ENGINEERING DEVELOPMENT OF SLURRY BUBBLE COLUMN REACTOR (SBCR) TECHNOLOGY

ENGINEERING DEVELOPMENT OF SLURRY BUBBLE COLUMN REACTOR (SBCR) TECHNOLOGY Twelfth Quarterly Report for January 1 - March 31, 1998 (Budget Year 3: October 1, 1997 September 3, 1998) Submitted to Air Products and Chemicals Contract No.: DE-FC 22 95 PC 9551 Chemical Reaction Engineering Laboratory Chemical Engineering Department Washington University i

ENGINEERING DEVELOPMENT OF SLURRY BUBBLE COLUMN REACTOR (SBCR) TECHNOLOGY Twelfth Quarterly Report Chemical Reaction Engineering Laboratory Contract No.: DE-FC 22 95 PC 9551 Budget Year 3 12 th Quarter for January 1 - March 31, 1998 Objectives for the Third Budget Year The main goal of this subcontract from the Department of Energy via Air Products to the Chemical Reaction Engineering Laboratory (CREL) at Washington University is to study the fluid dynamics of slurry bubble columns and address issues related to scale-up and design. The objectives for the third budget year (October 1, 1997 September 3, 1998) were set as follows: Further development of phenomenological models for liquid and gas flow. Testing of the models against available data from La Porte AFDU. Evaluating turbulent parameters in 18 inches diameter columns with and without internals using collected CARPT data in these columns. Development of relationships between fundamental and simpler practical models for industrial use. Further improvement in fundamental computational fluid dynamics models and testing the models against the CARPT/CT data. Preliminary assessment of differences in gas-liquid and gas-liquid-solid systems. Testing of the effect of the distributor on flow patterns. In this report, the research progress and achievements accomplished in the twelfth quarter (January 1 - March 31, 1998) are discussed. ii

ENGINEERING DEVELOPMENT OF SLURRY BUBBLE COLUMN REACTOR (SBCR) TECHNOLOGY Twelfth Quarterly Report Chemical Reaction Engineering Laboratory Contract No.: DE-FC 22 95 PC 9551 Budget Year 3 12 th Quarter for January 1 - March 31, 1998 OUTLINE OF THE ACCOMPLISHMENTS Turbulent Mixing Length Closure Model for Simulation of Flow in Bubble Columns Turbulent mixing length and k-epsilon closure models are used in CFDLIB to simulate the flow in bubble columns and to compare the predictions with the experimental measurements obtained by Computer Automated Radioactive Particle Tracking (CARPT) and Computer Tomography (CT). It was found that liquid velocity profiles can be predicted well using the mixing length closure, while the k- epsilon model, although modified for interfacial production of turbulence, did not result in good agreement with the measured velocity profile. The reasons for this are being explored. Neither the mixing length nor the k-epsilon model result in good agreement between predicted and observed time averaged gas holdup profile. However, the computations were based on a 2D-axisymetric model while the actual system is a 3D cylindrical column. Additional work on matching CFDLIB predictions and experimental data is in progress. Scale-up of Fluid Dynamic Parameters Systematic evaluation has been completed of the data for liquid velocity and gas holdup profiles obtained by Computer Automated Radioactive Particle Tracking (CARPT) and Computed Tomography (CT) as well as those reported in the literature in columns of 14 to 1 cm diameter over the range of gas superficial velocities between 2 cm/s and 8 cm/s. Relations for estimation of time averaged liquid velocity and gas holdup have been developed. Evaluation of data for turbulent eddy diffusivities obtained by CARPT for scale-up purposes has been initiated. iii

Comparison of Time Averaged Liquid (Slurry) Velocity Profiles in Gas-Liquid (GL) and Gas-Liquid-Solid (GLS) Slurry Bubble Columns Processing and analysis of slurry velocity profiles of the available CARPT data in gas-liquid-solid systems has been completed. Comparison between the time averaged liquid velocity profiles in bubble columns and time averaged slurry velocity profiles in slurry bubble columns obtained by CARPT is presented. The results in bubble columns and slurry bubble columns exhibit similar trends and the velocity profiles are within the same range of magnitude. The slurry systems studied were: air-water-glass beads; column diameter: 14 cm (6 inch); distributor: perforated plate with.4 mm diameter holes and.5% open area; particle size: 125-177 µm; solids loading: 7, 14, 2 % by mass; superficial gas velocity: 2, 5, 8, 14 cm/s. Computation of fluctuating velocities, Reynolds stresses and eddy diffusivities in slurry systems are in progress. Upon completion of slurry data processing comparison will be made with the results for the above quantities obtained in gas liquid systems at similar conditions. iv

ENGINEERING DEVELOPMENT OF SLURRY BUBBLE COLUMN REACTOR (SBCR) TECHNOLOGY Twelve Quarterly Report Chemical Reaction Engineering Laboratory Contract No.: DE-FC 22 95 PC 9551 Budget Year 3 12 th Quarter for January 1 - March 31, 1998 TABLE OF CONTENTS Section No. Page No. Objectives for the Third Budget Year ii Outline of the Accomplishments iii Table of Contents v 1. Turbulent Mixing Length Closure Model for Simulation of Flow in Bubble Columns 1 1.1 Introduction 1 1.2 Theoretical Background 1 1.3 Mixing Length in Bubble Columns 4 1.4 Governing Equations for Two-Phase Flow 4 1.5 Simulation Results 6 1.6 Conclusions 7 1.7 Nomenclature 8 1.8 References 9 2. Scale-up of Fluid Dynamic Parameters 12 2.1 Introduction 12 v

Section No. Page No. 2.2 Gas Holdup 13 2.3 Liquid Recirculating Velocity 15 2.4 Conclusions 18 2.5 References 18 3. Comparison of Time Averaged Liquid (Slurry) Velocity Profiles in Gas-Liquid (GL) and Gas-Liquid-Solid (GLS) Slurry Bubble Columns 21 3.1 Introduction 21 3.2 Experimental Conditions 21 3.3 Results and analysis 22 3.3.1 Time Averaged Axial Velocity Profiles 22 3.3.2 Time Averaged Radial Velocity profiles 24 3.4 Conclusions 26 3.5 Future Work 26 3.6 References 27 vi

