Article pubs.acs.org/IECR
Intensification of the Sasol SPD Reactor Realizing Potential Alex P. Vogel,* Herman G. Nel, Jacobus A. Stadler, Robin G. Jordi, and Berthold B. Breman† Sasol Technology, Research and Development Department, 1 Klasie Havenga Road, Sasolburg 1947, South Africa ABSTRACT: Intensification of slurry phase reactors can contribute significantly to capital cost reduction in the gas-to-liquid (GTL) process. It has previously been shown that the scope exists to potentially double the volumetric conversion of Sasol’s existing G1 commercial slurry phase reactors. Tests have successfully been completed in Sasol Technology’s semicommercial pilot plant that have demonstrated +50% (G2) and +100% (G3) reactor capacities. A G2 reactor design, based on lessons learned from the G1 ORYX GTL reactor, reduction of design margins and more effective layout of reactor internals, has been completed for GTL project execution. The combined use of computer-aided design tools (CAD, CMFD, FEA, CPFD, or DEM and 3D printing) has enabled a feasible conceptual G3 reactor design to be established. Future key focus areas include not only intensification of its production capacities but also economic optimization and cost-effective manufacturing and construction strategies.
1. INTRODUCTION Despite the global economic downturn at the end of the past decade and the subsequent struggle for worldwide financial recovery, the Sasol SPD process has retained a solid business case. The suppression of natural gas costs together with a modest recovery in oil price leaves an attractive price differential from which a gas-to-liquids (GTL) plant can still benefit. Financial discipline, however, is required in both capital cost (per barrel) reduction and project execution cost containment. Technology development is an area where capital costs can be reduced and project execution facilitated by effective equipment design. ORYX GTL (49% Sasol, 51% Qatar Petroleum shareholding) is the first GTL plant to utilize Sasol’s SPD reactor technology. This first of a kind, large scale GTL technology is now running in excess of design capacity with the Sasol’s first generation (G1) SPD reactor at the heart of the synthesis gas-to-diesel conversion process. The same G1 reactor technology has been used in the design of the Nigerian Escravos GTL plant which is currently in the commissioning phase. On the basis of the operational and business success of ORYX GTL, Sasol is pursuing additional GTL business in Uzbekistan (Oltin Y’Ol GTL in Tashkent) and the U. S. A. (Lake Charles, Louisiana). The reactor design poses significant challenges in design of the internal structures,which includes systems for gas feed injection, removal of the heat of reaction, and solid/liquid and liquid/gas separation systems. Manufacturing of such large vessels requires careful consideration of the manufacturing strategy depending on location, size, mass, and single piece shop versus modular site manufacturing as well as transport and erection logistics. Disclosure of intellectual property in both collaboration with industry experts and manufacturing community needs to be managed judiciously. Robust and high quality yet economical manufacturing processes, specifically by applying mass produced automated and robotic manufacturing techniques, are crucial in ensuring an economical offering. The relative capital cost breakdown of a typical GTL process is shown in Figure 1. These costs are the inside battery limit (IBL) capital costs. Depending on the location, infrastructural outside © 2013 American Chemical Society
Figure 1. Relative GTL process capital cost.
battery limit costs (OBL) can constitute a significant amount of the overall GTL plant cost. It can be seen that the SPD reactor, with associated tail gas processing, and the synthesis gas generation unit comprise approximately one-half of the capital cost. The SPD reactor makes up just more than one-fourth of the total amount. There is, therefore, a significant cost savings that can be realized through increasing the volumetric conversion efficiency of the SPD reactor. This translates into processing increased volumes of synthesis gas through similar reactor volumes and enables larger single train capacities that exploit economy of scale in the synthesis gas generation, air separation, and product work-up units. The current reactor shell diameter and weight are approaching construction and erection limitations. Intensification is, therefore, an essential enabler for larger single train capacities and, therefore, economy of scale benefits. The capital cost ($/barrel) of the reactor and, hence, the overall GTL plant is Special Issue: Recent Advances in Natural Gas Conversion Received: Revised: Accepted: Published: 1768
July 30, 2013 October 29, 2013 October 31, 2013 November 20, 2013 dx.doi.org/10.1021/ie402444f | Ind. Eng. Chem. Res. 2014, 53, 1768−1774
Industrial & Engineering Chemistry Research
Article
Figure 2. Void fraction vs gas velocity and solids concentration for a mimic G/L/S system (air−C9C11-paraffin mixture at 8 bara, ambient temperature, with varying solids volume fraction of catalyst support (gas-free basis)).
