2003 International Symposium on Hydrometallurgy Edited by C. Young TMS (The Minerals, Metals & Materials Society), 2003
CFD IN AUTOCLAVE CIRCUIT DESIGN Lanre Oshinowo, Lowy Gunnewiek and Kevin Fraser Hatch Associates Ltd. 2800 Speakman Drive Mississauga, Ontario, CANADA L5K 2R7 Abstract The trend in process engineering is to design compact, more efficient processes, there is the paramount requirement to get the job done right the first time going from the drawing board to full-scale commercial operation. To accomplish this goal, there is also the need for tools beyond the traditional engineering toolkit to evaluate designs through virtual prototyping, thereby reducing the risks associated with making design decisions. One of the most important tools that has recently come to the forefront of process design and development is Computational Fluid Dynamics (CFD). CFD has been used at HATCH to address the key process parameters that drive the design of hydrometallurgical unit operations. This paper will detail the role of CFD at HATCH in achieving a superior level of confidence in the process design of autoclave circuits. Specifically, the optimum application of multiphase modeling including hydrodynamic, heat and mass transfer to hydrometallurgy operations, the impact of non-Newtonian slurry rheology on autoclave performance, and the challenges of optimizing the mixing of key reactants into slurries in autoclave reactors, is discussed. Introduction Modern metallurgical operations require process intensification and higher efficiencies while striving to protect capital investment, market position and return on investment capital. With process enhancements and the application of new technology that pushes the envelope on materials of construction, new plants become a very expensive capital and risky investment. Hence, the efficiency and optimization of process design is paramount to achieving targets for the unit operations. And requires an in-depth evaluation and understanding of the process. The traditional approach of employing a combination of process experience, simplified analytical and empirical models with trial and error are no longer acceptable. A multidisciplinary group at Hatch is experienced in the design, construction and operation of modern hydrometallurgical facilities and autoclave circuit design. CFD is one of the indispensable tools utilized by Hatch and has been integrated into the autoclave circuit design practice and is used to manage the technological risk of unit operation design. CFD is the science of predicting fluid flow, heat transfer, mass transfer, chemical reactions, phase change, multiphase flow, and related phenomena by solving the mathematical equations that govern these processes. The results of CFD analyses are relevant engineering data used in conceptual studies of new designs, detailed process development, troubleshooting and redesign. Using CFD, many variations in design can be made, virtually, before deciding on an optimal configuration and committing to building a physical prototype. The commercial CFD software, FLUENT (1), is used at Hatch and for the work presented in this paper. Hydrometallurgical process operations involve the transport and conversion of an ore through various unit operations with water as the primary phase. When autoclaves are used in hydrometallurgical processes, the unit operations typically operate at temperature and pressure with corresponding chemical reactions. Unit operations in an autoclave circuit include mixers, settlers, clarifiers, hydrocyclones, off-gas systems, heat exchangers, flash vessels, and the autoclave(s). It is typically difficult to establish similarity between the commercial and lab scale
for the important dimensionless groups when testing on lab or pilot scale equipment. This makes CFD one of the only means to evaluate the performance of industrial-scale designs. The fluid flow phenomena in the autoclave circuit and in hydrometallurgical applications are complex due to the presence of multiple phases. The complexity of modeling multiphase systems is one of the reasons that CFD is not as widely deployed in the chemical and metallurgical process industry as it is in the aerospace and automotive industries. However, faster computers, better numerical models of more complex physics and more user-friendly commercial CFD codes has now made the challenging applications in the hydrometallurgical process more accessible than in the past (2). A survey of metallurgy literature on the subject of CFD reflects the rapidly growing trend with an order of magnitude increase over the past 10 years (See Figure 1). Two databases were used as a basis for the survey: The Engineering Compendex®, a comprehensive interdisciplinary engineering database referencing 5,000 engineering journals and conference materials and; the Metadex® index is a source for publications in the field of metallurgy and material sciences. The growth in usage is indicative of the utility of CFD as a tool for enabling engineers to design and troubleshoot systems when traditional correlations and rules-of-thumb are not. This paper will address the application of CFD to unit operations in the autoclave circuit. This paper is not fully comprehensive since many applications are yet to be addressed. However, it does provide an assessment of the application of CFD in the field of hydrometallurgy, in particular, the autoclave circuit. First, a description of the modeling methodology as pertaining to the multiphase flows will be discussed followed by the presentation and discussion of different applications.
