In case of single-string well completion with flowing fluid in the annulus (see Fig. 3) the HTC is defined by the following equation:
(1) |
\frac{1}{ d_{ti} \, U} = \frac{1}{d_{ti} \, U_{ti}} + \frac{1}{\lambda_t} \, \ln \frac{d_t}{d_{ti}} +
+ \frac{1}{\lambda_{a, \rm eff}} \ln \frac{d_{ci}}{d_t} +
\frac{1}{\lambda_c} \ln \frac{d_c}{d_{ci}} + \frac{1}{\lambda_{cem}} \ln \frac{d_w}{d_c} |
where
In case the annulus is filled with stagnant fluid the annulus fluid convection will be natural and the Convection Heat Transfer Multiplier
\epsilon_a(\rm Ra) is a function of Rayleigh number
\rm Ra.
In case the annulus fluid is moving the annulus fluid convection will be forced and the Convection Heat Transfer Multiplier
\epsilon_a can be approximated as: