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Computational fluid dynamic modelling of FCC riser: A review
Accepted Manuscript Title: Computational Fluid Dynamic Modelling of FCC Riser: A review Author: Milinkumar T. Shah Ranjeet P. Utikar Vishnu K. Pareek Geoffrey M. Evans Jyeshtharaj B. Joshi PII: DOI: Reference:
S0263-8762(16)30077-6 http://dx.doi.org/doi:10.1016/j.cherd.2016.04.017 CHERD 2263
To appear in: Received date: Revised date: Accepted date:
26-9-2015 19-4-2016 25-4-2016
Please cite this article as: Shah, M.T., Utikar, R.P., Pareek, V.K., Evans, G.M., Joshi, J.B.,Computational Fluid Dynamic Modelling of FCC Riser: A review, Chemical Engineering Research and Design (2016), http://dx.doi.org/10.1016/j.cherd.2016.04.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Draft manuscript: - Computational Flow Modelling of FCC Riser: A Review
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Computational Fluid Dynamic Modelling of FCC Riser: A review
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Milinkumar T Shah1, Ranjeet P Utikar1, Vishnu K Pareek1, Geoffrey M Evans2 and Jyeshtharaj B
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Joshi3 1
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Department of Chemical Engineering, Curtin University, Western Australia, Australia Department of Chemical Engineering, University of Newcastle, New South Wales, Australia 3 Homi Bhabha National Institute, India *Corresponding author: [email protected]
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Highlights
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(1) CFD models and experimental data of FCC riser are critically reviewed.
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(2) Governing equations and constitutive correlations of CFD models are explained.
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(3) Effect of important closure models on predictions is analysed.
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(4) Shortcomings of CFD models are identified and suggestions for future work are made.
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Abstract
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Design and scale-up of fluid catalytic cracking (FCC) riser is still largely empirical, owing to limited
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understanding of inherent multiphase flow in this equipment. The multiphase flow of FCC riser has
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therefore been extensively investigated both experimentally and computationally. The experiments
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have provided significant insight into gas-solid flow patterns inside cold-flow risers, but simultaneous
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observations on flow and performance parameters (conversion and yields) in FCC riser are rarely
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found in literature. Consequently, computational fluid dynamic (CFD) models of FCC riser that can
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simultaneously account for flow, interphase interactions, droplet vaporization and cracking kinetics
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have been developed. The CFD modelling of FCC riser, despite several efforts, has still remained a
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challenge as it requires careful consideration of governing equations and closure models. This review
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presents state-of-the-art in CFD modelling and experimental analysis of gas-solid hydrodynamics and
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reactive flow of FCC riser. The CFD models are explained in greater detail with governing equations,
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constitutive relations, and physical significance of all the terms. A brief review of DNS studies on
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cluster formation, gas-solid drag, and turbulent interactions is also presented. Impact of important
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closure models such as drag models, viscous stress models, boundary conditions, droplet vaporization
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models, and kinetic models on predictions is critically examined. The review identifies major
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shortcomings of current CFD models and makes detailed recommendations for future work.
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Keywords: Fluid catalytic cracking, riser, hydrodynamics, computation, simulation
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Content
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1. Introduction
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2. Gas-solid flow in FCC riser 2.1. “Core-annulus” radial profile
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2.2. “S-shape” axial profile
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2.3. Clusters
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2.4. Residence time distribution (RTD)
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2.5. Entry and exit effects
3.1. Eulerian-Eulerian model 3.1.1.Governing equations
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3.1.2.Constitutive equations
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3.2.4.Effect of boundary conditions
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3.2. Effect of closure models on flow predictions
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3. CFD models of gas-solid flow in riser
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3.2.1.Effect of drag models 3.2.2.Effect of gas phase stress models 3.2.3.Effect of KTGF models
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3.3. Shortcomings
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3.4. Eulerian-Lagrangian model
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3.5. Drift flux analysis
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4. Direct numerical simulations
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5. CFD models of a reactive flow in FCC riser 5.1. FCC riser performance
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5.2. Coupling of gas-solid flow model with droplet flow and vaporization models
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5.3. Coupling of gas-solid flow model and cracking kinetic model
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5.4. Predictions
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5.5. Shortcomings
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6. Recommendation for future work
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1. Introduction
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In petroleum refinery, an FCC unit converts low-value heavy residuals into valuable light products such as
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gas (C1-C4), gasoline (C5-C12), and diesel (C10-C15). In an FCC, a riser (Figure-1) is a long vertical pipe
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acting as a reactor where cracking reactions take place. In the FCC riser, steam, as an inert fluidizing
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medium, enters from the bottom and fluidizes regenerated catalyst. A few meters above the catalyst and
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steam inlets, hydrocarbon feedstock (vacuum gas oil - VGO, residue of vacuum distillation column) enters as
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a liquid spray through a set of atomizing nozzles. The fine droplets of the feedstock vaporize due to rapid
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mixing and heat transfer, and endothermic reactions then take place in the gas phase. The catalyst, droplets,
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and gas (hydrocarbon vapor and steam) concurrently flow upward along with reactions and droplet
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vaporization. This multiphase flow governs distribution of phases, temperature and concentrations, and in
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turn it dictates overall performance of the FCC riser. Consequently, the multiphase flow of FCC riser has
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been investigated both experimentally and computationally.
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Dimension and flow conditions (Buchanan, 1994; Berruti et al., 1995; Grace et al., 1997)
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Dimensions Height Diameter Operating conditions Inlet temperature of feedstock
30-40 m 1-2 m
150-300 ⁰C
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Inlet temperature of catalyst
Riser top temperature 500-550 ⁰C
Hydrocarbon Feedstock FCC Catalyst
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Steam
675-750 ⁰C
Solids circulation rate Catalyst to oil ratio Dispersion steam Pressure Solids residence time Catalyst particles Average size Particle density Bulk density Typical Umf Typical VT Geldart classification Feed droplets Droplet diameter
>250 kg/m2s 4-10 wt% 0-5 wt% 150-300 KPa 3-15 s 70 μm 1200-1700 kg/m3 750-1000kg/m3 0.001 m/s 0.1 m/s A up to 2000 μm
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Draft manuscript: - Computational Flow Modelling of FCC Riser: A Review Number of feed nozzles
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Figure-1: Schematic of FCC riser with dimensions and flow conditions Several experiments have been conducted to investigate gas-solid flow in riser. These experiments have
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shown (i) large variations in the volume fraction of the solids phase in different sections of riser, (ii) particle-
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scale heterogeneity due to formation of particle aggregates called 'clusters', (iii) considerable back mixing of
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the solids phase, and (iv) significant effects of entry and exit boundaries. While the experimental
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observations have provided significant understanding of the gas-solid flow patterns inside riser, they do not
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provide detailed information on hydrodynamics. In addition, experiments that provide observations of both
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flow and performance parameters (conversion and yields) in FCC riser are rarely found in literature. As a
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result, CFD models of riser have been developed. The CFD modelling of the riser flow involves careful
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selection and/or customization of the governing equations and closure models. Mostly two-fluid Eulerian-
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Eulerian gas-solid flow models have been used to model the gas-solid flow, while the two-fluid models
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coupled with cracking kinetics models have been used to model reactive flow in FCC riser. The two-fluid
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model is often extended by introducing feed droplet phase, which is modelled as either Eulerian or discrete
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Lagrangian phase. The model with the third (droplet) phase is coupled with appropriate droplet vaporization
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model. Predictions from such models are largely dependent on closure models. Multiple models are proposed
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in literature for solids phase properties, gas-solid drag force, viscous stresses, boundary conditions, droplet
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vaporization, cracking kinetics etc. In last few years, new closure models have been proposed based on
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multiscale approaches, cluster-based hypothesis, and direct numerical simulations. The closure models have
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been investigated in previous studies, who have recommended different closure models after comparing their
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predictions with experimental data. A systematic review of previous studies is necessary to identify most
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suitable set of closure models.
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Only a few reviews on CFD modelling of risers are available in literature. Berutti et al. (1995) has presented
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a detail review of flow patterns and models of gas-solid flow of the riser. Berruti et al. (1995) have
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thoroughly explained models that predict only axial variation of solids suspension density, and those that
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predict only radial variation of solids suspension density. Berruti et al. (1995) have briefly summarized
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previous works on CFD models of the gas-solid flow in riser. Godfrey et al. (1999) have evaluated the
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models that predict either axial or radial profiles by comparing predictions with experimental data. Wang
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(2009) has reviewed CFD models of a gas-solid flow focusing mainly on drag models available to capture
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sub-grid scale flow structures such as clusters. Wang et al. (2010) have critically reviewed applicability of a
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drag model based on the energy minimization multiscale (EMMS) approach in CFD simulations of riser.
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Gupta et al. (2010) have reviewed modelling of FCC riser by covering literature on models for cracking
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kinetics, droplet vaporization and hydrodynamics. The hydrodynamic modelling section of Gupta et al.
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(2010) doesn’t focus exclusively on CFD models. In last one decade, a large number of CFD studies of the
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riser flow have been published with them being mostly focused on evaluation and modification of different
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closure models. During this period, several studies have also been conducted using coupled CFD models to
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investigate alternate design and flow conditions in FCC riser. A comprehensive review of CFD models of
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FCC riser, particularly with focus on recent findings, is not available in literature.
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The current study presents a critical review of CFD models of FCC risers accompanying with analysis of
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experimental data. The review divides the available literature on this subject in two groups, those on gas-
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solid flow and those on reactive flow in FCC riser. The CFD models and experimental data published under
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both groups are comprehensively analysed. The CFD models are explained in detail with governing
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equations, constitutive relations, and physical significance of all the terms. A brief review on direct
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numerical simulation (DNS) studies on cluster formation, gas-solid drag, and turbulent interactions is also
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included. The impact of important closure models such as drag models, viscous stress models, boundary
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conditions, droplet vaporization models, and kinetic models on predictions is critically analysed. More
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specifically, conventional drag models vs. multiscale drag models, laminar vs. turbulent models for the gas
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phase, 2D vs. 3D boundary conditions, and no-slip vs. partial-slip wall boundary conditions are analysed for
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predictions of gas-solid flow in riser. Furthermore, uncertainty associated with the selection of droplet
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vaporization models and cracking kinetic models is also critically examined. Based on the thorough analysis,
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major shortcomings of current CFD models are explicitly brought out and detailed suggestions for future
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work are given.
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2. Gas-solid flow in FCC riser
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The gas-solid flow in FCC riser has been extensively investigated by cold-flow pilot-scale CFB setups. In
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these experiments, controlled quantities of the solids and gas (typically air) are circulated through a riser. As
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summarised in Table-1, these experiments are conducted for different riser dimensions, particle properties,
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and flow conditions (such as mass flux and fluidizing gas velocity). Measurements of the pressure, velocity,
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and volume fraction are taken at multiple locations along height and radial positions by using various
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invasive (pressure taps, optical probes and capacitance probe) or non-invasive (high speed videography,
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tomography, particle image velocimetry, electrical capacitance volume tomography, laser Doppler
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velocimetry, radioactive particle tracking and positron emission particle tracking) techniques. Though the
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operating conditions in these experiments do not resemble those in the actual FCC riser, the cold-flow
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experiments can still provide useful observations of inherent gas-solid hydrodynamics in FCC riser. Some of
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the important flow characteristics can be summarised as:
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Table-1
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Table-1: Cold-flow FCC riser experiments
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Yerushalmi et al. (1976) Rhodes and Geldart (1986) Ishii et al. (1989) Bader et al. (1988) Li et al. (1988) Pressure taps, Optical probes Ambler et al. (1990) Radioactive tracer detection Louge and Chang (1990) Pressure taps, Capacitance probes Bai et al. (1992) Pressure taps Yang et al. (1992) LDA Miller and Gidaspow (1992) X-ray densitometer, Extraction probe Brereton and Grace (1993) Needle capacitance probe Patience and Chaouki(1993) Radioactive tracer detection Horio and Kuroki (1994) High speed camera Wei et al. (1995) Optical fibre sensors Knowlton et al. (1995) Pressure taps Pugsley and Berruti (1996) Pressure taps Nieuwland et al. (1996b) Optical probes, Pressure taps Pugsley et al. (1997) Pressure taps Wei et al. (1998) LDA Cheng et al. (1998) LDA Noymer and Glicksman (1998) TIV Issangya et al. (2000) Pressure taps Bai et al. (1999) Optical fibre probes Mathiesen et al. (2000) LDA/PDA Smolders and Baeyens (2000) Electric conductivity of tracer Sharma et al. (2000) Pressure taps, Needle capacitance probe Pärssinen and Zhu (2001) Fibre optic probes Ibsen et al. (2002) LDV/PIV Harris et al. (2003) Light sensitive photomultiplier tube Zhang et al. (2003) Optical fibre probe, LDV Pandey et al. (2004) LDV Bhusarapu et al. (2005) CARPT and CT Mabrouk et al. (2007) RPT He et al. (2006) PIV Van de Velden et al. (2007) PEPT Kim et al. (2008) Pressure taps Yan et al. (2009) Phosphor tracer technique Chang et al. (2010) PEPT Wang et al. (2010) Pressure sensors Xu and Zhu (2011) High speed camera, Optical fibre probe Heynderickx et al. (2011) LDA Gao et al. (2012) Optical probes Pantzali et al. (2013) LDA Zhang et al. (2013) Pressure sensors Rodrigues et al. (2015) Pressure taps Monazam et al. (2016) Pressure taps Experimental observations: (a) Axial profiles of volume fraction of solids phase (b) Axial profiles of pressure drops (c) Axial profiles of velocity of solids phase (d) Radial profiles of volume fraction of solids phase (e) Radial profiles of velocity of solids phase (f) Observations on clusters (g) RTD (h) Effect of entries or exit configurations
Experimental setup and operating conditions Dt (m) H (m) dp (μm) Gs (kg/m2s) ug (m/s) 0.0762 7.3 60 52.90 3.65 0.152 6 64 8.5-107 2.5-4.5 0.05 2.79 60 10.7 1.29 0.305 12.2 76 147 9.1 0.09 10.5 54 14.3 1.52 0.05 3 106 124.305 4.5-7.1 0.197 7 61 17 2 0.140; 0.186 8 54, 280, 165, 31 30-180 2-8 0.140 11 54 26.56-119.43 1.5-6.5 0.075 6.58 75 12 2.89 0.152 9.3 148 42, 48, 62 6.5 0.083 5 277 20-140 4-8 0.2 1.6 61.3 0.016-0.6 0.15-0.6 0.2 1.6 61.3 0.016-0.6 0.15-0.6 0.20 14.2 76 485 5.2 0.05 5 208 51.3-700 8.5 0.054 8 129 100-300 10 0.1 and 0.2 6 and 12 220, 230, 71, 80 10-45; 10-85 4-6 0.186 8 54 200 2.3-6.2 0.186 8 54 200 2.3-6.2 0.159 (square) 2.44 69 25, 18 3, 6 0.762 6.1 70 18-325 4-8 0.0762; 0.102 6.1, 8.2 70 425 8 0.032 1 120, 185 0.8, 1, 1.2 0.1 6.5 90 5.19-34.1 2.82-4.92 0.15 11 70, 120 75 4, 4.9, 6 0.076 10 67 100, 300 8 0.02 2 250 0.45 0.14 (square) 5.8 25 1.3-4.5, 2-25.5 0.418 18 77 19-180 1.8-8 0.305 15.2 812 3.4-17.1 3.75-5.4 0.152 7.9 150 33.7, 36.9 3.9 and 4.5 0.52 1 250, 170 2, 12 2D, 0.05 x 1.5 1 335 5,10, 20 2-2.3 0.10 6.5 90 25, 89.7 3.6 and 9 0.05 4.5 70 7-300 0.2-9 0.186 10 78 40.8, 229.4 3.156, 5.989 0.16 7.9 120 5, 622 1, 10 0.27 (square) 10 330 113-165 15.5 0.019 x 0.114 7.6 67-288 50-200 3-8 0.1 8.765 77 3.0 2.48–7.43 0.095 and 0.14 2.2 139 0.94-1.25 0.1 8.7 77 1 3.5 and 5.3 0.316×0.08, 0.1×0.1 4.5, 4.3 350,175 12.7, 13.9, 16.1 4.4, 5.3, 5 0.3 18 300,250, 280 60 8-10 0.3 16.65 60, 230, 812 6.89-281 5.35-7.7 Abbreviations: LDA = Laser Doppler Anemometry PDA = Phase Doppler Anemometry PIV = Particle Image Velocimetry CARPT = Computer Aided Radioactive Particle Tracking CT = Computed Tomography RPT = Radioactive Particle Tracking TIV = Thermal Image Velocimetry PEPT = Positron Emission Particle Tracking
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Measurement technique Pressure taps, High-speed camera Pressure taps Optical fibre probes
ρs (kg/m3) 510.98 1800 1000 1714 1654 Sand 1545, 706, 750, 2660 1545 930 2650 2630 1780 1780 1712 2580 2540 2500, 2200, 2600, 1500 1398 1398 6970 1600 1600 2400 2200 1500 2400 4060 1398 189 2550 2500; 3400 2500 1740 1225 2260 2630 1877-2498 1550 2400 1550 2600 2650, 2600, 3300 2550, 1250, 189
Observations (f) (a) (a), (b), (f) (a), (d) (a), (e), (d) (g) (a), (b) (a) (d) € (b), (d), (e) (a) (a), (e), (g) (a), (f) (f) (b), (d), (e) (b) (d), (e) (b), (h) (a), (d), (e) (d), (h) (f) (a) (d) (d), (e) (g) (b), (e), (f) (a), (d), (e) (a), (b), (d) (g) (d), (e), (g) (f), (e) (d), (e) (a), (g) (e) (g) (a), (h) (e), (g) (g) (e) (f) (h) (a), (c), (d) (e) (h) (b) (a), (b), (h)
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2.1. “Core-annulus” radial profile
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Bader et al. (1988), Li et al. (1988), Miller and Gidaspow (1992), Yang et al. (1992), Nieuwland et al.
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(1996b), Knowlton et al. (1995), Mathiesen et al. (2000), Bhusarapu et al. (2005), and Wang et al. (2010)
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have reported radial profiles of the volume fraction and velocities of the solids phase. A lower volume
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fraction and higher velocity of the solids phase are observed at centre of riser (Figure-2). This region is
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referred as a “core” region, where the solids are carried upward due to flow of the gas. Contrary to the core
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region, a lower velocity or downward flow of the solids with a higher volume fraction of the solids are
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observed near wall. The region near wall is defined as an “annular” region. The heterogeneous radial
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distribution of velocity and volume fraction is widely known as the “core-annular” flow pattern. The higher
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solids volume fraction in the annular region is largely attributed to friction between flow and wall and energy
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dissipation due to particle-particle and particle-wall collisions. The solid segregation is also caused by
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formation of clusters (Noymer and Glicksman, 2000 and Pandey et al., 2004). Bader et al., (1988), Yang et
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al. (1992), Miller and Gidaspow (1992), Noymer and Glicksman (2000) and Pandey et al. (2004) have
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observed downward sliding motion of segregated particles near wall. Yang et al. (1992) have observed
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concurrent movement of phases in the core region, while they have observed counter current movement of
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the solids and gas near wall. The counter current movement of the phases lead to higher slip velocity near
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wall than that in core region (Yang et al., 1992). Experiments for various flow conditions and riser systems
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have revealed that the core region occupies almost 60-80% of cross-section with the annular region
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occupying rest 20-40%. Miller and Gidaspow (1992) have observed (Figure-2a and b) that an increase in the
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solids flux at a constant gas velocity results in higher solids volume fraction in both the core and annular
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regions; while an increase in the solids flux had a minor impact on velocity of the solids in the core region.
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Nieuwland et al. (1996b) have observed (Figure-2c and d) that an increase in velocity of the gas phase at a
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constant solids flux results in a lower solid volume fraction in both the core and annular regions. Perssinen
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and Zhu (2001) have reported the solids volume fraction at different heights, and observe that the values in
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both the core and annular regions decrease with an increase in the height.
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(c) (d) Figure-2: Core-annulus radial profiles, (a) and (b) effect of solids flux, (b) and (c) effect of gas velocity. 1
2.2. “S-shape” axial profile
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Li et al. (1988), Louge and Chang (1990), Pärssinen and Zhu (2001), Rhodes and Geldart (1986), Wei et al.
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(1998), Issangya et al. (2000) and Zhang et al. (2003) have reported axial variation in the solids volume
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fraction (Figure-3a). The axial profiles have shown an “S-shape” (Figure-3a and b) with three distinct
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regions (i) a dense bottom region, (ii) a dilute top section, and (iii) middle section presenting a transition
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from the dense to dilute flow. Experimental under various flow conditions in different riser systems have
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showed several similarities, i.e. the volume fraction of the solids in the dense bottom section is in a range of
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0.3-0.15, and that in the dilute top section is in a range of 0-0.05. The experimental data shows significant
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variations in the height of the transition from the dense to dilute flow (20-60% of the total height). Pärssinen
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and Zhu (2001) have found significant impact of the inlet gas velocity at a constant solids flux on axial
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profile the solid volume fraction (Figure-3c). A lower gas velocity gives a clear distinction between the
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dense and dilute region; while a higher gas velocity results in a smooth transition. Rhodes and Geldart (1986)
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and Issangya et al. (2000) have investigated the effect of the solids flux on axial profiles (Figure-3b). Rhodes
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and Geldart (1986) have found that a higher solids flux gives dense flow with higher values of the solids
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volume fraction than those from lower solids flux condition. Issangya et al. (2000) have found that a lower
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solids flux give a longer developing section than that resulted at a higher solids flux. Li et al. (1988) have
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investigated the effect of the solids inventory in CFB on axial profiles (Figure-3d). Notably, in Li et al.’s
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experiment, there is no mechanical valve that controls quantity of the solids circulated through the riser. Li et
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al. (1988) have found that a higher solids inventory in the CFB loop gave a longer dense phase and transition
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(d) (c) Figure-3: (a) “S” shape axial profiles of solids volume fraction, dimensionless height Vs. solid volume fraction; effect of (b) solids flux, (c) gas velocity, and (d) solid inventory on axial profiles of the solids volume fraction Miller and Gidaspow (1992); Knowlton et al. (1995); Sharma et al. (2000) and Ibsen et al. (2002) have
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reported variations in pressure drop along height, where it is observed that the bottom section of riser has
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higher pressure drop with lower values at the top (Figure-4). Miller and Gidaspow (1992) have found that the
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pressure drop in riser increases with increase in the solids flux (Figure-4a); while Sharma et al. (2000) have
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found that an increase in the gas velocity reduces the pressure drop in riser (Figure-4b).
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2.3. Clusters
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Yerushalmi et al. (1976) have observed segregation of particles and movement of the segregated solids
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within a dilute phase flow. They have characterized shape of the segregated solids as “strands”, “steamer”
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and “ribbons”. Later, Ishii et al. (1989) and Horio and Kuroki (1994) have reconfirmed presence of the
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particle segregations and defined them as “clusters”. The authors have observed that the clusters are present
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not only near wall but also in dilute phase at centre of riser. Ishii et al. (1989) and Horio and Kuroki (1994)
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have also observed that the shape of the clusters continuously changing with flow conditions. Soong et al.
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(1994) have measured instantaneous concentrations of the solids at various locations in riser, and give three
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criteria to identify the clusters, (1) solids concentration inside cluster must be significantly higher than local
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time–mean solids concentration; (2) perturbation caused by cluster must exist for significantly longer time
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than sampling time interval; (3) this perturbation must also be sensed by a sampling volume which has a
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characteristic length scale greater than one to two orders of particle diameter. Based on Soong et al.’s
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criteria, Noymer and Glicksman (1998); Sharma et al. (2000); Manyele et al. (2002); Liu et al. (2005); and
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He et al. (2006) have recorded measurements of cluster properties. More recently, Shaffer et al. (2010; 2013)
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have used high speed PIV to capture clusters and their movements along wall of riser. They have found large
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variations in cluster structures from several particles to several riser diameters. Furthermore, Shaffer et al.’s
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studies have also revealed that a presence of stream of the gas phase influences make-up and break-up of
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clusters near wall. Formation of clusters has two profound effects, (i) apparent solids diameter increases
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which leads to higher terminal velocity and (ii) gas tends to flow around clusters without penetrating inside
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the clusters (Li and Kwauk, 1994). Consequently, formation of clusters significantly impacts gas-solid drag
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in riser (discussed in section-3.2.1).
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2.4. Residence time distribution (RTD)
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Ambler et al. (1990), Patience and Chaouki (1993), Smolders and Baeyens (2000), Harris et al. (2003),
24
Mabrouk et al. (2007), Van de Velden et al. (2007) and Chan et al. (2010), have reported RTDs from
25
stimulus response experiments at various flow conditions. In the stimulus response experiments, a tracer is
26
injected at bottom of riser and its concentration at outlet is measured at different times after injection. Harris
27
et al. (2003) have measured RTD in a square riser by using a small portion of the solids particles as tracers,
28
and investigate the effect of three types of exit geometries, namely smooth, abrupt and highly refluxing, on
29
RTDs at various flow conditions. Figure-5(a) shows variations in the RTDs caused by variations in the gas
30
phase velocity for the smooth exit riser. Harris et al. (2003) have observed that an increase in the superficial
31
gas velocity decreases both mean residence time and variance of distribution over a range of investigated
32
solids fluxes. At a higher gas velocity, the RTD curves are narrow, relatively unskewed and having a
33
significant long tail. In contrast, at a lower gas velocity, the curves are broad with a long tail. Van de Valden
34
et al. (2007) have also reported RTDs for two operating gas velocities at a fixed solids flux (Figure-5b),
Ac ce
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where the RTD from a higher gas velocity is closer to that of ideal plug flow reactor; while the RTD from a
2
lower gas velocity is closer to that of the ideal mixed flow reactor.
us
cr
ip t
1
an
(a) Figure-5: Effect of gas velocity on residence time distribution (a) E(t) Vs. time and (b) F(t) Vs. t/ τ
(b)
M
; τ = half the injection time, approximately 1 s (Van de Valden et al., 2007) 2.5. Entry and exit effects
4
Bai et al. (1992), Brereton and Grace (1994), Zheng and Zhang (1994), Pugsley et al. (1997), Cheng et al.
5
(1998), Kim et al. (2008) and Mabrouk et al. (2008) have investigated the effect of exit configuration on riser
6
hydrodynamics. Cheng et al. (1998) and Kim et al. (2008) have also studied the effect on inlet
7
configurations. Figure-6(a) shows the effect of two types of exit configuration (abrupt exit – L or T-type exit,
8
and smooth exit – long radius bend type exit) on the axial profiles of pressure drop as observed by Pugsley et
9
al. (1997). It can be seen that the effect of the abrupt exit causes higher pressure drop in upper section of
10
riser, while the pressure drop in the bottom section with both types of the exit configurations are the same.
11
Pugsley et al. (1997) have also observed that the effect of the abrupt exit is only restricted to the top section,
12
and this effect is even higher for a lower solid circulated mass flux. Cheng et al. (1998) have also compared
13
axial profiles of the gas volume fraction from abrupt and smooth exits. Cheng et al. (1998) have found that
14
the abrupt exit gives a lower gas volume fraction near the exit, while values in the bottom section from the
15
two types of exits are in reasonable agreement. Cheng et al. (1998) have studied the effect of three types of
16
air entries in an internal nozzle type air inlet arrangement; While Kim et al. (2008) have compared three
17
different types (L-valve, J-valve and Loop-seal type) solid entries. Figure-6(b) shows the effect these three
18
types of solid entries on solid circulation rate vs. solid inventory plots (Kim et al., 2008). An increase in the
19
solid inventory increases the solid circulation rate in riser. At a higher value of the solid inventory, the values
20
of circulating rates from the L-valve and J-valve are in reasonable agreement. For an entire range of
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experimental values of the solid inventory (12-36 kg), the loop-seal type solid entry results in significantly
2
lower solid circulation rate than that in the other two types of entries.
(a)
an
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1
M
(b) Figure-6: (a) Effect of exit configuration, dimensionless height Vs. pressure drop per unit length (Gs = 85 kg/m2s and ug = 4.2 m/s); (b) Effect of solid phase entry, solid circulation rate Vs. solid inventory (ug = 7 m/s) Experimental observations show large flow structures such as radial and axial distributions extended across
4
length and width of riser. These structures are directly influenced by small scale flow phenomena such as
5
formation of clusters, particle-wall collisions and boundary effects. Capturing these multiple flow structures
6
that have disparate time and length scales in CFD predictions is a challenging task. Higher spatial resolution
7
using fine grid discretization of flow domain and lower time step for transient simulations are essential
8
simulation parameters for riser simulations. However, these parameters are generally constrained by
9
available computational resources. Hence careful selection of modelling approach and governing equations is
10
necessary. Each modelling approach needs closure models such as models for interphase interactions,
11
turbulent forces and boundary conditions. These closure models have been derived empirically or by
12
conducting high resolution sub-grid simulations or DNS. For each closure model, several models are
13
available in literature. Realistic prediction of riser flow critically depends on the selection of closure models.
14
For example, various drag models have been proposed to cater different flow conditions. But for industrial
15
scale riser simulation, a drag model that can capture clustering phenomena even with coarse grid spatial
16
discretization is essential. Similarly, proper inlet and outlet configurations of flow domain are required to
17
capture entry and exit effect. Moreover, capturing dissipation due to particle-wall collisions is critical in
18
configuring wall boundary conditions. Various modelling approaches, model equations and closure models
19
are discussed in detail in the next section.
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3. CFD models of gas-solid flow in riser
2
Different types of models of the gas-solid flow in riser have been proposed over last three decades. Harris
3
and Davidson (1994) have classified the models published before early 90’s into three categories, i.e. (i)
4
those that predict axial variation of suspension density, but not radial variation; (ii) those that predict radial
5
variation, but not axial variation; (iii) those that employ fundamental fluid dynamic equations for two phase
6
gas-solid flow. Among these three types of models, the category-(iii) models are most useful to investigate
7
the effect of local flow structures and design configurations (Harris and Davidson, 1994; and Berruti et al.,
8
1995). The models based on fundamental fluid dynamic equations can be further classified in two broad
9
categories, namely the Eulerian-Eulerian (E-E) or the Eulerian-Langragian (E-L) models. The E-E model
10
considers both the gas and solids phases to be continuous and fully interpenetrating. In the E-E model,
11
averaged Navier-Stokes equations of the mass, momentum and energy conservations are solved for both the
12
phases. Closure laws based on the kinetic theory of granular flow (KTGF) (Jenkins and Savage, 1983; Lun
13
and Savage, 1984; Lun et al., 1984) are used to calculate stresses in the solids phase. Coupling between the
14
momentum balance equations is modelled by using correlations for interphase forces; while coupling
15
between the energy balance equations is modelled by using correlations for heat transfer between the two
16
phases. The E-L model represents solids phase as a collection of discrete particles. The motion of each
17
individual particle is solved by Newton’s law, accounting for the effect of particle collisions and forces
18
acting on the particle by the gas. Solution of the force balance equations gives updated velocity and position
19
of each particle. In a further advanced E-L model, discrete element model (DEM), contact force due to
20
collisions between particles are also captured at a much shorter timescale by means of the empirical
21
coefficient of restitution and friction (hard sphere approach) or empirical spring stiffness and a friction
22
coefficient (soft-sphere approach) (Cundall and Strack, 1979; Tsuji et al., 1993; Deen et al., 2007). The
23
interactions between two phases are still modelled using interphase drag and heat transfer correlations
24
similar to those used in the E-E model. Use of the E-L approach requires tracking of billions of solid
25
particles by solving the force equation for each particle and then calculating contact forces between nearby
26
pairs of the solid particles. Hence, the E-L approach becomes computationally impractical for simulations of
27
industrial- or laboratory-scale risers. On the other hand, the E-E approach is computationally less expensive,
28
and hence, it has been widely used for the gas-solid flows in riser. Many of important simulation studies
29
using the E-E gas-solid models for riser simulations are summarised in Table-2.
30
Table-2
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Drag: (a) (b) (c) (d) (e) (f) (g) (h)
Wen and Yu (1966) Gidaspow et al. (1994) Syamlal – O’Brien (1987) EMMS (Li and Kwauk, 1994) SGS – Filtered drag Richardson and Zaki (1954) Arastoopour et al. (1990) Other
(b), (d) (c) (b), (e) (c) (a) (b), (d) (b), (c), (g) (b), (e) (d) (b), (d), (e) (b), (d) (a) (d) (d) (b)
NC NC (f) NC (e) NC (e)
(a) (a) (a) (a) (a) (a)
(c) (e) (c) (e) (c) (c)
(f) NC NC
(a) (a) (a)
(b) (b) NC NC (b)
(d) (b), (d) (a), (b), (c), (h)
(b),(c), (d) (a)
KTGF closures Collision Shear dissipation rate viscosity
Radial distribution function
Granular energy exchange
Investigations
Boundary condition Solids Walls (for inlets solids) (f) (d) (b) (c)
(b) (c) (a) (b) (a) (a) (a) (b)
(d) (j) (e) (c) (d) (j) (c) (c) (c) (f)
(b) (b) (d) (c) (b) (b) (b) (b) (c) (b)
(a) (a) (a) (a) (a) ((b)
(b) ((c) (e) (e) (d) (b) (d)
(b) (a) (b) (a) (a) (a) (b) (b) (b) ((c)
(a) (b) (a) (b) (a) (b)
(k) (c) (f) (c) (f),(g),(h) (c) (c)+(i)
(e) (b) (b) (b) (b) (b)
(b) (b),(c), (d) (a) (a)
(b) (d) (d) (d) (d) (b) (b)
(b) (b) (a), (c) (b) (b) (b)
(e) (c) (e)
(b) (a) (b)
(f) (c) (f)+(i)
(b) (b) (f)
(b) (a) (b)
(d) (b) (a), (b)
(b) (b)
(a), (b)
(b) (b) (a) (a) (a), (b)
(c) (e) (c)
(b) (b) (a) (b) (b)
(c)+(i) (b) (c) (f)+(i) (c)+(i)
(a) (e) (b) (f) (a)
(a) (a) (f) (b) (a)
(b) (d) (b) (b) (b), (c)
(a) (b) (b) (b) (a),(b)
(a), (f) (a), (b), (e), (f)
(a) (b) (a)
(c)
(b) (b) (a)
(c) (c)+(i) (c)
(b) (a) (c)
(a) (a) (a)
(b) (b) (c)
(b) (b) (b)
ip t
(a) (d) (c) (a) (c) (c) (c) (e)
M
an
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(a) (a) (a) (a) (a) (a) (a) (a)
ed
Shah et al. (2011b,c) Naren and Ranade (2011) Shuai et al. (2011) Benyahia (2012) Shah et al. (2011a) Chalermsinsuwan et al. (2013) Zhou and Wang (2014) Shah et al. (2015) Baharanchi et al. (2015)
Granular thermal conductivity
NC (b) NC (f) (b) (b) (f) (b) NC NC
pt
Igci et al. (2008) Lu et al. (2009) Benyahia, (2009)
Granular temperature formulation
(a) (f) (b) (b) (a) (f) (b) (b) (g) (b)
Ac ce
Arastoopour et al. (1990) Pita and Sundaresan (1993) Dasgupta et al. (1994) Nieuwland et al. (1996a) Samuelsberg and Hjertager (1996) Hrenya and Sinclair (1997) Dasgupta et al. (1998) Mathiesen et al. (2000) Neri and Gidaspow (2000) Benyahia et al. (2001) Agrawal et al. (2001) Huilin et al. (2003) Yang et al. (2003b) Huilin et al. (2005) Andrews IV et al. (2005) Jiradilok et al. (2006) Benyahia et al. (2007) Wang et al. (2007) Almuttahar and Taghipour (2008)
Gas phase turbulent
cr
Table-2: CFD models of cold-flow gas-solid flow in riser Drag
(b) (f) (d), (e) (d) (a) (a), (f) (a), (b) (b), (c) (a), (b), (c), (d)
(a)
(d), (e) (a), (c), (e), (f) (a)
Gas phase:
Granular temperature:
Granular shear viscosity:
Solids Inlets:
Investigations:
(a) NC
(a) Partial differential equation (Lun et al., 1984) (b) Algebraic equation (Syamlal et al., 1993)
(a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k)
(a) (b) (c) (d) (e)
Effect of (a) drag models (b) KTGF models (c) viscous models (d) inlet and/or outlet boundary conditions (e) wall boundary conditions (f) flow conditions
(b) Standard k- mixture model
(c) Standard k- dispersed model
Granular thermal conductivity: (a) (b) (c) (d) (e)
Lun et al. (1984) Syamlal et al. (1993) Gidaspow (1994) Nieuwland et al. (1996) Agrawal et al. (2001)
Lun et al. (1984) Syamlal et al. (1993) Gidaspow (1994) Hrenya and Sinclair (1997) Nieuwland et al. (1996) Agrawal et al. (2001) Blazer et al. (1996) Cao and Ahmadi (1995) Frictional viscosity (Schaeffer, 1987) Dasgupta et al. (1994) Yang et al. (2004)
Real 3D 2D- two-sided solids inlet 2D-single solids inlet Periodic One common inlet for gas and solids phases
Walls (for solids): (a) No-slip (b) Partial-slip (c) Free-slip
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(d) Standard k- per-phase model
Collision dissipation:
Radial distribution function:
(a) Jinkin and Sevage (1983) (b) Lun et al. (1984) (c) Nieuwland et al. (1996)
(a) (b) (c) (d) (e) (f)
(e) Modified k- model (f) Other
Lun and Sevage (1986) Sinclair and Jackson (1989) Gidaspow (1984) Ma and Ahmadi (1986) Iddir and Arastoopour (2005) Carnahan and Starling (1995)
Note: (1) All the studies are for cold flow in the riser. Consequently, energy balance is ignored. (2) All the studies use governing equations by Anderson and Jackson (1967). (3) All the studies have ignored interphase forces other than drag.
Granular energy exchange: Gidaspow (1994) Koch and Sangani (1999) Cao and Ahmadi (1995) Blazer et al. (1996)
cr
ip t
(a) (b) (c) (d)
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3.1. Eulerian-Eulerian model
2
In the formulation of the E-E model, local instantaneous equations are written for mass, momentum and
3
energy balances for each phase in each control volume. These equations can be solved by direct simulation
4
using size of control volume finer than the smallest length scales of the flow and a time step shorter than the
5
time scale of the fastest fluctuations. However, direct simulation would be computationally highly intensive.
6
Thus averaging of local instantaneous equations is applied. Generally, ensemble averaging (Enwald et al.,
7
1996) is applied to formulate averaged balance equations. The averaging of balance equations leads to
8
representation both phases as interpenetrating and continuous. The averaged equations then need extra
9
closure laws to close the set of equations. The closure laws for the continuous solids phase are derived using
10
the KTGF. Another set of closures are for the gas-solid interphase forces and heat exchanges. The closure
11
relations derived using the KTGF, interphase forces and heat exchanges are then incorporated into the
12
balance equations for the solids phase to achieve a close set of partial differential equations (PDEs).
13
3.1.1.
14
The governing equations for the E-E model consist of ensemble averaged Navier-Stokes equations (mass,
15
momentum and energy balances) for both the gas and catalyst phase. Several researchers have derived the
16
governing equations for two phase flows. Enwald et al. (1996) and van Wachem et al. (2001) have compared
17
the governing equations. Most of the gas-solid E-E simulation studies (as summarised in Table-2) have
18
referred their governing equations to Anderson and Jackson (1967). Therefore, in this study, we start from
19
the averaged balance equations of Anderson and Jackson (1967).
20
Mass balance equations:
21
The mass balance equation for the gas and solids phase can be written as:
23
cr
us
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an
Governing equations
Ac ce
22
ip t
1
eq.(1)
eq.(2)
24
Where, εg and εs are the volume fraction of the gas and solids phases; ρg and ρs are the densities of the gas
25
and solids phases; ug and us are the velocities of the gas and solids phases; mgs and msg are the mass transfer
26
terms from the gas to solids phase and the solid to gas phase respectively; and Sg and Ss are the source terms.
27
In the E-E model, both phases are considered as interpenetrating continua; and both the phases share the
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1
volume of flow domain. At any particular time therefore, a flow volume has εg of the gas phase and εs of the
2
solids phase with both volume fractions following:
3
For a simple gas-solid flow without mass transfer and mass sources, the continuity equations become:
ip t
4
eq.(3)
eq.(4)
us
cr
5
Momentum balance equations:
8
The conservation of momentum of the gas and solids phases is given by following equations:
ed
M
7
eq.(6)
Ac ce
pt
9
10
eq.(5)
an
6
eq.(7)
11
Where, P is the pressure that shared by both the phases;
and
are the stress tensor of the gas and solids
12
phases; g is the gravitational acceleration; FD, Flift and Fvm are the interphase forces such as drag force, lift
13
force and virtual mass forces respectively. Notably, in above equations, the force terms are positive for the
14
gas phase and negative for the solids phase.
15
Energy balance equations:
16
Energy conservation equation for the gaseous mixture phase:
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1
2
eq.(8)
Energy conservation equation for the solids phase:
eq.(9)
ip t
3
Where, hg and hs are the specific enthalpies of the gas and solids phases respectively; qg and qs are the heat
5
fluxes in the gas and solids phases respectively; Sgh and Ssh are the energy source terms; and ΔQgs and ΔQsg
6
are the heat exchanges between the gas and solids phases respectively.
7
3.1.2.
8
3.1.2.1 Interphase forces
9
The momentum balance equations are coupled with interphase force terms, which represent the interactions
10
between the gas and dispersed solids phases. These forces are generally caused by a relative motion between
11
the gas and solids phases.
12
Drag force
13
The gas-solid drag force can be written as:
us
pt
ed
M
an
Constitutive equations
Ac ce
14
cr
4
eq.(10)
15
Where, β is the interphase momentum transfer coefficient and
is the difference between the
16
velocities of the gas and solids phases, usually termed as slip velocity. The value of the drag coefficient
17
depends on volume fraction, particle diameter and slip velocity; and in turn, particle Reynolds number.
18
Several drag coefficient functions (Ergun, 1952; Wen and Yu, 1966; Gibilaro et al., 1985; Syamlal and
19
O’Brien, 1987; Syamlal et al., 1993; Di Felice, 1994; Gidaspow, 1994; Li and Kawauk, 1994; Andrews IV et
20
al., 2005; Beetstra et al., 2007; Igci et al., 2008; Igci and Sundaresan, 2008; Tenneti et al., 2011) have been
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proposed to cater different the gas-solid flow conditions. Comparison of the available drag models is
2
explained in section-3.2.1.
3
Virtual mass force
4
In the gas-solid flows in riser, the solids phase accelerates relative to the gas phase in the developing section.