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Figure 1. Number of publications on CFD on the Engineering Compendex and Metadex scientific publication databases. Modeling Multiphase Flow using CFD Modelling multiphase flows using CFD is complicated by the physics of the phenomena that makes the solution of said problems to be typically computationally expensive. Most multiphase models use empirical or semi-empirical descriptions of phase momentum, heat and mass interactions. Therefore, validation and verification of the models is required for each application. There are a number of models that are used to model multiphase flow: Lagrangian-Eulerian model, drift flux or slip mixture models, Eulerian and Eulerian Granular models. The applicability, and therefore, the choice of these models, is typically dependent on a knowledge of the volume concentration of the secondary solid phase in the primary fluid phase with the exception of the Eulerian models. The Lagrangian Eulerian model solves the equation of motion for the discrete particle trajectories. The coupling between the phases through drag
terms can be modeled but accumulation of particles cannot be modeled. The drift flux and slip mixture models are homogeneous mixture models for modeling multiphase flows. These models are ideally suited to modeling particles with relaxation times less than 0.001-0.01 seconds and in low concentrations. The Eulerian models are the most rigorous of the multiphase models and model the multiple phases as interpenetrating continua. A separate set of momentum equations is solved for each phase. The interaction between the phases is modeled through the momentum exchange terms and includes the drag exerted by the continuous phase on the dispersed phase. In the Eulerian Granular model, the granular momentum equation includes a solids stress tensor that is modeled based on the kinetic theory for granular flow. Numerics All transport equations are solved using second-order discretization and the typical residual convergence criteria are 1x10-4 for continuity, momentum and turbulence equations and 1x10-5 for the scalar equations. The residual computed by FLUENT's segregated solver is the imbalance in the equation solved at the cell center summed over all the computational cells and scaled by a factor representative of the flow rate of the variable through the domain. A scaled residual of 1x10-4 represents an error magnitude of approximately 0.01% in the transport equation. Validation and Verification Validation is essential to ensure that CFD can be used with confidence. Our approach is to validate the models based on the efficacy of the sub-models in predicting the macrohydrodynamics of the process. For example, the Eulerian Granular multiphase model requires sub-models for the interphase interactions of momentum, heat and mass transfer and the default models available in the CFD software FLUENT are not always applicable. If this occurs, additional models, determined by validation work to be more accurate, are added through custom subroutines. In this section, two applications of the Eulerian Granular multiphase model were validated against experimental data in the literature. Solids Suspension in Mixing Tanks Measurements of the axial distribution of solids concentration by Godfrey & Zhu (3) were considered for validation to determine the influence of agitation speed and particle diameter on the axial distribution of solids concentration. The axial distribution of solids is an important design requirement for autoclave design. A summary of the stirred tank geometry and liquid and solid property data are listed in Table I. Table I: Tank, impeller and material properties from Godfrey and Zhu (3). D – impeller diameter, C –off-bottom clearance, T – tank diameter, N – shaft speed, H – liquid level.
