Model prediction and optimization of dry pressure drop within Winpak

Accepted Manuscript Title: Model prediction and optimization of dry pressure drop within Winpak Author: Wenzhe Qi Kai Guo Huidian Ding Dan Li Chunjiang Liu PII: DOI: Reference:

S0255-2701(16)30492-5 http://dx.doi.org/doi:10.1016/j.cep.2017.04.020 CEP 6982

To appear in:

Chemical Engineering and Processing

Received date: Revised date: Accepted date:

7-10-2016 24-4-2017 28-4-2017

Please cite this article as: W. Qi, K. Guo, H. Ding, D. Li, C. Liu, Model prediction and optimization of dry pressure drop within Winpak, Chemical Engineering and Processing (2017), http://dx.doi.org/10.1016/j.cep.2017.04.020 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.

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Model Prediction and Optimization of Dry Pressure Drop within Winpak

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Wenzhe Qi1, 2, Kai Guo1, 2†, Huidian Ding3, Dan Li1, 2, Chunjiang Liu1, 2*

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1 School of Chemical Engineering and Technology, Tianjin University, Tianjin 300354, China 2 State Key Laboratory of Chemical Engineering (Tianjin University) 3 Research Institute of Petroleum Processing, SINOPEC, Beijing 100083, China

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AUTHOR INFORMATION Corresponding Author † [email protected] * [email protected] Tianjin University, School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, No. 135 Yaguan Road, Jinnan District, Tianjin 300354, China

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ABSTRACT The mechanism and optimization of the dry pressure drop within a novel structured packing, Winpak, was investigated by computational fluid dynamic simulations. The

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contribution of the dry pressure drop was decomposed into two components. The drag

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term was obtained according to an existing model. The frictional pressure drop was

simulated in a new representative elementary unit. Several structures of Winpak were

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designed to study the effect of the packing dimensions. Results indicate the windows

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on the packing sheets have significant effect. Accordingly, the cutting angle of windows was optimized to reduce dry pressure drop. A set of correlations for

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experimental data.

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predicting the dry pressure drop was established ultimately and validated by

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KEYWORDS: structured packing; dry pressure drop; CFD simulation; representative elementary unit; optimization

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1. Introduction Structured packing has been widely used for many decades in industrial separation process involving distillation (Spiegel and Meier, 2003), extraction (Fernandes et al.

high mass transfer efficiency and capacity (Olujić, 1999).

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2008), and carbon capture (Sebastia-Saez et al. 2013, 2014, 2015a, 2015b), for its

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The proper design of structured packing for specific industrial application and the optimization of packing geometries can be realized only when the transport

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mechanism within the packing is understood (Shilkin et al. 2005, 2006; Wolf et al.

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2014). It motivated the development of classical models, such as Billet model (Billet and Schultes, 1991, 1993, 1999), SRP model (Rocha et al. 1993, 1996) and Delft

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model (Olujić, 1997; Olujić et al. 1999), established by adjusting empirical

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correlations to measured values of great significance for predicting hydrodynamic

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behavior and mass transfer performance.

Study on dry pressure drop is generally the first and essential step for

understanding fundamental hydrodynamics behavior of a novel structured packing. Rocha et al. (1993) indicated that dry pressure drop has a positive correlation with wet pressure drop related to energy consumption and capacity. In view of this, it is necessary to investigate the mechanism of dry pressure drop within a packing. Since the last century, a mass of experiments have been carried out to get empirical correlations of various structured packings (Ding et al. 2014; Fair et al. 2000; Han et al. 2003; Iliuta et al. 2004; Robbins, 1991; Spiegel and Meier, 1992; Tsai et al. 2011; Woerlee et al. 2001). However, it is difficult to comprehend how gas flows within packings through experiments, which could enable us to evaluate hydrodynamic 3

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performance and optimize packing geometries. In addition, given the emergence of multifarious structured packings and operating conditions, the applicability of these models has been gradually limited on account of the laboratory conditions and high

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manufacturing costs of experimental apparatus (Said et al. 2011). Scholars attempted to propose theoretical approaches to predict pressure drops.

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Brunazzi and Paglianti (1997) explained that the pressure drop increases with the

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decrease of the column diameter since the diameter determines the number of gas flow bends across the wall. Another meaningful model by Olujić (1999) used in this

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study defined that the pressure drop is composed of three distinct components, of

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which pressure loss coefficients were regressed by experimental data. In recent years, computational fluid dynamic (CFD) method considered as “virtual

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experiments” has been widely used to study hydrodynamic characteristics inside

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structured packings (Kenig, 2008). However, it is too complex to simulate all transport phenomena in a full-scale packing column because of the costly computational expense derived from large scale difference between the characteristic sizes. Therefore, a lot of researches on packing column were carried out in three different scales (Raynal and Royon-Lebeaud, 2007; Sun et al. 2013), involving micro-scale (Gu et al. 2004; Haroun et al. 2010a, 2010b, 2012; Hoffmann et al. 2005; Hoffmann et al. 2006; Qi et al. 2013; Quan et al. 2015; Sebastia-Saez et al. 2014, 2015; Zhu et al. 2010; Ganguli and Kenig, 2011; Kenig et al. 2011), meso-scale (Armstrong et al. 2013; Ding et al. 2015; Fernandes et al. 2008; Larachi et al. 2003; Owens et al. 2013; Petre et al. 2003; Said et al. 2011; Sebastia-Saez et al. 2015b; 4

