Page 58 - Fundamentals of Reservoir Engineering

CONTENTS LVIII

kk′
jrw
α = j (10.76) 401
j
φ j (1 S − S wc j )
−
or
j
∂
′
q ρ w − q ρ w = Adx (ρ w S) Q ρ w (10.77) 407
w +
φ
w
w
w
x xdx t ∂
+
∂
∂ kk rw p ∂ S w
w = φ + Q w (10.78) 407
x ∂ µ w x ∂ t ∂
ro p
∂ kk ∂ o ∂ o S
= φ + Q o (10.79) 407
x ∂ µ o x ∂ t ∂
P = p o −p w (pseudo capillary pressure) (10.80) 408
°
c
S w + o S = 1 (10.81) 408
∂ S w ∂ o S
and + = 0 (10.82) 408
t ∂ t ∂
n n
1 kk rw (p n1 p n1 ) − kk rw (p n1 p n 1 )
+
+
+
+
2
−
+
(x) µ w
w,i 1 − w,i µ w
w,i − w,i 1
∆
i+ 1 2 i− 1 2 (10.83) 408
φ n1 n
+
= (S i w − S i w )
t ∆
n n
1 kk ro (p n1 p n1 ) − kk ro (p n1 p n1 )
+
+
+
+

2

−
+
(x) µ o
o,i 1 − o,i µ o
o,i − o,i 1
∆
i+ 1 2 i− 1 2 (10.84) 409
φ n1 n
+
= (S o,i − S o,i)
t ∆
+
,n 1
,n
°
+
P c °+ (S n1 n 1 − p n 1 ≈ P (S n w ) p= n o − p n w (10.85) 409
+
w ) p=
w
o
c
1 kk rw kk n n 1 p n 1 kk n ( P ° ,n P )
ro
ro
°
,n
+
+
2
o,i
(x) µ + µ o (p − w,i ) − µ o c,i 1 − c,i
+
∆
w i+ 1 2 i 1 + 2
(10.86) 409
n n
kk kk ro kk ro
n1
+
− rw + (p − p n1 ) − (P ° ,n ) = 0
+
w,i w,i 1 c,i 1
−
−
µ w µ o i+ 1 2 µ o i 1 + 2
q w = α (p wf – p w) (10.87) 413
dα n
n
+
+
q n1 = (α w,i + w,i ∆ t S w,i)(p wf,i − p n 1 ) (10.88) 414
w,i
w,i
dS w,i