Page 41 - Principles of Applied Reservoir Simulation 2E

26 Principles of Applied Reservoir Simulation

An example of mobility ratio is the mobility ratio of water to oil for a waterflood:

In this case, relative permeability to water is evaluated at residual oil saturation
S or, and relative permeability to oil is evaluated at connate water saturation S wc.
Notice that absolute permeability factors out of the expression for mobility ratio.
Consequently, mobility ratio can be calculated using either mobilities or relative
mobilities.

3.4 Fractional Flow

The fractional flow of water is the ratio of water production rate to total
production rate. In the case of an oil-water system, the fractional flow of water
is given by

/, = ~ = -^— (3.15)
*r <? w + <lo
where
fractional flow of water
f w
q w water volumetric flow rate [RB]
oil volumetric flow rate [RB]
q 0
total volumetric flow rate [RB]
q t
Notice that the flow rates are expressed in terms of reservoir volumes. The
fractional flow of oil/, and the fractional flow of water are related byf w= 1 -f 0
for an oil-water system. Based on the definition of fractional flow, we see that
fractional flow should be a value between 0 and 1.

Simplified Fractional Flow Equation
A simplified fractional flow equation is obtained by replacing flow rates
with Darcy's Law in the definition of fractional flow. If we neglect capillary
pressure and gravity for simplicity, we obtain