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Mixing indices allow scale-up of stirred tank slurry reactor conditions for equivalent homogeneity
Journal Pre-proof Mixing Indices Allow Scale-up of Stirred Tank Slurry Reactor Conditions for Equivalent Homogeneity S.T.L. Harrison, A. Kotsiopoulos, R. Stevenson, J.J. Cilliers
PII:
S0263-8762(19)30552-0
DOI:
https://doi.org/10.1016/j.cherd.2019.10.049
Reference:
CHERD 3909
To appear in:
Chemical Engineering Research and Design
Received Date:
21 July 2018
Revised Date:
13 September 2019
Accepted Date:
31 October 2019
Please cite this article as: Harrison STL, Kotsiopoulos A, Stevenson R, Cilliers JJ, Mixing Indices Allow Scale-up of Stirred Tank Slurry Reactor Conditions for Equivalent Homogeneity, Chemical Engineering Research and Design (2019), doi: https://doi.org/10.1016/j.cherd.2019.10.049
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Mixing Indices Allow Scale-up of Stirred Tank Slurry Reactor Conditions for Equivalent Homogeneity STL Harrisona*, A Kotsiopoulosa, R Stevensona, and JJ Cilliersb a
Centre for Bioprocess Engineering Research, Department of Chemical Engineering, University of Cape Town, Rondebosch 7701, South Africa b Royal School of Mines, Department of Earth Sciences and Engineering, Imperial College London, SW7 2AZ, U.K. *Corresponding Author: Fax: +27 21 650 5501, e-mail: [email protected]
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Highlights Mixing indices may be used to reduce energy needed to achieve slurry homogeneity Suspension quality most consistent in smaller vessels than in larger vessels Higher P/V ratios are achieved in smaller vessels with similar impeller tip speeds Inconsistencies in mixing attributed to limited mixing in the axial direction Less homogeneous suspension at low solids loading than at high loadings Abstract
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The influence of reactor scale, impeller tip speed and specific power on the overall homogeneity (multi-phasic mixing) of two dimensionally similar stirred tanks of 50 mm and 220 mm internal diameter (ID) are compared using data collected from electrical resistance tomography for 5 and 15% v/v 600 – 800 μm particle suspensions. The data collected is used to quantify the suspension quality of the system by defining mixing indices in the axial MIz and radial MIr directions as well as the overall mixing index MIo. Analyses across the vessels indicated that axial and radial homogeneity improved with increasing impeller tip speed for both large and small vessels with more consistent suspensions observed in the former. Improved homogeneity was consistently found in the 10 to 20% (v/v) solids loading range (data only shown for 15%) than at 5%, across both reactors. In either vessel, optimum homogeneity was achieved at impeller tip speeds ca. 20% lower than the critical suspension speed, as shown previously. Analysis of the local concentration of particles in the lowest region of the vessels indicated that absolute homogeneity was unattainable as the decreasing local concentration displayed an asymptotic character with increasing power per unit volume. The suspension quality during reactor scale-up was relatively consistent with specific power ratios P/V, while the same degree of homogeneity was not achieved when the impeller tip speed was kept constant.
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Keywords: Electrical resistance tomography (ERT), scale-up, solids suspension, specific power, solids concentration, impeller speed Introduction
Stirred tank reactors are prevalent in many industrial applications where a high degree of solid-fluid contact in the multi-phase reaction systems is necessary for optimum performance (Nienow, 1968; Oldshue, 1983; Shamlou and Koutsakos, 1989). Slurry reactors are typically a mixing system containing a particulate phase suspended in an aqueous solution through which a gaseous phase may be distributed. Understanding the dynamics and dispersion of solid fractions within these systems is important to maximise solid-liquid contact through enhanced solid suspensions, which ultimately
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improve multi-phase production efficiencies (Deveci, 2004; Harrison et al., 2012, 2003; Nemati and Harrison, 2000; Scholtz et al., 1997; Sissing and Harrison, 2003). Through mixing, multi-phase homogeneity is facilitated to affect improved reaction-medium contact time and hence efficiency. Knowledge of the mixing and suspension characteristics in the slurry reactor facilitates improved reactor design and provides important information on the influence of the main operating parameters on the reactor performance.
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Investigations into the distribution of phases in continuously stirred tank reactors, while varying key operating parameters, have previously been performed by applying a range of approaches such as direct sampling methods, magnetic resonance imaging and electrical resistance tomography (Barresi and Baldi, 1987; Bujalski et al., 1999; Carletti et al. 2014; Harrison et al., 2012; Illing and Harrison, 1999; Nasr-El-Din et al., 1996; Ochieng and Lewis, 2006; Shamlou and Koutsakos, 1989; Stevenson et al., 2010). However, investigations into the distribution of solids over the height of slurry reactors is sparse and is often limited to the case of low solids concentration using cloud height mechanisms (Bittorf and Kresta, 2003; Bujalski et al., 1999; Einenkel and Mersmann, 1977; Rieger and Ditl, 1994; Zehner and Tebel, 1984). Electrical resistance tomography (ERT) (McKee et al., 1995; Wilkinson et al., 2005) has been applied successfully to multi-phase environments achieving discrimination of slurries and gaseous slugs in pipelines, bubble columns, flotation cells and stirred tank reactors (Carletti et al., 2016; Fangary et al., 1998; Harrison et al., 2012; Jin et al., 2014; Meng et al., 2015; Paglianti et al.,2017; Sardeshpande et al., 2016; Wang and Cilliers, 1999; Xie et al., 2004). Discrete segregation of these phases using ERT promotes understanding of the mixing environment and the achieved suspension quality of these dynamic phases. Multiple dimensions are achievable allowing improved operational knowledge and control of stirred tank reactors for process optimisation (Harrison et al., 2012).
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Stirred tank reactors are often used in industrial applications where the mixing and the homogeneity of the particle suspension are governed by the operating conditions in the multi-phase system. Using geometrically similar reactors in the scale-up procedure is insufficient when attempting to replicate mixing characteristics observed in small-scale experiments. The dominant factors influencing particle homogeneity and liquid mixing in stirred tank slurry reactors are particle size and density, impeller design, impeller speed and tank geometry (Carletti et al., 2016; Fangary et al., 1998; Harrison et al., 2012; Paglianti et al., 2017). Increasing particle concentration increases the required impeller speed for complete suspension, thereby decreasing absolute homogeneity. The introduction of a gaseous phase decreases the power transferred from the impeller, thereby leading to a decrease in particle suspension and hence system homogeneity (Breucker et al., 1988; Frijlink et al., 1990; Rewatkar et al., 1991). Rates of mixing and reaction are interrelated, as turbulent motion in the vessel is often responsible for the dispersion of reactants in the vessel. Insufficient mixing and hence solid-liquid contact time, in the case of slurry reactors, may result in reduced reaction rates with poor product distribution and mass transfer limitations (Hill, 1976). The migration of a process from laboratory to pilot or industrial scale is therefore challenging (Li et al., 2005; Perry and Green, 2008). While it is necessary to have a framework for reactor scale-up on moving from the proof of concept phase to implementation, criteria for scale-down are equally important. These allow a relevant representation of the large-scale reactor to be made for fundamental studies to be performed at bench-scale. The key parameters affecting reactor scaling can also be determined. Scale-down studies are also increasingly of importance for
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rapid product development as they facilitate many miniaturised replicate experimental systems in the research phase (Betts et al., 2006; Buurman et al., 1986).
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As large-scale optimisation experiments can be expensive and time consuming, scale down systems are needed. Bench-scale studies to obtain reliable kinetics and effective conditions for maximum reactor performance are used to model commercial scale capacities. In this study, recent advancements in ERT detection technologies are applied and evaluated in a stirred tank environment to examine the influence of reactor scale on system homogeneity. Using a grid structure with an annular design, radial and axial concentration gradients are defined. Homogeneity is quantified in terms of radial, axial and overall mixing indices, as defined by Harrison et al. (2012) and compared as a function of solids loading across two reactor scales. This study provides insight into the critical operating parameters governing suspension in geometrically similar vessels during reactor scale-up or scale-down. Further, requirements for maximum homogeneity are considered.
Materials and methods The 50 mm ID and 220 mm ID stirred tank reactors
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Two geometrically similar (tank diameter T = working volume height H; T=H), flat bottom, Perspex stirred tank reactors were utilised for the homogeneity studies in slurry vessels. Stirred tank reactors with T = 220 mm and T = 50 mm internal diameters (ID) were fitted with four layers of 16 evenly spaced electrodes along the perimeter of the tanks (Harrison et al., 2012; Stevenson et al., 2010).
