Fig. 5.1 compares the simulated and real geometries.
All pictures of real packings were naturally distorted because of curved glass shape of the column body, which worked as a lens. This may give the false impression that the real column is more narrow than the simulated one.
5.6 Results 75
Figure 5.1: Simulation of the column filling process and comparison with the real one. Left image - process of filling, central image - simulated packing, right image - picture of real packing.
Comparisons between the simulated and experimental void fractions and specific areas are presented in Figs. 5.2 and 5.3, respectively. The error in all experimental volume fraction estimations did not exceed 4%. The error in the simulated results was approximately 5%.
These figures indicate that the simulated void fractions and specific areas are in good accordance with the experimental data for a wide region ofD/dratios.
To further test the performance of the method, packings consisting of spherical elements with 1 mm diameter were also simulated (black lines in the mentioned figures). The experimental data for spherical packings was taken from [46].
The green lines in Fig. 5.2 are the theoretical data for two structured packings of spheres.
The solid line stands for simple cubic packing, where elements form an orthogonal equidis-tant grid. The theoretical void fraction value is 1−π/6. The dotted line stands for a hexagonal close packing, where centers of spheres in each layer form an equidistant tri-angular grid (or hexagonal, if six triangles with a common vertex are combined). The elements of the next layer are located in crevices between the elements of the previous one. The theoretical void fraction value in this case is 1−π/(3√
2).
For small D/d ratios, the void fraction of the packing of spheres is close to that of the theoretical cubic packing, but as the relative column diameter increases, so does the
76 5. Packed-bed column
Figure 5.2: Void fraction for different column to element diameter rations
Figure 5.3: Void fraction for different column to element diameter ratios
density of the spherical packing.
The results demonstrate that the density of packing of the spherical elements is greater and the specific area smaller. This is also supported by the theoretical, experimental and numerical findings of other authors.
For spherical packing, also a more detailed comparison was possible. One widely used parameter to describe the structure of the packing is the radial porosity or void fraction.
It is defined as an average local void fraction at a specified distance from the column center-line. A significant number of experimental results related to measured radial
5.6 Results 77
porosity can be found in the literature. Here, the simulated data is compared with cases from [45]. Two cylindrical columns filled with monosized spheres were simulated. The diameter to sphere radius ratios of the columnsD/dwere 5.96 and 7.99.
Based on the data containing the coordinates of the spheres centers obtained after the simulations, it was possible to compute a height-averaged volume fraction for the column.
An example of the obtained values is presented in Fig. 5.4, which resembles an X-ray image taken along the column height. The darker parts indicate a higher density. The height-averaged solid fraction was averaged one more time along the angular coordinate to obtain the radial distribution. The void fraction was then computed as one minus the solid fraction. Fig. 5.5 compares the radial distribution of the void fraction of the simulated packings with the results taken from [45].
Figure 5.4: Height-averaged solid fraction distribution for column withD/d= 5.96. The darker the color, the higher the density.
The comparison demonstrates that the simulated spherical packings match real ones very accurately. The radial porosity in the near-wall region is in good agreement with the experiments. In the central region, there are small deviations from the experimental packing for the larger column.
The method can easily be extended for the pellets with arbitrary shapes, but to do so one should first subdivide their surface into triangles because general shapes are handled in Bullet Physics as a joint set of triangles.
This technique can be also used to design a real packed-bed column. The designer can simulate the packing to estimate the void fraction and specific area instead of building a prototype.
78 5. Packed-bed column
(a)D/d= 5.96 (b)D/d= 7.99
Figure 5.5: Distribution of radial porosity for a packed bed of monosized spheres.
5.7 Conclusion
The described method can be used for arbitrary shapes of packing elements and columns.
It is robust while maintaining almost real-time simulation for simple shapes. For rela-tively simple shapes such as the hollow cylinders used, no fine tuning is required - the method functions even with the simplest models. The implementation of more complex element shapes is possible, but requires more computational resources. The method has great potential in the field of the geometry preparation.
Although most of the routines were implemented in the toolbox, extensive coding is still required because every change in the parameters of the desired packing or the algorithm requires code editing and recompilation. This drawback can be overcome if more interest is shown by the research community, enabling people to share their compiled solutions and further improve the toolbox.