5
The inertia of the gas-phase encountered by the accelerating solids phase exerts a virtual mass force on the
6
particles.
ip t
1
eq.(11)
The term
denotes the phase material time derivation of the form,
M
an
8
us
cr
7
eq.(12)
ed
9
The virtual mass effect is significant when the secondary phase density is much smaller than the primary
11
phase density (i.e. bubble column). But in the riser, the solids phase density is much higher than the gas
12
phase, and therefore, most of the gas-solid models do not account for the virtual mass force.
13
Lift force
14
The lift force acts on the suspended particle mainly due to velocity gradients in the gas-phase, relative
15
velocity between the gas and solids phase, and rotation of the particles.
Ac ce
16
pt
10
eq.(13)
17
Where,
18
particle spacing and the value of drag force is much larger, the lift force has been ignored in the previously
19
proposed flow models.
is the lift coefficient.Assuming that the FCC particle diameter is much smaller than the inter-
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1
3.1.2.2. Gas phase stresses
2
The stresses in the gas phase are modelled by using either the laminar or turbulent model.
3
Considering laminar flow, the correlation for the gas phase stress tensor can be written as:
If the turbulent flow for the gas phase is considered then the stresses in the gas phase can be written as:
cr
5
eq.(14)
ip t
4
eq.(15)
an
us
6
Where, μg is the laminar viscosity; μt,g is the turbulent viscosity and k is the kinetic energy of the gas phase.
8
To close the equation of the turbulent stresses, a correlation for the turbulent viscosity and kinetic energy are
9
required.
M
7
Owing to their inherent complexity and scale of flow domain, the standard k- turbulent model has been
11
used (Dasgupta et al., 1998; Almuttahar and Taghipour, 2008; and Shah et al., 2011b) for the turbulent
12
properties. There are three different types of formulations that are possible for the standard k
13
model. The simplest k
14
for dissipation rate ( ). These equations are formulated for a single pseudo phase made of the mixture of the
15
gas and solids phases. This model then uses mixture properties to calculate the turbulence properties
16
(Dasgupta et al., 1998). The conservation equation for the kinetic energy and dissipation rate can be written
17
as:
turbulent
Ac ce
pt
ed
10
model has the two equations, one for the turbulent kinetic energy (k) and the other
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1
and that for the dissipations rate can be written as:
ip t
2
eq.(16)
eq.(17)
cr
3
Where, m denotes the mixture properties; k is the turbulent kinetic energy; is the turbulent dissipation rate;
5
ρm is the mixture density (
us
4
M
an
); and μm is the mixture viscosity (
ed
6
9
eq.(18)
eq.(19)
Ac ce
8
pt
7
).
eq.(20)
10
In above equations, Cμ, C1,ε, and C2,ε are constants; whereas σk and σε are the turbulent Prandtl numbers
11
(Lauder and Spalding, 1972). Dasgupta et al. (1994) have used 0.09, 1.45, 2.0, 1.3 and 1.0 for Cμ, C1ε, C2ε, σk
12
and σε respectively.
13
More complex k- turbulent model for the gas-solid flow is derived by accounting for the effect of dispersed
14
solid particles on the gas phase turbulent kinetic energy and dissipation rate (Bolio et al., 1995; Cao and Page 23 of 23 Page 23 of 114
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Ahmadi, 1995). In this model, the equations for k and
are solved for the gas phase and the interphase
2
turbulent momentum transfer is accounted using a closure term. This model is known as the k- dispersed
3
model, and its equations can be given by
ip t
1
eq.(21)
us
cr
4
6
Where,
are source terms for the influence of the dispersed phases on the continuous phase. The
7
equations for these source terms are (Elghobashi and Abou-Arab, 1983; Simonin and Viollet, 1990):
ed
M
and
eq.(22)
an
5
eq.(23)
Ac ce
pt
8
9
eq.(24)
10
Where, kgs is the variance in the velocity of the gas phase and dispersed solids phase; and C3e is a constant
11
having a value of 1.2.
12
Additionally, if the presence of solids has a significant impact on gas phase turbulence, the above equations
13
of k and
14
phase model.
for the gas phase are also solved for the solids phase. This model is then known as the k- per
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While the k- model is capable of useful predictions for engineering design and optimization, it requires
2
careful parametrization. There are two basic assumptions in the k- model, i.e. (i) isotropic turbulent
3
viscosity and (ii) simplifications due to Reynolds averaging. The assumption of isotropy is valid for many
4
flows, but not for those with strong separation or swirl. In flows where, the flow regime transitions occur, the
5
k- models do not provide the required accuracy. Therefore, other modelling approaches such as Reynolds
6
stress model (Lain et al., 2002; Lain and Garcia, 2006; Kuan et al., 2007 and Chu et al., 2011) and large eddy
7
simulation (LES) model (Mathiesen et al., 2000; Yamamoto et al., 2001; Huilin and Gidaspow, 2003; Ibsen
8
et al., 2004 and Vreman et al., 2009) have been used for the gas-solid flow. Such models are still
9
computationally expensive, particularly for full scale simulation of riser flow. Mostly, the RSM model is
10
used for gas-solid flow with strongly anisotropic flow of gas phase such as those in cyclone and pipe bends;
11
while the LES model has been used for dilute gas-solid flow in pipes.
12
In the RSM, the stress in the gas phase is given as sum of laminar and turbulent stresses. The laminar stress–
13
strain tensor can be given by eq. (14), while the turbulent stresses can be given by:
cr
us
an
M
ed pt
14
ip t
1
eq. (25)
Where, τt,g is the turbulent stresses in the gas phase; and
16
Similar to the k- two equation model, the RSM can also be implemented as either dispersed or mixture
17
model. In the RSM-dispersed model, the transport equation for the Reynolds-stress term is solved for only
18
the gas phase. The RSM transport equation can be given as:
Ac ce
15
is the Reynolds-stresses in the gas phase.
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1 2
eq.(26)
Where, u’ is the fluctuating velocity component; is the turbulent dissipation rate; and
4
stress terms due to turbulent interactions between phases.
cr
us M
is the Kronecker delta.
is given by modified model of Simonin and Viollet (1990):
ed
Where,
eq.(27)
eq.(28)
Ac ce
pt
7
can be given as (Cokljat et al. 2003):
an
5
6
is the Reynolds
ip t
3
8
Where, β is the drag coefficient; kgc is the gas-solid phase velocity covariant; k is the turbulent kinetic
9
energy; urel and udrift are relative and drift velocities respectively.
10
In the RSM-mixture model, the Reynolds-stress transport equation for the gas phase is solved, but without
11
term. Furthermore, properties of phase such as density and velocity are represented as mixture
12
properties. The RSM solves transport equations for six independent Reynolds stresses and one for the
13
turbulent dissipation. The transport equation of the turbulent dissipation is same as eq. (22). The RSM is
14
computationally more expensive than the k- model. The use of RSM avoids assumption of isotropy, but it
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1
still involves Reynolds averaging which may cause error estimation of double and triple correlation of
2
turbulent velocities.
3
Because of the restrictive assumptions made in the k- and RSM models, some deviations (upto 25%) occur
4
in the prediction of the three components of the mean flows. However, the major impact of the assumption is
5
seen in the predictions of k and
6
of the rates of agglomeration, breakage, heat transfer and mass transfer need to use the local values of k and
7
and hence the need for accurate predictions. The conservation equations for k and consists of 5 terms : rates
8
of (i) convective transport (ii) turbulent transport (iii) viscous transport (iv) productions and (v) dissipation.
9
While solving these conservation equations, the values of individual terms take such values that the overall
10
balance is satisfied. However, normally the rates of dissipation and turbulent transport are under-predicted
11
upto 70%. On contrast the rates convective transport and production together get over-predicted so as to
12
match the balance. These incorrect predictions of individual terms results into incorrect predictions of k and
ip t
cr
us
an
M
ed
in the range of ± 20% to ± 200% (Zoheb Khan, 2016).
pt
13
profiles. It may be pointed out that most of the models for the predictions
In the LES model, the flow of the gas is divided in two parts, (i) large-scale flow resolved by the
15
computation and (ii) sub-grid scale (SGS) fluctuations. The effect of SGS fluctuations on the large-scale
16
flow is accounted for by applying SGS closure for turbulent stresses. The gas phase stress can be given as
17
(Yamamoto et al., 2001):
18
Ac ce
14
19
Where µ is the gas phase viscosity; Sij is the strain rate tensor,
20
of the gas phase.
eq.(29)
is the SGS stress and u is the velocity
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1
The strain rate tensor can be given as:
2
eq.(30)
Using the Smagorinsky model (Smagorinsky, 1963), the SGS stress can be given as (Yamamoto et al.,
4
2001):
cr
eq.(31)
us
5
ip t
3
Where, Cs is the Smagorinsky constant;
8
be given as
is the filter size and fs is the damping function. The filter size can
M
7
pt
ed
and the damping coefficient can be given as:
eq.(33)
Ac ce
9
eq.(32)
an
6
10
Where, y+ is the distance from the wall in wall unit.
11
While we have provided an overview of LES formulation for the continuous phase, in multiphase flows,
12
even at laminar conditions, additional challenges arise due to small time and length scales involved in the
13
dispersed flow. These scales are further magnified in presence of turbulence. Thus it is important to capture
14
the microscopic phenomena that accounts for all the small scale interactions for development of accurate
15
multiphase model (Fox, 2012).
16
3.1.2.3. KTGF closure models
17
Using the continuum approach for the solids phase, the stresses in the solids phase are derived by making an
18
analogy between a random motion of particles and thermal motion of gas molecules. This approach is widely
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1
known as the KTGF (Jenkins and Savage, 1983; Lun et al., 1984). Unlike the kinetic theory of the dense gas
2
(Chapman and Cowling, 1970), the KTGF accounts for inelasticity of particle-particle collisions. The
3
intensity of the particle velocity fluctuations determines the stresses, viscosity and pressure of the solids
4
phase. Taking the analogy with the thermodynamic temperature of the gas, the random motion of particles is
5
represented by “granular temperature”, which is proportional to the mean quadratic velocity of the particle:
eq.(34)
cr
ip t
6
eq.(35)
us
7
Where, Θ is the granular temperature; c is fluctuating velocity of particle and EΘ is the fluctuating energy due
9
to random motion of particles.
an
8
The solids phase stresses depends on the magnitude of this fluctuating particle velocity. Thus, conservation
11
of the pseudo thermal energy of the solids phase associated with the fluctuating velocity is required. This
12
conservation equation can be given as:
ed
M
10
eq.(36)
Ac ce
pt
13
14
Where,
15
dissipated energy due to particle collision;
16
energy; and
17
The collisional dissipation energy can be written as (Lun et al., 1984):
represents generation of the energy by the solid stress tensor;
represents
is diffusion coefficient (or conductivity) for the granular
represents exchange of fluctuating energy between the gas and solids phases.
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1
2
eq.(37)
and the diffusion coefficient for the granular energy can be written as (Gidaspow, 1994):
eq.(38)
cr
ip t
3
4
Where,
5
The exchange of kinetic energy of random fluctuations in particle velocity to the gas phase is written as
6
(Gidaspow, 1994):
M
an
us
.
eq.(39)
ed
7
Syamlal et al. (1993) suggest an algebraic form of the granular temperature equations by neglecting
9
convection and diffusion terms. The algebraic form of the granular temperature equation can be written as
11
(Syamlal et al., 1993):
Ac ce
10
pt
8
eq.(40)
12
In above equations, ess is the coefficient of restitution for inelastic collisions between the particles; go,ss is the
13
radial distribution function, Ps is the solids pressure and
14
coefficient of restitution depends on the material properties, and its value for the FCC catalyst is not known.
15
As a result, this parameter works as an empirical tunning parameter. In previous simulations, the values of
16
the restitution coefficient between 0.7-0.99 have been used. The radial distribution function describes the
17
probability of finding two particles in close proximity. It is a correction factor that modifies the probability
18
of collisions between particles when the granular phase becomes dense. Its correlation given by Lun et al.
19
(1984) can be written as,
is the stress tensor for the solids phase. The
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1
2
eq.(41)
The stress tensor for the solids phase can be written as:
eq.(42)
cr
ip t
3
The solids pressure (Ps) represents the normal solids phase forces due to particle-particle interactions. The
5
solids pressure term is composed of a kinetic term and a second term due to the particle collisions. The solids
6
pressure term prevents the solids volume fraction from exceeding the maxing packing limit. The correlation
7
for the solids pressure can be written as (Lun et al., 1984):
an ed
written as (Lun et al., 1984):
pt
11
The solids bulk viscosity (λs) is the resistance of particle suspension against the compression, and it can be
eq.(44)
Ac ce
10
eq.(43)
M
8
9
us
4
12
The solid shear viscosity (µs) is made up of the collisional, frictional and kinetic parts. All the models for
13
solid shear viscosity yield practically the same solid shear viscosity at solid volume fraction greater than
14
0.25. For lower volume factions of the solids, the models start deviating from one another (Ahuja and
15
Patwardhan, 2008). The Gidaspow model (Gidaspow, 1994) for the solid shear viscosity neglects the
16
inelastic nature of particle collisions in the kinetic contribution of the total stress and the Gidaspow’s model
17
has been used in several previous studies. The model equations for the granular shear viscosities and its
18
collisional and kinetic components can be written as,
19
eq.(45)
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1
(Gidaspow, 1994)
eq.(46)
eq.(47)
ip t
2
3.1.2.4. Frictional viscosity
4
At high solid volume fraction, frictional stress resulting from inter-particles contacts is significant, and
5
therefore, frictional part is considered to calculate the solid shear viscosity. The frictional viscosity is
6
generally calculated using Schaeffer’s (Schaeffer, 1987) model.
an
us
cr
3
(Schaeffer, 1987)
eq.(48)
M
7
Where, θ is the angle of internal friction; Pfri is the frictional pressure; and I2D is the second invariant of the
9
deviatoric stress tensor. The frictional pressure is given as (Johnson and Jackson, 1987):
ed
8
eq.(49)
Ac ce
pt
10
11
Where, εs,min is the minimum solid volume fraction from where frictional stresses become important. Fr, n
12
and p are empirical constants which depend on material properties. The values of Fr, n and p are often taken
13
to be 0.05, 2 and 3 respectively (Ocone et al., 1993). Syamlal et al. (1993) have suggested a model the
14
frictional pressure, which is:
15
eq.(50)
16
In the above equation, A and n are empirical constants and their values are taken to be 1025 and 10
17
respectively (Syamlal et al. 1993).
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Notably, several alternate models are available for the radial distribution function, solids pressure, bulk
2
viscosity, shear viscosity, frictional viscosity, granular conductivity and granular energy diffusion
3
coefficient. Van Wachem et al. (2001) and Ahuja and Patwardhan (2008) have reviewed the available
4
models by plotting their values against the solids volume fraction.
5
3.1.2.5. Heat exchange
6
In the energy conservation equations, ΔQgs and ΔQsg are heat exchanges between the gas and solids phases.
7
The heat exchange between the gas and solids phase can be given as,
cr
ip t
1
eq.(51)
us
8
Where, hsg (= hgs) is heat transfer coefficient; Asi is interfacial area between the gas and solids phases; Ts is
10
the temperature of the solids and Tg is the temperature of the gas phase. The heat transfer coefficient can be
11
correlated to the Nusselt number by,
M
an
9
eq.(52)
ed
12
Where, Kg is the thermal conductivity of the gas phase; Nus is the Nusselt number for the solids phase; and dp
14
is the diameter of the particles.
15
Generally, an empirical correlation of Ranz and Marshall (1952) is used to derive the heat transfer
16
coefficients.
18
Ac ce
17
pt
13
(Ranz and Marshall, 1952)
Where, Rep is the particle Reynolds number; and Pr is the Prandtl number.
19
20
eq.(53)
eq.(54)
Where, Cpg is the heat capacity of the gas.
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1
The Ranz and Marshall model is based on the heat transfer between single particles moving in a stationary
2
gas. Table-3 summarises several other empirical models that have been derived for the fluidized bed
3
conditions. Notably, there is no model available for the heat transfer between the gas and solids under the
4
flow conditions of the riser. Table-3: Models for gas-solid heat transfer coefficient Ranz and Marshall (1952) Ranz and Marshall (1952) Kothari (1967)
ip t cr
Fixed bed
an
+
us
Gunn (1978)
Single particle
M
Kunni and Levenspiel (1991)
Fluidized bed (Rep = 1 -100) Fluidized bed (Rep = up to 105 Fluidized bed
5 3.2.
Effect of constitutive models on flow predictions
7
Table-2 shows that simulation studies have used different combination of the constitutive models, and the
8
different selections of the constitutive models have caused significant variations in flow predictions.
9
Therefore in this section, the impact of closure models on predictions of gas-solid riser flow is analysed.
Ac ce
pt
ed
6
10
3.2.1.
Effect of drag models
11
Available drag models for the riser flow can be divided in three categories, namely (i) conventional drag
12
models, (ii) multi-scale or cluster based drag models, and (iii) those derived from direct numerical
13
simulations. Table-4 summarises the available drag models with their correlations, methods of their
14
derivation and shortcomings. Conventionally, the Wen-Yu model (Wen and Yu, 1966), Gidaspow model
15
(Gidaspow, 1994), and Syamlal and O’Brian model (Syamlal and O’Brien, 1987 and Syamlal et al., 1993)
16
are used for riser simulations. The Gidaspow model is a combination of the Ergun (for εg<= 0.8) and the
17
Wen-Yu (for εg> 0.8) correlations. The Syamlal and O’Brian model is based on the velocity-volume fraction
18
correlations derived using sedimentation and fluidization experiments of Richardson and Zaki (1954) and
19
Garside and Al-Dibouni (1977). The conventional drag models are empirical correlations that derived from
20
experimental observations on settling velocities of a single particle in the liquid and pressure drops inside
21
packed bed of the solids. However, the flow in riser exhibits the formation of clusters (Yerushalmi et al., Page 34 of 34 Page 34 of 114
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1976; Yerushalmi and Cankurt, 1979; Hario and Kuroki, 1994), which coexist and interact with surrounding
2
dilute phase. Due to the presence of clusters, apparent diameter of the solids becomes higher, and terminal
3
velocity of the particles in the cluster then becomes higher. This leads to down flow of solids and higher
4
segregation of the solids near wall (Mueller and Reh, 1993; Nieuwland et al., 1996a, Noymer and
5
Glicksman, 2000; and Pandey et al., 2004). Furthermore, due to formation of the clusters, the gas tends to
6
flow around the clusters without penetrating inside them. This result in significant less resistance to flow (Li
7
and Kwauk, 1994) leading to reduction in gas-solid drag. In previous studies (Yang et al., 2003a,b; Andrew
8
IV et al., 2005; and Shah et al., 2011b,c), use of the conventional drag models in coarse grid riser simulations
9
has not captured axial and radial distribution phases accurately. These studies have attributed this drawback
10
to the use of coarse grid, where spatial resolution is insufficient to capture clusters. Agrawal et al. (2001)
11
have shown important of grid resolution to capture clusters. However, fine grid simulation of industrial-scale
12
riser is computationally intensive. Therefore, drag models specific to cater coarse grid riser simulations have
13
been derived by using different multiscale approaches. Wang (2009) has categorized methods for deriving
14
multiscale drag models for the Eulerian simulations of Geldart-A particles in six categories, i.e. empirical
15
correlation method, scaling factor method, structure-based method, modified Syamlal and O’Brien drag
16
correlation method, EMMS-model-based method, and correlative multi-scale method. Out of these methods,
17
the sub grid scale (SGS) approach (Sundaresan and co-workers) and energy minimization multi-scale
18
(EMMS) approach (Li and Kwauk and co-workers) have been often used in several previous studies.
19
In the SGS approach (Agrawal et al., 2001; Andrews IV et al., 2005; Igci et al., 2008; Igci and Sundaresan,
20
2008), the drag is derived by using numerical results from extremely fine grid simulations using a periodic
21
domain. Andrew IV et al. (2005) have conducted fine grid simulations of only a section of riser using
22
periodic boundary conditions, and the results have then been used to derive closures of the solids phase and
23
gas-solid drag. . Igci et al. (2008) have extended Andrew IV et al.’s work to show the effect of grid size,
24
known as filter size, on the closures derived from the fine grid simulations. These closures are then used in
25
coarse grid simulation of a full-scale riser (Benyahia, 2009). An alternative approach is the energy
26
minimization multi-scale (EMMS) model (Li and Kwauk, 1994; Xu and Li, 1998; Li et al., 1999; Yang et al.,
27
2003b). The EMMS approach divides the flow in three pseudo phases i.e. dilute phase, dense phase and
28
suspended clusters. The dilute phase represents individual particle in gas. The dense phase represents
29
particles and gas residing inside clusters; whereas the suspended clusters phase represents individual cluster
30
as a whole entity that moves in the gas phase. The EMMS calculates drag in each three pseudo phases by
31
using conventional Wen-Yu drag model. Drags in the dilute phase and dense phase are calculated by using
32
particle diameter, while drag in the suspended cluster phase is calculated by using cluster diameter. Addition
33
of three drags in three pseudo phases represents resultant EMMS drag in dilute gas-solid flow in riser.
34
However, calculation of the EMMS drag needs cluster diameter, fraction of solids forming the cluster and
35
slip velocities in three pseudo phases. Thus, EMMS drag largely relies on cluster parameters. Cluster
36
diameter in the EMMS is mostly calculated by empirical correlations and correlations based on different
37
hypothesis (Shah et al., 2011b); while fraction of solids and superficial velocity in cluster phase are
Ac ce
pt
ed
M
an
us
cr
ip t
1
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calculated by solving mass and energy balance equations for each pseudo phase. For detailed equations and
2
calculations of the EMMS drag, readers are referred to various published articles of Li and co-workers (Li
3
and Kwauk, 1994; Xu and Li, 1998; Li et al., 1999; Yang et al., 2003a, b; Wang, 2008; and Shah et al.,
4
2011b, c). Recently, numerical observations from DNS have been used to derive gas-solid drag correlations
5
(Hill et al., 2001b; Benyahia et al., 2006; Beetstra et al., 2007; Tenneti et al., 2011). DNS studies are
6
conducted by using lattice Boltzmann method (LBM) or immersed boundary method (IBM). In these studies,
7
particle resolved simulations of a periodic domain with several randomly positioned particles are conducted
8
to capture interphase exchange forces at the boundary of each particle. The numerically calculated particle-
9
scale forces are then used to calculate an averaged drag force in the flow domain.
Ac ce
pt
ed
M
an
us
cr
ip t
1
Page 36 of 36 Page 36 of 114
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Table-4: Gas-solid drag models Derived from Conventional drag models Gidaspow (1994)
Do not capture axial profile of the solid volume fraction (Yang et al., 2004; Wang et al., 2008; Benyahia, 2009; Shah et al., 2011; Baharanchi et al., 2015). Previous studies attributed this drawback to their inability to account for effect of clusters in coarse grid simulations. Actually, The Wen-Yu model is applicable to dilute flows (εg close to 1); while the Ergun is used for dense flows. Even the Syamlal-O’Brien is derived from a single particle drag. At intermediate range of solids A drag for multi-particle system is derived from single volume fraction (0.7 ≤ εs ≤ 0.95), these drag models particle drag, Dalla Valle (1948)’s equation for drag significantly over predict the drag force than the values coefficient for a single particle, Richardson and Zaki of multi-scale drag models. (1954)’s correlation between ratio (Vr) of terminal velocity of multi-particle to that of single particle with the gas volume fraction, and Garside and Al-Dibouni (1977)’s correlation between Vr and particle Reynolds number.
Uses Ergun model for εg less than 0.8 and Wen-Yu model for εg greater than 0.8. The Wen-Yu model has been derived from settling experiments of single particle in liquids, while the Ergun model has been derived pressure drop measurement in packed bed.
for εg> 0.8 (Wen and Yu, 1966) for εg<= 0.8 (Ergun, 1952b) If Res< 1000 Schiller &Nauman (1935)
ip t
= 0.44 If Res≥ 1000
us
cr
Syamlal-O’Brien (1987)
Multiscale drag models EMMS (Li and Kwauk, 1994)
for
> 0.748
<= 0.748
ed
for where,
M
an
if ε ≤ 0.85 if ε > 0.85 “a” and “b” are tunning constants that must be calibrated to match the minimum fluidization velocity for the solid particles in question (Syamalal and O’Brien 2003). Based on Umf calculated from the Ergun equation for 76 μm FCC particle and 1712 kg/m3 density, the values of “a” and “b” are 0.8 and 2.66.
is a correction factor and it can be calculated as,
Uses EMMS algorithm based on energy minimization of suspension and transportation in gas-solid riser flow. It requires cluster parameters such as fraction of solids in cluster, solid volume fraction of cluster, cluster diameter and slip velocity in clusters.
for 0.748 <εg<= 0.83
pt
for 0.83 <εg<= 0.86 for 0.86 <εg<= 0.94
Ac ce
for εg> 0.94 The equations for the corrections factors are for high solids flux (Gs = 489 kg/m2s, and ug = 5.2 m/s) as reported by Shah et al. (2014). These functions need to be recalculated using the EMMS algorithm (Li et al., 2011; Yang et al., 2003; Shah et al., 2011) for a given flow conditions and physical properties. SGS Anderew IV et al. (2005); Igci et al. (2008); Benyahia (2009)
Shortcomings
for
≤ 0.0.04083
Simulation results using very fine grid in periodic domain of a size comparable to control volume of the continuum simulations.
Capture both axial and radial profiles with some quantitative discrepancies (Yang et al., 2003; Benyahia, 2009; Igci et al., 2008 Shah et al., 2011). The EMMS requires cluster properties, of which detail measurements are not available. Furthermore, the EMMS correlation needs to be derived for riser with different flow conditions. Implementation of EMMS algorithm in each control volume using local flow conditions is computationally expensive. The SGS requires find grid simulations of a small flow domain and thus, the final drag function depend largely on grid size, as well as the simulated flow conditions (Igci et al., 2008; Benyahia, 2009). For riser simulation, this approach is computationally more expensive.
for 0.0.04083< ≤0.2589 for
>0.2589
Above drag equations are based on for high solids flux (Gs = 489 kg/m2s, and ug = 5.2 m/s) as reported by Benhyaia (2009) using dimensionless filter size gΔ/Vt2 = 2.056 where Δ = grid size = 0.014m, Vt = 18.46 m/s Models from DNS
Page 37 of 37 Page 37 of 114
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Beetstra et al. (2005)
LBM simulations of randomly arranged particles in periodic flow domain. Drag on individual particles is calculated at particle Reynolds number range of 21-105. The calculated drag values are used to derive a correlation between the drag, gas volume fraction and particle Reynolds number. IBM simulations of randomly arrange particles in periodic flow domain are conducted with flow conditions varies in a range of particle Reynolds number of 0-300. The calculated values of fluid-solid drag are used to derive drag correlation.
cr
ip t
Tenneti et al. (2011)
These drag models have not been extensively investigated by conducting riser simulations.
Ac ce
pt
ed
M
an
us
10
Drag values from Beetstra et al. (2005) are quite different from those of Tenneti et al. (2011) at high solids volume fraction and particle Reynolds number. Tenneti et al. (2011) have attributed the difference to insufficient grid resolution of Beetstra et al.’s simulations. Tenneti et al. (2011) have highlighted a need of high grid resolution to capture boundary layers between two particles, particularly at high solids volume fraction. Tenneti et al.’s drag model is based on particles arranged at random positions. Shah et al. (2013) have shown that drag values from particles arranged in cluster configurations are significantly lower than random configuration.
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In Table-4, the correlations for the EMMS and SGS are available for the flow conditions of high flux riser
2
(Gs = 489 kg/m2s, ug = 5.2 m/s, ρs = 1712 kg/m3, Inlet solid volume fraction = 0.5, Dt = 0.2 m and H = 14.2
3
m) of Knowlton et al. (1995).Using the correlations of Table-4, values of the drag coefficients are calculated
4
for a range of volume fraction at a given slip velocity of 0.57 m/s. The comparison of the calculated drag
5
coefficients is shown in Figure-7. It can be seen that the drag coefficients from the conventional models and
6
DNS agree with each other over a range of the volume fraction. But at the lower gas volume fraction, the
7
drag coefficients from the DNS studies are higher than those from the Wen-Yu and Ergun models. The
8
values from the Syamlal-O’Brien model are lower than those from the Wen-Yu, Ergun, BVK (Beetstra, van
9
der Hoef and Kuiper) and PUReIBM (Tenneti et al., 2011) models. The drag coefficient calculated from the
10
EMMS model is significantly lower in an intermediate range of the gas volume fraction of 0.7-1. At
11
minimum fluidizing and maximum gas volume fraction, the mathematic formulation of the EMMS model
12
forces the drag values to approach the values calculated by the conventional drag models. The values from
13
the SGS model are significantly lower than other drag models over entire range of the gas volume fraction,
14
and the SGS values further drifting lower at the gas volume fraction close to 1. While explanation of the
15
behaviour of the SGS model is not clear, it is noteworthy that the SGS correlation is a weak function of the
16
particle Reynolds number (Benyahia, 2009) and it relies mainly on grid size (known as filter size) used in
17
fine grid periodic simulations. In previous studies, the lower drag values from both the EMMS and SGS
18
models have been attributed for their ability to account for the clusters or volume fraction heterogeneity.
Ac ce
pt
ed
M
an
us
cr
ip t
1
Figure-7: Comparison of drag coefficients (Gs = 489 kg/m2s, ug = 5.2 m/s, Uslip = 0.57 m/s) 19
Yang et al. (2003a,b); Wang et al. (2008); Benyahia (2009), Shah et al., (2011b, c), Benyahia (2012), Wang
20
et al. (2012), Shah et al. (2015) and several others have compared predictions of axial and radial profiles
21
from the EMMS models with those from the Gidaspow drag model. Similarly, Andrews IV et al. (2005),
22
Benyahia (2009), Igci and Sundaresan (2008), and Igci and Sudaresan (2011) have compared predictions
23
from the SGS model with those from the Gidaspow and experimental data. Comparison by Shah et al. (2015) Page 39 of 39
Page 39 of 114
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is shown in Figure-8. For a low solid flux riser, the predicted axial profile from the Gidaspow model shows
2
that the values do not vary along height. This axial profile from the Gidaspow drag model shows complete
3
disagreement with the experimental data both qualitatively and quantitatively. On the other hand, the EMMS
4
model gives a dense bottom with higher solid volume fraction and lower values at the top (Figure-8) forming
5
the S-shape axial profile with reasonable qualitative agreements with the experimental data. For high flux
6
solids riser (Figure-8b), the pressure drop profiles predicted by both the Gidaspow and EMMS model
7
qualitatively agrees with the experimental data. Quantitatively, the predictions from the EMMS model are
8
closer to the experimental data at the bottom; while at the top, the values from the Gidaspow model are in
9
close agreement with the experimental data.
Ac ce
pt
ed
M
an
us
cr
ip t
1
(b)
(a)
Page 40 of 40
Page 40 of 114
us
cr
ip t
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an
(c) (d) Figure-8: Effect of drag model: (a) and (b) axial profiles of solids volume fraction at low solids flux and pressure drop at high solids flux respectively; (c) and (d) radial profiles of solids volume fraction at low and high flux respectively (Shah et al., 2015). Shah et al. (2015) have also compared the predicted radial profiles from the EMMS and Gidaspow models
2
with the experimental data (Figure-8c and d). The radial profiles from the EMMS model also give reasonable
3
qualitative agreements with the experimental data for two (low and high solids flux) flow conditions.
4
Quantitatively, the predictions from the EMMS still show some discrepancies between the predicted values
5
and experimental data. Shah et al. (2015) attributed these discrepancies to assumptions and empirical
6
correlations involved in calculations of the cluster parameters. Benyahia (2009) have also found
7
discrepancies between their predictions from the SGS drag model and experimental data, and the author has
8
attributed the discrepancies to the dependence of the SGS drag on the selection of the filter size. The
9
numerical drag models proposed by Beetstra et al. (2007) and Tenneti et al. (2011) have still not been tested
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by conducting riser simulations.
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(b) Figure-9: Effect of gas phase flow models, (a) radial profile of volume fraction of solids phase and (b) axial profile of volume fraction of solids phase. 3.2.2.
Effect of gas phase viscous model
2
Experimental data shows existence of both dense and dilute conditions inside the riser. The flow of the gas
3
phase in the dilute region is expected to be turbulent, while that in the dense region with narrow inter-particle
4
distances and in boundary layer around particles and clusters can be either laminar or turbulent. On the other
5
hand, clusters of the solid particles observed in riser can significantly dampen or enhance fluctuating velocity
6
of the gas phase. Hence, laminar model has also been used to model stresses in the gas phase. The gas phase
7
Reynolds number based on diameter of riser generally varies from 104 to 106; while the particle Reynolds
8
number that calculated from diameter of particle is less than 100. As a result, both the laminar and turbulent
9
models for the gas phase stresses are applied in CFD studies.
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10
Almuttahar and Taghipour (2008) have compared predictions from the laminar and k- mixture turbulent
11
models. It can be seen in Figure-9a that radial distributions of the solids volume fraction predicted by the
12
laminar model are closer to the experimental values than those from the k- turbulent model; whereas, the
13
predicted axial profiles from both the laminar and turbulent models show wide discrepancies with the
14
experimental values (Figure-9b). Almuttahar and Taghipour (2008) have attributed these discrepancies to the
15
considered 2D geometry, and recommend 3D simulations for accurate predictions. Benyahia et al. (2005)
16
have investigated three different gas-solids turbulence models. Two of these models are those of Balzer et al. Page 42 of 42
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(1996) and Cao and Ahmadi (1995) that account for the effect of gas turbulence through the use of a
2
modified k- model, whereas the third simulated model is of Agrawal et al. (2001) that does not model the
3
gas phase turbulence. Benyahia et al. (2005) have found only minor difference between the predicted radial
4
profiles from these models with and without gas phase turbulence.
5
Shah et al. (2015) have also compared predictions from the laminar, k-ε dispersed model and k-ε per phase
6
model for both high and low flux conditions. Shah et al. (2014) have found that predicted values from both
7
the laminar and k- dispersed models give reasonable agreement with the experimental data; while the per-
8
phase option slightly under predicted the values in the dense section and over predicted at the top section
9
(Figure-10a). For the high flux condition (Figure-10b), all three models predicted similar time-averaged axial
10
pressure drop profiles. Figure-10(c) and (d) shows the impact of three viscous stress models on instantaneous
11
contour plots of the solids volume fraction captured at 20s flow time. For both low and high flux conditions,
12
the contour plots from laminar and k- dispersed models give continuous flow structures with “cluster” and
13
“steamer” like solid structures appearing throughout the height. But the contour plots from k- per-phase
14
model give discontinuous solid structures, where zones of higher and lower solid volume fractions appear to
15
be stretched all the way from the wall to the centre of the riser. Furthermore for the low solids flux condition,
16
the contour plots from only laminar and k- dispersed model show a clear distinction between the dense
17
bottom and dilute top sections. Shah et al. (2015) have further compared instantaneous values of turbulent
18
kinetic energy of the gas phase and granular temperature of the solids phase at different heights. While Shah
19
et al. (2015) have shown different in predictions from the k- dispersed and per-phase models, they have not
20
given a detail analysis on reason for these differences.
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Laminar
k-ε dispersed
k-ε per-phase
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Laminar k-ε dispersed k-ε per-phase (d) High solids flux (Gs = 489 kg.m2s)
2
(c) Low solids flux (Gs = 14.3 kg.m s)
Figure-10: Effect of gas phase flow models on axial profiles, (a) volume fraction of solids phase at low solids flux condition; (b) pressure drop at high solids flux condition; and (c) and (d) Instantaneous contour plots of solid volume fraction (Shah et al., 2015). 3.2.3.
Effect of KTGF closure models
2
Table-2 shows that previous simulation studies have used the E-E model with the KTGF, where two types of
3
granular temperature conservation equations such as partial differential and algebraic have been used. In
4
either of these two selections, the model requires closure laws for the granular energy dissipation rate, radial
5
distribution function and solids bulk viscosity. If the partial differential equation for the granular temperature
6
is applied, then the closure law for the granular temperature conductivity is also required. Several models are
7
available for these KTGF closures. van Wachem et al. (2001) and Ahuja and Patwardhan (2008) have
8
explicitly calculated values of the solids phase KTGF properties from alternate closure models for a range of
9
the solids volume fraction of 0-0.65. For the solids volume fraction between 0-0.3, which is a typical range
10
of the solids volume fraction found in riser, these studies find only minor differences between the calculated
11
values from alternate closure models accept those from closure models proposed by Syamlal et al. (1993).
12
Consequently, the effects of alternate closure models for each of the KTGF parameters (such as the solid
13
pressure, frictional pressure, shear viscosity, granular viscosity, frictional viscosity, and radial distribution
14
function) on prediction of the riser hydrodynamics have not been investigated by conducting riser
15
simulations.
16
3.2.4.
17
3.2.4.1. Inlet boundary conditions
18
Boundary conditions have been used to specify numerical values at the boundary cells in CFD models. The
19
previous riser simulations (Table-2) employ three different types of flow domains such as periodic, 2D and
20
3D geometries. Using the periodic domain (Agrawal et al., 2001; Andrew IV et al., 2005; Benyahia et al.,
21
2009; Igci et al., 2008; Naren and Ranade, 2011), only a differential element of riser is considered and
22
computed values at the outlet boundary surface are passed to the inlet boundary at every time step. This type
23
of periodic flow domain is simulated to evaluate the effect of various closure models and flow conditions on
24
fully-developed radial profiles. In order to evaluate effect of model parameters on both axial and radial
25
profile, 2D and 3D flow domains with appropriate inlet and outlet boundary conditions are required. In these
26
simulations, inlets are configured with velocity-inlet boundary condition.
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Effect of boundary conditions
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1
At gas inlet, velocity of the gas phase equal to operating superficial gas velocity is specified with volume
2
fraction of solids phase equal to zero, while at solid inlet; average solid velocity at inlet is calculated from a
3
circulating solid mass flux by,
eq.(55)
ip t
4
Where, Gs is the solid flux circulating in riser, Ariser is the cross sectional area of riser, and Ainlet is the cross
6
sectional area of solid inlet. This boundary condition also needs a value of solids volume fraction which is
7
generally taken as the value at minimum fluidizing condition (0.5) or maximum packing condition (0.63).
8
Pressure-outlet boundary condition is most commonly used for the outlet. By specifying gauge pressure
9
equal to zero, the pressure at outlet is set as the atmospheric pressure.
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Previous CFD studies have been conducted by using both 2D and 3D flow domains. Furthermore, it can also
11
be observed that the previous simulations more choose 2D flow domain, as they are computationally more
12
feasible. Representation of an actual 3D riser using 2D domain then requires appropriate selection of the inlet
13
boundary conditions. Benyahia et al. (2001) have simulated a 2D geometry with one solid inlet (as
14
schematically shown in Figure-11a), mimicking the inlet configurations of the 3D boundary conditions of
15
experimental setup. In Benyahia et al.’s simulation, most of the solid particles are found to be concentrated at
16
the inlet side of the riser causing unsymmetrical radial distribution of the solid density (Figure-11b), which
17
did not agree with the core-annulus profile. Recently, Li et al. (2014a,b) have also observed accumulation of
18
the solids at one side of riser with one side inlet in 2D simulations. Since a 2D domain with one side inlet
19
cannot directly capture the asymmetric entry of solids to a continuously flowing riser, the 2D riser
20
simulations have been conducted using different types of boundary conditions for the inlets and outlets (Pita
21
and Sundaresan, 1993; Neri and Gidaspow, 2000; Benyahia et al., 2001; Yang et al., 2003; Almuttahar and
22
Taghipour, 2008).Benyahia et al. (2001), Yang et al. (2003) and Shah et al. (2012) have used two-sided
23
solids inlets for 2D riser simulations (Figure-12a). Shah et al. (2012) have compared the predictions from the
24
two-sided solids inlets in 2D simulations with both predictions from 3D simulations and experimental data
25
(Figure-11c), and found reasonable qualitative agreements between predictions and experimental data.
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(c) (b) Figure-11: (a) Schematic of 3D and 2D boundary conditions; (b) and (c) radial profile using one side solids inlet and two-sided solids inlets respectively. 1
3.2.4.2. Wall boundary conditions
2
For wall boundary condition, three alternatives (no-slip, free-slip or partial-slip) boundary conditions can be
3
used for an individual phase. Generally, no-slip boundary condition is used for the gas phase; whereas, each
4
of the three alternates have been considered for solids phase by previous studies. The no-slip boundary
5
condition for solids phase is set by equating the tangential and normal velocities of the solids to zero. The
6
partial-slip boundary condition can be configured using correlations developed by Sinclair and Jackson
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1
(Sinclair and Jackson, 1989) for the wall shear and Johnson and Jackson (Johnson and Jackson, 1987) for the
2
granular energy dissipation at wall. The wall shear boundary condition for the solids phase is given by rate of
3
axial momentum transferred to wall by the particles in a thin layer adjacent to wall surface (Sinclair and
4
Jackson, 1989):
eq.(56)
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5
Where,
is the specularity coefficient. Its value equal to zero denotes free slip or specular wall, and unity
7
denotes no-slip wall.
8
The granular energy at wall can be obtained by using equation of Johnson and Jackson (1987). The granular
9
energy flux can be positive (wall as sink) or negative (wall as source) depending upon the relative magnitude
10
of granular energy dissipation due to non-elastic collision between particle and wall, and generation of
11
granular energy due to shear at wall. The granular energy dissipation due to inelastic collision with wall can
12
be written as,
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eq.(57)
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14
Thus, the partials-slip condition for the solids phase requires two additional parameters i.e. the specularity
15
and wall restitution coefficients.
16
The selection of the wall boundary conditions for the solids phase dictates velocity and volume fraction near
17
wall, and hence, appropriate wall boundary condition is very critical for capturing the core-annulus radial
18
profile. Table-10 shows that the partial-slip (Johnson and Jackson, 1987) wall boundary condition for the
19
solids phase is overwhelmingly used in previous studies. However, the use of the partial-slip configuration
20
needs a specularity coefficient and particle-wall coefficient of restitution to calculate friction between the
21
wall and particles and energy dissipation in the particle-wall collisions respectively. The specularity
22
coefficient represents a fraction of collisions that transfers momentum to wall; while the coefficient of the
23
restitution represents the fraction of the energy dissipated in the particle-wall collisions. Both these
24
parameters are dependent on material properties particles and wall. The restitution coefficient has been
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measured from controlled experiments by Gorham and Kharaz (2000), Joseph et al. (2001), Kharaz et al.
2
(2001) and Mangwandi et al. (2007). However, values reported in these studies are for different particle sizes
3
and materials, not for FCC catalyst. Hui et al. (1984) and Li and Benyahia (2012) have mentioned that
4
experimental estimation of the specularity coefficient is not feasible. One way to determine the specularity
5
coefficient is to adjust this parameter to fit experimental data. Li and Benyahia (2012) have provided a model
6
for specularity coefficient as a function of the particle-wall restitution coefficient, the frictional coefficient
7
and the normalized slip velocity at the wall. Li and Benyahia’s model for specularity coefficient has not been
8
tested by conducting riser simulation.
ip t
1
cr
9
Benyahia et al. (2012); Almuttahar and Taghipour (2008); Wang et al. (2012) and Shah et al. (2015) have
11
investigated the effect of the specularity coefficient and coefficient of the restitution on flow predictions.
