The New, Generalized Material Balance as an Equation of a Straight Line: Part 1 - Applications to Undersaturated, Volumetric Reservoirs

Abstract

This work presents a general, straight-line method to estimate the original oil and gas in-place in a reservoir without restrictions on fluid composition. All past efforts are applicable to only restricted ranges of reservoir fluids. Our work supersedes these and is the first to be applicable to the full range of reservoir fluids - including volatile-oils and gas-condensates. Our work is based on the new generalized material-balance equation recently introduced by Walsh.¹ The superiority of the new method is illustrated by showing the error incurred by preexisting calculation methods. Guidelines are offered to help identify when preexisting calculation methods must be abandoned and when the new methods featured herein must be employed. The results of our work are summarized in a set of companion papers. Part 1 discusses applications to initially-undersaturated, volumetric reservoirs and Part 2 discusses applications to initially-saturated and non-volumetric reservoirs.*

Introduction

This work completes the search for a general, straight-line method to estimate the original oil and gas in-place. No restrictions are placed on initial fluid compositions. This breakthrough is made possible by the new, generalized material-balance equation (GMBE) recently introduced by Walsh.¹ Unlike the conventional material-balance equation (CMBE),^2-7 the GMBE uniquely accounts for volatilized-oil is the stock-tank oil content of the free reservoir gas-phase. By including both dissolved-gas and volatilized-oil, the GMBE is uniquely applicable to the full range of reservoir fluids. Because our straight-line method is based on the GMBE, it too is applicable to the full range of reservoir fluids. All preexisting straight-line methods are applicable to only restricted ranges of reservoir fluids. This restriction is now no longer necessary.

This work leads to a new and improved method of analyzing reservoir performance. Together with Walsh's work,¹ it leads to a complete and comprehensive understanding of the influence of phase behavior on reservoir performance. It also leads to a new, improved, and innovative way to teach reservoir engineering.

The results of our work are summarized in a set of companion papers. Part 1 presents the mathematical development and discusses applications to initially-undersaturated, volumetric reservoirs, initially-undersaturated reservoirs are those whose initial but not necessarily final pressure is greater than the saturation (dew or bubble point) pressure. Volumetric reservoirs are those whose hydrocarbon pore volume does not change. Part 2 discusses applications to initially-saturated and non-volumetric reservoirs. Initially-saturated reservoirs include, but are not restricted to, gas-cap reservoirs; non-volumetric reservoirs include, but are not restricted to, water-influx reservoirs. Part 1 is restricted to simple expansion-drive reservoirs and Part 2 discusses combination-drive reservoirs.

Background

Interest in developing straight-line methods to estimate petroleum reserves began with the development of p/z-plots to estimate gas reserves in dry-gas reservoirs. This well-known method of estimating gas reserves was in common practice by the 1940's.⁸ Since this time, there has been considerable interest in developing straight-line mmethods for other types of petroleum reservoirs.