The method is not restricted to the usage of the above-mentioned Bullet Physics tool-box. Any other available commercial or free libraries designed for multibody dynamic simulations can be used (PhysX, Havok, etc.), or one’s own code. Bullet Physics was chosen because of its availability and open source.
Chapter VI
Summary
The main objective of this work was to investigate how mathematical modeling could be utilized to assist the study of various chemical apparata, focusing on cases with complex spatial structures. With the fast development of computers in recent years, it has become possible to use more complex models in chemical engineering. These models can give very detailed information on processes in chemical apparata. In many cases, the shape of the active zone is rather complex, which makes it impossible to study phenomena in situ.
In this study, it was shown that for different cases encountered in chemical engineering, mathematical modeling can provide valuable information about the performance of the setup. It was also demonstrated that in some cases, such modeling is the only way to obtain the desired data. At some point, these models meet barriers not only because of computer limitations, but also barriers related to the complexity of the reactor geometry.
Solutions to overcome this issue were presented in the research.
The study of the microplate reactor showed that it is possible to model complex cases with multiphase flows by using modern CFD approaches. Due to good agreement with experimental data, the model can be applied to study similar cases. As was shown, this approach can be used, for example, to optimize the geometry of a microreactor. The results also demonstrated how a reduction from 3D to 2D is possible while maintaining good agreement with experimental data. Without this approach, the solution of the problem would have taken much more CPU time. The reduction significantly decreases time and memory requirements, enabling the simulation of larger reactor domains.
Mass transfer coefficient estimations showed that the model can describe experimental data very well and that the parameter identifiability is sufficient. The model used to describe the mass transfer process was rather simple compared with the CFD model above. It was possible to obtain the empirical expressions in order to fit the experimental data.
Results from the micromixer and microtube reactor models showed how CFD simulations can, in some cases, help to clarify the underlynig modeling assumptions. It was shown that such an approach can be beneficial for cases where precise results are not needed,
79
80 6. Summary
but rather one has to ensure that certain values or the operation range do not exceed particular limits. Consequently, it can be stated that modeling, even as heavy as CFD, can be successively used to quickly estimate the performance of processing equipment to obtain an overview on what actually should be considered and what equipment can be fully or partially omitted from the consideration in a particular case.
Results from the packed-bed column case show that modern computers are powerful enough to be successfully used for 3D multibody dynamic simulations. These simulations are quite a straightforward approach to generate complex unstructured packed beds by utilizing the underlying physics of the column filling process with the packing elements.
The approach does not add excessive overheads to the study of packed beds because it uses nearly ready-made software tools. It was demonstrated, that packings generated in this way have all of the properties of real ones, but can be directly used for CFD simulations without complicated approaches such as tomography to obtain a numerical representation of the packing geometry.
The modeling of flows and other phenomena in complex geometries is difficult and still rarely applied in academic research or in real chemical engineering applications. Exper-imental measurements and simple models are the main sources of data in the industry.
The reason is the excessive overall time needed to develop and implement complex mod-els. However, more methodologies aiming to speed up the process are emerging: faster, accurate and robust models, as well as fast-to-implement software. They can make the application of more complicated models in the industry more attractive. The research described in this thesis is a contribution to this development.
Bibliography
[1] Al-Rawashdeha, M., Hessela, V., Loba, P., Mevissena, K., and Schon-felda, F. Pseudo 3-D simulation of a falling film microreactor based on realistic channel and film profiles. Chemical Engineering Science 63, 21 (2008), 5149–5159.
[2] Ansys Inc. ANSYS CFX Reference Guide, Release 12.0, 2009.
[3] Ansys Inc. ANSYS FLUENT User’s Guide, Release 12.0, 2009.
[4] Ansys Inc. ANSYS DesignModeler User Guide, Release 14.0, 2011.
[5] Ansys Inc. ANSYS Meshing User’s Guide, Release 14.5, 2012.
[6] Bagi, K.An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies. Granular Matter 7 (2005), 31–43.
[7] Bothe, D., Lojewski, A., and Warnecke, H.-J. Computational analysis of an instantaneous chemical reaction in a t-microreactor. AIChE Journal 56, 6 (2010), 1406–1415.