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Both reactors were agitated using six-bladed Rushton turbines (blade length = 0.26D; blade height = 0.21D; disk diameter = 0.67D) with dimensionally similar tank to impeller diameter ratios and clearance (D = T/2; C = T/3). Four baffles were present (B = 0.1T). Stainless steel components of the impeller were insulated with black enamel paint and Loctite®, a rubberized paint, to ensure nonconductivity of metallic surfaces. This ensured that the metallic surfaces would contribute similarly to the conductivity distribution as the non-conducting Perspex tank walls and baffles. Solid and liquid phase
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The 600 – 850 μm sieved size fraction of quartzite particles used in the conductivity trials was characterised by a volumetric mean diameter of 857 µm and a mode of 754 µm with a d50 of 790 µm. These particulates were washed with nitric acid in a stirred tank reactor over two weeks to bleach and remove any fines and metal content. The solid particles were subsequently calcined at 550oC for 20 hours after additional washing to remove any traces of acid. Particle size fractions of 5, 10, 15 and 20% v/v were suspended in 0.1 g.L-1 NaCl solution at room temperature (20oC) for ERT analysis. The addition of NaCl electrolyte ensured that adequate image reconstruction could be achieved (Fangary et al., 1998). The ERT measurement system The ERT system, operating at 3 kHz, employed a current-pulse technique developed by Wilkinson et al. (2005) with data acquisition speeds up to 1000 frames per second. A bi-directional current was
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injected across the excitation electrode pairs in the measuring sequence and maintained during positive and negative half cycles. Voltage differences were captured by a multiplexor on the remaining electrode pairs where the signals were buffered and read by an analogue to digital converter. The resulting potential differences between pickup electrode pairs reflected the conductivity in the plane of measurement (Harrison et al., 2012). The bi-directional current utilised by the system minimised electrode polarisation.
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The reconstruction code in this study used a modified Newton-Raphson algorithm over a 712 and 764 element mesh for the 220 mm ID and 50 mm ID tanks, respectively. These meshes have irregular elements and thus 12 radial subdivisions in each 16-electrode plane (L1 – L4) were created to calculate the radial profiles barring the baffle area and impeller zone as illustrated in Harrison et al. (2012). The mesh was constructed with radial symmetry with each plane considered as seven concentric rings (Harrison et al., 2012). This translated to the averaging of conductivity data in radial distances from r/R = 0.55 (50 mm ID) or 0.63 (220 mm ID) to 1.0 from each of the radial subdivisions within the specific electrode plane. The averaged data were converted to radial concentration profiles using the Maxwell equation (Eq. 1), which relates the difference in the measured conductivity and the conductivity of the liquid phase to particle concentrations (Fangary et al., 1998; Maxwell, 1873). 𝜎𝑚 − 𝜎𝑝 𝜎𝑚 − 𝜎 =𝑓 (1) 2𝜎𝑚 + 𝜎 2𝜎𝑚 + 𝜎𝑝
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where σ is the conductivity of the clear liquid medium or particles denoted by the subscripts m and p, respectively, while f is the volume fraction of particles in the vessel. In the quartzite tests, σp was assumed to be zero.
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Data averaged over the radial distance for each electrode layer were used to determine the axial concentration profiles of which comprehensive detail is presented in Harrison et al. (2012). Calibration of the ERT detection system, in the absence of the quartzite particles, was performed in the presence of the reactor baffles, impeller and shaft at either 236 rpm or 304 rpm for the 220 mm ID tank, and at 200 rpm for the 50 mm ID tank. One hundred frames (220 mm ID tank) and fifty frames (50 mm ID tank) of data were recorded during calibration and averaged prior to reconstruction. The fifty frames in the smaller vessel were found to be consistent with data presented by the 100 frame system and was therefore considered suitable in subsequent measurements.
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At the high impeller tip speeds examined, the liquid surface level in the 50 mm tank fluctuated intermittently near the uppermost electrode layer L4 due to fluid turbulence and surface aeration. Further contributing to the varying surface, the small height differential between the liquid surface and layer L4 led to greater measurement error at high speeds resulting in decreased resistance in L4. Only the last two data points of the uppermost layer L4 near the vessel wall were therefore selected as representative. Consequently, conductivity data in the stirred tank reactors were extracted at radial distances r/R = 0.55 to 0.96 for the 50 mm ID reactor.
Further analysis of the system Specific power (P/V) was also investigated with the power input for the Rushton turbines extracted from the graphical relationship between power number Np and Reynolds number NRe (Perry and
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Green, 2008) and reproduced using correlations developed by Nagata (1975). For each of the solid concentrations considered the power number was determined using slurry densities as a function of both the solid and liquid densities. Over the considered range, high Reynolds numbers are achieved with power numbers for the Rushton turbine remaining similar across the investigated impeller speeds and thus approximated at Np = 5. The critical suspension velocity Njs was calculated according to Zwietering's correlation of 1958 (van der Westhuizen and Deglon, 2008): 𝑁𝑗𝑠 = 𝑆𝑑𝑝0.20 𝐵0.13 𝜈 0.10 𝑔0.45 (
𝜌𝑠 − 𝜌𝐿 0.45 −0.85 ) 𝐷 𝜌𝐿
(2)
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where dp is the particle diameter [μm], B the solid-liquid mass ratio [ms.mL-1], ν the kinematic viscosity [m2.s-1], g the gravitational acceleration [m.s-2], and ρs and ρL [kg.m-3] the density of the solid and liquid fractions. D [m] is the impeller diameter and S is a function of the relative ratio (D/T); the ratio (C/T) of the impeller clearance C [m] to the reactor diameter and the impeller type. The S parameter used to in these calculations were set at 4 in accordance with findings by Armenante and Nagamine (1998) for an equivalent 6-bladed Rushton turbine.
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Results and Discussion
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In the presence of solids, a maximum in the NP-NRe curve is generally observed at the critical suspension velocity Njs (Bohnet and Niesmak, 1980). Njs is presented in Table 1 as a function of solids loading demonstrating that the power per unit volume P/V required to achieve complete suspension should increase for all impeller speeds tested in the 50 and 220 mm ID tank with increasing of presence of solids.
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Experiments were conducted in the 220 mm ID reactor using impeller tip speeds ranging from 1.36 to 2.65 m.s-1. (equivalent impeller speeds 236 – 480 rpm, respectively) For comparative studies in the 50 mm ID tank, relatively slow impeller tip speeds were initially investigated. Preliminary experiments were conducted at 0.63 m.s-1 at an equivalent impeller speed of 480 rpm with 5% v/v quartzite particles to determine whether satisfactory suspensions and turbulent conditions similar to those achieved in the larger vessel could be attained (Figure 1).
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Minimal suspension occurred with particles remaining unsuspended in the reactor. As turbulent conditions defined by Reynolds numbers similar to those achieved in the 220 mm ID tank could not be replicated in the 50 mm ID tank owing to the extreme agitation speeds required, comparative experiments were based on impeller tip speed. As such, stirring speeds between 1038 and 2024 rpm were maintained in the 50 mm ID stirred reactor with Reynolds numbers and power input per unit volume for each of these vessels presented in Table 2. Interestingly, the solid fraction in the L4 plane exceeded the upper planes (L2 and L3) toward the tank wall. This irregularity was likely due to selfaeration causing the entrainment of air bubbles through the liquid phase resulting in higher solid concentrations being detected. This was phenomenon was particularly evident in the 50 mm ID vessel and further noted in subsequent tests at higher stirring speeds.
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Particle suspensions at impeller tip speeds presented in Table 2 and corresponding to a study previously conducted in the 220 mm ID vessel are shown in Figure 2 (d – f) (Harrison et al., 2012). Harrison et al. (2012) previously showed that overall homogeneity of suspended particles in stirred tank reactors (220 mm diameter) was a strong function of the reactor solids loading, particle size and impeller speed. The suspension quality improved with increasing impeller speed and solids concentration while the inverse was noted with increasing particle size. To examine the influence of reactor scale, the suspension of quartzite particles in both the 50 mm and 220 mm ID stirred tanks were compared using ERT. The difference or similarity in particle homogeneity in the dimensionally similar vessels and contrasting hydrodynamic environments in the axial and radial directions, were investigated.
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Radial concentration profiles for 50 mm ID and 220 mm ID stirred tank reactors
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The radial concentration profiles for 5% and 15% v/v of quartzite particles for both reactor configurations are presented in Figures 2 and 3, respectively. Fluctuations in the concentration profiles are observed for each of the vessels with radial and axial position. At equivalent tip speeds and relative axial position in the reactor, greater homogeneity is observed in the 50 mm ID vessel, evidenced by the narrow horizontal variance in the radial profiles in Figure 2 (a – c). Also, the concentration profiles in the smaller vessel across conductivity layers L1 – L4 in Figure 2 (a – c) are more consistent than those in the 220 mm ID tank (Figure 2 d – f), indicating greater axial homogeneity in the former.
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On increasing the volume fraction to 15% v/v, the observed variance in both the radial and axial directions is amplified in the larger tank while greater consistency in the radial concentration profiles is observed with increasing impeller speed in the small vessel (Figure 3). Operating both vessels at either volume fraction, the particle concentration in the 50 mm ID tank increases toward the vessel wall in the lower segment of the vessel (L1 in Figure 2 and Figure 3 a – c) while marginally decreasing or remaining constant in the rest of the layers L2 – L4 on approaching the tank wall. This is in contrast to the decrease in particle concentration towards the wall in the 220 mm ID tank.
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The improved suspension quality in the smaller tank, illustrated by the flatter and more closely spaced lines representing radial and axial homogeneity respectively, is attributed to the specific power P/V. Higher P/V ratios in the 50 mm ID tank provide more regular suspensions compared to the 220 mm ID tank, which is further highlighted by the enhanced homogeneity in the smaller vessel when the volume fraction is increased from 5% to 15% v/v (Figure 2 and Figure 3). In Figure 2 and Figure 3, it is clear that the radial and axial profiles are more consistent in the 50 mm ID tank than in the 220 mm ID vessel. In the subsequent sections, the suspension quality of the tanks is rated according to mixing indices in both the vertical and horizontal planes as a means to establish the basis for the improved homogeneity in the smaller vessel. The influence of the impeller tip speed and specific power P/V on the uniformity of the suspension within the reactors are therefore investigated.
