Chromatography; Convection–diffusion–reaction; Packed-bed; Reduced-order modeling; Stabilized space–time finite elements; Convection-diffusion-reaction; Dispersion coefficient; Fast simulation; Flow and transport; High definition; Inhomogeneities; Reduced order modelling; Reduced-order model; Space time finite element; Stabilized space–time finite element; Chemical Engineering (all); Computer Science Applications
Abstract :
[en] Numerical simulations of chromatography are conventionally performed using reduced-order models that homogenize aspects of flow and transport in the radial and angular dimensions. This enables much faster simulations at the expense of lumping the effects of inhomogeneities into a column dispersion coefficient, which requires calibration via empirical correlations or experimental results. We present a high-definition model with spatially resolved geometry. A stabilized space–time finite element method is used to solve the model on massively parallel high-performance computers. We simulate packings with up to 10,000 particles. The impact of particle size distribution on velocity and concentration profiles as well as breakthrough curves is studied. Our high-definition simulations provide unique insight into the process. The high-definition data can also be used as a source of ground truth to identify and calibrate appropriate reduced-order models that can then be applied for process design and optimization.
Disciplines :
Chemical engineering
Author, co-author :
Rao, Jayghosh Subodh; Forschungszentrum Jülich, IBG-1: Biotechnology, Jülich, Germany ; Chair for Computational Analysis of Technical Systems (CATS), RWTH Aachen University, Aachen, Germany ; JARA - Center for Simulation and Data Science, Germany
Püttmann, Andreas; Forschungszentrum Jülich, IBG-1: Biotechnology, Jülich, Germany ; Chair for Computational Analysis of Technical Systems (CATS), RWTH Aachen University, Aachen, Germany
Khirevich, Siarhei; Department of Chemistry, Philipps-University Marburg, Marburg, Germany ; Ali I. Al-Naimi Petroleum Engineering Research Center, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
Tallarek, Ulrich; Department of Chemistry, Philipps-University Marburg, Marburg, Germany
Geuzaine, Christophe ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Applied and Computational Electromagnetics (ACE)
Behr, Marek ; Chair for Computational Analysis of Technical Systems (CATS), RWTH Aachen University, Aachen, Germany ; JARA - Center for Simulation and Data Science, Germany
von Lieres, Eric ; Forschungszentrum Jülich, IBG-1: Biotechnology, Jülich, Germany ; JARA - Center for Simulation and Data Science, Germany
Language :
English
Title :
High-definition simulation of packed-bed liquid chromatography
This work was conducted during the Ph.D. studies of Andreas Püttmann and Jayghosh Rao. The authors gratefully acknowledge the funding and support of the JARA-SSD program. The authors also gratefully acknowledge the computing time granted through JARA on the supercomputer JURECA ( Centre, 2018; Jülich Supercomputing Centre, 2021 ) at Forschungszentrum Jülich. Figures 1 and 2 reprinted from Püttmann et al. (2014) with permission from Elsevier.
Baker, M., Young, P., Tabor, G., Image based meshing of packed beds of cylinders at low aspect ratios using 3d MRI coupled with computational fluid dynamics. Comput. Chem. Eng. 35:10 (2011), 1969–1977, 10.1016/j.compchemeng.2011.03.017.
Bu, S., Yang, J., Zhou, M., Li, S., Wang, Q., Guo, Z., On contact point modifications for forced convective heat transfer analysis in a structured packed bed of spheres. Nucl. Eng. Des. 270 (2014), 21–33, 10.1016/j.nucengdes.2014.01.001.
Campello, E.M.B., Cassares, K.R., Rapid generation of particle packs at high packing ratios for dem simulations of granular compacts. Lat. Am. J. Solids Struct. 13:1 (2016), 23–50, 10.1590/1679-78251694.
Carta, G., Ubiera, A., Particle-size distribution effects in batch adsorption. AIChE J. 49:12 (2003), 3066–3073, 10.1002/aic.690491208.
Centre, J.S., JURECA: Modular supercomputer at Jülich Supercomputing Centre. J. Large-Scale Res. Facil., 4(A132), 2018, 10.17815/jlsrf-4-121-1.
Daneyko, A., Hlushkou, D., Khirevich, S., Tallarek, U., From random sphere packings to regular pillar arrays: Analysis of transverse dispersion. J. Chromatogr. A 1257 (2012), 98–115, 10.1016/j.chroma.2012.08.024 URL http://www.ncbi.nlm.nih.gov/pubmed/22921359.
Daneyko, A., Khirevich, S., Höltzel, A., Seidel-Morgenstern, A., Tallarek, U., From random sphere packings to regular pillar arrays: Effect of the macroscopic confinement on hydrodynamic dispersion. J. Chromatogr. A 1218:45 (2011), 8231–8248, 10.1016/j.chroma.2011.09.039 URL http://www.ncbi.nlm.nih.gov/pubmed/21982445.