[8] Brackbill, J., Kothe, D., and Zemach, C. A continuum method for modeling surface tension. Journal of Computational Physics 100, 2 (June 1992), 335–354.
[9] Bretherton, F. P. The motion of long bubbles in tubes. Journal of Fluid Me-chanics 10, 2 (1961), 166–188.
[10] Caulkin, R., Ahmad, A., Fairweather, M., Jia, X., and Williams, R. Dig-ital predictions of complex cylinder packed columns. Computers and Chemical En-gineering 33, 1 (2009), 10–21.
[11] Chen, G., and Kharif, C.Two-dimensional Navier-Stokes simulation of breaking waves. Physics of Fluids 11, 1 (1999), 121–133.
[12] Chii-Dong, H., Hsuan, C., Hsi-Jen, C., Cheng-Liang, C., Hsieh-Hsung, L., and Yin-Yu, C. CFD simulation of the two-phase flow for a falling film microre-actor. International Journal of Heat and Mass Transfer 54 (2011), 3740–3748.
[13] Cui, L., and O’Sullivan, C. Analysis of a triangulation based approach for specimen generation for discrete element simulations. Granular Matter 5, 3 (2003), 135–145.
81
82 BIBLIOGRAPHY
[14] Cundall, P. A computer model for simulating progressive, large scale movements in blocky rock systems. InProceeding of International Symposium on Rock Fracture (1971).
[15] Deshmukh, S. R., Mhadeshwar, A. B., and Vlachos, D. G. Microreactor modeling for hydrogen production from ammonia decomposition on ruthenium. In-dustrial and Engineering Chemical Research 43, 12 (2004), 2986–2999.
[16] Ebrahimi, F., Kolehmainen, E., Laari, A., Haario, H., Semyonov, D., and Turunen, I. Determination of kinetics of percarboxylic acids synthesis in a microrector by mathematical modeling. Chemical Engineering Science 71 (2012), 531–538.
[17] Ehrfeld, W., Golbig, K., Hessel, V., Lowe, H., and Richter, T. Charac-terization of mixing in micromixers by a test reaction: single mixing units and mixer arrays. Industrial and Engineering Chemistry Research 38 (1999), 1075–1082.
[18] Fard, M. H., Zivdar, M., Rahimi, R., Esfahany, M. N., Afacan, A., Nan-dakumar, K., and Chuang, K. T. CFD simulation of mass transfer efficiency and pressure drop in a structured packed distillation column. Chemical Engineering and Technology 30, 7 (2007), 854–861.
[19] Feng, Y., Han, K., and Owen, D. Filling domains with disks: an advancing front approach. International Journal for Numerical Methods in Engineering 56 (2003), 699–713.
[20] Fernandes, J., Lisboa, P. F., Simoes, P. C., Mota, J. P., and Saatdjian, E. Application of CFD in the study of supercritical fluid extraction with structured packing: Wet pressure drop calculations. The Journal of Supercritical Fluids 50 (2009), 61–68.
[21] Gethin, D., Yang, X.-S., and Lewis, R. A two dimensional combined dis-crete and finite element scheme for simulating the flow and compaction of systems comprising irregular particulates.Computer Methods in Applied Mechanics and En-gineering 195, 41–43 (2006), 5552–5565.
[22] Graton, L. C., and Fraser, H. J. Systematic packing of spheres: With particu-lar relation to porosity and permeability. Journal of Geology 43, 8 (1935), 785–909.
[23] Gupta, R., Fletcher, D. F., and Haynes, B. S. On the CFD modelling of Taylor flow in microchannels. Chemical Engineering Science 64 (2009), 2941–2950.
[24] Haario, H., Laine, M., Mira, A., and Saksman, E. DRAM: Efficient adaptive MCMC, Statistics and Computing. Statistics and Computing 16, 4 (2006), 339–354.
[25] Haario, H., Saksman, E., and Tamminen, J.An adaptive Metropolis algorithm.
Bernoulli 7, 2 (2001), 223–242.
[26] Haggstrom, O., and Meester, R. Nearest neighbour and hard sphere models in continuum percolation. Random Structures and Algorithms 9 (1996), 295–315.