2. EXPERIMENTAL SECTION It has been previously mentioned2 that a new semicommercial reactor, termed the slurry phase distillate design reactor (SPDDR), was being constructed in Sasolburg, South Africa. The construction and commissioning of this reactor has successfully been completed. The reactor may be reconfigured to represent a variety of different heat, liquid, and gas removal systems and is used to develop design data of an optimized, fully integrated reactor system. A broad range of process conditions and processing options are allowed, such as gas velocity, composition, hold-up, and distribution, catalyst loading and concentration, slurry bed height, and reactor pressure and temperature. This enables demonstration of the production capacity achievable and design parameters for future generations of commercial slurry bed reactors. A test program was carried out in two phases to demonstrate the capacity targeted for the second (G2) and third (G3) generation reactor designs. Relative to the ORYX GTL generation 1 (G1) reactor design capacity, the targets were • G2: 150% • G3: 200% The synthesis feed gas flow and catalyst concentrations were increased stepwise to reach the target conditions in two separate reactor demonstrations. The process conditions (gas feed rate, catalyst concentration, catalyst activity, temperature) were changed in a coordinated way in order to keep the synthesis gas conversion within a tolerable variance of ±5 percentage points. Cocatalyst deactivates in a nonlinear fashion to approximately 60% of its initial activity over a 30 day period under realistic Fischer−Tropsch synthesis conditions.9−11 As a result, the catalyst mass in the reactor is increased as the run progresses to maintain optimum conversion at fixed feed gas rate and composition, within a normal operating temperature band of 1−2 °C. The mass of catalyst that can be added to the reactor is therefore a function of the activity of the catalyst already in the reactor and the activity of the catalyst to be loaded. Adding catalyst of a lower activity enables catalyst to be added at a faster rate, thus reducing the time taken to reach the test conditions of increased inventory. If catalyst of a higher activity is loaded, smaller additions by mass or longer time periods between additions are required to allow time for the incumbent inventory
thereby reduced. The liquid natural gas (LNG) industry has shown a proven track record of reducing specific capital investment by pushing single train capacities.1 This paper addresses the challenge of increasing the synthesis gas (H2 + CO) processing capacity of a slurry bed reactor through a test program of progressively increasing the gas feed rate to and the catalyst concentration in the reactor. It has previously been shown2 that the volumetric conversion efficiency of slurry phase reactors can be increased substantially. This is achieved by maintaining a constant reactor volume through the relative increases in gas velocity and catalyst concentration. It can be seen (Figure 2)3,4 that changes in slurry phase void fraction is affected in opposite directions by increases in gas velocity (synthesis gas) and solids (catalyst) concentration. As gas velocity is increased, so does void fraction, whereas an increase in solids concentration affects a decrease in void fraction. In the study carried out in Figure 2, gas hold-ups were measured in a 6 in. diameter, 4 m height bubble column using gas disengagement techniques. This effect has also been established in open literature and captured reasonably well by various literature correlations.5−8 Although similar effects have been reported in the open literature and captured by various correlations, extrapolation to intensified conditions often predicted excessive gas hold-ups, which dissuaded other technology developers from explore such extreme operating conditions. Nevertheless. it was shown in this study that through careful management of increases in both gas velocity and solids concentration, a constant height of the slurry phase could be maintained, thereby enhancing its gas processing capacity. A combination of fundamental studies, cold model tests, and semicommercial reactor demonstrations indicated that a doubling of the production capacity of the Sasol SPD reactors was feasible. Although the hydrodynamic considerations of such a capacity increase are attainable, a challenge remains in the development of a practical reactor mechanical design for commercial implementation. Further cold model studies have shown substantial scope beyond doubling the reactor capacity from a strictly hydrodynamic point of view. This study shows integrated demonstration of the hydrodynamic conditions at increased production capacity as well as the associated slurry bed reactor design methodology. 1769
dx.doi.org/10.1021/ie402444f | Ind. Eng. Chem. Res. 2014, 53, 1768−1774
Industrial & Engineering Chemistry Research
Article
Figure 3. G2 demonstration: catalyst inventory and gas velocity.
