Page 106 - Introduction to Petroleum Engineering

ONE‐DIMENSIONAL WATER-OIL DISPLACEMENT 91

1.00

0.80
Water fractional flow 0.60

0.40

0.20

0.00
0.00 0.20 0.40 0.60 0.80 1.00
Water saturation
FIgURE 5.6 Fractional flow for oil–water displacement with relative permeabilities shown
in Figure 5.5.

Fractional flow of water depends on mobility ratio, buoyancy effects relative to
oil, and the gradients of capillary pressure between oil and water. Here, we neglect
buoyancy and capillary pressure effects. Substituting Equations 5.6 and 5.7 for water
and oil flow rates into Equation 5.13 gives

1
f = (5.15)
w µ k ( )
S
1 + w ro o
S
k ( ) µ o
rw
w
Thus, for a given pair of water and oil viscosities, fractional flow depends only on
water saturation through the saturation dependence of the relative permeabilities.
The fractional flow relationship for the relative permeabilities of Figure 5.5, with
water viscosity of 0.9 cp and oil viscosity of 8.0 cp, is shown in Figure 5.6.

Example 5.3 Fractional Flow
A well produces 1000 STB/day oil and 100 STB/day water. What is the
fractional flow of water?
Answer
q 100
f = q + w q o = 100 +1000 = 0 091
.
w
w

5.5 ONE‐DIMENSIONAL WATER-OIL DISPLACEMENT

Fractional flow is a useful concept for modeling water–oil displacement in one
dimension. Although actual reservoirs are not one‐dimensional, understanding the
basics of displacements in one dimension is a good start on understanding more