A Two-Dimensional Reservoir Simulator for Expansion-Drive Reservoirs

Abstract

ABSTRACT The application of reservoir simulation to mimic the behavior of reservoirs is widely accepted in the petroleum industry. The technique involves planning, constructing and operating a model whose behavior approximates the behavior of the actual (real) reservoir. Often, mathematical equations (i.e., a model) are developed and employed to understand the performance of the real (physical) reservoir. In this paper, a two-dimensional numerical reservoir simulator is developed for expansion-drive reservoirs. Cumulative production at bubble point is computed as a sum of expansion from each cell, based on average reservoir pressure and oil rate from the well. The average reservoir pressure is weighted based on stock tank oil that remains in the reservoir and each cell. Subsequently, plots were generated for average reservoir pressure versus time and cumulative production from each cell versus time. Also, wellbore pressure at mid-horizontal well was plotted against time on Cartesian and semi-log graphs. Furthermore, area plots were generated using color differentiation to illustrate how the reservoir pressure is depleting with time. Simulation studies performed using the developed simulator show a rapid pressure decline as would be expected for an expansion-drive reservoir due to the insignificant compressibilities that typify rocks and liquids. In addition, the reservoir volume estimated from the Cartesian and semi-log plots correctly matched the material balance estimate. Finally, the estimated recovery factor at bubble point (about 2% of the stock tank oil originally in place, STOIIP) agrees with published values in widely-circulated literatures - demonstrating the weakness of rock and liquid expansion as a primary drive mechanism. The reservoir simulator developed in this work can be used by reservoir engineers to understand depletion in under-saturated oil reservoirs whose primary production is driven by rock and liquid expansion.