1. TURBULENT MIXING LENGTH CLOSURE MODEL FOR SIMULATION OF FLOW IN BUBBLE COLUMNS 1.1 Introduction The Prandtl mixing length model is a semi-empirical model for closure of the momentum equations for turbulent flow. This model has also been used in some of the existing CFD codes for simulation of two- or multiphase flows, basically for the reason of simplicity and unavailability of realistic higher order turbulent closure models. In the present study, we first re-examine the fundamentals and limits of applicability of this type of closure in single phase turbulent flows. Then we investigate the applicability of the mixing length model in the case of two-phase flow in bubble columns. The final objective of this work is to propose and formulate models for the observed fluctuating flows in bubble columns which will be guided by experimental investigations. These models can then be implemented in the CFDLIB codes and used to predict the average and instantaneous velocity and phase distributions in bubble columns. The first step in this study is a preliminary evaluation of the predictive capability of the currently used closure models. 1.2 Theoretical Background One of the simplest but most widely used closure forms for turbulent flows is derived from the mixing-length hypothesis. Prandtl (1925) visualized a simplified model for turbulent fluid motion in which fluid particles coalesce into lumps that cling together and move as a unit. In shear flow, the lumps retain their x-directed momentum for a distance in the y direction, l mix, that he called the mixing length (Figure 1.1). In an analogy to the molecular momentum transport process, with Prandtl s lumps of fluid replacing the molecules, and l mix replacing the molecular mean free path, the turbulent shear stress can be written as: 1 ρu u = ρv l 2 x y mix mix U y (1.1) where v mix is the mixing velocity. This formulation is not complete because the mixing velocity should be specified. Prandtl further postulated that: v mix = constant. l mix U y (1.2) Because l mix is not a physical property of the fluid, the constant in eq. (1.2) and the factor ½ in eq. (1.1) can be absorbed in the mixing length. Thus, Prandtl s mixing length hypothesis leads to: 1

y U(y) Q x 2lmix P Figure 1.1: Schematic of a shear flow ρ = µ U ux u y t y (1.3) where µ t is the eddy viscosity given by: µ = ρl t 2 mix U y (1.4) A relationship for the cross correlation of fluctuating velocity follows by combining eqs. (1.3) and (1.4) into the following equation: u u = l x y mix U y 2 (1.5) It can be shown that the mixing velocity, v mix, must be proportional to an appropriate average of u, the fluctuating velocity, such as the RMS value defined by urms = ( u ) 2 Also, Townsend (1976) stated that in all turbulent shear flows, experimental measurements indicate: u u 4u u.,, (1.6) x y rms x rms y Consequently, if urms, y ~ vmix, comparison of eqs. (1.2), (1.5) and (1.6) reveals that the mixing length model implies that u rms, x and u rms, y are of the same order of magnitude. This is only approximately true for these types of flow, since u rms, x is usually 25% to 75% lager than u rms, y. 1 2. 2

The above formulation still remains incomplete as long as the mixing length remain unspecified since the Boussinesq s empirical eddy viscosity has been replaced with Prandtl mixing length. Prandtl further assumed that for flows near solid boundaries the mixing length is proportional to the distance from the surface, y. For free shear flows such as jets, wakes and mixing layers, the mixing length is proportional to the width of the layer, δ. However, each of these flows requires a different coefficient of proportionality between l mix and δ. The appropriateness of the mixing length hypothesis was examined by Wilcox (1994). Since a direct analogy to the molecular transport process has been assumed, two basic assumptions are made: specifically, it is assumed that the Boussinesq approximation for eddy viscosity holds, and that the turbulence is unaltered by the mean shear. Unfortunately, neither condition is rigorously satisfied. Regarding the Boussinesq approximation, its applicability depends on the Knudsen number being small. The Knudsen number, K n, is defined as the ratio of the mean free path to the characteristic length scale of the mean flow. The latter scale can be defined by: L du dy 2 d U dy 2 (1.7) Close to a solid boundary, for example, the mixing length is approximately proportional to the distance from the surface, y. Specifically, measurements indicate that l. 41 mix y. In the same vicinity of the solid boundary, the velocity follows the well-known law of the wall (Schlichting, 1979), and the velocity gradient varies inversely with y. Consequently, the Knudsen number, K n, is of order one, i.e., K n lmix = L 41. (1.8) Hence, the linear stress/strain-rate relation of eq. (1.1) is suspect. Concerning the effect of the mean shear flow on turbulence, the assumed lifetime of Prandtl s lumps of fluid is l mix. Using equations (1-2) for the estimate of mixing velocity indicates that this time is proportional to du dy l ~ v mix du dy v mix 1. Hence: mix (1.9) Equation (1.9) tells us that the lumps of fluid will undergo changes as they travel between the points P and Q (shown in Figure 1.1) towards y =. Thus, the theoretical foundation of the mixing length hypothesis is not strong. On one hand, a turbulence model built on this formulation is unlikely to possess a very wide range of applicability. On the other hand, as the entire formulation is basically empirical, the usefulness and the justification of its approximations ultimately lies in how well the model performs in applications. 3

Despite its theoretical shortcomings, the mixing length model is able to reproduce experimental measurements quite well, especially in the case of free shear flows, like the far wake, the mixing layer and the jet. All three of these flows are self preserving flows. The mixing length model can easily be calibrated for each specific class of these flows, and the model predictions are consistent with measurements provided that the departure from the data used to calibrate the mixing length is not too large (Wilcox, 1994). 1.3 Mixing Length in Bubble Columns The physical meaning of the mixing length in bubble columns is not yet well understood. The bubble-liquid and bubble-bubble interactions are important potential factors that can influence the magnitude of the mixing length. Gas phase properties such as the mean bubble size and bubble size distribution, as well as the mean gas hold-up and gas hold-up profile determine the local and global flow structures. On one hand, the motion of the interstitial liquid phase is limited by multiple bubble-liquid interfaces, which can modify the turbulence structure in the bulk of the liquid phase. On the other hand, bubbles, while rising in liquid, create a high degree of agitation which tends to increase the turbulence, and hence, can increase the turbulence length scale in the liquid phase. Therefore, studying and understanding the relationship between the mixing length and bubble size and hold-up distribution is of vital importance. The mixing length model, as described above, has been implemented in the CFDLIB code and has been used extensively for modeling the liquid phase flow in bubble columns. So far, a constant mixing length has been used in these studies. However, measurements by CARPT and CT techniques at CREL have revealed that the mixing length values are not constant. The mixing length profiles can be determined from these measurements at different experimental conditions and generalized correlations can be proposed based on these data. In the present work, we perform simulations using CFDLIB code with a constant mixing length closure model to preliminarily evaluate the applicability of such a model and the sensitivity of the results to the magnitude of the mixing length. The governing equations and the implementation of this model in CFDLIB are presented first. 1.4 Governing Equations for Two-Phase Flow The ensemble averaged continuity or mass balance equation for phase k in the absence of chemical reaction, phase change and interfacial mass exchange can be written as: ρ t k k k +. ρ u = (1.1) k k k k where ρ = α ρ is the apparent density of phase k, ρ phase k material indicator, defined by: α k = 1 if material k is present otherwise is material density, and α k (1.11) is 4

