Page 203 - Fundamentals of Reservoir Engineering

STABILIZED INFLOW EQUATIONS 141

qµ r
r
p − p wf = oh ln r < ≤ r h
r
w
2kh w r
π
qµ oc r
r
and p − p h = ln r ≤ < r e
r
h
2kh r h
π
and in particular
qµ r
p − p = oh ln h (6.16)
wf
h
2kh r
π
w
qµ r
and p − p h = oc ln e (6.17)
e
2kh
r
π
h
Since there is continuity of pressure at r = r h, then equs. (6.16) and (6.17) will yield,
upon addition
q r r
p − p = µ ln h + µ ln e
wf
e
2kh oh r w oc r h (6.18)
π
qµ oc µ oh r h r
e
= ln + ln
2kh µ oc r w r h
π
and since the inflow equation for an unstimulated well is
qµ r
oc
p − p wf = 2kh ln r e w
e
π
Then the effect on the productivity index due to steam soaking can be expressed as
PI stimulated well
PI ratio increase =
PI unstimulated well
r
ln e
r
= w
µ oh ln r h + ln r e
µ oc r w r h

and using typical field data in the above formula, i.e.

= 113° F = 525° F
T r T s
= 980 cp = 3.2 cp
µ oc µ oh
= 382 ft = 65 ft
r e r h
= 0.23 ft
r w
Then

382
In
PI ratio increase = .23 = 4.14
3.2 In 65 In 382
980 .23 65