Open Access Open Access  Restricted Access Subscription or Fee Access

Modeling and Simulation of Transport and Biological Reaction in Fluid-Saturated Porous Media

(*) Corresponding author

Authors' affiliations



Several procedures are recommended for the treatment of polluted sites. It has been observed that biological remediation (biodegradation) is a promising, economical, fast, and functional procedure, which can be used as a new treatment technique for polluted sites. It entails providing nutritive substrates like oxygen and nitrogen to bacteria in each environment to stimulate their activity. This work will consider the transport of a pollutant coupled with the phenomenon of biodegradation, which is the decomposition of organic matter by microorganisms such as bacteria, fungi, or algae, in a saturated porous medium. The mathematical model under consideration is composed of three independent equations linked together, each with its own stability and convergence conditions, making the system difficult to solve numerically. Our model will be solved as a nonlinear system of coupled partial differential equations. Therefore, our objective is to develop a strategy that will allow approaching this type of problems and producing results that are more efficient. The technique used here is based on the operator splitting method, which is an effective method to solve this kind of complex models. The primary idea behind this strategy is to break down a complex problem into smaller subsystems, known as division sub-problems, and solve each one using the proper numerical method. In the literature, there are not enough details on the programs to translate the numerical methods used. There is only software ready to do that. In this context, we developed our own code capable of simulating this type of problem. The transport problem is approximated by a finite difference scheme- the first order accurate FDM for time, the second order accurate FDM for space and for diffusion equation and first order backward FDN for the term of advection - and the biological equations, which are presented using Monod kinetics, are solved by a Rung-Kutter method of order 4. The operator splitting method employed in this simulation is validated using an example of transport and biodegradation with first order kinetics (case of low contaminant concentration) that admits an analytical solution in saturated porous media. The numerical and analytical results are in perfect agreement, and this can prove the efficiency of the splitting method as well as the validation of our developed code.
Copyright © 2022 Praise Worthy Prize - All rights reserved.


Transport; Biodegradation; Saturated Porous Media; Finite Different Scheme; Splitting Technique; Runge-Kutta Method

Full Text:



Geng, X., An, C., Lee, K., & Boufadel, M. C. (2022). Modeling oil biodegradation and bioremediation within beaches. Current Opinion in Chemical Engineering, 35, 100751.

M. L. Brusseau, M. Q. Hu, J.-M. Wang, R. M. Maier, Biodegradation during Contaminant Transport in Porous Media. 2. The Influence of Physicochemical Factors, Environ. Sci. Technol., vol. 33, no 1, p. 96 103, janv. 1999.

B. Kim, I. W. Seo, S. Kwon, S. H. Jung, et Y. Choi, Modelling one-dimensional reactive transport of toxic contaminants in natural rivers, Environmental Modelling & Software, vol. 137, p. 104971, March 2021.

Escuder-Gilabert, Laura, Martín-Biosca, Yolanda, Perez-Baeza, Mireia, et al. Trimeprazine is enantioselectively degraded by an activated sludge in ready biodegradability test conditions. Water Research, 2018, vol. 141, p. 57-64.

L. S. J. Bell et P. J. Binning, A split operator approach to reactive transport with the forward particle tracking Eulerian Lagrangian localized adjoint method, Advances in Water Resources, vol. 27, no 4, p. 323 334, avr. 2004.

A. S. Kim, Complete analytic solutions for convection-diffusion-reaction-source equations without using an inverse Laplace transform, Sci Rep, vol. 10, no 1, p. 8040, Dec. 2020.

Y. Fu, W. J. Kao, Drug release kinetics and transport mechanisms of non-degradable and degradable polymeric delivery systems, Expert Opinion on Drug Delivery, vol. 7, no 4, p. 429 444, April 2010.

A. Agouzal, K. Allali, et S. Binna, Numerical analysis of in-situ biodegradation model in porous media, Journal of Computational and Applied Mathematics, vol. 344, p. 190 228, Dec. 2018.

Bear, Jacob. Modeling phenomena of flow and transport in porous media. Vol. 1. Cham: Springer International Publishing, 2018.

Liu, Y., Zhang, X., Xu, Y., Liu, Q., & Cao, W. Transport Behaviors of Biochar Particles in Saturated Porous Media Under Dc Electric Field. Huu hao and Cao, Weimin, Transport Behaviors of Biochar Particles in Saturated Porous Media Under Dc Electric Field, 2022.

E. Bahar, G. Gürarslan, Numerical Solution of Advection-Diffusion Equation Using Operator Splitting Method, International Journal of Engineering & Applied Sciences, vol. 9, no 4, p. 76 88, Dec. 2017.

A. Taigbenu, J. A. Liggett, An Integral Solution for the Diffusion-Advection Equation, Water Resour. Res., vol. 22, no 8, p. 1237 1246, août 1986.

D. Lanser, J. G. Verger, Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling, Journal of Computational and Applied Mathematics, p. 16, 1999.

I. El Arabi, A. Chafi, et S. K. Alami, Numerical simulation of the SIR and Lotka-Volterra models used in biology, in 2019 International Conference on Intelligent Systems and Advanced Computing Sciences (ISACS), Taza, Morocco, Dec. 2019, p. 1-4.

Guo, D., You, S., Li, F., & Liu, Y. (2021). Engineering carbon nano catalysts towards efficient degradation of emerging organic contaminants via persulfate activation: A review. Chinese Chemical Letters.

I. El Arabi, A. Chafi, and S. K. Alami, Numerical simulation of the advection-diffusion-reaction equation using finite difference and operator splitting methods: Application on the 1D transport problem of contaminant in saturated porous media, E3S Web Conf., vol. 351, p. 01003, 2022.

I. E. Arabi, A. Chafi, and S. K. Alami, Numerical Simulation of the Advection-diffusion Equation using Finite Difference and Operator Splitting Methods, Advances in Communication Technology, Computing and Engineering, pp. 685-692, 2022

E. Universitat Politécnica de Valencia, Universitat Politécnica de Valencia, ING. Agua, vol. 18, no. 1, p. ix, Sep. 2014.

McLachlan R I, Quispel R (2002) Splitting methods, Acta Number. 11: 341-434.

Hairer E, Lubich C, and Wanner G (2006) Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd Ed, Springer (Berlin).

Holden H, Karlsen K H, Lie K A, and Risebro N H (2010) Splitting Methods for Partial Differential Equations with Rough Solutions, European Mathematical Society (Zurich).

S. A. Kammouri, M. Elhatri, and M. N. Kabbaj, A Numerical Simulation of Transport and Biodegradation in Saturated Porous Media, in 2009 International Conference on Advanced Information Networking and Applications Workshops, Bradford, United Kingdom, May 2009, pp. 914-917.

S. Krautle, General multi-species reactive transport problems in porous media: Efficient numerical approaches and existence of global solutions, Habilitation Thesis, 2008.

Mazzeo DEC, Matsumoto ST, Levy CE, de Angelis DdF, Marin-Morales MA (2013) Application of micronucleus test and comet assay to evaluate BTEX biodegradation. Chemosphere 90:1030-1036.

Feisther VA, Ulson de Souza AA, Trigueros DEG, Mello JMM, Oliveira D, Ulson Guelli, de Souza SMA (2015) Biodegradation kinetics of benzene, toluene, and xylene compounds: microbial growth and evaluation of models. Bioprocess Biosyst Eng 38:1233-1241.

CONAMA (2011) Brazilian National Council for the Environment-Resolution no. 430, of May 2011.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2024 Praise Worthy Prize