Numerical analysis of liquid-solid adsorption model
Abstract
In this paper, the numerical algorithms for solution of pore volume and surface diffusion model of adsorption systems are constructed and investigated. The approximation of PDEs is done by using the finite volume method for space derivatives and ODE15s solvers for numerical integration in time. The analysis of adaptive in time integration algorithms is presented. The main aim of this work is to analyze the sensitivity of the solution with respect to the main parameters of the mathematical model. Such a control analysis is done for a linearized and normalized mathematical model. The obtained results are compared with simulations done for a full nonlinear mathematical model.
Keyword : numerical algorithms, finite volume method, adsorption models, sensitivity analysis
How to Cite
Leonavičienė, T., Čiegis, R., Baltrėnaitė, E., & Chemerys, V. (2019). Numerical analysis of liquid-solid adsorption model. Mathematical Modelling and Analysis, 24(4), 598-616. https://doi.org/10.3846/mma.2019.036
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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M. Belhachemi and F. Addoun. Comparative adsorption isotherms and modeling of methylene blue onto activated carbons. Applied Water Science, 1(3–4):111– 117, 2011. https://doi.org/10.1007/s13201-011-0014-1
E. Alberdi Celaya, J.J. Anza Aguirrezabala and P. Chatzipantelidis. Implementation of adaptive bdf2 formula and comparison with the matlab ode15s. Procedia Computer Science, 29:1014–1026, 2014. https://doi.org/10.1016/j.procs.2014.05.091
R. Ciegis and N. Tumanova.ˇ Numerical solution of parabolic problems with nonlocal boundary conditions. Numerical Functional Analysis and Optimization, 31(12):1318–1329, 2010. https://doi.org/10.1080/01630563.2010.526734
K. Eriksson, D. Estep, P. Hansbo and C. Johnson. Computational Differential Equations. Cambridge University Press, 1996.
W. Hundsdorfer and J.G. Verwer. Numerical Solution of Time-Dependent Advection-Difusion-Reaction Equations. Springer Series in Computational Mathematics, 33. Springer, Berlin, Heidelberg, New York, Tokyo, 2003.
O. Iliev, Z. Lakdawala, K.H.L. Neßler, T. Prill, Y. Vutov, Y. Yang and J. Yao. On the pore-scale modeling and simulation of reactive transport in 3d geometries. Mathematical Modelling and Analysis, 22(5):671–694, 2017. https://doi.org/10.3846/13926292.2017.1356759
I. Kangro and H. Kalis. On mathematical modelling of the solid-liquid mixtures transport in porous axial-symmetrical container with Henry and Langmuir sorption kinetics. Mathematical Modelling and Analysis, 23(4):554–567, 2018. https://doi.org/10.3846/mma.2018.033
M. Kavand, N. Asasian, M. Soleimani, T. Kaghazchi and R. Bardestani. Filmpore-[concentration-dependent] surface diffusion model for heavy metal ions adsorption: Single and multi-component systems. Process Safety and Environmental Protection, 107:486–497, 2017. https://doi.org/10.1016/j.psep.2017.03.017
L. Largitte and R. Pasquier. A review of the kinetics adsorption models and their application to the adsorption of lead by an activated carbon. Chemical Engineering Research and Design, 109:495–504, 2016. https://doi.org/10.1016/j.cherd.2016.02.006
R. Ocampo-Perez, R. Leyva-Ramos, P. Alonso-Davila, J. Rivera-Utrilla and M. Sanchez-Polo. Modeling adsorption rate of pyridine onto granular activated carbon. Chemical Engineering Journal, 165(1):133–141, 2010. https://doi.org/10.1016/j.cej.2010.09.002
V. Russo, R. Tesser, D. Masiello, M. Trifuoggi and M. Di Serio. Further verification of adsorption dynamic intraparticle model (ADIM) for fluid-solid adsorption kinetics in batch reactors. Chemical Engineering Journal, 283:1197–1202, 2016. https://doi.org/10.1016/j.cej.2015.08.066
V. Russo, R. Tesser, M. Trifuoggi, M. Giugni and M. Di Serio. A dynamic intraparticle model for fluid-solid adsorption kinetics. Computers and Chemical Engineering, 74:66–74, 2015. https://doi.org/10.1016/j.compchemeng.2015.01.001
V. Russo, M. Trifuoggi, M. Di Serio and R. Tesser. Fluid-solid adsorption in bach and continuous processing: a review and insights into modeling. Chemical Engineering Technology, 40(5):799–820, 2017. https://doi.org/10.1002/ceat.201600582
J.M. Sanz-Serna and S. Larsson. Shadows, chaos, and saddles. Applied Numerical Mathematics, 13:181–190, 1993. https://doi.org/10.1016/0168-9274(93)90141-D
P.R. Souza, G.L. Dotto and N.P.G. Salau. Detailed numerical solution of pore volume and surface diffusion model in adsorption systems. Chemical Engineering Research and Design, 122:298–307, 2017. https://doi.org/10.1016/j.cherd.2017.04.021
H.H. Tran, F.A. Roddick and J.A. O’Donnell. Comparison of chromatography and desiccant silica gels for the adsorption of metal ions–I. adsorption and kinetics. Water Research, 33(13):2992–3000, 1999. https://doi.org/10.1016/S00431354(99)00017-2