The ensemble averaged momentum balance equation for phase k subject to the same above cited assumptions is given by (CFDLIB workshop, CFD 97 Conference): k k ρ u k k k +. ρ u u = rate of change t k θ p mean pressure θ k + ρ k g [ ( p p) I τ] + α +. α τ k. α ρ u u k k k k k body force interphase exchange average stress Reynolds stress (1.12) k = α is the volume fraction of phase k, p = p is the average pressure, p is pressure in phase k, and τ is phase k stress tensor. The interfacial momentum exchange is modeled by using the drag force for a single sphere. Its final form is given by: [ ( p p) I + ] F = C u u k kl k l 3 fluid l k τ α θ θ ρ d ( ul uk ) (1.13) 4 d where C d is the drag force coefficient. For modeling of Reynolds stresses, the widely used Boussinesq closure is assumed. This introduces an eddy viscosity which relates the Reynolds stresses to the mean velocity as shown bellow: k k k k k 2 k k α ρ u u = ρ k I νt S (1.14) 3 where k k k T 2 k S = u + ( u ) ( u ) I 3 p (1.15) The Boussinesq assumption reduces the closure problem to the modeling of the eddy viscosity, ν t and the turbulent kinetic energy, k. The eddy viscosity is modeled by the Prandtl mixing form as: { } l 2 tr S. S (1.16) ν t mix k k The length l mix can be chosen as a characteristic physical length to model all scales of turbulence or as a grid cell size to model sub-grid-scale turbulence. By neglecting the k-terms in equation (1.14), the Reynolds stresses can be written as a function of the turbulent viscosity and the mean shear rate, as given by the following expression: α ρ 2 k k k { mix ( ) } u u = ρ l tr S. S S (1.17) k k k k k 5

A more sophisticated form (using a higher order closure) of the eddy viscosity can be computed from the turbulent kinetic energy, k and its dissipation rate, ε : νt C k 2 = µ (1.18) ε This form requires the knowledge of k and ε locally. The transport equation for turbulent kinetic energy can be used and has following form (CFDLIB workshop, CFD 97 Conference; Hinze, 1975): ρ k k Dk Dt νt k k =. k + ρ νt tr( u. u ) ρ ε σ k k k k ( ) + β U F + θ θ ρ τ χ k χ k k kl kl k l l l k k (1.19) However, closure for ε must also be supplied. A point-wise or algebraic model can be constructed from the mixing length: 3 k 2 k = 3 4 (1.2) ε µ C k l mix In this case, the mixing length is still unknown and must be estimated. Therefore, the set of equations (1.18) and (1.19) does not represent a fully predictive model. Finally, an improved model can be constructed by writing a transport equation for the dissipation rate, ε also, which can be written by analogy to single phase turbulent flow. For a two-phase flow, this takes the form: ρ k k Dε Dt k k k { Cε1 ttr( u u ) Cε2 } ν σ ε ρ ε k t k k =. + ν. ε k k ε ρ + C β U F θ θ τ χ k χ 3 + k k ( ) k kl kl k l l l k k (1.21) The set of equations (1.18), (1.19) and (1.21) constitute a fully predictive twoequation turbulence model. 1.5 Simulation Results Gas-liquid flow in a two-dimensional bubble column was simulated using the CFDLIB code (version 97), with the mixing length closure form given by eq. (1.16). The properties of an air-water system at the ambient pressure and temperature were used. The column width and height were 14 cm and 15 cm, respectively. The initial liquid height was 1 cm. The assumed bubble diameter used for the calculation of the drag force was.5 cm. Simulations were performed using a superficial gas velocity of 12 cm/s. Constant mixing length values of.5 and 1 cm were used in eq. (1.16). A similar case was also run with the k-epsilon closure model, as described by eqs. (1.18), (1.19) and (1.21). All of the simulations were performed with a Cartesian grid of 3 x 15 cells. The typical time step in these simulations was of the order of 1-4 to 1-3 sec. The simulation results were saved in 1 second intervals, up to 5 seconds. The velocity and hold-up values were then averaged between t = 1 and t = 5 sec. 6

