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| Fig. 1. Dual-barrier well completion schematic |
The Heat Transfer Coefficient (HTC) is defined by the following equation:
\frac{1}{ r_{ti} \, U} = \frac{1}{r_{ti} \, U_{ti}} + \frac{1}{r_{ti} \, U_t} +
\frac{1}{d_{ann} \, U_{ann}} +
\frac{1}{r_{ci} \, U_c} + \frac{1}{r_c \, U_{cem}} |
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 | |
| wellbore radius by drilling bit | |
| Tubing Wall Conductive Heat Transfer Coefficient | |
| Annular Flow Heat Transfer Coefficient | |
| Casing Wall Conductive Heat Transfer Coefficient | |
| Cement Conductive Heat Transfer Coefficient | |
| annular hydraulic diameter | |
| thermal conductivity of fluid moving through the tubing | |
| thermal conductivity of fluid in the annulus | |
| thermal conductivity of tubing material | |
| thermal conductivity of casing material | |
| thermal conductivity of cement |
The equation can be written explicitly as:
\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
| effective thermal conductivity of the annulus | |
| Natural Convection Heat Transfer Multiplier |
Physics / Thermodynamics / Heat Transfer / Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model
[ Thermal conductivity ] [ Nusselt number (Nu) ] [ Natural Convection Heat Transfer Multiplier ]