Page 132 - Fundamentals of Reservoir Engineering

CHAPTER 3

MATERIAL BALANCE APPLIED TO OIL RESERVOIRS

3.1 INTRODUCTION

The Schilthuis material balance equation has long been regarded as one of the basic
tools of reservoir engineers for interpreting and predicting reservoir performance.

In this chapter, the zero dimensional material balance is derived and subsequently
applied, using mainly the interpretative technique of Havlena and Odeh, to gain an
understanding of reservoir drive mechanisms under primary recovery conditions.
Finally, some of the uncertainties attached to estimation of in-situ pore compressibility,
a basic component in the material balance equation, are qualitatively discussed.

Although the classical material balance techniques, once applied, have now largely
been superseded by numerical simulators, which are essentially multi-dimensional,
multi-phase, dynamic material balance programs, the classical approach is well worth
studying since it provides a valuable insight into the behaviour of hydrocarbon
reservoirs.

3.2 GENERAL FORM OF THE MATERIAL BALANCE EQUATION FOR A
HYDROCARBON RESERVOIR

1
The general form of the material balance equation was first presented by Schilthuis in
1941. The equation is derived as a volume balance which equates the cumulative
observed production, expressed as an underground withdrawal, to the expansion of the
fluids in the reservoir resulting from a finite pressure drop. The situation is depicted in
fig. 3.1 in which (a) represents the fluid volume at the initial pressure p i in a reservoir
which has a finite gascap. The total fluid volume in this diagram is the hydrocarbon
pore volume of the reservoir (HCPV). Fig. 3.1 (b) illustrates the effect of reducing the
pressure by an amount ∆p and allowing the fluid volumes to expand, in an artificial
sense, in the reservoir. The original HCPV is still drawn in this diagram as the solid
line. Volume A is the increase due to the expansion of the oil plus originally dissolved
gas, while volume increase B is due to the expansion of the initial gascap gas. The
third volume increment C is the decrease in HCPV due to the combined effects of the
expansion of the connate water and reduction in reservoir pore volume as already
discussed in Chapter 1, sec. 7.
If the total observed surface production of oil and gas is expressed in terms of an
underground withdrawal, evaluated at the lower pressure p, (which means effectively,