12
While Benyahia et al. (2012); Almuttahar and Taghipour (2008) and Wang et al. (2012) have found only
13
minor effect of the coefficient of the restitution on the predicted axial and radial profiles; the authors found
14
significant impact of the specularity coefficient. Shah et al. (2015) have investigated a wide range of
15
specularity coefficients from 0.1 to 0.0001 in riser with low and high solids flux conditions (Figure-12). As
16
shown in Figure-12(a) and (b), a lower specularity coefficient of 0.0001 gave axial profiles of the solids
17
volume fraction (in the low solids flux riser) and pressure drop (in the high solids flux riser) that reasonably
18
agree with the experimental data. Figure-12(b) and (c) shows the effect of the specularity coefficients on
19
radial profiles at low and high solids flux conditions (Shah et al., 2015). While the specularity coefficient of
20
0.0001 also predicted experimental values in dilute section of the low solids flux riser; in dense bottom
21
region of the low solids flux riser, a higher specularity coefficient of 0.1 gave good agreement between the
22
predictions and experimental data. Shah et al. (2014) have concluded that the impact of the specularity
23
coefficient on the flow predictions has varied with the flow conditions. Therefore, this parameter must be
24
adjusted with the flow conditions.
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(a)
(b)
High solids flux
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Low solids flux
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(b) (c) Figure 12. Effect of wall boundary condition, (a) height of riser Vs. volume fraction of solid, and (b) height of riser Vs. pressure drop, (c) volume fraction of solid Vs. radial position (low solid flux riser, Gs = 14.3 kg/m2s), and (d) volume fraction of solid Vs. radial position (high solid flux riser, Gs = 489 kg/m2s) 1
3.3. Shortcomings
2
Following shortcomings of the E-E based CFD models of riser can be stated.
3
(1) The treatment of the solids phase as a fluid in the E-E approach requires several closure models that are
4
derived by using the KTGF. For each closure law, several models are proposed in literature. A selection
5
of appropriate closure models is critical to achieve close quantitative agreements between the predictions
6
and experimental data. Various combinations of the closure models (see Table-2) have been used in the
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1
past to get closer agreements with the experimental data at various flow conditions. Clear guidelines for
2
selection of KTGF closures are not available.
3 (2) The dominant closure in the E-E model is the interphase drag. Both conventional models and multiscale
5
drag models have been used. For coarse grid simulations, conventional drag models could not predict
6
experimental observations quantitatively. The multiscale structure dependent drag models such as the
7
EMMS and SGS drag models have shown significant improvements in predictions of axial and radial
8
profiles at different flow conditions (Yang et al., 2003; Benyahia, 2009; Shah et al., 2011b,c; and Shah et
9
al., 2015). However, the SGS model is computationally expensive, and the application of the EMMS
10
drag model needs local values of cluster properties such as size and volume fraction at a given flow
11
conditions. So far, experimental observations on structure of clusters (shape, size and volume fraction) at
12
different flow conditions are not available.
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(3) Predicted radial profiles from different simulation studied show reasonable qualitative agreements with
15
experimental data with some quantitative discrepancies. To eliminate such discrepancies, most of
16
previous efforts have been devoted to investigate the gas-solid drag model; while the effect of the lift
17
force has not been investigated.
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(4) Both the laminar and turbulent models for viscous stresses in the gas phase have been used in two-fluid
20
models of riser. Interestingly, both these models could give reasonable qualitative agreements with
21
experimental data in previous studies. Shah et al. (2015) showed that different types of the k- turbulent
22
models (dispersed and per phase models) for the gas phase gave similar time-averaged values, but
23
instantaneous flow structures are quite different. Further analysis suggested that turbulent kinetic energy
24
and dissipation rate predicted by the k- dispersed and per phase models are different by orders of
25
magnitude. Without detail time-averaged and instantaneous data on velocities and volume fraction, it is
26
difficult to conclude on suitability of use of the laminar or type of turbulent model.
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1 (5) As described in Table-2, almost all previous studies have used partial-slip wall boundary conditions,
3
which has been able to capture the core-annulus distributions of the solids phase. But, this wall boundary
4
conditions required empirical constant such as secularity coefficient, experimental value of which is also
5
not available. Therefore, most of the studies used this parameter for fine-tuning of the predictions. Li and
6
Benyahia (2012) have provided a model for specularity coefficient as a function of the particle-wall
7
restitution coefficient, the frictional coefficient and the normalized slip velocity at the wall. Such
8
correlation between the specularity coefficient and flow conditions needs further investigation by
9
conducting riser simulation.
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(6) Extensive simulation works have been conducted using 2D domain of riser due to computational
12
feasibility, while experiments are mostly conducted using 3D cylindrical riser. Furthermore, in the 2D
13
geometry, different types of assumptions such as two-sided inlets for the solids phase and bottom inlet
14
for the gas phase, single bottom inlet for gas and solids phases, and cycle boundary conditions to
15
maintain a constant solid holdup have been used. Shah et al. (2012) have showed that the inlet boundary
16
conditions in 2D domain significantly affect profiles in so-called fully developed region (at top section
17
of riser). Therefore, to avoid uncertainty arising from the assumed 2D boundary conditions, it is
18
necessary to evaluate effect of closure models in exact 3D geometry.
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3.4. Eulerian-Lagrangian model
20
In E-L model, the gas phase is represented as a continuous phase for which the averaged mass and
21
momentum balance equations are solved. These equations are similar to those discussed in the E-E model
22
(section-3.1.1.). The particle phase is considered as discrete particle. For individual particle, Newton’s force
23
balance equation is solved. The force balance equation around individual particle can be written as:
25
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(eq. 58)
(eq. 59)
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1
(eq. 60)
Where, xp is the position of particle p; Mp is the mass of particle, vp is the velocity of particle, Fp is the total
3
force on particle, Fd is the drag force on particle, Fc is the contact force on particle, Tp is the total torque on
4
particle, Ip is the moment of inertia of particle, Ω is the angular velocity of particle.
5
The drag force term on a particle residing in kth control volume can be written as (Garg and Dietiker, 2013):
cr
ip t
2
(eq. 61)
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Where, Pg,k is the gas pressure in kth control volume, vp is the volume of parcel, β is the drag coefficient, Xp
8
is the location of parcel, ug(Xp) is the velocity of the gas phase at location Xp, and up is the velocity of parcel.
9
In the Eulerian equation for the gas phase, the drag force term can be calculated as:
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(eq. 62)
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Where, vk is the volume of kth control volume, and np is the total number of particles in kth control volume.
12
Table-5 lists CFD studies of riser using the E-L gas-solid flow model. It can be seen that there are five
13
different types of modelling approaches have been adopted within the E-L framework. These approaches are
14
(i) discrete particle model (DPM), (ii) discrete element model (DEM)-hard sphere, (iii) DEM- soft sphere,
15
(vi) multiphase particle in cell (MP-PIC) and (v) dense discrete particle model (DDPM). Helland et al.
16
(2000) and Mansoori et al. (2005) have adopted DPM approach by considering only the drag force and
17
gravity force in the force balance equation for the particle phase. Zhou et al. (2002), Zhou et al. (2007), He et
18
al. (2009) and Cheng and Jin (2010) have used DEM approach. The DEM approach considers the contact
19
forces due to particle-particle and particle-wall collisions. In this approach, the contact forces can be
20
calculated by either hard-sphere (Allen and Tildesley, 1989) or soft-sphere (Cundall and Stack, 1979) model.
21
In the hard-sphere model, collisions are considered to be binary and instantaneous. The time step is
22
determined by the minimum collision time between any one pair of particles. Consequently, the time step is
23
directly proportional to the mean free path or inversely proportional to the particle volume fraction. Due to
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consideration of binary collisions, this approach is more suitable to dilute gas-solid flow (Garg et al., 2012).
2
For a dense gas-solid flow, the hard-sphere approach requires much smaller time-scale. Furthermore, a dense
3
flow is characterized by collisions and persistent contact between multiple particles. In the soft-sphere
4
model, the particles are allowed to overlap each other. The overlap between the two particles is represented
5
as a system of springs and dashpots in both normal and tangential directions. Here, the contact force on a
6
particle is calculated as a sum of conservative force represented by spring and dissipative forces represented
7
by dashpot. To calculate conservative and dissipative forces, stiffness of spring and damping coefficient of
8
dashpot are used. The spring stiffness, damping coefficient and overlap between particles are used to
9
calculate the time step. For detail formulation of the soft-sphere approach, readers are refer to Cundall and
cr
ip t
1
Stack (1979); Tsuji et al. (1993); Deen et al. (2007); Zhu et al. (2008) and Garg et al. (2012).
11
Vegendla et al (2011), Li et al. (2012), Chen et al. (2013), Wang et al. (2014) and Jiang et al. (2014) have
12
used multi-phase particle-in-cell (MP-PIC) method (Andrews andO’Rourke,1996; Snider,2001; Benyahia
13
and Galvin,2010) to simulate the gas-solid flow in riser. In MP-PIC method, particles are represented by
14
parcels where each parcel contains a certain number of real particles of the same diameter and density
15
(Snider, 2001). In implementation of MP-PIC, the effect of several particles forming a parcel is manifested
16
through solids volume fraction in the drag force term. The drag force on parcel residing in kth control volume
17
can be calculated similar to the drag force on each particle. However, the Eulerian drag force term can be
18
calculated as:
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eq.(63)
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Where, vk is the volume of kth control volume, NT is the total number of parcels in kth control volume and np is
21
the number of particles in a parcel.
22
The interactions between particles are considered through the solid phase normal stress but not directly
23
through particle contact forces (Li et al. 2012), while particle-wall interactions are modelled by using bounce
24
back rules where the particle-wall restitution factor is used for energy dissipation. In the MP-PIC method, the
25
collision force term is calculated as (Li et al., 2012 and Garg and Dietiker, 2013):
26
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(eq. 64)
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1
Where, Ps is the solids pressure which is calculated by,
2
(eq. 65)
Where, ps* and α are model parameters, whose recommended ranges are 1-100 Pa (Garg and Dietiker, 2013)
4
and 2-5 (Auzerais et al., 1988) respectively. Clote et al. (2010) have used slightly different approach where
5
solids pressure term appearing in above equation is calculated by used of the KTGF approach. This approach
6
is called as DDPM.
7
Different E-L modelling approaches can be evaluated in terms of (i) computational feasibility and (ii) their
8
ability to capture physical phenomena. Due to consideration of all real particles in riser, E-L approach
9
without contact forces (mentioned as DPM in Table-5) or DEM approach becomes computationally
10
impractical for real riser system. Consequently, most of DEM studies (see Table-5) have been conducted for
11
significantly less number of particles, scaled-down geometries or large sized particles. On the other hand,
12
MP-PIC approach considers flow of parcels number of which is significantly lower than number of real
13
particles. In addition, the MP-PIC approach does not take particle collision model explicitly and therefore, a
14
longer time step can be adopted for the particle phase. As a result, the MP-PIC approach becomes
15
computationally more feasible for riser simulations.
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Table-5: CFD studies of risers using E-L models Modelling approaches (a) (b) (a) (b)
Drag model (a) (a) (c) (a)
Number of particles × 10-3 250 >7
Investigations
>7
(c)
(b)
40
Effect of inlet gas velocity Effect of coefficient of restitution and friction coefficient Effect of operational, particle properties and geometrical parameters on clusters
0.02
0.14 (2D)
100
1400
He et al. (2009) Cloete et al. (2010) Wu et al. (2010) Zhao et al. (2010) Vegendla et al (2011) Li et al. (2012)
0.05 × 0.015 0.076 0.05 0.1 0.1 0.05, 0.09
0.3 0.4 (2D) 2 (2D) 2-6 m 1 2.79, 10.5
335 67 500 500, 520 77 60, 54
2500 1500 1500 950, 2620 1550 1000, 930
(b) (d) (c) (c) (e) (e)
(b) (a) (c) (c) (b) (d)
40-200 -
Chen et al. (2013)
0.09, 0.2, 0.3
54, 76 , 140
930, 1712, 2600
(e)
(b)
-
Wang et al. (2014)
0.4
10.5, 14.2 (2D) 8.35 (3D) 3
(e)
(b)
400, 540, 890
Jiang et al. (2014)
0.42 × 0.92
5.8
200-1000
2620
(e)
(a)
-
Shi et al. (2015) Shi et al. (2015)
0.152 0.15
7.9 3
2550 2222
(e) (e)
(b) (b)
-
Modelling approaches:
cr
us
an
279, 291
150 160
ip t
0.37 (2D)
M
Particle ρs (kg/m3) 2400 2650 1020 2650
Dp (µm) 126 700, 1200 500 700
Solids residence time, effect of flow parameters Effect of number particles in parcel Effect of drag model and particle-wall restitution coefficient Axial and radial volume fraction profiles Distribution of particles in binary and polydispersed solids along height Distribution of solids concentration at inlet and in standpipe Analysis of solids RTDs and back mixing Effect of exit geometry
Drag model: Wen-Yu Gidaspow De Felice EMMS
Ac ce
DPM- Discrete particle model DEM (Discrete element method) - hard sphere DEM-soft sphere DDPM – Dense discrete phase model MP-PIC – Multi phase particle-in-cell
ed
Zhang et al. (2008)
Riser dimensions H (m) 1 0.378
pt
Helland et al. (2000) Zhou et al. (2002) Mansoori et al. (2005) Zhou et al. (2007)
Dt (m) 0.1 0.07 0.0305 0.07
Page 56 of 56
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3.5. Drift flux analysis
2
Various drag force formulations and their relative merits are described in section 3.2.1. While using any one
3
of the drag laws, it is necessary to have a priori knowledge of cluster size distribution (CSD). Obviously, the
4
CSD depends upon the type of particle, size distribution, age of the catalyst, solid loading, column diameter,
5
superficial gas velocity, physical properties of the raw material, etc. Thus the development of procedures for
6
the estimation of the CSD is a formidable task. However, this problem can be addressed (though not with
7
desired rigor) with the help of drift flux model and measurements by the gamma ray densitometry. In a
8
rigorous manner, the DNS has a capability of predicting cluster size distribution and the corresponding drag
9
forces and the subject is discussed in detail in section 4.
cr
ip t
1
In order to address the problem of relation between the CSD and the drag force, drift flux analysis can be
11
applied for the FCC riser for the representation of the combined effect of superficial gas velocity, solids
12
circulating flux, column dimensions and physical properties of gas and solids on the solid holdup and
13
velocity profiles. The drift flux model for two-phase flow, proposed by Zuber and Findlay (1969), correlates
14
the averaged volume fractions of solids with the superficial velocities.
an
us
10
eq. (66)
ed
M
15
pt
16
17
Where,
18
superficial velocity of gas, and c0 and c1 are the drift flux constants. The values of c0 and c1 indicate the
19
quality of radial profile of the solid phase and the slip velocity respectively. The original model of Zuber and
20
Findlay (1969) considers the continuous phase profile to be flat. However, it is known to have strong
21
circulatory flows (upflow in the central region and down flow near the column wall). Under these conditions
22
the drift flux constants take the following forms (Thakre and Joshi, 1999; Joshi, 2001; and Ekambara et al.,
23
2005).
Ac ce
is the time-averaged holdup of solids inside riser, Vs is the superficial velocity of solids, VG is the
24
25
;
eq. (67)
Page 57 of 57 Page 57 of 114
Draft manuscript: - Computational Flow Modelling of FCC Riser: A Review
Where Vslip is the relative velocity between two phases,
is the instantaneous volume fraction of the
2
dispersed phase, εg is the instantaneous volume fraction of the continuous phase and ug are the interstitial true
3
velocities of the solid and gas phases velocity of solids.
4
The values of the drift flux constants can be estimated by using experimental data. The cold flow
5
experiments have reported several sets of radial and axial profiles of volume fraction and velocities of the
6
solids phase at different superficial gas velocity and solid fluxes. These data can be used to plot
vs.
cr
ip t
1
to estimate c0 and c1 for a given combination of operating conditions and column dimensions. The
8
coefficient c0 represents the transverse volume fraction profile, while the coefficient c1 represents the slip
9
velocity. CFD predictions of FCC riser must give values of holdup and slip velocity that satisfy the values of
10
c0 and c1 for a given operating condition and column dimensions. As the slip can be adjusted by the drag
11
coefficient, the value of c1 can be used for the estimation of representative slip velocity of drag coefficient of
12
the solid particles (which includes the cluster size distributions) and the gas. This slip velocity can be used
13
for the estimation of drag force.
14
It is further recommended that the gamma ray densitometry be used for the measurement of radial εs profile
15
at 5 to 10 locations in the FCC riser. These be substituted in the CFD simulation for getting profiles of
16
and
17
drift flux constant c0 which enables the estimation of c1 at a given location and hence the axial variation of
18
the CSD and the drag force. It may be emphasized that, the abovementioned procedure is iterative and needs
19
to begin with some reasonable value of drag coefficient.
20
4.
21
In riser flow, clustering is an important phenomenon which includes continuous formation and breakup of
22
clusters and complex interactions between fluid turbulence and dispersed solids phase. The formation of
23
clusters dictates intrinsic hydrodynamics, and therefore, understanding the clustering phenomenon is critical.
24
Due to small spatial and temporal scale of the clusters, experimental investigation to resolve the clustering
25
phenomenon under flow conditions of riser is currently impractical. Consequently, several investigators have
Ac ce
pt
ed
M
an
us
7
at various axial locations. Thus, the knowledge of ug, us, εg and εs can be used for the estimation of
Direct numerical simulations (DNS)
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adopted DNS approach. Two different numerical approaches, namely lattice Boltzmann method (LBM) and
2
immersed boundary method (IBM) have been previously used to conduct DNS of fluid-solid suspensions.
3
The LBM has been used by Hill et al. (2001a,b); van der Hoef et al. (2005); Beetstra et al. (2007); Yin and
4
Sundaresan (2009); and Shah et al. (2013). In the LBM, a flow domain is represented by number of lattices
5
and flow of fluid is calculated by updating velocity distribution at each lattice by using Boltzmann’s velocity
6
distribution function. Flow of particles is resolved by applying Newton’s force balance equation. Force
7
interactions between fluid and particle are then calculated from the velocity distributions at boundary nodes
8
and velocity of particles. The IBM has been used by Uhlmann (2005); Garg et al. (2010) and Tenneti et al.
9
(2011) to study the drag between the gas and solids phases. In the IBM, fluid is represented in an Eulerian
10
framework, whereas particles are represented in a Lagrangian framework. The Eulerian variables are defined
11
on a Cartesian mesh, and the Lagrangian variables are defined on a curvilinear mesh that moves freely
12
through the Cartesian mesh without being constrained to adapt to it in any way at all. The fluid-solid
13
interactions are accounted via a smoothed approximation to the Dirac delta function (Peskin, 2002). For
14
simplicity, previous DNS studies on the clustering can be divided into two categories, i.e. (i) those focus on
15
the impact of the clusters on the fluid-particle drag and (ii) those focus on the interactions between the
16
turbulent and clusters.
17
Hill et al. (2001a,b); van der Hoef et al. (2005); Beetstra et al. (2007); Yin and Sundaresan (2009); and
18
Tenneti et al. (2011) have adopted the DNS approach to investigate the drag force in solid-fluid suspensions
19
by simulating flow passing through a fixed assembly of randomly located mono- or bi-dispersed solid
20
particles inside a 3-D cubical flow domain with periodic boundary conditions. These studies calculated
21
effective drag force in gas-solid suspensions, and then, compared the calculated drag force with that obtained
22
from the conventional drag models such as the Wen-Yu, Syamlal-O’Brien, and Gidaspow models. Such
23
comparison has been made at various solid volume fraction and particle Reynlods numbers. The authors
24
observed wide discrepancies between the drag values from the DNS and the conventional models.
25
Consequently, Hill et al. (2001a,b), Beetstra et al. (2007) and Tenneti et al. (2011) have given a modified
26
drag correlations derived from the DNS results. Beetstra et al. (2006); Zhang et al. (2011); and Shah et al.
27
(2013) have conducted DNS of cluster configurations inside a cubical flow domain. Zhang et al. (2011) and
28
Shah et al. (2013) have observed that the calculated drag for cluster configurations is significantly lower than
29
that from random configurations. The reduction in drag due to the presence of cluster increases with an
30
increase in the solid volume fraction and particle Reynolds number. Main drawbacks of these studies are that
31
(i) cluster properties (sized, shape, number of particles) have been assumed, (ii) clusters have been treated as
32
stationary, and (iii) limited number of particles (32-1000) in a small flow domain (10-20 times particle
33
diameter) have been considered. To remove these limitations, simulations should be performed for a large
34
flow domain with several thousand free-flowing solid particles, which not only interact with surrounding
35
fluid but also experience particle-particle collisions.
Ac ce
pt
ed
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ip t
1
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Xu and Subramanian (2010); Derksen (2012); Prevel et al. (2013) and Nicolai et al. (2014) have used DNS
2
approach to study influence of turbulence in fluid phase on the clustering phenomenon. Xu and Subramanian
3
(2010) have used IBM to simulate a flow with particle Reynolds number of 50 and the ratio of the particle
4
diameter to Kolmogorov scale of 5.5. In this study, numerical results for turbulent flow past fixed
5
assemblies, uniform and cluster configurations, of solid particles are analysed. It is found that clustered
6
configurations enhance the level of fluid-phase turbulent kinetic energy (TKE) more than uniform
7
configurations. This increase is attributed to a lower dissipation rate in the clustered particle configuration.
8
The simulations also reveal that the particle-fluid interactions result in anisotropic fluid-phase turbulence due
9
to the anisotropic nature of the interphase TKE transfer and dissipation tensors. Derksen (2012) has used the
10
LBM combined with the IBM to simulate fully coupled solid-liquid flow in a periodic, cubical 3-D domain
11
with homogeneous isotropic turbulence and 5000 spherical particles. In Derksen’s study, particles are made
12
sticky with a tendency to aggregate by a square-well potential, which is a function of a distance of interaction
13
and binding energy. In these simulations, the particles also interact with each other via interacting fluid and
14
through hard-sphere collisions. Derksen (2012) has investigated the impact of both the particle-particle
15
interactions and turbulent intensity on aggregate size distributions. It is found that a small increase in
16
velocity, volume fraction of the solids phase resulted in a single large aggregate with a size comparable to
17
size of the domain. In addition, friction coefficient related to hard-sphere collisions is found to have
18
influence on aggregate size distributions. Prevel et al. (2013) have performed DNS to investigate flow of
19
solids particles under the effect of hairpin vortices in a laminar boundary layer and the preferential
20
accumulation of particles close to wall. In this study, the Navier-Stokes equations are solved for the fluid
21
phase, along with Lagrangian tracking of 200,000 particles. In these simulations, hairpin vortices are
22
generated in a controlled way by a hemisphere protuberance mounted on the lower wall in an initial laminar
23
boundary layer. The authors observed preferential aggregation of outward moving particles in low speed
24
fluid regions between standing vortex and external vortex, and in high shear region between legs of the
25
hairpin vortex. They observe the ejection of the particles from high span wise vorticity region at the head of
26
hairpin vortices. Nicolai et al. (2014) have investigated flow of particles in homogenously sheared turbulent
27
to gain insight into structure and statistical properties of clusters. Nicolai et al. (2014) have performed both
28
experiments and DNS to record particle positions under turbulent flow conditions. In this experiment, a
29
homogeneous shear flow was generated in central part of recirculating water channel, and spherical glass
30
beads are injected in the channel. The instantaneous concentration is measured by imaging the positions of
31
particles using high resolution CCD camera. Both the experimental and numerical datasets are further
32
analysed by statistical methods such as the voronoi decomposition method and the Angular Distribution
33
Function (ADF). The particle snapshots indicate that particles tend to aggregate into thin clusters outside
34
vortex cores, and that the mean velocity gradient induces an evident preferential orientation on the particle
35
clusters. The voronoi analysis gave characteristic dimension of regions which may be identified as clusters
36
and voids. The use of the ADF approach gives further characterization of geometry of the clusters by
37
estimating anisotropy content of particle files at changing the scale of observations. Recently, Joshi and
Ac ce
pt
ed
M
an
us
cr
ip t
1
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Nandkumar (2015) have made several suggestions for future work which will enable additional
2
understanding in the mechanism of formation/break-up of clusters using DNS simulations.
3
The subject of transition from homogeneous to heterogeneous dispersions have been addressed by many
4
previous studies (Anderson and Jackson, 1967; Didwania and Homsy, 1982; Batchelor, 1988; Thorat et al.,
5
1998; Joshi et al., 2001; Sundaresan, 2003; Thorat and Joshi, 2004; Ghatage et al., 2014). All these studies
6
use the theory of linear stability which consists of the following steps (1) the starting point is one
7
dimensional governing equations of continuity and motion for multiphase system (2) use Reynolds averaging
8
procedure for turbulent dispersion and introduce dispersion coefficients for individual phases (3) eliminate
9
pressure term with the assumption that it is shared by the multiple phases (4) linearization (5) introduction of
10
purturbation variables (6) simplification of all the equations in the form of single equation having one
11
dependent purturbation variable (continuous phase hold-up) (7) application of the theory of linear stability.
12
Joshi et al (2001) have compared all the experimental data on transition in gas fluidized bed and have shown
13
very good agreement with the predictions of the theory of linear stability. Further, there has been a long time
14
need for understanding the origin of disturbance. In this context of transitions, Derksen and Sundaresan,
15
(2007) have performed DNS simulations and established the reasons for initiation of clustering. This
16
pioneering work needs to be taken forward for understanding transitions in FCC risers. The analysis needs to
17
be performed separately (1) for the entry region of complex geometry and (ii) the pneumatic transport region.
18
In addition to the modulation of turbulence, the effect of turbulence on particle aggregation has been
19
analysed (Xu and Subramaniam, 2010; Derksen, 2012). Accordingly, the core-annulus phenomenon in the
20
FCC has been explained. Wei et al. (2013), Shnip et al. (1992) and Derksen and Sundaresan (2007) have
21
made useful contributions on the prediction of onset of transition to heterogeneity from homogeneity.
22
Further, such a transition has been shown to follow enhancement in particle setting velocity due to possible
23
particle aggregation/generation of strong convection currents in the continuous phase. However, like
24
turbulence modulation, the phenomena of aggregation as well as the onset of transition have not been
25
quantitatively understood and substantial additional work is needed.
26
5.
27
CFD studies of a reactive flow in the FCC riser (listed in Table-9) can be classified in two categories, i.e. (i)
28
those who ignore droplet phase by assuming instantaneous vaporization of feedstock (Theologos and
29
Markatos, 1993; Theologos et al., 1997; Gao et al., 1999; Benyahia et al., 2003; Das Sharma et al., 2006;
30
Lopes et al., 2011; ad Li et al., 2013), and (ii) those who consider the flow of feed droplets and vaporization
31
(Gao et al., 2004; Mortignoni and Lasa, 2001; Nayak et al., 2005; Behjat et al., 2011; and Chang et al.,
32
2012). The studies in the first category use the E-E gas-solid flow models coupled with cracking kinetics
33
models; while those in the second category use the E-E gas-solid flow model coupled with droplet phase
34
model (either Eulerian or Lagrangian), droplet vaporization model, and cracking kinetics model. Simulation
Ac ce
pt
ed
M
an
us
cr
ip t
1
CFD models of a reactive flow in FCC riser
Page 61 of 61 Page 61 of 114
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predictions of these models are often compared with the FCC riser performance data (conversion and yields)
2
available in literature.
3
Table-6
Ac ce
pt
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an
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ip t
1
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Table-6: CFD studies of a reactive flow in the FCC riser Riser Modelling approach geometry
4
Cracking kinetics
Momentum transfer
Mass transfer
Heat transfer
Molar expansion
Investigations
Capability of their CFD model Effect of number of feed nozzles Effect of droplet size Effect of water injection at 10m height Droplet concentration near feed inlet zone Effect of droplet size Capability of their CFD model Capability of their CFD model Radial distributions at various heights Effect of droplet size and CTO ratio Capability of their CFD model Performance of two stage riser system; effect of operating conditions Comparison between riser and downer reactors Comparison between phenomenological model with heterogeneous reactive 1-D flow model Profiles of catalyst volume fraction near entry section of riser Feed entry with a mixing section in two stage riser systems Effect of operating conditions and droplet size Effect of operating conditions Comparison between predictions from rotating fluidized bed and conventional riser Effect of catalyst size distributions in FCC riser Effect of reaction temperature and effect of CTO Effect of feedstock and catalyst temperature, effect of CTO
3-D 3-D 3-D 3-D
E-E E-E E-E E-E
Lump kinetics model 3 10 3 13
Deactivation (a) (b) (a) (b)
(a) (a) (a) (a)
NC NC NC NC
(a)+(d) (a)+(d)+(e) (a)+(d)+(e) (a)
NC NC NC Ideal gas
Gao et al. (2001)
3-D
E-E-E
13
(b)
(a)+(b)
Vaporization
(a)+(c)+(d)
Ideal gas
Benyahia et al. (2003) Chang and Zhou (2003) Das et al. (2003)
2-D 3-D 3-D
E-E E-E-E E-E
3 4 12
(a)
(a) (a) (a)
NC Vaporization NC
NC (a)+(b)+(c)+(d) (f)
NC Ideal gas NC
Nayak et al. (2005)
3-D
E-L-L
4, 10
(b)
(a)+(b)
Vaporization
(a)+(b)+(c)+(d)
Ideal gas
Souza et al. (2006) Lan et al. (2009)
2-D 2-D
Well mixed single phase E-E
6 14
(a)
NC
(a)+(d) (a)+(d)
NC Ideal gas
Wu et al. (2010)
2-D
E-L
4
(a)
(a)
NC
(a) + (d)
Ideal gas
Zhu et al. (2011)
1-D
E-E
4
(b)
(a)
NC
(a)+(d)
Ideal gas
Lopes et al. (2011)
3-D
E-E
4
(b)
(a)
NC
(a)+(d)
Ideal gas
Gan et al. (2011)
3-D
E-E
11
(b)
(a)
NC
(a)+(d)
Ideal gas
Behjat et al. (2011)
3-D
E-E-L
4
(a)
(a)+(b)+(c)
Vaporization
(a)+(b)+(c)+(d)
Ideal gas
Chang et al. (2012) Trujillo and De Wilde (2012)
3-D Rotating fluidized bed
E-E-E E-E
12 10
(a) (b)
(a)+(b)+(c) (a)
Vaporization NC
(a)+(b)+(c)+(d) (a)+(d)
Ideal gas Ideal gas
Li et al. (2013)
3-D
E-E
14
(b)
(a)
NC
(a)
Ideal gas
Chang et al. (2014)
3-D
E-E
9
(a)
NC
(a)
Ideal gas
Alvarez-Castro et al. (2015a, b)
3-D
E-E
12
(a)
NC
(a)
Ideal gas
cr
us an
(b) (b)
M
ed pt
Ac ce
(b)
ip t
Theologos and Markatos (1993) Theologos et al. (1997) Theologos et al. (1999) Gao et al. (1999a,b)
(b)
Modelling approach:
Deactivation:
Heat transfer:
E-E: Gas and solids phases E-E-E: Gas, solids and liquid phases E-E-L: Gas and solids as continua, droplets as a discrete phase E-L-L: Gas as a continuum, solids and droplets as discrete phases E-L: Gas as continuum and solids as discrete phase Well mixed single phase
Based on residence time of catalyst Based on coke concentration
Gas-solid heat transfer resistance Gas-liquid heat transfer resistance Solid-droplet heat transfer Heat of reactions Effect of droplet vaporization on enthalpy of hydrocarbon gases Imposed temperature profiles
Momentum transfer: Gas-solid drag Gas-droplet drag Solid-droplet collisions
Page 63 of 63 Page 63 of 114
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5.1. FCC riser performance
2
Paraskos et al. (1976), Shah et al. (1977), Corella et al. (1986), and Bollas et al. (2002) have conducted pilot-
3
scale experiments of FCC plant; while Theologos et al. (1997), Ali et al. (1997), Derouin et al. (1997), Gao
4
et al. (2001), and Yang et al. (2009) have reported commercial FCC plant data. The available FCC plant data
5
can also be divided in two categories, one for which variation of conversion, yields and/or temperature are
6
reported along height of riser (Shah et al., 1977; Derouin et al., 1977) and the other for which the data only at
7
the riser exit are available (Paraskos et al., 1976; Corella et al., 1986; Ali et al., 1997; Bollas et al., 2002;
8
Yang et al., 2009).
M
an
us
cr
ip t
1
ed
(a) (b) Figure-13: (a) Conversion and yield Vs. dimensionless height; (b) Gas oil conversion Vs. gasoline yield (Shah et al., 1977: height = 30 m, diameter = 0.85 m, C/O = 7.06, pressure = 3.04 atm, catalyst dia = 68 μm, feed oil flow rate = 11.87 kg/s, catalyst flow rate = 83.09 kg/s; Derouin et al., 1997: height = 30 m, Diameter = 0.7-1 m, C/O = 5.5, pressure = 3.15atm, catalyst dia = 60-70μm, feed oil flow rate = 55-109 kg/s, catalyst flow rate = 300-600 kg/s) Figure-13(a) shows conversion of gas oil and yield of gasoline along height given in Shah et al. (1977) and
10
Derouin et al. (1997). Both the data sets show a steep rise in the conversion and yield in initial 20-40% of the
11
riser height, and then the profiles plateau. However, quantitative values in these two data sets are quite
12
different. Shah et al. (1977) have shown rise in conversion up to 45% and yield up to 67%; while Derouin et
13
al. (1997) have reported rise in conversion up to 72% and yield up to 48%. The discrepancies between the
14
two data sets, despite similar riser geometries, can be attributed to flow conditions. The feed and catalyst
15
flow rates in Derouin et al.’s riser system is almost 5-10 times higher than those used by Shah et al. (1977).
16
Furthermore, the Catalyst to oil ratio (CTO) in Shah et al.’s experiments is 7 compared to 5.5 in Derouin et
17
al.’s riser system. Figure-13(b) shows the gasoline yield against the gas oil conversion from the two data
18
sets. A significantly higher selectivity of the gasoline was reported by Shah et al. (1977). This suggests that
19
both higher CTO and lower flow rates of both feed and catalyst result in higher selectivity of the gasoline.
20
Paraskos et al. (1976) have conducted pilot-scale FCC riser experiments at isothermal condition, and
21
reported 14 data sets for varying CTO (6.82-8.6) and flowing space time (1.12-59.80). They report the
22
conversion at exit in range of 40% - 78% and yield in range of 31.3% - 53%. Ali et al. (1997) have reported
23
commercial FCC plant data, in which conversion of gas oil, and yields of gasoline, gas and coke components
Ac ce
pt
9
Page 64 of 64 Page 64 of 114
Draft manuscript: - Computational Flow Modelling of FCC Riser: A Review
at exit are 73, 44, 23.45, 5.8 wt % respectively. Furthermore, Ali et al. (1997) also report an exit temperature
2
of 795 K. Gao et al. (2001) have reported yields of five-lumps at two exit temperatures in a commercial FCC
3
riser systems. In Gao et al.’s data, yields of heavy fuel oil, light fuel oil, gasoline, gas and coke are 42, 18.5,
4
27.9, 7.7 and 3.9 wt % at 504 ˚C and 404.4, 18.8, 29.7, 7.8 and 3.3 wt % at 496 ˚C.
5
5.2. Coupling of gas-solid flow model with droplet flow and vaporization models
6
In FCC riser, feedstock is injected through atomizing nozzles in the form of micron-sized droplets. After
7
entering, the feed droplets vaporize upon making contact with hot catalyst and steam. The vaporisation of
8
feedstock controls distribution of temperatures and concentration of gas oil in bottom section of riser.
9
Therefore, it is critical to model the droplet phase along with the gas-solid flow. In previous studies, the
10
droplet phase was modelled by using either Eulerian (Gao et al., 2001; Mortignoni and Lasa, 2001; and
11
Chang et al., 2012) or Langrangian approach (Nayak et al., 2005 and Behjat et al. 2011).
12
Eulerian approach for the droplet phase: If the Eulerian approach is used, the E-E gas-solid model is
13
modified with a third set of mass, momentum and energy balance equations for the droplet phase. The gas-
14
droplet and the solids-droplet momentum and heat transfer are modelled by using correlations for the
15
interphase drag (Table-4) and heat exchange (Table-3). Gao et al. (2001) and Chang et al. (2012) used
16
following mass balance equations for the three-phase flow.
19
cr
us
an
M
ed pt
18
Ac ce
17
ip t
1
eq.(68)
eq.(69)
eq.(70)
20
Where, d denotes the droplet phase; and mdg (
) is the mass transfer from the droplet phase to gas
21
phase due to droplet vaporization. Gao et al. (2001) and Chang et al. (2012) used following momentum
22
balance equations for the three-phase flow.
Page 65 of 65 Page 65 of 114
Draft manuscript: - Computational Flow Modelling of FCC Riser: A Review
eq.(71)
2
eq.(72)
ip t
1
eq.(73)
Here, FD,sg (=
5
gas, droplet-gas, solid-droplet respectively. Chang et al. (2012) used the Syamlal-O’Brien drag model,
6
whereas Gao et al. (2001) used the Wen-Yu drag models to calculate the drag forces.
7
The energy balance equations for the three phases can be written as,
10
) are the drag force exchanges between the solid-
M
ed pt Ac ce
9
) and FD,sd (=
an
4
8
), FD,dg (=
us
cr
3
eq.(74)
eq.(75)
eq.(76)
11
Where, ΔQgs(= ̶ ΔQsg), ΔQdg (= ̶ ΔQgd) and ΔQds (= ̶ ΔQsd) are heat exchange terms between the gas and
12
catalyst phases and the gas and droplet phases respectively. Sgh is the energy source term in the gas phase
13
energy balance equation due to the endothermic heat of reaction. The equations of ΔQgs (= ̶ ΔQsg), are given
14
in the section 3.1.1.5. The heat exchange between the gas and droplet phase can be given as,
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1
eq.(77)
Where, hgd (= hdg) is the heat transfer coefficient; Adi is the interfacial area between the gas and solids phases;
3
Tg is the temperature of the gas phase; Td is the temperature of the droplet phase and hfg is the heat of
4
vaporization of the droplet phase. The heat transfer coefficient can be correlated to the Nusselt number,
5
which is further correlated by the droplet Reynolds number and Prandtl number according Ranz and
6
Marshall (1952). Chang et al. (2012) have used correlation of Gunn (1978) to calculate the Nusselt number;
7
while Gao et al. (2001) and Theologos and Markatos (1993) have used a correlation of Kothari (1967) for the
8
particle Nusselt number.
9
Lagrangian approach for the droplet phase: In the Lagrangian approach (Nayak et al., 2005 and Behjat et al.
10
2011), force and energy balance equations for each droplet are solved separately. The force balance equation
11
on an individual droplet can be written as,
an
us
cr
ip t
2
eq.(78)
M
12
Where, md is the mass of the droplet, ud is the velocity of the droplet, t is the flow time, FD is the drag force
14
on the droplet, Fg is the gravity force, and Fothers are acceleration forces such as lift force, virtual mass force,
15
pressure force, etc. For each droplet, the position and velocity is updated at every time step.
16
Nayak et al. (2005) have considered forces on the droplet due to continuous phase pressure gradient.
17
Furthermore, Nayak et al. (2005) have used drag model of Morsi and Alexander (1972). Nayak et al.’s
18
equation for force balance is,
pt
Ac ce
19
ed
13
eq.(79)
20
Where, CD is the drag coefficient, vd is the volume of the droplet, ρcont is the density of continuous phase
21
(only the gas phase was considered as continuous phase by Nayak et al., 2005 and Behjat et al., 2011), ucont is
22
the velocity of the continuous phase, and ρd is the density of the droplet phase. As tracking individual droplet
23
is computationally infeasible, Nayak et al. (2005) and Behjat et al. (2011) have considered flow of packets of
24
several droplets. Then, an equivalent diameter of the packet is used to calculate interphase drag and heat
25
exchange terms.
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Regardless of approach used for the droplet phase, heat exchange between the continuous phase and the
2
droplet phase causes variation in droplet size and temperature, which is calculated by using a suitable droplet
3
vaporization model. Available droplet vaporization models can be classified in two categories, namely
4
homogeneous where droplets are assumed to receive heat only from the surrounding hot gases (Abramzon
5
and Sirignano, 1989; Renksizbulut and Bussmann, 1993; Buchanan, 1994; Miller et al., 1998; Abramzon and
6
Sazhin, 2006) and heterogeneous which involves the effect of direct collisions between droplet and hot solid
7
particles (Buchanan, 1994; Nayak et al., 2005). Recently, Nguyen et al. (2015) have presented a detailed
8
review of all droplet vaporization models. In this review, the models proposed by Ranz and Marshall (1952),
9
Buchanan (1994) and Nayak et al. (2005), which have been previously used in the FCC riser simulations,
ip t
1
have been compared.
11
The feed droplets are generally injected at a temperature lower than the vaporization temperature; as a result,
12
the vaporization of droplets occurs in three steps, namely inert heating, vaporization and boiling. For inert
13
heating step, the governing equation for heat transfer can be given as,
an
us
cr
10
eq.(80)
M
14
And the heat transfer coefficient for the inert heating step can be calculated by following equations.
16
According to Ranz and Marshall (1952) and Buchanan (1994),
18
19
20
21
pt Ac ce
17
ed
15
eq.(81)
And according to Nayak et al. (2005),
eq.(82)
For vaporization step, the equations for mass transfer can be written as,
eq.(83)
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1
Where, K is the mass transfer coefficient; Ci,s and Ci, cont are the concentrations of vaporizing component at
2
surface of the droplet and in the bulk of the continuous phase respectively; and MWi is the molecular weight
3
of vaporizing component. According to Ranz and Marshall and Nayak et al.’s models, the mass transfer
4
coefficient can be calculated by,
cr
For the vaporization step, the equations for heat transfer can be written as,
7
And heat transfer for the vaporization step can be calculated by,
9
(Ranz and Marshall, 1952)
ed
M
an
8
us
6
eq.(84)
ip t
5
(Nayak et al. (2005)
Notably, Buchanan (1994) only considered the inert heating and boiling steps.
12
For the boiling step, equations can be written as,
Ac ce
11
13
(Ranz and Marshall, 1952; and Buchanan, 1994)
14
15
eq.(86)
eq.(87)
pt
10
eq.(85)
(Nayak et al., 2005)
eq.(88)
eq.(89)
In eq.(57), Nu can be calculated by,
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(Ranz and Marshall, 1952)
3
with
(Buchanan, 1994) – Heterogeneous
In eq.(58), Nueff can be calculated by,
an
4
(Buchanan, 1994) – Homogeneous
eq.(91)
ip t
with
cr
2
eq.(90)
eq.(92)
us
1
(Nayak et al. (2005)
M
5
eq.(93)
Buchanan (1994) has considered two hypothetical limiting cases for heterogeneous vaporization, i.e.
