Page 41 - Fundamentals of Reservoir Engineering

CONTENTS XLI

Cumulative Production
t = Effective flowing time = (7.14) 156
Final flow rate

r
dimensionless radius r D = (7.15) 161
r
w
kt
dimensionless time t D = (7.16) 161
φµ cr w 2

2kh
π
and dimensionless pressure p(r ,t ) = (p − p ) (7.17) 161
r,t
D
D
D
i
qµ
1 ∂ r ∂ p ∂ p D (7.18) 161
D

r D r ∂ D D r ∂ D = t ∂ D
2kh
π
(p − p ) = p (t ) + S (7.19) 161
i
wf
D
D
qµ
kt
t D = 0.000264 2 t in hours (7.20) 162
−
φµ cr w
kt
t D = 0.00634 2 t in days (7.21) 162
−
φµ cr w
kh
p D = 7.08 × 10 − 3 (p − p ) (7.22) 163
i
wf
qB o
µ
4t
t
p D () = 1 2 ln D (7.23) 164
D
γ
t
p D () = 1 2 (ln t + 0.809) (7.24) 164
D
D
4A r 2
p(t ) = 1 2 ln 2 + 2 t π D w (7.25) 164
D
D
γ Cr w A
A
r 2 kt
t = t w = (7.26) 165
DA
D
A φµ cA
4A
p(t ) = 1 ln + 2 t (7.27) 165
π
D D 2 2 DA
γ Cr w
A
r 2 4t r / A
2
π
Ct w ≈ e D w (7.28) 165
AD
A
4t
π
Ct ≈ e DA (7.29) 165
ADA
kt
t = ≈ 0.1 (7.30) 165
DA
φµ cA