Development of Finite Difference Explicit and Implicit Numerical Reservoir Simulator for Modelling Single Phase Flow in Porous Media

Abstract

Every petroleum reservoir requires some means of predicting future performances as well as optimizing recovery of hydrocarbons under various operating conditions. Moreover, there is a need to simulate fluid flow in porous media due to the uncertainty and heterogeneity that is associated with petroleum reservoirs. Therefore, this study developed 1D finite difference explicit and implicit numerical reservoir simulator for modeling single phase flow in porous media. The explicit and implicit simulator developments consist of physical modeling, mathematical modeling, discretization of the models with finite difference scheme and transformation of the models into computer algorithms. Matlab codes were written to describe the fluid flow process to obtain the reservoir pressure distributions for each grid block at each timestep calculation. The explicit formulation linear equation was solved by the direct method while the implicit method was solved by the Jacobi iterative method. The numerical examples graphical plots generated from the simulator illustrate the average reservoir pressure depletion for the finite difference grid blocks. The plots for both the explicit and implicit method indicate decline in average reservoir pressure with time. The explicit and implicit simulators show that the implicit formulation is unconditionally stable than the explicit formulation. This is because the explicit method under certain conditions generates errors in the numerical solutions which tend to go zero during subsequent timestep calculations. Additionally, the porosity sensitivity analyses performed show that the average reservoir pressure decline as the porosity decreases from 30% to 10%. Material balance method was used to determine the average reservoir pressure decline for a one-year production period. The estimated recovery factor at the bubble point pressure is 0.68% of the original oil in place. This low recovery factor is a characteristic of an expansion-drive reservoir which has the least efficient recovery mechanism. Finally, the 1D explicit and implicit finite difference numerical simulators for predicting single phase flow reservoir pressure distributions during production periods are stepping stone towards implementing multiphase fluid flow formulations.