Solving the models is computationally expensive and generates large data files. High-end 64-bit multicore workstations are applied with parallel processing capabilities on either in-house blade type clusters or external high performance computing platforms involving hundreds of processing cores, low-latency interconnects, terabytes of RAM memory, and large data storage capacities. In particular, modern CMFD solver software exhibits very good scalability on such parallel processing hardware platforms.12 Additional complexities arise in CMFD simulations owing to the supplementary physics inherent in multiphase reactive fluid flows and interfacial interactions13 as well as the enhanced mesh quality requirements for numerical stability, improved convergence and fidelity in the full 3D meshes used. Sasol Technology usually applies the Reynolds-averaged Navier−Stokes equation (RANS) approach to CMFD in intensification studies using either Boussinesq hypothesis-based k−ε14 and k−ω15 models or Reynolds stress transport models16 in situations where highly swirling and stress dominated flows are anticipated. Depending on the focus of the analysis, both volume of fluids and Eulerian multiphase models are applied, the former usually in analyses involving flow transients in the ducts, conduits, and subdomains where a refined mesh is not too computationally prohibitive. For whole column models, quadrature method of moments (QMOM) population balance modeling17−19 or multifield models are applied. These models are combined with suitably validated drag and nondrag closure modeling to capture force effects including virtual mass (mainly to enhance numerical stability), lift, turbulent dispersion and wall forces,20−22 and particle−fluid and particle−particle interactions, among others, typically incorporated by proprietary user defined functions (UDFs). Supplementary UDFs are coded to further configure the solver to assist in the initialization of the flow field, species concentration, and phase volume fraction profiles, to model mass and energy interfacial transport processes,23 to implement bubble coalescence24,25 and breakup26,27 models and chemical reaction submodels, and to extract solution data during the computer run for postprocessing applications.
to deactivate. Catalyst additions of either fresh (active) or spent (less active) catalyst were used depending on the targeted catalyst inventory and time frame required for the test. Simulation is a valuable tool complementing conventional experimental or piloting as well as fundamental or analytical design tools, often referred to as virtual prototyping. Such simulation methods provide highly detailed and visual insights to often complex and integrated problems and have the potential to accelerate development time and reduce the capital investment required for concept-development engineering phases. These simulation tools require the user to specify physical models, boundary conditions, and fluid medium properties in approximating actual parameters. In validating the simulation specifications and results obtained, it is very valuable to have experimental programs, often at cold model and prototype scales, to generate data for comparison, ensuring validity and boosting the confidence that engineers in industry have in such results obtained. Advanced simulation tools applied specifically for slurry phase reactor development include • CMFD (computational multiphase fluid dynamics), in which the interactions between multiple fluids, in this instance catalyst, syngas, and FT wax, and its boundary walls are analyzed. • FEA (finite element analysis) is applied for evaluation of structural, thermal, and modal stress and strain effects of reactor internals. • CPFD or DEM (computational particle fluid dynamics or discrete element method) is applied for cases where particle−particle interactions govern physical interactions. • CAD (computer-aided drafting) is extensively applied for form, fit, and assembly conceptual work, being a simulation precursor in preparation of domains for simulation. Realistic 3D geometry is prepared prior to defeaturing for generating physics appropriate mesh discretization of domains. The simulation tools are highly integrated in allowing for shared, parametric geometries and data transfer, such as particle−fluid or fluid−structure interactions, which may be solved by either uni- or bidirectional links. In analyzing the data files, the designer has the freedom of probing the domain at virtually any point, slice, or zone in assessing for example velocity profiles, solids concentrations, temperatures, pressures, and stresses in the structures.