7
infinitely fast heat transfer during collision (limiting case-1) and hard-sphere collision (limiting case-2). In
8
the hard-sphere collision vaporization, Buchanan (1994) has considered elastic collision between droplets
9
and catalyst particles; while in the infinitely fast case, Buchanan (1994) has considered instantaneous transfer
10
of all possible heat from catalyst to droplets. The model equations for Buchanan’s heterogeneous case
11
mentioned above are for the hard-sphere collision model. For Buchanan’s infinitely fast case, the governing
12
equations can be given as,
14
pt
Ac ce
13
ed
6
for the inert heating step
eq.(94)
for the boiling step
eq.(95)
15
The model equations for inert heating and boiling steps are solved using finite element method with a time-
16
step size of 1 × 10-5 s to calculate vaporization times for the flow conditions given by Buchanan (1994). The Page 70 of 70 Page 70 of 114
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calculations are conducted for the Buchanan-homogeneous, Buchanan-heterogeneous (case-1 and case-2),
2
Ranz and Marshall and Nayak et al. models. The comparison of the calculated vaporization times is shown in
3
Figure-14. To show the fidelity of the calculation method, the calculated values of this study for the
4
Buchanan models are also compared with those reported by Buchanan (1994). Good agreement between the
5
calculations of this study and those of Buchanan (1994) is achieved. Figure-14(a) shows that the inert heating
6
times for the Buchanan-homogeneous and Ranz and Marshall models are the same, but the vaporization time
7
of the Buchanan-homogeneous model is approximately three times longer than that of the Ranz and Marshall
8
model. This can be attributed to the significant reduction in the Nusselt number caused by a factor
9
of
ip t
1
cr
, whose value is 1.94 at the simulated flow conditions. This means that the Nusselt
number of Buchanan-homogeneous model is almost half of that in the Ranz and Marshall model. Figure-
11
14(b) shows the comparison of calculated vaporization times from the heterogeneous models. The
12
Buchanan-case-1 (infinitely fast vaporization) gives total vaporization time of 0.9 milliseconds; while the
13
Buchanan-case-2 (hard-collision model) yields vaporization time of 17 milliseconds. The Nayak et al. model
14
yields intermediate value of 5.7 milliseconds. The decrease in the droplet vaporization time using the
15
Buchanan case-2 can be attributed to the use of modified droplet Reynolds number equation (see eq.61),
16
which consists of particle density and particle volume fraction; and hence, the use of the modified droplet
17
Reynolds number results in significant higher heat transfer coefficient. In the calculation for the Nayak et al.
18
model, the Nusselt number equation is modified by using particle Reynolds number (see eq.56), and this also
19
resulted in the higher value for the heat transfer coefficient. As a result, the Nayak et al. model also gives
20
significantly shorter duration for the droplet vaporization. It is noteworthy that the Nayak et al. model has an
21
empirical constant, whose value, as recommended by Nayak et al. (2015), is taken to be 14 in our
22
calculations. But this empirical constant brings further uncertainty to Nayak et al vaporization model.
Ac ce
pt
ed
M
an
us
10
Figure-14: Droplet diameter Vs. time (a) homogeneous models (b) heterogeneous models (flow conditions of
Page 71 of 71 Page 71 of 114
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Buchanan et al., 1994: droplet dia. = 300 μm, temp of cont. phase = 811 K, temp of droplet = 700 K, gasdroplet slip velocity = 6.1 m/s, gas-solid slip velocity = 6.1 m/s)
The calculated vaporization times from the simulated models are in milliseconds, and this can be considered
2
as a valid reason for the instantaneous vaporization assumption by several CFD studies. However, the above
3
calculation is for single droplet under a particular flow conditions. In reality, multiple droplets and variation
4
in flow conditions would have significant impact on the droplet vaporization time. The comparison of the
5
models shows wide discrepancies in the computed vaporization times (Figure-14). In previous simulation
6
studies (Table-6), Behjat et al. (2011a, b) and Chang et al. (2012) have used homogeneous vaporization
7
model; while Nayak et al. (2005) have compared their own model with Buchanan’s heterogeneous
8
vaporization model. None of these studies have validated their predictions of droplet vaporization time or
9
height, as experimental data on droplet vaporization height or time in FCC riser are not available in
10
literature. Few studies have reported experimental data of homogeneous droplet vaporization under
11
controlled conditions. Experimental data are available for homogeneous vaporization of water (Ranz and
12
Marshall, 1952), decane (Wong and Lin, 1992) and heptane (Nomura et al., 1996). Nguyen et al. (2015) have
13
compared calculated values from the Ranz and Marshall model with the experimental data. Nguyen et al.
14
(2015) have found that the Ranz and Marshall model could predict the data for vaporization of water but it
15
significantly under predicts the vaporization time for hydrocarbon droplets. As experimental data on
16
homogeneous or heterogeneous vaporization of FCC feed droplets are not available, comparisons of
17
calculated values with those of Buchanan (1994) are considered in this section.
18
5.3. Coupling between gas-solid flow model and cracking kinetic model
19
Catalytic cracking involves conversion of heavier hydrocarbons in the vaporized feedstock to lighter
20
products in the presence of hot zeolite catalyst. The vaporized feed contains thousands of species and hence
21
the cracking results into a similar number of cracked products. The cracking reactions also produce coke and
22
heavy hydrocarbons that deposit on the surface of catalyst reducing its activity. Describing the kinetics of
23
such a complex process in entirety is rather difficult task. Therefore, traditionally, a lump kinetic approach
24
has been adopted to describe the kinetics of catalytic cracking.
25
Weekman Jr (1968) and Wojciechowski (1968) have proposed the first lumped kinetic model, a 3-lump
26
model, which divides reaction mixture in gas oil, gasoline and light gases-coke components. Weekman Jr
27
(1968) has also estimated rate constants and deactivation coefficient by using experimental data. Further,
28
Weekman Jr and Nace (1970) have estimated kinetic parameters of the 3-lump model using moving bed
29
experiments. They also compare the kinetic parameters from fixed bed and moving bed experiments. All
30
these estimates of the kinetic parameters are based on only one type of feedstock. Nace et al. (1971) have
31
reported range of 3-lump kinetic parameters based on experiments with different types of feedstock. Voltz et
32
al. (1971) have given correlations to calculate variations in rate constants with the concentration of aromatic
Ac ce
pt
ed
M
an
us
cr
ip t
1
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and naphthenic components of feedstock. Paraskos et al. (1976) and Shah et al. (1977) and Corella et al.
2
(1986) have conducted pilot-scale riser experiments to estimate 3-lump kinetic parameters. In these three
3
pilot-scale experimental studies, residence times of the catalyst are significantly lower than those in the fixed
4
bed experiments of Nace et al. (1971). Furthermore, Paraskos et al. (1976), Shah et al. (1977) and Corella et
5
al. (1986) have used a governing (component balance) equation for the plug flow to calculate yields and
6
conversion. Due to different equations and operating conditions, the estimated 3-lump kinetic parameters
7
widely differ from each other. Lee et al. (1989) have proposed a 4-lump model and estimated kinetic
8
parameters by using micro-activity test (MAT) experiment data. Lee et al. (1989) have also investigated the
9
effect of temperature on the kinetic parameters, and consequently gave values of frequency factors and
10
activation energies for the 4-lump model. Gianetto et al. (1994), Pitault et al. (1994), Ancheyta-Juárez et al.
11
(1997), Abul-Hamayel (2003) have proposed different sets of the 4-lump kinetic parameters. Ancheyta-
12
Juárez et al. (1997) have further extended the work and provide rate constants for the 5-lump model. Bollas
13
et al. (2007) have also given kinetic parameters for the 5-lump model, but Bollas et al.’s model considers
14
additional cracking reaction of the LPG lump to the dry gas which is not considered by Ancheyta-Juárez et
15
al. (1997). Their model also considers tc–n type catalyst deactivation. To remove the dependence of the
16
kinetic parameters on charged feedstock, Jacobs et al. (1976) have proposed a 10-lump scheme; in which the
17
gas oil lump is further divided into heavy fuel oil consisting of paraffinic, naphthenic and aromatic lumps.
18
Jacobs et al. (1976) also use reaction rate equation different from previous 3-lump studies. Apart from the
19
lumped kinetic models, cracking kinetics models based on single-event kinetics (Froment, 1992; Feng et al.,
20
1993), molecular lump approach (Pitault et al., 1994), neural networks (McGreavy et al., 1994), and pseudo-
21
component approach (Liguras and Allen, 1989b, Gupta et al., 2007) are also available in the literature.
Ac ce
pt
ed
M
an
us
cr
ip t
1
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Hari et al. (1995) 582.84
0.97-2.87 10.3-39.2 18.5-40.1
23.76 684 5688
15.12 845.28 2412
Ej (kJ/mol) 68.2495 89.2164 64.5750 52.7184 115.4580 72.2526 51.6726 117.7050
Abul-Hamayel (2003) Ej (kJ/mol) 121.-743 117.208 35-158 79.534 21-60 62.79 12-104 142.324 3-20 125.58
Ancheyta-Juarez et al. (1997) Ej (kJ/mol) 699 57.3482 125.28 52.7436 50.4 31.8136 33.48 65.7202 0.000072 66.5574
92-281
315
cr
(Pre-exp. Factor) 7.978×105 4.549×106 3.765×104 3.255×103 79.57 1.937×106 4.308×103 3.017×108
us
k12 (hr-1) (wt%-1) k13 (hr-1) (wt%-1) k14 (hr-1) (wt%-1) k23 (hr-1) k24 (hr-1) k1 (hr-1) (wt%-1) k2 (hr-1) α (hr-1)
Corella et al. (1985) 432
75.348
an
VGOGasoline VGOGas VGOCoke GasolineGas GasolineCoke Reacn 1+2+3 Reacn 3+4 Deactivation (ϕ=e-αtc)
Nace et al. (1970) 7.7-33.5
ip t
Table-7: 3-, 4-, and 5- lump kinetic parameters derived from controlled fixed bed experiments. 3-lump kinetic parameters Weekman (1968) VGOGasoline k12 (hr-1) (wt%-1) VGOGas + coke k13 (hr-1) (wt%-1) k23 (hr-1) GasolineGas + coke k1 (hr-1) (wt%-1) 143 and 194 Reacn 1+2 -αtc 18.8 and 21.8 Deactivation (ϕ=e ) α (hr-1) 4-lump kinetic parameters Lee et al. (1989)
5-lump kinetic parameters
ed
699 128.52 0.36 50.4 21.96 11.52 0.000072 7.2 315
pt
22
k12 (hr-1) (wt%-1) k13 (hr-1) (wt%-1) k14 (hr-1) (wt%-1) k15 (hr-1) (wt%-1) k23 (hr-1) k24 (hr-1) k25 (hr-1) K34 (hr-1) α (hr-1)
Ej (kJ/mol) 57.3208 52.3 49.3712 31.7984 73.22 45.1872 66.5256 39.748
Ac ce
VGOGasoline VGOLPG VGODry gas VGOCoke GasolineLPG GasolineDry gas GasolineCoke LPGDry gas Deactivation (ϕ=e-αtc)
M
Ancheyta-Juarez et al. (1997)
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Of all the kinetic models proposed, the lump kinetic models are most appropriate for CFD simulations; and
2
hence, they have been overwhelmingly used by previous CFD studies. However, selection of lump model
3
and its kinetic parameters is a tricky task as several sets of kinetic parameters for a given lump model are
4
reported in literature. These kinetic parameters are estimated from experiments using different feedstock,
5
catalyst, reactor type, and operating conditions. The kinetic parameters of 3, 4 and 5-lump models are
6
compared in Table-7. Notably, these listed parameters have been derived only from fixed-bed experiments
7
and similar operating conditions of temperature and CTO. Despite similar experimental conditions for their
8
estimation, large differences between the values of these kinetic parameters can be seen. The differences in
9
the kinetic parameters can be attributed to not only type of feedstock and catalyst properties but also
cr
governing component mass balance equations used in their estimation.
Ac ce
pt
ed
M
an
us
10
ip t
1
Figure-15: Model prediction (of gasoil conversion wt%) Vs. Experimental data of Nace et al. (1971) 11
Figure-15 shows a parity plot for calculated predictions using listed kinetic parameters of the 3-, 4- and 5-
12
lump models against the experimental data of Nace et al. (1971), who have reported gas oil conversion vs.
13
space time for 16 different feedstock at two different run times (1.25 and 5 min). The predictions (shown in
14
Figure-15) are calculated by using the equation for gas oil conversion given by Lee et al. (1989). As
15
expected, the predictions from the 3-lump parameters of Nace et al. (1971) are very close to the experimental
16
values. The 4-lump kinetic parameters of Lee et al. (1989) give predictions within ±20% errors, while the
17
predictions from all other sets of kinetic parameters show wide discrepancy. The error in predictions using
18
parameters of Weekman Jr (1968) and Lee et al. (1989) is due to the fact that these parameters are derived
19
only for one type of feedstock while the experimental data of Nace et al. (1971) is for different types of
20
feedstock. In addition, the parameters of Weekman Jr (1968) are derived from conversion and yield data vs.
Page 75 of 75
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liquid hourly space velocity, while experimental data of Nace et al. (1971) is available against weight hourly
2
space velocity. The discrepancy in using the kinetic parameters of Hari et al. (1995), Abul-Hamayel (2003)
3
and Ancheyta-Juárez et al. (1997) can be attributed to their use of governing equation that does not account
4
for the effect of space velocity sufficiently. In CFD simulation of riser, each cell has different flow
5
conditions; while the available kinetic parameters are only valid for range of operating conditions. The above
6
analysis shows that significant uncertainty in CFD predictions is associated by direct use of the kinetic
7
parameters of previous studies. Therefore, one should review of all available kinetic data its validity over a
8
range of operating conditions of interest.
9
In a CFD model, number of species in the gas phase depends on the selection of lump kinetic model. Change
10
in mass fraction of each species (lump) is calculated by using a separate component balance equation that
11
can be written as::
an
us
cr
ip t
1
eq.(96)
M
12
Where, yj is the mass fraction of the jth species; and rj is the net rate of the production of the jth species. The rj
14
can be calculated by:
ed
13
eq.(97)
pt
15
Where, Mw,i is the molecular weight of the jth species; k is the total number of cracking reactions; and ri,j is
17
the rate of production of the jth species in the ith reaction. In a generalised form, the rate of consumption of a
18
reactant jthlump in ith reaction can be given by
19
Ac ce
16
eq.(98)
20
Where, kij is the rate constant of consumption of jth lump in ith reaction; cj is the concentration of jth lump, n is
21
the order of the reaction; and
22
VGO cracking reactions and zero for all other cracking reactions.
is catalyst deactivation function. The value of n is assumed to be one for the
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1
There are two other types of rate equations are available in the literature, which can be written as:
2
(for 3-lump model of Pachovsky and Wojciechowski, 1971)
eq.(99)
Where, n is one for the VGO cracking reactions; n is zero for all other cracking reactions, cj0 is initial
4
concentration of pure lump j. The value of n for the VGO cracking implies that the cracking of the VGO is
5
easier for the initially vaporized fraction and it becomes progressively difficult as the VGO travels upward in
6
the riser.
us
cr
ip t
3
(for 10-lump model of Jacob et al., 1976)
eq.(100)
an
7
Where, ρc/εg is the mass density of the catalyst relative to the gas volume; kh is the heavy aromatic ring
9
adsorption coefficient; and CAh is the concentration of aromatic ring in heavy fuel oil. In this rate equation,
10
influence of the adsorption of heavy aromatic ring on the catalyst active sites and consequently on the rate of
11
the reaction is considered.
12
In all three types of rate equations, the catalyst deactivation function ( ) can be given either as a function of
13
residence time of the catalyst (tc) or concentration of the coke on the catalyst. In addition, several different
14
types of deactivation functions are available in the literature (see Table-8).
Ac ce
pt
ed
M
8
Table-8: Models for catalyst deactivation Weekman Jr.(1969) α and n are the rate constants.
Jacob et al. (1976)
= partial pressure of oil at inlet; α, β, γ = constants Krambeck (1991) b = empirical constant Ccoke= coke concentration (kg coke/kg cat) Farag et al. (1993) Kc = deactivation constant (kg catalyst/kmol) Ccoke= coke concentration (kmol/m3)
Page 77 of 77
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Pitault et al. (1995) Ccoke concentration in wt% A and B are empirical constants. As mentioned-above, rate constants used in the rate equations are estimated by lab-scale or pilot-scale
2
experimental data. Change in mass fraction of various species results in change in volume of the gas.
3
Furthermore, variation in the temperature and pressure conditions also brings in change in volume of the gas.
4
Volumetric expansion in gas phase is generally calculated by using the ideal gas law to calculate gas density
5
as:
cr
ip t
1
eq.(101)
an
us
6
Gas density calculated from mass fraction of various species is used in the mass and momentum balance
8
equations for the gas phase.
9
Coke deposition on catalyst surface causes change in catalyst activity and density. Change in the catalyst
10
activity due to the presence of coke is incorporated by using deactivation model as described in the kinetic
11
model section. In most CFD models (Table-9), the coke is assumed as a separate lump in the gas phase
12
instead of a separate solids phase.
13
The cracking reactions are endothermic, and their effect on the temperature is accounted for by a source term
14
in the enthalpy balance equation (Sgh in eq.43) for the gas phase. Heat of reaction is used to calculate the
15
source term. Chang et al. (2012) used the value of this source term equal to 9.127×103 KJ/kg of coke
16
produced; while Theologos and Markatos (1993) and Theologos et al. (1997) have used a constant value of
17
300 KJ/kg of hydrocarbon converted and 465 KJ/kg of feed respectively. Nayak et al. (2005) and Behjat et
18
al. (2011) have used reference enthalpy or heat of formation of each lump of the four-lump model to
19
calculate the heat of reaction in each control volume. In Nayak et al. (2005), the heat of formation values of
20
each lump are back calculated from heat of reactions estimated by Han and Chung (2000).
21
5.4. Predictions
22
The CFD models have been used to evaluate various designs and operational alternatives. Some of important
23
predictions can be summarised as follows.
Ac ce
pt
ed
M
7
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(1) Effect of CTO: Nayak et al. (2005), Wu et al. (2010), Zhu et al. (2011) and Behjat et al. (2011b) have
2
investigated the effect of CTO on the performance of FCC riser. Nayak et al. (2005) have found that an
3
increase in CTO from 6 to 12 increases the conversion 70 to 79%. Zhu et al. (2011) have also found that
4
the increase in CTO from 5 to 9 increases the yield of gasoline from 45% to 60%. Zhu et al. (2011) also
5
report negligible the effect of CTO on the yield of coke. Wu et al. (2010) have investigated the effect of
6
CTO (in a range of 5-20) on the clustering phenomenon and residence time of catalyst in the FCC riser
7
by using Langrangian approach. They note that increase in CTO results in higher clustering, suggesting
8
higher back mixing in riser. Wu et al. (2010) have further observed that an increase in CTO from 5 to 15
9
almost doubles the residence time of the catalyst phase in riser.
cr
ip t
1
us
10
(2) Effect of feed nozzles: Theologos et al. (1997), Theologos et al. (1999) and Li et al. (2013) have
12
investigated the effect of feed nozzle configurations and droplet size on the performance of FCC riser.
13
Theologos et al. (1997) have investigated 3 and 12-nozzle configurations, and found that the 12-nozzle
14
configurations increases gasoline fraction at outlet from 45 wt % to 48 wt %. Theologos et al. (1999)
15
have investigated the effect of three different feed droplet sizes (30, 100 and 500 μm) on vaporization,
16
cracking reaction initiation, selectivity and overall performance. They have found that a higher degree of
17
atomization (lower droplet size) gives faster feed vaporization and initialization of the cracking
18
reactions. Nayak et al. (2005) have also found that an increase in the droplet size from less than 400 μm
19
to 2mm results in decrease in the conversion from 85% to less than 70%. As the initial droplet size is
20
reduced, more uniformity in temperature profiles is achieved with higher conversion rates and gasoline
21
selectivity. Li et al. (2013) have analysed the effect of jet velocity (41.7, 62.5, and 83.3 m/s), positions
22
(the distance between the nozzle opening and walls - 3.5, 4.5, and 5.5 m) and angle of feed injection
23
nozzles (15°, 30°, and 45°) on flow field and cracking reactions in the feedstock mixing zone of riser.
24
Their simulations suggest that a higher jet velocity significantly increases inhomogeneity in radial
25
distributions of velocity and volume fraction of the solids phase. A higher angle of nozzles gives more
26
homogeneous radial distribution of the gas phase temperature. However, the angle of nozzles does not
27
impact axial distribution of the solids volume fraction. Increasing the distance between nozzle opening
28
and walls also has marginal impact on flow field. Decreasing the injection angle from 60˚ to 45˚
29
increases the conversion of VGO from 94.8% to 95.7% and the yield of coke from 8.25% to 8.56%
30
(Chang et al., 2012).
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1
(3) Effect of temperature: Zhu et al. (2011) have studied the effects of inlet temperatures of the catalyst
2
phase (600, 850 and 1000K) on the yields and conversions. Low inlet temperature of 600K for the
3
catalyst phase gives the conversion of approximately 20% and yield of the gasoline of approximately
4
15%. Increase in the inlet temperature to 1000 K then resulted in the fractional conversion of
5
approximately 80% and the yield of the gasoline of approximately 60%.
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(4) Effect of catalyst: Behjat et al. (2011) have studied the effect of catalyst deactivation on mass fraction of
8
various species. They compare predicted variation in the mass fraction along height using a CFD model
9
with and without deactivation of catalyst. The mass fraction of gas oil at outlet is almost 10% higher
10
when catalyst deactivation is considered, suggesting lower conversion of gas oil. Corresponding
11
reduction (approximately 10%) in mass fraction of gasoline at the outlet is also observed. Catalyst
12
deactivation affects light gases lump the most as its mass fraction decreases by approximately 50%.
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13
(5) Effect of riser geometry: Gao et al. (1999, 2001) have found that an optimum yield of desirable FCC
15
products is achieved at a riser height that is less than 10 m above feed inlet. Beyond this height,
16
excessive cracking reactions result in increased yield of by-products such as gas and coke at the expense
17
of desirable products. They have also suggested that injection of water as a reaction-terminating medium
18
above optimum riser height can be an effective option for optimizing the yield of desirable products. Lan
19
et al. (2009) have used CFD model to investigate performance of a two stage riser technology, where
20
two risers with different diameter and length replace conventional single riser. Gan et al. (2011) have
21
further investigated the impact of change in the diameter and nozzles in the two stage FCC risers. In this
22
study, the feed injection zone was fitted with a section with a diameter twice that of riser. Gan et al.
23
(2011) concluded that the changing diameter riser provides more mixing and is well suitable for the fast
24
reactions occurring at the feed injection section. Lopes et al. (2011) have analysed flow patterns near the
25
inlet section of the riser, and found a large-scale inhomogeneity in the distribution of solids volume
26
fraction near the catalyst inlet. Chang et al. (2012) have proposed use of an airlift loop mixer at the inlet
27
section of riser to improve hydrodynamics and mixing. Trujillo and Wilde (2012) have compared
28
performance of riser with a rotating fluidized bed in static geometry configuration, where solids are
29
injected in radially inward direction and VGO is injected in radially tangential direction. Due to intense
30
mixing in rotating fluidized bed configuration, significant process intensification is achieved in terms of
31
the bed height and corresponding rector volume required for a given conversion.
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5.5. Shortcomings
2
(1) CFD models of FCC riser have not been thoroughly validated against experimental data. Bottleneck in
3
this aspect comes from unavailability of a comprehensive set of experimental data. Experiments which
4
give measurements on both hydrodynamics and conversions at multiple locations in a given riser systems
5
are not available in literature. Consequently, several models have been validated against the
6
experimental data of cold-flow riser and few models have been validated against the available plant data.
7
Without thorough validation, the CFD models have only been used for qualitative analysis of the effect
8
design alternatives or operating conditions on the FCC performance.
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(2) There is a lack of coherence between evaluation of closure models for gas-solid flow in riser and coupled
11
CFD models for reactive flow in FCC riser. Recommendations on the selection of closure models and
12
modifications of these models provided by the gas-solid flow modelling efforts have not been
13
implemented in the coupled CFD models of FCC riser. For example, it has been repeatedly shown that
14
the multiscale drag models such as the EMMS and SGS models significantly improve flow predictions.
15
Despite of this, most of the coupled CFD models (Table-6) have used the Gidaspow drag models.
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(3) Most of the coupled CFD models (Table-6) have ignore the droplet phase by assuming instantaneous
18
vaporization. While this assumption makes the model and computation less complex, ignoring the
19
droplet phase leads to inaccurate predictions in more critical bottom section of the riser.
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(4) The coupled CFD models of Theologos et al. (1997), Gao et al. (2000), Behjat et al. (2011) have
22
considered homogeneous fast vaporization of feed droplets, while Nayak et al. (2005) have implemented
23
a mechanistic heterogeneous model for droplet vaporization. The comparison (see Figure-13) of the
24
vaporization models for single droplet vaporization under FCC conditions shows wide differences in the
25
predicted vaporization times. The selection of the vaporization model therefore needs to be validated by
26
comparing predicted droplet vaporization height with real FCC riser. Without such validation, the
27
predictions of the impact of the droplet diameter or design configuration of feed nozzles on FCC
28
performance remain unconvincing.
29
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1
(5) The gas-solid heat transfer coefficient is mostly calculated using Ranz and Marshall (1952). Behjat et al.
2
(2011) have used a correlation of Gunn (1978), whereas Theologos and Markatos (1993) and Theologos
3
et al. (1997) have used a correlation of Kothari (1967). It is necessary to evaluate the effect of various
4
heat transfer coefficient models on predictions. Currently, systematic study on the effect of the heat
5
transfer models on FCC performance is not available.
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(6) All the coupled CFD models (Table-6) have used lump kinetic models for cracking reactions. For each
8
lump kinetic model, several sets of estimated kinetic parameters are available in the literature. These
9
parameters have been derived by different catalyst, feedstock, operating conditions and flow conditions.
10
The comparison of the 3, 4, and 5-lump kinetic parameters (Figure-14) shows that different sets of
11
kinetic parameters do not predict experimental values of the gas oil conversion reported by Nace et al.
12
(1971). This clearly suggests that the available kinetic parameters are just tuned for a specific set(s) of
13
experimental data, and they do not represent intrinsic kinetic but they are highly influenced by other heat
14
and mass transfer processes.
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(7) Selection of appropriate set of kinetic parameters is not adequately explained in the previous CFD
17
models. Furthermore, none of the previous studies have investigated the sensitivity of predictions on
18
kinetic parameters. The selection of the kinetic parameters has been arbitrary in the previous efforts. For
19
example, Nayak et al. (2005) have used kinetic constants of Pitault et al. (1994) and activation energy of
20
Lee et al. (1989) for the four-lump kinetic model, though experimental data used to estimate the kinetic
21
constants and activation energy by Pitault et al. (1994) and Lee et al. (1989) have been quite different.
22
Nayak et al.’s modelling approach to couple cracking kinetics has been followed by Behjat et al. (2011)
23
and Lopez et al. (2011).
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(8) The volume expansion due to vaporization of feedstock and cracking reactions can significantly change
26
the hydrodynamics in the riser. Many studies (Theologos and Markatos, 1993; Theologos et al., 1997;
27
Theologos et al., 1999; Chang and Zhou 2003; and Das et al., 2003) have ignored the volume expansion
28
in their model.
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6. Recommendation for future work
2
This review identifies several shortcomings related to the selection of the KTGF closure models, modelling
3
of interphase exchange and turbulent forces, model dependency on several empirical constants, uncertainty
4
over the selection of the droplet vaporization model under riser flow conditions, uncertainty over the
5
selection of kinetic parameters for a given lump kinetic model and lack of experimental data for validation of
6
CFD models. All these shortcomings must be addressed in future research for development of accurate and
7
reliable computational model for FCC riser. Following suggestions are useful for future considerations:
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(1)
KTGF: Riser simulations have been predominantly conducted by using the E-E model with the
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KTGF approach, which requires several closure models to represent rheology of the solids phase.
11
Several alternate models have been proposed for every closure term of solids phase properties.
12
Consequently, different models have used a different combination of closure laws. There are very
13
few comparative studies which have investigated the influence of available alternate models on flow
14
predictions of riser flow. In future, a detailed study that compares influence of all KTGF closure
15
models on flow predictions at various riser flow conditions should be carried out. Such study can
16
provide a guide line for selection of a set of closure models that are suitable for riser simulations.
18
(2)
Use of discrete particle model: On the basis of published CFD models, the KTGF approach appears
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to be reasonable basis for estimating closure models for solids phase. Future work should include
20
discrete particle method (DPM) or discrete element method (DEM) to simulate the flow of the solids
21
phase. In DEM, the particle-particle and particle-walls collisions are captured by calculating contact
22
forces on each particle using the soft-sphere or hard-sphere approach. Both these approach use
23
spring stiffness and damping coefficient, which are derived from the material properties of the
24
solids. The DEM approach will ensure a realistic resolution of the solids phase without use of the
25
KTGF closure models. This approach is computationally more expensive; but due to recent advances
26
in high performance computing facilities and advances in DEM tools with ability to track millions of
27
particles in the flow domain, it is now possible to conduct DEM simulations of riser. In this
28
direction, DEM models for riser flow have been reported by Zhang et al. (2008), Wu et al. (2010)
29
and Chu and Yu (2012). However, these studies either use scaled-down geometry or consider
30
significantly lower number of particles then those found in actual FCC riser system.
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(3)
Use of multiscale drag: Gas-solid drag model is the dominant closure model that significantly affects flow predictions. Previous studies have shown that use of multiscale drag models (such as EMMS
3
and SGS-filtered models) has considerably improved flow predictions (radial and axial profiles of
4
solids volume fraction) than those from the conventional drag models (Benayahia, 2009; Shah et al.,
5
2014). Despite their usefulness, the multiscale drag models have not been used by published coupled
6
CFD models for FCC riser. Therefore, future simulations of FCC riser should use multiscale drag
7
models instead of the conventional drag models.
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(4)
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Resolution of clusters: Aggregation of particles, formation/break-up of clusters, and turbulentparticle interactions are key phenomena in upward gas-solid flow inside the riser. These phenomena
11
occur at meso-scale. Developing closure laws applicable to the riser that sufficiently account for
12
these meso-scale phenomena is a major challenge.
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Recently, Shaffer et al. (2013) used high-speed PIV images to capture clusters away from the walls.
15
Shaffer et al. (2013) and Coco et al. (2013) have provided direct and indirect measurements for
16
cluster properties. As mentioned in Section-4, Nicolai et al. (2014) have performed experiments to
17
investigate particle aggregation under turbulent flow conditions. More measurements like these are
18
required to characterise clusters in the riser flow. Another useful approach is particle resolved DNS,
19
where fluid-particle and inter particle interactions can be investigated by applying first principles.
20
Current, numerical observations from DNS are limited to several thousand particles positioned at
21
fixed locations in a fictitious cubical flow domain with periodic boundary conditions. DNS with
22
large number of particles, bigger size of flow domain, and free movement of particles that
23
experience both drag and collisional forces should be performed. The suggested simulations would
24
provide numerical observations to characterize clusters with respect to flow conditions. Numerical
25
results from DNS can then become input to multiscale drag, as well as particle turbulent models used
26
in the FCC simulations..
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(5)
LES for turbulent parameters: In the k- turbulent models, extreme assumption of isotropy is made,
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parameters are estimated on the basis of some ideal flow. In gas-solid flow, the effect of the solids
2
on the gas phase turbulent properties is significant. Capturing such effect in turbulent closure models
3
used in the two fluid model is critical, and hence it is proposed to undertake LES simulations. In
4
LES of gas-solid flow (Yomamoto et al., 2001; and Vreman et al., 2009), the gas phase is modelled
5
as a continuous phase whereas the solids are modelled by using Lagrangian approach. The gas phase
6
turbulent is modelled by using the LES model with the Smagorinski SGS model (section-3.1.2.2.) or
7
improved Smagorinski model (Boivin et al., 2000). Here, the average balance equation of the gas
8
phase and the force balance equations for the solids are coupled with the drag force term. This type
9
of simulations can be used to estimate the effect of the solids phase on turbulent properties of the gas
10
phase. Such estimates of turbulent properties can be made for different flow conditions at number
11
locations in riser (say at 10 points), which should be selected on the basis of various ranges of power
12
consumption per unit mass as well as solids volume fraction. Interpolated values of these turbulence
13
parameters can be used in the two fluid models for the riser simulation.
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14 (6)
Drift flux analysis: The cold-flow experiments and simulation studies have reported several sets of
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15
radial and axial profiles of volume fraction and velocity of the solids phase. These concentration
17
profiles will enable the estimation of drift flux constants c0 and c1 (section-3.5.). The coefficient c0
18
represents the transverse volume fraction profile and the value of c1 represents the slip velocity.
19
These values will give additional basis for confirmation of drag coefficient.
21
(7)
For the detailed understanding of transport phenomenon in FCC risers, it is recommended to identify
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22
the turbulent structures (together with the size and shape distribution) and their dynamics (together
23
with velocity and energy distributions). For this purpose, the procedures are given by Kulkarni et al.
24
(2001) and Joshi et al (2009). Mathpati and Joshi (2007) and Mathpati et al (2009) have described
25
the relationships between the structure dynamics and the transport phenomena.
26 27
(8)
Entry section: It is seen from experimental and simulation results that the concentration and
28
temperature profiles drop exponentially in the initial few meter height of the FCC riser. This
29
suggests that most of the variation in concentration and temperature occurs in the entry region,
30
which probably further indicates that majority of cracking reactions also occur in the entry section.
31
Therefore, the performance of riser strongly depends on the performance of entry section. Hence, a Page 85 of 85
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1
comprehensive research on the entry section is necessary. The future work should include (a)
2
transient 3D measurement of concentration and velocity profiles of gas and solids phase, (b)
3
dynamic pressure measurement, (c) time series analysis of all variables in order to extract flow
4
parameters, and (d) CFD simulation and validation with experimental measurements of the entry
5
section.
7
(9)
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Pilot scale experiments: This review found a serious deficit of reliable plant experiment data in open literature. Future work should include an extensive experimental program for estimation of three
9
dimensional profiles in riser flow domain. For reactive flow, simultaneous measurements of
10
concentration, temperature, pressure, and catalyst volume fraction are required; while for
11
hydrodynamics, axial and radial profiles of both volume fraction and velocity in a single riser system
12
are desired.
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In conclusion, CFD modelling of FCC riser has come a long way, but it has still remained an art due to use
14
of various combinations of closure models and boundary conditions without rigorous experimental
15
validation. We feel that more fundamental work that consists of both numerical modelling and
16
experimentation is necessary to create greater understanding of underlying phenomena. Both simulations and
17
experiments can be conducted at various scales. At particle and cluster scale, DNS can provide more
18
observations on the interphase interactions and droplet vaporization. At equipment scale, pilot-scale
19
experimentations can provide much needed data for validation. Derivations of fundamental correlations for
20
interphase forces, turbulent interactions and droplet vaporization along with an extensive validation using
21
experiments are critical for development of more reliable computational models of FCC riser.
22
7. Nomenclature
23 24 25 26 27 28 29 30 31 32 33 34 35 36
Asi Ad Ariser Ainlet CAh CD0 Ci,s Ci,cont cμ, c1ε, c2ε cj cj0 c0 and c1 Cl Cp
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Interfacial area between gas and solids, m2 Droplet surface area, m2 Cross sectional area of riser, m2 Cross sectional area of inlet of riser, m2 Concentration of heavy aromatic ring in heavy fuel oil, kg/m3 Drag coefficient of a particle Concentration of vaporizing component at the droplet surface, kmol/m3 Concentration of vaporizing component in the bulk of the continuous phase, kmol/m3 Constant in k-ϵ model Concentration of jth lump in gas phase, kg/m3 Initial concentration of jth lump in gas phase, kg/m3 Drift flux constants Lift coefficient Heat capacity, J/kg K Page 86 of 86
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Smagorinsky constant Diameter of riser, m Diameter of particle, m Diameter of droplet, m Diameter of solids, m Fluctuating energy due to random motion of particle, kg/m3 s Activation energy of ith reaction, J/mol Coefficient of restitution of particle collisions Coefficient of restitution of particle-wall collisions Contact force on particle, kg/m s2 Drag force, kg/m s2 Drag on a particle, kg/m s2 Gravitational force, kg/m s2 Force on particle, kg/m s2 Lift force, kg/m s2 Empirical constant in frictional pressure equation Vitual mass force, , kg/m s2 Damping coefficient Generation of turbulent kinetic energy due to shear in the gas phase, kg m2/s2 Solids flux, kg/m2s Gravitational acceleration, m/s2 Radial distribution function Height of riser, m Specific enthalpy, J/kg Heat transfer coefficient, J/kg m2 K Heat of vaporization, kJ/kg Thermal conductivity, J/m K Mass transfer coefficient, m/s Gas-solid phase velocity variant Rate constant of consumption of jth lump in ith reaction, m3reactant/m3cat s Heavy aromatic ring absorption coefficient Turbulent kinetic energy, m2/s2 Conductivity for granular temperature, kg/m s Moment of inertia of particle Unit tensor Second invariant of the deviatoric stress tensor Total number of parcels in kth control volume Nusselt number Effective Nusselt number (Nayak et al., 2005) Order of reaction Empirical constant in frictional pressure equation Number of particles in a parcel Molecular weight, kg/kmol Mass, kg Pressure, kg/m s2 Solids pressure due to friction, kg/m s2 Solids pressure, kg/m s2 Empirical constant in frictional pressure equation Model parameter in solids pressure equation Prandtl number Heat flux, kJ/m2 s Heat exchanges, kJ/kg s Universal gas constant, J/kmol K
pt
Cs Dt dp dd ds EΘ Ej ess ew Fc FD Fd,p Fg Fp Flift Fr Fv,m fs Gk,g Gs g go,ss H h h hfg K K Kgc Kij Kh k kΘs Ip I̿ I2D NT Nu Nueff n n np MW m P Pfri Ps p ps* Pr q ΔQ R
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
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cr
Model parameter in solids pressure equation Volume fraction Maximum packing limit Minimum solid volume fraction from where friction between particle is dominant Time-averaged holdup of solids Density, kg/m3 Stress tensor, kg/m s2 Drag coefficient, kg/m2 s Filter size Kronecker delta Viscosity, kg/m s Turbulent viscosity, kg/m s Bulk viscosity of solids phase, kg/m s Component of bulk viscosity of solids phase due to collision between particles, kg/m s Component of bulk viscosity of solids phase due to friction, kg/m s Component of bulk viscosity of solids phase due to free motion of particles, kg/m s Turbulent dissipation rate, m2/s3 Interphase turbulent kinetic energy source term, m2/s2 Interphase turbulent energy dissipation source term, m2/s2 Reynolds stress due to turbulent interactions between phases Turbulent Prandtlnumber Granular temperature, m2/s2 Dissipation of granular energy due to inelastic collision between particles, kg/m3 s
pt
Greek letters α ε εs,max εs,min εs ρ τ β Δs δij μ μg,t μs μs,col μs,fri μs,kin ϵ Πk Πε Π(R,ij) σk, σε Θ γΘs
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Rij Reynold stresses, kg/m s2 Rep Particle Reynolds number Particle Reynolds number Res Droplet Reynolds number Red Rate of consumption of jth lump in ith reaction, kg/m3s rij S Source term in mass balances, kg/m3 Sh Source term in enthalpy balances, kg/m3 Strain rate Sij T Temperature, K Torque on particle, kg m3/s2 Tp t Time, s u Velocity, m/s Velocity of the gas phase at location Xp ug(Xp) up Velocity of parcel u’ Fluctuating velocity, m/s u Velocity, m/s Relative velocity, m/s urel Drift velocity, m/s udrift SGS stress, , kg/m s2 (u_i^' u_j^' ) ̅^SGS Us Slip velocity, m/s Volume of the droplet, m3 vd Volume of kth control volume, m3 vk Volume of parcel, m3 vp V Superficial velocity, m/s Slip velocity, m/s Vslip Location of parcel Xp y Mass fraction Distance from wall in wall unit y+
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ϕgs λs ϕ ϕ θ τs,w γ(Θs,w) Ω
Exchange of kinetic energy of random fluctuations in particle velocity to gas phase, kg m2/s2 Shear viscosity of solids phase, kg/m s Specularity coefficient Catalyst deactivation factor Angle of internal friction Wall shear, kg/m s2 Dissipation of granular energy due to inelastic collision between particles and wall, kg/m3 s Angular velocity of particle, rad/s
Subscripts g s SGS m p w d gs sg gd dg sd ds cont i
gas phase solids phase Sub grid scale mixture properties Parcel Wall Droplet From gas phase to solids phase From solids phase to gas phase From gas phase to droplet phase From droplet phase to gas phase From solids phase to droplet phase From droplet phase to solids phase Continuous phase Vaporizing phase
26
8. References
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Abramzon, B., Sirignano, W., 1989. Droplet vaporization model for spray combustion calculations.
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Abramzon, B., Sazhin, S., 2006. Convective vaporization of a fuel droplet with thermal radiation absorption.
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Fuel 85, 32-46.
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Agrawal, K., Loezos, P.N., Syamlal, M., Sundaresan, S., 2001. The role of meso-scale structures in rapid
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gas–solid flows. Journal of Fluid Mechanics 445, 151-185.
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Ahuja, G.N., Patwardhan, A.W., 2008. CFD and experimental studies of solids hold-up distribution and
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circulation patterns in gas–solid fluidized beds. Chemical Engineering Journal 143, 147-160.
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Ali, H., Rohani, S., 1997. Dynamic modeling and simulation of a riser-type fluid catalytic cracking unit.
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Alvarez-Castro, H., Matos, E., Mori, M., Martignoni, W., Ocone, R., 2015. Evaluation of the Performance of
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the Riser in the Fluid Catalytic Cracking Process. Petroleum Science and Technology 33, 579-587.
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Alvarez-Castro, H., Matos, E., Mori, M., Martignoni, W., Ocone, R., 2015. Analysis of Process Variables via
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CFD to Evaluate the Performance of a FCC Riser. International Journal of Chemical Engineering 2015.
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Allen, M.P., Tildesley, D.J., 1989. Computer simulation of liquids. Oxford university press.
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Ambler, P., Milne, B., Berruti, F., Scott, D., 1990. Residence time distribution of solids in a circulating
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Ancheyta-Juárez, J., López-Isunza, F., Aguilar-Rodríguez, E., Moreno-Mayorga, J.C., 1997. A strategy for
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Anderson, T.B., Jackson, R., 1967. Fluid mechanical description of fluidized beds. Equations of motion.
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Industrial & Engineering Chemistry Fundamentals 6, 527-539.
