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

Abstract

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.