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Baten and Krishna, 2002; Chen, 2009; Haghshenas Fard, 2007; Hosseini, 2012; Nikou and Ehsani, 2008; Shojaee, 2011; Shojaee et al. 2012)and macro-scale (Fourati et al. 2013). Previous studies have validated that meso-scale simulations can be efficiently

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used to study the gas flow pattern and predict the dry pressure drop in representative elementary units (REUs) of a structured packing (Dai et al. 2012; Rafati Saleh et al.

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2011; Raynal et al. 2004). Petre et al. (2003) and Larachi et al. (2003) tailored the

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structured packing as a combination of four REUs, corresponding to four principal regions: the entrance of layer, criss-crossing junction, two-layer transition and

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channel-wall transition. Based on the work by Petre et al. (2003) and Larachi et al.

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(2003), Raynal et al. (2004) studied the influence of mesh size on CFD simulation of the dry pressure drop. Simulation results showed high dependence on the mesh size

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larger than 0.5mm. Said et al. (2011) and Amstrong et al. (2013) used a similar REU

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to study the effects of geometries on dry pressure drop within B1-250.45 Montz-Pak packing, and the predicted values by fitting equations are consistent with experimental data. Lautenschleger et al. (2015) developed a CFD-based optimization approach towards the reduction of dry pressure drops within a novel structured packing PD 10. Winpak is a novel structured packing based on multibaffled plate that invented by

our research group (Liu et al. 2014). It has been recognized as a high efficient mass transfer unit for the windows on the packing sheets improving the liquid distribution and the surface renewal (Sun et al. 2013). Many experiments were carried out to study the hydraulic behavior of this structured packing (Li et al. 2012; Li and Liu, 2011; Xiang et al. 2016). However, the pressure drop within Winpak is found to be relative 5

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high, which limits its industrial application with strict hydraulic restrictive conditions. A structural optimization strategy for reducing the dry pressure drop was proposed by Ding et al. (2015), who investigated the Winpak-based modular catalytic structured

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packing (MCSP) by meso-scale CFD simulation. However, Ding’s model cannot describe precisely the mechanism of dry pressure drop within Winpak because of the

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structural difference between Winpak and Winpak-based MCSP. As a consequence,

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the optimization of packing geometries cannot be accomplished either.

The current work, therefore, aims at studying the mechanism of the dry pressure

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drop within Winpak. The dry pressure drop is decomposed into two components. The

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drag component is calculated on the basis of Olujic’s work (1999). The frictional pressure drop is simulated in a new REU by means of three-dimensional CFD

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simulations. Several structures of Winpak are designed to investigate the effects of the

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packing dimensions. An optimal structure is proposed later through analyzing the resistance of the windows. Correlations for frictional pressure loss coefficient, considering all effects, are established by REU-based simulated data. The total dry pressure drop is predicted by the combination of the two components and the prediction model is validated by published (Li et al. 2012; Li and Liu, 2011) and supplemental experimental data.

2. Methodology 2.1 Packing used The basic geometry of Winpak is shown in Fig. 1. There are several flow-guiding 6

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cut-out windows on the crests and troughs of the packing sheet which can guide liquid from one side to another. The most commonly used packing is 500X-type, of which

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the dimensions are listed in Tab. 1.

2.2 Calculation strategy of dry pressure drop

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Fig. 2 shows that the pressure drop can break down into two independent

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contributions: frictional component due to gas-liquid interactions and gas-gas interactions between packing sheets, and drag component due to gas flow direction

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changes near the wall regions and between adjacent packing layers. The total pressure

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drop across the entire column is regarded as the sum of these two components (Olujić, 2009), determined by loss coefficient of frictional and drag components, (ζf and ζdc),

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gas density ρg, as well as the gas interstitial velocity uint.

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∆P = (ζ f + ζ dc ) uint =

2 ρguint

2

uspf

ε sin α

(1)

(2)

where uspf is gas superficial velocity based on an empty column. ε and α are porosity and inclination angle of the packing respectively. In Eqs. 1-2, ζf and ζdc are unknown parameters, which are investigated

respectively in subsequent sections to calculate the pressure drop within Winpak. 2.2.1 Pressure drop for the drag component Winpak is still the reformation of traditional corrugated sheets. It means the similarity of pressure drops due to gas flow direction changes between the novel 7

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packing and the traditional corrugated sheet structured packings (Armstrong et al. 2013; Olujić, 1999; Said et al. 2011). Therefore, the pressure loss coefficient for drag pressure drop can be calculated by the previously proposed correlation: hpb hpe

(ξ bulk + Ψξ wall )

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ζ dc =

(3)

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0.445 0.31  4092uLs  hpb  + 4715 ( cos α ) 1.63 0.779 0.44 1.76 ( cos α ) + Ψ  = + 34.19uLs cos α )  (   hpe  Re Gint    

