Page 227 - Fundamentals of Enhanced Oil and Gas Recovery

Waterflooding 215

k rwA =μ dp=dx k rw =μ

q w w w
f w 5 5 5
q o 1 q w k roA =μ o dp=dx 1 k rwA =μ w dp=dx k ro =μ 1 k rw =μ w
o
1
5
1 1 k ro μ =k rw μ
w o
(7.46)

k o =k w is a function of saturation; hence, for constant viscosity, f w is just a function of
saturation [20].Wu [20] also considered studying the Buckley Leverett flow in a
one-dimensional radial system, where a fluid flowing radially toward (or away from) a
vertical well in a radially symmetric manner as illustrated in Fig. 7.4.
The mass balance equation for the fluid phase is given as

@ ðρqÞ @
pqj 2 pqj 1 dr 5 2πrhdr ð[ρÞ (7.47)
r
r
@t @t
Wu [20] suggested that if Darcy’s law for multipurpose flow is applied for radial
flow in the above equation, then we have
kk ro @P o
q o 52 2πh (7.48)
μ o @r

kk rw @P w
q w 52 2πh (7.49)
μ w @r
Then, one can obtain the corresponding fractional flow equation to water in a
radial flow system as
1 2 2πhkk ro =q t μ r@P c =@r

f w 5 o (7.50)
1 1 k ro μ =k rw μ o
w

Figure 7.4 A control volume in a circular reservoir with a well located in the center [1].