BIBLIOGRAPHY 83
[27] Han, K., Feng, Y., and Owen, D. Sphere packing with a geometric based compression algorithm. Powder Technology 155 (2005), 33–41.
[28] Hardt, S., and Schonfeld, F.Laminar mixing in different interdigital micromix-ers: II. numerical simulations. AIChE Journal 49, 3 (2003), 578–584.
[29] Harries, N., Burns, J. R., Barrow, D. A., and Ramshaw, C. A numerical model for segmented flow in a microreactor.International Journal of Heat and Mass Transfer (2003), 3313–3322.
[30] Hastings, W. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 (1970), 97–109.
[31] Hessel, V., Hardt, S., Lowe, H., and Schonfeld, F. Laminar mixing in different interdigital micromixers: I. experimental characterization. AIChE Journal 49, 3 (2003), 566–577.
[32] Hirt, C. W., and Nichols, B. D.Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39 (1981), 201–225.
[33] IGES/PDES Organization. Formerly ANS US PRO/IPO-100-1996, Initial Graphics Exchange Specification, IGES 5.3, September 1996.
[34] Jerier, J.-F., Imbault, D., Donze, F.-V., and Doremus, P. A geometric algo-rithm based on tetrahedral meshes to generate a dense polydisperse sphere packing.
Granular Matter 11 (2009), 43–52.
[35] Jia, X., and Williams, R. A packing algorithm for particles of arbitrary shapes.
Powder Technology 120 (2001), 175–186.
[36] Jiangbo, C., Chunjiang, L., Xigang, Y., and Guocong, Y. CFD simulation of flow and mass transfer in structured packing distillation columns. Separation Science and Engineering 17, 3 (2009), 381–388.
[37] Kashid, M. N., Agar, D. W., and Turek, S. CFD modelling of mass trans-fer with and without chemical reaction in the liquid-liquid slug flow microreactor.
Chemical Engineering Science 62 (2007), 5102–5109.
[38] Keyser, M., Conradie, M., Coertzen, M., and Dyk, J. V. Effect of coal particle size distribution on packed bed pressure drop and gas flow distribution.
Fuel 85, 10–11 (2006), 1439–1445.
[39] Kositanont, C., Putivisutisak, S., Praserthdam, P., Assabumrungrat, S., Yamada, H., and Tagawa, T. Flow pattern of liquid multiphase flow in microreactors with different guideline structures. Journal of Chemical Engineering of Japan 44, 9 (2011), 649–652.
[40] Lichtner, P. Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems. Geochemica et Cosmochemica Acta 49 (1985), 779–800.
84 BIBLIOGRAPHY
[41] Lo, S., and Wang, W. Generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3D domain. Computer Methods in Applied Mechanics and Engineering 194 (2005), 5002–5018.
[42] Lopes, R. J. G., and Quinta-Ferreira, R. M. Volume-of-fluid-based model for multiphase flow in high-pressure trickle-bed reactor: Optimization of numerical parameters. AIChE Journal 55, 11 (2009), 2920–2933.
[43] Mase, S., Moller, J., Stoyan, D., Waagepeterse, R., and Doge, G. Pack-ing densities and simulated temperPack-ing for hard core Gibbs point processes. Annals of the Institute of Statistical Mathematics 53 (2001), 661–680.
[44] Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E. Equations of state calculations by fast computing machines. Jour-nal of Chemical Physics 21 (1953), 1087–1092.
[45] Mueller, G. E. Radial void fraction distributions in randomly packed fixed beds of uniformly sized spheres in cylindrical containers. Powder Technology 72 (1992), 269–275.
[46] Mueller, G. E. Numerical simulation of packed beds with monosized spheres in cylindrical containers. Powder Technology 92, 2 (1997), 179–183.
[47] Nijemeisland, M., and Dixon, A. G. Comparison of CFD simulations to exper-iment for convective heat transfer in a gas-solid fixed bed. Chemical Engineering Journal 82 (2001), 231–246.
[48] Nijemeisland, M., and Dixon, A. G. CFD study of fluid flow and wall heat transfer in a fixed bed of spheres. AIChE Journal 50, 5 (2004), 906–921.