3. RESULTS 3.1. Reactor Intensification Tests. The increases in the catalyst inventory and gas velocity during the G2 test are shown in Figure 3, together with the target value of 150% of G1. The 1770
dx.doi.org/10.1021/ie402444f | Ind. Eng. Chem. Res. 2014, 53, 1768−1774
Industrial & Engineering Chemistry Research
Article
Figure 4. G2 demonstration: relative H2 + CO conversion.
Figure 5. G3 demonstration: catalyst inventory and gas velocity.
Figure 6. G3 demonstration: relative H2 + CO conversion.
The relative synthesis gas (H2 + CO) conversion is shown in Figure 4. It can be seen that the conversion level was kept within 5% of the target through management of catalyst mass, catalyst activity, gas feed rate, and reactor temperature.
gradual, relative increases in both catalyst inventory and gas velocity can be seen prior to reaching values of 155% for catalyst inventory and 170% for gas velocity. All the data is represented by a three-point rolling average. The time period for the test stretches over several months. 1771
dx.doi.org/10.1021/ie402444f | Ind. Eng. Chem. Res. 2014, 53, 1768−1774
Industrial & Engineering Chemistry Research
Article
Once the G2 demonstration had been successfully completed, preparations for the G3 test were made. Some time was spent stabilizing the reactor with a more active catalyst, requiring a slightly higher gas velocity to manage synthesis gas conversion. Catalyst mass and gas velocity were then increased together to elevate the reactor to G3 conditions (Figure 5). Conditions were maintained at 200% G1 while a variety of design measurements and sustainability tests were conducted. The lower variability in conversion was a result of the G3 test using a larger catalyst mass addition of less active catalyst toward the end of the demonstration. This methodology allowed the target inventory to be reached within a reasonable period of time without having to wait for smaller catalyst additions to slowly deactivate, permitting the addition of subsequent batches. It can be seen from Figure 6 that the synthesis gas conversion was managed within ±1%. The reactor operates in a region where there are not yet any mass transfer limitations that could inhibit the advantage of reactor intensification. This was seen from apparent catalyst activities as back-calculated from detailed reactor models, which were in line with the activities as expected on the basis of catalyst activity runs in hydrodynamically well-defined microreactors that had no mass transfer limitations and well-mixed gas and liquid phases. The mass transfer submodel as used in the detailed reactor model also predicts rather insignificant mass transfer limitations at intensified conditions. This finding is in contrast to a previous study28 that predicted a significant decrease in the liquid phase mass transfer of H2 and CO and is more in support of Vandu et al.,29 who found an increase in mass transfer at all solids loading up to superficial gas velocities of 0.4−0.5m/s. They, however, reported a flattening off or even a decrease in mass transfer at velocities above 0.5 m/s. 3.2. FEA and CMFD. In illustrating the capacity and typical deliverables obtained from FEA and CMFD in support of the slurry bed reactor development program, two case studies are given. Large diameter slurry reactors for commercial design, typically 10 m in diameter and up to 60 m in total height, have specific challenges in providing support structures for suspending hundreds of tons of internals. Such internals are exposed to forces and dynamics during reactor start-up, normal operation, trip, and shutdown conditions. Loads on the internals include coincident thermal transients and the pressure, gravity, and dynamic loads associated with starting up, operating, and shutting down fluidized slurry domains. In assessing the combined loading, FEA is a valuable tool for the mechanical engineer when considering alternatives and optimization of these structures. Figure 7 below depicts a conceptual internal structure showing an amplified deformation plot. CMFD is used to assess overall reactor performance including start-up transients, bed expansion, catalyst and syngas distribution, and gas disengagement as well as more targeted smaller scale analyses aimed at optimization of the performance of reactor internal structures and the associated operating procedures. An example of such a commercial scale CMFD reactor study was a 3D four phase Euler−Euler full transient analysis of the first five minutes after start-up from slumped state. This study captured the dominant internal geometrical structures within the reactor using tetrahedral mesh decomposition. The realizable k−ε turbulence model, phase-coupled SIMPLE pressure velocity coupling and QUICK spatial discretization applied to the momentum and volume fraction equations were utilized. The
Figure 7. Reactor internal structure finite element analysis.
