ISSN(Online): 2319-8753 ISSN (Print): 2347-6710 International Journal of Innovative Research in Science, Engineering and Technology (An ISO 3297: 2007 Certified Organization) Vol. 5, Issue 11, November 2016 Copyright to IJIRSET Discrete Modeling of Solute Transport in a Homogeneous Porous Medium S Semmar, N Bendjaballah-Lalaoui Department of Chemical Engineering, University of Science and Technology Houari Boumediene (USTHB) , Algeria 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. Keywords: Modeling, Analytical solution, Solute transport, Physical non equilibrium, Porous media. Nomenclature BTC breakthrough curve. CDE convection dispersion equation. CM classical model. MIM mobile-immobile model. PNE physical non equilibrium. C concentration of solute in contact with an aggregate [M L-3].   Laplace transforms of C. D0 molecular diffusion coefficient in free water [L2T-1]. d diameter of column [L]. dp diameter of a soil particle [L]. F (t) function of the BTC from step inputs. G(s) global transfer function for the column. G(T) transfer function in time domain. g_k (s) transfer function for cell k. J number of mixing cells. K_im ratio of immobile water fraction to mobile water fraction k_M mass transfer coefficient [T-1]. L length of column [L]. M mass of the porous medium [M]. N number of observation concentration data. Q volumetric flow rate [L3T-1]. R2 correlation coefficient. Sp area of a soil particle [L2]. s Laplace transform parameter. t_M characteristic mass transfer time [T].