Numerical simulation of a nonlinear diffusion type equation in a two phase media with linear porosity and permeability model

Abstract

Predicting and understanding the behavior of pressure is important in reservoir maintenance and evaluation. This work studies the behavior of fluid pressure in a reservoir by numerical simulation of the pressure diffusion type equation in a two phase media with a linear porosity and permeability model. Because the porosity and permeability are pressure dependent, the resulting diffusion type equation is nonlinear and is solved using a backward-forward finite difference method. The simulation code was ran using a constant porosity and permeability model and a linear porosity and permeability model. The results from the linear porosity and permeability model was compared to that of the constant porosity and permeability model. In both cases the pressure gradient was greatest at the wellbore and decreases as the radial distances away from the wellbore increases. The pressure in both cases also decreased with time. However, at each location and time the pressure drop was lower in the linear porosity and permeability model than with the constant porosity and permeability. The backward-forward finite difference method proved to be useful in solving numerically the nonlinear diffusion type equation. This work can be applied in the oil and gas industry to predict pressure behavior in reservoirs and make investment decisions, production and maintenance decision.