model was solved with an implicit first order transient formulation using 5 ms time steps, allowing up to 80 intertemporal subiterations to drive absolute residuals down to at least 5 × 10−4. This analysis required a total of 170 000 CPU hours using 80 cores on ten nodes of a high-performance computer cluster followed by detailed postprocessing. Figure 8
Figure 8. SPR phase velocity profiles at 260 s.
illustrates some details of the reactor geometry, as well as the gas phase, liquid phase, and catalyst phase velocities on respective volume fraction isosurfaces and a contour plane through the reactor. Rapid prototyping (3D printing) also allows for construction of reactor parts in engineering plastics. A number of these additive manufacturing methods have been commercialized, varying as to material tolerances, physical properties, build speed, and transparency. The parts are quickly produced directly from engineering desks, applied for conceptual demonstration, manufacturability, maintenance reviews, and functional testing.
4. DISCUSSION As a result of the success of demonstration both of a G2 (150%) and G3 (200%) capacity, reactor design studies for these two 1772
dx.doi.org/10.1021/ie402444f | Ind. Eng. Chem. Res. 2014, 53, 1768−1774
Industrial & Engineering Chemistry Research
Article
3D printing allows for scaled, yet highly realistic, parts often not achievable by conventional (subtractive) manufacturing techniques in either plastic or metal components. This contributes to a significant reduction in time for product development, alternative design optimization, and cost savings.
capacities were conducted. The G2 reactor design was based on lessons learned from the G1 ORYX GTL reactor (Figure 9),
5. CONCLUSIONS By extending the knowledge base of void fraction, catalyst concentration, and feed gas velocity, the SPDDR demonstration program has shown that a slurry bed reactor capacity of 200% of the G1 ORYX GTL reactor design is possible. Computer-aided tools (CAD, CMFD, CMPD, and FEA) have proved to be invaluable in designing state-of-the-art commercial slurry phase reactors. Combining the SPDDR test program results with computational tools has enabled the mechanical design of a G2 reactor of 150% capacity to be completed for use in current GTL projects. A conceptual design of a 200% G3 capacity reactor has also been done and will be progressed to be available for inclusion in future GTL endeavors. In developing reactors for future designs, key focus areas include (i) intensification of its production capacities, (ii) economic optimization targeting a unit cost per barrel benefit, and (iii) a cost-effective manufacturing and construction strategy.
■
AUTHOR INFORMATION
Corresponding Author
*Address: P.O. Box 1, Sasolburg 1947, South Africa. Phone: +27 16 960 2766. Fax: +27 11 522 4894. E-mail: alex.vogel@sasol. com. Present Address †
Sasol Technology, Research and Development Division, PO Box 328, NL-7500 AH, Enschede, The Netherlands. Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. All authors contributed equally.
Figure 9. G1 ORYX GTL reactor.
Notes
The authors declare no competing financial interest.
