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Discrete Modeling of Solute Transport in a Homogeneous Porous Medium

Abstract

This work presents the study of one-dimensional and unidirectional transport of non-reactive solute through a saturated and homogeneous porous medium in a laboratory column. Based on the discrete approach, two models were discussed. The first called classical model (CM) established when local thermodynamic equilibria are reached; however, the second was the mobile/immobile model (MIM). This model takes into account the physical non-equilibrium (PNE), so the pore space is divided into “mobile” and “immobile” flow regions with first-order mass transfer between these two regions. The objective of this work is the determination of the analytical solution of the transport equation for both models using Inverse Laplace transforms based on the method of residues. Validation of each equation is made through a calculation code that we developed in MATLAB to optimize the experimental breakthrough curves (BTCs). The results obtained show that for a moderate flow rate (Q= 5ml/min) the BTCs present an asymmetry, the assumption of physical equilibrium on which the CM model based, is sometimes inadequate. This justified the application of the MIM model.

S Semmar, N Bendjaballah-Lalaoui

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