The New, Generalized Material Balance as an Equation of a Straight Line: Part 2 - Applications to Saturated and Non-Volumetric Reservoirs

Abstract

This paper is the second in a two-part series of papers which features practical applications of the generalized material-balance equation. Applications to initially-saturated and non-volumetric reservoirs are discussed in this paper (Part 2); applications to initially-undersaturated, volumetric reservoirs are discussed in Part 1. Graphical methods to estimate the original oil and gas in-place are presented. The graphical methods are general and are applicable to the full range of reservoir fluids of interest. Example calculations are carried out for gas-cap and water-influx reservoirs. These examples, along with those discussed in Part 1, demonstrate the extraordinary power of the generalized material-balance equation.*

Introduction

We continue the work started in Part 1¹ by considering applications of the generalized material-balance equation² (GMBE) 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. The end-product of this work is to demonstrate that straight-line methods offered herein are applicable to the full range of reservoir fluids and to a wide range of reservoir conditions. The consequences of ignoring volatilized-oil are also the focus of this work. Volatilized-oil is the stock-tank oil content of the free reservoir gas-phase. Because our nomenclature purposely follows Havlena and Odeh's,³ virtually all of their algebraic rearrangements of the conventional material-balance equation (CMBE) are equally valid to our work; however, unlike their work, our work is applicable to the full range of reservoir fluids - including volatile-oil and gas-condensates.

For purposes of illustration, we examine a reservoir containing a volatile-oil. The system properties are identical to those discussed in Part 1 except we now extend our study to gas-cap and water-drive systems. Thus, all of the specific conditions noted in Part 1 also apply here. Although we restrict our attention to a volatile-oil system, our conclusions are generic and apply equally well to gas-condensate systems. The extraordinary power of the GMBE will become evident in the examples we consider.

Our approach to study the GMBE is to: (1) consider an example volatile-oil reservoir fluid, (2) develop an equation-of-state (EOS) fluid property description to accurately model its phase behavior, (3) carry out numerical PVT experiments to determine the necessary fluid properties such as B_o, B_g, R_s, and R_v, (4) carry out numerical simulations to predict the performance of different hypothetical reservoirs, and (5) apply graphical methods to estimate the OOIP and OGIP and compare these estimates with the actual OOIP and OGIP. The example reservoirs we study include gas-cap and water-influx reservoirs. All EOS computations carried out here use the Zudkevitch-Joffe⁴ modification of the Redlich-Kwong⁵ EOS; all reservoir performance simulations use the numerical model⁶ discussed in Part 1.

Collectively, these works (Parts 1 and 2) complete the search for a general, straight-line method to estimate the OOIP and OGIP in a reservoir without restrictions on fluid composition. They lead to a new and improved method to analyze reservoir performance. Together with Walsh's work,² they lead to a complete and comprehensive understanding of the influence of phase behavior on reservoir performance. They also provide a new, improved, and innovative way to teach reservoir engineering.