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Andrews, M., O'rourke, P., 1996. The multiphase particle-in-cell (MP-PIC) method for dense particulate
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flows. International Journal of Multiphase Flow 22, 379-402.
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Andrews IV, A.T., Loezos, P.N., Sundaresan, S., 2005. Coarse-grid simulation of gas-particle flows in
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vertical risers. Industrial & Engineering Chemistry Research 44, 6022-6037.
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Arastoopour, H., Pakdel, P., Adewumi, M., 1990. Hydrodynamic analysis of dilute gas--solids flow in a
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Auzerais, F., Jackson, R., Russel, W., 1988. The resolution of shocks and the effects of compressible
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Bader, R., Findlay, J., Knowlton, T., 1988. Gas/solids flow patterns in a 30.5-cm-diameter circulating
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Baharanchi, A.A., Gokaltun, S., Dulikravich, G., 2015. Performance improvement of existing drag models in
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Yerushalmi, J., Cankurt, N., 1979. Further studies of the regimes of fluidization. Powder Technology 24,
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187-205.
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Yin, X., Sundaresan, S., 2009. Fluid‐particle drag in low‐Reynolds‐number polydisperse gas–solid
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suspensions. AIChE Journal 55, 1352-1368.
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Yamamoto, Y., Potthoff, M., Tanaka, T., Kajishima, T., Tsuji, Y., 2001. Large-eddy simulation of turbulent
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18
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S0263-8762(16)30077-6 http://dx.doi.org/doi:10.1016/j.cherd.2016.04.017 CHERD 2263
To appear in: Received date: Revised date: Accepted date:
26-9-2015 19-4-2016 25-4-2016
Please cite this article as: Shah, M.T., Utikar, R.P., Pareek, V.K., Evans, G.M., Joshi, J.B.,Computational Fluid Dynamic Modelling of FCC Riser: A review, Chemical Engineering Research and Design (2016), http://dx.doi.org/10.1016/j.cherd.2016.04.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Draft manuscript: - Computational Flow Modelling of FCC Riser: A Review
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Computational Fluid Dynamic Modelling of FCC Riser: A review
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Milinkumar T Shah1, Ranjeet P Utikar1, Vishnu K Pareek1, Geoffrey M Evans2 and Jyeshtharaj B
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Joshi3 1
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Department of Chemical Engineering, Curtin University, Western Australia, Australia Department of Chemical Engineering, University of Newcastle, New South Wales, Australia 3 Homi Bhabha National Institute, India *Corresponding author: [email protected]
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Highlights
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(1) CFD models and experimental data of FCC riser are critically reviewed.
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(2) Governing equations and constitutive correlations of CFD models are explained.
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(3) Effect of important closure models on predictions is analysed.
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(4) Shortcomings of CFD models are identified and suggestions for future work are made.
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Abstract
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Design and scale-up of fluid catalytic cracking (FCC) riser is still largely empirical, owing to limited
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understanding of inherent multiphase flow in this equipment. The multiphase flow of FCC riser has
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therefore been extensively investigated both experimentally and computationally. The experiments
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have provided significant insight into gas-solid flow patterns inside cold-flow risers, but simultaneous
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observations on flow and performance parameters (conversion and yields) in FCC riser are rarely
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found in literature. Consequently, computational fluid dynamic (CFD) models of FCC riser that can
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simultaneously account for flow, interphase interactions, droplet vaporization and cracking kinetics
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have been developed. The CFD modelling of FCC riser, despite several efforts, has still remained a
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challenge as it requires careful consideration of governing equations and closure models. This review
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presents state-of-the-art in CFD modelling and experimental analysis of gas-solid hydrodynamics and
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reactive flow of FCC riser. The CFD models are explained in greater detail with governing equations,
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constitutive relations, and physical significance of all the terms. A brief review of DNS studies on
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cluster formation, gas-solid drag, and turbulent interactions is also presented. Impact of important
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closure models such as drag models, viscous stress models, boundary conditions, droplet vaporization
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models, and kinetic models on predictions is critically examined. The review identifies major
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shortcomings of current CFD models and makes detailed recommendations for future work.
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Keywords: Fluid catalytic cracking, riser, hydrodynamics, computation, simulation
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Content
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1. Introduction
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2. Gas-solid flow in FCC riser 2.1. “Core-annulus” radial profile
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2.2. “S-shape” axial profile
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2.3. Clusters
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2.4. Residence time distribution (RTD)
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2.5. Entry and exit effects
3.1. Eulerian-Eulerian model 3.1.1.Governing equations
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3.1.2.Constitutive equations
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3.2.4.Effect of boundary conditions
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3.2.1.Effect of drag models 3.2.2.Effect of gas phase stress models 3.2.3.Effect of KTGF models
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3.3. Shortcomings
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3.4. Eulerian-Lagrangian model
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3.5. Drift flux analysis
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4. Direct numerical simulations
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5. CFD models of a reactive flow in FCC riser 5.1. FCC riser performance
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5.2. Coupling of gas-solid flow model with droplet flow and vaporization models
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5.3. Coupling of gas-solid flow model and cracking kinetic model
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5.4. Predictions
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5.5. Shortcomings
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6. Recommendation for future work
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1. Introduction
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In petroleum refinery, an FCC unit converts low-value heavy residuals into valuable light products such as
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gas (C1-C4), gasoline (C5-C12), and diesel (C10-C15). In an FCC, a riser (Figure-1) is a long vertical pipe
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acting as a reactor where cracking reactions take place. In the FCC riser, steam, as an inert fluidizing
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medium, enters from the bottom and fluidizes regenerated catalyst. A few meters above the catalyst and
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steam inlets, hydrocarbon feedstock (vacuum gas oil - VGO, residue of vacuum distillation column) enters as
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a liquid spray through a set of atomizing nozzles. The fine droplets of the feedstock vaporize due to rapid
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mixing and heat transfer, and endothermic reactions then take place in the gas phase. The catalyst, droplets,
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and gas (hydrocarbon vapor and steam) concurrently flow upward along with reactions and droplet
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vaporization. This multiphase flow governs distribution of phases, temperature and concentrations, and in
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turn it dictates overall performance of the FCC riser. Consequently, the multiphase flow of FCC riser has
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been investigated both experimentally and computationally.
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Dimension and flow conditions (Buchanan, 1994; Berruti et al., 1995; Grace et al., 1997)
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Dimensions Height Diameter Operating conditions Inlet temperature of feedstock
30-40 m 1-2 m
150-300 ⁰C
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Inlet temperature of catalyst
Riser top temperature 500-550 ⁰C
Hydrocarbon Feedstock FCC Catalyst
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Steam
675-750 ⁰C
Solids circulation rate Catalyst to oil ratio Dispersion steam Pressure Solids residence time Catalyst particles Average size Particle density Bulk density Typical Umf Typical VT Geldart classification Feed droplets Droplet diameter
>250 kg/m2s 4-10 wt% 0-5 wt% 150-300 KPa 3-15 s 70 μm 1200-1700 kg/m3 750-1000kg/m3 0.001 m/s 0.1 m/s A up to 2000 μm
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Draft manuscript: - Computational Flow Modelling of FCC Riser: A Review Number of feed nozzles
4-12
Figure-1: Schematic of FCC riser with dimensions and flow conditions Several experiments have been conducted to investigate gas-solid flow in riser. These experiments have
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shown (i) large variations in the volume fraction of the solids phase in different sections of riser, (ii) particle-
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scale heterogeneity due to formation of particle aggregates called 'clusters', (iii) considerable back mixing of
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the solids phase, and (iv) significant effects of entry and exit boundaries. While the experimental
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observations have provided significant understanding of the gas-solid flow patterns inside riser, they do not
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provide detailed information on hydrodynamics. In addition, experiments that provide observations of both
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flow and performance parameters (conversion and yields) in FCC riser are rarely found in literature. As a
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result, CFD models of riser have been developed. The CFD modelling of the riser flow involves careful
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selection and/or customization of the governing equations and closure models. Mostly two-fluid Eulerian-
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Eulerian gas-solid flow models have been used to model the gas-solid flow, while the two-fluid models
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coupled with cracking kinetics models have been used to model reactive flow in FCC riser. The two-fluid
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model is often extended by introducing feed droplet phase, which is modelled as either Eulerian or discrete
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Lagrangian phase. The model with the third (droplet) phase is coupled with appropriate droplet vaporization
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model. Predictions from such models are largely dependent on closure models. Multiple models are proposed
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in literature for solids phase properties, gas-solid drag force, viscous stresses, boundary conditions, droplet
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vaporization, cracking kinetics etc. In last few years, new closure models have been proposed based on
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multiscale approaches, cluster-based hypothesis, and direct numerical simulations. The closure models have
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been investigated in previous studies, who have recommended different closure models after comparing their
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predictions with experimental data. A systematic review of previous studies is necessary to identify most
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suitable set of closure models.
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Only a few reviews on CFD modelling of risers are available in literature. Berutti et al. (1995) has presented
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a detail review of flow patterns and models of gas-solid flow of the riser. Berruti et al. (1995) have
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thoroughly explained models that predict only axial variation of solids suspension density, and those that
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predict only radial variation of solids suspension density. Berruti et al. (1995) have briefly summarized
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previous works on CFD models of the gas-solid flow in riser. Godfrey et al. (1999) have evaluated the
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models that predict either axial or radial profiles by comparing predictions with experimental data. Wang
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(2009) has reviewed CFD models of a gas-solid flow focusing mainly on drag models available to capture
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sub-grid scale flow structures such as clusters. Wang et al. (2010) have critically reviewed applicability of a
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drag model based on the energy minimization multiscale (EMMS) approach in CFD simulations of riser.
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Gupta et al. (2010) have reviewed modelling of FCC riser by covering literature on models for cracking
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kinetics, droplet vaporization and hydrodynamics. The hydrodynamic modelling section of Gupta et al.
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(2010) doesn’t focus exclusively on CFD models. In last one decade, a large number of CFD studies of the
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riser flow have been published with them being mostly focused on evaluation and modification of different
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closure models. During this period, several studies have also been conducted using coupled CFD models to
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investigate alternate design and flow conditions in FCC riser. A comprehensive review of CFD models of
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FCC riser, particularly with focus on recent findings, is not available in literature.
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The current study presents a critical review of CFD models of FCC risers accompanying with analysis of
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experimental data. The review divides the available literature on this subject in two groups, those on gas-
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solid flow and those on reactive flow in FCC riser. The CFD models and experimental data published under
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both groups are comprehensively analysed. The CFD models are explained in detail with governing
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equations, constitutive relations, and physical significance of all the terms. A brief review on direct
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numerical simulation (DNS) studies on cluster formation, gas-solid drag, and turbulent interactions is also
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included. The impact of important closure models such as drag models, viscous stress models, boundary
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conditions, droplet vaporization models, and kinetic models on predictions is critically analysed. More
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specifically, conventional drag models vs. multiscale drag models, laminar vs. turbulent models for the gas
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phase, 2D vs. 3D boundary conditions, and no-slip vs. partial-slip wall boundary conditions are analysed for
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predictions of gas-solid flow in riser. Furthermore, uncertainty associated with the selection of droplet
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vaporization models and cracking kinetic models is also critically examined. Based on the thorough analysis,
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major shortcomings of current CFD models are explicitly brought out and detailed suggestions for future
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work are given.
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2. Gas-solid flow in FCC riser
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The gas-solid flow in FCC riser has been extensively investigated by cold-flow pilot-scale CFB setups. In
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these experiments, controlled quantities of the solids and gas (typically air) are circulated through a riser. As
21
summarised in Table-1, these experiments are conducted for different riser dimensions, particle properties,
22
and flow conditions (such as mass flux and fluidizing gas velocity). Measurements of the pressure, velocity,
23
and volume fraction are taken at multiple locations along height and radial positions by using various
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invasive (pressure taps, optical probes and capacitance probe) or non-invasive (high speed videography,
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tomography, particle image velocimetry, electrical capacitance volume tomography, laser Doppler
26
velocimetry, radioactive particle tracking and positron emission particle tracking) techniques. Though the
27
operating conditions in these experiments do not resemble those in the actual FCC riser, the cold-flow
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experiments can still provide useful observations of inherent gas-solid hydrodynamics in FCC riser. Some of
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the important flow characteristics can be summarised as:
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Table-1
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Table-1: Cold-flow FCC riser experiments
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Yerushalmi et al. (1976) Rhodes and Geldart (1986) Ishii et al. (1989) Bader et al. (1988) Li et al. (1988) Pressure taps, Optical probes Ambler et al. (1990) Radioactive tracer detection Louge and Chang (1990) Pressure taps, Capacitance probes Bai et al. (1992) Pressure taps Yang et al. (1992) LDA Miller and Gidaspow (1992) X-ray densitometer, Extraction probe Brereton and Grace (1993) Needle capacitance probe Patience and Chaouki(1993) Radioactive tracer detection Horio and Kuroki (1994) High speed camera Wei et al. (1995) Optical fibre sensors Knowlton et al. (1995) Pressure taps Pugsley and Berruti (1996) Pressure taps Nieuwland et al. (1996b) Optical probes, Pressure taps Pugsley et al. (1997) Pressure taps Wei et al. (1998) LDA Cheng et al. (1998) LDA Noymer and Glicksman (1998) TIV Issangya et al. (2000) Pressure taps Bai et al. (1999) Optical fibre probes Mathiesen et al. (2000) LDA/PDA Smolders and Baeyens (2000) Electric conductivity of tracer Sharma et al. (2000) Pressure taps, Needle capacitance probe Pärssinen and Zhu (2001) Fibre optic probes Ibsen et al. (2002) LDV/PIV Harris et al. (2003) Light sensitive photomultiplier tube Zhang et al. (2003) Optical fibre probe, LDV Pandey et al. (2004) LDV Bhusarapu et al. (2005) CARPT and CT Mabrouk et al. (2007) RPT He et al. (2006) PIV Van de Velden et al. (2007) PEPT Kim et al. (2008) Pressure taps Yan et al. (2009) Phosphor tracer technique Chang et al. (2010) PEPT Wang et al. (2010) Pressure sensors Xu and Zhu (2011) High speed camera, Optical fibre probe Heynderickx et al. (2011) LDA Gao et al. (2012) Optical probes Pantzali et al. (2013) LDA Zhang et al. (2013) Pressure sensors Rodrigues et al. (2015) Pressure taps Monazam et al. (2016) Pressure taps Experimental observations: (a) Axial profiles of volume fraction of solids phase (b) Axial profiles of pressure drops (c) Axial profiles of velocity of solids phase (d) Radial profiles of volume fraction of solids phase (e) Radial profiles of velocity of solids phase (f) Observations on clusters (g) RTD (h) Effect of entries or exit configurations
Experimental setup and operating conditions Dt (m) H (m) dp (μm) Gs (kg/m2s) ug (m/s) 0.0762 7.3 60 52.90 3.65 0.152 6 64 8.5-107 2.5-4.5 0.05 2.79 60 10.7 1.29 0.305 12.2 76 147 9.1 0.09 10.5 54 14.3 1.52 0.05 3 106 124.305 4.5-7.1 0.197 7 61 17 2 0.140; 0.186 8 54, 280, 165, 31 30-180 2-8 0.140 11 54 26.56-119.43 1.5-6.5 0.075 6.58 75 12 2.89 0.152 9.3 148 42, 48, 62 6.5 0.083 5 277 20-140 4-8 0.2 1.6 61.3 0.016-0.6 0.15-0.6 0.2 1.6 61.3 0.016-0.6 0.15-0.6 0.20 14.2 76 485 5.2 0.05 5 208 51.3-700 8.5 0.054 8 129 100-300 10 0.1 and 0.2 6 and 12 220, 230, 71, 80 10-45; 10-85 4-6 0.186 8 54 200 2.3-6.2 0.186 8 54 200 2.3-6.2 0.159 (square) 2.44 69 25, 18 3, 6 0.762 6.1 70 18-325 4-8 0.0762; 0.102 6.1, 8.2 70 425 8 0.032 1 120, 185 0.8, 1, 1.2 0.1 6.5 90 5.19-34.1 2.82-4.92 0.15 11 70, 120 75 4, 4.9, 6 0.076 10 67 100, 300 8 0.02 2 250 0.45 0.14 (square) 5.8 25 1.3-4.5, 2-25.5 0.418 18 77 19-180 1.8-8 0.305 15.2 812 3.4-17.1 3.75-5.4 0.152 7.9 150 33.7, 36.9 3.9 and 4.5 0.52 1 250, 170 2, 12 2D, 0.05 x 1.5 1 335 5,10, 20 2-2.3 0.10 6.5 90 25, 89.7 3.6 and 9 0.05 4.5 70 7-300 0.2-9 0.186 10 78 40.8, 229.4 3.156, 5.989 0.16 7.9 120 5, 622 1, 10 0.27 (square) 10 330 113-165 15.5 0.019 x 0.114 7.6 67-288 50-200 3-8 0.1 8.765 77 3.0 2.48–7.43 0.095 and 0.14 2.2 139 0.94-1.25 0.1 8.7 77 1 3.5 and 5.3 0.316×0.08, 0.1×0.1 4.5, 4.3 350,175 12.7, 13.9, 16.1 4.4, 5.3, 5 0.3 18 300,250, 280 60 8-10 0.3 16.65 60, 230, 812 6.89-281 5.35-7.7 Abbreviations: LDA = Laser Doppler Anemometry PDA = Phase Doppler Anemometry PIV = Particle Image Velocimetry CARPT = Computer Aided Radioactive Particle Tracking CT = Computed Tomography RPT = Radioactive Particle Tracking TIV = Thermal Image Velocimetry PEPT = Positron Emission Particle Tracking
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Measurement technique Pressure taps, High-speed camera Pressure taps Optical fibre probes
ρs (kg/m3) 510.98 1800 1000 1714 1654 Sand 1545, 706, 750, 2660 1545 930 2650 2630 1780 1780 1712 2580 2540 2500, 2200, 2600, 1500 1398 1398 6970 1600 1600 2400 2200 1500 2400 4060 1398 189 2550 2500; 3400 2500 1740 1225 2260 2630 1877-2498 1550 2400 1550 2600 2650, 2600, 3300 2550, 1250, 189
Observations (f) (a) (a), (b), (f) (a), (d) (a), (e), (d) (g) (a), (b) (a) (d) € (b), (d), (e) (a) (a), (e), (g) (a), (f) (f) (b), (d), (e) (b) (d), (e) (b), (h) (a), (d), (e) (d), (h) (f) (a) (d) (d), (e) (g) (b), (e), (f) (a), (d), (e) (a), (b), (d) (g) (d), (e), (g) (f), (e) (d), (e) (a), (g) (e) (g) (a), (h) (e), (g) (g) (e) (f) (h) (a), (c), (d) (e) (h) (b) (a), (b), (h)
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2.1. “Core-annulus” radial profile
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Bader et al. (1988), Li et al. (1988), Miller and Gidaspow (1992), Yang et al. (1992), Nieuwland et al.
3
(1996b), Knowlton et al. (1995), Mathiesen et al. (2000), Bhusarapu et al. (2005), and Wang et al. (2010)
4
have reported radial profiles of the volume fraction and velocities of the solids phase. A lower volume
5
fraction and higher velocity of the solids phase are observed at centre of riser (Figure-2). This region is
6
referred as a “core” region, where the solids are carried upward due to flow of the gas. Contrary to the core
7
region, a lower velocity or downward flow of the solids with a higher volume fraction of the solids are
8
observed near wall. The region near wall is defined as an “annular” region. The heterogeneous radial
9
distribution of velocity and volume fraction is widely known as the “core-annular” flow pattern. The higher
10
solids volume fraction in the annular region is largely attributed to friction between flow and wall and energy
11
dissipation due to particle-particle and particle-wall collisions. The solid segregation is also caused by
12
formation of clusters (Noymer and Glicksman, 2000 and Pandey et al., 2004). Bader et al., (1988), Yang et
13
al. (1992), Miller and Gidaspow (1992), Noymer and Glicksman (2000) and Pandey et al. (2004) have
14
observed downward sliding motion of segregated particles near wall. Yang et al. (1992) have observed
15
concurrent movement of phases in the core region, while they have observed counter current movement of
16
the solids and gas near wall. The counter current movement of the phases lead to higher slip velocity near
17
wall than that in core region (Yang et al., 1992). Experiments for various flow conditions and riser systems
18
have revealed that the core region occupies almost 60-80% of cross-section with the annular region
19
occupying rest 20-40%. Miller and Gidaspow (1992) have observed (Figure-2a and b) that an increase in the
20
solids flux at a constant gas velocity results in higher solids volume fraction in both the core and annular
21
regions; while an increase in the solids flux had a minor impact on velocity of the solids in the core region.
22
Nieuwland et al. (1996b) have observed (Figure-2c and d) that an increase in velocity of the gas phase at a
23
constant solids flux results in a lower solid volume fraction in both the core and annular regions. Perssinen
24
and Zhu (2001) have reported the solids volume fraction at different heights, and observe that the values in
25
both the core and annular regions decrease with an increase in the height.
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2.2. “S-shape” axial profile
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Li et al. (1988), Louge and Chang (1990), Pärssinen and Zhu (2001), Rhodes and Geldart (1986), Wei et al.
3
(1998), Issangya et al. (2000) and Zhang et al. (2003) have reported axial variation in the solids volume
4
fraction (Figure-3a). The axial profiles have shown an “S-shape” (Figure-3a and b) with three distinct
5
regions (i) a dense bottom region, (ii) a dilute top section, and (iii) middle section presenting a transition
6
from the dense to dilute flow. Experimental under various flow conditions in different riser systems have
7
showed several similarities, i.e. the volume fraction of the solids in the dense bottom section is in a range of
8
0.3-0.15, and that in the dilute top section is in a range of 0-0.05. The experimental data shows significant
9
variations in the height of the transition from the dense to dilute flow (20-60% of the total height). Pärssinen
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and Zhu (2001) have found significant impact of the inlet gas velocity at a constant solids flux on axial
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profile the solid volume fraction (Figure-3c). A lower gas velocity gives a clear distinction between the
2
dense and dilute region; while a higher gas velocity results in a smooth transition. Rhodes and Geldart (1986)
3
and Issangya et al. (2000) have investigated the effect of the solids flux on axial profiles (Figure-3b). Rhodes
4
and Geldart (1986) have found that a higher solids flux gives dense flow with higher values of the solids
5
volume fraction than those from lower solids flux condition. Issangya et al. (2000) have found that a lower
6
solids flux give a longer developing section than that resulted at a higher solids flux. Li et al. (1988) have
7
investigated the effect of the solids inventory in CFB on axial profiles (Figure-3d). Notably, in Li et al.’s
8
experiment, there is no mechanical valve that controls quantity of the solids circulated through the riser. Li et
9
al. (1988) have found that a higher solids inventory in the CFB loop gave a longer dense phase and transition
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(d) (c) Figure-3: (a) “S” shape axial profiles of solids volume fraction, dimensionless height Vs. solid volume fraction; effect of (b) solids flux, (c) gas velocity, and (d) solid inventory on axial profiles of the solids volume fraction Miller and Gidaspow (1992); Knowlton et al. (1995); Sharma et al. (2000) and Ibsen et al. (2002) have
2
reported variations in pressure drop along height, where it is observed that the bottom section of riser has
3
higher pressure drop with lower values at the top (Figure-4). Miller and Gidaspow (1992) have found that the
4
pressure drop in riser increases with increase in the solids flux (Figure-4a); while Sharma et al. (2000) have
5
found that an increase in the gas velocity reduces the pressure drop in riser (Figure-4b).
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2.3. Clusters
2
Yerushalmi et al. (1976) have observed segregation of particles and movement of the segregated solids
3
within a dilute phase flow. They have characterized shape of the segregated solids as “strands”, “steamer”
4
and “ribbons”. Later, Ishii et al. (1989) and Horio and Kuroki (1994) have reconfirmed presence of the
5
particle segregations and defined them as “clusters”. The authors have observed that the clusters are present
6
not only near wall but also in dilute phase at centre of riser. Ishii et al. (1989) and Horio and Kuroki (1994)
7
have also observed that the shape of the clusters continuously changing with flow conditions. Soong et al.
8
(1994) have measured instantaneous concentrations of the solids at various locations in riser, and give three
9
criteria to identify the clusters, (1) solids concentration inside cluster must be significantly higher than local
10
time–mean solids concentration; (2) perturbation caused by cluster must exist for significantly longer time
11
than sampling time interval; (3) this perturbation must also be sensed by a sampling volume which has a
12
characteristic length scale greater than one to two orders of particle diameter. Based on Soong et al.’s
13
criteria, Noymer and Glicksman (1998); Sharma et al. (2000); Manyele et al. (2002); Liu et al. (2005); and
14
He et al. (2006) have recorded measurements of cluster properties. More recently, Shaffer et al. (2010; 2013)
15
have used high speed PIV to capture clusters and their movements along wall of riser. They have found large
16
variations in cluster structures from several particles to several riser diameters. Furthermore, Shaffer et al.’s
17
studies have also revealed that a presence of stream of the gas phase influences make-up and break-up of
18
clusters near wall. Formation of clusters has two profound effects, (i) apparent solids diameter increases
19
which leads to higher terminal velocity and (ii) gas tends to flow around clusters without penetrating inside
20
the clusters (Li and Kwauk, 1994). Consequently, formation of clusters significantly impacts gas-solid drag
21
in riser (discussed in section-3.2.1).
22
2.4. Residence time distribution (RTD)
23
Ambler et al. (1990), Patience and Chaouki (1993), Smolders and Baeyens (2000), Harris et al. (2003),
24
Mabrouk et al. (2007), Van de Velden et al. (2007) and Chan et al. (2010), have reported RTDs from
25
stimulus response experiments at various flow conditions. In the stimulus response experiments, a tracer is
26
injected at bottom of riser and its concentration at outlet is measured at different times after injection. Harris
27
et al. (2003) have measured RTD in a square riser by using a small portion of the solids particles as tracers,
28
and investigate the effect of three types of exit geometries, namely smooth, abrupt and highly refluxing, on
29
RTDs at various flow conditions. Figure-5(a) shows variations in the RTDs caused by variations in the gas
30
phase velocity for the smooth exit riser. Harris et al. (2003) have observed that an increase in the superficial
31
gas velocity decreases both mean residence time and variance of distribution over a range of investigated
32
solids fluxes. At a higher gas velocity, the RTD curves are narrow, relatively unskewed and having a
33
significant long tail. In contrast, at a lower gas velocity, the curves are broad with a long tail. Van de Valden
34
et al. (2007) have also reported RTDs for two operating gas velocities at a fixed solids flux (Figure-5b),
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where the RTD from a higher gas velocity is closer to that of ideal plug flow reactor; while the RTD from a
2
lower gas velocity is closer to that of the ideal mixed flow reactor.
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1
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(a) Figure-5: Effect of gas velocity on residence time distribution (a) E(t) Vs. time and (b) F(t) Vs. t/ τ
(b)
M
; τ = half the injection time, approximately 1 s (Van de Valden et al., 2007) 2.5. Entry and exit effects
4
Bai et al. (1992), Brereton and Grace (1994), Zheng and Zhang (1994), Pugsley et al. (1997), Cheng et al.
5
(1998), Kim et al. (2008) and Mabrouk et al. (2008) have investigated the effect of exit configuration on riser
6
hydrodynamics. Cheng et al. (1998) and Kim et al. (2008) have also studied the effect on inlet
7
configurations. Figure-6(a) shows the effect of two types of exit configuration (abrupt exit – L or T-type exit,
8
and smooth exit – long radius bend type exit) on the axial profiles of pressure drop as observed by Pugsley et
9
al. (1997). It can be seen that the effect of the abrupt exit causes higher pressure drop in upper section of
10
riser, while the pressure drop in the bottom section with both types of the exit configurations are the same.
11
Pugsley et al. (1997) have also observed that the effect of the abrupt exit is only restricted to the top section,
12
and this effect is even higher for a lower solid circulated mass flux. Cheng et al. (1998) have also compared
13
axial profiles of the gas volume fraction from abrupt and smooth exits. Cheng et al. (1998) have found that
14
the abrupt exit gives a lower gas volume fraction near the exit, while values in the bottom section from the
15
two types of exits are in reasonable agreement. Cheng et al. (1998) have studied the effect of three types of
16
air entries in an internal nozzle type air inlet arrangement; While Kim et al. (2008) have compared three
17
different types (L-valve, J-valve and Loop-seal type) solid entries. Figure-6(b) shows the effect these three
18
types of solid entries on solid circulation rate vs. solid inventory plots (Kim et al., 2008). An increase in the
19
solid inventory increases the solid circulation rate in riser. At a higher value of the solid inventory, the values
20
of circulating rates from the L-valve and J-valve are in reasonable agreement. For an entire range of
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experimental values of the solid inventory (12-36 kg), the loop-seal type solid entry results in significantly
2
lower solid circulation rate than that in the other two types of entries.
(a)
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(b) Figure-6: (a) Effect of exit configuration, dimensionless height Vs. pressure drop per unit length (Gs = 85 kg/m2s and ug = 4.2 m/s); (b) Effect of solid phase entry, solid circulation rate Vs. solid inventory (ug = 7 m/s) Experimental observations show large flow structures such as radial and axial distributions extended across
4
length and width of riser. These structures are directly influenced by small scale flow phenomena such as
5
formation of clusters, particle-wall collisions and boundary effects. Capturing these multiple flow structures
6
that have disparate time and length scales in CFD predictions is a challenging task. Higher spatial resolution
7
using fine grid discretization of flow domain and lower time step for transient simulations are essential
8
simulation parameters for riser simulations. However, these parameters are generally constrained by
9
available computational resources. Hence careful selection of modelling approach and governing equations is
10
necessary. Each modelling approach needs closure models such as models for interphase interactions,
11
turbulent forces and boundary conditions. These closure models have been derived empirically or by
12
conducting high resolution sub-grid simulations or DNS. For each closure model, several models are
13
available in literature. Realistic prediction of riser flow critically depends on the selection of closure models.
14
For example, various drag models have been proposed to cater different flow conditions. But for industrial
15
scale riser simulation, a drag model that can capture clustering phenomena even with coarse grid spatial
16
discretization is essential. Similarly, proper inlet and outlet configurations of flow domain are required to
17
capture entry and exit effect. Moreover, capturing dissipation due to particle-wall collisions is critical in
18
configuring wall boundary conditions. Various modelling approaches, model equations and closure models
19
are discussed in detail in the next section.
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3. CFD models of gas-solid flow in riser
2
Different types of models of the gas-solid flow in riser have been proposed over last three decades. Harris
3
and Davidson (1994) have classified the models published before early 90’s into three categories, i.e. (i)
4
those that predict axial variation of suspension density, but not radial variation; (ii) those that predict radial
5
variation, but not axial variation; (iii) those that employ fundamental fluid dynamic equations for two phase
6
gas-solid flow. Among these three types of models, the category-(iii) models are most useful to investigate
7
the effect of local flow structures and design configurations (Harris and Davidson, 1994; and Berruti et al.,
8
1995). The models based on fundamental fluid dynamic equations can be further classified in two broad
9
categories, namely the Eulerian-Eulerian (E-E) or the Eulerian-Langragian (E-L) models. The E-E model
10
considers both the gas and solids phases to be continuous and fully interpenetrating. In the E-E model,
11
averaged Navier-Stokes equations of the mass, momentum and energy conservations are solved for both the
12
phases. Closure laws based on the kinetic theory of granular flow (KTGF) (Jenkins and Savage, 1983; Lun
13
and Savage, 1984; Lun et al., 1984) are used to calculate stresses in the solids phase. Coupling between the
14
momentum balance equations is modelled by using correlations for interphase forces; while coupling
15
between the energy balance equations is modelled by using correlations for heat transfer between the two
16
phases. The E-L model represents solids phase as a collection of discrete particles. The motion of each
17
individual particle is solved by Newton’s law, accounting for the effect of particle collisions and forces
18
acting on the particle by the gas. Solution of the force balance equations gives updated velocity and position
19
of each particle. In a further advanced E-L model, discrete element model (DEM), contact force due to
20
collisions between particles are also captured at a much shorter timescale by means of the empirical
21
coefficient of restitution and friction (hard sphere approach) or empirical spring stiffness and a friction
22
coefficient (soft-sphere approach) (Cundall and Strack, 1979; Tsuji et al., 1993; Deen et al., 2007). The
23
interactions between two phases are still modelled using interphase drag and heat transfer correlations
24
similar to those used in the E-E model. Use of the E-L approach requires tracking of billions of solid
25
particles by solving the force equation for each particle and then calculating contact forces between nearby
26
pairs of the solid particles. Hence, the E-L approach becomes computationally impractical for simulations of
27
industrial- or laboratory-scale risers. On the other hand, the E-E approach is computationally less expensive,
28
and hence, it has been widely used for the gas-solid flows in riser. Many of important simulation studies
29
using the E-E gas-solid models for riser simulations are summarised in Table-2.
30
Table-2
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Drag: (a) (b) (c) (d) (e) (f) (g) (h)
Wen and Yu (1966) Gidaspow et al. (1994) Syamlal – O’Brien (1987) EMMS (Li and Kwauk, 1994) SGS – Filtered drag Richardson and Zaki (1954) Arastoopour et al. (1990) Other
(b), (d) (c) (b), (e) (c) (a) (b), (d) (b), (c), (g) (b), (e) (d) (b), (d), (e) (b), (d) (a) (d) (d) (b)
NC NC (f) NC (e) NC (e)
(a) (a) (a) (a) (a) (a)
(c) (e) (c) (e) (c) (c)
(f) NC NC
(a) (a) (a)
(b) (b) NC NC (b)
(d) (b), (d) (a), (b), (c), (h)
(b),(c), (d) (a)
KTGF closures Collision Shear dissipation rate viscosity
Radial distribution function
Granular energy exchange
Investigations
Boundary condition Solids Walls (for inlets solids) (f) (d) (b) (c)
(b) (c) (a) (b) (a) (a) (a) (b)
(d) (j) (e) (c) (d) (j) (c) (c) (c) (f)
(b) (b) (d) (c) (b) (b) (b) (b) (c) (b)
(a) (a) (a) (a) (a) ((b)
(b) ((c) (e) (e) (d) (b) (d)
(b) (a) (b) (a) (a) (a) (b) (b) (b) ((c)
(a) (b) (a) (b) (a) (b)
(k) (c) (f) (c) (f),(g),(h) (c) (c)+(i)
(e) (b) (b) (b) (b) (b)
(b) (b),(c), (d) (a) (a)
(b) (d) (d) (d) (d) (b) (b)
(b) (b) (a), (c) (b) (b) (b)
(e) (c) (e)
(b) (a) (b)
(f) (c) (f)+(i)
(b) (b) (f)
(b) (a) (b)
(d) (b) (a), (b)
(b) (b)
(a), (b)
(b) (b) (a) (a) (a), (b)
(c) (e) (c)
(b) (b) (a) (b) (b)
(c)+(i) (b) (c) (f)+(i) (c)+(i)
(a) (e) (b) (f) (a)
(a) (a) (f) (b) (a)
(b) (d) (b) (b) (b), (c)
(a) (b) (b) (b) (a),(b)
(a), (f) (a), (b), (e), (f)
(a) (b) (a)
(c)
(b) (b) (a)
(c) (c)+(i) (c)
(b) (a) (c)
(a) (a) (a)
(b) (b) (c)
(b) (b) (b)
ip t
(a) (d) (c) (a) (c) (c) (c) (e)
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(a) (a) (a) (a) (a) (a) (a) (a)
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Shah et al. (2011b,c) Naren and Ranade (2011) Shuai et al. (2011) Benyahia (2012) Shah et al. (2011a) Chalermsinsuwan et al. (2013) Zhou and Wang (2014) Shah et al. (2015) Baharanchi et al. (2015)
Granular thermal conductivity
NC (b) NC (f) (b) (b) (f) (b) NC NC
pt
Igci et al. (2008) Lu et al. (2009) Benyahia, (2009)
Granular temperature formulation
(a) (f) (b) (b) (a) (f) (b) (b) (g) (b)
Ac ce
Arastoopour et al. (1990) Pita and Sundaresan (1993) Dasgupta et al. (1994) Nieuwland et al. (1996a) Samuelsberg and Hjertager (1996) Hrenya and Sinclair (1997) Dasgupta et al. (1998) Mathiesen et al. (2000) Neri and Gidaspow (2000) Benyahia et al. (2001) Agrawal et al. (2001) Huilin et al. (2003) Yang et al. (2003b) Huilin et al. (2005) Andrews IV et al. (2005) Jiradilok et al. (2006) Benyahia et al. (2007) Wang et al. (2007) Almuttahar and Taghipour (2008)
Gas phase turbulent
cr
Table-2: CFD models of cold-flow gas-solid flow in riser Drag
(b) (f) (d), (e) (d) (a) (a), (f) (a), (b) (b), (c) (a), (b), (c), (d)
(a)
(d), (e) (a), (c), (e), (f) (a)
Gas phase:
Granular temperature:
Granular shear viscosity:
Solids Inlets:
Investigations:
(a) NC
(a) Partial differential equation (Lun et al., 1984) (b) Algebraic equation (Syamlal et al., 1993)
(a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k)
(a) (b) (c) (d) (e)
Effect of (a) drag models (b) KTGF models (c) viscous models (d) inlet and/or outlet boundary conditions (e) wall boundary conditions (f) flow conditions
(b) Standard k- mixture model
(c) Standard k- dispersed model
Granular thermal conductivity: (a) (b) (c) (d) (e)
Lun et al. (1984) Syamlal et al. (1993) Gidaspow (1994) Nieuwland et al. (1996) Agrawal et al. (2001)
Lun et al. (1984) Syamlal et al. (1993) Gidaspow (1994) Hrenya and Sinclair (1997) Nieuwland et al. (1996) Agrawal et al. (2001) Blazer et al. (1996) Cao and Ahmadi (1995) Frictional viscosity (Schaeffer, 1987) Dasgupta et al. (1994) Yang et al. (2004)
Real 3D 2D- two-sided solids inlet 2D-single solids inlet Periodic One common inlet for gas and solids phases
Walls (for solids): (a) No-slip (b) Partial-slip (c) Free-slip
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(d) Standard k- per-phase model
Collision dissipation:
Radial distribution function:
(a) Jinkin and Sevage (1983) (b) Lun et al. (1984) (c) Nieuwland et al. (1996)
(a) (b) (c) (d) (e) (f)
(e) Modified k- model (f) Other
Lun and Sevage (1986) Sinclair and Jackson (1989) Gidaspow (1984) Ma and Ahmadi (1986) Iddir and Arastoopour (2005) Carnahan and Starling (1995)
Note: (1) All the studies are for cold flow in the riser. Consequently, energy balance is ignored. (2) All the studies use governing equations by Anderson and Jackson (1967). (3) All the studies have ignored interphase forces other than drag.
Granular energy exchange: Gidaspow (1994) Koch and Sangani (1999) Cao and Ahmadi (1995) Blazer et al. (1996)
cr
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(a) (b) (c) (d)
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3.1. Eulerian-Eulerian model
2
In the formulation of the E-E model, local instantaneous equations are written for mass, momentum and
3
energy balances for each phase in each control volume. These equations can be solved by direct simulation
4
using size of control volume finer than the smallest length scales of the flow and a time step shorter than the
5
time scale of the fastest fluctuations. However, direct simulation would be computationally highly intensive.
6
Thus averaging of local instantaneous equations is applied. Generally, ensemble averaging (Enwald et al.,
7
1996) is applied to formulate averaged balance equations. The averaging of balance equations leads to
8
representation both phases as interpenetrating and continuous. The averaged equations then need extra
9
closure laws to close the set of equations. The closure laws for the continuous solids phase are derived using
10
the KTGF. Another set of closures are for the gas-solid interphase forces and heat exchanges. The closure
11
relations derived using the KTGF, interphase forces and heat exchanges are then incorporated into the
12
balance equations for the solids phase to achieve a close set of partial differential equations (PDEs).
13
3.1.1.
14
The governing equations for the E-E model consist of ensemble averaged Navier-Stokes equations (mass,
15
momentum and energy balances) for both the gas and catalyst phase. Several researchers have derived the
16
governing equations for two phase flows. Enwald et al. (1996) and van Wachem et al. (2001) have compared
17
the governing equations. Most of the gas-solid E-E simulation studies (as summarised in Table-2) have
18
referred their governing equations to Anderson and Jackson (1967). Therefore, in this study, we start from
19
the averaged balance equations of Anderson and Jackson (1967).
20
Mass balance equations:
21
The mass balance equation for the gas and solids phase can be written as:
23
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Governing equations
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22
ip t
1
eq.(1)
eq.(2)
24
Where, εg and εs are the volume fraction of the gas and solids phases; ρg and ρs are the densities of the gas
25
and solids phases; ug and us are the velocities of the gas and solids phases; mgs and msg are the mass transfer
26
terms from the gas to solids phase and the solid to gas phase respectively; and Sg and Ss are the source terms.
27
In the E-E model, both phases are considered as interpenetrating continua; and both the phases share the
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1
volume of flow domain. At any particular time therefore, a flow volume has εg of the gas phase and εs of the
2
solids phase with both volume fractions following:
3
For a simple gas-solid flow without mass transfer and mass sources, the continuity equations become:
ip t
4
eq.(3)
eq.(4)
us
cr
5
Momentum balance equations:
8
The conservation of momentum of the gas and solids phases is given by following equations:
ed
M
7
eq.(6)
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10
eq.(5)
an
6
eq.(7)
11
Where, P is the pressure that shared by both the phases;
and
are the stress tensor of the gas and solids
12
phases; g is the gravitational acceleration; FD, Flift and Fvm are the interphase forces such as drag force, lift
13
force and virtual mass forces respectively. Notably, in above equations, the force terms are positive for the
14
gas phase and negative for the solids phase.
15
Energy balance equations:
16
Energy conservation equation for the gaseous mixture phase:
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1
2
eq.(8)
Energy conservation equation for the solids phase:
eq.(9)
ip t
3
Where, hg and hs are the specific enthalpies of the gas and solids phases respectively; qg and qs are the heat
5
fluxes in the gas and solids phases respectively; Sgh and Ssh are the energy source terms; and ΔQgs and ΔQsg
6
are the heat exchanges between the gas and solids phases respectively.
7
3.1.2.
8
3.1.2.1 Interphase forces
9
The momentum balance equations are coupled with interphase force terms, which represent the interactions
10
between the gas and dispersed solids phases. These forces are generally caused by a relative motion between
11
the gas and solids phases.
12
Drag force
13
The gas-solid drag force can be written as:
us
pt
ed
M
an
Constitutive equations
Ac ce
14
cr
4
eq.(10)
15
Where, β is the interphase momentum transfer coefficient and
is the difference between the
16
velocities of the gas and solids phases, usually termed as slip velocity. The value of the drag coefficient
17
depends on volume fraction, particle diameter and slip velocity; and in turn, particle Reynolds number.