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where uLs is the liquid superficial velocity which is inappreciable when the focus is dry pressure drop, and hpb is packed bed height. Wall correction factor Ψ represents

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the fraction of gas flow channels ending at walls determined by packing element

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height hpe, column diameter dc and inclination angle α:

 2 hpe2  Ψ= − d   π dc2 tan α  c tan 2 α 

0.5

+

2  hpe    π  dc tan α 

(4)

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2hpe

The ignorance of liquid phase effects leads to the simplification of Eq. 3:

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0.445  hpb  4715Ψ ( cos α ) 1.63 = 1.76 ( cos α ) +   hpe  ReGint 

ζ dc

(5)

where ReGint can be defined as:

ReGint =

uint ρ g d

µ

(6)

2.2.2 Frictional pressure drop

The dry pressure drop within Winpak has distinct features because of the

occurrence of windows. It is reasonable to deem that windows can enhance the gas disturbance leading to higher dry pressure drop. Therefore, it is necessary to consider the windows’ contribution to the frictional pressure drop. The pressure drop of frictional term can be calculated as: 8

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2 ρ uint ρu 2 ∆Pf = ζf = ξgg int hpb 2hpb 2

(7)

where the pressure loss coefficient, ξgg, due to gas-gas interactions is the focus of

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REU-based simulations.

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2.3 Representative elementary unit

Presenting an appropriate simulation model is a significant priority for obtaining

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the pressure loss coefficient for gas-gas interactions, ξgg. An applicable REU enables

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us to capture the flow dynamics within the structured packing at acceptable computational costs. Considering the gas could flow through windows to the other

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side, a hexahedral construction shown in Fig. 3 is determined as the REU, including

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two packing sheets and four windows in each sheet. The boundaries of the

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hexahedron were extended by 0.2 millimeter from packing sheets for better gridding and setting periodic boundary more easily. The effect of this construction is negligible because the pressure drop is mainly caused by the packing sheets and windows on it. The translational periodic boundary condition that gas flow leaving one face of the

unit would reintroduce to the opposite face is used to guarantee the fully developed gas flow. Arrows with the same color in Fig. 3 symbolize corresponding periodic boundaries. The dry pressure drop per unit height within the REU obtained by this periodic condition could represent the frictional dry pressure drop at column scale, even though the physical model is mesoscale. Therefore, the loss coefficient derived from the REU-based simulation, given as Eq. 8, could be used to calculate the total frictional dry pressure drop across an entire column. 9

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ξ gg =

2∆PREU 2 l ρ uint

(8)

Founded on the construction of 500X-type Winpak, nineteen structures including four inclination angles, three sizes of windows, and four opening angles with three

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kinds of channel heights were designed. Detailed structural parameters are listed in

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Tab. 2-4.

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2.4 CFD model

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The key point of the simulation is dry pressure drop in the REU. Therefore, the single-phase air streams are assumed to be impressible and isothermal with a density

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of 1.225 kg/m3 and a viscosity of 1.7894×10-5 Pa·s. The equation for mass conservation is given as (Batchelor, 2000):

∂ρ + ∇ ⋅ ρv = 0 ∂t

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d

( )

(9)

The conservation of momentum is described as:

()

∂ ρ v + ∇ ⋅ ρ vv = −∇P + ∇ ⋅ τ ∂t

( )

(

)

(10)

where the stress tensor τ is:



(

T

)

2



τ = µ  ∇v + ∇v − ∇ ⋅ vI  3  

(11)

The flow field in the novel packing is complex because of the corrugated sheets and windows on them. RNG k-ε model is used to close the Navier-stokes equation. This is because the RNG k-ε model has shown better performance of handling low-Reynolds-number and near-wall flows in Winpak (Ding et al. 2015). It is similar 10

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in form to the standard k-ε model with a particular differential equation for turbulent viscosity where v̂=µeff/µ and Cv≈100. Details of CFD settings are presented in Tab. 5.

 νɵ dνɵ  = 1.72 3  νɵ − 1 + Cν

(12)

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 ρ2 d  εµ 

Fig. 4 compares the simulated results accuracy for three different mesh sizes, 0.3

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mm, 0.5 mm and 0.6 mm in the element of 500X-type Winpak. The computing time

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ranged from tens of minutes for the 0.6 mm mesh to several days for the 0.3 mm mesh. The simulated values are consistent with experimental data for mesh smaller than 0.5

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mm. The average relative error between experimental data and simulated values

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obtained using 0.5 mm mesh is merely 5.1%. Therefore, the remaining simulations are performed using 0.5 mm mesh to keep the accuracy and to obtain faster results than

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the more refined mesh.

3. Results and discussion 3.1 Gas flow patterns

In order to comprehend directly the mechanism of the dry pressure drop, the gas

flow pattern is shown in Fig. 5. The 500X-type packing with F=2 is used as the representative sample. The favorite gas flow direction is that going through the inclination angle. In addition, the streamlines are more disturbed than that within the traditional packing sheets because of the gas flowing through or bypassing the window with a greater true velocity, which may be the major contribution to dry pressure drop. 11

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3.2 Effect of geometries The effect of geometries on dry pressure drop is shown in Fig. 6. Fig. 6a reflects that the smaller the inclination angle is, the larger the dry pressures drop will be,

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which is in line with previous work. It is obvious that the dry pressure drop increases sharply if the flux capacity is larger. The reason is that the interstitial velocity

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increases with the decrease of the inclination angle. The resulting increase in the gas

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turbulence leads to the significant rising of the pressure loss due to the frictional resistance.