[49] Osher, S., and Sethian, J. A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computa-tional Physics 79, 1 (1988), 12–49.
[50] Qian, D., and Lawal, A. Numerical study on gas and liquid slugs for Taylor flow in a T-junction microchannel. Chemical Engineering Science 61 (2006), 7609–7625.
[51] Ratchananusorn, W., Semyonov, D., Gudarzi, D., Kolehmainen, E., and Turunen, I. Hydrodynamics and mass transfer studies on a plate microreactor.
Chemical Engineering and Processing: Process Intensification 50 (2011), 1186–1192.
[52] Reddy, R. K., and Joshi, J. B. CFD modeling of pressure drop and drag coeffi-cient in fixed and expanded beds. Chemical Engineering Research and Design 86, 5 (2008), 444–453.
[53] Rusche, H.Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions. PhD thesis, Imperial Colledge, London, 2002.
[54] Semyonov, D., Ratchananusorn, W., and Turunen, I. Hydrodynamic mod-ell of a microstructured plate microreactor. Computers and Chemical Engineering Journal 52 (2013), 145–154.
BIBLIOGRAPHY 85
[55] Sorel, E. La Rectification de l’Alcool. Gauthier-Villars et fils, Paris, 1894.
[56] Steefel, C., and Lasaga, A.A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems.American Journal of Science 294 (1994), 529–592.
[57] Stoyan, D. Models of random systems of non-intersecting spheres. In Prague Stochastics’98 (1998), pp. 543–547.
[58] Szymkiewicz, A. Modelling Water Flow in Unsaturated Porous Media. Accounting for Nonlinear Permeability and Material Heterogeneity. Springer, 2012.
[59] Taha, T., and Cui, Z. F. CFD modelling of slug flow inside square capillaries.
Chemical Engineering Science 61 (2006), 665–675.
[60] Tseng, S.-Y., Yang, A.-S., Lee, C.-Y., and Hsieh, C.-Y. CFD-based opti-mization of a diamond-obstacles inserted micromixer with boundary protrusions.
Engineering Applications of Computational Fluid Mechanics 5, 2 (2011), 210–222.
[61] van Baten, J., Ellenberger, J., and Krishna, R. Radial and axial disper-sion of the liquid phase within a KATAPAK-SR structure: experiments vs. CFD simulations. Chemical Engineering Science 56, 3 (2001), 813–821.
[62] van Baten, J., and Krishna, R. CFD simulations of mass transfer from taylor bubbles rising in circular capillaries.Chemical Engineering Science 59(2004), 2535–
2545.
[63] Vold, M. J. The sediment volume in dilute dispersions of spherical particles.
Journal of Physical Chemistry 64, 11 (1960), 1616–1619.
[64] White, J. A CFD simulation on how the different sizes of silica gel will affect the adsorption performance of silica gel. Modelling and Simulation in Engineering (2012).
[65] Williams, J., Hocking, G., and Mustoe, G. The theoretical basis of the discrete element method. In NUMETA 1985, Numerical Methods of Engineering, Theory and Applications (1985), A. Balkema, Ed.
[66] www.bulletphysics.com, Bullet Physics Toolbox main page.
[67] www.openfoam.com, OpenFOAM main page.
[68] Yeh, G., and Tripathi, V. A critical evaluation of recent developments in hy-drogeochemical transport models of reactive multi-chemical components. Water Resources Research 25 (1989), 93–108.
[69] Youngs, D. L. Time-dependent multi-material flow with large fluid distortion.
Numerical methods for fluid dynamics 24 (1982), 273–285.
[70] Yuan, Y., Han, M., Cheng, Y., Wang, D., and Jin, Y. Experimental and CFD analysis of two-phase cross/countercurrent flow in the packed column with a novel internal. Chemical Engineering Science 60, 22 (2005), 6210–6216.
86 BIBLIOGRAPHY
[71] Ziegenbalg, D., Kompter, C., Schonfeld, F., and Kralisch, D. Evalua-tion of different micromixers by CFD simulaEvalua-tions for the anionic polymerisaEvalua-tion of styrene. Green Processing and Synthesis 1, 2 (April 2012), 211–214.
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