Dixon, A.G., Nijemeisland, M., Stitt, E.H., Packed tubular reactor modeling and catalyst design using computational fluid dynamics. Adv. Chem. Eng., 2006, 307–389, 10.1016/s0065-2377(06)31005-8.
Dixon, A.G., Nijemeisland, M., Stitt, E.H., Systematic mesh development for 3D CFD simulation of fixed beds: Contact points study. Comput. Chem. Eng. 48 (2013), 135–153, 10.1016/j.compchemeng.2012.08.011.
Dorai, F., Moura Teixeira, C., Rolland, M., Climent, E., Marcoux, M., Wachs, A., Fully resolved simulations of the flow through a packed bed of cylinders: Effect of size distribution. Chem. Eng. Sci. 129 (2015), 180–192, 10.1016/j.ces.2015.01.070.
Dziennik, S.R., Belcher, E.B., Barker, G.A., DeBergalis, M.J., Fernandez, S.E., Lenhoff, A.M., Nondiffusive mechanisms enhance protein uptake rates in ion exchange particles. Proc. Natl. Acad. Sci. 100:2 (2003), 420–425, 10.1073/pnas.0237084100.
Eppinger, T., Seidler, K., Kraume, M., DEM-CFD simulations of fixed bed reactors with small tube to particle diameter ratios. Chem. Eng. J. 166:1 (2011), 324–331, 10.1016/j.cej.2010.10.053.
Eppinger, T., Wehinger, G.D., A generalized contact modification for fixed-bed reactor CFD simulations. Chem. Ing. Tech., 2020, 10.1002/cite.202000182.
Georgalli, G.A., Reuter, M.A., A particle packing algorithm for packed beds with size distribution. Granul. Matter 10:4 (2008), 257–262, 10.1007/s10035-008-0097-z.
Gerontas, S., Shapiro, M.S., Bracewell, D.G., Chromatography modelling to describe protein adsorption at bead level. J. Chromatogr. A 1284 (2013), 44–52, 10.1016/j.chroma.2013.01.102.
Geuzaine, C., Remacle, J.-F., Gmsh : a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Internat. J. Numer. Methods Engrg., 2009, 1–24.
Guiochon, G., Felinger, A., Shirazi, D.G., Katti, A.M., Fundamentals of Preparative and Nonlinear Chromatography. second ed., 2006, Elsevier Academic Press, Amsterdam.
Hlushkou, D., Bruns, S., Seidel-Morgenstern, A., Tallarek, U., Morphology-transport relationships for silica monoliths: From physical reconstruction to pore-scale simulations. J. Sep. Sci. 34:16–17 (2011), 2026–2037, 10.1002/jssc.201100158.
Hlushkou, D., Bruns, S., Tallarek, U., High-performance computing of flow and transport in physically reconstructed silica monoliths. J. Chromatogr. A 1217:23 (2010), 3674–3682, 10.1016/j.chroma.2010.04.004.
Hlushkou, D., Tallarek, U., Analysis of microstructure–effective diffusivity relationships for the interparticle pore space in physically reconstructed packed beds. J. Chromatogr. A 1581–1582 (2018), 173–179, 10.1016/j.chroma.2018.11.003.
Hubbuch, J., Linden, T., Knieps, E., Thömmes, J., Kula, M.-R., Dynamics of protein uptake within the adsorbent particle during packed bed chromatography. Biotechnol. Bioeng. 80:4 (2002), 359–368, 10.1002/bit.10500.
Hubbuch, J., Linden, T., Knieps, E., Thömmes, J., Kula, M.-R., Mechanism and kinetics of protein transport in chromatographic media studied by confocal laser scanning microscopy. J. Chromatogr. A 1021:1–2 (2003), 105–115, 10.1016/j.chroma.2003.08.092.
Jerier, J.-F., Imbault, D., Donze, F.-V., Doremus, P., A geometric algorithm based on tetrahedral meshes to generate a dense polydisperse sphere packing. Granul. Matter 11:1 (2008), 43–52, 10.1007/s10035-008-0116-0.
Jodrey, W.S., Tory, E.M., Computer simulation of close random packing of equal spheres. Phys. Rev. A 32:4 (1985), 2347–2351, 10.1103/physreva.32.2347.
Jülich Supercomputing Centre, W.S., JURECA: Data centric and booster modules implementing the modular supercomputing architecture at Jülich Supercomputing Centre. J. Large-Scale Res. Facil., 7(A182), 2021, 10.17815/jlsrf-7-182.
Jungreuthmayer, C., Steppert, P., Sekot, G., Zankel, A., Reingruber, H., Zanghellini, J., Jungbauer, A., The 3D pore structure and fluid dynamics simulation of macroporous monoliths: High permeability due to alternating channel width. J. Chromatogr. A 1425 (2015), 141–149, 10.1016/j.chroma.2015.11.026.
