In case of dual-barrier 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

outer radius of tubing (with outer radius )

inner diameter of the tubing (with inner radius )

tubing wall thickness

outer radius of casing (with outer radius )

inner diameter of the casing (with inner radius )

casing wall thickness

thermal conductivity of tubing material

thermal conductivity of fluid moving through the tubing

effective thermal conductivity of the annulus 

Natural Convection Heat Transfer Multiplier

thermal conductivity of fluid in the annulus

heat transfer coefficient (HTC)
between inner surface of tubing and moving fluid


See also


Physics / Thermodynamics / Heat Transfer /  Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model

Thermal conductivity ] [ Nusselt number (Nu) ]