In case of dual-barrier single-string completion with fluid (stagnant or moving) filling in the annulus (see Fig. 1) the HTC is defined by the following equation:
| ||
Fig. 1. |
where
outer radius of tubing | ||
inner radius of the tubing | ||
tubing wall thickness | ||
outer radius of casing | ||
inner radius of the casing | ||
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 | ||
Tubing Wall Conductive Heat Transfer Coefficient | ||
Annular Flow Heat Transfer Coefficient | ||
Casing Wall Conductive Heat Transfer Coefficient | ||
Cement Conductive Heat Transfer Coefficient |
\frac{1}{ r_{ti} \, U} = \frac{2}{\lambda \, {\rm Nu}_{ti}} + \frac{1}{\lambda_t} \, \ln \frac{r_t}{r_{ti}} + + \frac{1}{\lambda_{ann} \, {\rm Nu}_{ann}} + \frac{1}{\lambda_c} \ln \frac{r_c}{r_{ci}} + \frac{1}{\lambda_{cem}} \ln \frac{r_w}{r_c} |
where
outer radius of tubing | ||
inner radius of the tubing | ||
tubing wall thickness | ||
outer radius of casing | ||
inner radius of the casing | ||
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 | ||
Annular Flow Heat Transfer Coefficient |
Physics / Thermodynamics / Heat Transfer / Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model
[ Thermal conductivity ] [ Nusselt number (Nu) ]