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Axial and radial homogeneity
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Various methods have been proposed to describe the mixing in slurry vessels quantitatively using ERT (Fangary et al., 1998; Hosseini et al., 2010; Mann et al., 2001; McKee et al., 1995; Stevenson et al., 2006; Williams et al., 1996). However, these approaches only quantify homogeneity in the axial direction and not mixing quality in the radial direction (Hosseini et al., 2010; Williams et al., 1996). The quantitative description of radial homogeneity requires a suitable computational grid that reflects the reactor geometry, specifically an annular grid in preference to a regular square grid. In our previous study, mixing indices were developed that quantify the uniformity of particle concentration; radially, axially and overall (Harrison et al., 2012). The overall mixing index MI was quantified by calculating the normalised standard deviation of the particle volume fraction in each of the annuli across the conductivity planes (Harrison et al., 2012). Similarly, the axial MIz and radial MIr mixing indices were determined. Data validation was achieved through correlation of the volume fraction of particulates across all regions of the reactor (derived from the conductivity data), and the experimental volume fraction.
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In Figure 2 and Figure 3, both axial and radial variance in quartzite volume fractions in each of the vessels is shown. The axial mixing index MIz is defined as the normalised, average standard deviation of volume fraction across the seven annuli, weighted by annulus area. The radial mixing index MIr is calculated from the normalised, average standard deviation in each of the four planes. The change in the axial MIz and radial MIr mixing indices, and hence the mixing performance, with impeller tip speed for 5% and 15% v/v fractions of 600 – 800 μm quartzite particles for either vessel configuration are presented in Figure 4. Low mixing indices in these figures indicate high homogeneity while high mixing indices represent low homogeneity.
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In agreement with Figure 3, the axial MIz and radial MIr mixing indices in Figure 4 indicate that the smaller vessel has greater axial (Figure 4 a-b) and radial (Figure 4 c-d) homogeneity than the larger tank at the equivalent tip speed. Homogeneity improves in both reactors with increasing solid fractions. Similar axial mixing indices MIz are achieved at higher impeller tip speeds (Figure 4). The most notable difference in homogeneity between the two vessels is in the axial plane (Figure 4 a-b). The axial homogeneity of the smaller and larger vessels increases with increasing tip speed. However, at low solid concentration in the 50 mm ID vessel at high impeller tip speeds there was a departure in this trend. This was likely due to the entrainment of air through the vessel at high impeller speed decreasing the electrical resistance in the lower layers (L4) leading to poor axial mixing. Inhomogeneity across the vessel is mainly attributed to inefficient axial mixing, possibly due to the increased wall resistance at high particle concentrations (at ca. r/R ≥ 0.77 in Figure 3a–c for the smaller tank). At low volume fractions poor mixing in the axial plane is attributed to the solids accumulating around the impeller (radial distance r/R < 0.7 Figure 2). However, in the 220 mm tank, the axial and radial mixing indices are similar for 15% v/v solids. In general, homogeneity improves at higher impeller tip speeds (Figure 4). It is important to note that, in both vessels, the highest homogeneity is achieved at impeller tip speeds below the critical suspension speeds Njs at high solids concentrations. (see Table 1 and Figure 4). No further improvement in either the axial or radial homogeneity is achieved by increasing the impeller speeds above ca. 80% of the critical suspension speed. This is consistent with the prior findings of
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Harrison et al. (2012).
Overall system homogeneity
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The overall mixing index is presented in Figure 5 as a function of specific power P/V (Figure 5a), impeller tip speed (Figure 5b) and the ratio of the impeller tip speed to the Zwietering critical suspension speed N/Njs (Figure 5c). It is clear from Figure 5 that the homogeneity in both tanks is improved with increasing specific power P/V, impeller tip speed and N/Njs, noted by the decreasing trend of the overall mixing index MIo over the entire range (excepting at 5% solids loading in the 50 mm ID reactor). The suspension quality in the 220 mm ID tank improved when the particle concentration was increased from 5% to 15% v/v. This result was due to, as seen in Figure 2 and Figure 3 (d–f), the increased presence of particles in the upper regions L4 of the mixing vessel with increasing particle loading. However, when comparing the mixing profiles of the larger vessel to the smaller vessel, the 50 mm ID tank has greater homogeneity for the same P/V ratio and impeller tip speed relative to the larger vessel for the 15% v/v fraction but not the 5% v/v fraction (Figure 5). The poor homogeneity observed in both vessels, especially the 50 mm ID tank, containing 5 % v/v solids is due to the large axial variance as seen in Figure 2 between conductivity layers L1 – L4, particularly in the top region of the reactor, L3 and L4, where little to no quartzite particles are observed with increasing impeller speed. In either configuration, the solid fraction accumulates within or below the impeller zone L1 and L2.
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Maintaining the specific power constant during scale-up, the Reynolds number in the larger tank increases by a factor of 7.2 while the rotational speed N in the larger tank decreases to 0.37 of that in the 50 mm ID tank. The peripheral tip speed of the impeller in the larger tank is 1.6 times greater (see Table 3, Figure 6 a). Maintaining the impeller tip speed constant, the Reynolds number and rotational speed increase as with maintaining the specific power constant; however, the increase in the Reynolds number is less pronounced (see Table 3, Figure 6 b). The decreased factor by which the degree of turbulence in the larger reactor changes with respect to the 50 mm ID reactor at constant impeller tip speed can be inferred from the lower overall homogeneity shown in Figure 5. The suspension quality is significantly reduced when the tip speed is kept constant (Figure 5 b) compared to when the P/V ratio is maintained steady (Figure 5 a) when the 50 mm ID tank is scaled-up to 200 mm ID. Therefore, maintaining the same impeller tip speed is not a reliable measure for scaling procedures to obtain the same suspension quality at scale-up or scale-down. However, even though the fluid dynamics differs during scale-up or scale-down, the homogeneity in both vessels is similar at low P/V ratios for the same volume fraction and approach relatively similar homogeneity with increasing specific power with improved suspension quality (Figure 5 a).
According to Buurman et al. (1986), eddy sizes 3 to 5 times greater than the particle size are required to transport a solid particle with diameters between 100 μm and 2 mm. In stirred tanks, impeller dimensions typically govern the size of the largest eddies produced, while the smallest eddy sizes depend on the energy dissipation range. Turbulent flow and hence high Reynolds numbers result from the cascade of energy from large scale to small scale eddies and is responsible for particle lift-off. In both the 50 mm or 220 mm vessels, the Kolmogorov eddy lengths η, calculated as function of the kinematic viscosity ν (m2.s-1) of the slurry and the turbulent power dissipation per mass of liquid ε
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(W.kg-1) in accordance with Eq. 3 (Kolmogorov, 1941), are smaller than the particle size range 600 – 800 μm required to suspend the particles (η50 < 51 μm; η200 < 24 μm over the specified agitation range). 0.25
𝜈3 (3) 𝜂=( ) 𝜀 The fluctuating velocity, a function of the impeller tip speed in either tank is similar. However, the largest eddy sizes are approximately 1.45 times smaller in the 50 mm vessel, which would support the observed similarity in homogeneity in the two vessels with increasing specific power P/V (Figure 5). This would indicate that maintaining the same overall mixing index to achieve the required particle dispersion during scaling procedures is achievable when power per unit volume is kept constant at the desired homogeneity. However, the exceedingly high power input required to maintain the desired homogeneity during scale-up may not always be economically practical (Villadsen et al., 2011).
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Influence of specific power on local particle concentration
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To further investigate the influence of power per unit volume on system homogeneity, the concentration of particles in the lowest electrode layer L1 of the vessel was studied. The objective was to examine the degree of suspension of particles as they migrate to the higher portions of the vessel L2 – L4 with increasing specific power P/V.
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In Figure 7, it is shown that the volume fraction of solids in the lowest layer in the reactor L1 decreases with increasing power per unit volume in both reactor configurations. In either vessel, the volume fraction approaches an asymptotic value at high P/V ratios indicating that complete uniformity of solid particles in the stirred vessels is unattainable but rather an optimal suspension quality is achieved. This decreasing trend is in accordance to studies by Buurman et al. (1986).
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When comparing the 5% v/v solids concentration in both tanks, the volume fraction of solids in the 220 mm ID vessel approaches optimum homogeneity at lower P/V ratios even though the suspension quality across the remaining conductivity layers L2 – L4 is poorer than is achieved at higher solid concentrations (Figures 2, 5 & 7). However, complete homogeneous condition is achieved in the smaller 50 mm ID vessel as the power per unit volume approaches ca. 24 W.L-1 with 5% v/v solids (Figure 7a). The Reynolds number in the larger tank is at least 7.2 times greater than in the smaller vessel at any given P/V ratio (Figure 6), which may aid homogenisation, does not necessarily aid particle lift off (see L1 in Figure 2 d–f). Consequently, optimal but not complete suspension concentration in the 220 mm ID vessel would be obtained at lower P/V ratios than in the 50 mm ID tank (Figure 7). Examining the 15% v/v fraction in both vessels, neither system attains the average solids concentration in the agitation range studied. However, the solids concentration in the 220 mm ID tank consistently approaches optimum uniformity at lower P/V ratios than in the smaller vessel even though it is less homogeneous across the entire vessel at the same specific power.
Conclusions
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The influence of reactor conditions and scale effects on the suspension of quartzite particles in both the 50 mm and 220 mm ID tank was successfully analysed using ERT. Radial and axial profiles were detected using ERT for a 50 mm and 220 mm ID tank. These were converted to radial, axial and overall mixing indices. Using these, the influence of scale, specific power, impeller speed and impeller tip speed on the suspension quality of the system was determined.
