GAS MATERIAL BALANCE: RECOVERY FACTOR

The material balance equation, for any hydrocarbon system, is simply a volume balance which equates the total production to the difference between the initial volume of hydrocarbons in the reservoir and the current volume. In gas reservoir engineering the equation is very simple and will now be considered for the separate cases in which there is no water influx into the reservoir and also when there is a significant degree of influx.

a) Volumetric depletion reservoirs

The term volumetric depletion, or simply depletion, applied to the performance of a reservoir means that as the pressure declines, due to production, there is an insignificant amount of water influx into the reservoir from the adjoining aquifer. This, in turn, implies that the aquifer must be small (refer sec. 1.4). Thus the reservoir volume occupied by hydrocarbons (HCPV) will not decrease during depletion. An expression for the hydrocarbon pore volume can be obtained from equ. (1.26) as

The ratio Gp/G is the fractional gas recovery at any stage during depletion and, if the gas expansion factor E, in equ. (1.34), is evaluated at the proposed abandonment pressure then the corresponding value of Gp/G is the gas recovery factor. Before describing how the material balance equation is used in practice, it is worthwhile reconsidering the balance expressed by equ. (1.33) more thoroughly.

Implicit in the equation is the assumption that because the water influx is negligible then the hydrocarbon pore volume remains constant during depletion. This, however, neglects two physical phenomena which are related to the pressure decline. Firstly, the connate water in the reservoir will expand and secondly, as the gas (fluid) pressure declines, the grain pressure increases in accordance with equ. (1.4). As a result of the latter, the rock particles will pack closer together and there will be a reduction in the pore volume.

These two effects can be combined to give the total change in the hydrocarbon pore volume as

where Vw and Vf represent the initial connate water volume and pore volume (PV), respectively. The negative sign is necessary since an expansion of the connate water leads to a reduction in the HCPV. These volume changes can be expressed, using equ. (1.11), in terms of the water and pore compressibilities, where the latter is defined as

That is, the inclusion of the term accounting for the reduction in the hydrocarbon pore volume, due to the connate water expansion and pore volume reduction, only alters the material balance by 1.3% and is therefore frequently neglected. The reason for its omission is because the water and pore compressibilities are usually, although not always, insignificant in comparison to the gas compressibility, the latter being defined in sec. 1.6 as approximately the reciprocal of the pressure.

As described in Chapter 3, sec. 8, however, pore compressibility can sometimes be very large in shallow unconsolidated reservoirs and values in excess of 100 × 10−6 / psi have been measured, for instance, in the Bolivar Coast fields in Venezuela. In such reservoirs it would be inadmissible to omit the pore compressibility from the gas material balance.