The averaged radial profiles of axial liquid velocity and gas hold-up obtained from the simulations with the mixing length values of.5 and 1 cm are shown in Figures 1.2 and 1.3. The experimental values for liquid velocities and gas hold-up measured in a three-dimensional cylindrical bubble column of 14 cm diameter for the same gas superficial velocity are also shown in Figures 1.2 and 1.3. It can be observed that an increase in the mixing length decreases the magnitude of the averaged liquid velocity in the central region of the column significantly. However, the effect is relatively smaller in the region near the wall where liquid flows downward. The same increase in mixing length has a much lesser effect on the averaged hold-up distribution. It can also be noted that the simulated velocity profiles in a two-dimensional column show the same trend as the velocity profiles in a real three-dimensional column, while the shape and magnitude of the two-dimensional simulated gas hold-up profiles are significantly different from those obtained in a real three-dimensional column. The simulated two-dimensional averaged velocity profile using the k-epsilon model is also compared with the experimental data in Figure 1.4 for the 3D column. The calculated velocity profiles in this case have a much flatter shape than the profiles obtained from the mixing length closure model. The use of the k-epsilon model was found to have a negligible effect on the gas hold-up profile. 1.6 Conclusions The mixing length turbulent closure model has been successful in the prediction of the self preserving single phase shear flows, and with some modifications has also been used for wall bounded flows. Due to its simplicity this kind of model has also been included in the two-phase flow simulation code. Moreover, the mixing length can also be evaluated by experimental facilities such as Computer-Aided Radioactive Particle Tracking (CARPT). This justifies its use as an empirical closure model in two-phase flow. In the present work, we used a mixing length closure model, as well as a k-epsilon model in order to predict the flow field in bubble columns, the main objectives being evaluation of the code, examining the sensitivity of the computations to the value of mixing length used as a constant, and also, to judge the performance of higher order models. The results obtained for the time averaged liquid velocity and gas hold-up radial profiles indicate that the value of the mixing length can significantly influence the prediction of the averaged velocity field in bubble columns. The results also showed that the use of a k-epsilon closure model resulted in very high turbulent viscosities and a poor prediction of the liquid velocity. One of the possible reasons for this disagreement can be the fact that the high Reynolds number k-epsilon model has been developed for shear induced turbulence, while bubble-induced turbulence has a major role in the production of the velocity fluctuations in bubble columns. Although, the effect of the interfacial slip has been introduced as an additional source term into the k-epsilon equations, the production of the turbulence kinetic energy by shear remains the dominant source in these equations. The study and modeling of the turbulence generated by the bubble phase is the subject of future work. 7

Another important remark is that the results of a 2D simulation can not directly be compared to the 3D flow field in a real column. The reasonable agreement between the measured and the predicted axial liquid velocity profiles is somewhat misleading and should not be used to derive any conclusion related to the performance and validity of the closure models. Both visual observations and experimental investigations of the flow in 2D and 3D bubble columns indicate major differences between the flow structure in these flows (Mudde et al., 1997, Lin et al., 1996). In a 3D bubble column, large bubble clusters undergo a helical motion in the mid-section between the center and the wall, and a large amount of smaller bubbles are induced toward the center of the column by this helical motion. In a 2D bubble column, the flow in the third dimension is non-existent, and the helical motion of the large bubbles is reduced to a snakelike motion, with the smaller bubbles trapped in the intermittent large scale vortices created by this flow close to the column wall. No significant hold-up peak is observed at the column center (Lin et al. 1996 and observations at CREL). Therefore, the comparison of the simulations with experimental data requires the experimental investigation of the flow field in a 2D column. This subject will also be included in future work. 1.7 Nomenclature C D C ε1, C ε2, C 3 C µ d p F kl G K K n l mix L P Re U u mix U V v mix x y Greek letters α β χ δ ε µ Dynamic viscosity Drag force coefficient Constants in eq. (2) Constant in eq. (18) Bubble diameter Drag Force Gravity constant Turbulent kinetic energy per unit mass Knudsen number Prandtl mixing length Flow length scale Pressure Reynolds number Velocity Mixing velocity in direction x Mean velocity in the main direction (x) in a shear flow Velocity in direction y Mixing velocity in direction y Direction of the main flow direction normal to the main flow Phase indicator Momentum exchange coeffiicient Momentum exchange term Thickness of boundary layer Dissipation rate of turbulence kinetic energy 8

ν Kinematic viscosity ρ Density θ Volume fraction τ Shear stress, particle relaxation time Subscripts or superscripts Pure material or phase l, k Phases k, l P Particle or bubble T Mathematical symbols < > ' D I T Tr Turbulent Ensemble average operator Fluctuation about mean Substantial differentiation operator Partial differentiation operator Differentiation operator Unit tensor Transpose of a vector Trace of a tensor 1.8 References CFDLIB Workshop, CFD 97 Conference in Victoria, British Columbia, Canada, May (1997). Degaleesan S. Fluid Dynamic Measurements and Modeling of Liquid Backmixing in Bubble columns D.Sc. Thesis, Washington University, St. Louis (1997). Hinze, J.O., Turbulence, 2 nd ed., McGraw-Hill, New York, (1975). Lin T.J., Reese J., Hong T., Fan L. S. Quantitative Analysis and Computation of Two- Dimensional Bubble Columns, AIChE Journal, 42, 31 (1996) Mudde R.F., Lee D. J., Reese J., Fan L. S. Role of Coherent Structures on Reynolds Stresses in a 2-D Bubble Column, AIChE Journal, 43 (4), 913-926 (1997). Prandtl L. Über die ausgebildete Turbulenz, ZAMM, 5, 136-139 (1925). Townsend A. A. The Structure of the Turbulent Shear Flow, Second Ed., Cambridge University Press, Cambridge (1976). Wilcox D. C. Turbulence Modeling for CFD, Second Ed., DWC Industries, Inc., La Cañada, California (1994). 9

4 Liquid velocity (cm/s) 2-2 lmix =.5 cm lmix = 1 cm Measured -4.2.4.6.8 1 r/r Figure 1.2: Simulated time averaged radial profiles of liquid axial velocity using different mixing length values. System: air-water; reactor diameter: 14 cm; superficial gas velocity: 12 cm/s..4.3 Gas hold-up.2.1 lmix =.5 cm lmix = 1 cm Measured.2.4.6.8 1 r/r Figure 1.3: Simulated time averaged gas hold-up profiles using different mixing length values. System: air-water; reactor diameter: 14 cm; superficial gas velocity: 12 cm/s. 1

4 Liquid velocity (cm/s) 2-2 Measured k-epsilon -4.2.4.6.8 1 r/r Figure 1.4: Simulated time averaged radial profiles of liquid axial velocity using k- epsilon model. System: air-water; reactor diameter:14 cm; superficial gas velocity: 12 cm/s. 11

