Page 308 - Principles of Applied Reservoir Simulation 2E

Part V: Technical Supplements 293

process is expensive and most relative permeability data are obtained on restored
state cores in the laboratory.
In principle, three-phase relative permeability should be used when oil,
water, and gas are flowing simultaneously. As a practical matter, the difficulty
of accurately measuring three-phase relative permeabilities often makes their
use meaningless. It is often sufficient to work with the two-phase relative
permeability curves only.
Despite their shortcomings, it may be of interest to perform a simulation
using a set of three-phase relative permeability curves. For this case, WINB4D
contains an option for computing a three-phase oil relative permeability curve
using water-oil and gas-oil relative permeability curves. As with most calcula-
tions of this type, we assume:
a. The water relative permeability curve (k^ obtained for a water-oil
system depends only on water saturation, and
b. The gas relative permeability curve (k rg) obtained for a gas-oil
system depends only on gas saturation.
The validity of these assumptions depends on such factors as wettability
and degree of consolidation. Given the above assumptions, £ w and k rg for water-
oil and gas-oil systems, respectively, are also valid for a water-gas-oil system.
The three-phase oil relative permeability k ro3 is calculated as

, (^row + ^rw) (krog + *rp ,* _,_ L \
k^ = - 1 £- - (k rw + k rg) (28J)
*row
where

k row - oil relative permeability for water-oil system
= oil relative permeability for gas-oil system
k mg
k* row= oil relative permeability for water-oil system evaluated
at the oil saturation corresponding to irreducible water
saturation
Equation (28.1) is based on the work by Stone [1973], and it corresponds to
Model II of Dietrich and Bonder [1976]. For a discussion of alternative models
of three-phase oil relative permeability, see Blunt [1999].
When the three-phase calculation is activated, the user must be sure the
input water-oil and gas-oil relative permeability curves are realistic. For example,