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.
Fluid flow in petroleum reservoirs (porous media) is very complex phenomena, and as such analytical solutions to mathematical models are only obtainable after making simplifying assumptions regarding reservoir geometry, properties and boundary conditions. However, simplifications of this nature are often invalid for most fluid flow problems and in many cases, it is impossible to develop analytical solutions for practical issues due to the complex behaviors of multiphase flow, nonlinearity of the governing equations, and the heterogeneity and irregular shape of a reservoir system. Due to these limitations in the use of analytical method, these models must be solved with numerical methods such as finite difference.
Reservoir simulation is one of the most effective tools for reservoir engineers that involves developing mathematical equations or computable procedure that are employed to understand the behaviour of the real reservoir (Darman, 1999). Today, numerical reservoir simulation is regularly used as a valuable tool to help make investment decisions on major exploitation and development projects. These decisions include determining commerciality, optimizing field development plans and initiating secondary and enhanced oil recovery methods on major oil and gas projects. Proper planning is made possible by use of reservoir simulation; it can be used effectively in the early stages of development before the pool is placed on production so that unnecessary expenditures can be avoided.
When crude oil is discovered, in order to have proper understanding of reservoir behaviour and predict future performance, it is necessary to have knowledge of the driving mechanisms that control the behaviour of fluids within reservoirs. The overall performance of oil reservoirs is largely determined by the nature of the energy available for moving the oil to the wellbore. The recovery of hydrocarbons from an oil reservoir is commonly recognized to occur in several recovery stages. They are: Primary recovery, Secondary recovery, Tertiary recovery (Enhanced Oil Recovery, EOR), and Infill recovery. Primary recovery is the recovery of hydrocarbons from the reservoir using the natural energy of the reservoir as a drive. The term refers to the production of hydrocarbons from a reservoir without the use of any process (such as fluid injection) to supplement the natural energy of the reservoir (Ahmed, 2006).