| (1) | \frac{1}{ r_{ti} \, U} = \frac{1}{r_c \, \alpha_{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 | |
\alpha_{ci} | heat exchange coefficient between inner surface of casing and moving fluid |
In case of single-string well completion with stagnant fluid in the annulus (see Fig. 1):
| (2) | \frac{1}{ r_{ti} \, U} = \frac{1}{r_{ti} \, \alpha_{ti}} + \frac{1}{\lambda_t} \, \ln \frac{r_t}{r_{ti}} + \frac{1}{r_t \, \alpha_{to}} + \frac{1}{r_c \, \alpha_{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 |
|
h_t | tubing wall thickness | |
r_{ti} = r_t - h_t | inner radius of tubing | |
\lambda_t | thermal conductivity of tubing material | |
\alpha_{ti} | heat exchange coefficient between inner surface of tubing and moving fluid | |
\alpha_{to} | heat exchange coefficient between outer surface of tubing and fluid moving in annulus | Fig. 1. Schematic of a typical multi-layer structure around well completion |
Heat exchange coefficients are related to unitless Nusselt number:
|
|
|
where
\lambda | thermal conductivity of fluid moving through the tubing |
\lambda_a | thermal conductivity of fluid in the annulus |
See also
Physics / Thermodynamics / Heat Transfer
[ Heat exchange coefficient ] [ Thermal conductivity ]