Numerical Solution of the Material Balance Equations of Compartmented Gas Reservoirs

Abstract

Summary This paper presents a robust and rigorous method for the numerical solution of the material balance equations of compartmented gas reservoirs. The method is based on the integral form of the material balance equations and employs an implicit, iterative solution procedure. The proposed method enables extension of traditional p/z analysis of single gas reservoirs to complex, compartmented gas reservoirs. Example calculations of the depletion of a compartmented reservoir show how the p/z is affected by crossflow, reservoir size, and depletion rate. The depletion behavior can be rationalized by the observation that depletion of a compartmented reservoir at a constant rate tends to develop a semisteady state. A field example is presented that illustrates the capabilities of the extended material balance for the analysis of the past performance of compartmented reservoirs.