A Generalized Approach to Reservoir Material Balance Calculations

Abstract

This work completes the search for a generalized material balance equation. No restrictions are placed on reservoir fluid compositions. Unlike the conventional material balance equation, the new equation specifically accounts for volatilized-oil and, therefore, is uniquely applicable to the full range of fluids, including volatile-oils and gas-condensates. Equally important, the new material balance equation retains the same simplicity with which the conventional material balance equation has become known. The new, generalized material balance equation is featured here by showing how it is used to predict reservoir performance and estimate reserves in example volatile-oil and gas-condensate reservoirs. In comparison, the conventional material balance equation is shown to lead to erroneous results. The new, generalized material balance equation leads to an improved method of reservoir performance analysis.

Introduction

Material balance calculations are a useful method of reservoir performance analysis. They are routinely used to estimate oil and gas reserves and predict future reservoir performance. Schilthuis ^(l), in 1936, was among the first to formulate and apply material balances. Inherent in his and others' use of material balances were the following assumptions: (1) at most, there are two hydrocarbon phases: oil and gas, (2) at most, there are two hydrocarbon components: stock-tank oil and separator (surface) gas, (3) the reservoir oil-phase consists of stock-tank oil and separator-gas, (4) the reservoir gas-phase consists of only separator-gas and no stock-tank oil, and (5) there are no compositional gradients within the system. Assumptions 1 and 2 define the popular two-hydrocarbon- component formulation. Assumption 3 effectively accounts for the effects of dissolved- or solution-gas. Assumption 4 ignores the possibility of volatilized-oil and. therefore, restricts application to black-oils and dry-gases and precludes application to volatile-oils, gas-condensates, or wet-gases. Volatilized-oil is the stock-tank oil content of the free reservoir gas-phase, Assumption 5 means that the system is effectively treated as a tank with no gradients; accordingly, Coats ⁽²⁾ and others have sometimes referred to this type of model as a tank or zero-dimensional model. Despite their apparent oversimplicity, early tank models found widespread use in reservoir engineering applications ^{( 3-16)}.

As time progressed, more sophisticated material balance models evolved, each striving for greater generality. Eventually, following the advent of digital computers, the material balance equations were discretized and the first generation of multi-dimensional, black-oil, finite-difference reservoir simulators were developed in the 1960's ^(17-19). These models, like their zero-dimensional counterparts, could effectively simulate black-oil and dry-gas reservoirs but could 1I0t model volatile-oil and gas-condensate reservoirs. To address this limitation, Cook et al ²⁰ in 1974 introduced a volatile-oil, finite-difference simulator. Their formulation retained the simplicity of two hydrocarbon components, but allowed for volatilized-oil. Consequently, their formulation was applicable to the full range of reservoir fluids. The resulting formulation was applicable to the full range of reservoir fluids. Coats(21) later, in 1986, verified the applicability of the black- and volatile-oil approaches in reservoir simulation by showing agreement with a fully-compositional, equation-of-state (EOS) reservoir simulator.