Page 181 - Fundamentals of Enhanced Oil and Gas Recovery

169
Thermal Recovery Processes

Approximate U to by the following equation.

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r to r to ln r to =r ti 1 r to ln r co =r ci r to ln r hd =r co
U to 5 1 1 1 1 (5.103)
r ti h f k htub h nc 1h r k hcas k hcem
In most cases, h f , k htub , and k hcas are so large that previous equation can be approx-
imated by
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1 r to ln r hd =r co

U to 5 1 (5.104)
ð h nc 1h r Þ k hcem
5.2.10.2 Radiation Heat-Transfer Rate/L
Evaluation of U to with approximated equation requires estimation of h r and h c . Heat
transfer coefficient for radiation, h r ,isgiven by
2 2
h r 5 σF tci ðT to 1 T ci ÞðT to 1 T ci Þ (5.105)
where
1 1 r ti 1
5 1 2 1 (5.106)
F tci ε to r ci ε ci
where ε to is the emissivity of external tubing surface, (2), ε ci is the emissivity of inter-
nal casing surface, (2), T is the absolute T ( R), σ is the Stefan Boltzmann constant

29 2 4
(51.713 3 10 Btu/h ft R ).
5.2.10.3 Heat Transfer-Rate Through Wellbore/L

T ci 5 T h 1 r to U to ln r hd ðT s 2 T h Þ (5.107)
k hcem r co
To calculate h r , the values of T to and T ci are required.
T ci is correlated to T h and T s using the above equation. It should be mentioned
that T ci and T h are dependent on U to and also time.

5.2.10.4 Natural Convection Heat-Transfer Rate
The heat transfer coefficient for natural convection, h c , is given by the following equa-
8
4
tion (Applicable 5 3 10 , N Gr N Pr , 7.2 3 10 ):
k nc
(5.108)
h nc 5
r to ln r ci =r to