2. SCALE-UP OF FLUID DYNAMIC PARAMETERS 2.1 Introduction The design and scale-up of bubble column reactors are very important in chemical industry. Studies of the effects of equipment scale and operating conditions on the fluid dynamic parameters by using experimental data obtained by Computer Automated Radioactive Particle Tracking (CARPT) and Computed Tomograghy (CT) and from the literature will aid in the design and scale-up of bubble column reactors. Our specific focus is on utilizing the available hydrodynamics information to model liquid mixing in bubble columns in the churn-turbulent flow regime. In this regard, the fluid dynamic parameters of interest are the gas holdup and holdup profile, the liquid recirculation velocity and liquid turbulence which can be quantified by the turbulent eddy diffusivities. Gas holdup plays an important role in bubble column fluid dynamics. The global gas holdup determines the residence time of the gas phase and the pressure drop in the system. The local gas holdup, determined by the bubble size and number density, influences the rate of liquid recirculation and mass transfer across the gas-liquid interface. It is the non-uniform gas holdup distribution, resulting from the various forces acting on gas bubbles, that drives the flow in the system, inducing the generation of turbulent eddies, phase interactions and liquid recirculation. Gas holdup is closely dependent on bubble sizes, their distribution and frequency of formation. These in turn depend on a number of factors: 1) the operating conditions, such as the superficial velocities, pressure and temperature of the system, 2) process specific variables, such as the physical properties of the individual phases, and 3) column geometry which includes the column diameter, distributor type and type of internals, if any. Numerous experimental studies reported in the literature discuss the effects of the various parameters, stated above, on gas holdup. These fall into two categories: global or overall gas holdup and local void fraction measurements. Global holdup measurements, owing to their relative ease of obtaining data, have been the predominant subject of research and experimental study. Investigations in various systems (e.g., Krishna and Ellenberger 1996; Wilkinson et al. 1992; Reilly el al. 1994; Hammer et al. 1984), under different operating conditions, have aided in understanding the effects of system parameters and process variables on global gas holdup, and have resulted in several correlations (Degaleesan, S. 1997). However, there is yet no single correlation that performs well under all process conditions. Reports on measurement of local void fractions and their spatial distribution are more recent and still relatively scarce. Nottenkamper et al. (1983), Menzel et al. (199), De Lasa et al. (1984), Kumar (1994) and Groen et al. (1995), among others (Degaleesan, S. 1997), have used different techniques to measure the local void fraction and in some cases bubble sizes and phase velocities in bubble columns. Such local measurements have predominantly been used to study air-water systems under atmospheric conditions, due to simplicity of the system. Recently Adkins et al. (1996) obtained measurements of local void fraction profiles in 12

slurry bubble columns operating under industrial conditions, using Nuclear Gauge Densitometry (NGD), to study the effects of pressure and temperature on the local gas holdup profile. They showed that, at high gas velocities (1-12 cm/s) the overall gas holdup increases with pressure. However, the radial gas holdup profile at high pressure is similar (parabolic) to that in an air-water system, at atmospheric pressure. For the design and modeling of industrial bubble column reactors using phenomenological models, information on the local fluid dynamics parameters, in addition to global parameters (such as the gas holdup), is needed at industrial conditions of interest. While there exists abundant experimental information on the global gas holdup in different systems (liquid and gas properties, presence of solids, high temperature and pressure), information on the local holdup and holdup profiles, and other local fluid dynamic parameters, is still currently restricted to air-water systems. For example, measurements of the local liquid velocities have so far been made only in atmospheric air-water systems ((Hills 1974; Nottenkamper et al. 1983; Franz et al. 1984; Menzel et al. 199; Devanathan et al. 199; etc.). This is mainly due to the difficulties associated with applying the different experimental techniques, for local measurements, to industrially relevant systems (Kumar et al. 1997). In light of these limitations, the objective of this report is to consolidate the global holdup characteristics, for which there is abundant experimental data in a variety of operating and process conditions, with the information on holdup distribution and other fluid dynamic parameters, existing only for air-water systems. The aim is to develop a basis for the approximate characterization of churn-turbulent bubble columns, which enables the estimation of certain local fluid dynamic parameters in industrial systems, based on measurements of these parameters in air-water atmospheric systems. It is well known that changes in distributor and trace impurities (in air-water systems) can affect two-phase flows considerably. Nevertheless, it is expected that such effects are more pronounced for bubbly flows and tend to diminish in the churn-turbulent flow regime. The proposed analysis is hence applied only to the churn-turbulent flow regime, in large diameter columns, greater than 1 cm in diameter. In small diameter columns, at high gas velocities slugging flow occurs, which is characteristically different from churn-turbulent flows (Shah et al. 1982). 2.2 Gas Holdup The influence of gas velocity and column diameter on the overall gas holdup in air-water bubble columns, is considered in this section. The study is based on experimental data for the global gas holdup from the present investigation and the literature. To this date a generally accepted holdup correlation in terms of dimensionless group is not available. As a general rule, gas holdup increases with superficial gas velocity. The absolute value of gas holdup at low gas velocities in the bubbly flow regime is affected by the type of distributor used and the presence of trace contaminants in the water. However, with increase in gas velocity, well into the heterogeneous flow regime, these differences 13

diminish. Gas holdup dependence on superficial gas velocity can be expressed in the form ε g n U g (2.1) where the exponent n depends on the flow regime (Shah et al.1982). Most studies from the literature suggest that total gas holdup does not depend on the diameter of the column, for columns that are 15 cm or greater in diameter (for example, Reith et al. 1968; Akita and Yoshida 1973; Wilkinson et al. 1991). The experimental data considered in most of these investigations are for gas velocities below 2 cm/s. DeSwart (1996), shows that the effect of column diameter, while negligible at low gas velocities, becomes noticeable in the churn-turbulent regime at higher velocities ( 2 cm/s). These observations are in agreement with experimental measurements for the global gas holdup by Nottenkamper et al. (1983), as shown in Figure 2.1 along with data obtained by Degaleesan (1997) in air-water data (Reilly 1994; Guy et al. 1986; Myers 1986; Reith et al. 1968, Kumar 1994). It is seen from Figure 2.1 that at low gas velocities there is no prominent effect of column diameter on the global gas holdup. With increase in gas velocity the effect becomes apparent and at very high velocities, much greater than 2 cm/s, there is a significant influence of column diameter on holdup. The existing correlations (other than the correlation for large bubbles by Krishna and Ellenberger (1996)) do not account for such diameter effects (Figure 2.1). Figure 2.1 Average gas holdup as a function of column diameter and superficial gas velocity (Solid line represent equation 2.2) The experimental data for the global gas holdup, shown in Figure 2.1, is correlated to 14

