Page 173 - Well Logging and Formation Evaluation

Reservoir Engineering Issues 163

Exercise 11.2. Material Balance of Undersaturated
Oil Reservoir

Consider a reservoir with negligible water drive (W = 0). Bubble point is
200 bar.
3
7
If N = 10 standard m ,
B oi = 1.3,
B o at 250 bar = 1.25,
S w = 0.2,
-5
Cf= 10.0 * 10 l/bar,
-5
C w = 4.4*10 l/bar, and
P i = 300 bar,
how much oil will have been produced when the reservoir pressure has
dropped to 250 bar?

11.4 DARCY’S LAW

For linear flow, an empirical equation developed by Darcy is as follows:

k ) (
*
∂
u =-( m * ∂ p x + r* g ∂ z x) (11.4.1)
∂
where:
u = flow velocity in m/s
2
2
k = permeability in m (note that 1 darcy is 10 -12 m )
-3
m= viscosity, in Pa (note that 1cp = 10 Pa)
p = pressure of flowing phase, in Pa
z = vertical distance upward, in m
x = distance in the direction of flow, in m
g = gravitational constant (9.81), in m/s 2
r= density of the flowing phase.

For purely horizontal flow over a distance L (having pressure drop DP)
with area A, this equation reduces to:

k )
Q =-( m * D P A L (11.4.2)
*
3
where Q is flow rate measured in m /s. The above equation also approx-
imately applies in so-called Darcy units, where Q is in cc/sec, k is in
2
darcies, A is in cm , m is in cp, P is in atmospheres, and L is in cm. The