Page 87 - Fundamentals of Reservoir Engineering
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SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 26
The ratio G p/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 G p/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
d(HCPV) = − dV w +dV f (1.36)
where V w and V f 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
1 ∂ V
c =− f (1.4)
f
V f ∂ (GP)
where GP is the grain pressure which is related to the fluid pressure by
d(FP) = − d(GP)
therefore
1 ∂ V 1 ∂ V
c =− f = f (1.37)
f
V f ∂ (FP) f V ∂ p
where p is the fluid pressure. Equation (1.36) can now be expressed as
d(HCPV) = c w V w dp + c f V f dp
or, as a reduction in hydrocarbon pore volume as
d(HCPV) = − (c w V w + c f V f ) ∆p (1.38)
where ∆p = p i − p, the drop in fluid (gas) pressure. Finally, expressing the pore and
connate water volumes as
HCPV G
V = PV = =
f
(1 S ) E (1 S )
−
−
wc
i
wc
and
