Page 271 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

240 Reservoir Engineering

5. Compute the cumulative gas produced at pressure p;

(5-1 64)

where I$ is the instantaneous gas-oil ratio computed at pressure p,.
Usually three judicious guesses are made for the value (N )* and the cor-
responding values of (GP)* computed by both step 2 and step 5. bhen the values
for (Gp)* are plotted against the assumed values for (Ne)*, the intersection of
the curve indicates the cumulative gas and oil production that will satisfy both
equations. In actual application the method is usually simplified further by
equating the incremental gas production (Gp& - (Gp)l rather than (Gp)* itself.
This equality signifies that at each pressure step the cumulative gas, as deter-
mined by the volumetric balance is the same as the quantity of gas produced
from the reservoir, as controlled by the relative permeability ratio of the rock,
which in turn depends on the total liquid saturation .

The Muskat Method
The Schilthuis and Tamer forms of material balance have been expressed in
integral form. An approach presented by Muskat [251] expresses the material
balance in terms of finite pressure differences in small increments. The changes
in variables that affect production are evaluated at any stage of depletion or
pressure. The assumption is made that values of the variables will hold for a
small drop in pressure, and the incremental recovery can be calculated for the
small pressure drop. The variables are recalculated at the lower pressure, and
the process is continued to any desired abandonment pressure. If the PVT data
and the gas-oil relative permeabilities are known at any liquid saturation, the
unit recovery by pressure depletion can be computed from a differential form
of the material balance equation:

(5165)
dP

From the change in saturation at any pressure, the reservoir saturation at that
time can be related to the change in oil production and the instantaneous gas-
oil ratio. Calculations can be facilitated if the terms in the numerator that are
functions of pressure only (Bg, Bo, R,) are determined for various depletion
pressures. Pressure increments of 10 psi or less may be necessary for acceptable
accuracy [180].
Predicting Primary Recovery in Water-Drive ReservoIra
In the prediction of performance caused by water influx, predictions of water
encroachment are made independent of material balance. The extent of water
encroachment depends on the characteristics of the aquifer and is a function
of the pressure history and time [252]. While several methods are available to
predict water drive performance, some [197] feel that the theory of unsteady-