account for effects of column diameter and gas velocity on the global gas holdup, which results in the following equation:.474.626dc ε g =. 7U g (in cgs units) (2.2) At low gas velocities, the above equation results in global gas holdup values which are in broad agreement with predictions of literature correlations (Reilly et al. 1986; Hammer et al. 1984). At higher gas velocities, it is able to capture the effects of column diameter, as observed from the data of Nottenkamper et al.(1983), which represent the only data in the open literature for gas holdup at very high gas velocities in air-water systems. Additional data in large diameter columns at high gas velocities is necessary to verify Equation 2.2. 2.3 Liquid Recirculating Velocity Time averaged results from various experimental techniques indicate the existence of global liquid recirculation in the time averaged sense, with liquid flowing upward in the central region of the column, and downward near the wall. In the well developed region, (middle section in large L/D columns), this is represented by a recirculating axial liquid velocity profile, with negligible radial velocities. Liquid recirculation in its simplest form is modeled using the one dimensional recirculation model (Kumar 1994) for predicting the time-averaged axial liquid velocity profile. This model requires as input the radial gas holdup profile and a closure for the turbulent shear stress (typically using either eddy viscosity or mixing length). Experimental measurements are used to supply the input radial holdup profile to the model. For example, using the difference in Nuclear Gauge Densitometry (NGD) and pressure drop determined mean holdups one can construct a radial gas holdup profile (Degleesan 1997). The mixing length (or eddy viscosity) is the other unknown, to which the model is found to be very sensitive (Kumar 1994). Various attempts have been made at developing functional forms for the eddy viscosity (Ueyama and Miyauchi 1979) and mixing length (Clark et al. 1987; Luo and Svendsen 1991; Rice and Geary 199) required for solving the one dimensional model. However, Kumar (1994) shows that there is truly no universal expression for the mixing length or the eddy viscosity that can be successfully used under a wide range of operating conditions, to predict the liquid recirculating velocity profile. In the present investigation the effect of scale on liquid recirculation in air-water atmospheric systems, is studied by considering a mean liquid recirculation velocity or an average liquid upflow velocity, defined as: u rec * r u ( r) ε ( r) rdr z = * r l l ε ( r) rdr (2.3) where r * represents the radial position of flow inversion. The above expression holds for the case of batch liquid (U l =) and in situations of low superficial liquid velocities, such as those typically encountered in bubble column operations, where U l <<. u rec 15

Experimental data for the liquid velocity profile (u z (r)) and the holdup profile (ε l (r)), from the literature and the present investigation, are used to calculate u rec for various operating conditions (U g, and D c > 1 cm) in air-water systems. The results are plotted in Figure 2.2. Assuming the following functional form for the dependence of u rec on column diameter and gas velocity, u rec m D U c n g (2.4) and performing a regression using the data from CARPT/CT (CT data for the holdup profile is taken from Kumar (1994)), and data from Nottenkamper et al. (1983) at U g =82.3 cm/s, yields m=n=.4. Thereby we arrive at the following expression for : u rec u ( cm / s) = 2. 2D U.4.4 rec c g (2.5) u rec Liquid circulation velocity,, calculated from the above equation compares reasonably well with the data of Menzel et al. (199) and Nottenkamper et al. (1983) at U g = 32.4 cm/s, as shown in Figure 2.2. A similar dependency of (U g D c ).33 has been reported by Joshi and Sharma (1979) and Zehner (1982) for the liquid circulation velocity that was derived based on the assumption of the existence of multiple circulation cells. Koide et al. (1979) report a dependency of D.5 c and U.28 g for the centerline liquid velocity. Equation 2.5, developed here, can be used to estimate the mean recirculation liquid velocity in an air-water bubble column (D c > 1 cm), at atmospheric pressure operating in the churn turbulent flow regime. It is evident, however, from Figure 2.2, that much more data is needed to confirm the proposed correlation. Hence, extension of the data base especially to larger gas velocities and larger diameter columns is necessary. 16

Figure 2.2 Effect of superficial gas velocity and column diameter on mean liquid recirculating velocity With the knowledge of the mean recirculation velocity, u rec, and the holdup profile, it is possible to calculate the liquid recirculation velocity profile in the column by a procedure described in Figure 2.3. The one dimensional model of Kumar et al. (1994) is considered here. An estimate of the mixing length profile (Kumar et al. 1994) is assumed and used in the one dimensional model, along with a known holdup distribution, to calculate the liquid recirculating velocity profile, u z (r). The centerline velocity, u z (), and therefore the mean, u will depend on the mixing length profile used. The average recirculating rec velocity, u rec, est, calculated from u z (r) using Equation 2.3, is compared with the estimated mean recirculation velocity, urec, calc, obtained from Equation 2.5, for a given superficial gas velocity and column diameter. The mixing length profile is suitably adjusted until urec, calc = urec, est, which then yields an approximate value for the required radial profile of the axial liquid velocity. Using the above procedure, the liquid velocity profile can be evaluated, provided the radial gas holdup profile in the column is known. (This is obtainable from NGD and pressure drop measurements). 17

2.4 Conclusions Figure 2.3 Determination of the liquid recirculating velocity profile, u z (r), with knowledge of ε l (ξ ) and In this report scale up issues have been discussed for the fluid dynamics parameters, such as gas holdup and liquid recirculating velocity in the churn turbulent flow regime in large diameter columns (> 1 cm). Using experimental data, from the present work and from the literature, equations have been developed for the prediction of the mean liquid recirculating velocity in airwater atmospheric systems. The scale up issues for the time average eddy diffusivities and a methodology which enables the estimation of the mean liquid recirculating velocity, in the churn turbulent flow regime, in systems of industrial interest, e.g., high pressure and high temperature, using the data generated in air water systems are being developed and will be reported later. 2.5 References Adkins, D. R., K. A. Shollenberger, T. J. O Hern and J. R. Torczynski, Pressure Effects on Bubble Column Flow Characteristics, ANS Proceedings of the National Heat Transfer Conference, THD-Vol. 9, 318-325 (1996). Clark, N. N., C. M. Atkinson and R. L. C. Flemmer, Turbulent Circulation in Bubble Columns, AIChE Journal, Vol. 33, 575-578 (1987). u rec 18