Geometry Single, pitched-blade turbine (four blades at 45°) D = T/3; C = T/5 N = 1000, 1600 rpm T = H = 0.154 m
Liquid Solids
Properties ρ = 1096 kg/m3 µ = 1.76 cp ρ = 2480 kg/m3 d50 = 231, 390µm
No-slip boundary conditions (u=v=w=0) for both phases are applied on the tank walls and shaft with the latter having a prescribed rotational velocity. The free surface of the suspension is described by zero gradients of velocity and all other variables. Since the shear stress is zero, the free surface can be interpreted as a slip wall. The impellers were modeled implicitly using internal boundary conditions based on laser Doppler velocimetry (LDV) data supplied by the impeller manufacturers. The impellers can also be modeled explicitly in three-dimensions using
the multiple reference frames or sliding mesh models but add to the computational expense of the calculations. Due to the simplicity of the mixing tank geometry and the implicit treatment of the impellers, the stirred tanks were set up as 2D axisymmetric models with a transport equation for swirl. The system was also modelled in 3D for comparison. To account for the presence of the baffles, the tangential velocity is reduced to zero in the baffle region. By modeling the mixing tank in two dimensions, the simulation runtime is considerably reduced. The 2D computational grids consisted of approximately 3,000 cells. Figure 2 shows the flow field and volume fraction distribution of 390 µm particles in the tank with an agitation speed of 1000 rpm. The axial pumping impeller establishes a single flow loop in the bottom half of the vessel. The cloud height of the suspension is constrained to this region. Figure 3(a) shows the axial profiles of normalized solids concentration X (local solids concentration/average solids concentration, the average solids concentration was 12vol%) for 390 µm particles at 1000 and 1600-rpm agitation speeds. The solids concentration measurements were made mid-way between the impeller and the baffle. Both the 2D and 3D CFD predictions of the solids concentration profiles are in good agreement with the experimental measurements and the cloud height is predicted correctly. At the lower agitation speed, the solids are not completely suspended and a cloud height forms as shown by the transition in the axial concentration profile. The height of the particle cloud coincides with the change in direction in the bulk flow pattern (see Figure 2(a)). As the agitator speed is increased to 1600 rpm, the suspension becomes more homogeneous or completely suspended and no appreciable transition in the axial concentration profile is observed. Figure 3(b) shows the axial profiles of normalized solids concentration X for 231 and 390 µm particles at an agitation speed of 1000 rpm. There is good agreement between the predictions and the experimental measurements. As the particle diameter decreases, the drag and slip velocity decrease allowing the solids phase to be transported more easily by the continuous phase increasing the dispersion of solids in the tank. Therefore, by reducing the particle diameter, at constant impeller speed, the suspension becomes more complete. The agreement with experimental data from the literature is very good demonstrating that CFD can be used to predict the suspension of solids, including the velocity distribution of the solids and liquid, and the cloud height of the suspension. (-)
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Figure 2: Flow Field Distribution at N = 1000 rpm and 390 µm particles (a) Liquid flow field vectors: 0 - 0.95 m/s (b) Solids Volume Fraction showing the cloud height just past mid-way up the tank.
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Figure 3: Axial distribution of solids concentration (a) Influence of agitation speed (Particle diameter of 390 µm) (b) Influence of particle diameter (Agitation speed of 1000 rpm). Experimental data from Godfrey and Zhu (3). Z is normalized height in the vessel. CFD grid sizes are shown in parentheses. Liquid-Solid Fluidization The fluidization or suspension of a solid by a liquid using non-mechanical means provides another rigorous test for the Eulerian Granular model. An example of a conical fluidized was selected due to the complex flow regimes that develop as the flow in the bed increases. At low superficial liquid velocities, the bed remains in a fixed state. As the velocity in increased, the smaller cross-section at the bottom of the reactor allows for the liquid superficial velocity to exceed the minimum fluidization of the solids. The bottom part of the bed is fluidized while the top remains fixed until the liquid velocity is increased sufficiently to fluidize the entire bed. The data for validation was obtained from Maruyama and Sato (4) who performed experimental studies in a conical vessel 90 cm in height, a 3 cm diameter distributor at the cone bottom, and a cone angle of 15.2°. The liquid used was tap water and the solids are glass beads with an average diameter of 189 µm and density of 2,486 kg/m3. A 2D axisymmetric CFD model of the bed was used and the solution was obtained as a transient simulation. However, the data presented is time-averaged for comparison with the experimental data. Figure 4(a) shows the CFD and experimental bed height as a function of superficial velocity at the liquid distributor. The prediction of overall void fraction is excellent over a wide range of water flow rates: from the fixed, low velocity to the fluidized, higher velocity flow regimes. Figure 4(b) shows the CFD and experimental bed pressure drop. At low superficial velocity, the conical bed is fixed. As the liquid velocity is increased, the superficial velocity exceeds the minimum fluidization velocity and the fluidization is initiated. The pressure is a maximum at this point. As the superficial velocity is increased further, the bed becomes fully fluidized. There is good agreement between the CFD multiphase model and the experimental pressure drop in the fluidized bed. The fixed bed pressure drop determined from the Ergun equation is shown for comparison and highlights why it cannot be used to predict the pressure drop in the fluidized flow regime. Figure 5 shows the root mean square liquid volume fraction in the bed. This highlights the portion of the bed where the presence of higher liquid volume fraction predominates. The pattern shows that the liquid preferentially channels up the center of the bed and disengages forming a spout at the bed surface. Maruyama and Sato (4) made similar observations.