■
increasing reactor capacity by reducing design margins and more effective layout of reactor internals. The G3 reactor conceptual design followed from a sound design basis established for the G2 reactor. A greater level of ingenuity was required for this design as it challenges some of the traditional mechanical constraints and introduces some novel reactor design concepts. The resulting innovative designs realized a reduced install cost of heat- and mass-transfer areas in the reactor while keeping the shell cost constant. A more detailed level of cost analysis, design review, and testing was also required. A combined use of computer-aided design tools (CAD, CMFD, FEA, CPFD, or DEM and 3D printing) and SPDDR test work has enabled a feasible conceptual G3 reactor design to be established. The ability for engineers to manufacture internals used for physical testing has a benefit in quickly constructing and adapting parts for functional testing in a variety of cold-flow piloting models. Prototyping of parts has a benefit when manufactured in transparent materials, allowing for visual observation and validation of CFD flow patterns. Physics observed includes phase interactions in densely packed zones and FEA analysis of imposed forces related to transients associated with resuspension and slumping of fluidized slurry beds.
■
ABBREVIATIONS εG = void fraction (dimensionless) uG = gas velocity (m/s) k = turbulent kinetic energy (m2/s2) ε = turbulent dissipation rate (m2/s3) ω = specific dissipation rate (s−1) REFERENCES
(1) Foss, M. M. Introduction to LNG: An Overview on Liquefied Natural Gas (LNG), Its Properties, the LNG Industry, and Safety Considerations; Energy Economics Research at the Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Center for Energy Economics: Austin, TX, 2012; p 21 [Online] http:// www.beg.utexas.edu/energyecon/ INTRODUCTION%20TO%20LNG%20Update%202012.pdf (accessed Oct 11, 2013). (2) Vogel, A. P.; Steynberg, A. P.; Breman, B. B. Intensification of Commercial Slurry Phase Reactors. Studies in Surface Science and Catalysts, Natural Gas Conversion VIII 2007, 167, 61. (3) Breman, B. B. Process for Producing at Least One Product from at Least One Gaseous Reactant from a Slurry Bed. PCT WO2012/168829 A1, December 13, 2012. 1773
dx.doi.org/10.1021/ie402444f | Ind. Eng. Chem. Res. 2014, 53, 1768−1774
Industrial & Engineering Chemistry Research
Article
(27) Wang, T.; Wang, J.; Jin, Y. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chem. Eng. Sci. 2003, 58, 4629−4637. (28) Lemoine, R.; Behkish, A.; Sehabiague, L.; Heintz, Y. J.; Oukacib, R.; Morsi, B. An algorithm for predicting the hydrodynamic and mass transfer parameters in bubble column and slurry bubble column reactors. Fuel Process. Technol. 2008, 89, 322−343. (29) Vandu, C.; Van den Berg, B.; Krishna, R. Gas-liquid mass transfer in a slurry bubble column at high slurry concentrations and high gas velocities. Chem. Eng. Technol. 2005, 28 (9), 998−1002.
