Page 43 - Principles of Applied Reservoir Simulation 2E

28 Principles of Applied Reservoir Simulation

a dip angle of formation
g gravitational constant
If we differentiate capillary pressure for a water-wet system with respect to
position x along the dipping bed, we find

dx dx dx

Combining Eqs. (3.19) and (3.20) gives

Akk
ru M»
where we have used = q 0 + q w. If we write the density difference as
q t
Ap = P w - P 0, (3.22)

collect terms, and simplify we obtain
li BP
q t
~t > o , cow sina (3.23)
Ak\ k k Akk dx
ro rw /
Rearranging and collecting terms gives the fractional flow to water f w in
conventional oilfield units:

Akk dp
1+0.001127 0.433(Y ~Yjsina
(3.24)

k u
r w P O

2
A cross-sectional area of flow system [ft ]
k absolute permeability [md]
relative permeability to oil
k ro
k m relative permeability to water
oil viscosity [cp]
|J, 0
water viscosity [cp]
\l w
P cow oil-water capillary pressure [psi] = P 0 - P w