Page 182 - Fundamentals of Enhanced Oil and Gas Recovery

170 Forough Ameli et al.

where

k hc 0:333 0:074
5 0:049ðN Gr N Pr Þ N Pr (5.109)
k ha
r ci 2 r to Þgβρ 2
ð an ðT to 2 T ci Þ
N Gr 5 (5.110)
μ 2
an
C an μ
N Pr 5 an (5.111)
k ha

5.2.10.5 Unit Definitions in h nc Term
N Gr 5 Grashof number (2)
N Pr 5 Prandtl number 5 ν/α 5 (μ/ρ)/(k/ρc P )(2)
C an 5 heat capacity of fluid in annulus at average annulus temperature (Btu/
lbm F)

k ha 5 thermal conductivity of air in the annulus at average T,P in annulus (Btu/
hft F)

K hc 5 equivalent thermal conductivity of fluids in the annulus with natural con-
vection effects at average T,P in annulus (Btu/h ft F)

β 5 thermal expansion coefficient of fluids in the annulus at average T,P in annulus

(1/ R)
2
8
g 5 gravity acceleration (54.17 3 10 ft/h )

μ an 5viscosity of fluids in the annulus at average T,P in annulus (1/ R)
hT annulus i 5 (T ci 1 T to )/2.
The step-by-step procedure to calculate heat loss to wellbore:
1. Give an initial guess for U to based on T s or T to (depending on well completion)
2. Determine f(t)
3. Calculate T h
4. Calculate T ci
5. Guess h r and h c
6. Calculate the updated U to
7. Compare the calculated and the initial value for U to
8. Determine the value of heat loss while the error criterion for U to is met.

Example 5.2: Heat loss from wellbore

Consider tubing with 3.5v in which gas in injected at temperature of 600 F. The casing
is N-80. The air pressure is 14.7 psia. The casing is cemented in a hole of 12v diameter.
Thedepth of thereservoir is 3000 ft. Thepacker sizeis9.625v. The average temperature
of subsurface is 100 F. Determine the overall heat transfer coefficient, the mean temper-

ature of the casing, the value of heat loss from the wellbore after 21 days of injection.