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Figure 5. RMS void fraction in the bed for a distributor superficial velocity of 10 cm/s. Application Areas There are a number of different application areas in hydrometallurgy that CFD can be applied to, including flotation, milling, leaching, solid-liquid separation (slurry transport, clarifiers, decantation, and filtration), precipitation processes, ion exchange processes, heat exchangers, and other processes sensitive to hydrodynamics. The following section describes briefly the application of CFD to the design or trouble-shooting of selected unit operations in the autoclave circuit. Scale-up/Scale-Down Criteria for Solids Suspension The problem of how to scale-up solids suspension systems has not been adequately solved, despite much research. The commonly used scale-up exponent is -0.85, suggested by Zwietering (5), which results in a decreasing power input per unit volume when the process is scaled up. Corpstein et al. (6) refined this further by linking the scale-up exponent to the particle settling velocity, which addressed the problem of the seemingly inconsistent values for the scale-up exponent found in the literature. Later, unpublished work by the same researchers
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suggested that the scale-up exponent is also affected by scale itself, although to a much lesser degree than it is affected by particle settling velocity. Furthermore, it was observed in experiments that the scale-up exponents for just-suspended speed and to obtain the same relative cloud height were actually different. Therefore, the scale-up methods used to predict the conditions for suspension are not necessarily suited for predicting the solids distribution uniformity in the vessel, which is of principal importance for process performance and is the main parameter predicted by CFD. Another issue that destabilizes the foundation of the Zwietering-type correlations used by engineers, including agitator vendors, is that the correlations are based on solid material types, such as glass or sand, with much lower specific gravities of the materials typically found in the hydrometallurgical process industry. The present case is an investigation into an existing design and the planned modifications for the agitation system in an autoclave reactor. The autoclave had experienced operational difficulties due to the possibility of incomplete suspension. The d80 of the solids was 150 µm and was 30wt% or 8.5vol% of the reactor contents. The particle size distribution in the feed slurry, with a solids specific gravity of approximately 5, was higher after process start-up than the original design values and the large size fractions were not being suspended with the existing agitation system (impellers, shaft and drive motor). However, complete suspension was a design requirement for the autoclave, and process performance would be compromised with poor suspension. A lab study by the agitator vendor was performed to evaluate the performance of the impellers. The lab tests involved making qualitative visual observations of the solids on the bottom of the vessel. CFD was used to model the scale-down and scale-up configurations using the Eulerian Granular model in FLUENT 6 and grid refinement in the impeller region and at the walls. The grid sizes are in the range of 4,000 to 8,000 quadrilateral cells depending on the level of refinement in the regions of interest. Existing Autoclave – Commercial Scale The existing configuration has an impeller/tank-diameter (D/T) ratio of 0.4, and off-bottom clearance/tank-diameter (C/T) ratio of 0.36. Figure 6(a) shows the predicted liquid flow distribution in the existing commercial-scale reactor illustrating the axial pumping characteristics of the dual down-pumping hydrofoil impellers. Adding solids to the calculations severely disrupts the single flow loop on either side of the impellers as shown in Figure 6 (b). Two distinct flow loops are observed; one for each impeller. Figure 6(c) shows the distribution of the solids and the complete lack of suspension at the bottom of the autoclave verifying the operational performance of the autoclave.
(a) Velocity Vectors (Liquid only; No solids in the autoclave)
(b) Velocity Vectors (Liquid and solids in the autoclave)
(c) Distribution of solids volume fraction
Figure 6. The flow and solids distribution in the commercial-scale autoclave reactor – design configuration.
