Page 164 - Fundamentals of Enhanced Oil and Gas Recovery

152 Forough Ameli et al.

Figure 5.3 Boberg Lantz model.

@T
at r-N; 5 0 (5.66)
@r
h @T
at z 5 ; 5 0 (5.67)
2 @r
@T
at z-N; 5 0 (5.68)
@r
Using the superposition principle in this model:

Tr; zÞ 5 TrðÞTðzÞ (5.69)
ð
TrðÞ for 0 # r # r h (5.70)
TzðÞ for 0 # z # h (5.71)

(5.72)
T D 5 T Dr T Dz
Introducing dimensionless parameters in Boberg Lantz model:
Temperature:

TrðÞ 2 T R
T Dr 5 (5.73)
T s 2 T R
TzðÞ 2 T R
T Dz 5 (5.74)
T s 2 T R
Time:

αðt 2 t i Þ
t Dr 5 (5.75)
2
r h
αðt 2 t i Þ
(5.76)
2
t Dz 5
h=2