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Results indicated that the overall mixing of 5% and 15% v/v quartzite particles in the 50 mm tank was more consistent than the 220 mm tank. The consistency in the smaller vessel, when operating the vessels at the same impeller tip speed, was attributed to the higher power input per unit volume. When operating the vessels at the same P/V ratios or equivalent tip speeds, the smaller vessel was found to be more homogeneous than the larger vessel. This was indicated by low overall mixing indices. Lower and more consistent radial mixing indices compared to axial mixing indices indicated that the overall homogeneity of the system was limited by mixing in the axial direction. This was ascribed to shear resistance near the vessel wall. Both radial and axial homogeneities were more uniform in the smaller vessel with increasing solids concentration denoted by the reduced variance in the horizontal and vertical radial concentration profiles.
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Of particular interest was the finding that a 5% (v/v) solids loading resulted in a less homogeneous suspension than a 15% loading at the same impeller speed across both reactor scales. This was supported in the 220 mm reactor across 10 to 20% solids loading.
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At the lowest conductivity layer L1, the 220 mm ID tank approached optimal suspension concentration at lower P/V ratios than achieved in the 50 mm ID tank. This was due to the increased turbulence in the large tank resulting in the development of larger eddies from the larger impeller compared to the smaller vessel. Absolute homogeneity was unattainable as the decreasing local concentration in the layer L1 approached a limiting concentration with increasing power per unit volume.
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Homogeneity achieved across the two reactor scales and concentrations correlated well with power input per unit volume. Similar minimum overall mixing index, representing similar maximum homogeneity, was attained across the reactors at 15% solids. Similarly, the data correlated well to the ratio of impeller speed to critical impeller speed for suspension (N/Njs). Conversely, poor correlation was found with impeller tip speed.
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In both reactor configurations, optimum homogeneity was achieved at ca. 80% of the critical suspension speeds indicating that further increase in the impeller speed does not further enhance system homogeneity, irrespective of reactor scale. On using P/V as a scale-up criterion, it was demonstrated that, under all conditions explored, no further improvement in suspension homogeneity was achieved on increasing the P/V above 10 W.L-1. This provides a useful estimate of energy required for suspension homogeneity. This study thus guides the selection of operating variables within the stirred tank slurry reactor to optimise tank homogeneity with respect to the suspension of the solid phase, while facilitating improved energy efficiency. Through use of mixing indices, homogeneity may be quantified, assisting rigorous process design. Particularly, through the scale experiments, scale down approaches are
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validated, whereas the consistency of homogeneity of suspension with scale has previously remained poorly quantified. The integration of quantification of suspension homogeneity with reaction rate and extent may now be considered. Acknowledgements
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The authors gratefully acknowledge the funding contribution of the National Research Foundation South African Research Chair Initiative (GUN 64778) funding of the SARChI chair in Bioprocess Engineering and the NRF Postdoctoral Innovation awards (Grant: 85138).
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Carletti, C., Montante, G., De Blasio, C., Paglianti, A., 2016. Liquid mixing dynamics in slurry stirred tanks based on electrical resistance tomography. Chemical Engineering Science 152, 478–487. doi:10.1016/j.ces.2016.06.044 Deveci, H., 2004. Effect of particle size and shape of solids on the viability of acidophilic bacteria during mixing in stirred tank reactors. Hydrometallurgy 71, 385–395. Einenkel, W.D., Mersmann, A., 1977. Erforderliche Drekzaken zum Suspendieren ia Riihrnerben. Verfahrenstechnik 11, 90–94. Fangary, Y., Williams, R., Neil, W., Bond, J., Faulks, I., 1998. Application of electrical resistance tomography to detect deposition in hydraulic conveying systems. Powder technology 95, 61–66.
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Frijlink, J., Bakker, A., Smith, J., 1990. Suspension of solid particles with gassed impellers. Chemical Engineering Science 45, 1703–1718. Harrison, S.T.L., Sissing, A., Raja, S., Pearce, S.J.A., Lamaignere, V., Nemati, M., 2003. Solids loading in the bioleach slurry reactor: mechanisms through which particulate parameters influence slurry bioreactor performance, in: Proceedings of the 15th International Biohydrometallurgy Symposium, Athens, Greece. Harrison, S.T.L., Stevenson, R., Cilliers, J.J., 2012. Assessing solids concentration homogeneity in Rushton-agitated slurry reactors using electrical resistance tomography (ERT). Chemical Engineering Science 71, 392–399. doi:10.1016/j.ces.2011.10.053
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Hill, J.C., 1976. Homogeneous turbulent mixing with chemical reaction. Annual review of fluid Mechanics 8, 135–161. Hosseini, S., Patel, D., Ein-Mozaffari, F., Mehrvar, M., 2010. Study of solid–liquid mixing in agitated tanks through electrical resistance tomography. Chemical Engineering Science 65, 1374–1384. doi:10.1016/j.ces.2009.10.007
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McKee, S.L., Williams, R.A., Boxman, A., 1995. Development of solid-liquid mixing models using tomographic techniques. The Chemical Engineering Journal and the Biochemical Engineering Journal 56, 101–107. Meng, J., Xie, W., Brennan, M., Runge, K., Bradshaw, D., 2015. Measuring turbulence in a flotation cell using electrical resistance tomography. Measurement Science and Technology 26, 115305. Nagata, S., 1975. Mixing: principles and applications. Kodansha Ltd. , Tokyo, Japan. Nasr-El-Din, H.A., MacTaggart R S, Masliyah, J.H., 1996. Local solids concentration measurement in a slurry mixing tank. Chemical Engineering Science 51, 1209–1220.
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Nemati, M., Harrison, S.T.L., 2000. Effect of solid loading on thermophilic bioleaching of sulfide minerals. Journal of Chemical Technology and Biotechnology 75, 526–532. Nienow, A.W., 1968. Suspension of solid particles in turbine agitated baffled vessels. Chemical Engineering Science 23, 1453–1459. doi:10.1016/0009-2509(68)89055-4 Ochieng, A., Lewis, A.E., 2006. CFD simulation of solids off-bottom suspension and cloud height. Hydrometallurgy 82, 1–12. doi:10.1016/j.hydromet.2005.11.004 Oldshue, J., 1983. Fluid mixing technology. McGraw-Hill Publications Co., New York, USA.
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Paglianti A., Carletti C., Buscilio A., Montane G., 2017. Solid distribution and mixing time in stirred tanks: the case of floating particles. Canadian Journal of Chemical Engineering 95(9), 17891799. doi: 10.1002/cjce.22854 Perry, R.H., Green, D.W., 2008. Perry’s Chemical Engineers’ Handbook, McGrawHill Professional Publishing, Chemical Engineers Handbook. McGraw-Hill. doi:10.1036/0071511334
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Scholtz, N.J., Pandit, A.B., Harrison, S.T.L., 1997. The effect of solids suspension on microbial cell disruption, in: Bioreactor & Bioprocess Fluid Dynamics. pp. 199–216. Shamlou, P.A., Koutsakos, E., 1989. Solids suspension and distribution in liquids under turbulent agitation. Chemical Engineering Science 44, 529–542. doi:10.1016/0009-2509(89)85030-4
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Sissing, A., Harrison, S.T.L., 2003. Thermophilic mineral bioleaching performance : A compromise between maximizing mineral loading and maximizing microbial growth and activity. The Journal of The South African Institute of Mining and Metallurgy 139–142.
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Stevenson, R., Harrison, S.T.L., Mantle, M.D., Sederman, A.J., Moraczewski, T.L., Johns, M.L., 2010. Analysis of partial suspension in stirred mixing cells using both MRI and ERT. Chemical Engineering Science 65, 1385–1393. doi:10.1016/j.ces.2009.10.006 Stevenson, R., Harrison, S.T.L., Miles, N., Cilliers, J.J., 2006. Examination of swirling flow using electrical resistance tomography. Powder Technology 162, 157–165. doi:10.1016/j.powtec.2005.11.008 van der Westhuizen, A.P., Deglon, D.A., 2008. Solids suspension in a pilot-scale mechanical flotation cell: A critical impeller speed correlation. Minerals Engineering 21, 621–629. doi:10.1016/j.mineng.2007.12.010 Villadsen, J., Nielsen, J., Lidén, G., 2011. Bioreaction Engineering Principles, 3rd ed. Springer Science+Business Media.
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Wilkinson, A.J., Randall, E.W., Cilliers, J.J., Durrett, D.R., Naidoo, T., Long, T., 2005. A 1000measurement frames/second ERT data capture system with real-time visualization. IEEE Sensors Journal 5, 300–307. doi:10.1109/JSEN.2004.842445 Williams, R.A., Jia, X., McKee, S.L., 1996. Development of slurry mixing models using resistance tomography. Powder Technology 87, 21–27. doi:10.1016/0032-5910(95)03077-8 Zehner, P., Tebel, K.H., 1984. Hydrodynamik beim Suspendieren in Rührbehälter, Mischvorgänge. Freising.
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Zwietering, T.N., 1958. Suspending of solid particles in liquid by agitators. Chemical Engineering Science 8, 244–253.
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Figure 1: Radial concentration profiles for 5% v/v fraction of 600 – 800 μm quartzite particles in a 50 mm ID tank at 480 rpm (impeller tip speed 0.63 m.s-1).
