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| Fig. 1. Dual-barrier well completion schematic |
The Heat Transfer Coefficient (HTC) of dual-barrier well completion is defined by the following equation:
| (1) | \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
r_t | outer radius of the tubing |
r_{ti} | inner radius of the tubing |
h_t = r_t - r_{ti} | tubing wall thickness |
r_c | outer radius of the casing |
r_{ci} | inner radius of the casing |
h_c = r_c - r_i | casing wall thickness |
r_w | wellbore radius by drilling bit |
\displaystyle U_{ti} = \frac{\lambda}{2 \, r_{ti}} \, {\rm Nu}_{ti} | |
\displaystyle U_t = \frac{\lambda_t}{r_{ti} \cdot \ln (r_t/r_{ti})} | Tubing Wall Conductive Heat Transfer Coefficient |
\displaystyle U_{ann} = \frac{\lambda_{ann}}{d_{ann}} \, {\rm Nu}_{ann} | Annular Flow Heat Transfer Coefficient |
\displaystyle U_c = \frac{\lambda_c}{r_{ci} \cdot \ln (r_c/r_{ci})} | Casing Wall Conductive Heat Transfer Coefficient |
\displaystyle U_{cem} = \frac{\lambda_{cem}}{r_c \cdot \ln (r_w/r_c)} | Cement Conductive Heat Transfer Coefficient |
d_{ann} = r_{ci}-r_t | annular hydraulic diameter |
\lambda | thermal conductivity of fluid moving through the tubing |
\lambda_{ann} | thermal conductivity of fluid in the annulus |
\lambda_t | thermal conductivity of tubing material |
\lambda_с | thermal conductivity of casing material |
\lambda_{cem} | thermal conductivity of cement |
The equation (1) can be written explicitly as:
| (2) | \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} |
See also
Physics / Thermodynamics / Heat Transfer / Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model
[ Single-barrier well completion Heat Transfer Coefficient @model ]
[ Thermal conductivity ] [ Nusselt number (Nu) ] [ Natural Convection Heat Transfer Multiplier ]