18
Several drag coefficient functions (Ergun, 1952; Wen and Yu, 1966; Gibilaro et al., 1985; Syamlal and
19
O’Brien, 1987; Syamlal et al., 1993; Di Felice, 1994; Gidaspow, 1994; Li and Kawauk, 1994; Andrews IV et
20
al., 2005; Beetstra et al., 2007; Igci et al., 2008; Igci and Sundaresan, 2008; Tenneti et al., 2011) have been
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proposed to cater different the gas-solid flow conditions. Comparison of the available drag models is
2
explained in section-3.2.1.
3
Virtual mass force
4
In the gas-solid flows in riser, the solids phase accelerates relative to the gas phase in the developing section.
5
The inertia of the gas-phase encountered by the accelerating solids phase exerts a virtual mass force on the
6
particles.
ip t
1
eq.(11)
The term
denotes the phase material time derivation of the form,
M
an
8
us
cr
7
eq.(12)
ed
9
The virtual mass effect is significant when the secondary phase density is much smaller than the primary
11
phase density (i.e. bubble column). But in the riser, the solids phase density is much higher than the gas
12
phase, and therefore, most of the gas-solid models do not account for the virtual mass force.
13
Lift force
14
The lift force acts on the suspended particle mainly due to velocity gradients in the gas-phase, relative
15
velocity between the gas and solids phase, and rotation of the particles.
Ac ce
16
pt
10
eq.(13)
17
Where,
18
particle spacing and the value of drag force is much larger, the lift force has been ignored in the previously
19
proposed flow models.
is the lift coefficient.Assuming that the FCC particle diameter is much smaller than the inter-
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1
3.1.2.2. Gas phase stresses
2
The stresses in the gas phase are modelled by using either the laminar or turbulent model.
3
Considering laminar flow, the correlation for the gas phase stress tensor can be written as:
If the turbulent flow for the gas phase is considered then the stresses in the gas phase can be written as:
cr
5
eq.(14)
ip t
4
eq.(15)
an
us
6
Where, μg is the laminar viscosity; μt,g is the turbulent viscosity and k is the kinetic energy of the gas phase.
8
To close the equation of the turbulent stresses, a correlation for the turbulent viscosity and kinetic energy are
9
required.
M
7
Owing to their inherent complexity and scale of flow domain, the standard k- turbulent model has been
11
used (Dasgupta et al., 1998; Almuttahar and Taghipour, 2008; and Shah et al., 2011b) for the turbulent
12
properties. There are three different types of formulations that are possible for the standard k
13
model. The simplest k
14
for dissipation rate ( ). These equations are formulated for a single pseudo phase made of the mixture of the
15
gas and solids phases. This model then uses mixture properties to calculate the turbulence properties
16
(Dasgupta et al., 1998). The conservation equation for the kinetic energy and dissipation rate can be written
17
as:
turbulent
Ac ce
pt
ed
10
model has the two equations, one for the turbulent kinetic energy (k) and the other
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1
and that for the dissipations rate can be written as:
ip t
2
eq.(16)
eq.(17)
cr
3
Where, m denotes the mixture properties; k is the turbulent kinetic energy; is the turbulent dissipation rate;
5
ρm is the mixture density (
us
4
M
an
); and μm is the mixture viscosity (
ed
6
9
eq.(18)
eq.(19)
Ac ce
8
pt
7
).
eq.(20)
10
In above equations, Cμ, C1,ε, and C2,ε are constants; whereas σk and σε are the turbulent Prandtl numbers
11
(Lauder and Spalding, 1972). Dasgupta et al. (1994) have used 0.09, 1.45, 2.0, 1.3 and 1.0 for Cμ, C1ε, C2ε, σk
12
and σε respectively.
13
More complex k- turbulent model for the gas-solid flow is derived by accounting for the effect of dispersed
14
solid particles on the gas phase turbulent kinetic energy and dissipation rate (Bolio et al., 1995; Cao and Page 23 of 23 Page 23 of 114
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Ahmadi, 1995). In this model, the equations for k and
are solved for the gas phase and the interphase
2
turbulent momentum transfer is accounted using a closure term. This model is known as the k- dispersed
3
model, and its equations can be given by
ip t
1
eq.(21)
us
cr
4
6
Where,
are source terms for the influence of the dispersed phases on the continuous phase. The
7
equations for these source terms are (Elghobashi and Abou-Arab, 1983; Simonin and Viollet, 1990):
ed
M
and
eq.(22)
an
5
eq.(23)
Ac ce
pt
8
9
eq.(24)
10
Where, kgs is the variance in the velocity of the gas phase and dispersed solids phase; and C3e is a constant
11
having a value of 1.2.
12
Additionally, if the presence of solids has a significant impact on gas phase turbulence, the above equations
13
of k and
14
phase model.
for the gas phase are also solved for the solids phase. This model is then known as the k- per
Page 24 of 24 Page 24 of 114
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While the k- model is capable of useful predictions for engineering design and optimization, it requires
2
careful parametrization. There are two basic assumptions in the k- model, i.e. (i) isotropic turbulent
3
viscosity and (ii) simplifications due to Reynolds averaging. The assumption of isotropy is valid for many
4
flows, but not for those with strong separation or swirl. In flows where, the flow regime transitions occur, the
5
k- models do not provide the required accuracy. Therefore, other modelling approaches such as Reynolds
6
stress model (Lain et al., 2002; Lain and Garcia, 2006; Kuan et al., 2007 and Chu et al., 2011) and large eddy
7
simulation (LES) model (Mathiesen et al., 2000; Yamamoto et al., 2001; Huilin and Gidaspow, 2003; Ibsen
8
et al., 2004 and Vreman et al., 2009) have been used for the gas-solid flow. Such models are still
9
computationally expensive, particularly for full scale simulation of riser flow. Mostly, the RSM model is
10
used for gas-solid flow with strongly anisotropic flow of gas phase such as those in cyclone and pipe bends;
11
while the LES model has been used for dilute gas-solid flow in pipes.
12
In the RSM, the stress in the gas phase is given as sum of laminar and turbulent stresses. The laminar stress–
13
strain tensor can be given by eq. (14), while the turbulent stresses can be given by:
cr
us
an
M
ed pt
14
ip t
1
eq. (25)
Where, τt,g is the turbulent stresses in the gas phase; and
16
Similar to the k- two equation model, the RSM can also be implemented as either dispersed or mixture
17
model. In the RSM-dispersed model, the transport equation for the Reynolds-stress term is solved for only
18
the gas phase. The RSM transport equation can be given as:
Ac ce
15
is the Reynolds-stresses in the gas phase.
Page 25 of 25 Page 25 of 114
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1 2
eq.(26)
Where, u’ is the fluctuating velocity component; is the turbulent dissipation rate; and
4
stress terms due to turbulent interactions between phases.
cr
us M
is the Kronecker delta.
is given by modified model of Simonin and Viollet (1990):
ed
Where,
eq.(27)
eq.(28)
Ac ce
pt
7
can be given as (Cokljat et al. 2003):
an
5
6
is the Reynolds
ip t
3
8
Where, β is the drag coefficient; kgc is the gas-solid phase velocity covariant; k is the turbulent kinetic
9
energy; urel and udrift are relative and drift velocities respectively.
10
In the RSM-mixture model, the Reynolds-stress transport equation for the gas phase is solved, but without
11
term. Furthermore, properties of phase such as density and velocity are represented as mixture
12
properties. The RSM solves transport equations for six independent Reynolds stresses and one for the
13
turbulent dissipation. The transport equation of the turbulent dissipation is same as eq. (22). The RSM is
14
computationally more expensive than the k- model. The use of RSM avoids assumption of isotropy, but it
Page 26 of 26 Page 26 of 114
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1
still involves Reynolds averaging which may cause error estimation of double and triple correlation of
2
turbulent velocities.
3
Because of the restrictive assumptions made in the k- and RSM models, some deviations (upto 25%) occur
4
in the prediction of the three components of the mean flows. However, the major impact of the assumption is
5
seen in the predictions of k and
6
of the rates of agglomeration, breakage, heat transfer and mass transfer need to use the local values of k and
7
and hence the need for accurate predictions. The conservation equations for k and consists of 5 terms : rates
8
of (i) convective transport (ii) turbulent transport (iii) viscous transport (iv) productions and (v) dissipation.
9
While solving these conservation equations, the values of individual terms take such values that the overall
10
balance is satisfied. However, normally the rates of dissipation and turbulent transport are under-predicted
11
upto 70%. On contrast the rates convective transport and production together get over-predicted so as to
12
match the balance. These incorrect predictions of individual terms results into incorrect predictions of k and
ip t
cr
us
an
M
ed
in the range of ± 20% to ± 200% (Zoheb Khan, 2016).
pt
13
profiles. It may be pointed out that most of the models for the predictions
In the LES model, the flow of the gas is divided in two parts, (i) large-scale flow resolved by the
15
computation and (ii) sub-grid scale (SGS) fluctuations. The effect of SGS fluctuations on the large-scale
16
flow is accounted for by applying SGS closure for turbulent stresses. The gas phase stress can be given as
17
(Yamamoto et al., 2001):
18
Ac ce
14
19
Where µ is the gas phase viscosity; Sij is the strain rate tensor,
20
of the gas phase.
eq.(29)
is the SGS stress and u is the velocity
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1
The strain rate tensor can be given as:
2
eq.(30)
Using the Smagorinsky model (Smagorinsky, 1963), the SGS stress can be given as (Yamamoto et al.,
4
2001):
cr
eq.(31)
us
5
ip t
3
Where, Cs is the Smagorinsky constant;
8
be given as
is the filter size and fs is the damping function. The filter size can
M
7
pt
ed
and the damping coefficient can be given as:
eq.(33)
Ac ce
9
eq.(32)
an
6
10
Where, y+ is the distance from the wall in wall unit.
11
While we have provided an overview of LES formulation for the continuous phase, in multiphase flows,
12
even at laminar conditions, additional challenges arise due to small time and length scales involved in the
13
dispersed flow. These scales are further magnified in presence of turbulence. Thus it is important to capture
14
the microscopic phenomena that accounts for all the small scale interactions for development of accurate
15
multiphase model (Fox, 2012).
16
3.1.2.3. KTGF closure models
17
Using the continuum approach for the solids phase, the stresses in the solids phase are derived by making an
18
analogy between a random motion of particles and thermal motion of gas molecules. This approach is widely
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1
known as the KTGF (Jenkins and Savage, 1983; Lun et al., 1984). Unlike the kinetic theory of the dense gas
2
(Chapman and Cowling, 1970), the KTGF accounts for inelasticity of particle-particle collisions. The
3
intensity of the particle velocity fluctuations determines the stresses, viscosity and pressure of the solids
4
phase. Taking the analogy with the thermodynamic temperature of the gas, the random motion of particles is
5
represented by “granular temperature”, which is proportional to the mean quadratic velocity of the particle:
eq.(34)
cr
ip t
6
eq.(35)
us
7
Where, Θ is the granular temperature; c is fluctuating velocity of particle and EΘ is the fluctuating energy due
9
to random motion of particles.
an
8
The solids phase stresses depends on the magnitude of this fluctuating particle velocity. Thus, conservation
11
of the pseudo thermal energy of the solids phase associated with the fluctuating velocity is required. This
12
conservation equation can be given as:
ed
M
10
eq.(36)
Ac ce
pt
13
14
Where,
15
dissipated energy due to particle collision;
16
energy; and
17
The collisional dissipation energy can be written as (Lun et al., 1984):
represents generation of the energy by the solid stress tensor;
represents
is diffusion coefficient (or conductivity) for the granular
represents exchange of fluctuating energy between the gas and solids phases.
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1
2
eq.(37)
and the diffusion coefficient for the granular energy can be written as (Gidaspow, 1994):
eq.(38)
cr
ip t
3
4
Where,
5
The exchange of kinetic energy of random fluctuations in particle velocity to the gas phase is written as
6
(Gidaspow, 1994):
M
an
us
.
eq.(39)
ed
7
Syamlal et al. (1993) suggest an algebraic form of the granular temperature equations by neglecting
9
convection and diffusion terms. The algebraic form of the granular temperature equation can be written as
11
(Syamlal et al., 1993):
Ac ce
10
pt
8
eq.(40)
12
In above equations, ess is the coefficient of restitution for inelastic collisions between the particles; go,ss is the
13
radial distribution function, Ps is the solids pressure and
14
coefficient of restitution depends on the material properties, and its value for the FCC catalyst is not known.
15
As a result, this parameter works as an empirical tunning parameter. In previous simulations, the values of
16
the restitution coefficient between 0.7-0.99 have been used. The radial distribution function describes the
17
probability of finding two particles in close proximity. It is a correction factor that modifies the probability
18
of collisions between particles when the granular phase becomes dense. Its correlation given by Lun et al.
19
(1984) can be written as,
is the stress tensor for the solids phase. The
Page 30 of 30 Page 30 of 114
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1
2
eq.(41)
The stress tensor for the solids phase can be written as:
eq.(42)
cr
ip t
3
The solids pressure (Ps) represents the normal solids phase forces due to particle-particle interactions. The
5
solids pressure term is composed of a kinetic term and a second term due to the particle collisions. The solids
6
pressure term prevents the solids volume fraction from exceeding the maxing packing limit. The correlation
7
for the solids pressure can be written as (Lun et al., 1984):
an ed
written as (Lun et al., 1984):
pt
11
The solids bulk viscosity (λs) is the resistance of particle suspension against the compression, and it can be
eq.(44)
Ac ce
10
eq.(43)
M
8
9
us
4
12
The solid shear viscosity (µs) is made up of the collisional, frictional and kinetic parts. All the models for
13
solid shear viscosity yield practically the same solid shear viscosity at solid volume fraction greater than
14
0.25. For lower volume factions of the solids, the models start deviating from one another (Ahuja and
15
Patwardhan, 2008). The Gidaspow model (Gidaspow, 1994) for the solid shear viscosity neglects the
16
inelastic nature of particle collisions in the kinetic contribution of the total stress and the Gidaspow’s model
17
has been used in several previous studies. The model equations for the granular shear viscosities and its
18
collisional and kinetic components can be written as,
19
eq.(45)
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1
(Gidaspow, 1994)
eq.(46)
eq.(47)
ip t
2
3.1.2.4. Frictional viscosity
4
At high solid volume fraction, frictional stress resulting from inter-particles contacts is significant, and
5
therefore, frictional part is considered to calculate the solid shear viscosity. The frictional viscosity is
6
generally calculated using Schaeffer’s (Schaeffer, 1987) model.
an
us
cr
3
(Schaeffer, 1987)
eq.(48)
M
7
Where, θ is the angle of internal friction; Pfri is the frictional pressure; and I2D is the second invariant of the
9
deviatoric stress tensor. The frictional pressure is given as (Johnson and Jackson, 1987):
ed
8
eq.(49)
Ac ce
pt
10
11
Where, εs,min is the minimum solid volume fraction from where frictional stresses become important. Fr, n
12
and p are empirical constants which depend on material properties. The values of Fr, n and p are often taken
13
to be 0.05, 2 and 3 respectively (Ocone et al., 1993). Syamlal et al. (1993) have suggested a model the
14
frictional pressure, which is:
15
eq.(50)
16
In the above equation, A and n are empirical constants and their values are taken to be 1025 and 10
17
respectively (Syamlal et al. 1993).
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Notably, several alternate models are available for the radial distribution function, solids pressure, bulk
2
viscosity, shear viscosity, frictional viscosity, granular conductivity and granular energy diffusion
3
coefficient. Van Wachem et al. (2001) and Ahuja and Patwardhan (2008) have reviewed the available
4
models by plotting their values against the solids volume fraction.
5
3.1.2.5. Heat exchange
6
In the energy conservation equations, ΔQgs and ΔQsg are heat exchanges between the gas and solids phases.
7
The heat exchange between the gas and solids phase can be given as,
cr
ip t
1
eq.(51)
us
8
Where, hsg (= hgs) is heat transfer coefficient; Asi is interfacial area between the gas and solids phases; Ts is
10
the temperature of the solids and Tg is the temperature of the gas phase. The heat transfer coefficient can be
11
correlated to the Nusselt number by,
M
an
9
eq.(52)
ed
12
Where, Kg is the thermal conductivity of the gas phase; Nus is the Nusselt number for the solids phase; and dp
14
is the diameter of the particles.
15
Generally, an empirical correlation of Ranz and Marshall (1952) is used to derive the heat transfer
16
coefficients.
18
Ac ce
17
pt
13
(Ranz and Marshall, 1952)
Where, Rep is the particle Reynolds number; and Pr is the Prandtl number.
19
20
eq.(53)
eq.(54)
Where, Cpg is the heat capacity of the gas.
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1
The Ranz and Marshall model is based on the heat transfer between single particles moving in a stationary
2
gas. Table-3 summarises several other empirical models that have been derived for the fluidized bed
3
conditions. Notably, there is no model available for the heat transfer between the gas and solids under the
4
flow conditions of the riser. Table-3: Models for gas-solid heat transfer coefficient Ranz and Marshall (1952) Ranz and Marshall (1952) Kothari (1967)
ip t cr
Fixed bed
an
+
us
Gunn (1978)
Single particle
M
Kunni and Levenspiel (1991)
Fluidized bed (Rep = 1 -100) Fluidized bed (Rep = up to 105 Fluidized bed
5 3.2.
Effect of constitutive models on flow predictions
7
Table-2 shows that simulation studies have used different combination of the constitutive models, and the
8
different selections of the constitutive models have caused significant variations in flow predictions.
9
Therefore in this section, the impact of closure models on predictions of gas-solid riser flow is analysed.
Ac ce
pt
ed
6
10
3.2.1.
Effect of drag models
11
Available drag models for the riser flow can be divided in three categories, namely (i) conventional drag
12
models, (ii) multi-scale or cluster based drag models, and (iii) those derived from direct numerical
13
simulations. Table-4 summarises the available drag models with their correlations, methods of their
14
derivation and shortcomings. Conventionally, the Wen-Yu model (Wen and Yu, 1966), Gidaspow model
15
(Gidaspow, 1994), and Syamlal and O’Brian model (Syamlal and O’Brien, 1987 and Syamlal et al., 1993)
16
are used for riser simulations. The Gidaspow model is a combination of the Ergun (for εg<= 0.8) and the
17
Wen-Yu (for εg> 0.8) correlations. The Syamlal and O’Brian model is based on the velocity-volume fraction
18
correlations derived using sedimentation and fluidization experiments of Richardson and Zaki (1954) and
19
Garside and Al-Dibouni (1977). The conventional drag models are empirical correlations that derived from
20
experimental observations on settling velocities of a single particle in the liquid and pressure drops inside
21
packed bed of the solids. However, the flow in riser exhibits the formation of clusters (Yerushalmi et al., Page 34 of 34 Page 34 of 114
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1976; Yerushalmi and Cankurt, 1979; Hario and Kuroki, 1994), which coexist and interact with surrounding
2
dilute phase. Due to the presence of clusters, apparent diameter of the solids becomes higher, and terminal
3
velocity of the particles in the cluster then becomes higher. This leads to down flow of solids and higher
4
segregation of the solids near wall (Mueller and Reh, 1993; Nieuwland et al., 1996a, Noymer and
5
Glicksman, 2000; and Pandey et al., 2004). Furthermore, due to formation of the clusters, the gas tends to
6
flow around the clusters without penetrating inside them. This result in significant less resistance to flow (Li
7
and Kwauk, 1994) leading to reduction in gas-solid drag. In previous studies (Yang et al., 2003a,b; Andrew
8
IV et al., 2005; and Shah et al., 2011b,c), use of the conventional drag models in coarse grid riser simulations
9
has not captured axial and radial distribution phases accurately. These studies have attributed this drawback
10
to the use of coarse grid, where spatial resolution is insufficient to capture clusters. Agrawal et al. (2001)
11
have shown important of grid resolution to capture clusters. However, fine grid simulation of industrial-scale
12
riser is computationally intensive. Therefore, drag models specific to cater coarse grid riser simulations have
13
been derived by using different multiscale approaches. Wang (2009) has categorized methods for deriving
14
multiscale drag models for the Eulerian simulations of Geldart-A particles in six categories, i.e. empirical
15
correlation method, scaling factor method, structure-based method, modified Syamlal and O’Brien drag
16
correlation method, EMMS-model-based method, and correlative multi-scale method. Out of these methods,
17
the sub grid scale (SGS) approach (Sundaresan and co-workers) and energy minimization multi-scale
18
(EMMS) approach (Li and Kwauk and co-workers) have been often used in several previous studies.
19
In the SGS approach (Agrawal et al., 2001; Andrews IV et al., 2005; Igci et al., 2008; Igci and Sundaresan,
20
2008), the drag is derived by using numerical results from extremely fine grid simulations using a periodic
21
domain. Andrew IV et al. (2005) have conducted fine grid simulations of only a section of riser using
22
periodic boundary conditions, and the results have then been used to derive closures of the solids phase and
23
gas-solid drag. . Igci et al. (2008) have extended Andrew IV et al.’s work to show the effect of grid size,
24
known as filter size, on the closures derived from the fine grid simulations. These closures are then used in
25
coarse grid simulation of a full-scale riser (Benyahia, 2009). An alternative approach is the energy
26
minimization multi-scale (EMMS) model (Li and Kwauk, 1994; Xu and Li, 1998; Li et al., 1999; Yang et al.,
27
2003b). The EMMS approach divides the flow in three pseudo phases i.e. dilute phase, dense phase and
28
suspended clusters. The dilute phase represents individual particle in gas. The dense phase represents
29
particles and gas residing inside clusters; whereas the suspended clusters phase represents individual cluster
30
as a whole entity that moves in the gas phase. The EMMS calculates drag in each three pseudo phases by
31
using conventional Wen-Yu drag model. Drags in the dilute phase and dense phase are calculated by using
32
particle diameter, while drag in the suspended cluster phase is calculated by using cluster diameter. Addition
33
of three drags in three pseudo phases represents resultant EMMS drag in dilute gas-solid flow in riser.
34
However, calculation of the EMMS drag needs cluster diameter, fraction of solids forming the cluster and
35
slip velocities in three pseudo phases. Thus, EMMS drag largely relies on cluster parameters. Cluster
36
diameter in the EMMS is mostly calculated by empirical correlations and correlations based on different
37
hypothesis (Shah et al., 2011b); while fraction of solids and superficial velocity in cluster phase are
Ac ce
pt
ed
M
an
us
cr
ip t
1
Page 35 of 35 Page 35 of 114
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calculated by solving mass and energy balance equations for each pseudo phase. For detailed equations and
2
calculations of the EMMS drag, readers are referred to various published articles of Li and co-workers (Li
3
and Kwauk, 1994; Xu and Li, 1998; Li et al., 1999; Yang et al., 2003a, b; Wang, 2008; and Shah et al.,
4
2011b, c). Recently, numerical observations from DNS have been used to derive gas-solid drag correlations
5
(Hill et al., 2001b; Benyahia et al., 2006; Beetstra et al., 2007; Tenneti et al., 2011). DNS studies are
6
conducted by using lattice Boltzmann method (LBM) or immersed boundary method (IBM). In these studies,
7
particle resolved simulations of a periodic domain with several randomly positioned particles are conducted
8
to capture interphase exchange forces at the boundary of each particle. The numerically calculated particle-
9
scale forces are then used to calculate an averaged drag force in the flow domain.
Ac ce
pt
ed
M
an
us
cr
ip t
1
Page 36 of 36 Page 36 of 114
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Table-4: Gas-solid drag models Derived from Conventional drag models Gidaspow (1994)
Do not capture axial profile of the solid volume fraction (Yang et al., 2004; Wang et al., 2008; Benyahia, 2009; Shah et al., 2011; Baharanchi et al., 2015). Previous studies attributed this drawback to their inability to account for effect of clusters in coarse grid simulations. Actually, The Wen-Yu model is applicable to dilute flows (εg close to 1); while the Ergun is used for dense flows. Even the Syamlal-O’Brien is derived from a single particle drag. At intermediate range of solids A drag for multi-particle system is derived from single volume fraction (0.7 ≤ εs ≤ 0.95), these drag models particle drag, Dalla Valle (1948)’s equation for drag significantly over predict the drag force than the values coefficient for a single particle, Richardson and Zaki of multi-scale drag models. (1954)’s correlation between ratio (Vr) of terminal velocity of multi-particle to that of single particle with the gas volume fraction, and Garside and Al-Dibouni (1977)’s correlation between Vr and particle Reynolds number.
Uses Ergun model for εg less than 0.8 and Wen-Yu model for εg greater than 0.8. The Wen-Yu model has been derived from settling experiments of single particle in liquids, while the Ergun model has been derived pressure drop measurement in packed bed.
for εg> 0.8 (Wen and Yu, 1966) for εg<= 0.8 (Ergun, 1952b) If Res< 1000 Schiller &Nauman (1935)
ip t
= 0.44 If Res≥ 1000
us
cr
Syamlal-O’Brien (1987)
Multiscale drag models EMMS (Li and Kwauk, 1994)
for
> 0.748
<= 0.748
ed
for where,
M
an
if ε ≤ 0.85 if ε > 0.85 “a” and “b” are tunning constants that must be calibrated to match the minimum fluidization velocity for the solid particles in question (Syamalal and O’Brien 2003). Based on Umf calculated from the Ergun equation for 76 μm FCC particle and 1712 kg/m3 density, the values of “a” and “b” are 0.8 and 2.66.
is a correction factor and it can be calculated as,
Uses EMMS algorithm based on energy minimization of suspension and transportation in gas-solid riser flow. It requires cluster parameters such as fraction of solids in cluster, solid volume fraction of cluster, cluster diameter and slip velocity in clusters.
for 0.748 <εg<= 0.83
pt
for 0.83 <εg<= 0.86 for 0.86 <εg<= 0.94
Ac ce
for εg> 0.94 The equations for the corrections factors are for high solids flux (Gs = 489 kg/m2s, and ug = 5.2 m/s) as reported by Shah et al. (2014). These functions need to be recalculated using the EMMS algorithm (Li et al., 2011; Yang et al., 2003; Shah et al., 2011) for a given flow conditions and physical properties. SGS Anderew IV et al. (2005); Igci et al. (2008); Benyahia (2009)
Shortcomings
for
≤ 0.0.04083
Simulation results using very fine grid in periodic domain of a size comparable to control volume of the continuum simulations.
Capture both axial and radial profiles with some quantitative discrepancies (Yang et al., 2003; Benyahia, 2009; Igci et al., 2008 Shah et al., 2011). The EMMS requires cluster properties, of which detail measurements are not available. Furthermore, the EMMS correlation needs to be derived for riser with different flow conditions. Implementation of EMMS algorithm in each control volume using local flow conditions is computationally expensive. The SGS requires find grid simulations of a small flow domain and thus, the final drag function depend largely on grid size, as well as the simulated flow conditions (Igci et al., 2008; Benyahia, 2009). For riser simulation, this approach is computationally more expensive.
for 0.0.04083< ≤0.2589 for
>0.2589
Above drag equations are based on for high solids flux (Gs = 489 kg/m2s, and ug = 5.2 m/s) as reported by Benhyaia (2009) using dimensionless filter size gΔ/Vt2 = 2.056 where Δ = grid size = 0.014m, Vt = 18.46 m/s Models from DNS
Page 37 of 37 Page 37 of 114
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Beetstra et al. (2005)
LBM simulations of randomly arranged particles in periodic flow domain. Drag on individual particles is calculated at particle Reynolds number range of 21-105. The calculated drag values are used to derive a correlation between the drag, gas volume fraction and particle Reynolds number. IBM simulations of randomly arrange particles in periodic flow domain are conducted with flow conditions varies in a range of particle Reynolds number of 0-300. The calculated values of fluid-solid drag are used to derive drag correlation.
cr
ip t
Tenneti et al. (2011)
These drag models have not been extensively investigated by conducting riser simulations.
Ac ce
pt
ed
M
an
us
10
Drag values from Beetstra et al. (2005) are quite different from those of Tenneti et al. (2011) at high solids volume fraction and particle Reynolds number. Tenneti et al. (2011) have attributed the difference to insufficient grid resolution of Beetstra et al.’s simulations. Tenneti et al. (2011) have highlighted a need of high grid resolution to capture boundary layers between two particles, particularly at high solids volume fraction. Tenneti et al.’s drag model is based on particles arranged at random positions. Shah et al. (2013) have shown that drag values from particles arranged in cluster configurations are significantly lower than random configuration.
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In Table-4, the correlations for the EMMS and SGS are available for the flow conditions of high flux riser
2
(Gs = 489 kg/m2s, ug = 5.2 m/s, ρs = 1712 kg/m3, Inlet solid volume fraction = 0.5, Dt = 0.2 m and H = 14.2
3
m) of Knowlton et al. (1995).Using the correlations of Table-4, values of the drag coefficients are calculated
4
for a range of volume fraction at a given slip velocity of 0.57 m/s. The comparison of the calculated drag
5
coefficients is shown in Figure-7. It can be seen that the drag coefficients from the conventional models and
6
DNS agree with each other over a range of the volume fraction. But at the lower gas volume fraction, the
7
drag coefficients from the DNS studies are higher than those from the Wen-Yu and Ergun models. The
8
values from the Syamlal-O’Brien model are lower than those from the Wen-Yu, Ergun, BVK (Beetstra, van
9
der Hoef and Kuiper) and PUReIBM (Tenneti et al., 2011) models. The drag coefficient calculated from the
10
EMMS model is significantly lower in an intermediate range of the gas volume fraction of 0.7-1. At
11
minimum fluidizing and maximum gas volume fraction, the mathematic formulation of the EMMS model
12
forces the drag values to approach the values calculated by the conventional drag models. The values from
13
the SGS model are significantly lower than other drag models over entire range of the gas volume fraction,
14
and the SGS values further drifting lower at the gas volume fraction close to 1. While explanation of the
15
behaviour of the SGS model is not clear, it is noteworthy that the SGS correlation is a weak function of the
16
particle Reynolds number (Benyahia, 2009) and it relies mainly on grid size (known as filter size) used in
17
fine grid periodic simulations. In previous studies, the lower drag values from both the EMMS and SGS
18
models have been attributed for their ability to account for the clusters or volume fraction heterogeneity.
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Figure-7: Comparison of drag coefficients (Gs = 489 kg/m2s, ug = 5.2 m/s, Uslip = 0.57 m/s) 19
Yang et al. (2003a,b); Wang et al. (2008); Benyahia (2009), Shah et al., (2011b, c), Benyahia (2012), Wang
20
et al. (2012), Shah et al. (2015) and several others have compared predictions of axial and radial profiles
21
from the EMMS models with those from the Gidaspow drag model. Similarly, Andrews IV et al. (2005),
22
Benyahia (2009), Igci and Sundaresan (2008), and Igci and Sudaresan (2011) have compared predictions
23
from the SGS model with those from the Gidaspow and experimental data. Comparison by Shah et al. (2015) Page 39 of 39
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is shown in Figure-8. For a low solid flux riser, the predicted axial profile from the Gidaspow model shows
2
that the values do not vary along height. This axial profile from the Gidaspow drag model shows complete
3
disagreement with the experimental data both qualitatively and quantitatively. On the other hand, the EMMS
4
model gives a dense bottom with higher solid volume fraction and lower values at the top (Figure-8) forming
5
the S-shape axial profile with reasonable qualitative agreements with the experimental data. For high flux
6
solids riser (Figure-8b), the pressure drop profiles predicted by both the Gidaspow and EMMS model
7
qualitatively agrees with the experimental data. Quantitatively, the predictions from the EMMS model are
8
closer to the experimental data at the bottom; while at the top, the values from the Gidaspow model are in
9
close agreement with the experimental data.
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(b)
(a)
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(c) (d) Figure-8: Effect of drag model: (a) and (b) axial profiles of solids volume fraction at low solids flux and pressure drop at high solids flux respectively; (c) and (d) radial profiles of solids volume fraction at low and high flux respectively (Shah et al., 2015). Shah et al. (2015) have also compared the predicted radial profiles from the EMMS and Gidaspow models
2
with the experimental data (Figure-8c and d). The radial profiles from the EMMS model also give reasonable
3
qualitative agreements with the experimental data for two (low and high solids flux) flow conditions.
4
Quantitatively, the predictions from the EMMS still show some discrepancies between the predicted values
5
and experimental data. Shah et al. (2015) attributed these discrepancies to assumptions and empirical
6
correlations involved in calculations of the cluster parameters. Benyahia (2009) have also found
7
discrepancies between their predictions from the SGS drag model and experimental data, and the author has
8
attributed the discrepancies to the dependence of the SGS drag on the selection of the filter size. The
9
numerical drag models proposed by Beetstra et al. (2007) and Tenneti et al. (2011) have still not been tested
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by conducting riser simulations.
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(b) Figure-9: Effect of gas phase flow models, (a) radial profile of volume fraction of solids phase and (b) axial profile of volume fraction of solids phase. 3.2.2.
Effect of gas phase viscous model
2
Experimental data shows existence of both dense and dilute conditions inside the riser. The flow of the gas
3
phase in the dilute region is expected to be turbulent, while that in the dense region with narrow inter-particle
4
distances and in boundary layer around particles and clusters can be either laminar or turbulent. On the other
5
hand, clusters of the solid particles observed in riser can significantly dampen or enhance fluctuating velocity
6
of the gas phase. Hence, laminar model has also been used to model stresses in the gas phase. The gas phase
7
Reynolds number based on diameter of riser generally varies from 104 to 106; while the particle Reynolds
8
number that calculated from diameter of particle is less than 100. As a result, both the laminar and turbulent
9
models for the gas phase stresses are applied in CFD studies.
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1
10
Almuttahar and Taghipour (2008) have compared predictions from the laminar and k- mixture turbulent
11
models. It can be seen in Figure-9a that radial distributions of the solids volume fraction predicted by the
12
laminar model are closer to the experimental values than those from the k- turbulent model; whereas, the
13
predicted axial profiles from both the laminar and turbulent models show wide discrepancies with the
14
experimental values (Figure-9b). Almuttahar and Taghipour (2008) have attributed these discrepancies to the
15
considered 2D geometry, and recommend 3D simulations for accurate predictions. Benyahia et al. (2005)
16
have investigated three different gas-solids turbulence models. Two of these models are those of Balzer et al. Page 42 of 42
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(1996) and Cao and Ahmadi (1995) that account for the effect of gas turbulence through the use of a
2
modified k- model, whereas the third simulated model is of Agrawal et al. (2001) that does not model the
3
gas phase turbulence. Benyahia et al. (2005) have found only minor difference between the predicted radial
4
profiles from these models with and without gas phase turbulence.
5
Shah et al. (2015) have also compared predictions from the laminar, k-ε dispersed model and k-ε per phase
6
model for both high and low flux conditions. Shah et al. (2014) have found that predicted values from both
7
the laminar and k- dispersed models give reasonable agreement with the experimental data; while the per-
8
phase option slightly under predicted the values in the dense section and over predicted at the top section
9
(Figure-10a). For the high flux condition (Figure-10b), all three models predicted similar time-averaged axial
10
pressure drop profiles. Figure-10(c) and (d) shows the impact of three viscous stress models on instantaneous
11
contour plots of the solids volume fraction captured at 20s flow time. For both low and high flux conditions,
12
the contour plots from laminar and k- dispersed models give continuous flow structures with “cluster” and
13
“steamer” like solid structures appearing throughout the height. But the contour plots from k- per-phase
14
model give discontinuous solid structures, where zones of higher and lower solid volume fractions appear to
15
be stretched all the way from the wall to the centre of the riser. Furthermore for the low solids flux condition,
16
the contour plots from only laminar and k- dispersed model show a clear distinction between the dense
17
bottom and dilute top sections. Shah et al. (2015) have further compared instantaneous values of turbulent
18
kinetic energy of the gas phase and granular temperature of the solids phase at different heights. While Shah
19
et al. (2015) have shown different in predictions from the k- dispersed and per-phase models, they have not
20
given a detail analysis on reason for these differences.
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(b)
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Laminar
k-ε dispersed
k-ε per-phase
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Laminar k-ε dispersed k-ε per-phase (d) High solids flux (Gs = 489 kg.m2s)
2
(c) Low solids flux (Gs = 14.3 kg.m s)
Figure-10: Effect of gas phase flow models on axial profiles, (a) volume fraction of solids phase at low solids flux condition; (b) pressure drop at high solids flux condition; and (c) and (d) Instantaneous contour plots of solid volume fraction (Shah et al., 2015). 3.2.3.
Effect of KTGF closure models
2
Table-2 shows that previous simulation studies have used the E-E model with the KTGF, where two types of
3
granular temperature conservation equations such as partial differential and algebraic have been used. In
4
either of these two selections, the model requires closure laws for the granular energy dissipation rate, radial
5
distribution function and solids bulk viscosity. If the partial differential equation for the granular temperature
6
is applied, then the closure law for the granular temperature conductivity is also required. Several models are
7
available for these KTGF closures. van Wachem et al. (2001) and Ahuja and Patwardhan (2008) have
8
explicitly calculated values of the solids phase KTGF properties from alternate closure models for a range of
9
the solids volume fraction of 0-0.65. For the solids volume fraction between 0-0.3, which is a typical range
10
of the solids volume fraction found in riser, these studies find only minor differences between the calculated
11
values from alternate closure models accept those from closure models proposed by Syamlal et al. (1993).
12
Consequently, the effects of alternate closure models for each of the KTGF parameters (such as the solid
13
pressure, frictional pressure, shear viscosity, granular viscosity, frictional viscosity, and radial distribution
14
function) on prediction of the riser hydrodynamics have not been investigated by conducting riser
15
simulations.
16
3.2.4.
17
3.2.4.1. Inlet boundary conditions
18
Boundary conditions have been used to specify numerical values at the boundary cells in CFD models. The
19
previous riser simulations (Table-2) employ three different types of flow domains such as periodic, 2D and
20
3D geometries. Using the periodic domain (Agrawal et al., 2001; Andrew IV et al., 2005; Benyahia et al.,
21
2009; Igci et al., 2008; Naren and Ranade, 2011), only a differential element of riser is considered and
22
computed values at the outlet boundary surface are passed to the inlet boundary at every time step. This type
23
of periodic flow domain is simulated to evaluate the effect of various closure models and flow conditions on
24
fully-developed radial profiles. In order to evaluate effect of model parameters on both axial and radial
25
profile, 2D and 3D flow domains with appropriate inlet and outlet boundary conditions are required. In these
26
simulations, inlets are configured with velocity-inlet boundary condition.
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Effect of boundary conditions
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1
At gas inlet, velocity of the gas phase equal to operating superficial gas velocity is specified with volume
2
fraction of solids phase equal to zero, while at solid inlet; average solid velocity at inlet is calculated from a
3
circulating solid mass flux by,
eq.(55)
ip t
4
Where, Gs is the solid flux circulating in riser, Ariser is the cross sectional area of riser, and Ainlet is the cross
6
sectional area of solid inlet. This boundary condition also needs a value of solids volume fraction which is
7
generally taken as the value at minimum fluidizing condition (0.5) or maximum packing condition (0.63).
8
Pressure-outlet boundary condition is most commonly used for the outlet. By specifying gauge pressure
9
equal to zero, the pressure at outlet is set as the atmospheric pressure.
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Previous CFD studies have been conducted by using both 2D and 3D flow domains. Furthermore, it can also
11
be observed that the previous simulations more choose 2D flow domain, as they are computationally more
12
feasible. Representation of an actual 3D riser using 2D domain then requires appropriate selection of the inlet
13
boundary conditions. Benyahia et al. (2001) have simulated a 2D geometry with one solid inlet (as
14
schematically shown in Figure-11a), mimicking the inlet configurations of the 3D boundary conditions of
15
experimental setup. In Benyahia et al.’s simulation, most of the solid particles are found to be concentrated at
16
the inlet side of the riser causing unsymmetrical radial distribution of the solid density (Figure-11b), which
17
did not agree with the core-annulus profile. Recently, Li et al. (2014a,b) have also observed accumulation of
18
the solids at one side of riser with one side inlet in 2D simulations. Since a 2D domain with one side inlet
19
cannot directly capture the asymmetric entry of solids to a continuously flowing riser, the 2D riser
20
simulations have been conducted using different types of boundary conditions for the inlets and outlets (Pita
21
and Sundaresan, 1993; Neri and Gidaspow, 2000; Benyahia et al., 2001; Yang et al., 2003; Almuttahar and
22
Taghipour, 2008).Benyahia et al. (2001), Yang et al. (2003) and Shah et al. (2012) have used two-sided
23
solids inlets for 2D riser simulations (Figure-12a). Shah et al. (2012) have compared the predictions from the
24
two-sided solids inlets in 2D simulations with both predictions from 3D simulations and experimental data
25
(Figure-11c), and found reasonable qualitative agreements between predictions and experimental data.
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(c) (b) Figure-11: (a) Schematic of 3D and 2D boundary conditions; (b) and (c) radial profile using one side solids inlet and two-sided solids inlets respectively. 1
3.2.4.2. Wall boundary conditions
2
For wall boundary condition, three alternatives (no-slip, free-slip or partial-slip) boundary conditions can be
3
used for an individual phase. Generally, no-slip boundary condition is used for the gas phase; whereas, each
4
of the three alternates have been considered for solids phase by previous studies. The no-slip boundary
5
condition for solids phase is set by equating the tangential and normal velocities of the solids to zero. The
6
partial-slip boundary condition can be configured using correlations developed by Sinclair and Jackson
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1
(Sinclair and Jackson, 1989) for the wall shear and Johnson and Jackson (Johnson and Jackson, 1987) for the
2
granular energy dissipation at wall. The wall shear boundary condition for the solids phase is given by rate of
3
axial momentum transferred to wall by the particles in a thin layer adjacent to wall surface (Sinclair and
4
Jackson, 1989):
eq.(56)
cr
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5
Where,
is the specularity coefficient. Its value equal to zero denotes free slip or specular wall, and unity
7
denotes no-slip wall.
8
The granular energy at wall can be obtained by using equation of Johnson and Jackson (1987). The granular
9
energy flux can be positive (wall as sink) or negative (wall as source) depending upon the relative magnitude
10
of granular energy dissipation due to non-elastic collision between particle and wall, and generation of
11
granular energy due to shear at wall. The granular energy dissipation due to inelastic collision with wall can
12
be written as,
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eq.(57)
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14
Thus, the partials-slip condition for the solids phase requires two additional parameters i.e. the specularity
15
and wall restitution coefficients.
16
The selection of the wall boundary conditions for the solids phase dictates velocity and volume fraction near
17
wall, and hence, appropriate wall boundary condition is very critical for capturing the core-annulus radial
18
profile. Table-10 shows that the partial-slip (Johnson and Jackson, 1987) wall boundary condition for the
19
solids phase is overwhelmingly used in previous studies. However, the use of the partial-slip configuration
20
needs a specularity coefficient and particle-wall coefficient of restitution to calculate friction between the
21
wall and particles and energy dissipation in the particle-wall collisions respectively. The specularity
22
coefficient represents a fraction of collisions that transfers momentum to wall; while the coefficient of the
23
restitution represents the fraction of the energy dissipated in the particle-wall collisions. Both these
24
parameters are dependent on material properties particles and wall. The restitution coefficient has been
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measured from controlled experiments by Gorham and Kharaz (2000), Joseph et al. (2001), Kharaz et al.
