Page 48 - Principles of Applied Reservoir Simulation 2E

Part I: Reservoir Engineering Primer 33

A*
A* A 7

=
Az Ar

In the limit as A*, Aj, Az, and A? go to zero, Eq. (4.5) becomes the
continuity equation
dJ x dJ v dJ z dC,
y (A &}
\*T,Oj
dx dy dz dt
The oil, water, and gas phases each satisfy a mass conservation equation having
the form of Eq. (4.6).

4.2 Flow Equations for Three-Phase Flow

The flow equations for an oil, water, and gas system are determined by
specifying the fluxes and concentrations of the conservation equations for each
of the three phases. A flux in a given direction can be written as the density of
the fluid times its velocity in the given direction. Letting the subscripts o, w, and
g denote oil, water, and gas, respectively, the fluxes become:

D
B

(A, - -^ (4.8)

g (
B B B
are formation volume
where R so and R sw are gas solubilities; B 0, B w, and B g
factors; the subscript sc denotes standard conditions (usually 60°F and 14.7 psia
in oilfield units); and p denotes fluid densities. The velocities v are assumed
to be Darcy velocities and their x components are