Page 141 - Fundamentals of Reservoir Engineering

MATERIAL BALANCE APPLIED TO OIL RESERVOIRS 80

p b = 3330 psi B ob = 1.2511 rb/stb

Therefore, the average compressibility of the undersaturated oil between initial and
bubble point pressure is

−
B − B 1.2511 1.2417 6
−
×
c = ob oi = = 11.3 10 /psi
o
B ∆ p 1.2417(4000 3330)
−
oi
The recovery at bubble point pressure can be calculated using equ. (3.18) as
N p B oi p
e
N = B c ∆
b p ob
where

1
c = (11.3 0.8 3 0.2 8.6 × − 6
) 10 /psi
+
×
+ ×
e
.8
= 22.8 10 − 6
×
and therefore,
1.2417
6
−
Recovery = × 22.8 10 × (4000 3330)
−
×
1.2511
or 1.52% of the original oil in place. Considering that the 670 psi pressure drop
represents about 17% of the initial, absolute pressure, the oil recovery is extremely
low. This is because the effective compressibility is small providing the reservoir
contains just liquid oil and water. The situation will, however, be quite different once the
pressure has fallen below bubble point.

b) Below bubble point pressure (saturated oil)

Below the bubble point pressure gas will be liberated from the saturated oil and a free
gas saturation will develop in the reservoir. To a first order of approximation the gas
compressibility is c g ≈ 1/p, as described in Chapter 1, sec. 6. Therefore, using the data
of exercise 3.1, the minimum value of the free gas phase compressibility will occur at
-6
the bubble point pressure and will be equal to 1/p b = 1/3330 = 300 × 10 /psi. This is
two orders of magnitude greater than the water compressibility and 35 times greater
than the pore compressibility and, as a result, the latter two are usually neglected in the
material balance equation. The manner in which the reservoir will now behave is
illustrated by the following exercise.

EXERCISE 3.2 SOLUTION GAS DRIVE; BELOW BUBBLE POINT PRESSURE

The reservoir described in exercise 3.1 will be produced down to an abandonment
pressure of 900 psia.

1) Determine an expression for the recovery at abandonment as a function of the
cumulative gas oil ratio R p.