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Examples

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In case of flow in a simple one-casing well completion (see Fig. 1) the HTC is defined by the following equation:

\frac{1}{ d_{ci} \, U} =  \frac{1}{d_{ci} \, U_{ci}} + \frac{1}{\lambda_c} \ln \frac{d_c}{d_{ci}} + \frac{1}{\lambda_{\rm cem}} \ln \frac{d_w}{d_c} 

where

thermal conductivity of the casing material

thermal conductivity of cement

Nusselt number for the moving wellbore fluid with account of its contact with inner surface of the casing

In case of single-string well completion with flowing fluid in the annulus (see Fig. 3) the HTC is defined by the following equation:

\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 

In case the annulus fluid is moving the annulus fluid convection will be forced and the Convection Heat Transfer Multiplier 

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