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The effect of opening angles with different channel heights is shown in Figs. 6b-d.

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Increased opening angle can reduce the dry pressure drop with the same channel height. The reduction of specific surface area of the packing and the slight increase in

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porosity resulting in larger gas flow space and lower frictional resistance is a

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reasonable explanation. On the other hand, detailed analysis of specific values indicates that the dry pressure drop does not dramatically decrease continually with the increase of the channel height with the same opening angle, which disagrees with the previous viewpoint. It is because when the channel height increases, the size of the window increases as well, which remarkably enlarges the resistance within the already small channel.

It is obvious that the window dimension cannot be changed greatly because of the size limit of the packing sheet. Fig. 6e illustrates the effect of the window dimensions on dry pressure drop. The window height, q, only has little effect, while shortening the window width, m, remarkably reduces the pressure drop. It indicates that slender 12

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windows can reduce the flow resistance because of the smaller solid area vertical to the gas flow direction.

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3.3 Optimization The windows of Winpak may play a great role in dry pressure drop. Fig. 7

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confirms that gas flow has to overcome the much greater resistance when flowing

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through windows. It inspires us to optimize the structure of the window to increase the flux capacity. The slender structure of the window (smaller m or larger q) can

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reduce the dry pressure drop. However, an extremely small m will result in the

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reduction of area for liquid to flow through. Also, an extremely large q may reduce the number of windows on the whole packing, which will reduce the probability of

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liquid flowing to the opposite side. These two influences are adverse to the liquid

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distribution and may have negative effect on mass transfer efficiency. Therefore, ensuring constant m and q is the latent premise for designing an optimal structure of windows.

The vertical relationship of the two sides of the window (γ=90°), shown in Fig. 1,

just facilitates the manufacture of Winpak. Actually, this cutting angle can be changed easily by adjusting the die without changing the projected lengths of corresponding sides of the window at the original location (m and q). Therefore, two supplemental cutting angles, 120° and 150°, shown in Fig. 8, are chosen to investigate whether larger angle can optimize dry pressure drop. Fig. 9 shows the comparison of dry pressure drops between the optimal and original packing. It is clear that the optimal 13

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packing with larger angle, 150°, can significantly reduce dry pressure drop by up to 40%. Fig. 10 makes a clear explanation that increasing the cutting angle can lead to the significant reduction of the resistance of windows. It is because the optimal

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window decreases the solid area which is vertical to the gas flow direction. In addition to the lower pressure drop, the optimal structure is unlikely to have considerable

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negative impact on the liquid distribution and mass transfer efficiency. Therefore,

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increasing the cutting angle, γ, is a feasible optimization strategy for reducing dry

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3.4 The Determination of prediction model

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pressure drop.

According to Petre et al. (2003), a non-Ergun-like correlation could be better used

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to describe the pressure loss coefficient of structured packings. So, a non-Ergun-like

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correlation validated by Said et al. (2011) and Amstrong et al. (2013) is chosen to describe the coefficient for frictional component. n

C2  3  C1 ξgg =  n1 + n2  Re   Re

(13)

where the parameters, C1 and C2, incorporate correlative factors of pressure drop. Said et al. (2011) and Amstrong et al. (2013) proposed correlations for these parameters given as Eqs. 14-15 and Eqs. 16-17, respectively. C1 = Γ1 cos (α )

Γ2

(14)

C2 = θ1 cos (α ) 2 + θ 3 cos (α ) 4

(15)

C1 = Γ1h Γ2 b Γ3 cos (α )

(16)

θ

θ

Γ4

14

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C2 = θ1hθ 2 bθ3 cos (α ) 4 + θ5 hθ6 bθ7 cos (α ) 8 θ

θ

(17)

In these correlations, the effects of the channel base b, the channel height h and the inclination angle α are considered. But the effect of windows is not considered.

Γ

C2 = θ1hθ 2 bθ3 cos (α ) 4 mθ5 qθ6 sin ( β ) 7 θ

θ

Γ8

(18)

(19)

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C1 = Γ1h Γ2 b Γ3 cos (α ) 4 +Γ 5 h Γ6 b Γ7 cos (α )

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Therefore, new correlations are proposed to describe all effects of packing geometries.

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For all packings studied in this work, including the original and the optimized packings, over 100 cases with different operation conditions and packing geometries

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were simulated. The genetic algorithm was executed to get new coefficients fitting

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correlations 13, 18, and 19. Fitting parameters are listed in Tab. 6. The parity plot in Fig. 11 indicates that the predicted frictional pressure drops are highly consistent with

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simulated data. The majority of the prediction lies within 10% of the simulated data.