Figure 2: Radial concentration profiles for 5% volume fraction of 600 - 800 μm quartzite particles for the 50 mm (a - c) and 220 mm (d - f) ID stirred tank reactors.
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Figure 3: Radial concentration profiles for 15% volume fraction of 600 – 800 μm quartzite particles for the 50 mm (a-c) and 220 mm (d-f) ID stirred tank reactors.
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Figure 4: The influence of impeller tip speed on the (a & b) axial MIz (L1–L4) and (c & d) radial MIr (L1– L4) mixing index for 5 % (a & c) and 15% v/v (b & d) suspension of 600 – 850 μm quartzite particles in 50 and 220 mm ID vessels.
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Figure 5: The influence of specific power (a), impeller tip speed (b) and ratio of the impeller speed to the critical suspension speed N/Njs (c) on the overall homogeneity for a suspension of 600 - 800 μm quartzite particles in the 50 and 220 mm ID stirred tanks.
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Figure 6: Reynolds numbers as a function of the slurry density in the 50 and 220 mm ID tanks at the same (a) specific power P/V and (b) impeller tip speed.
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Figure 7: Examining the influence of increasing specific power P/V on local particle concentration in conductivity layer L1: a. 50 mm ID tank, b. 220 mm ID tank
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Table 1: Critical suspension speeds Njs for a 600 – 850 μm fraction in 50 and 220 mm ID tanks calculated using the critical suspension theory developed by Zwietering (1958) Volume fraction [%] 5 10 15 20
Njs 50 mm [rpm] [m.s-1] 1665 2.16 1835 2.37 1949 2.52 2039 2.64
Njs 220 mm [rpm] [m.s-1] 473 2.72 521 3.00 553 3.19 579 3.33
Table 2: Reynolds numbers, impeller tip speeds and power per unit volume (P/V) for the 220 mm ID and 50 mm ID stirred tank reactors at equivalent (i) impeller tip speed and (ii) power per unit volume for vessels loaded with 15% v/v of 600 – 800 μm particles.
Re220 (x 104) 8.17 10.53 12.22 15.93 18.94
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Tip speed [m.s-1] 1.36 1.75 2.03 2.65 3.15
(ii) at equivalent P/V Required Resultant impeller Re50 speed [rpm] (x 104) 634 1.13 816 1.46 948 1.70 1235 2.21 1469 2.63
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Impeller speed [rpm] 236 304 353 460 547
50 mm ID Tank (i) at equivalent tip speed P/V Required Resultant P/V -1 [W.L ] impeller Re50 [W.L-1] 4 speed [rpm] (x 10 ) 1.70 1038 1.86 7.48 3.64 1338 2.39 16.03 5.70 1553 2.78 25.06 12.61 2024 3.62 55.48 21.20 2407 4.31 93.31
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220 mm ID Tank
Table 3: Properties of a continuous stirred tank reactor on scale-up from 50 to 220 mm ID. 50 mm ID V = 0.098 L
Power (P) Specific Power (P/V) Speed (N) Turbine Diameter (D) Pumping Capacity (Q) Q/V Tip Speed (ND) Re (ρND2/μ)
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
220 mm ID V = 8.36 L P/V constant 85 1.0 0.37 4.4 31.7 0.37 1.6 7.2
ND constant 19 0.2 0.2 4.4 19.4 0.2 1.0 4.4
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Property
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PII:
S0263-8762(19)30552-0
DOI:
https://doi.org/10.1016/j.cherd.2019.10.049
Reference:
CHERD 3909
To appear in:
Chemical Engineering Research and Design
Received Date:
21 July 2018
Revised Date:
13 September 2019
Accepted Date:
31 October 2019
Please cite this article as: Harrison STL, Kotsiopoulos A, Stevenson R, Cilliers JJ, Mixing Indices Allow Scale-up of Stirred Tank Slurry Reactor Conditions for Equivalent Homogeneity, Chemical Engineering Research and Design (2019), doi: https://doi.org/10.1016/j.cherd.2019.10.049
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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. © 2019 Published by Elsevier.
Mixing Indices Allow Scale-up of Stirred Tank Slurry Reactor Conditions for Equivalent Homogeneity STL Harrisona*, A Kotsiopoulosa, R Stevensona, and JJ Cilliersb a
Centre for Bioprocess Engineering Research, Department of Chemical Engineering, University of Cape Town, Rondebosch 7701, South Africa b Royal School of Mines, Department of Earth Sciences and Engineering, Imperial College London, SW7 2AZ, U.K. *Corresponding Author: Fax: +27 21 650 5501, e-mail: [email protected]
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Highlights Mixing indices may be used to reduce energy needed to achieve slurry homogeneity Suspension quality most consistent in smaller vessels than in larger vessels Higher P/V ratios are achieved in smaller vessels with similar impeller tip speeds Inconsistencies in mixing attributed to limited mixing in the axial direction Less homogeneous suspension at low solids loading than at high loadings Abstract
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The influence of reactor scale, impeller tip speed and specific power on the overall homogeneity (multi-phasic mixing) of two dimensionally similar stirred tanks of 50 mm and 220 mm internal diameter (ID) are compared using data collected from electrical resistance tomography for 5 and 15% v/v 600 – 800 μm particle suspensions. The data collected is used to quantify the suspension quality of the system by defining mixing indices in the axial MIz and radial MIr directions as well as the overall mixing index MIo. Analyses across the vessels indicated that axial and radial homogeneity improved with increasing impeller tip speed for both large and small vessels with more consistent suspensions observed in the former. Improved homogeneity was consistently found in the 10 to 20% (v/v) solids loading range (data only shown for 15%) than at 5%, across both reactors. In either vessel, optimum homogeneity was achieved at impeller tip speeds ca. 20% lower than the critical suspension speed, as shown previously. Analysis of the local concentration of particles in the lowest region of the vessels indicated that absolute homogeneity was unattainable as the decreasing local concentration displayed an asymptotic character with increasing power per unit volume. The suspension quality during reactor scale-up was relatively consistent with specific power ratios P/V, while the same degree of homogeneity was not achieved when the impeller tip speed was kept constant.
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Keywords: Electrical resistance tomography (ERT), scale-up, solids suspension, specific power, solids concentration, impeller speed Introduction
Stirred tank reactors are prevalent in many industrial applications where a high degree of solid-fluid contact in the multi-phase reaction systems is necessary for optimum performance (Nienow, 1968; Oldshue, 1983; Shamlou and Koutsakos, 1989). Slurry reactors are typically a mixing system containing a particulate phase suspended in an aqueous solution through which a gaseous phase may be distributed. Understanding the dynamics and dispersion of solid fractions within these systems is important to maximise solid-liquid contact through enhanced solid suspensions, which ultimately
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improve multi-phase production efficiencies (Deveci, 2004; Harrison et al., 2012, 2003; Nemati and Harrison, 2000; Scholtz et al., 1997; Sissing and Harrison, 2003). Through mixing, multi-phase homogeneity is facilitated to affect improved reaction-medium contact time and hence efficiency. Knowledge of the mixing and suspension characteristics in the slurry reactor facilitates improved reactor design and provides important information on the influence of the main operating parameters on the reactor performance.
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Investigations into the distribution of phases in continuously stirred tank reactors, while varying key operating parameters, have previously been performed by applying a range of approaches such as direct sampling methods, magnetic resonance imaging and electrical resistance tomography (Barresi and Baldi, 1987; Bujalski et al., 1999; Carletti et al. 2014; Harrison et al., 2012; Illing and Harrison, 1999; Nasr-El-Din et al., 1996; Ochieng and Lewis, 2006; Shamlou and Koutsakos, 1989; Stevenson et al., 2010). However, investigations into the distribution of solids over the height of slurry reactors is sparse and is often limited to the case of low solids concentration using cloud height mechanisms (Bittorf and Kresta, 2003; Bujalski et al., 1999; Einenkel and Mersmann, 1977; Rieger and Ditl, 1994; Zehner and Tebel, 1984). Electrical resistance tomography (ERT) (McKee et al., 1995; Wilkinson et al., 2005) has been applied successfully to multi-phase environments achieving discrimination of slurries and gaseous slugs in pipelines, bubble columns, flotation cells and stirred tank reactors (Carletti et al., 2016; Fangary et al., 1998; Harrison et al., 2012; Jin et al., 2014; Meng et al., 2015; Paglianti et al.,2017; Sardeshpande et al., 2016; Wang and Cilliers, 1999; Xie et al., 2004). Discrete segregation of these phases using ERT promotes understanding of the mixing environment and the achieved suspension quality of these dynamic phases. Multiple dimensions are achievable allowing improved operational knowledge and control of stirred tank reactors for process optimisation (Harrison et al., 2012).
