In this work we present a problematic associated with fluid flow, transport and particle retention processes in porous media. In particular, we highlight the filtration and adsorption phenomena which occur during particle injection in porous media. This work main goal is to deduct a mathematical and computational modeling of deep bed filtration and particle adsorption. Having the mathematical model been deducted, based on differential equations, analytical solutions for particular cases of the filtration coefficient are obtained. For the computational model, the high order finite volume method of Kurganov & Tadmor (KT) is proposed in order to obtain numerical solutions for the particle transport equation, and the Runge-Kutta method is used for the retention kinetics. Finally, numerical simulations for the filtration process are proposed making it possible to understand filtration, as well as evaluating the optimal properties of the proposed finite volume method.