Page 39 - Fundamentals of Reservoir Engineering

CONTENTS XXXIX

q 2 kh
π
PI = = (6.8) 137
p − p wf r e 1
e
µ ln − + S
r w 2
e r
pdV

p = w r (6.9) 138
e r
dV
w r

2 e r
p = 2 prdr (6.10) 138
r e w r

2
2 qµ e r r r
pp = . r ln − 2 dr (6.11) 138

−
wf
r e 2 2kh w r r w 2r e
π
qµ r 3
pp wf = ln e − + S (6.12) 139
−
2kh r w 4
π
1 ∂ r ∂ p = 0 (6.13) 139

r
r ∂ r ∂
qµ r 3
pp wf = ln e − (6.14) 140
−
2kh r′ w 4
π
r′ = r e −s (6.15) 140
w
w
qµ r
oh
p − p wf = 2kh ln r h w (6.16) 141
h
π
qµ r
and p − p h = oc ln e (6.17) 141
e
r
2kh
π
h
q r r
p − p wf = µ oh ln h + µ oc ln e
e
2kh r w r h (6.18) 141
π
qµ oc µ oh r h r
e
= ln + ln
2kh µ oc r w r h
π
k − k a r a
e
S = In (6.19) 142
k a r w
qµ 1 r π 2
pp wf = ln e 3/ 2 (6.20) 144
−
2
2kh 2 π r e

π
w
4r e 2 4A 4A (6.21) 144
π
3/2 2
4 e r w = 56.32r w 2 = γ 31.6r w 2
π