A comparative study between finite difference explicit and implicit method for predicting pressure distribution in a petroleum reservoir

Abstract

Predicting pressure distribution in a petroleum reservoir is principal to the reservoir’s evaluation and maintenance, as pressure changes with space and time. A convenient approach to effectively achieve this task is to formulate fluid flow equations based on the reservoir characteristics and solve them numerically. Numerical method provides solutions to mathematical fluid flow models developed in a reservoir simulation. This study provides numerical solutions, using both finite difference explicit and implicit method, to a mathematical model by developing MATLAB codes to ascertain the pressure distribution for a singlephase, one-dimensional, slightly compressible fluid flow in a petroleum reservoir. Series of numerical simulations were carried out during the first year of production using timestep sizes of 1, 2 and 3 days, respectively. The explicit method gave poor result (negative values for pressures) for timestep of 1 day, an outcome that is not accurate to describe the problem being solved but gave acceptable pressure results for timestep of 2 and 3 days. This shows that the efficacy of the explicit method is reliant on the chosen timestep and simulation time. In contrast, the implicit method gave a quite satisfactory results for all timesteps, and including less than 1 day, confirming the robustness and unconditionally stable nature of the implicit method. A commercial simulator (CMG software) was also employed to build a one-dimensional black oil model to validate the aforesaid results of which a close match was observed between the simulator results and the numerical solutions. This study provides insights to reservoir’s pressure profile during hydrocarbon recovery beforehand so that efficient pressure maintenance decisions can be made to achieve economic hydrocarbon recovery throughout the life of the reservoir.

Keywords: finite difference formulation; explicit and implicit method; petroleum reservoir; pressure distribution; numerical reservoir simulation