Page 156 - Fundamentals of Enhanced Oil and Gas Recovery

144 Forough Ameli et al.

Kgα @y
@x
q 52 (5.16)
@y
mν s
@t

@y
U 52 cosθ (5.17)
@t
x
@y
tanθ 5 (5.18)
@x

@q @y
5 φΔS o (5.19)
@x @t
t x

KgαφΔS o @y=@q
q 52 t (5.20)
mν s
SAGD-oil production rate from 1/2 chamber is as follows:
ð q ð h2y
KgαφΔS o
qdq 5 dy (5.21)
0 0 mν s
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2KgαφΔS o ðh 2 yÞ
q 5 (5.22)
mν s

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2KgαφΔS o h
q 5 (5.23)
y
mν s
ð
fx; y; tÞ 5 0 ðAt SAGD interfaceÞ (5.24)

@x @t @y
52 1 ðshape of interface vs timeÞ (5.25)
@t @y @x
y x t

@x 21 2 @y=@t
x
5 5 (5.26)
@t @y=@x @t=@y @y=@x
y t x t

2 Kgα @y=@x
q 5 t (5.27)
mν s @y=@t
x
Kgα 2 @y=@t

x
5 (5.28)
qmν s @y=@x
t