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. A mathematical model is obtained based on differential equations, and analytical solutions considering particular cases of the filtration coefficient are obtained. The high order finite volume scheme based on Kurganov & Tadmor (KT) method is proposed in order to obtain numerical solutions for the particle transport equation, and the Runge-Kutta method is used for the retention kinetics. Furthermore, 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. Finally, we use the proposed mathematical and numerical model along with an optimization technique to quantify the model’s effective coefficients based on effluent and retained particle concentrations profiles obtained experimentally.