For the pipeline flow Heat Transfer Coefficient is related to dimensionless Nusselt number:
| (1) | U = \frac{\lambda}{r_{i}} \, {\rm Nu}_{ti} |
where
{\rm Nu} | Nusselt number |
r_{i} | pipeline inner radius |
\lambda | thermal conductivity of flowing fluid |
In case of simple one-casing well completion (see Fig. 1) the HTC is defined by the following equation:
| (2) | \frac{1}{ r_{ti} \, U} = \frac{1}{r_c \, U_{ci}} + \frac{1}{\lambda_c} \ln \frac{r_c}{r_{ci}} + \frac{1}{\lambda_{cem}} \ln \frac{r_w}{r_c} |
where
r_w | wellbore radius | |
r_c | outer radius of casing | |
h_c | casing thickness | |
r_{ci}= r_c - h_c | inner radius of casing | |
\lambda_c | thermal conductivity of casing material | |
\lambda_{cem} | thermal conductivity of cement | |
\lambda_a | thermal conductivity of wellbore fluid | |
\displaystyle U_{ci} = \frac{\lambda_a}{r_{ci}} \, {\rm Nu}_{ci} | heat transfer coefficient (HTC) between inner surface of casing and moving fluid | |
{\rm Nu}_{ci} | Nusselt number between inner surface of casing and stagnant fluid in annulus | Fig. 1. Schematic of a typical multi-layer structure around simple one-casing well completion |
In case of single-string well completion with stagnant fluid in the annulus (see Fig. 2) the HTC is defined by the following equation:
| (3) | \frac{1}{ r_{ti} \, U} = \frac{1}{r_{ti} \, U_{ti}} + \frac{1}{\lambda_t} \, \ln \frac{r_t}{r_{ti}} + \frac{1}{r_t \, U_{to}} + \frac{1}{r_c \, U_{ci}} + \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 tubing | |
h_t = r_t - r_{ti} | tubing wall thickness | |
r_c | outer radius of casing | |
r_{ci} | inner radius of casing | |
h_c = r_c - r_{ci} | casing wall thickness | |
\lambda_t | thermal conductivity of tubing material | |
\lambda | thermal conductivity of fluid moving through the tubing | |
\lambda_a | thermal conductivity of fluid in the annulus | |
\displaystyle U_{ti} = \frac{\lambda}{r_{ti}} \, {\rm Nu}_{ti} | heat transfer coefficient (HTC) | |
\displaystyle U_{to} = \frac{\lambda_a}{r_{t}} \, {\rm Nu}_{to} | heat transfer coefficient (HTC) | |
\displaystyle U_{ci} = \frac{\lambda_a}{r_{ci}} \, {\rm Nu}_{ci} | heat transfer coefficient (HTC) | Fig. 2. Schematic of a typical multi-layer structure around single-string well completion |
See also
Physics / Thermodynamics / Heat Transfer / Heat Transfer Coefficient (HTC)
[ Thermal conductivity ][ Nusselt Number ]