De Lasa, H. I., S. L. P. Lee and M. A. Bergougnou, Bubble Measurement in Three- Phase Fluidized Beds Using a U-Shaped Optical Fiber, Can. J. Chem. Eng., Vol. 62, 165-169 (1984). Devanathan, N., D. Moslemian and M. P. Dudukovic, Flow Mapping in Bubble Columns Usin CARPT, Chem. Eng. Sci., Vol. 45, 2285-2291 (199). De Swart, J. W. A., Scale-up of a Fischer-tropsch Slurry Reactor, Ph. D. Thesis, University of Amsterdam, The Netherlands (1996). Degaleesan, S., Fluid Dynamic Measurements and Modeling of Liquid Mixing in Bubble Columns, D. Sc. Thesis, Washington University, St. Louis, MO (1997). Franz, K., T. Borner, H. J. Kantorek and R. Buchholz, Flow Structures in Bubble Columns, Ger. Chem. Eng., Vol. 7, 365-374 (1984). Groen, J. S., R. F. Mudde and H. E. A. van den Akker, Time Depandent Behavior of the Flow in a Bubble Column, Trans. Inst. Chem. Engr., A9-A16 (1995). Guy, C., P. J. Carreau and J. Paris, Mixing Characteristics and Gas Holdup of a Bubble column, Can J. Chem. Eng., Vol. 64, 23-35 (1986). Hammer, H., H. schrag, K. Hektor, K. Schonau, W. Kuster, A. Soemarno, U. Sahabi and W. Napp, New Sub-Functions on Hydrdynamics, Heat and Mass Transfer for Gas/ Liquid and Gas/liquid/solid Chemical and Biochemical Reactors, Frontiers in Chemical Reaction Engineering, 464-474 (1984). Hills, J. H., Radial Non-Uniformity of Velocity and Coidage in a Bubble Column, Trans. Inst. Chem. Engrs., Vol. 52, 1-9 (1974). Joshi, J. B. and M. M. Sharma, A Circulation Cell Model for Bubble Columns, Trans. Inst. Chem. Engrs., Vol. 57, 244-251 (1979). Kumar, S. B., N. Devanathan, D. Moslemian and M. P. Dudukovic, Effect of Scale on Liquid Recirculation in Bubble Columns, Chem. Eng. Sci., Vol 49, 5637-5652 (1994). Kumar, S. B., M. P. Dudukovic and B. A. Toseland, Measurement Techniques for Local and Global Fluid Dynamic Quantities in Two and Three Phase Systems, Non- Invasive Monitoring of Multiphase Flows, Edited by J. Chaouki, F. Larachi and M. P. Dudukovic, Elsevier, Chapter1, 1-46 (1997). Krishna, R., J. W. A. de Swart, J. Ellenberger, G. B. Martina and C. Maretto, Gas Holdup in Slurry Bubble Columns: Effect of Column Diameter and Slurry Concentrations, AIChE Journal, Vol. 33, 311-316 (1997a). 19

Koide, J., S. Morooka, K. Ueyama, A. Matsura, F. Yamashita, S. Jwamoto, Y. Kato, H. Inoue, M. Shigeti, S. Suzuki and T. Akehata, Behavior of Bubble in Large Scale Bubble Columns, J. Chem. Eng. Of Japan, Vol. 12, 98-14 (1979). Luo, H. and H. F. Svendsen, Turbulent Circulation in Bubble Columns from Eddy Viscosity Distributions of Single-Phase Pipe Flow, Can. J. Chem. Eng., Vol. 69, 1389-1394 (1991). Menzel, T., T. in der Weide, O. Staudacher, O. Wein and U. Onken, Reynolds Shear Stress for Modeling of Bubble Column Reactors, Ind. Eng. Chem. Res., Vol. 29, 988-994 (199). Myers, K. J., Liquid-Phase Mixing in Churn-Turbulent Bubble Columns, D. Sc. Thesis, Washington University, St. Louis, MO (1986). Nottenkamper, R., A. Steiff and P.-M. Weinspach, Experimental Investigation of Hydrodynamics of Bubble Columns, Ger. Chem. Eng., Vol. 6, 147-155 (1983). Reilly, I. G., D. S. Scott, T. J. W. de Bruin, A. Jain and J. Piskorz, Correlation for Gas Holdup in Turbulent Coalescing Bubble Columns, Can. J. Chem. Eng., Vol. 64, 75-717 (1986). Reilly, I. G., D. S. Scott, T. J. W. de Bruin and D. MacIntyre, The Role of Gas Momentum in Determining Gas Holdup and Hydrodynamic Flow Regimes in Bubble Column Operations, Can. J. Chem. Eng., Vol. 72, 3-12 (1994). Reith, T. S. Renken and B. A. Israel, Gas Holdup and Axial Mixing in the Fluid Phase of Bubble Columns, Chem. Eng. Sci., Vol. 23, 619-629 (1968). Rice, R. G. and N. W. Geary, Prediction of Liquid Circulation in Viscous Bubble Columns, AIChE Joural, Vol. 36, 1339-1348 (199). Shah, Y. T., B. G. Kelkar, S. P. Godbole and W. D. Deckwer, Design Parameter estimations for Bubble Column Reactors, AIChE Journal, Vol. 28, 353-379 (1982). Ueyama, K. and T. Miyauchi, Properties of Recirculating Turbulent Two Phase Flow in Gas Bubble Columns, AIChE Journal, Vol. 25, 258-265 (1979). Wilkinson, P. M., A. P. Spek and L. L. van Dierendonck, Design Parameters Estimation for Scale-up of High-Pressure Bubble Columns, AIChE Journal, Vol. 38, 544-554 (1992). Zehner, P., Impuls-, Stoff- und Warmetransport in Basensaulen, Chem. Ing. Tech., Vol. 54, 248-251 (1982). 2