2
(2001) and Mangwandi et al. (2007). However, values reported in these studies are for different particle sizes
3
and materials, not for FCC catalyst. Hui et al. (1984) and Li and Benyahia (2012) have mentioned that
4
experimental estimation of the specularity coefficient is not feasible. One way to determine the specularity
5
coefficient is to adjust this parameter to fit experimental data. Li and Benyahia (2012) have provided a model
6
for specularity coefficient as a function of the particle-wall restitution coefficient, the frictional coefficient
7
and the normalized slip velocity at the wall. Li and Benyahia’s model for specularity coefficient has not been
8
tested by conducting riser simulation.
ip t
1
cr
9
Benyahia et al. (2012); Almuttahar and Taghipour (2008); Wang et al. (2012) and Shah et al. (2015) have
11
investigated the effect of the specularity coefficient and coefficient of the restitution on flow predictions.
12
While Benyahia et al. (2012); Almuttahar and Taghipour (2008) and Wang et al. (2012) have found only
13
minor effect of the coefficient of the restitution on the predicted axial and radial profiles; the authors found
14
significant impact of the specularity coefficient. Shah et al. (2015) have investigated a wide range of
15
specularity coefficients from 0.1 to 0.0001 in riser with low and high solids flux conditions (Figure-12). As
16
shown in Figure-12(a) and (b), a lower specularity coefficient of 0.0001 gave axial profiles of the solids
17
volume fraction (in the low solids flux riser) and pressure drop (in the high solids flux riser) that reasonably
18
agree with the experimental data. Figure-12(b) and (c) shows the effect of the specularity coefficients on
19
radial profiles at low and high solids flux conditions (Shah et al., 2015). While the specularity coefficient of
20
0.0001 also predicted experimental values in dilute section of the low solids flux riser; in dense bottom
21
region of the low solids flux riser, a higher specularity coefficient of 0.1 gave good agreement between the
22
predictions and experimental data. Shah et al. (2014) have concluded that the impact of the specularity
23
coefficient on the flow predictions has varied with the flow conditions. Therefore, this parameter must be
24
adjusted with the flow conditions.
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(a)
(b)
High solids flux
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Low solids flux
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(b) (c) Figure 12. Effect of wall boundary condition, (a) height of riser Vs. volume fraction of solid, and (b) height of riser Vs. pressure drop, (c) volume fraction of solid Vs. radial position (low solid flux riser, Gs = 14.3 kg/m2s), and (d) volume fraction of solid Vs. radial position (high solid flux riser, Gs = 489 kg/m2s) 1
3.3. Shortcomings
2
Following shortcomings of the E-E based CFD models of riser can be stated.
3
(1) The treatment of the solids phase as a fluid in the E-E approach requires several closure models that are
4
derived by using the KTGF. For each closure law, several models are proposed in literature. A selection
5
of appropriate closure models is critical to achieve close quantitative agreements between the predictions
6
and experimental data. Various combinations of the closure models (see Table-2) have been used in the
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1
past to get closer agreements with the experimental data at various flow conditions. Clear guidelines for
2
selection of KTGF closures are not available.
3 (2) The dominant closure in the E-E model is the interphase drag. Both conventional models and multiscale
5
drag models have been used. For coarse grid simulations, conventional drag models could not predict
6
experimental observations quantitatively. The multiscale structure dependent drag models such as the
7
EMMS and SGS drag models have shown significant improvements in predictions of axial and radial
8
profiles at different flow conditions (Yang et al., 2003; Benyahia, 2009; Shah et al., 2011b,c; and Shah et
9
al., 2015). However, the SGS model is computationally expensive, and the application of the EMMS
10
drag model needs local values of cluster properties such as size and volume fraction at a given flow
11
conditions. So far, experimental observations on structure of clusters (shape, size and volume fraction) at
12
different flow conditions are not available.
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13
(3) Predicted radial profiles from different simulation studied show reasonable qualitative agreements with
15
experimental data with some quantitative discrepancies. To eliminate such discrepancies, most of
16
previous efforts have been devoted to investigate the gas-solid drag model; while the effect of the lift
17
force has not been investigated.
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(4) Both the laminar and turbulent models for viscous stresses in the gas phase have been used in two-fluid
20
models of riser. Interestingly, both these models could give reasonable qualitative agreements with
21
experimental data in previous studies. Shah et al. (2015) showed that different types of the k- turbulent
22
models (dispersed and per phase models) for the gas phase gave similar time-averaged values, but
23
instantaneous flow structures are quite different. Further analysis suggested that turbulent kinetic energy
24
and dissipation rate predicted by the k- dispersed and per phase models are different by orders of
25
magnitude. Without detail time-averaged and instantaneous data on velocities and volume fraction, it is
26
difficult to conclude on suitability of use of the laminar or type of turbulent model.
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1 (5) As described in Table-2, almost all previous studies have used partial-slip wall boundary conditions,
3
which has been able to capture the core-annulus distributions of the solids phase. But, this wall boundary
4
conditions required empirical constant such as secularity coefficient, experimental value of which is also
5
not available. Therefore, most of the studies used this parameter for fine-tuning of the predictions. Li and
6
Benyahia (2012) have provided a model for specularity coefficient as a function of the particle-wall
7
restitution coefficient, the frictional coefficient and the normalized slip velocity at the wall. Such
8
correlation between the specularity coefficient and flow conditions needs further investigation by
9
conducting riser simulation.
cr
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(6) Extensive simulation works have been conducted using 2D domain of riser due to computational
12
feasibility, while experiments are mostly conducted using 3D cylindrical riser. Furthermore, in the 2D
13
geometry, different types of assumptions such as two-sided inlets for the solids phase and bottom inlet
14
for the gas phase, single bottom inlet for gas and solids phases, and cycle boundary conditions to
15
maintain a constant solid holdup have been used. Shah et al. (2012) have showed that the inlet boundary
16
conditions in 2D domain significantly affect profiles in so-called fully developed region (at top section
17
of riser). Therefore, to avoid uncertainty arising from the assumed 2D boundary conditions, it is
18
necessary to evaluate effect of closure models in exact 3D geometry.
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3.4. Eulerian-Lagrangian model
20
In E-L model, the gas phase is represented as a continuous phase for which the averaged mass and
21
momentum balance equations are solved. These equations are similar to those discussed in the E-E model
22
(section-3.1.1.). The particle phase is considered as discrete particle. For individual particle, Newton’s force
23
balance equation is solved. The force balance equation around individual particle can be written as:
25
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(eq. 58)
(eq. 59)
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1
(eq. 60)
Where, xp is the position of particle p; Mp is the mass of particle, vp is the velocity of particle, Fp is the total
3
force on particle, Fd is the drag force on particle, Fc is the contact force on particle, Tp is the total torque on
4
particle, Ip is the moment of inertia of particle, Ω is the angular velocity of particle.
5
The drag force term on a particle residing in kth control volume can be written as (Garg and Dietiker, 2013):
cr
ip t
2
(eq. 61)
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6
Where, Pg,k is the gas pressure in kth control volume, vp is the volume of parcel, β is the drag coefficient, Xp
8
is the location of parcel, ug(Xp) is the velocity of the gas phase at location Xp, and up is the velocity of parcel.
9
In the Eulerian equation for the gas phase, the drag force term can be calculated as:
ed
(eq. 62)
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7
Where, vk is the volume of kth control volume, and np is the total number of particles in kth control volume.
12
Table-5 lists CFD studies of riser using the E-L gas-solid flow model. It can be seen that there are five
13
different types of modelling approaches have been adopted within the E-L framework. These approaches are
14
(i) discrete particle model (DPM), (ii) discrete element model (DEM)-hard sphere, (iii) DEM- soft sphere,
15
(vi) multiphase particle in cell (MP-PIC) and (v) dense discrete particle model (DDPM). Helland et al.
16
(2000) and Mansoori et al. (2005) have adopted DPM approach by considering only the drag force and
17
gravity force in the force balance equation for the particle phase. Zhou et al. (2002), Zhou et al. (2007), He et
18
al. (2009) and Cheng and Jin (2010) have used DEM approach. The DEM approach considers the contact
19
forces due to particle-particle and particle-wall collisions. In this approach, the contact forces can be
20
calculated by either hard-sphere (Allen and Tildesley, 1989) or soft-sphere (Cundall and Stack, 1979) model.
21
In the hard-sphere model, collisions are considered to be binary and instantaneous. The time step is
22
determined by the minimum collision time between any one pair of particles. Consequently, the time step is
23
directly proportional to the mean free path or inversely proportional to the particle volume fraction. Due to
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consideration of binary collisions, this approach is more suitable to dilute gas-solid flow (Garg et al., 2012).
2
For a dense gas-solid flow, the hard-sphere approach requires much smaller time-scale. Furthermore, a dense
3
flow is characterized by collisions and persistent contact between multiple particles. In the soft-sphere
4
model, the particles are allowed to overlap each other. The overlap between the two particles is represented
5
as a system of springs and dashpots in both normal and tangential directions. Here, the contact force on a
6
particle is calculated as a sum of conservative force represented by spring and dissipative forces represented
7
by dashpot. To calculate conservative and dissipative forces, stiffness of spring and damping coefficient of
8
dashpot are used. The spring stiffness, damping coefficient and overlap between particles are used to
9
calculate the time step. For detail formulation of the soft-sphere approach, readers are refer to Cundall and
cr
ip t
1
Stack (1979); Tsuji et al. (1993); Deen et al. (2007); Zhu et al. (2008) and Garg et al. (2012).
11
Vegendla et al (2011), Li et al. (2012), Chen et al. (2013), Wang et al. (2014) and Jiang et al. (2014) have
12
used multi-phase particle-in-cell (MP-PIC) method (Andrews andO’Rourke,1996; Snider,2001; Benyahia
13
and Galvin,2010) to simulate the gas-solid flow in riser. In MP-PIC method, particles are represented by
14
parcels where each parcel contains a certain number of real particles of the same diameter and density
15
(Snider, 2001). In implementation of MP-PIC, the effect of several particles forming a parcel is manifested
16
through solids volume fraction in the drag force term. The drag force on parcel residing in kth control volume
17
can be calculated similar to the drag force on each particle. However, the Eulerian drag force term can be
18
calculated as:
ed
M
an
us
10
eq.(63)
pt
19
Where, vk is the volume of kth control volume, NT is the total number of parcels in kth control volume and np is
21
the number of particles in a parcel.
22
The interactions between particles are considered through the solid phase normal stress but not directly
23
through particle contact forces (Li et al. 2012), while particle-wall interactions are modelled by using bounce
24
back rules where the particle-wall restitution factor is used for energy dissipation. In the MP-PIC method, the
25
collision force term is calculated as (Li et al., 2012 and Garg and Dietiker, 2013):
26
Ac ce
20
(eq. 64)
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1
Where, Ps is the solids pressure which is calculated by,
2
(eq. 65)
Where, ps* and α are model parameters, whose recommended ranges are 1-100 Pa (Garg and Dietiker, 2013)
4
and 2-5 (Auzerais et al., 1988) respectively. Clote et al. (2010) have used slightly different approach where
5
solids pressure term appearing in above equation is calculated by used of the KTGF approach. This approach
6
is called as DDPM.
7
Different E-L modelling approaches can be evaluated in terms of (i) computational feasibility and (ii) their
8
ability to capture physical phenomena. Due to consideration of all real particles in riser, E-L approach
9
without contact forces (mentioned as DPM in Table-5) or DEM approach becomes computationally
10
impractical for real riser system. Consequently, most of DEM studies (see Table-5) have been conducted for
11
significantly less number of particles, scaled-down geometries or large sized particles. On the other hand,
12
MP-PIC approach considers flow of parcels number of which is significantly lower than number of real
13
particles. In addition, the MP-PIC approach does not take particle collision model explicitly and therefore, a
14
longer time step can be adopted for the particle phase. As a result, the MP-PIC approach becomes
15
computationally more feasible for riser simulations.
Ac ce
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ip t
3
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Table-5: CFD studies of risers using E-L models Modelling approaches (a) (b) (a) (b)
Drag model (a) (a) (c) (a)
Number of particles × 10-3 250 >7
Investigations
>7
(c)
(b)
40
Effect of inlet gas velocity Effect of coefficient of restitution and friction coefficient Effect of operational, particle properties and geometrical parameters on clusters
0.02
0.14 (2D)
100
1400
He et al. (2009) Cloete et al. (2010) Wu et al. (2010) Zhao et al. (2010) Vegendla et al (2011) Li et al. (2012)
0.05 × 0.015 0.076 0.05 0.1 0.1 0.05, 0.09
0.3 0.4 (2D) 2 (2D) 2-6 m 1 2.79, 10.5
335 67 500 500, 520 77 60, 54
2500 1500 1500 950, 2620 1550 1000, 930
(b) (d) (c) (c) (e) (e)
(b) (a) (c) (c) (b) (d)
40-200 -
Chen et al. (2013)
0.09, 0.2, 0.3
54, 76 , 140
930, 1712, 2600
(e)
(b)
-
Wang et al. (2014)
0.4
10.5, 14.2 (2D) 8.35 (3D) 3
(e)
(b)
400, 540, 890
Jiang et al. (2014)
0.42 × 0.92
5.8
200-1000
2620
(e)
(a)
-
Shi et al. (2015) Shi et al. (2015)
0.152 0.15
7.9 3
2550 2222
(e) (e)
(b) (b)
-
Modelling approaches:
cr
us
an
279, 291
150 160
ip t
0.37 (2D)
M
Particle ρs (kg/m3) 2400 2650 1020 2650
Dp (µm) 126 700, 1200 500 700
Solids residence time, effect of flow parameters Effect of number particles in parcel Effect of drag model and particle-wall restitution coefficient Axial and radial volume fraction profiles Distribution of particles in binary and polydispersed solids along height Distribution of solids concentration at inlet and in standpipe Analysis of solids RTDs and back mixing Effect of exit geometry
Drag model: Wen-Yu Gidaspow De Felice EMMS
Ac ce
DPM- Discrete particle model DEM (Discrete element method) - hard sphere DEM-soft sphere DDPM – Dense discrete phase model MP-PIC – Multi phase particle-in-cell
ed
Zhang et al. (2008)
Riser dimensions H (m) 1 0.378
pt
Helland et al. (2000) Zhou et al. (2002) Mansoori et al. (2005) Zhou et al. (2007)
Dt (m) 0.1 0.07 0.0305 0.07
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3.5. Drift flux analysis
2
Various drag force formulations and their relative merits are described in section 3.2.1. While using any one
3
of the drag laws, it is necessary to have a priori knowledge of cluster size distribution (CSD). Obviously, the
4
CSD depends upon the type of particle, size distribution, age of the catalyst, solid loading, column diameter,
5
superficial gas velocity, physical properties of the raw material, etc. Thus the development of procedures for
6
the estimation of the CSD is a formidable task. However, this problem can be addressed (though not with
7
desired rigor) with the help of drift flux model and measurements by the gamma ray densitometry. In a
8
rigorous manner, the DNS has a capability of predicting cluster size distribution and the corresponding drag
9
forces and the subject is discussed in detail in section 4.
cr
ip t
1
In order to address the problem of relation between the CSD and the drag force, drift flux analysis can be
11
applied for the FCC riser for the representation of the combined effect of superficial gas velocity, solids
12
circulating flux, column dimensions and physical properties of gas and solids on the solid holdup and
13
velocity profiles. The drift flux model for two-phase flow, proposed by Zuber and Findlay (1969), correlates
14
the averaged volume fractions of solids with the superficial velocities.
an
us
10
eq. (66)
ed
M
15
pt
16
17
Where,
18
superficial velocity of gas, and c0 and c1 are the drift flux constants. The values of c0 and c1 indicate the
19
quality of radial profile of the solid phase and the slip velocity respectively. The original model of Zuber and
20
Findlay (1969) considers the continuous phase profile to be flat. However, it is known to have strong
21
circulatory flows (upflow in the central region and down flow near the column wall). Under these conditions
22
the drift flux constants take the following forms (Thakre and Joshi, 1999; Joshi, 2001; and Ekambara et al.,
23
2005).
Ac ce
is the time-averaged holdup of solids inside riser, Vs is the superficial velocity of solids, VG is the
24
25
;
eq. (67)
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Where Vslip is the relative velocity between two phases,
is the instantaneous volume fraction of the
2
dispersed phase, εg is the instantaneous volume fraction of the continuous phase and ug are the interstitial true
3
velocities of the solid and gas phases velocity of solids.
4
The values of the drift flux constants can be estimated by using experimental data. The cold flow
5
experiments have reported several sets of radial and axial profiles of volume fraction and velocities of the
6
solids phase at different superficial gas velocity and solid fluxes. These data can be used to plot
vs.
cr
ip t
1
to estimate c0 and c1 for a given combination of operating conditions and column dimensions. The
8
coefficient c0 represents the transverse volume fraction profile, while the coefficient c1 represents the slip
9
velocity. CFD predictions of FCC riser must give values of holdup and slip velocity that satisfy the values of
10
c0 and c1 for a given operating condition and column dimensions. As the slip can be adjusted by the drag
11
coefficient, the value of c1 can be used for the estimation of representative slip velocity of drag coefficient of
12
the solid particles (which includes the cluster size distributions) and the gas. This slip velocity can be used
13
for the estimation of drag force.
14
It is further recommended that the gamma ray densitometry be used for the measurement of radial εs profile
15
at 5 to 10 locations in the FCC riser. These be substituted in the CFD simulation for getting profiles of
16
and
17
drift flux constant c0 which enables the estimation of c1 at a given location and hence the axial variation of
18
the CSD and the drag force. It may be emphasized that, the abovementioned procedure is iterative and needs
19
to begin with some reasonable value of drag coefficient.
20
4.
21
In riser flow, clustering is an important phenomenon which includes continuous formation and breakup of
22
clusters and complex interactions between fluid turbulence and dispersed solids phase. The formation of
23
clusters dictates intrinsic hydrodynamics, and therefore, understanding the clustering phenomenon is critical.
24
Due to small spatial and temporal scale of the clusters, experimental investigation to resolve the clustering
25
phenomenon under flow conditions of riser is currently impractical. Consequently, several investigators have
Ac ce
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an
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7
at various axial locations. Thus, the knowledge of ug, us, εg and εs can be used for the estimation of
Direct numerical simulations (DNS)
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adopted DNS approach. Two different numerical approaches, namely lattice Boltzmann method (LBM) and
2
immersed boundary method (IBM) have been previously used to conduct DNS of fluid-solid suspensions.
3
The LBM has been used by Hill et al. (2001a,b); van der Hoef et al. (2005); Beetstra et al. (2007); Yin and
4
Sundaresan (2009); and Shah et al. (2013). In the LBM, a flow domain is represented by number of lattices
5
and flow of fluid is calculated by updating velocity distribution at each lattice by using Boltzmann’s velocity
6
distribution function. Flow of particles is resolved by applying Newton’s force balance equation. Force
7
interactions between fluid and particle are then calculated from the velocity distributions at boundary nodes
8
and velocity of particles. The IBM has been used by Uhlmann (2005); Garg et al. (2010) and Tenneti et al.
9
(2011) to study the drag between the gas and solids phases. In the IBM, fluid is represented in an Eulerian
10
framework, whereas particles are represented in a Lagrangian framework. The Eulerian variables are defined
11
on a Cartesian mesh, and the Lagrangian variables are defined on a curvilinear mesh that moves freely
12
through the Cartesian mesh without being constrained to adapt to it in any way at all. The fluid-solid
13
interactions are accounted via a smoothed approximation to the Dirac delta function (Peskin, 2002). For
14
simplicity, previous DNS studies on the clustering can be divided into two categories, i.e. (i) those focus on
15
the impact of the clusters on the fluid-particle drag and (ii) those focus on the interactions between the
16
turbulent and clusters.
17
Hill et al. (2001a,b); van der Hoef et al. (2005); Beetstra et al. (2007); Yin and Sundaresan (2009); and
18
Tenneti et al. (2011) have adopted the DNS approach to investigate the drag force in solid-fluid suspensions
19
by simulating flow passing through a fixed assembly of randomly located mono- or bi-dispersed solid
20
particles inside a 3-D cubical flow domain with periodic boundary conditions. These studies calculated
21
effective drag force in gas-solid suspensions, and then, compared the calculated drag force with that obtained
22
from the conventional drag models such as the Wen-Yu, Syamlal-O’Brien, and Gidaspow models. Such
23
comparison has been made at various solid volume fraction and particle Reynlods numbers. The authors
24
observed wide discrepancies between the drag values from the DNS and the conventional models.
25
Consequently, Hill et al. (2001a,b), Beetstra et al. (2007) and Tenneti et al. (2011) have given a modified
26
drag correlations derived from the DNS results. Beetstra et al. (2006); Zhang et al. (2011); and Shah et al.
27
(2013) have conducted DNS of cluster configurations inside a cubical flow domain. Zhang et al. (2011) and
28
Shah et al. (2013) have observed that the calculated drag for cluster configurations is significantly lower than
29
that from random configurations. The reduction in drag due to the presence of cluster increases with an
30
increase in the solid volume fraction and particle Reynolds number. Main drawbacks of these studies are that
31
(i) cluster properties (sized, shape, number of particles) have been assumed, (ii) clusters have been treated as
32
stationary, and (iii) limited number of particles (32-1000) in a small flow domain (10-20 times particle
33
diameter) have been considered. To remove these limitations, simulations should be performed for a large
34
flow domain with several thousand free-flowing solid particles, which not only interact with surrounding
35
fluid but also experience particle-particle collisions.
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Xu and Subramanian (2010); Derksen (2012); Prevel et al. (2013) and Nicolai et al. (2014) have used DNS
2
approach to study influence of turbulence in fluid phase on the clustering phenomenon. Xu and Subramanian
3
(2010) have used IBM to simulate a flow with particle Reynolds number of 50 and the ratio of the particle
4
diameter to Kolmogorov scale of 5.5. In this study, numerical results for turbulent flow past fixed
5
assemblies, uniform and cluster configurations, of solid particles are analysed. It is found that clustered
6
configurations enhance the level of fluid-phase turbulent kinetic energy (TKE) more than uniform
7
configurations. This increase is attributed to a lower dissipation rate in the clustered particle configuration.
8
The simulations also reveal that the particle-fluid interactions result in anisotropic fluid-phase turbulence due
9
to the anisotropic nature of the interphase TKE transfer and dissipation tensors. Derksen (2012) has used the
10
LBM combined with the IBM to simulate fully coupled solid-liquid flow in a periodic, cubical 3-D domain
11
with homogeneous isotropic turbulence and 5000 spherical particles. In Derksen’s study, particles are made
12
sticky with a tendency to aggregate by a square-well potential, which is a function of a distance of interaction
13
and binding energy. In these simulations, the particles also interact with each other via interacting fluid and
14
through hard-sphere collisions. Derksen (2012) has investigated the impact of both the particle-particle
15
interactions and turbulent intensity on aggregate size distributions. It is found that a small increase in
16
velocity, volume fraction of the solids phase resulted in a single large aggregate with a size comparable to
17
size of the domain. In addition, friction coefficient related to hard-sphere collisions is found to have
18
influence on aggregate size distributions. Prevel et al. (2013) have performed DNS to investigate flow of
19
solids particles under the effect of hairpin vortices in a laminar boundary layer and the preferential
20
accumulation of particles close to wall. In this study, the Navier-Stokes equations are solved for the fluid
21
phase, along with Lagrangian tracking of 200,000 particles. In these simulations, hairpin vortices are
22
generated in a controlled way by a hemisphere protuberance mounted on the lower wall in an initial laminar
23
boundary layer. The authors observed preferential aggregation of outward moving particles in low speed
24
fluid regions between standing vortex and external vortex, and in high shear region between legs of the
25
hairpin vortex. They observe the ejection of the particles from high span wise vorticity region at the head of
26
hairpin vortices. Nicolai et al. (2014) have investigated flow of particles in homogenously sheared turbulent
27
to gain insight into structure and statistical properties of clusters. Nicolai et al. (2014) have performed both
28
experiments and DNS to record particle positions under turbulent flow conditions. In this experiment, a
29
homogeneous shear flow was generated in central part of recirculating water channel, and spherical glass
30
beads are injected in the channel. The instantaneous concentration is measured by imaging the positions of
31
particles using high resolution CCD camera. Both the experimental and numerical datasets are further
32
analysed by statistical methods such as the voronoi decomposition method and the Angular Distribution
33
Function (ADF). The particle snapshots indicate that particles tend to aggregate into thin clusters outside
34
vortex cores, and that the mean velocity gradient induces an evident preferential orientation on the particle
35
clusters. The voronoi analysis gave characteristic dimension of regions which may be identified as clusters
36
and voids. The use of the ADF approach gives further characterization of geometry of the clusters by
37
estimating anisotropy content of particle files at changing the scale of observations. Recently, Joshi and
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Nandkumar (2015) have made several suggestions for future work which will enable additional
2
understanding in the mechanism of formation/break-up of clusters using DNS simulations.
3
The subject of transition from homogeneous to heterogeneous dispersions have been addressed by many
4
previous studies (Anderson and Jackson, 1967; Didwania and Homsy, 1982; Batchelor, 1988; Thorat et al.,
5
1998; Joshi et al., 2001; Sundaresan, 2003; Thorat and Joshi, 2004; Ghatage et al., 2014). All these studies
6
use the theory of linear stability which consists of the following steps (1) the starting point is one
7
dimensional governing equations of continuity and motion for multiphase system (2) use Reynolds averaging
8
procedure for turbulent dispersion and introduce dispersion coefficients for individual phases (3) eliminate
9
pressure term with the assumption that it is shared by the multiple phases (4) linearization (5) introduction of
10
purturbation variables (6) simplification of all the equations in the form of single equation having one
11
dependent purturbation variable (continuous phase hold-up) (7) application of the theory of linear stability.
12
Joshi et al (2001) have compared all the experimental data on transition in gas fluidized bed and have shown
13
very good agreement with the predictions of the theory of linear stability. Further, there has been a long time
14
need for understanding the origin of disturbance. In this context of transitions, Derksen and Sundaresan,
15
(2007) have performed DNS simulations and established the reasons for initiation of clustering. This
16
pioneering work needs to be taken forward for understanding transitions in FCC risers. The analysis needs to
17
be performed separately (1) for the entry region of complex geometry and (ii) the pneumatic transport region.
18
In addition to the modulation of turbulence, the effect of turbulence on particle aggregation has been
19
analysed (Xu and Subramaniam, 2010; Derksen, 2012). Accordingly, the core-annulus phenomenon in the
20
FCC has been explained. Wei et al. (2013), Shnip et al. (1992) and Derksen and Sundaresan (2007) have
21
made useful contributions on the prediction of onset of transition to heterogeneity from homogeneity.
22
Further, such a transition has been shown to follow enhancement in particle setting velocity due to possible
23
particle aggregation/generation of strong convection currents in the continuous phase. However, like
24
turbulence modulation, the phenomena of aggregation as well as the onset of transition have not been
25
quantitatively understood and substantial additional work is needed.
26
5.
27
CFD studies of a reactive flow in the FCC riser (listed in Table-9) can be classified in two categories, i.e. (i)
28
those who ignore droplet phase by assuming instantaneous vaporization of feedstock (Theologos and
29
Markatos, 1993; Theologos et al., 1997; Gao et al., 1999; Benyahia et al., 2003; Das Sharma et al., 2006;
30
Lopes et al., 2011; ad Li et al., 2013), and (ii) those who consider the flow of feed droplets and vaporization
31
(Gao et al., 2004; Mortignoni and Lasa, 2001; Nayak et al., 2005; Behjat et al., 2011; and Chang et al.,
32
2012). The studies in the first category use the E-E gas-solid flow models coupled with cracking kinetics
33
models; while those in the second category use the E-E gas-solid flow model coupled with droplet phase
34
model (either Eulerian or Lagrangian), droplet vaporization model, and cracking kinetics model. Simulation
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1
CFD models of a reactive flow in FCC riser
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predictions of these models are often compared with the FCC riser performance data (conversion and yields)
2
available in literature.
3
Table-6
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Table-6: CFD studies of a reactive flow in the FCC riser Riser Modelling approach geometry
4
Cracking kinetics
Momentum transfer
Mass transfer
Heat transfer
Molar expansion
Investigations
Capability of their CFD model Effect of number of feed nozzles Effect of droplet size Effect of water injection at 10m height Droplet concentration near feed inlet zone Effect of droplet size Capability of their CFD model Capability of their CFD model Radial distributions at various heights Effect of droplet size and CTO ratio Capability of their CFD model Performance of two stage riser system; effect of operating conditions Comparison between riser and downer reactors Comparison between phenomenological model with heterogeneous reactive 1-D flow model Profiles of catalyst volume fraction near entry section of riser Feed entry with a mixing section in two stage riser systems Effect of operating conditions and droplet size Effect of operating conditions Comparison between predictions from rotating fluidized bed and conventional riser Effect of catalyst size distributions in FCC riser Effect of reaction temperature and effect of CTO Effect of feedstock and catalyst temperature, effect of CTO
3-D 3-D 3-D 3-D
E-E E-E E-E E-E
Lump kinetics model 3 10 3 13
Deactivation (a) (b) (a) (b)
(a) (a) (a) (a)
NC NC NC NC
(a)+(d) (a)+(d)+(e) (a)+(d)+(e) (a)
NC NC NC Ideal gas
Gao et al. (2001)
3-D
E-E-E
13
(b)
(a)+(b)
Vaporization
(a)+(c)+(d)
Ideal gas
Benyahia et al. (2003) Chang and Zhou (2003) Das et al. (2003)
2-D 3-D 3-D
E-E E-E-E E-E
3 4 12
(a)
(a) (a) (a)
NC Vaporization NC
NC (a)+(b)+(c)+(d) (f)
NC Ideal gas NC
Nayak et al. (2005)
3-D
E-L-L
4, 10
(b)
(a)+(b)
Vaporization
(a)+(b)+(c)+(d)
Ideal gas
Souza et al. (2006) Lan et al. (2009)
2-D 2-D
Well mixed single phase E-E
6 14
(a)
NC
(a)+(d) (a)+(d)
NC Ideal gas
Wu et al. (2010)
2-D
E-L
4
(a)
(a)
NC
(a) + (d)
Ideal gas
Zhu et al. (2011)
1-D
E-E
4
(b)
(a)
NC
(a)+(d)
Ideal gas
Lopes et al. (2011)
3-D
E-E
4
(b)
(a)
NC
(a)+(d)
Ideal gas
Gan et al. (2011)
3-D
E-E
11
(b)
(a)
NC
(a)+(d)
Ideal gas
Behjat et al. (2011)
3-D
E-E-L
4
(a)
(a)+(b)+(c)
Vaporization
(a)+(b)+(c)+(d)
Ideal gas
Chang et al. (2012) Trujillo and De Wilde (2012)
3-D Rotating fluidized bed
E-E-E E-E
12 10
(a) (b)
(a)+(b)+(c) (a)
Vaporization NC
(a)+(b)+(c)+(d) (a)+(d)
Ideal gas Ideal gas
Li et al. (2013)
3-D
E-E
14
(b)
(a)
NC
(a)
Ideal gas
Chang et al. (2014)
3-D
E-E
9
(a)
NC
(a)
Ideal gas
Alvarez-Castro et al. (2015a, b)
3-D
E-E
12
(a)
NC
(a)
Ideal gas
cr
us an
(b) (b)
M
ed pt
Ac ce
(b)
ip t
Theologos and Markatos (1993) Theologos et al. (1997) Theologos et al. (1999) Gao et al. (1999a,b)
(b)
Modelling approach:
Deactivation:
Heat transfer:
E-E: Gas and solids phases E-E-E: Gas, solids and liquid phases E-E-L: Gas and solids as continua, droplets as a discrete phase E-L-L: Gas as a continuum, solids and droplets as discrete phases E-L: Gas as continuum and solids as discrete phase Well mixed single phase
Based on residence time of catalyst Based on coke concentration
Gas-solid heat transfer resistance Gas-liquid heat transfer resistance Solid-droplet heat transfer Heat of reactions Effect of droplet vaporization on enthalpy of hydrocarbon gases Imposed temperature profiles
Momentum transfer: Gas-solid drag Gas-droplet drag Solid-droplet collisions
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5.1. FCC riser performance
2
Paraskos et al. (1976), Shah et al. (1977), Corella et al. (1986), and Bollas et al. (2002) have conducted pilot-
3
scale experiments of FCC plant; while Theologos et al. (1997), Ali et al. (1997), Derouin et al. (1997), Gao
4
et al. (2001), and Yang et al. (2009) have reported commercial FCC plant data. The available FCC plant data
5
can also be divided in two categories, one for which variation of conversion, yields and/or temperature are
6
reported along height of riser (Shah et al., 1977; Derouin et al., 1977) and the other for which the data only at
7
the riser exit are available (Paraskos et al., 1976; Corella et al., 1986; Ali et al., 1997; Bollas et al., 2002;
8
Yang et al., 2009).
M
an
us
cr
ip t
1
ed
(a) (b) Figure-13: (a) Conversion and yield Vs. dimensionless height; (b) Gas oil conversion Vs. gasoline yield (Shah et al., 1977: height = 30 m, diameter = 0.85 m, C/O = 7.06, pressure = 3.04 atm, catalyst dia = 68 μm, feed oil flow rate = 11.87 kg/s, catalyst flow rate = 83.09 kg/s; Derouin et al., 1997: height = 30 m, Diameter = 0.7-1 m, C/O = 5.5, pressure = 3.15atm, catalyst dia = 60-70μm, feed oil flow rate = 55-109 kg/s, catalyst flow rate = 300-600 kg/s) Figure-13(a) shows conversion of gas oil and yield of gasoline along height given in Shah et al. (1977) and
10
Derouin et al. (1997). Both the data sets show a steep rise in the conversion and yield in initial 20-40% of the
11
riser height, and then the profiles plateau. However, quantitative values in these two data sets are quite
12
different. Shah et al. (1977) have shown rise in conversion up to 45% and yield up to 67%; while Derouin et
13
al. (1997) have reported rise in conversion up to 72% and yield up to 48%. The discrepancies between the
14
two data sets, despite similar riser geometries, can be attributed to flow conditions. The feed and catalyst
15
flow rates in Derouin et al.’s riser system is almost 5-10 times higher than those used by Shah et al. (1977).
16
Furthermore, the Catalyst to oil ratio (CTO) in Shah et al.’s experiments is 7 compared to 5.5 in Derouin et
17
al.’s riser system. Figure-13(b) shows the gasoline yield against the gas oil conversion from the two data
18
sets. A significantly higher selectivity of the gasoline was reported by Shah et al. (1977). This suggests that
19
both higher CTO and lower flow rates of both feed and catalyst result in higher selectivity of the gasoline.
20
Paraskos et al. (1976) have conducted pilot-scale FCC riser experiments at isothermal condition, and
21
reported 14 data sets for varying CTO (6.82-8.6) and flowing space time (1.12-59.80). They report the
22
conversion at exit in range of 40% - 78% and yield in range of 31.3% - 53%. Ali et al. (1997) have reported
23
commercial FCC plant data, in which conversion of gas oil, and yields of gasoline, gas and coke components
Ac ce
pt
9
Page 64 of 64 Page 64 of 114
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at exit are 73, 44, 23.45, 5.8 wt % respectively. Furthermore, Ali et al. (1997) also report an exit temperature
2
of 795 K. Gao et al. (2001) have reported yields of five-lumps at two exit temperatures in a commercial FCC
3
riser systems. In Gao et al.’s data, yields of heavy fuel oil, light fuel oil, gasoline, gas and coke are 42, 18.5,
4
27.9, 7.7 and 3.9 wt % at 504 ˚C and 404.4, 18.8, 29.7, 7.8 and 3.3 wt % at 496 ˚C.
5
5.2. Coupling of gas-solid flow model with droplet flow and vaporization models
6
In FCC riser, feedstock is injected through atomizing nozzles in the form of micron-sized droplets. After
7
entering, the feed droplets vaporize upon making contact with hot catalyst and steam. The vaporisation of
8
feedstock controls distribution of temperatures and concentration of gas oil in bottom section of riser.
9
Therefore, it is critical to model the droplet phase along with the gas-solid flow. In previous studies, the
10
droplet phase was modelled by using either Eulerian (Gao et al., 2001; Mortignoni and Lasa, 2001; and
11
Chang et al., 2012) or Langrangian approach (Nayak et al., 2005 and Behjat et al. 2011).
12
Eulerian approach for the droplet phase: If the Eulerian approach is used, the E-E gas-solid model is
13
modified with a third set of mass, momentum and energy balance equations for the droplet phase. The gas-
14
droplet and the solids-droplet momentum and heat transfer are modelled by using correlations for the
15
interphase drag (Table-4) and heat exchange (Table-3). Gao et al. (2001) and Chang et al. (2012) used
16
following mass balance equations for the three-phase flow.
19
cr
us
an
M
ed pt
18
Ac ce
17
ip t
1
eq.(68)
eq.(69)
eq.(70)
20
Where, d denotes the droplet phase; and mdg (
) is the mass transfer from the droplet phase to gas
21
phase due to droplet vaporization. Gao et al. (2001) and Chang et al. (2012) used following momentum
22
balance equations for the three-phase flow.
Page 65 of 65 Page 65 of 114
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eq.(71)
2
eq.(72)
ip t
1
eq.(73)
Here, FD,sg (=
5
gas, droplet-gas, solid-droplet respectively. Chang et al. (2012) used the Syamlal-O’Brien drag model,
6
whereas Gao et al. (2001) used the Wen-Yu drag models to calculate the drag forces.
7
The energy balance equations for the three phases can be written as,
10
) are the drag force exchanges between the solid-
M
ed pt Ac ce
9
) and FD,sd (=
an
4
8
), FD,dg (=
us
cr
3
eq.(74)
eq.(75)
eq.(76)
11
Where, ΔQgs(= ̶ ΔQsg), ΔQdg (= ̶ ΔQgd) and ΔQds (= ̶ ΔQsd) are heat exchange terms between the gas and
12
catalyst phases and the gas and droplet phases respectively. Sgh is the energy source term in the gas phase
13
energy balance equation due to the endothermic heat of reaction. The equations of ΔQgs (= ̶ ΔQsg), are given
14
in the section 3.1.1.5. The heat exchange between the gas and droplet phase can be given as,
Page 66 of 66 Page 66 of 114
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1
eq.(77)
Where, hgd (= hdg) is the heat transfer coefficient; Adi is the interfacial area between the gas and solids phases;
3
Tg is the temperature of the gas phase; Td is the temperature of the droplet phase and hfg is the heat of
4
vaporization of the droplet phase. The heat transfer coefficient can be correlated to the Nusselt number,
5
which is further correlated by the droplet Reynolds number and Prandtl number according Ranz and
6
Marshall (1952). Chang et al. (2012) have used correlation of Gunn (1978) to calculate the Nusselt number;
7
while Gao et al. (2001) and Theologos and Markatos (1993) have used a correlation of Kothari (1967) for the
8
particle Nusselt number.
9
Lagrangian approach for the droplet phase: In the Lagrangian approach (Nayak et al., 2005 and Behjat et al.
10
2011), force and energy balance equations for each droplet are solved separately. The force balance equation
11
on an individual droplet can be written as,
an
us
cr
ip t
2
eq.(78)
M
12
Where, md is the mass of the droplet, ud is the velocity of the droplet, t is the flow time, FD is the drag force
14
on the droplet, Fg is the gravity force, and Fothers are acceleration forces such as lift force, virtual mass force,
15
pressure force, etc. For each droplet, the position and velocity is updated at every time step.
16
Nayak et al. (2005) have considered forces on the droplet due to continuous phase pressure gradient.
17
Furthermore, Nayak et al. (2005) have used drag model of Morsi and Alexander (1972). Nayak et al.’s
18
equation for force balance is,
pt
Ac ce
19
ed
13
eq.(79)
20
Where, CD is the drag coefficient, vd is the volume of the droplet, ρcont is the density of continuous phase
21
(only the gas phase was considered as continuous phase by Nayak et al., 2005 and Behjat et al., 2011), ucont is
22
the velocity of the continuous phase, and ρd is the density of the droplet phase. As tracking individual droplet
23
is computationally infeasible, Nayak et al. (2005) and Behjat et al. (2011) have considered flow of packets of
24
several droplets. Then, an equivalent diameter of the packet is used to calculate interphase drag and heat
25
exchange terms.
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Regardless of approach used for the droplet phase, heat exchange between the continuous phase and the
2
droplet phase causes variation in droplet size and temperature, which is calculated by using a suitable droplet
3
vaporization model. Available droplet vaporization models can be classified in two categories, namely
4
homogeneous where droplets are assumed to receive heat only from the surrounding hot gases (Abramzon
5
and Sirignano, 1989; Renksizbulut and Bussmann, 1993; Buchanan, 1994; Miller et al., 1998; Abramzon and
6
Sazhin, 2006) and heterogeneous which involves the effect of direct collisions between droplet and hot solid
7
particles (Buchanan, 1994; Nayak et al., 2005). Recently, Nguyen et al. (2015) have presented a detailed
8
review of all droplet vaporization models. In this review, the models proposed by Ranz and Marshall (1952),
9
Buchanan (1994) and Nayak et al. (2005), which have been previously used in the FCC riser simulations,
ip t
1
have been compared.
11
The feed droplets are generally injected at a temperature lower than the vaporization temperature; as a result,
12
the vaporization of droplets occurs in three steps, namely inert heating, vaporization and boiling. For inert
13
heating step, the governing equation for heat transfer can be given as,
an
us
cr
10
eq.(80)
M
14
And the heat transfer coefficient for the inert heating step can be calculated by following equations.
16
According to Ranz and Marshall (1952) and Buchanan (1994),
18
19
20
21
pt Ac ce
17
ed
15
eq.(81)
And according to Nayak et al. (2005),
eq.(82)
For vaporization step, the equations for mass transfer can be written as,
eq.(83)
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1
Where, K is the mass transfer coefficient; Ci,s and Ci, cont are the concentrations of vaporizing component at
2
surface of the droplet and in the bulk of the continuous phase respectively; and MWi is the molecular weight
3
of vaporizing component. According to Ranz and Marshall and Nayak et al.’s models, the mass transfer
4
coefficient can be calculated by,
cr
For the vaporization step, the equations for heat transfer can be written as,
7
And heat transfer for the vaporization step can be calculated by,
9
(Ranz and Marshall, 1952)
ed
M
an
8
us
6
eq.(84)
ip t
5
(Nayak et al. (2005)
Notably, Buchanan (1994) only considered the inert heating and boiling steps.
