Page 135 - Fundamentals of Reservoir Engineering

MATERIAL BALANCE APPLIED TO OIL RESERVOIRS 74

The total volume change due to these combined effects can be mathematically
expressed as

d(HCPV) = dV w + dV f (1.36)

or, as a reduction in the hydrocarbon pore volume, as

d (HCPV) = (c w V w + c f V f ) ∆p (1.38)

where V f is the total pore volume = HCPV/(1 − S wc)

and V w is the connate water volume = V f × S wc = (HCPV)S wc/(1 − S wc).

Since the total HCPV, including the gascap, is

(1+m)NB oi (rb) (3.4)

then the HCPV reduction can be expressed as

cS + c
− d(HCPV) = (1 m)NB oi w wc f ∆ p (3.5)
+
−
1S wc
This reduction in the volume which can be occupied by the hydrocarbons at the
lower pressure, p, must correspond to an equivalent amount of fluid production
expelled from the reservoir, and hence should be added to the fluid expansion
terms.

d) Underground withdrawal

The observed surface production during the pressure drop ∆p is N p stb of oil and
N p R p scf of gas. When these volumes are taken down to the reservoir at the
reduced pressure p, the volume of oil plus dissolved gas will be N pB o rb. All that
is known about the total gas production is that, at the lower pressure, N p R s scf
will be dissolved in the N p stb of oil. The remaining produced gas, N p (R p − R s) scf
is therefore, the total amount of liberated and gascap gas produced during the
pressure drop ∆p and will occupy a volume N(R p − R s)B g rb at the lower pressure.
The total underground withdrawal term is therefore

N p (B o + (R p − R s)B g) (rb) (3.6)

Therefore, equating this withdrawal to the sum of the volume changes in the
reservoir, equs. (3.1 ), (3.2), (3.3) and (3.5), gives the general expression for the
material balance as

(B − B ) (R − R ) B g
+
oi
si
s
o
N(B + (R − R )B ) = NB oi +
p
o
p
s
g
B oi
B cS + c (3.7)

m g − 1 + (1 m) w wc f ∆ (W − W )B
+
p +
B 1 S e p w

gi
− wc