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:
| (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 tubing |
|
r_{ti} | inner radius of the tubing | |
h_t = r_t - r_{ti} | tubing wall thickness | |
r_c | outer radius of casing | |
r_{ci} | inner radius of the casing | |
h_c = r_c - r_i | casing wall thickness | |
\lambda_t | thermal conductivity of tubing material | |
\lambda | thermal conductivity of fluid moving through the tubing | |
\lambda_{ann} = \lambda_a \cdot \epsilon_a | effective thermal conductivity of the annulus | |
\epsilon_a | Natural Convection Heat Transfer Multiplier | |
\lambda_a | thermal conductivity of fluid in the annulus | |
\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 |
| (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} |
where
r_t | outer radius of tubing | |
r_{ti} | inner radius of the tubing | |
h_t = r_t - r_{ti} | tubing wall thickness | |
r_c | outer radius of casing | |
r_{ci} | inner radius of the casing | |
h_c = r_c - r_i | casing wall thickness | |
\lambda_t | thermal conductivity of tubing material | |
\lambda | thermal conductivity of fluid moving through the tubing | |
\lambda_{ann} = \lambda_a \cdot \epsilon_a | effective thermal conductivity of the annulus | |
\epsilon_a | Natural Convection Heat Transfer Multiplier | |
\lambda_a | thermal conductivity of fluid in the annulus | |
\displaystyle U_{ti} = \frac{\lambda}{2 \, r_{ti}} \, {\rm Nu}_{ti} | ||
\displaystyle U_{ann} = \frac{\lambda}{2 \, r_t} \, {\rm Nu}_{ann} | Annular Flow Heat Transfer Coefficient |
See also
Physics / Thermodynamics / Heat Transfer / Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model
[ Thermal conductivity ] [ Nusselt number (Nu) ]