Page 228 - Fundamentals of Enhanced Oil and Gas Recovery

216 Mohammad Ali Ahmadi

The equation above is the water fractional flow equation for the displacement of
oil by water in a one-dimensional radial system [20]. If we neglect the capillary-
pressure gradient along the radii, the fractional flow equation is reduced to
1
f w 5 (7.51)
1 1 k ro μ =k rw μ
w o
This expression is practically the same equation as the expression for fractional
flow in a linear system. This tells us categorically that the fractional flow in a one-
dimensional radial flow system is also a function of water saturation through the satu-
ration dependence on relative permeability. When fluid viscosities are constant, the
mass conservation of a one-dimensional flow and displacement in a radial system is
rewritten as follows:

1 @f w @s w
2 q t 5 2πhφ (7.52)
r @r @t
For Buckley Leverett solution in one-dimensional linear flow, an expression

@S w =@t is obtained and solved as

2
2
r 5 r 1 W i U df w (7.53)
s w w
πhφ dS w S w
It is important to note that Buckley Leverett solution in a radial flow system
depends on but not solely on the assumption that the effect of the capillary-pressure

gradient @P c =@r is small and negligible.

7.4 IMPORTANCE AND CAPABILITY OF FRACTIONAL FLOW
IN RADIAL FLOW SYSTEM
The fractional flow is of great importance, because with the fractional flow, at
any given point in time in the reservoir, we can calculate both the oil and water flow
rates, and it depicts reservoir flow conditions. With the help of Buckley Leverette
who developed the frontal advance equation, we can determine water cut and recov-
ery after breakthrough. Also, with the fractional flow cure, we can determine the
mobility ratio (which is the ratio of the relative permeability of the rock to the viscos-
ity of the fluid), bearing in mind that the lower the mobility ratio, the higher the
recovery efficiency. Low mobility ratio also gives a good sweep efficiency. These two
parameters enhance the oil recovery process.
Paul and Franklin [27] understood the importance of the above subject and there-
fore modified the work of Stiles [28] by developing equations based on the radial