Page 301 - Principles of Applied Reservoir Simulation 2E

286 Principles of Applied Reservoir Simulation

Gas

V j? R v
SO
-V • „-„„,*?„ 2 -4. 1 . m._ LJ_ Li. L, -* K ' -
ij
R 0 ° v
-D 15
^ ^
^ (27.3)
a | g + ^o
' a, j 5 5 0
g
Letting the subscript / denote o (oil), w (water), and g (gas), the symbols in Eqs.
(27.1) to (27.3) have the following definitions:
= formation volume factor of phase i
B t
q i = mass flow rate per unit reservoir volume of phase /
= solubility of gas in oil
R so
= solubility of gas in water
R sw
5, = saturation of phase i
v, = Darcy's velocity of phase i
Pise ~ density of phase i at standard conditions
<j) = porosity
Three additional equations - called auxiliary equations - are employed
when solving the preceding fluid flow equations. They are the saturation
constraint
+ + S g=l (27.4)
S 0 S w

and the capillary pressure relationships

P
c OW(S w) = P 0 - P w (27.5)

P cgo(S g) = P 8 ' P 0 (27.6)
where P, is the pressure of phase i, P cow is the oil-water capillary pressure, and
P cgo is the gas-oil capillary pressure.
Darcy's velocity for phase / is

(27.7)