Jurtz, N., Kraume, M., Wehinger, G.D., Advances in fixed-bed reactor modeling using particle-resolved computational fluid dynamics (CFD). Rev. Chem. Eng. 35:2 (2019), 139–190, 10.1515/revce-2017-0059.
Karthik, G.M., Buwa, V.V., Effect of particle shape on fluid flow and heat transfer for methane steam reforming reactions in a packed bed. AIChE J. 63:1 (2016), 366–377, 10.1002/aic.15542.
Khirevich, S., High-Performance Computing of Flow, Diffusion, and Hydrodynamic Dispersion in Random Sphere Packings. (Ph.D. thesis), 2011, Philipps-Universität Marburg.
Khirevich, S., Daneyko, A., Höltzel, A., Seidel-Morgenstern, A., Tallarek, U., Statistical analysis of packed beds, the origin of short-range disorder, and its impact on eddy dispersion. J. Chromatogr. A 1217:28 (2010), 4713–4722, 10.1016/j.chroma.2010.05.019 URL http://www.ncbi.nlm.nih.gov/pubmed/20570271.
Khirevich, S., Höltzel, A., Ehlert, S., Seidel-Morgenstern, A., Tallarek, U., Large-scale simulation of flow and transport in reconstructed HPLC-microchip packings. Anal. Chem. 81:12 (2009), 4937–4945 URL http://www.ncbi.nlm.nih.gov/pubmed/19459621.
Khirevich, S., Höltzel, A., Hlushkou, D., Seidel-Morgenstern, A., Tallarek, U., Structure-transport analysis for particulate packings in trapezoidal microchip separation channels. Lab Chip 8:11 (2008), 1801–1808.
Khirevich, S., Höltzel, A., Hlushkou, D., Tallarek, U., Impact of conduit geometry and bed porosity on flow and dispersion in noncylindrical sphere packings. Anal. Chem. 79:24 (2007), 9340–9349, 10.1021/ac071428k.
Li, L., Yan, X., Yang, J., Wang, Q., Computational study of chromatography performance in ordered packed beds with spherical or ellipsoidal particles. Energy Procedia 75 (2015), 3322–3327, 10.1016/j.egypro.2015.07.719.
Li, L., Yan, X., Yang, J., Wang, Q., Numerical investigation on band-broadening characteristics of an ordered packed bed with novel particles. Appl. Energy 185 (2017), 2168–2180, 10.1016/j.apenergy.2016.03.045.
Ljunglöf, A., Hjorth, R., Confocal microscopy as a tool for studying protein adsorption to chromatographic matrices. J. Chromatogr. A 743:1 (1996), 75–83, 10.1016/0021-9673(96)00290-7.
Ljunglöf, A., Thömmes, J., Visualising intraparticle protein transport in porous adsorbents by confocal microscopy. J. Chromatogr. A 813:2 (1998), 387–395, 10.1016/s0021-9673(98)00378-1.
Lubachevsky, B.D., Stillinger, F.H., Geometric properties of random disk packings. J. Stat. Phys. 60:5–6 (1990), 561–583, 10.1007/bf01025983.
Mantle, M., Sederman, A., Gladden, L., Single- and two-phase flow in fixed-bed reactors: MRI flow visualisation and lattice-Boltzmann simulations. Chem. Eng. Sci. 56:2 (2001), 523–529, 10.1016/s0009-2509(00)00256-6.
Martinez, A., Kuhn, M., Briesen, H., Hekmat, D., Enhancing the X-ray contrast of polymeric biochromatography particles for three-dimensional imaging. J. Chromatogr. A 1590 (2019), 65–72, 10.1016/j.chroma.2018.12.065.
Montesinos, R., Tejedamansir, A., Guzman, R., Ortega, J., Schiesser, W., Analysis and simulation of frontal affinity chromatography of proteins. Sep. Purif. Technol. 42:1 (2005), 75–84, 10.1016/j.seppur.2004.03.014.
Mościński, J., Bargieł, M., Rycerz, Z.A., Jacobs, P.W.M., The force-biased algorithm for the irregular close packing of equal hard spheres. Mol. Simul. 3:4 (1989), 201–212, 10.1080/08927028908031373.
Pashchenko, D., Karpilov, I., Mustafin, R., Numerical calculation with experimental validation of pressure drop in a fixed-bed reactor filled with the porous elements. AIChE J., 66(5), 2020, 10.1002/aic.16937.
Pauli, L., Behr, M., On stabilized space-time FEM for anisotropic meshes: Incompressible Navier-Stokes equations and applications to blood flow in medical devices. Internat. J. Numer. Methods Fluids 85:3 (2017), 189–209, 10.1002/fld.4378.
