From predicting the flow of water entering the tunnel to geothermal reservoirs and waste dumps, identifying the flow pattern in rock environments is of great importance. Various numerical and experimental methods are used to study the flow pattern in rock environments. Numerical methods have been widely used due to the lack of limitations on the dimensions of the simulated environment. In this study, a Matlab program was developed to study the flow pattern in a dual permeability environment. First, a two-dimensional model with a cross-sectional fault was developed. Then, disregarding the effects of gravity, a cross-sectional fault model was implemented from the southwest to the northeast on the porous environment, and then injection and exploitation were defined as two terms of source and discharge from the two initial and final points of the fault. The pressure equations were implicitly solved, and then the saturation percentage was explicitly calculated for each cell. Given the pressure and saturation percentage, the velocity field for the entire model was obtained. After that, the flow lines were identified and used, along with the transit time parameter, to interpret the fluid behavior in the environment.