3. COMPARISON OF TIME AVERAGED LIQUID (SLURRY) VELOCITY PROFILES IN GAS-LIQUID (G-L) AND GAS-LIQUID-SOLID (G-L-S) SLURRY BUBBLE COLUMNS 3.1 Introduction Slurry bubble column reactors are presently used for a wide range of reactions in both chemical and biochemical industry. The successful design and scale up of bubble column reactors require understanding of multiphase fluid dynamics and its influence on phase mixing and transport characteristics. However, due to the complexity of flow dynamics involved slurry bubble column reactors are not yet fully understood. Considerable effort has been directed towards the computational fluid dynamics modeling of both two- and three-phase bubble column systems. Multiphase turbulence still remains a major unresolved problem. Due to that fact, phenomenological models are still widely used to describe two phase flows. These models require prior knowledge of the flow structure. However, although both G-L and G-L-S slurry systems are not yet fully understood, much of the experimental and modeling work done until today refers to G-L systems. Possible and logical starting approach in slurry modeling is to investigate extrapolation of gas-liquid scale-up and design experimental correlations and modeling techniques to slurry, pseudo two-phase, systems. Recently, CARPT technique has been recognized as a powerful tool for acquiring accurate and reliable experimental data for the liquid phase velocity and turbulent parameters. Over the past few years our laboratory adopted and improved the CARPT technique. Both, gas-liquid and gas-liquid-solid slurry systems have been studied. In this report we will try to summarize our findings by comparing time averaged axial and radial velocity profiles in gas-liquid and gas-liquid-solid systems. 3.2 Experimental Conditions The effect of column diameter, gas superficial velocity, sparger design and solids loading on liquid/slurry velocity have been studied. The operating conditions used for G-L and G-L-S slurry systems are listed in Table 3.1 and 3.2, respectively. Sparger design specifications used in the experiments are listed in Table 3.3. Column diameter in inch (cm) G-L system Table 3.1: Operating conditions used for study of G-L systems 4 (1.2) 6 (14) air - 5% water /5% isopropanol (density:.917 g/cm 3 ;viscosity: 2.78 cp) air water (density:.998 g/cm 3 ; viscosity:.95 cp) Gas superficial velocity 4-12 2.4-12 range, cm/s Liquid mode batch batch Sparger perforated plate, bubble cap perforated plate 21

Radioactive particle Scandium Sc 46 sealed in neutrally buoyant 2.38 mm polypropylene sphere Scandium Sc 46 sealed in neutrally buoyant 2.38 mm polypropylene sphere Table 3.2: Operating conditions used for study of G-L-S slurry systems Column diameter in inch 4 (1.2) 6 (14) (cm) G-L-S system air - 5% water /5% isopropanol air - water - glass beads - alumina Gas superficial velocity 2-8 2-14 range, cm/s Slurry mode batch batch Solid particle diameter (µm) 4-16 125-177 Solids loading, wt. % 1 (density:.986 g/cm 3 ; viscosity: 3.5 cp) 7, 14 and 2 (density: 1.47, 1.1 and 1.15 g/cm 3 ; viscosity: 1.2, 1.11, 1.2 cp, respectively) Sparger sintered plate perforated plate perforated plate Radioactive particle Scandium Sc 46 sealed in neutrally buoyant 2.38 mm polypropylene sphere Scandium Sc 46 weight matched to 15 µm glass bead particle Table 3.3: Sparger designs used in G-L and G-L-S systems studies Column diameter, inch 4 6 Sintered plate (SP) Pore size: D H =2µm Perforated plate (PP) Number of holes: N H =94 Number of holes: N H =61 Hole diameter: D H =.5mm Hole diameter: D H =.4mm Pattern: Hexagonal Pattern: 3 concentric circles 15 mm apart Bubble cap (BC) Nozzle diameter: D N =1.27cm Cap diameter: D C =2.7cm Cap height: H C =7.cm Cap clearance: 3.cm 3.3 Results and Analysis 3.3.1 Time Averaged Axial Velocity Profiles A sample of the processed data is included to show some of the effects of the operating conditions. The 4 inch column data shows (Fig. 3.1.a) that a change from perforated plate 22

to a bubble cap sparger affects gas-liquid flow considerably (1% variation in centerline liquid velocity). A change from sintered plate to perforated plate also affects the flow in the gas-liquid system but to a lesser extent (not shown) but considerably more than in the gas-liquid-solid system (shown in Figure 3.1). The variation in gas superficial velocity also has a smaller influence on the time averaged axial velocity profiles in slurries than in G-L systems (Fig. 3.1.b). In line with this finding the effect of gas superficial velocity is more noticeable in slurries with lower (7 wt.%) than higher (2 wt.%) solids loading. As shown in Figure 3.2.a, a change in solids loading, while keeping the superficial gas velocity constant, changes the axial slurry velocity profiles up to only 2% (6 inch column). In both columns and systems a fully developed axial velocity profile was reached after approximately 2 column diameters in slurries (Fig. 3.2.b) compared to approximately 1 diameter in G-L systems. In the 4 inch column, for the air-alcohol solution systems (smaller bubble size) the velocity inversion point occurred between r/r=.6 and.65 in both G-L and slurry systems (Fig. 3.1.a and 3.1.b). In the 6 inch column with air-water systems (larger bubble size) the velocity inversion point occurred around r/r=.7 in G-L and around r/r=.65 (even.6 in 2 wt.%) in slurry systems (Fig. 3.2.a). This must be the effect of different liquid physical properties (bubble size distribution is greatly effected by liquid density, viscosity, surface tension and solids loading) and different velocity/loading ratio (ratio between inertial and gravity/buoyancy forces). In our experiments the addition of alcohol caused a big change in surface tension (primary effect) and some change in density and viscosity (secondary effect) of liquid. Dc=4in. 4 3 2 Axial Velocity Profiles Z=36.9cm pp-u8-gl bc-u8-gl sp-u8-gls pp-u8-gls Dc=4in. 4 3 2 Axial Velocity Profiles Z=36.9cm pp-u8-gl pp-u8-gls pp-u4-gl pp-u4-gls Uax, cm/s 1 Uax, cm/s 1-1 -1-2 -3 a)..2.4.6.8 1. r/r -2-3 b)..2.4.6.8 1. r/r Figure 3.1: Influence of sparger design (a) and superficial gas velocity (b) on time averaged axial velocity profiles of G-L and G-L-S slurry systems. (pp, bc and sp are defined in Table 3.3, u8 indicates superficial gas velocity of 8 cm/s and u4 of 4 cm/s. Solid loading is 1% wt). 23