12
For the boiling step, equations can be written as,
Ac ce
11
13
(Ranz and Marshall, 1952; and Buchanan, 1994)
14
15
eq.(86)
eq.(87)
pt
10
eq.(85)
(Nayak et al., 2005)
eq.(88)
eq.(89)
In eq.(57), Nu can be calculated by,
Page 69 of 69 Page 69 of 114
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(Ranz and Marshall, 1952)
3
with
(Buchanan, 1994) – Heterogeneous
In eq.(58), Nueff can be calculated by,
an
4
(Buchanan, 1994) – Homogeneous
eq.(91)
ip t
with
cr
2
eq.(90)
eq.(92)
us
1
(Nayak et al. (2005)
M
5
eq.(93)
Buchanan (1994) has considered two hypothetical limiting cases for heterogeneous vaporization, i.e.
7
infinitely fast heat transfer during collision (limiting case-1) and hard-sphere collision (limiting case-2). In
8
the hard-sphere collision vaporization, Buchanan (1994) has considered elastic collision between droplets
9
and catalyst particles; while in the infinitely fast case, Buchanan (1994) has considered instantaneous transfer
10
of all possible heat from catalyst to droplets. The model equations for Buchanan’s heterogeneous case
11
mentioned above are for the hard-sphere collision model. For Buchanan’s infinitely fast case, the governing
12
equations can be given as,
14
pt
Ac ce
13
ed
6
for the inert heating step
eq.(94)
for the boiling step
eq.(95)
15
The model equations for inert heating and boiling steps are solved using finite element method with a time-
16
step size of 1 × 10-5 s to calculate vaporization times for the flow conditions given by Buchanan (1994). The Page 70 of 70 Page 70 of 114
Draft manuscript: - Computational Flow Modelling of FCC Riser: A Review
calculations are conducted for the Buchanan-homogeneous, Buchanan-heterogeneous (case-1 and case-2),
2
Ranz and Marshall and Nayak et al. models. The comparison of the calculated vaporization times is shown in
3
Figure-14. To show the fidelity of the calculation method, the calculated values of this study for the
4
Buchanan models are also compared with those reported by Buchanan (1994). Good agreement between the
5
calculations of this study and those of Buchanan (1994) is achieved. Figure-14(a) shows that the inert heating
6
times for the Buchanan-homogeneous and Ranz and Marshall models are the same, but the vaporization time
7
of the Buchanan-homogeneous model is approximately three times longer than that of the Ranz and Marshall
8
model. This can be attributed to the significant reduction in the Nusselt number caused by a factor
9
of
ip t
1
cr
, whose value is 1.94 at the simulated flow conditions. This means that the Nusselt
number of Buchanan-homogeneous model is almost half of that in the Ranz and Marshall model. Figure-
11
14(b) shows the comparison of calculated vaporization times from the heterogeneous models. The
12
Buchanan-case-1 (infinitely fast vaporization) gives total vaporization time of 0.9 milliseconds; while the
13
Buchanan-case-2 (hard-collision model) yields vaporization time of 17 milliseconds. The Nayak et al. model
14
yields intermediate value of 5.7 milliseconds. The decrease in the droplet vaporization time using the
15
Buchanan case-2 can be attributed to the use of modified droplet Reynolds number equation (see eq.61),
16
which consists of particle density and particle volume fraction; and hence, the use of the modified droplet
17
Reynolds number results in significant higher heat transfer coefficient. In the calculation for the Nayak et al.
18
model, the Nusselt number equation is modified by using particle Reynolds number (see eq.56), and this also
19
resulted in the higher value for the heat transfer coefficient. As a result, the Nayak et al. model also gives
20
significantly shorter duration for the droplet vaporization. It is noteworthy that the Nayak et al. model has an
21
empirical constant, whose value, as recommended by Nayak et al. (2015), is taken to be 14 in our
22
calculations. But this empirical constant brings further uncertainty to Nayak et al vaporization model.
Ac ce
pt
ed
M
an
us
10
Figure-14: Droplet diameter Vs. time (a) homogeneous models (b) heterogeneous models (flow conditions of
Page 71 of 71 Page 71 of 114
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Buchanan et al., 1994: droplet dia. = 300 μm, temp of cont. phase = 811 K, temp of droplet = 700 K, gasdroplet slip velocity = 6.1 m/s, gas-solid slip velocity = 6.1 m/s)
The calculated vaporization times from the simulated models are in milliseconds, and this can be considered
2
as a valid reason for the instantaneous vaporization assumption by several CFD studies. However, the above
3
calculation is for single droplet under a particular flow conditions. In reality, multiple droplets and variation
4
in flow conditions would have significant impact on the droplet vaporization time. The comparison of the
5
models shows wide discrepancies in the computed vaporization times (Figure-14). In previous simulation
6
studies (Table-6), Behjat et al. (2011a, b) and Chang et al. (2012) have used homogeneous vaporization
7
model; while Nayak et al. (2005) have compared their own model with Buchanan’s heterogeneous
8
vaporization model. None of these studies have validated their predictions of droplet vaporization time or
9
height, as experimental data on droplet vaporization height or time in FCC riser are not available in
10
literature. Few studies have reported experimental data of homogeneous droplet vaporization under
11
controlled conditions. Experimental data are available for homogeneous vaporization of water (Ranz and
12
Marshall, 1952), decane (Wong and Lin, 1992) and heptane (Nomura et al., 1996). Nguyen et al. (2015) have
13
compared calculated values from the Ranz and Marshall model with the experimental data. Nguyen et al.
14
(2015) have found that the Ranz and Marshall model could predict the data for vaporization of water but it
15
significantly under predicts the vaporization time for hydrocarbon droplets. As experimental data on
16
homogeneous or heterogeneous vaporization of FCC feed droplets are not available, comparisons of
17
calculated values with those of Buchanan (1994) are considered in this section.
18
5.3. Coupling between gas-solid flow model and cracking kinetic model
19
Catalytic cracking involves conversion of heavier hydrocarbons in the vaporized feedstock to lighter
20
products in the presence of hot zeolite catalyst. The vaporized feed contains thousands of species and hence
21
the cracking results into a similar number of cracked products. The cracking reactions also produce coke and
22
heavy hydrocarbons that deposit on the surface of catalyst reducing its activity. Describing the kinetics of
23
such a complex process in entirety is rather difficult task. Therefore, traditionally, a lump kinetic approach
24
has been adopted to describe the kinetics of catalytic cracking.
25
Weekman Jr (1968) and Wojciechowski (1968) have proposed the first lumped kinetic model, a 3-lump
26
model, which divides reaction mixture in gas oil, gasoline and light gases-coke components. Weekman Jr
27
(1968) has also estimated rate constants and deactivation coefficient by using experimental data. Further,
28
Weekman Jr and Nace (1970) have estimated kinetic parameters of the 3-lump model using moving bed
29
experiments. They also compare the kinetic parameters from fixed bed and moving bed experiments. All
30
these estimates of the kinetic parameters are based on only one type of feedstock. Nace et al. (1971) have
31
reported range of 3-lump kinetic parameters based on experiments with different types of feedstock. Voltz et
32
al. (1971) have given correlations to calculate variations in rate constants with the concentration of aromatic
Ac ce
pt
ed
M
an
us
cr
ip t
1
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and naphthenic components of feedstock. Paraskos et al. (1976) and Shah et al. (1977) and Corella et al.
2
(1986) have conducted pilot-scale riser experiments to estimate 3-lump kinetic parameters. In these three
3
pilot-scale experimental studies, residence times of the catalyst are significantly lower than those in the fixed
4
bed experiments of Nace et al. (1971). Furthermore, Paraskos et al. (1976), Shah et al. (1977) and Corella et
5
al. (1986) have used a governing (component balance) equation for the plug flow to calculate yields and
6
conversion. Due to different equations and operating conditions, the estimated 3-lump kinetic parameters
7
widely differ from each other. Lee et al. (1989) have proposed a 4-lump model and estimated kinetic
8
parameters by using micro-activity test (MAT) experiment data. Lee et al. (1989) have also investigated the
9
effect of temperature on the kinetic parameters, and consequently gave values of frequency factors and
10
activation energies for the 4-lump model. Gianetto et al. (1994), Pitault et al. (1994), Ancheyta-Juárez et al.
11
(1997), Abul-Hamayel (2003) have proposed different sets of the 4-lump kinetic parameters. Ancheyta-
12
Juárez et al. (1997) have further extended the work and provide rate constants for the 5-lump model. Bollas
13
et al. (2007) have also given kinetic parameters for the 5-lump model, but Bollas et al.’s model considers
14
additional cracking reaction of the LPG lump to the dry gas which is not considered by Ancheyta-Juárez et
15
al. (1997). Their model also considers tc–n type catalyst deactivation. To remove the dependence of the
16
kinetic parameters on charged feedstock, Jacobs et al. (1976) have proposed a 10-lump scheme; in which the
17
gas oil lump is further divided into heavy fuel oil consisting of paraffinic, naphthenic and aromatic lumps.
18
Jacobs et al. (1976) also use reaction rate equation different from previous 3-lump studies. Apart from the
19
lumped kinetic models, cracking kinetics models based on single-event kinetics (Froment, 1992; Feng et al.,
20
1993), molecular lump approach (Pitault et al., 1994), neural networks (McGreavy et al., 1994), and pseudo-
21
component approach (Liguras and Allen, 1989b, Gupta et al., 2007) are also available in the literature.
Ac ce
pt
ed
M
an
us
cr
ip t
1
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Hari et al. (1995) 582.84
0.97-2.87 10.3-39.2 18.5-40.1
23.76 684 5688
15.12 845.28 2412
Ej (kJ/mol) 68.2495 89.2164 64.5750 52.7184 115.4580 72.2526 51.6726 117.7050
Abul-Hamayel (2003) Ej (kJ/mol) 121.-743 117.208 35-158 79.534 21-60 62.79 12-104 142.324 3-20 125.58
Ancheyta-Juarez et al. (1997) Ej (kJ/mol) 699 57.3482 125.28 52.7436 50.4 31.8136 33.48 65.7202 0.000072 66.5574
92-281
315
cr
(Pre-exp. Factor) 7.978×105 4.549×106 3.765×104 3.255×103 79.57 1.937×106 4.308×103 3.017×108
us
k12 (hr-1) (wt%-1) k13 (hr-1) (wt%-1) k14 (hr-1) (wt%-1) k23 (hr-1) k24 (hr-1) k1 (hr-1) (wt%-1) k2 (hr-1) α (hr-1)
Corella et al. (1985) 432
75.348
an
VGOGasoline VGOGas VGOCoke GasolineGas GasolineCoke Reacn 1+2+3 Reacn 3+4 Deactivation (ϕ=e-αtc)
Nace et al. (1970) 7.7-33.5
ip t
Table-7: 3-, 4-, and 5- lump kinetic parameters derived from controlled fixed bed experiments. 3-lump kinetic parameters Weekman (1968) VGOGasoline k12 (hr-1) (wt%-1) VGOGas + coke k13 (hr-1) (wt%-1) k23 (hr-1) GasolineGas + coke k1 (hr-1) (wt%-1) 143 and 194 Reacn 1+2 -αtc 18.8 and 21.8 Deactivation (ϕ=e ) α (hr-1) 4-lump kinetic parameters Lee et al. (1989)
5-lump kinetic parameters
ed
699 128.52 0.36 50.4 21.96 11.52 0.000072 7.2 315
pt
22
k12 (hr-1) (wt%-1) k13 (hr-1) (wt%-1) k14 (hr-1) (wt%-1) k15 (hr-1) (wt%-1) k23 (hr-1) k24 (hr-1) k25 (hr-1) K34 (hr-1) α (hr-1)
Ej (kJ/mol) 57.3208 52.3 49.3712 31.7984 73.22 45.1872 66.5256 39.748
Ac ce
VGOGasoline VGOLPG VGODry gas VGOCoke GasolineLPG GasolineDry gas GasolineCoke LPGDry gas Deactivation (ϕ=e-αtc)
M
Ancheyta-Juarez et al. (1997)
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Of all the kinetic models proposed, the lump kinetic models are most appropriate for CFD simulations; and
2
hence, they have been overwhelmingly used by previous CFD studies. However, selection of lump model
3
and its kinetic parameters is a tricky task as several sets of kinetic parameters for a given lump model are
4
reported in literature. These kinetic parameters are estimated from experiments using different feedstock,
5
catalyst, reactor type, and operating conditions. The kinetic parameters of 3, 4 and 5-lump models are
6
compared in Table-7. Notably, these listed parameters have been derived only from fixed-bed experiments
7
and similar operating conditions of temperature and CTO. Despite similar experimental conditions for their
8
estimation, large differences between the values of these kinetic parameters can be seen. The differences in
9
the kinetic parameters can be attributed to not only type of feedstock and catalyst properties but also
cr
governing component mass balance equations used in their estimation.
Ac ce
pt
ed
M
an
us
10
ip t
1
Figure-15: Model prediction (of gasoil conversion wt%) Vs. Experimental data of Nace et al. (1971) 11
Figure-15 shows a parity plot for calculated predictions using listed kinetic parameters of the 3-, 4- and 5-
12
lump models against the experimental data of Nace et al. (1971), who have reported gas oil conversion vs.
13
space time for 16 different feedstock at two different run times (1.25 and 5 min). The predictions (shown in
14
Figure-15) are calculated by using the equation for gas oil conversion given by Lee et al. (1989). As
15
expected, the predictions from the 3-lump parameters of Nace et al. (1971) are very close to the experimental
16
values. The 4-lump kinetic parameters of Lee et al. (1989) give predictions within ±20% errors, while the
17
predictions from all other sets of kinetic parameters show wide discrepancy. The error in predictions using
18
parameters of Weekman Jr (1968) and Lee et al. (1989) is due to the fact that these parameters are derived
19
only for one type of feedstock while the experimental data of Nace et al. (1971) is for different types of
20
feedstock. In addition, the parameters of Weekman Jr (1968) are derived from conversion and yield data vs.
Page 75 of 75
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liquid hourly space velocity, while experimental data of Nace et al. (1971) is available against weight hourly
2
space velocity. The discrepancy in using the kinetic parameters of Hari et al. (1995), Abul-Hamayel (2003)
3
and Ancheyta-Juárez et al. (1997) can be attributed to their use of governing equation that does not account
4
for the effect of space velocity sufficiently. In CFD simulation of riser, each cell has different flow
5
conditions; while the available kinetic parameters are only valid for range of operating conditions. The above
6
analysis shows that significant uncertainty in CFD predictions is associated by direct use of the kinetic
7
parameters of previous studies. Therefore, one should review of all available kinetic data its validity over a
8
range of operating conditions of interest.
9
In a CFD model, number of species in the gas phase depends on the selection of lump kinetic model. Change
10
in mass fraction of each species (lump) is calculated by using a separate component balance equation that
11
can be written as::
an
us
cr
ip t
1
eq.(96)
M
12
Where, yj is the mass fraction of the jth species; and rj is the net rate of the production of the jth species. The rj
14
can be calculated by:
ed
13
eq.(97)
pt
15
Where, Mw,i is the molecular weight of the jth species; k is the total number of cracking reactions; and ri,j is
17
the rate of production of the jth species in the ith reaction. In a generalised form, the rate of consumption of a
18
reactant jthlump in ith reaction can be given by
19
Ac ce
16
eq.(98)
20
Where, kij is the rate constant of consumption of jth lump in ith reaction; cj is the concentration of jth lump, n is
21
the order of the reaction; and
22
VGO cracking reactions and zero for all other cracking reactions.
is catalyst deactivation function. The value of n is assumed to be one for the
Page 76 of 76
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1
There are two other types of rate equations are available in the literature, which can be written as:
2
(for 3-lump model of Pachovsky and Wojciechowski, 1971)
eq.(99)
Where, n is one for the VGO cracking reactions; n is zero for all other cracking reactions, cj0 is initial
4
concentration of pure lump j. The value of n for the VGO cracking implies that the cracking of the VGO is
5
easier for the initially vaporized fraction and it becomes progressively difficult as the VGO travels upward in
6
the riser.
us
cr
ip t
3
(for 10-lump model of Jacob et al., 1976)
eq.(100)
an
7
Where, ρc/εg is the mass density of the catalyst relative to the gas volume; kh is the heavy aromatic ring
9
adsorption coefficient; and CAh is the concentration of aromatic ring in heavy fuel oil. In this rate equation,
10
influence of the adsorption of heavy aromatic ring on the catalyst active sites and consequently on the rate of
11
the reaction is considered.
12
In all three types of rate equations, the catalyst deactivation function ( ) can be given either as a function of
13
residence time of the catalyst (tc) or concentration of the coke on the catalyst. In addition, several different
14
types of deactivation functions are available in the literature (see Table-8).
Ac ce
pt
ed
M
8
Table-8: Models for catalyst deactivation Weekman Jr.(1969) α and n are the rate constants.
Jacob et al. (1976)
= partial pressure of oil at inlet; α, β, γ = constants Krambeck (1991) b = empirical constant Ccoke= coke concentration (kg coke/kg cat) Farag et al. (1993) Kc = deactivation constant (kg catalyst/kmol) Ccoke= coke concentration (kmol/m3)
Page 77 of 77
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Pitault et al. (1995) Ccoke concentration in wt% A and B are empirical constants. As mentioned-above, rate constants used in the rate equations are estimated by lab-scale or pilot-scale
2
experimental data. Change in mass fraction of various species results in change in volume of the gas.
3
Furthermore, variation in the temperature and pressure conditions also brings in change in volume of the gas.
4
Volumetric expansion in gas phase is generally calculated by using the ideal gas law to calculate gas density
5
as:
cr
ip t
1
eq.(101)
an
us
6
Gas density calculated from mass fraction of various species is used in the mass and momentum balance
8
equations for the gas phase.
9
Coke deposition on catalyst surface causes change in catalyst activity and density. Change in the catalyst
10
activity due to the presence of coke is incorporated by using deactivation model as described in the kinetic
11
model section. In most CFD models (Table-9), the coke is assumed as a separate lump in the gas phase
12
instead of a separate solids phase.
13
The cracking reactions are endothermic, and their effect on the temperature is accounted for by a source term
14
in the enthalpy balance equation (Sgh in eq.43) for the gas phase. Heat of reaction is used to calculate the
15
source term. Chang et al. (2012) used the value of this source term equal to 9.127×103 KJ/kg of coke
16
produced; while Theologos and Markatos (1993) and Theologos et al. (1997) have used a constant value of
17
300 KJ/kg of hydrocarbon converted and 465 KJ/kg of feed respectively. Nayak et al. (2005) and Behjat et
18
al. (2011) have used reference enthalpy or heat of formation of each lump of the four-lump model to
19
calculate the heat of reaction in each control volume. In Nayak et al. (2005), the heat of formation values of
20
each lump are back calculated from heat of reactions estimated by Han and Chung (2000).
21
5.4. Predictions
22
The CFD models have been used to evaluate various designs and operational alternatives. Some of important
23
predictions can be summarised as follows.
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(1) Effect of CTO: Nayak et al. (2005), Wu et al. (2010), Zhu et al. (2011) and Behjat et al. (2011b) have
2
investigated the effect of CTO on the performance of FCC riser. Nayak et al. (2005) have found that an
3
increase in CTO from 6 to 12 increases the conversion 70 to 79%. Zhu et al. (2011) have also found that
4
the increase in CTO from 5 to 9 increases the yield of gasoline from 45% to 60%. Zhu et al. (2011) also
5
report negligible the effect of CTO on the yield of coke. Wu et al. (2010) have investigated the effect of
6
CTO (in a range of 5-20) on the clustering phenomenon and residence time of catalyst in the FCC riser
7
by using Langrangian approach. They note that increase in CTO results in higher clustering, suggesting
8
higher back mixing in riser. Wu et al. (2010) have further observed that an increase in CTO from 5 to 15
9
almost doubles the residence time of the catalyst phase in riser.
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(2) Effect of feed nozzles: Theologos et al. (1997), Theologos et al. (1999) and Li et al. (2013) have
12
investigated the effect of feed nozzle configurations and droplet size on the performance of FCC riser.
13
Theologos et al. (1997) have investigated 3 and 12-nozzle configurations, and found that the 12-nozzle
14
configurations increases gasoline fraction at outlet from 45 wt % to 48 wt %. Theologos et al. (1999)
15
have investigated the effect of three different feed droplet sizes (30, 100 and 500 μm) on vaporization,
16
cracking reaction initiation, selectivity and overall performance. They have found that a higher degree of
17
atomization (lower droplet size) gives faster feed vaporization and initialization of the cracking
18
reactions. Nayak et al. (2005) have also found that an increase in the droplet size from less than 400 μm
19
to 2mm results in decrease in the conversion from 85% to less than 70%. As the initial droplet size is
20
reduced, more uniformity in temperature profiles is achieved with higher conversion rates and gasoline
21
selectivity. Li et al. (2013) have analysed the effect of jet velocity (41.7, 62.5, and 83.3 m/s), positions
22
(the distance between the nozzle opening and walls - 3.5, 4.5, and 5.5 m) and angle of feed injection
23
nozzles (15°, 30°, and 45°) on flow field and cracking reactions in the feedstock mixing zone of riser.
24
Their simulations suggest that a higher jet velocity significantly increases inhomogeneity in radial
25
distributions of velocity and volume fraction of the solids phase. A higher angle of nozzles gives more
26
homogeneous radial distribution of the gas phase temperature. However, the angle of nozzles does not
27
impact axial distribution of the solids volume fraction. Increasing the distance between nozzle opening
28
and walls also has marginal impact on flow field. Decreasing the injection angle from 60˚ to 45˚
29
increases the conversion of VGO from 94.8% to 95.7% and the yield of coke from 8.25% to 8.56%
30
(Chang et al., 2012).
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(3) Effect of temperature: Zhu et al. (2011) have studied the effects of inlet temperatures of the catalyst
2
phase (600, 850 and 1000K) on the yields and conversions. Low inlet temperature of 600K for the
3
catalyst phase gives the conversion of approximately 20% and yield of the gasoline of approximately
4
15%. Increase in the inlet temperature to 1000 K then resulted in the fractional conversion of
5
approximately 80% and the yield of the gasoline of approximately 60%.
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(4) Effect of catalyst: Behjat et al. (2011) have studied the effect of catalyst deactivation on mass fraction of
8
various species. They compare predicted variation in the mass fraction along height using a CFD model
9
with and without deactivation of catalyst. The mass fraction of gas oil at outlet is almost 10% higher
10
when catalyst deactivation is considered, suggesting lower conversion of gas oil. Corresponding
11
reduction (approximately 10%) in mass fraction of gasoline at the outlet is also observed. Catalyst
12
deactivation affects light gases lump the most as its mass fraction decreases by approximately 50%.
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13
(5) Effect of riser geometry: Gao et al. (1999, 2001) have found that an optimum yield of desirable FCC
15
products is achieved at a riser height that is less than 10 m above feed inlet. Beyond this height,
16
excessive cracking reactions result in increased yield of by-products such as gas and coke at the expense
17
of desirable products. They have also suggested that injection of water as a reaction-terminating medium
18
above optimum riser height can be an effective option for optimizing the yield of desirable products. Lan
19
et al. (2009) have used CFD model to investigate performance of a two stage riser technology, where
20
two risers with different diameter and length replace conventional single riser. Gan et al. (2011) have
21
further investigated the impact of change in the diameter and nozzles in the two stage FCC risers. In this
22
study, the feed injection zone was fitted with a section with a diameter twice that of riser. Gan et al.
23
(2011) concluded that the changing diameter riser provides more mixing and is well suitable for the fast
24
reactions occurring at the feed injection section. Lopes et al. (2011) have analysed flow patterns near the
25
inlet section of the riser, and found a large-scale inhomogeneity in the distribution of solids volume
26
fraction near the catalyst inlet. Chang et al. (2012) have proposed use of an airlift loop mixer at the inlet
27
section of riser to improve hydrodynamics and mixing. Trujillo and Wilde (2012) have compared
28
performance of riser with a rotating fluidized bed in static geometry configuration, where solids are
29
injected in radially inward direction and VGO is injected in radially tangential direction. Due to intense
30
mixing in rotating fluidized bed configuration, significant process intensification is achieved in terms of
31
the bed height and corresponding rector volume required for a given conversion.
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5.5. Shortcomings
2
(1) CFD models of FCC riser have not been thoroughly validated against experimental data. Bottleneck in
3
this aspect comes from unavailability of a comprehensive set of experimental data. Experiments which
4
give measurements on both hydrodynamics and conversions at multiple locations in a given riser systems
5
are not available in literature. Consequently, several models have been validated against the
6
experimental data of cold-flow riser and few models have been validated against the available plant data.
7
Without thorough validation, the CFD models have only been used for qualitative analysis of the effect
8
design alternatives or operating conditions on the FCC performance.
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(2) There is a lack of coherence between evaluation of closure models for gas-solid flow in riser and coupled
11
CFD models for reactive flow in FCC riser. Recommendations on the selection of closure models and
12
modifications of these models provided by the gas-solid flow modelling efforts have not been
13
implemented in the coupled CFD models of FCC riser. For example, it has been repeatedly shown that
14
the multiscale drag models such as the EMMS and SGS models significantly improve flow predictions.
15
Despite of this, most of the coupled CFD models (Table-6) have used the Gidaspow drag models.
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(3) Most of the coupled CFD models (Table-6) have ignore the droplet phase by assuming instantaneous
18
vaporization. While this assumption makes the model and computation less complex, ignoring the
19
droplet phase leads to inaccurate predictions in more critical bottom section of the riser.
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(4) The coupled CFD models of Theologos et al. (1997), Gao et al. (2000), Behjat et al. (2011) have
22
considered homogeneous fast vaporization of feed droplets, while Nayak et al. (2005) have implemented
23
a mechanistic heterogeneous model for droplet vaporization. The comparison (see Figure-13) of the
24
vaporization models for single droplet vaporization under FCC conditions shows wide differences in the
25
predicted vaporization times. The selection of the vaporization model therefore needs to be validated by
26
comparing predicted droplet vaporization height with real FCC riser. Without such validation, the
27
predictions of the impact of the droplet diameter or design configuration of feed nozzles on FCC
28
performance remain unconvincing.
29
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1
(5) The gas-solid heat transfer coefficient is mostly calculated using Ranz and Marshall (1952). Behjat et al.
2
(2011) have used a correlation of Gunn (1978), whereas Theologos and Markatos (1993) and Theologos
3
et al. (1997) have used a correlation of Kothari (1967). It is necessary to evaluate the effect of various
4
heat transfer coefficient models on predictions. Currently, systematic study on the effect of the heat
5
transfer models on FCC performance is not available.
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(6) All the coupled CFD models (Table-6) have used lump kinetic models for cracking reactions. For each
8
lump kinetic model, several sets of estimated kinetic parameters are available in the literature. These
9
parameters have been derived by different catalyst, feedstock, operating conditions and flow conditions.
10
The comparison of the 3, 4, and 5-lump kinetic parameters (Figure-14) shows that different sets of
11
kinetic parameters do not predict experimental values of the gas oil conversion reported by Nace et al.
12
(1971). This clearly suggests that the available kinetic parameters are just tuned for a specific set(s) of
13
experimental data, and they do not represent intrinsic kinetic but they are highly influenced by other heat
14
and mass transfer processes.
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15
(7) Selection of appropriate set of kinetic parameters is not adequately explained in the previous CFD
17
models. Furthermore, none of the previous studies have investigated the sensitivity of predictions on
18
kinetic parameters. The selection of the kinetic parameters has been arbitrary in the previous efforts. For
19
example, Nayak et al. (2005) have used kinetic constants of Pitault et al. (1994) and activation energy of
20
Lee et al. (1989) for the four-lump kinetic model, though experimental data used to estimate the kinetic
21
constants and activation energy by Pitault et al. (1994) and Lee et al. (1989) have been quite different.
22
Nayak et al.’s modelling approach to couple cracking kinetics has been followed by Behjat et al. (2011)
23
and Lopez et al. (2011).
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(8) The volume expansion due to vaporization of feedstock and cracking reactions can significantly change
26
the hydrodynamics in the riser. Many studies (Theologos and Markatos, 1993; Theologos et al., 1997;
27
Theologos et al., 1999; Chang and Zhou 2003; and Das et al., 2003) have ignored the volume expansion
28
in their model.
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6. Recommendation for future work
2
This review identifies several shortcomings related to the selection of the KTGF closure models, modelling
3
of interphase exchange and turbulent forces, model dependency on several empirical constants, uncertainty
4
over the selection of the droplet vaporization model under riser flow conditions, uncertainty over the
5
selection of kinetic parameters for a given lump kinetic model and lack of experimental data for validation of
6
CFD models. All these shortcomings must be addressed in future research for development of accurate and
7
reliable computational model for FCC riser. Following suggestions are useful for future considerations:
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(1)
KTGF: Riser simulations have been predominantly conducted by using the E-E model with the
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8
KTGF approach, which requires several closure models to represent rheology of the solids phase.
11
Several alternate models have been proposed for every closure term of solids phase properties.
12
Consequently, different models have used a different combination of closure laws. There are very
13
few comparative studies which have investigated the influence of available alternate models on flow
14
predictions of riser flow. In future, a detailed study that compares influence of all KTGF closure
15
models on flow predictions at various riser flow conditions should be carried out. Such study can
16
provide a guide line for selection of a set of closure models that are suitable for riser simulations.
18
(2)
Use of discrete particle model: On the basis of published CFD models, the KTGF approach appears
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to be reasonable basis for estimating closure models for solids phase. Future work should include
20
discrete particle method (DPM) or discrete element method (DEM) to simulate the flow of the solids
21
phase. In DEM, the particle-particle and particle-walls collisions are captured by calculating contact
22
forces on each particle using the soft-sphere or hard-sphere approach. Both these approach use
23
spring stiffness and damping coefficient, which are derived from the material properties of the
24
solids. The DEM approach will ensure a realistic resolution of the solids phase without use of the
25
KTGF closure models. This approach is computationally more expensive; but due to recent advances
26
in high performance computing facilities and advances in DEM tools with ability to track millions of
27
particles in the flow domain, it is now possible to conduct DEM simulations of riser. In this
28
direction, DEM models for riser flow have been reported by Zhang et al. (2008), Wu et al. (2010)
29
and Chu and Yu (2012). However, these studies either use scaled-down geometry or consider
30
significantly lower number of particles then those found in actual FCC riser system.
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(3)
Use of multiscale drag: Gas-solid drag model is the dominant closure model that significantly affects flow predictions. Previous studies have shown that use of multiscale drag models (such as EMMS
3
and SGS-filtered models) has considerably improved flow predictions (radial and axial profiles of
4
solids volume fraction) than those from the conventional drag models (Benayahia, 2009; Shah et al.,
5
2014). Despite their usefulness, the multiscale drag models have not been used by published coupled
6
CFD models for FCC riser. Therefore, future simulations of FCC riser should use multiscale drag
7
models instead of the conventional drag models.
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(4)
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8
Resolution of clusters: Aggregation of particles, formation/break-up of clusters, and turbulentparticle interactions are key phenomena in upward gas-solid flow inside the riser. These phenomena
11
occur at meso-scale. Developing closure laws applicable to the riser that sufficiently account for
12
these meso-scale phenomena is a major challenge.
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Recently, Shaffer et al. (2013) used high-speed PIV images to capture clusters away from the walls.
15
Shaffer et al. (2013) and Coco et al. (2013) have provided direct and indirect measurements for
16
cluster properties. As mentioned in Section-4, Nicolai et al. (2014) have performed experiments to
17
investigate particle aggregation under turbulent flow conditions. More measurements like these are
18
required to characterise clusters in the riser flow. Another useful approach is particle resolved DNS,
19
where fluid-particle and inter particle interactions can be investigated by applying first principles.
20
Current, numerical observations from DNS are limited to several thousand particles positioned at
21
fixed locations in a fictitious cubical flow domain with periodic boundary conditions. DNS with
22
large number of particles, bigger size of flow domain, and free movement of particles that
23
experience both drag and collisional forces should be performed. The suggested simulations would
24
provide numerical observations to characterize clusters with respect to flow conditions. Numerical
25
results from DNS can then become input to multiscale drag, as well as particle turbulent models used
26
in the FCC simulations..
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28
29
(5)
LES for turbulent parameters: In the k- turbulent models, extreme assumption of isotropy is made,
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parameters are estimated on the basis of some ideal flow. In gas-solid flow, the effect of the solids
2
on the gas phase turbulent properties is significant. Capturing such effect in turbulent closure models
3
used in the two fluid model is critical, and hence it is proposed to undertake LES simulations. In
4
LES of gas-solid flow (Yomamoto et al., 2001; and Vreman et al., 2009), the gas phase is modelled
5
as a continuous phase whereas the solids are modelled by using Lagrangian approach. The gas phase
6
turbulent is modelled by using the LES model with the Smagorinski SGS model (section-3.1.2.2.) or
7
improved Smagorinski model (Boivin et al., 2000). Here, the average balance equation of the gas
8
phase and the force balance equations for the solids are coupled with the drag force term. This type
9
of simulations can be used to estimate the effect of the solids phase on turbulent properties of the gas
10
phase. Such estimates of turbulent properties can be made for different flow conditions at number
11
locations in riser (say at 10 points), which should be selected on the basis of various ranges of power
12
consumption per unit mass as well as solids volume fraction. Interpolated values of these turbulence
13
parameters can be used in the two fluid models for the riser simulation.
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14 (6)
Drift flux analysis: The cold-flow experiments and simulation studies have reported several sets of
M
15
radial and axial profiles of volume fraction and velocity of the solids phase. These concentration
17
profiles will enable the estimation of drift flux constants c0 and c1 (section-3.5.). The coefficient c0
18
represents the transverse volume fraction profile and the value of c1 represents the slip velocity.
19
These values will give additional basis for confirmation of drag coefficient.
21
(7)
For the detailed understanding of transport phenomenon in FCC risers, it is recommended to identify
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22
the turbulent structures (together with the size and shape distribution) and their dynamics (together
23
with velocity and energy distributions). For this purpose, the procedures are given by Kulkarni et al.
24
(2001) and Joshi et al (2009). Mathpati and Joshi (2007) and Mathpati et al (2009) have described
25
the relationships between the structure dynamics and the transport phenomena.
26 27
(8)
Entry section: It is seen from experimental and simulation results that the concentration and
28
temperature profiles drop exponentially in the initial few meter height of the FCC riser. This
29
suggests that most of the variation in concentration and temperature occurs in the entry region,
30
which probably further indicates that majority of cracking reactions also occur in the entry section.
31
Therefore, the performance of riser strongly depends on the performance of entry section. Hence, a Page 85 of 85
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1
comprehensive research on the entry section is necessary. The future work should include (a)
2
transient 3D measurement of concentration and velocity profiles of gas and solids phase, (b)
3
dynamic pressure measurement, (c) time series analysis of all variables in order to extract flow
4
parameters, and (d) CFD simulation and validation with experimental measurements of the entry
5
section.
7
(9)
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6
Pilot scale experiments: This review found a serious deficit of reliable plant experiment data in open literature. Future work should include an extensive experimental program for estimation of three
9
dimensional profiles in riser flow domain. For reactive flow, simultaneous measurements of
10
concentration, temperature, pressure, and catalyst volume fraction are required; while for
11
hydrodynamics, axial and radial profiles of both volume fraction and velocity in a single riser system
12
are desired.
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8
In conclusion, CFD modelling of FCC riser has come a long way, but it has still remained an art due to use
14
of various combinations of closure models and boundary conditions without rigorous experimental
15
validation. We feel that more fundamental work that consists of both numerical modelling and
16
experimentation is necessary to create greater understanding of underlying phenomena. Both simulations and
17
experiments can be conducted at various scales. At particle and cluster scale, DNS can provide more
18
observations on the interphase interactions and droplet vaporization. At equipment scale, pilot-scale
19
experimentations can provide much needed data for validation. Derivations of fundamental correlations for
20
interphase forces, turbulent interactions and droplet vaporization along with an extensive validation using
21
experiments are critical for development of more reliable computational models of FCC riser.
22
7. Nomenclature
23 24 25 26 27 28 29 30 31 32 33 34 35 36
Asi Ad Ariser Ainlet CAh CD0 Ci,s Ci,cont cμ, c1ε, c2ε cj cj0 c0 and c1 Cl Cp
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Interfacial area between gas and solids, m2 Droplet surface area, m2 Cross sectional area of riser, m2 Cross sectional area of inlet of riser, m2 Concentration of heavy aromatic ring in heavy fuel oil, kg/m3 Drag coefficient of a particle Concentration of vaporizing component at the droplet surface, kmol/m3 Concentration of vaporizing component in the bulk of the continuous phase, kmol/m3 Constant in k-ϵ model Concentration of jth lump in gas phase, kg/m3 Initial concentration of jth lump in gas phase, kg/m3 Drift flux constants Lift coefficient Heat capacity, J/kg K Page 86 of 86
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Smagorinsky constant Diameter of riser, m Diameter of particle, m Diameter of droplet, m Diameter of solids, m Fluctuating energy due to random motion of particle, kg/m3 s Activation energy of ith reaction, J/mol Coefficient of restitution of particle collisions Coefficient of restitution of particle-wall collisions Contact force on particle, kg/m s2 Drag force, kg/m s2 Drag on a particle, kg/m s2 Gravitational force, kg/m s2 Force on particle, kg/m s2 Lift force, kg/m s2 Empirical constant in frictional pressure equation Vitual mass force, , kg/m s2 Damping coefficient Generation of turbulent kinetic energy due to shear in the gas phase, kg m2/s2 Solids flux, kg/m2s Gravitational acceleration, m/s2 Radial distribution function Height of riser, m Specific enthalpy, J/kg Heat transfer coefficient, J/kg m2 K Heat of vaporization, kJ/kg Thermal conductivity, J/m K Mass transfer coefficient, m/s Gas-solid phase velocity variant Rate constant of consumption of jth lump in ith reaction, m3reactant/m3cat s Heavy aromatic ring absorption coefficient Turbulent kinetic energy, m2/s2 Conductivity for granular temperature, kg/m s Moment of inertia of particle Unit tensor Second invariant of the deviatoric stress tensor Total number of parcels in kth control volume Nusselt number Effective Nusselt number (Nayak et al., 2005) Order of reaction Empirical constant in frictional pressure equation Number of particles in a parcel Molecular weight, kg/kmol Mass, kg Pressure, kg/m s2 Solids pressure due to friction, kg/m s2 Solids pressure, kg/m s2 Empirical constant in frictional pressure equation Model parameter in solids pressure equation Prandtl number Heat flux, kJ/m2 s Heat exchanges, kJ/kg s Universal gas constant, J/kmol K
pt
Cs Dt dp dd ds EΘ Ej ess ew Fc FD Fd,p Fg Fp Flift Fr Fv,m fs Gk,g Gs g go,ss H h h hfg K K Kgc Kij Kh k kΘs Ip I̿ I2D NT Nu Nueff n n np MW m P Pfri Ps p ps* Pr q ΔQ R
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
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cr
Model parameter in solids pressure equation Volume fraction Maximum packing limit Minimum solid volume fraction from where friction between particle is dominant Time-averaged holdup of solids Density, kg/m3 Stress tensor, kg/m s2 Drag coefficient, kg/m2 s Filter size Kronecker delta Viscosity, kg/m s Turbulent viscosity, kg/m s Bulk viscosity of solids phase, kg/m s Component of bulk viscosity of solids phase due to collision between particles, kg/m s Component of bulk viscosity of solids phase due to friction, kg/m s Component of bulk viscosity of solids phase due to free motion of particles, kg/m s Turbulent dissipation rate, m2/s3 Interphase turbulent kinetic energy source term, m2/s2 Interphase turbulent energy dissipation source term, m2/s2 Reynolds stress due to turbulent interactions between phases Turbulent Prandtlnumber Granular temperature, m2/s2 Dissipation of granular energy due to inelastic collision between particles, kg/m3 s
pt
Greek letters α ε εs,max εs,min εs ρ τ β Δs δij μ μg,t μs μs,col μs,fri μs,kin ϵ Πk Πε Π(R,ij) σk, σε Θ γΘs
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Rij Reynold stresses, kg/m s2 Rep Particle Reynolds number Particle Reynolds number Res Droplet Reynolds number Red Rate of consumption of jth lump in ith reaction, kg/m3s rij S Source term in mass balances, kg/m3 Sh Source term in enthalpy balances, kg/m3 Strain rate Sij T Temperature, K Torque on particle, kg m3/s2 Tp t Time, s u Velocity, m/s Velocity of the gas phase at location Xp ug(Xp) up Velocity of parcel u’ Fluctuating velocity, m/s u Velocity, m/s Relative velocity, m/s urel Drift velocity, m/s udrift SGS stress, , kg/m s2 (u_i^' u_j^' ) ̅^SGS Us Slip velocity, m/s Volume of the droplet, m3 vd Volume of kth control volume, m3 vk Volume of parcel, m3 vp V Superficial velocity, m/s Slip velocity, m/s Vslip Location of parcel Xp y Mass fraction Distance from wall in wall unit y+
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ϕgs λs ϕ ϕ θ τs,w γ(Θs,w) Ω
Exchange of kinetic energy of random fluctuations in particle velocity to gas phase, kg m2/s2 Shear viscosity of solids phase, kg/m s Specularity coefficient Catalyst deactivation factor Angle of internal friction Wall shear, kg/m s2 Dissipation of granular energy due to inelastic collision between particles and wall, kg/m3 s Angular velocity of particle, rad/s
Subscripts g s SGS m p w d gs sg gd dg sd ds cont i
gas phase solids phase Sub grid scale mixture properties Parcel Wall Droplet From gas phase to solids phase From solids phase to gas phase From gas phase to droplet phase From droplet phase to gas phase From solids phase to droplet phase From droplet phase to solids phase Continuous phase Vaporizing phase
26
8. References
27
Abul-Hamayel, M.A., 2003. Kinetic modeling of high-severity fluidized catalytic cracking☆. Fuel 82, 1113-
28
1118.
29
Abramzon, B., Sirignano, W., 1989. Droplet vaporization model for spray combustion calculations.
30
International Journal of Heat and Mass Transfer 32, 1605-1618.
31
Abramzon, B., Sazhin, S., 2006. Convective vaporization of a fuel droplet with thermal radiation absorption.
32
Fuel 85, 32-46.
33
Agrawal, K., Loezos, P.N., Syamlal, M., Sundaresan, S., 2001. The role of meso-scale structures in rapid
34
gas–solid flows. Journal of Fluid Mechanics 445, 151-185.
35
Ahuja, G.N., Patwardhan, A.W., 2008. CFD and experimental studies of solids hold-up distribution and
36
circulation patterns in gas–solid fluidized beds. Chemical Engineering Journal 143, 147-160.
37
Ali, H., Rohani, S., 1997. Dynamic modeling and simulation of a riser-type fluid catalytic cracking unit.
38
Chemical Engineering & Technology 20, 118-130.
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Almuttahar, A., Taghipour, F., 2008. Computational fluid dynamics of high density circulating fluidized bed
2
riser: Study of modeling parameters. Powder Technology 185, 11-23.
3
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