Environmental Engineering Reference
In-Depth Information
There are several alternatives in formulation of the partial differential
equations in the above system including (i) formulation in phase pressures,
(ii) formulation in phase pressure and saturation, and (iii) formulation in
global pressure (Crichlow, 1977; Dake, 1978; Aziz and Settari, 1979; King,
1992; Chen et al., 2006; Aarnes et al., 2007). When formulated in phase
pressures, simultaneous solution techniques can be used to solve the sys-
tem of equations. When formulated in phase pressure and saturation, the
implicit pressure explicit saturation (IMPES) technique can be used to
solve the system of equations. Finally, to reduce the coupling in the system,
equations can be formulated in global pressure (Crichlow, 1977; Dake,
1978; Aziz and Settari, 1979; King, 1992; Chen et al., 2006; Aarnes et al.,
2007).
5.8.6
Formulation in Phase Pressure (Oil Pressure) and
Saturation (Water Saturation)
Capillary pressure is a function of water saturation and the direction of sat-
uration change (drainage or imbibition). Different empirical correlations
between saturation and capillary pressure have been developed including
the Brooks and Corey (Brooks and Corey, 1964; Corey, 1994) correlation
expressed as:
(
)
1/ l
(5.93)
PPS
C
=
d
w
Where, P C is capillary pressure, P d is entry capillary pressure, and l is
related to the pore size distribution of the porous medium (in the range of
0.2 to 3.0).
Relative permeability coefficients are correlated to wetting phase satura-
tion (usually water saturation). As discussed in section 5.8.3, these coef-
ficients are determined either experimentally for specific porous medium
of interest or empirical correlations can be used as an alternative. There
are several empirical expressions for relative permeability coefficients as
a function of wetting phase saturation including the Brooks and Corey
(Brooks and Corey, 1964; Corey, 1994) correlation given as:
23 l
l
+
(5.94)
k
=
S
rww
,
w
2
+
l
(
)
2
(5.95)
k
=
S
11
S
l
roo
,
o
o
 
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