Page 205 - Fundamentals of Reservoir Engineering

STABILIZED INFLOW EQUATIONS 143

qµ r
p − p wf = ln a
a
2k h
π
a r w
and

qµ r 1
p e − p a = 2k h ln r e a − 2
a
π

At r = r a, there is continuity of pressure, therefore, adding the above equations

qµ r 1 k r
p − p wf = ln e − + e ln a
e
2k h r a 2 k a r w
π
e
qµ r 1 r r k r
= ln e − + ln e − ln e + e ln a
2k h r w 2 r a r w k a r w
e
π
i.e.

qµ r 1 k r

p − p = ln e − + e − 1 ln a
e
wf
2 k h r w 2 k a r w
π
e
which must be equivalent to

qµ r e 1
p − p wf = 2k h ln r w − 2 + S
e
π

e
and therefore

k − k r
S = e a ln a
k r
a w
2
which is an alternative expression for the skin factor presented by Craft and Hawkins .

2) Before stimulation

4.333
S = (100 1)ln = 254.02
−
1
0.333
while the skin factor after stimulation is

(1 10) 10.333
−
S = ln = − 3.09
2
10 0.333
and since