Fluid flow invasion is governed by the characteristics of the pore structure in the porous media. The flow is restricted due to the increase of net stresses near borehole after drilling. Understanding the fluid flow at the pore scale becomes an important aspect of successful operations such as matrix acidizing or fluid formation treatment. The aim of this work is to demonstrate the ability of using Lattice-Boltzmann formulations to solve the complex fluid flow system in the porous medium as compared to a Darcy type of flow analysis using geomechanical approaches. The simulations were performed at the same physical scale. The reduction of pore size at the vicinity of the borehole is approximated using different geometrical domains to mimic the fluid invasion process as a result of change in net stresses.