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The total dry pressure drop across an entire column could be predicted by adding

up the two components. The experimental data published in previous work (Li et al. 2012; Li and Liu, 2011) and some supplemental measured values of packings with different dimensions are used to validate the model. The column is the same as the one used by Li et al. (2012). It is set with a diameter of 0.4 m, a total packing height of 1.2 m and a packing element height of 0.2 m. Fig.12 shows a good agreement between predicted values and the experimental data. The average relative error between predicted values and experimental data is 6.9%. Therefore, the validity of the prediction model is finally confirmed.

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4. Conclusion In this work, three-dimensional CFD calculations are conducted to predicting dry pressure drop within Winpak. The conclusions of this study can be drawn as follows:

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(1) A new hexahedral periodic structure, regarded as the REU of Winpak, is established to describe the mechanism of the frictional dry pressure loss.

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(2) The smaller inclination angle or the smaller opening angle can decrease dry

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pressure drop, which is consistent with the mainstream views.

(3) The windows on the crests and troughs of packing sheets have considerable

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impacts on dry pressure drop. In view of this, an optimized cutting angle of

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windows is designed to be 150°, leading to dry pressure drop reducing by up to 40% without sacrificing the advantages of windows.

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(4) A set of correlations, considering all aspects of packing dimensions, are

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proposed to predict the pressure drop of entire column and validated by experimental data. An average relative error of 6.9% proves the availability of the comprehensive predicting model.

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Acknowledgments The authors acknowledge the National Basic Research Program of China (973 Program No. 2012CB720500), the National High Technology Research and

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Development Program of China (863 Program No. 2015BAC04B01) and China Postdoctoral Science Foundation Funded Project (No. 2016M601263) for financial

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support.

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[Pa] [m] [m] [m/s] [m s-1] [m s-1] [m s-1]

→

v

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cr

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Greek letters α [°] β [°] γ [°] Γi δ [mm] ∆P [Pa] ∆PREU [Pa] ε µ [Pa s] ζdc ζf θi ξgg [m-1] ξbulk

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[m] [m]

packed bed height packing element height unit tensor REU height window width constant pressure window height Reynolds number packing side length gas interstitial velocity liquid superficial velocity gas superficial velocity Parameter =µeff/µ  velocity vector in mass conservation equation

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[m] [m]

F factor=

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hpb hpe I l m ni P q ReGint s uint uLs uspf v̂

channel base parameter ≈100 constant column diameter

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Nomenclature Symbols b [m] Cv Ci dc [m] F [Pa0.5]

ξwall ρg τ̿ Ψ

[kg m-3] [N m-2]

inclination angle opening angle cutting angle constant packing thickness total pressure drop pressure drop of REU packing porosity gas viscosity loss coefficient due to drag component loss coefficient due to frictional component constant pressure drop coefficient due to gas-gas interactions loss coefficient due to gas direction change between packing layers loss coefficient due to the wall regions gas density stress tensor wall correction factor 18

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References

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(1) Spiegel, L., Meier, W., 2003. Distillation columns with structured packings in the next decade. Chem. Eng. Res. Des. 81(1), 39-47. (2) Fernandes, J., Simões, P. C., Mota, J. P., Saatdjian, E., 2008. Application of CFD in the study of supercritical fluid extraction with structured packing: dry pressure drop calculations. J. Supercrit. Fluid. 47(1), 17-24. (3) Sebastia-Saez, D., Gu, S., Ranganathan, P., Papadikis, K., 2013. 3D modeling of hydrodynamics and physical mass transfer characteristics of liquid film flows in structured packing elements. Int. J. Greenh. Gas Con. 19, 492-502. (4) Sebastia-Saez, D., Gu, S., Ranganathan, P,; Papadikis, K., 2015. Micro-scale CFD modeling of reactive mass transfer in falling liquid films within structured packing materials. Int. J. Greenh. Gas Con. 33, 40-50. (5) Sebastia-Saez, D., Gu, S., Ranganathan, P., Papadikis, K., 2014. Micro-scale CFD study about the influence of operative parameters on physical mass transfer within structured packing elements. Int. J. Greenh. Gas Con. 28, 180-188. (6) Sebastia-Saez, D., Gu, S., Ranganathan, P., Papadikis, K., 2015. Meso-scale CFD study of the pressure drop, liquid hold-up, interfacial area and mass transfer in structured packing materials. Int. J. Greenh. Gas Con. 42, 388-399. (7) Olujić, Ž., Kamerbeek, A. B., De Graauw, J., 1999. A corrugation geometry based model for efficiency of structured distillation packing. Chem. Eng. Process. 38(4), 683-695. (8) Shilkin, A., Kenig, E. Y., 2005. A new approach to fluid separation modelling in the columns equipped with structured packings. Chem. Eng. J. 110(1), 87-100. (9) Shilkin, A., Kenig, E. Y., Olujić, Ž., 2006. Hydrodynamic‐ analogy‐ based model for efficiency of structured packing columns. AIChE J. 52(9), 3055-3066. (10) Wolf, T. S., Bradtmöller, C., Scholl, S., Kenig, E. Y., 2014. Hydrodynamic-Analogy-Based Modeling Approach for Distillative Separation of Organic Systems with Elevated Viscosity. Chem. Eng. Tech. 37(12), 2065-2072. (11) Billet, R., Schultes, M., 1991. Modelling of pressure drop in packed columns. Chem. Eng. Technol. 14(2), 89-95. (12) Billet, R., Schultes, M., 1993. Predicting mass transfer in packed columns. Chem. Eng. Technol. 16(1), 1-9. (13) Billet, R., Schultes, M., 1999. Prediction of mass transfer columns with dumped and arranged packings: updated summary of the calculation method of Billet and Schultes. Chem. Eng. Res. Des. 77(6), 498-504. (14) Rocha, J. A., Bravo, J. L., Fair, J. R., 1993. Distillation columns containing structured packings: a comprehensive model for their performance. 1. Hydraulic models. Ind. Eng. Chem. Res. 32(4), 641-651. (15) Rocha, J. A., Bravo, J. L., Fair, J. R., 1996. Distillation columns containing structured packings: a comprehensive model for their performance. 2. Mass-transfer model. Ind. Eng. Chem. Res. 35(5), 1660-1667. (16) Olujić, Ž., 1997. Development of a complete simulation model for predicting the hydraulic and separation performance of distillation columns equipped with structured 19