Püttmann, A., Nicolai, M., Behr, M., von Lieres, E., Stabilized space–time finite elements for high-definition simulation of packed bed chromatography. Finite Elem. Anal. Des. 86 (2014), 1–11, 10.1016/j.finel.2014.03.001.
Püttmann, A., Schnittert, S., Naumann, U., von Lieres, E., Fast and accurate parameter sensitivities for the general rate model of column liquid chromatography. Comput. Chem. Eng. 56 (2013), 46–57, 10.1016/j.compchemeng.2013.04.021 URL http://linkinghub.elsevier.com/retrieve/pii/S0098135413001440.
Qamar, S., Uche, D.U., Khan, F.U., Seidel-Morgenstern, A., Analysis of linear two-dimensional general rate model for chromatographic columns of cylindrical geometry. J. Chromatogr. A 1496 (2017), 92–104, 10.1016/j.chroma.2017.03.048.
Rasmuson, A., The effect of particles of variable size, shape and properties on the dynamics of fixed beds. Chem. Eng. Sci. 40:4 (1985), 621–629, 10.1016/0009-2509(85)80006-3.
Rastegar, S.O., Gu, T., Empirical correlations for axial dispersion coefficient and peclet number in fixed-bed columns. J. Chromatogr. A 1490 (2017), 133–137, 10.1016/j.chroma.2017.02.026.
Rebughini, S., Cuoci, A., Maestri, M., Handling contact points in reactive CFD simulations of heterogeneous catalytic fixed bed reactors. Chem. Eng. Sci. 141 (2016), 240–249, 10.1016/j.ces.2015.11.013.
Schnittert, S., Winz, R., von Lieres, E., Development of a 3D model for packed bed liquid chromatography in micro-columns. 2009 Third UKSim European Symposium on Computer Modeling and Simulation, 2009, IEEE, 10.1109/ems.2009.62 URL http://dx.doi.org/10.1109/ems.2009.62.
Schröder, M., Von Lieres, E., Hubbuch, J., Direct quantification of intraparticle protein diffusion in chromatographic media. J. Phys. Chem. B 110:3 (2006), 1429–1436.
Sederman, A., Alexander, P., Gladden, L., Structure of packed beds probed by magnetic resonance imaging. Powder Technol. 117:3 (2001), 255–269, 10.1016/s0032-5910(00)00374-0.
Sullivan, S., Sani, F., Johns, M., Gladden, L., Simulation of packed bed reactors using lattice Boltzmann methods. Chem. Eng. Sci. 60:12 (2005), 3405–3418, 10.1016/j.ces.2005.01.038.
Tallarek, U., Hlushkou, D., Höltzel, A., Solute sorption, diffusion, and advection in macro–mesoporous materials: Toward a realistic bottom-up simulation strategy. J. Phys. Chem. C 126:5 (2022), 2336–2348, 10.1021/acs.jpcc.1c10137.
Tallarek, U., Hlushkou, D., Rybka, J., Höltzel, A., Multiscale simulation of diffusion in porous media: From interfacial dynamics to hierarchical porosity. J. Phys. Chem. C 123:24 (2019), 15099–15112, 10.1021/acs.jpcc.9b03250.
Wehinger, G.D., Eppinger, T., Kraume, M., Detailed numerical simulations of catalytic fixed-bed reactors: Heterogeneous dry reforming of methane. Chem. Eng. Sci. 122 (2015), 197–209, 10.1016/j.ces.2014.09.007.
Wehinger, G.D., Fütterer, C., Kraume, M., Contact modifications for CFD simulations of fixed-bed reactors: Cylindrical particles. Ind. Eng. Chem. Res. 56:1 (2016), 87–99, 10.1021/acs.iecr.6b03596.
Yang, K., Bai, S., Sun, Y., Protein adsorption dynamics in cation-exchange chromatography quantitatively studied by confocal laser scanning microscopy. Chem. Eng. Sci. 63:16 (2008), 4045–4054, 10.1016/j.ces.2008.05.013.
Yang, K., Shi, Q.-H., Sun, Y., Modeling and simulation of protein uptake in cation exchanger visualized by confocal laser scanning microscopy. J. Chromatogr. A 1136:1 (2006), 19–28, 10.1016/j.chroma.2006.09.036.
Zhao, G., Zhang, L., Bai, S., Sun, Y., Analysis of hydrophobic charge induction displacement chromatography by visualization with confocal laser scanning microscopy. Sep. Purif. Technol. 82 (2011), 138–147, 10.1016/j.seppur.2011.09.002.
Zobel, N., Eppinger, T., Behrendt, F., Kraume, M., Influence of the wall structure on the void fraction distribution in packed beds. Chem. Eng. Sci. 71 (2012), 212–219, 10.1016/j.ces.2011.12.029.