Lab Scale – Existing Configuration The lab test rig was a 1/8th scale model of the commercial scale autoclave (diameter, liquid height and impeller diameters). The shaft speed was scaled based on power per unit volume. Figure 7(a) shows the flow distribution with the liquid and solids in the autoclave. The double flow loop is observed at the lab scale as well. Figure 7(b) shows the distribution of the solids in the lab-scale autoclave. The suspension of the solids is slightly better than in the commercial scale though there is not off-bottom suspension. The lab tests verified that the solids were not off-bottom. This demonstrates that the level of agitation is insufficient.
(a) Velocity Vectors (liquid and solids)
(b) Distribution of solids volume fraction
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Figure 7. The flow and solids distribution in the lab scale autoclave reactor – design configuration. Lab Scale – Proposed Configuration Based on the suspension achieved with the level of agitation in the existing configuration, the proposed improvement to the autoclave agitation was to increase the power per unit volume to the autoclave. The bottom impeller was changed to a high-solidity hydrofoil and the impeller diameter was increased to a D/T of 0.5. Figure 8(a) shows the flow distribution with the liquid and solids with the proposed mixer configuration in the lab-scale autoclave. The double flow loop is not completely eliminated. Figure 8 (b) shows an improved distribution of the solids in the lab-scale autoclave. However, there is not off-bottom suspension. The lab tests verified that the solids were not off-bottom. Further lab tests were run to show that lowering the impellers and increasing the shaft speed could achieve complete off-bottom suspension. However, these additional modifications would require a much larger motor (4 times the size of the existing motor) and a larger shaft seal to handle the larger shaft diameter and length. Commercial Scale-Up The lab-scale proposed configuration was scaled-up at constant power per unit volume. The actual process conditions are modelled so that the liquid phase properties of density and viscosity at operating temperature and pressure are used in the analysis. Figure 9(a) shows the flow pattern in the commercial-scale autoclave with the proposed mixer configuration. The proposed mixer configuration is under-sized and unable to establish the single- loop flow pattern needed to distribute the solids throughout the autoclave. Figure 9 (b) shows the resulting distribution of solids. The suspension in the commercial-scale is worse than the lab-scale indicating that the vendor-proposed changes will not work in the field and the scale-up methodology used is flawed. Further modification to the mixer configuration, including lowering the off-bottom clearance and increasing the shaft speed, should be considered to improve the distribution of the solids suspension in the vertical autoclave.
(a) Velocity Vectors (liquid and solids)
(b) Distribution of solids volume fraction
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Figure 8. The flow and solids distribution in the lab scale autoclave reactor – proposed configuration.
(a) Velocity Vectors (liquid and solids)
(b) Distribution of solids volume fraction
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Figure 9. The flow and solids distribution in the commercial-scale autoclave reactor – proposed configuration. Non-Newtonian Blending of Acid into Slurry In pressure acid leaching autoclaves, highly concentrated sulphuric acid is injected into the slurry. The acid must be rapidly blended by the mixer configuration, since the leach kinetics are typically fast, and to avoid contact of poorly mixed blobs of high concentration sulphuric acid with the mixer or autoclave walls to minimize corrosion. Due to the small particle size and medium solids loading (24 – 35 wt%), the particles remain relatively uniformly suspended for a period of time far less than the hold-up time of the slurry in the autoclave. As such, the slurry can be considered homogeneous with a non-Newtonian fluid rheology, i.e., shear thinning with a yield stress. The apparent slurry viscosity is an order of magnitude greater than the acid viscosity, increasing the difficulty of mixing between the two fluids. In order to characterize the behaviour of the autoclave with respect to the dispersion of acid into the slurry, the transient dispersion of acid using an acid tracer was modelled. Chemical reaction and mass transfer are neglected in order to simulate the worst-case scenario. An ideal reactor is a well-mixed one, or CSTR, so the deviation of the reactor residence time distribution (RTD)
