Page 42 - Principles of Applied Reservoir Simulation 2E

Part I: Reservoir Engineering Primer 27

/. - - - (3.16)
kkAdP klA dP

where ^ is cross-sectional area and /^ is the pressure of phase L Since capillary
pressure is neglected, we have the equality of phase pressures P w = P 0 so that

Equation (3.17) can be expressed in terms of mobilities as
1 1

^£ ¥z i+jjl ( 3;l8 )
k.
rw
The construction of Eq. (3.18) is based on the following simplifying assump-
tions: Darcy's Law adequately describes flow rate, and capillary pressure and
gravity are negligible. Given these assumptions, we can calculate/,, at reservoir
conditions.

Fractional Flow Equation with Gravity
Gravity can be included in the fractional flow equation as follows. First,
let us consider the two-phase flow of oil and water in a tilted linear system.
Darcy's Law including capillary pressure and gravity effects for linear flow is

(3.19)
kkA
ro
P 0gsina
dx
^
• u ^
where