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Stirred tank reactors are often used in industrial applications where the mixing and the homogeneity of the particle suspension are governed by the operating conditions in the multi-phase system. Using geometrically similar reactors in the scale-up procedure is insufficient when attempting to replicate mixing characteristics observed in small-scale experiments. The dominant factors influencing particle homogeneity and liquid mixing in stirred tank slurry reactors are particle size and density, impeller design, impeller speed and tank geometry (Carletti et al., 2016; Fangary et al., 1998; Harrison et al., 2012; Paglianti et al., 2017). Increasing particle concentration increases the required impeller speed for complete suspension, thereby decreasing absolute homogeneity. The introduction of a gaseous phase decreases the power transferred from the impeller, thereby leading to a decrease in particle suspension and hence system homogeneity (Breucker et al., 1988; Frijlink et al., 1990; Rewatkar et al., 1991). Rates of mixing and reaction are interrelated, as turbulent motion in the vessel is often responsible for the dispersion of reactants in the vessel. Insufficient mixing and hence solid-liquid contact time, in the case of slurry reactors, may result in reduced reaction rates with poor product distribution and mass transfer limitations (Hill, 1976). The migration of a process from laboratory to pilot or industrial scale is therefore challenging (Li et al., 2005; Perry and Green, 2008). While it is necessary to have a framework for reactor scale-up on moving from the proof of concept phase to implementation, criteria for scale-down are equally important. These allow a relevant representation of the large-scale reactor to be made for fundamental studies to be performed at bench-scale. The key parameters affecting reactor scaling can also be determined. Scale-down studies are also increasingly of importance for
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rapid product development as they facilitate many miniaturised replicate experimental systems in the research phase (Betts et al., 2006; Buurman et al., 1986).
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As large-scale optimisation experiments can be expensive and time consuming, scale down systems are needed. Bench-scale studies to obtain reliable kinetics and effective conditions for maximum reactor performance are used to model commercial scale capacities. In this study, recent advancements in ERT detection technologies are applied and evaluated in a stirred tank environment to examine the influence of reactor scale on system homogeneity. Using a grid structure with an annular design, radial and axial concentration gradients are defined. Homogeneity is quantified in terms of radial, axial and overall mixing indices, as defined by Harrison et al. (2012) and compared as a function of solids loading across two reactor scales. This study provides insight into the critical operating parameters governing suspension in geometrically similar vessels during reactor scale-up or scale-down. Further, requirements for maximum homogeneity are considered.
Materials and methods The 50 mm ID and 220 mm ID stirred tank reactors
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Two geometrically similar (tank diameter T = working volume height H; T=H), flat bottom, Perspex stirred tank reactors were utilised for the homogeneity studies in slurry vessels. Stirred tank reactors with T = 220 mm and T = 50 mm internal diameters (ID) were fitted with four layers of 16 evenly spaced electrodes along the perimeter of the tanks (Harrison et al., 2012; Stevenson et al., 2010).
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Both reactors were agitated using six-bladed Rushton turbines (blade length = 0.26D; blade height = 0.21D; disk diameter = 0.67D) with dimensionally similar tank to impeller diameter ratios and clearance (D = T/2; C = T/3). Four baffles were present (B = 0.1T). Stainless steel components of the impeller were insulated with black enamel paint and Loctite®, a rubberized paint, to ensure nonconductivity of metallic surfaces. This ensured that the metallic surfaces would contribute similarly to the conductivity distribution as the non-conducting Perspex tank walls and baffles. Solid and liquid phase
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The 600 – 850 μm sieved size fraction of quartzite particles used in the conductivity trials was characterised by a volumetric mean diameter of 857 µm and a mode of 754 µm with a d50 of 790 µm. These particulates were washed with nitric acid in a stirred tank reactor over two weeks to bleach and remove any fines and metal content. The solid particles were subsequently calcined at 550oC for 20 hours after additional washing to remove any traces of acid. Particle size fractions of 5, 10, 15 and 20% v/v were suspended in 0.1 g.L-1 NaCl solution at room temperature (20oC) for ERT analysis. The addition of NaCl electrolyte ensured that adequate image reconstruction could be achieved (Fangary et al., 1998). The ERT measurement system The ERT system, operating at 3 kHz, employed a current-pulse technique developed by Wilkinson et al. (2005) with data acquisition speeds up to 1000 frames per second. A bi-directional current was
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injected across the excitation electrode pairs in the measuring sequence and maintained during positive and negative half cycles. Voltage differences were captured by a multiplexor on the remaining electrode pairs where the signals were buffered and read by an analogue to digital converter. The resulting potential differences between pickup electrode pairs reflected the conductivity in the plane of measurement (Harrison et al., 2012). The bi-directional current utilised by the system minimised electrode polarisation.
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The reconstruction code in this study used a modified Newton-Raphson algorithm over a 712 and 764 element mesh for the 220 mm ID and 50 mm ID tanks, respectively. These meshes have irregular elements and thus 12 radial subdivisions in each 16-electrode plane (L1 – L4) were created to calculate the radial profiles barring the baffle area and impeller zone as illustrated in Harrison et al. (2012). The mesh was constructed with radial symmetry with each plane considered as seven concentric rings (Harrison et al., 2012). This translated to the averaging of conductivity data in radial distances from r/R = 0.55 (50 mm ID) or 0.63 (220 mm ID) to 1.0 from each of the radial subdivisions within the specific electrode plane. The averaged data were converted to radial concentration profiles using the Maxwell equation (Eq. 1), which relates the difference in the measured conductivity and the conductivity of the liquid phase to particle concentrations (Fangary et al., 1998; Maxwell, 1873). 𝜎𝑚 − 𝜎𝑝 𝜎𝑚 − 𝜎 =𝑓 (1) 2𝜎𝑚 + 𝜎 2𝜎𝑚 + 𝜎𝑝
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where σ is the conductivity of the clear liquid medium or particles denoted by the subscripts m and p, respectively, while f is the volume fraction of particles in the vessel. In the quartzite tests, σp was assumed to be zero.
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Data averaged over the radial distance for each electrode layer were used to determine the axial concentration profiles of which comprehensive detail is presented in Harrison et al. (2012). Calibration of the ERT detection system, in the absence of the quartzite particles, was performed in the presence of the reactor baffles, impeller and shaft at either 236 rpm or 304 rpm for the 220 mm ID tank, and at 200 rpm for the 50 mm ID tank. One hundred frames (220 mm ID tank) and fifty frames (50 mm ID tank) of data were recorded during calibration and averaged prior to reconstruction. The fifty frames in the smaller vessel were found to be consistent with data presented by the 100 frame system and was therefore considered suitable in subsequent measurements.
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At the high impeller tip speeds examined, the liquid surface level in the 50 mm tank fluctuated intermittently near the uppermost electrode layer L4 due to fluid turbulence and surface aeration. Further contributing to the varying surface, the small height differential between the liquid surface and layer L4 led to greater measurement error at high speeds resulting in decreased resistance in L4. Only the last two data points of the uppermost layer L4 near the vessel wall were therefore selected as representative. Consequently, conductivity data in the stirred tank reactors were extracted at radial distances r/R = 0.55 to 0.96 for the 50 mm ID reactor.
Further analysis of the system Specific power (P/V) was also investigated with the power input for the Rushton turbines extracted from the graphical relationship between power number Np and Reynolds number NRe (Perry and
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Green, 2008) and reproduced using correlations developed by Nagata (1975). For each of the solid concentrations considered the power number was determined using slurry densities as a function of both the solid and liquid densities. Over the considered range, high Reynolds numbers are achieved with power numbers for the Rushton turbine remaining similar across the investigated impeller speeds and thus approximated at Np = 5. The critical suspension velocity Njs was calculated according to Zwietering's correlation of 1958 (van der Westhuizen and Deglon, 2008): 𝑁𝑗𝑠 = 𝑆𝑑𝑝0.20 𝐵0.13 𝜈 0.10 𝑔0.45 (
𝜌𝑠 − 𝜌𝐿 0.45 −0.85 ) 𝐷 𝜌𝐿
(2)
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where dp is the particle diameter [μm], B the solid-liquid mass ratio [ms.mL-1], ν the kinematic viscosity [m2.s-1], g the gravitational acceleration [m.s-2], and ρs and ρL [kg.m-3] the density of the solid and liquid fractions. D [m] is the impeller diameter and S is a function of the relative ratio (D/T); the ratio (C/T) of the impeller clearance C [m] to the reactor diameter and the impeller type. The S parameter used to in these calculations were set at 4 in accordance with findings by Armenante and Nagamine (1998) for an equivalent 6-bladed Rushton turbine.
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Results and Discussion
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In the presence of solids, a maximum in the NP-NRe curve is generally observed at the critical suspension velocity Njs (Bohnet and Niesmak, 1980). Njs is presented in Table 1 as a function of solids loading demonstrating that the power per unit volume P/V required to achieve complete suspension should increase for all impeller speeds tested in the 50 and 220 mm ID tank with increasing of presence of solids.
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Experiments were conducted in the 220 mm ID reactor using impeller tip speeds ranging from 1.36 to 2.65 m.s-1. (equivalent impeller speeds 236 – 480 rpm, respectively) For comparative studies in the 50 mm ID tank, relatively slow impeller tip speeds were initially investigated. Preliminary experiments were conducted at 0.63 m.s-1 at an equivalent impeller speed of 480 rpm with 5% v/v quartzite particles to determine whether satisfactory suspensions and turbulent conditions similar to those achieved in the larger vessel could be attained (Figure 1).
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Minimal suspension occurred with particles remaining unsuspended in the reactor. As turbulent conditions defined by Reynolds numbers similar to those achieved in the 220 mm ID tank could not be replicated in the 50 mm ID tank owing to the extreme agitation speeds required, comparative experiments were based on impeller tip speed. As such, stirring speeds between 1038 and 2024 rpm were maintained in the 50 mm ID stirred reactor with Reynolds numbers and power input per unit volume for each of these vessels presented in Table 2. Interestingly, the solid fraction in the L4 plane exceeded the upper planes (L2 and L3) toward the tank wall. This irregularity was likely due to selfaeration causing the entrainment of air bubbles through the liquid phase resulting in higher solid concentrations being detected. This was phenomenon was particularly evident in the 50 mm ID vessel and further noted in subsequent tests at higher stirring speeds.