from the ideal RTD is used to quantify the behaviour of the reactor and the efficacy of the blending/mixing process. To produce an RTD, a pulse of acid is made into the compartment and the concentration of acid is monitored at the overflow to the second compartment as a function of time. The RTD or exit-age distribution of the acid indicates whether the reactor is well-behaved: rapid and complete blending of the acid into the slurry. The impellers are modelled in 3D to allow the power draw to be computed explicitly and compared to the vendor data, and the acid concentration on the blade surfaces can be determined. The time-dependent sliding mesh model was used to compute the transient flowfield and time-dependent dispersion of acid into the autoclave. Due to the range of Reynolds numbers resulting from the pseudoplastic rheology of the slurry, it was necessary to model turbulence in the autoclave. The boundary condition for all solid surfaces (walls) is a zero slip condition. A rotational speed is applied to the impellers and shaft surfaces. The free surface (liquid level) is modelled as a slip boundary. The overflow is modelled as a pressure-outlet. The computational domain consisted of approximately 1 million cells. Figure 10 is a time-sequence of acid injection into the autoclave showing the dispersion of the acid in the flow field. Figure 11 shows the exit age distribution of the acid pulse injection monitored at the overflow for two acid injection locations (Configuration A and B) compared with an ideal CSTR. Configuration A shows a significant overshoot of the ideal CSTR RTD indicative of acid short-circuiting to the outlet without adequate blending in the compartment. Short-circuiting leads to underutilization of the acid and compartment. Configuration B shows an improvement of the RTD with minimal short-circuiting occurring. The ideal CSTR RTD starts at unity and decays asymptotically since the assumption is that the tracer is instantly blended uniformly throughout the autoclave. In actuality, the RTD starts at zero since it takes a finite amount of time for the tracer to travel from the tip of the acid injection lance to the overview outlet. This the reason for the short time-lag in the RTD signals for configurations A and B at the start of the distribution.
Figure 10. Time sequence showing the injection of acid (iso-surface of constant acid mass fraction equal to 0.0001) into the autoclave ( Eθ = E t , θ = t / t , E = C / ò Cdt , residence time t = ò tCdt / ò Cdt , C is acid concentration and t is time). For an ideal CSTR, Eθ = exp(− θ) .
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Figure 11. Exit age distribution of acid tracer as a function of dimensionless time. Note different abscissa values. Splash Tower Performance Splash towers or direct contact heat exchangers eliminate the impermeable barrier between the hot and cold fluids in conventional heat exchangers by directly contacting the fluids. The advantages are simple design, less corrosion, lower maintenance costs, higher specific transfer areas, and higher transfer rates (7).In addition to the high heat transfer rates obtained by direct contact, the direct contact heat exchangers can handle fouling materials, such as slurries. Figure 12 shows a schematic of a splash tower used to condense steam to heat up slurry. In addition to hydrometallurgy applications, direct contact heat exchangers are used in geothermal power stations for feed water heating, in condensers of space vehicle power units, in flash evaporation units for water desalination, and in the chemical and food industries (8). Despite the widespread use, rigorous design methodologies are lacking (9).
Hatch has developed and implemented, in several successful installations worldwide, a design methodology for splash towers and has used CFD to optimize the hydrodynamics and heat transfer. Splash towers are designed with the intent to maximize contact between the cold slurry and hot condensable vapour. As with counter-current flow in columnar unit operations, there is a maximum throughput of both phases at which point the column is said to be flooded. As spreading over the splash plates increases the surface area of the cold slurry, flooding occurs at lower gas flow rates. Flooding correlations exist (10) for horizontal splash plate in narrow columns but not for towers typical of an autoclave circuit. The splash plates must also be inclined to allow the yield stress slurry to flow. Ultimately, the heat transfer characteristics are affected by the hydrodynamics in the splash tower though the methodology and results of the splash tower heat transfer will not be presented here. Due to the complexity of the hydrodynamics, primarily a consequence of the difference in dimensions between the film (in order of millimetres thick on the splash plate) to the diameter of the vessel (in order of meters), it was necessary to reduce the problem into solvable parts. The first step is to establish the mechanism of slurry flow as it is introduced onto the splash plate. Next, the trajectory of the slurry sheet leaving one plate the next is studied. Finally, the overall heat transfer performance is modeled with counter-current steam and slurry flow where the slurry flow is modelled as discrete particles with plastic normal and elastic tangential restitution coefficients on impact with the splash plates.