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cr

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packings. Chem. Biochem. Eng. Q. 11(1), 31-46. (17) Iliuta, I., Petre, C. F., Larachi, F., 2004. Hydrodynamic continuum model for two-phase flow structured-packing-containing columns. Chem. Eng. Sci. 59(4), 879-888. (18) Tsai, R. E., Seibert, A. F., Eldridge, R. B., Rochelle, G. T., 2011. A dimensionless model for predicting the mass‐transfer area of structured packing. AIChE J. 57(5), 1173-1184. (19) Fair, J. R., Seibert, A. F., Behrens, M., Saraber, P. P., Olujić, Ž., 2000. Structured packing performance experimental evaluation of two predictive models. Ind. Eng. Chem. Res. 39(6), 1788-1796. (20) Woerlee, G. F., Berends, J., Olujić, Ž., de Graauw, J., 2001. A comprehensive model for the pressure drop in vertical pipes and packed columns. Chem. Eng. J. 84(3), 367-379. (21) Robbins, L. A., 1991. Improve pressure-drop prediction with a new correlation. Chem. Eng. Prog. 87(5), 87-90. (22) Ding, H. D., Xiang, W. Y., Song, N., Liu, C. J., Yuan, X. G., 2014. Hydrodynamic behavior and residence time distribution of industrial-scale bale packings. Chem. Eng. Technol. 37(7), 1127-1136. (23) Han, M., Lin, H., Yuan, Y., Wang, D., Jin, Y., 2003. Pressure drop for two phase counter-current flow in a packed column with a novel internal. Chem. Eng. J. 94(3), 179-187. (24) Spiegel, L., Meier, W. A., 1992. Generalized pressure drop model for structured packings. Inst. Chem. Eng. Synp. Ser. 128, B85-B94. (25) Said, W., Nemer, M., Clodic, D., 2011. Modeling of dry pressure drop for fully developed gas flow in structured packing using CFD simulations. Chem. Eng. Sci. 66(10), 2107-2117. (26) Brunazzin, E., Paglianti, A., 1997. Mechanistic pressure drop model for columns containing structured packings. AIChE J. 43(2), 317-327. (27) Olujić, Ž., 1999. Effect of column diameter on pressure drop of a corrugated sheet structured packing. Chem. Eng. Res. Des. 77(6), 505-510. (28) Kenig, E. Y., 2008. Complementary modelling of fluid separation processes. Chem. Eng. Res. Des. 86(9), 1059-1072. (29) Raynal, L., Royon-Lebeaud, A., 2007. A multi-scale approach for CFD calculations of gas–liquid flow within large size column equipped with structured packing. Chem. Eng. Sci. 62(24), 7196-7204. (30) Sun, B., He, L., Liu, B. T., Gu, F., Liu, C. J., 2013. A new multi‐scale model based on CFD and macroscopic calculation for corrugated structured packing column. AIChE J. 59(8), 3119-3130. (31) Quan, X. Y., Geng, Y., Yuan, P. F., Huang, Z., Liu, C. J., 2015. Experiment and simulation of the shrinkage of falling film upon direct contact with vapor. Chem. Eng. Sci. 135, 52-60. (32) Gu, F., Liu, C. J., Yuan, X. G., Yu, G. C., 2004. CFD simulation of liquid film flow on inclined plates. Chem. Eng. Technol. 27(10), 1099-1104. (33) Qi, R., Lu, L., Yang, H., Qin, F., 2013. Investigation on wetted area and film 20