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Particle suspensions at impeller tip speeds presented in Table 2 and corresponding to a study previously conducted in the 220 mm ID vessel are shown in Figure 2 (d – f) (Harrison et al., 2012). Harrison et al. (2012) previously showed that overall homogeneity of suspended particles in stirred tank reactors (220 mm diameter) was a strong function of the reactor solids loading, particle size and impeller speed. The suspension quality improved with increasing impeller speed and solids concentration while the inverse was noted with increasing particle size. To examine the influence of reactor scale, the suspension of quartzite particles in both the 50 mm and 220 mm ID stirred tanks were compared using ERT. The difference or similarity in particle homogeneity in the dimensionally similar vessels and contrasting hydrodynamic environments in the axial and radial directions, were investigated.
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Radial concentration profiles for 50 mm ID and 220 mm ID stirred tank reactors
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The radial concentration profiles for 5% and 15% v/v of quartzite particles for both reactor configurations are presented in Figures 2 and 3, respectively. Fluctuations in the concentration profiles are observed for each of the vessels with radial and axial position. At equivalent tip speeds and relative axial position in the reactor, greater homogeneity is observed in the 50 mm ID vessel, evidenced by the narrow horizontal variance in the radial profiles in Figure 2 (a – c). Also, the concentration profiles in the smaller vessel across conductivity layers L1 – L4 in Figure 2 (a – c) are more consistent than those in the 220 mm ID tank (Figure 2 d – f), indicating greater axial homogeneity in the former.
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On increasing the volume fraction to 15% v/v, the observed variance in both the radial and axial directions is amplified in the larger tank while greater consistency in the radial concentration profiles is observed with increasing impeller speed in the small vessel (Figure 3). Operating both vessels at either volume fraction, the particle concentration in the 50 mm ID tank increases toward the vessel wall in the lower segment of the vessel (L1 in Figure 2 and Figure 3 a – c) while marginally decreasing or remaining constant in the rest of the layers L2 – L4 on approaching the tank wall. This is in contrast to the decrease in particle concentration towards the wall in the 220 mm ID tank.
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The improved suspension quality in the smaller tank, illustrated by the flatter and more closely spaced lines representing radial and axial homogeneity respectively, is attributed to the specific power P/V. Higher P/V ratios in the 50 mm ID tank provide more regular suspensions compared to the 220 mm ID tank, which is further highlighted by the enhanced homogeneity in the smaller vessel when the volume fraction is increased from 5% to 15% v/v (Figure 2 and Figure 3). In Figure 2 and Figure 3, it is clear that the radial and axial profiles are more consistent in the 50 mm ID tank than in the 220 mm ID vessel. In the subsequent sections, the suspension quality of the tanks is rated according to mixing indices in both the vertical and horizontal planes as a means to establish the basis for the improved homogeneity in the smaller vessel. The influence of the impeller tip speed and specific power P/V on the uniformity of the suspension within the reactors are therefore investigated.
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Axial and radial homogeneity
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Various methods have been proposed to describe the mixing in slurry vessels quantitatively using ERT (Fangary et al., 1998; Hosseini et al., 2010; Mann et al., 2001; McKee et al., 1995; Stevenson et al., 2006; Williams et al., 1996). However, these approaches only quantify homogeneity in the axial direction and not mixing quality in the radial direction (Hosseini et al., 2010; Williams et al., 1996). The quantitative description of radial homogeneity requires a suitable computational grid that reflects the reactor geometry, specifically an annular grid in preference to a regular square grid. In our previous study, mixing indices were developed that quantify the uniformity of particle concentration; radially, axially and overall (Harrison et al., 2012). The overall mixing index MI was quantified by calculating the normalised standard deviation of the particle volume fraction in each of the annuli across the conductivity planes (Harrison et al., 2012). Similarly, the axial MIz and radial MIr mixing indices were determined. Data validation was achieved through correlation of the volume fraction of particulates across all regions of the reactor (derived from the conductivity data), and the experimental volume fraction.
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In Figure 2 and Figure 3, both axial and radial variance in quartzite volume fractions in each of the vessels is shown. The axial mixing index MIz is defined as the normalised, average standard deviation of volume fraction across the seven annuli, weighted by annulus area. The radial mixing index MIr is calculated from the normalised, average standard deviation in each of the four planes. The change in the axial MIz and radial MIr mixing indices, and hence the mixing performance, with impeller tip speed for 5% and 15% v/v fractions of 600 – 800 μm quartzite particles for either vessel configuration are presented in Figure 4. Low mixing indices in these figures indicate high homogeneity while high mixing indices represent low homogeneity.
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In agreement with Figure 3, the axial MIz and radial MIr mixing indices in Figure 4 indicate that the smaller vessel has greater axial (Figure 4 a-b) and radial (Figure 4 c-d) homogeneity than the larger tank at the equivalent tip speed. Homogeneity improves in both reactors with increasing solid fractions. Similar axial mixing indices MIz are achieved at higher impeller tip speeds (Figure 4). The most notable difference in homogeneity between the two vessels is in the axial plane (Figure 4 a-b). The axial homogeneity of the smaller and larger vessels increases with increasing tip speed. However, at low solid concentration in the 50 mm ID vessel at high impeller tip speeds there was a departure in this trend. This was likely due to the entrainment of air through the vessel at high impeller speed decreasing the electrical resistance in the lower layers (L4) leading to poor axial mixing. Inhomogeneity across the vessel is mainly attributed to inefficient axial mixing, possibly due to the increased wall resistance at high particle concentrations (at ca. r/R ≥ 0.77 in Figure 3a–c for the smaller tank). At low volume fractions poor mixing in the axial plane is attributed to the solids accumulating around the impeller (radial distance r/R < 0.7 Figure 2). However, in the 220 mm tank, the axial and radial mixing indices are similar for 15% v/v solids. In general, homogeneity improves at higher impeller tip speeds (Figure 4). It is important to note that, in both vessels, the highest homogeneity is achieved at impeller tip speeds below the critical suspension speeds Njs at high solids concentrations. (see Table 1 and Figure 4). No further improvement in either the axial or radial homogeneity is achieved by increasing the impeller speeds above ca. 80% of the critical suspension speed. This is consistent with the prior findings of
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Harrison et al. (2012).
Overall system homogeneity
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The overall mixing index is presented in Figure 5 as a function of specific power P/V (Figure 5a), impeller tip speed (Figure 5b) and the ratio of the impeller tip speed to the Zwietering critical suspension speed N/Njs (Figure 5c). It is clear from Figure 5 that the homogeneity in both tanks is improved with increasing specific power P/V, impeller tip speed and N/Njs, noted by the decreasing trend of the overall mixing index MIo over the entire range (excepting at 5% solids loading in the 50 mm ID reactor). The suspension quality in the 220 mm ID tank improved when the particle concentration was increased from 5% to 15% v/v. This result was due to, as seen in Figure 2 and Figure 3 (d–f), the increased presence of particles in the upper regions L4 of the mixing vessel with increasing particle loading. However, when comparing the mixing profiles of the larger vessel to the smaller vessel, the 50 mm ID tank has greater homogeneity for the same P/V ratio and impeller tip speed relative to the larger vessel for the 15% v/v fraction but not the 5% v/v fraction (Figure 5). The poor homogeneity observed in both vessels, especially the 50 mm ID tank, containing 5 % v/v solids is due to the large axial variance as seen in Figure 2 between conductivity layers L1 – L4, particularly in the top region of the reactor, L3 and L4, where little to no quartzite particles are observed with increasing impeller speed. In either configuration, the solid fraction accumulates within or below the impeller zone L1 and L2.
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Maintaining the specific power constant during scale-up, the Reynolds number in the larger tank increases by a factor of 7.2 while the rotational speed N in the larger tank decreases to 0.37 of that in the 50 mm ID tank. The peripheral tip speed of the impeller in the larger tank is 1.6 times greater (see Table 3, Figure 6 a). Maintaining the impeller tip speed constant, the Reynolds number and rotational speed increase as with maintaining the specific power constant; however, the increase in the Reynolds number is less pronounced (see Table 3, Figure 6 b). The decreased factor by which the degree of turbulence in the larger reactor changes with respect to the 50 mm ID reactor at constant impeller tip speed can be inferred from the lower overall homogeneity shown in Figure 5. The suspension quality is significantly reduced when the tip speed is kept constant (Figure 5 b) compared to when the P/V ratio is maintained steady (Figure 5 a) when the 50 mm ID tank is scaled-up to 200 mm ID. Therefore, maintaining the same impeller tip speed is not a reliable measure for scaling procedures to obtain the same suspension quality at scale-up or scale-down. However, even though the fluid dynamics differs during scale-up or scale-down, the homogeneity in both vessels is similar at low P/V ratios for the same volume fraction and approach relatively similar homogeneity with increasing specific power with improved suspension quality (Figure 5 a).