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Hot slurry OUT Figure 12. Splash tower used to condense steam on a slurry. A 3D CFD analysis of the slurry impingement on a splash plate was performed to determine the characteristics of the film formation on the baffle and predict the lip loading. The slurry-steam flow was modelled using the VOF model for the free-surface flow. This approach solves a single momentum equation and an equation for the volume fraction. A phase is either present in a computational cell with a volume fraction of 1 or it is not and the volume fraction is zero. If the volume fraction is between 0 and 1, then the interface between the phases exists in the cell and a tracking scheme is implemented to refine the interface shape. The explicit scheme employed here is the geo-reconstruct interface-tracking method. The slurry is introduced to the plate through a distributor and the 3D model represents the top-most splash plate in the tower. The slurry was modeled as a non-Newtonian fluid with a yield stress and shear-thinning properties. The time-dependent VOF calculation was run until the slurry film height reached a steady value as determined from the average slurry volume fraction at the exit boundary of the 380,000 unstructured hexahedral cell computational domain shown in Figure 13.
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Figure 14 shows the slurry-steam interface. The slurry jets impinge on the splash plate and spread into a sheet that leaves the edge of the plate. The main features of the flow show that the slurry film is not uniformly distributed at the edge of the plate. The non-uniform distribution results in a variation of the film velocity at the edge of the plate since the flow is still developing. As such, simple 1D analytical models describing flow down an inclined plate will not capture the correct film thickness and velocity of the film. Figure 15 shows the temperature distribution in the splash plate due to the cooling of the slurry film. The results are used by design engineers to size the heat exchanger and better understand how to design for stress in the splash plates. Splash plate
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Figure 14. Slurry-steam interface at an instant in the transient VOF solution showing the jets of slurry impinging on the inclined splash plate. °C
Figure 15. Splash plate temperature distribution and slurry-steam interface.
Future work will predict splash tower performance using the Eulerian multiphase model by directly integrating the interfacial area available for heat and mass transfer. The results of a 2D, “cold” flow, simulation is shown in Figure 16. The counter-current flow of steam and slurry is shown. The variation in the slurry velocity in the film on the splash plate leads to a variation in the trajectory of the slurry in the film impacting the subsequent plate over a wide area. Overall, the CFD modeling of the splash towers has produced better designed units for contact between the slurry and the steam and have reduced the risk by verifying the splash tower hydrodynamic capacity and heat transfer performance.
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Figure 16. Slurry volume fraction and steam pathlines in a splash tower. Summary The application of CFD to modelling unit operations in the autoclave circuit to improve and enhance process design is a reality. Recent advances in the capabilities of commercial CFD software, in particular FLUENT, has enabled engineers at HATCH to understand the performance of the design and perform pre-construction optimization based on the results of CFD analysis.
1 Fluent Inc., Lebanon, NH, USA. Available at http://www.fluent.com 2 A. Bakker, A. Haidari and L. Oshinowo, “Realize Greater Benefits from CFD”, Chemical Eng. Progress, March 2001, pg.45-53, 2001, http://www.cepmagazine.org/pdf/030145.pdf 3. J.C. Godfrey, Z.M. Zhu, “Measurement of particle-liquid profiles in agitated tanks”, AIChE Symposium Series. 299, (1994), 181-185.
4 Maruyama, T. and Sato, H., “Liquid fluidization in conical vessels”, The Chemical Engineering Journal, 46, (1991) 15-21 5 T.N. Zwietering, “Suspending solid particles in liquid by agitators,” Chemical Engineering, 8 (1958), 244-253. 6 R. Corpstein, J.B. Fasano and K.J. Myers, “The high-efficiency road to liquid-solid agitation,” Chemical Engineering, 10 (1994), 138-144. 7 S. Sideman and D. Moalem-Maron, “Direct Contact Condensation,” Advances in Heat Transfer, Volume 15, Academic Press, (1982), 227-281. 8 A.P. Solodov, “Calculation Models of Heat Transfer with Contact-Type Condensation,” Teploenergetika, v. 37, n. 10, (1990) 12-16. 9 F. Kreith and R.F. Boehm (Eds.), “Direct Contact Heat Transfer.” (1988). 10 J.R., Fair, “Designing Direct-Contact Coolers/Condensers,” Chemical Engineering, June 12, (1972), 91- 100.
