Material Balance in Volumetric Gas Reservoirs

For a volumetric gas reservoir, Eq. (4.13) can be reduced to a simple application of a straight line involving the gas produced, its composition, and the reservoir pressure. This relationship is routinely used by reservoir engineers to predict recoveries from volumetric reservoirs. Since there is neither water encroachment nor water production in this type of a reservoir, Eq. (4.13) reduces to

Using Eq. (2.15) and substituting expressions for B_g and B_gi into Eq. (4.14), the following is obtained:

Noting that production is essentially an isothermal process (i.e., the reservoir temperature remains constant), then Eq. (4.15) is reduced to

This can be rearranged as

Because p_i, z_i, and G are constants for a given reservoir, Eq. (4.16) suggests that a plot of p/z as the ordinate versus G_p as the abscissa would yield a straight line, with

This plot is shown in Fig. 4.2.

If p/z is set equal to zero, which would represent the production of all the gas from a reservoir, then the corresponding G_p equals G, the initial gas in place. The plot could also be extrapolated to any abandonment p/z to find the initial reserve. Usually this extrapolation requires at least 3 years of accurate pressure depletion and gas production data.

Figure 4.2 also contains a plot of cumulative gas production G_p versus pressure. As indicated by Eq. (4.16), this is not linear, and extrapolations from the pressure-production data may be in considerable error. Because the minimum value of the gas deviation factor generally occurs near 2500 psia, the extrapolations will be low for pressures above 2500 psia and high for pressures below 2500 psia. Equation (4.16) may be used graphically, as shown in Fig. 4.2, to find the initial gas in place or the reserves at any pressure for any selected abandonment pressure. For example, at 1000 psia (or p/z = 1220) abandonment pressure, the initial reserve is 4.85 MMM SCF. At 2500 psia (or p/z = 3130), the (remaining) reserve is 4.85 less 2.20—that is, 2.65 MMM SCF.

Figure 4.2 Comparison of theoretical values of p and p/z plotted versus cumulative production from a volumetric gas reservoir.