According to Buurman et al. (1986), eddy sizes 3 to 5 times greater than the particle size are required to transport a solid particle with diameters between 100 μm and 2 mm. In stirred tanks, impeller dimensions typically govern the size of the largest eddies produced, while the smallest eddy sizes depend on the energy dissipation range. Turbulent flow and hence high Reynolds numbers result from the cascade of energy from large scale to small scale eddies and is responsible for particle lift-off. In both the 50 mm or 220 mm vessels, the Kolmogorov eddy lengths η, calculated as function of the kinematic viscosity ν (m2.s-1) of the slurry and the turbulent power dissipation per mass of liquid ε
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(W.kg-1) in accordance with Eq. 3 (Kolmogorov, 1941), are smaller than the particle size range 600 – 800 μm required to suspend the particles (η50 < 51 μm; η200 < 24 μm over the specified agitation range). 0.25
𝜈3 (3) 𝜂=( ) 𝜀 The fluctuating velocity, a function of the impeller tip speed in either tank is similar. However, the largest eddy sizes are approximately 1.45 times smaller in the 50 mm vessel, which would support the observed similarity in homogeneity in the two vessels with increasing specific power P/V (Figure 5). This would indicate that maintaining the same overall mixing index to achieve the required particle dispersion during scaling procedures is achievable when power per unit volume is kept constant at the desired homogeneity. However, the exceedingly high power input required to maintain the desired homogeneity during scale-up may not always be economically practical (Villadsen et al., 2011).
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Influence of specific power on local particle concentration
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To further investigate the influence of power per unit volume on system homogeneity, the concentration of particles in the lowest electrode layer L1 of the vessel was studied. The objective was to examine the degree of suspension of particles as they migrate to the higher portions of the vessel L2 – L4 with increasing specific power P/V.
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In Figure 7, it is shown that the volume fraction of solids in the lowest layer in the reactor L1 decreases with increasing power per unit volume in both reactor configurations. In either vessel, the volume fraction approaches an asymptotic value at high P/V ratios indicating that complete uniformity of solid particles in the stirred vessels is unattainable but rather an optimal suspension quality is achieved. This decreasing trend is in accordance to studies by Buurman et al. (1986).
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When comparing the 5% v/v solids concentration in both tanks, the volume fraction of solids in the 220 mm ID vessel approaches optimum homogeneity at lower P/V ratios even though the suspension quality across the remaining conductivity layers L2 – L4 is poorer than is achieved at higher solid concentrations (Figures 2, 5 & 7). However, complete homogeneous condition is achieved in the smaller 50 mm ID vessel as the power per unit volume approaches ca. 24 W.L-1 with 5% v/v solids (Figure 7a). The Reynolds number in the larger tank is at least 7.2 times greater than in the smaller vessel at any given P/V ratio (Figure 6), which may aid homogenisation, does not necessarily aid particle lift off (see L1 in Figure 2 d–f). Consequently, optimal but not complete suspension concentration in the 220 mm ID vessel would be obtained at lower P/V ratios than in the 50 mm ID tank (Figure 7). Examining the 15% v/v fraction in both vessels, neither system attains the average solids concentration in the agitation range studied. However, the solids concentration in the 220 mm ID tank consistently approaches optimum uniformity at lower P/V ratios than in the smaller vessel even though it is less homogeneous across the entire vessel at the same specific power.
Conclusions
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The influence of reactor conditions and scale effects on the suspension of quartzite particles in both the 50 mm and 220 mm ID tank was successfully analysed using ERT. Radial and axial profiles were detected using ERT for a 50 mm and 220 mm ID tank. These were converted to radial, axial and overall mixing indices. Using these, the influence of scale, specific power, impeller speed and impeller tip speed on the suspension quality of the system was determined.
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Results indicated that the overall mixing of 5% and 15% v/v quartzite particles in the 50 mm tank was more consistent than the 220 mm tank. The consistency in the smaller vessel, when operating the vessels at the same impeller tip speed, was attributed to the higher power input per unit volume. When operating the vessels at the same P/V ratios or equivalent tip speeds, the smaller vessel was found to be more homogeneous than the larger vessel. This was indicated by low overall mixing indices. Lower and more consistent radial mixing indices compared to axial mixing indices indicated that the overall homogeneity of the system was limited by mixing in the axial direction. This was ascribed to shear resistance near the vessel wall. Both radial and axial homogeneities were more uniform in the smaller vessel with increasing solids concentration denoted by the reduced variance in the horizontal and vertical radial concentration profiles.
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Of particular interest was the finding that a 5% (v/v) solids loading resulted in a less homogeneous suspension than a 15% loading at the same impeller speed across both reactor scales. This was supported in the 220 mm reactor across 10 to 20% solids loading.
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At the lowest conductivity layer L1, the 220 mm ID tank approached optimal suspension concentration at lower P/V ratios than achieved in the 50 mm ID tank. This was due to the increased turbulence in the large tank resulting in the development of larger eddies from the larger impeller compared to the smaller vessel. Absolute homogeneity was unattainable as the decreasing local concentration in the layer L1 approached a limiting concentration with increasing power per unit volume.
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Homogeneity achieved across the two reactor scales and concentrations correlated well with power input per unit volume. Similar minimum overall mixing index, representing similar maximum homogeneity, was attained across the reactors at 15% solids. Similarly, the data correlated well to the ratio of impeller speed to critical impeller speed for suspension (N/Njs). Conversely, poor correlation was found with impeller tip speed.
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In both reactor configurations, optimum homogeneity was achieved at ca. 80% of the critical suspension speeds indicating that further increase in the impeller speed does not further enhance system homogeneity, irrespective of reactor scale. On using P/V as a scale-up criterion, it was demonstrated that, under all conditions explored, no further improvement in suspension homogeneity was achieved on increasing the P/V above 10 W.L-1. This provides a useful estimate of energy required for suspension homogeneity. This study thus guides the selection of operating variables within the stirred tank slurry reactor to optimise tank homogeneity with respect to the suspension of the solid phase, while facilitating improved energy efficiency. Through use of mixing indices, homogeneity may be quantified, assisting rigorous process design. Particularly, through the scale experiments, scale down approaches are
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validated, whereas the consistency of homogeneity of suspension with scale has previously remained poorly quantified. The integration of quantification of suspension homogeneity with reaction rate and extent may now be considered. Acknowledgements
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The authors gratefully acknowledge the funding contribution of the National Research Foundation South African Research Chair Initiative (GUN 64778) funding of the SARChI chair in Bioprocess Engineering and the NRF Postdoctoral Innovation awards (Grant: 85138).
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Figure 1: Radial concentration profiles for 5% v/v fraction of 600 – 800 μm quartzite particles in a 50 mm ID tank at 480 rpm (impeller tip speed 0.63 m.s-1).
Figure 2: Radial concentration profiles for 5% volume fraction of 600 - 800 μm quartzite particles for the 50 mm (a - c) and 220 mm (d - f) ID stirred tank reactors.
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Figure 3: Radial concentration profiles for 15% volume fraction of 600 – 800 μm quartzite particles for the 50 mm (a-c) and 220 mm (d-f) ID stirred tank reactors.
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Figure 4: The influence of impeller tip speed on the (a & b) axial MIz (L1–L4) and (c & d) radial MIr (L1– L4) mixing index for 5 % (a & c) and 15% v/v (b & d) suspension of 600 – 850 μm quartzite particles in 50 and 220 mm ID vessels.
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Figure 5: The influence of specific power (a), impeller tip speed (b) and ratio of the impeller speed to the critical suspension speed N/Njs (c) on the overall homogeneity for a suspension of 600 - 800 μm quartzite particles in the 50 and 220 mm ID stirred tanks.
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Figure 6: Reynolds numbers as a function of the slurry density in the 50 and 220 mm ID tanks at the same (a) specific power P/V and (b) impeller tip speed.
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Figure 7: Examining the influence of increasing specific power P/V on local particle concentration in conductivity layer L1: a. 50 mm ID tank, b. 220 mm ID tank
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Table 1: Critical suspension speeds Njs for a 600 – 850 μm fraction in 50 and 220 mm ID tanks calculated using the critical suspension theory developed by Zwietering (1958) Volume fraction [%] 5 10 15 20
Njs 50 mm [rpm] [m.s-1] 1665 2.16 1835 2.37 1949 2.52 2039 2.64
Njs 220 mm [rpm] [m.s-1] 473 2.72 521 3.00 553 3.19 579 3.33
Table 2: Reynolds numbers, impeller tip speeds and power per unit volume (P/V) for the 220 mm ID and 50 mm ID stirred tank reactors at equivalent (i) impeller tip speed and (ii) power per unit volume for vessels loaded with 15% v/v of 600 – 800 μm particles.
Re220 (x 104) 8.17 10.53 12.22 15.93 18.94
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Tip speed [m.s-1] 1.36 1.75 2.03 2.65 3.15
(ii) at equivalent P/V Required Resultant impeller Re50 speed [rpm] (x 104) 634 1.13 816 1.46 948 1.70 1235 2.21 1469 2.63
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Impeller speed [rpm] 236 304 353 460 547
50 mm ID Tank (i) at equivalent tip speed P/V Required Resultant P/V -1 [W.L ] impeller Re50 [W.L-1] 4 speed [rpm] (x 10 ) 1.70 1038 1.86 7.48 3.64 1338 2.39 16.03 5.70 1553 2.78 25.06 12.61 2024 3.62 55.48 21.20 2407 4.31 93.31
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Table 3: Properties of a continuous stirred tank reactor on scale-up from 50 to 220 mm ID. 50 mm ID V = 0.098 L
Power (P) Specific Power (P/V) Speed (N) Turbine Diameter (D) Pumping Capacity (Q) Q/V Tip Speed (ND) Re (ρND2/μ)
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
220 mm ID V = 8.36 L P/V constant 85 1.0 0.37 4.4 31.7 0.37 1.6 7.2
ND constant 19 0.2 0.2 4.4 19.4 0.2 1.0 4.4
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Property
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