In case of flow in a simple one-casing well completion (see Fig. 1) the HTC is defined by the following equation:
| (1) | \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
d_w = 2 \cdot r_w | wellbore diameter (with radius r_w) | |
d_c = 2 \cdot r_c | outer diameter of the casing (with outer radius r_c) | |
d_{ci} = 2 \cdot r_{ci} | inner diameter of the casing (with inner radius r_{ci}) | |
h_c = r_c - r_i | casing wall thickness | |
\lambda_c | thermal conductivity of the casing material | |
\lambda_{cem} | thermal conductivity of cement | |
\lambda | thermal conductivity of wellbore fluid | |
\displaystyle U_{ci} = \frac{\lambda}{d_{ci}} \, {\rm Nu}_{ci} | heat transfer coefficient (HTC) between inner surface of the casing and moving fluid | |
{\rm Nu}_{ci} | Nusselt number for the moving wellbore fluid with account of its contact with inner surface of the casing | Fig. 1. Schematic of a typical multi-layer structure around single-barrier (casing) well completion |
See also
Physics / Thermodynamics / Heat Transfer / Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model