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thickness for falling film liquid desiccant regeneration system. Appl. Energ. 112, 93-101. (34) Haroun, Y., Legendre, D., Raynal, L., 2010. Volume of fluid method for interfacial reactive mass transfer: Application to stable liquid film. Chem. Eng. Sci. 65(10), 2896-2909. (35) Haroun, Y., Legendre, D., Raynal, L., 2010. Direct numerical simulation of reactive absorption in gas–liquid flow on structured packing using interface capturing method. Chem. Eng. Sci. 65(1), 351-356. (36) Haroun, Y., Raynal, L., Legendre, D., 2012. Mass transfer and liquid hold-up determination in structured packing by CFD. Chem. Eng. Sci. 75, 342-348. (37) Zhu, M., Liu, C. J., Zhang, W. W., Yuan, X. G., 2010. Transport phenomena of falling liquid film flow on a plate with rectangular holes. Ind. Eng. Chem. Res. 49(22), 11724-11731. (38) Hoffmann, A., Ausner, I., Repke, J. U., Wozny, G., 2005. Fluid dynamics in multiphase distillation processes in packed towers. Comput. Chem. Eng. 29(6), 1433-1437. (39) Hoffmann, A., Ausner, I., Wozny, G., 2006. Detailed investigation of multiphase (gas–liquid and gas–liquid–liquid) flow behaviour on inclined plates. Chem. Eng. Res. Des. 84(2), 147-154. (40) Ganguli, A. A., Kenig, E. Y., 2011 A CFD-based approach to the interfacial mass transfer at free gas–liquid interfaces. Chem. Eng. Sci. 66(14), 3301-3308. (41) Kenig, E. Y., Ganguli, A. A., Atmakidis, T., Chasanis, P., 2011. A novel method to capture mass transfer phenomena at free fluid–fluid interfaces. Chem. Eng. Process. 50(1), 68-76. (42) Petre, C. F., Larachi, F., Iliuta, I., Grandjean, B., 2003. Pressure drop through structured packings: Breakdown into the contributing mechanisms by CFD modeling. Chem. Eng. Sci. 58(1), 163-177. (43) Larachi, F., Petre, C. F., Iliuta, I., Grandjean, B., 2003. Tailoring the pressure drop of structured packings through CFD simulations. Chem. Eng. Process. 42(7), 535-541. (44) Armstrong, L. M., Gu, S., Luo, K. H., 2013. Dry pressure drop prediction within Montz-pak B1-250.45 packing with varied inclination angles and geometries. Ind. Eng. Chem. Res. 52(11), 4372-4378. (45) Owens, S. A., Perkins, M. R., Eldridge, R. B., Schulz, K. W., Ketcham, R. A., 2013. Computational fluid dynamics simulation of structured packing. Ind. Eng. Chem. Res. 52(5), 2032-2045. (46) Ding, H. D., Li, J. M., Xiang, W. Y., Liu, C. J., 2015. CFD simulation and optimization of Winpak-based modular catalytic structured packing. Ind. Eng. Chem. Res. 54(8), 2391-2403. (47) V Van Baten, J. M., Krishna, R., 2002. Gas and liquid phase mass transfer within KATAPAK-S® structures studied using CFD simulations. Chem. Eng. Sci. 57(9), 1531-1536. (48) Haghshenas Fard, M., Zivdar, M., Rahimi, R., Nasr Esfahani, M., Afacan, A., Nandakumar, K., Chuang, K. T., 2007. CFD simulation of mass transfer efficiency 21

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and pressure drop in a structured packed distillation column. Chem. Eng. Technol. 30(7), 854-861. (49) Nikou, M. K., Ehsani, M. R., 2008. Turbulence models application on CFD simulation of hydrodynamics, heat and mass transfer in a structured packing. Int. Commun. Heat Mass, 35(9), 1211-1219. (50) Chen, J. B., Liu, C. J., Yuan, X. G., Yu, G. C., 2009. CFD simulation of flow and mass transfer in structured packing distillation columns. Chinese J. Chem. Eng. 2009, 17(3), 381-388. (51) Shojaee, S., Hosseini, S. H., Razavi, B. S., 2012. Computational fluid dynamics simulation of multiphase flow in structured packings. J. Appl. Math. in press. (52) Hosseini, S. H., Shojaee, S., Ahmadi, G., Zivdar, M., 2012. Computational fluid dynamics studies of dry and wet pressure drops in structured packings. J. Ind. Eng. Chem. 18(4), 1465-1473. (53) Shojaee, S., Hosseini, S. H., Rafati, A., Ahmadi, G., 2011. Prediction of the effective area in structured packings by computational fluid dynamics. Ind. Eng. Chem. Res. 50(18), 10833-10842. (54) Fourati, M., Roig, V., Raynal, L., 2013. Liquid dispersion in packed columns: experiments and numerical modeling. Chem. Eng. Sci. 100, 266-278. (55) Dai, C., Lei, Z., Li, Q., Chen, B., 2012. Pressure drop and mass transfer study in structured catalytic packings. Sep. Purif. Technol. 98, 78-87. (56) Rafati Saleh, A., Hosseini, S. H., Shojaee, S., Ahmadi, G., 2011. CFD studies of pressure drop and increasing capacity in MellapakPlus 752. Y structured packing. Chem. Eng. Technol. 34(9), 1402-1412. (57) Raynal, L., Boyer, C., Ballaguet, J. P., 2004. Liquid holdup and pressure drop determination in structured packing with CFD simulations. Can. J. Chem. Eng. 82(5), 871-879. (58) Lautenschleger, A., Olenberg, A., Kenig, E. Y., 2015. A systematic CFD-based method to investigate and optimise novel structured packings. Chem. Eng. Sci. 122, 452-464. (59) Liu, C., Ding, H., Guo, K., Zhang, T., Yuan, X., He, L., 2014. Ultra-low pressure drop packing sheet with flow-guiding cut-out windows and structured packing. EP2708281. (60) Sun, B., Zhu, M., Liu, B. T., Liu, C. J., Yuan, X. G., 2013. Investigation of falling liquid film flow on novel structured packing. Ind. Eng. Chem. Res. 52(13), 4950-4956. (61) Li, X., Liu, C. J., Yuan, X. G., 2012. Hydrodynamics and mass transfer behavior of a novel structured packing with diversion windows. Adv. Mater. Res. 391-392, 1459-1463. (62) Li, X., Liu, C. J., 2011. Hydrodynamics behavior of structured packing with diversion windows. Chem. Ind. Eng. Prog. 30, 298-302. (63) Xiang, W. Y., Li, J. M., Ding, H. D., Liu, C. J., 2016. Experimental investigation of liquid axial and radial dispersion in Winpak modular catalytic structured packing. Ind. Eng. Chem. Res. 55(6), 1768-1777. (64) Batchelor, G. K., 2000. An introduction to fluid dynamics; Cambridge university 22

