Page 44 - Principles of Applied Reservoir Simulation 2E

Part I: Reservoir Engineering Primer 29

x direction of linear flow [ft]
a dip angle of formation [degrees]
oil specific gravity (water =1)
Y 0
water specific gravity (water = 1 )
j w
The general expression forf w includes all three terms governing immiscible
displacement, namely the viscous term (k ro/k rw) (|i w/ (1 0 ) , the capillary pressure
(
term d P coJ$x, and the gravity term Y W ~Y 0 ) sin a,
It is interesting to note that the capillary pressure and gravity terms are
multiplied by II q t in Eq. (3.24). Most waterfloods have sufficiently high flow
rates that capillary pressure and gravity effects can be neglected, leaving the
simplified expression:
_ L __
f a
, ^ k ro V« (3.25)
••- - • •

Equation (3.25) is in agreement with Eq. (3.18), as it should be.

Gas Fractional Flow
A similar analysis can be performed to determine the fractional flow of
gasjC The result for a gas-oil system is
Akk dP
1+0.001127 — ^ - 0.433 (Y ~Y 0
f _- U ° Q ' dx } (3.26)
t
l + £
k u.
rg ~o
where

k rg relative permeability to gas
M-g gas viscosity [cp]

P cgo gas-oil capillary pressure = P g-P 0 [psi]
gas specific gravity [water = 1]
Y g
q g gas volumetric flow rate [RB/D]
q t' total volumetric flow rate = q 0 + q g [RB/D]
Immiscible displacement of oil by gas is analogous to water displacing oil with