A-THREE DIMENSIONAL NUMERICAL SIMULATOR FOR EXPANSION-DRIVE RESERVOIRS
Every simulation study is a unique process, starting from the geological model and reservoir description to the final analysis of recovery factor optimizations. In petroleum engineering area, numerical reservoir simulators are often employed to obtained meaningful and reliable solutions for most actual cases due to extreme complexity of reservoir systems.
In this work, a three-dimensional numerical reservoir simulator is developed for expansion-drive reservoirs. The governing equation is discretized using finite difference approach; conjugate gradient method with the aid of MATLAB 9.0.0R code is used to solve the system of linear equations to obtain reservoir pressure for each cell, until bubble point pressure is reached; cumulative production at bubble point is computed as sum of expansion from each cell and oil production rate is determined at each time step. The average reservoir pressure is determined as a weighted average based on the stock tank oil that is left in the reservoir, and finally the recovery factor at the bubble point pressure is computed.
Contour plots (with colour map to ease the user’s assimilation and interpretation of the simulator results), of reservoir pressure depletion with time were generated for different number of finite-difference grid blocks. The results indicate that the more the number of grid blocks used, the more accurate the numerical solution and the more detailed the description of the reservoir fluid distribution. The plot of average reservoir pressure against time shows a rapid decline in the average reservoir pressure due to the negligible compressibility associated with rock and liquid expansion-drive reservoirs. The estimated oil cumulative production of 236MSTB was recovered in 1180days up to the bubble point using the developed simulator. Furthermore, sensitivity analysis was performed to investigate the impact of key reservoir parameters the average reservoir pressure.
1.1 General Introduction
Reservoir simulation is the science of combining physics, mathematics, reservoir engineering, and computer programming to develop a tool for predicting hydrocarbon reservoir performance under various operating strategies (Aziz, K. and Settari, A. 1979).
The practice of reservoir simulation has been in existence since the beginning of petroleum engineering in the 1930’s. But the term “numerical simulation” only became common in the early 1960’s as predictive methods evolved into relatively sophisticated computer programs. These computer programs represented a major advancement because they allowed solution of large sets of finite-difference equations describing two- and three-dimensional, transient, multiphase flow in heterogeneous porous media. This advancement was made possible by the rapid evolution of large-scale, high-speed digital computers and development of numerical mathematical methods for solving large systems of finite-difference equations