(4) Breman, B. B. Process for Producing at Least One Product from at Least One Gaseous Reactant from a Slurry Bed. PCT WO2012/168830 A1, December 13, 2012. (5) Behkish, A.; Lemoine, R.; Oukaci, R.; Morsi, B. I. Novel correlations for gas holdup in large-scale slurry bubble column reactors operating under elevated pressures and temperatures. Chem. Eng. J. 2006, 115, 157−171. (6) De Swart, J. W. A. Scale-up of a Fischer−Tropsch Slurry reactor. Ph.D. Dissertation, University of Amsterdam, 1996. (7) Krishna, R.; van Baten, J. M.; Urseanu, M. I.; Ellenberger, J. Design and scale-up of the bubble column slurry reactor for Fischer−Tropsch synthesis. Chem. Eng. Sci. 2001, 56, 537. (8) Luo, X.; Lee, D. J.; Lau, R.; Yang, G. Q.; Fan, L.-S. Maximum stable bubble size and gas hold up in high-pressure slurry bubble column. AIChE J. 1999, 45, 665−680. (9) Saib, A. M.; Moodley, D. J.; Ciobîcă, I. M.; Hauman, M. M.; Sigwebela, B. H.; Weststrate, C. J.; Niemantsverdriet, J. W.; van de Loosdrecht, J. Fundamental understanding of deactivation and regeneration of cobalt Fischer−Tropsch synthesis catalysts. Cataly. Today 2010, 154 (3−4), 271−282. (10) Saib, A. M.; Borgna, A.; van de Loosdrecht, J.; van Berge, P. J.; Niemantsverdriet, J. W. XANES study of the susceptibility of nano-sized cobalt crystallites to oxidation during realistic Fischer−Tropsch synthesis. Appl. Catal., A: Gen. 2006, 312, 12. (11) van de Loosdrecht, J.; Balzhinimaev, B.; Dalmon, J.-A.; Niemantsverdriet, J. W.; Tsybulya, S. V.; Saib, A. M.; van Berge, P. J.; Visagie, J. L. Cobalt Fischer−Tropsch synthesis: Deactivation by oxidation? Catal. Today 2007, 123 (1−4), 293−302. (12) Browell, R.; Hutchings, B. Bigger, Better, Faster: HPC Technology. ANSYS Advantage 2011, 5 (3), 6−8. (13) Jakobsen, H. A. Chemical Reactor Modeling; Springer-Verlag: Berlin, Germany, 2008. (14) Shih, T.-H.; Liou, W. W.; Shabbir, A.; Yang, Z.; Zhu, J. A New k-ε Eddy-Viscosity Model for High Reynolds Number Turbulent Flows − Model Development and Validation. Comput. Fluids 1995, 24, 227−238. (15) Menter, F. R. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA J. 1994, 32, 1598−1605. (16) Launder, B. E. Second-Moment Closure and Its Use in Modeling Turbulent Industrial Flows. Int. J. Numer. Methods Fluids 1989, 9, 963− 985. (17) Chen, P.; Sanyal, J.; Duduković, M. P. Numerical simulation of bubble columns flows: effect of different breakup and coalescence closures. Chem. Eng. Sci. 2005, 60, 1085−1101. (18) Marchisio, D. L.; Virgil, R. D.; Fox, R. O. Quadrature Method of Moments for Aggregation-Breakage Processes. J. Colloid Interface Sci. 2003, 258, 322−334. (19) Troshko, A. A.; Zdravistch, F. CFD modeling of slurry bubble column reactors for Fischer−Tropsch synthesis. Chem. Eng. Sci. 2009, 64, 892−903. (20) Antal, S. P.; Lahey, R. T.; Flaherty, J. E. Analysis of Phase Distributions in Fully Developed Laminar Bubbly Two-Phase Flow. Int. J. Multiphase Flow 1991, 17, 635−652. (21) Jacobsen, H. A.; Grevskott, S.; Svendsen, H. F. Modeling of Vertical Bubble-Driven flows. Ind. Eng. Chem. Res. 1997, 36, 4052−4074. (22) Jacobsen, H. A.; Lindborg, H.; Dorao, C. A. Modeling of Bubble Column Reactors: Progress and Limitations. Ind. Eng. Chem. Res. 2005, 44, 5107−5151. (23) Taylor, R.; Krishna, R. Multicomponent Mass Transfer; John Wiley: New York, 1993. (24) Luo, H. Coalescence, Breakup and Liquid Circulation in Bubble Column Reactors. Ph.D. Dissertation, Norges Tekniske Høgskole, Trondheim, Norway, 1993. (25) Chen, P.; Duduković, M. P.; Sanyal, J. Three-dimensional simulation of bubble column flows with bubble coalescence and breakup. AIChE J. 2005, 51, 696−712. (26) Lehr, F.; Millies, M.; Mewes, D. Bubble-Size Distributions and Flow Fields in Bubble Columns. AIChE J. 2002, 48, 2426−2443. 1774
dx.doi.org/10.1021/ie402444f | Ind. Eng. Chem. Res. 2014, 53, 1768−1774
