Page 88 - Fundamentals of Reservoir Engineering

SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 27

GS
V w = PV × S wc = wc
E(1 S )
−
wc
i
the reduction in hydrocarbon pore volume, equ. (1.38), can be included in equ. (1.33),
to give

G p (c S wc + c ) p E (1.39)
∆
w
f
G = 1− 1 − 1 S wc E i
−

−6
as the modified material balance. Inserting the typical values of c w = 3 × 10 /psi,
−6
c f = 10 × 10 /psi and S wc = 0.2 in this equation, and considering a large pressure drop
of ∆p = 1000 psi; the term in parenthesis becomes
(3 .2 10) 6 3
×
+
−
1 − × 10 × 10 = 1 0.013
−
0.8
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
−6
unconsolidated reservoirs and values in excess of 100 × 10 / 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.
In a reservoir which contains only liquid oil, with no free gas, allowance for the connate
water and pore compressibility effects must be included in the material balance since
these compressibilities have the same order of magnitude as the liquid oil itself (refer
Chapter 3, sec. 5).

In the majority of cases the material balance for a depletion type gas reservoir can
adequately be described using equ. (1.35). This equation indicates that there is a linear
relationship between p/Z and the fractional recovery G p/G, or the cumulative production
G p, as shown in fig. 1.10(a) and (b), respectively. These diagrams illustrate one of the
basic techniques in reservoir engineering which is, to try to reduce any equation, no
matter how complex, to the equation of a straight line; for the simple reason that linear
functions can be readily extrapolated, whereas non-linear functions, in general, cannot.
Thus a plot of p versus G p/G or G p, would have less utility than the representations
shown in fig. 1.10, since both would be non-linear.