Page 162 - Fundamentals of Enhanced Oil and Gas Recovery

150 Forough Ameli et al.

To calculate the mean temperature, use the following correlation proposed by
Boberg and Lantz [35]. It is emphasized that this equation is an approximation for our
media and is actually represented for the cylindrical shape volumes.

ð
ð
T avg 5 T R 1 T s 2 T R Þ½f HD f VD 1 2 f PD Þ 2 f PD Š (5.53)
f HD , f VD , and f PD are dimensionless parameters indicating radial loss, vertical loss, and
exhausted energy from the fluids, respectively. These parameters are function of time.
They were introduced by Boberg and Lantz [35] graphically in terms of dimensionless
time or as error and gamma functions. To simplify calculations, the following equa-
tions are represented:
1
f HD 5 (5.54)
1 1 5t DH
αðt 2 t inj Þ
t DH 5 (5.55)
2
R h
1
f VD 5 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (5.56)
1 1 5t DV
4αðt 2 t inj Þ
t DV 5 (5.57)
h t 2
To calculate the amount of the energy removed by the fluid, this equation is
introduced:
ð t
1
f PD 5 Q P dt (5.58)
2Q max 0
Q max is the maximum amount of heat transfer to the reservoir. This parameter is
calculated as follows:
The value of the heat loss to overburden minus the summation of the heat
remaining in the reservoir and the value of heat injected to the reservoir in the pres-
ent time step.

r ffiffiffiffiffiffiffiffiffiffi
2 T soak
Q max 5 H inj 1 H last 2 πR h K R ðT s 2 T R Þ (5.59)
πa
The amount of H last is substituted from the last time step. The value of heat injec-
tion in each cycle is calculated as follows:
(5.60)
H inj 5 350Q i Q s t inj
To calculate the rate of heat transfer, use the following equation (5.2):
Q P 5 5:615ðq o M o1 q w M w ÞðT avg 2 T R Þ (5.61)