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press.

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Figures

Figure 1 The geometry of Winpak

24

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Figure 2 Contributions of the dry pressure drop within Winpak

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Figure 3 The representative elementary unit with periodic boundaries

26

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Figure 4 The comparison between experimental pressure drops and simulated values with different

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mesh sizes over a range of F factors.

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Figure 5 Typical gas flow pattern within Winpak

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Figure 6 Dry pressure drops for different geometries (a) for varied inclination angles, various opening angles with channel heights (b) 6 mm; (c) 9 mm; (d) 12 mm, and (e) for diverse window dimensions

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Figure 7 Dry pressure drops at different REU heights in various operating conditions

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ip t

cr

Figure 8 Geometries of Winpak with various cutting angles of the windows (a) γ=90°, (b) γ=120°,

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(c) γ= 150°

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Figure 9 Comparison of dry pressure drops between original and optimal structures

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structures

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Figure 10 Comparison of pressure drops at different REU heights between original and optimal

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Figure 11 Parity plot of predicted pressure drops vs. the simulated data

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Figure 12 Parity plot of predicted pressure drops vs. experimental data

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Tables Table 1 Dimensions of 500X-type Winpak

2b

α

δ

β

m

q

γ

ε

12mm

10mm

60°

0.2mm

79.61°

4mm

8mm

90°

0.95

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cr

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2h

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Table 2 Dimensions of packings with varied inclination angles

2h/mm

2b/mm

β/°

m/mm

q/mm

l/mm

30

12

10

79.61

4

8

25.4

40

12

10

79.61

4

8

32.54

50

12

10

79.61

4

8

38.7

60

12

10

79.61

4

8

ip t

α/°

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d

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cr

43.7

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Table 3 Dimensions of packings for varied opening angles and channel heights

2h/mm

2b/mm

α/°

m/mm

q/mm

l/mm

60

12

6.928

60

4

8

17.7

60

18

10.392

60

5

10

26.4

60

24

13.86

60

8.75

15

35.0

79.61

12

10

60

4

8

79.61

18

15

60

5

10

79.61

24

20

60

8.75

90

12

12

60

4

90

18

18

60

90

24

24

60

120

12

20.78

60

120

18

31.18

60

120

24

41.57

cr

37.9

50.4

8

30.4

us

15

5

10

45.4

8.75

15

60.4

4

8

52.4

5

10

78.3

8.75

15

104.3

an

M

25.4

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d

60

ip t

β/°

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Table 4 Dimensions of packings for varied window structures

q/mm

2h/mm

2b/mm

α/°

β/°

l/mm

4

8

12

10

60

79.61

25.4

2

8

12

10

60

79.61

25.4

4

5

12

10

60

79.61

25.4

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cr

ip t

m/mm

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Table 5 Details of CFD settings

Translational periodic boundary condition

Turbulence model

RNG k-ε

Pressure-velocity coupling

SIMPLEC

Pressure

Second order

ip t

Boundary conditions

Momentum, Turbulent kinetic energy，

Second-order upwind discretization

cr

Turbulent dissipation rate 10-6

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Residuals for convergence

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Table 6 Coefficients best fitting equations 13, 18, and 19 for predicting the dry pressure drop

Γi

θi

ni

1

0.106

516.593

2.170

2

-14.232

0.980

9.259

3

-10.683

-24.554

0.048

4

55.084

-83.722

5

84.794

15.468

6

42.713

-10.260

7

-30.596

15.121

8

-193.561

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i

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Highlights:

2. A new REU for Winpak was proposed to simulate the dry pressure drop.

cr

3. The windows of Winpak were optimized to reduce the dry pressure drop.

ip t

1. Mechanism of the dry pressure drop within a novel structured packing was studied.

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4. Correlations considering all factors were built to predict the dry pressure drop.

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