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:

\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

	outer radius of tubing
	inner radius of the tubing
	tubing wall thickness
	outer radius of casing
	inner radius of the casing
	casing wall thickness
	thermal conductivity of tubing material
	thermal conductivity of fluid moving through the tubing
	effective thermal conductivity of the annulus
	Natural Convection Heat Transfer Multiplier
	thermal conductivity of fluid in the annulus
	Pipe Flow Heat Transfer Coefficient
	Tubing Wall Conductive Heat Transfer Coefficient
	Annular Flow Heat Transfer Coefficient
	Casing Wall Conductive Heat Transfer Coefficient
	Cement Conductive Heat Transfer Coefficient

\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_{ann}} +
\frac{1}{\lambda_c} \ln \frac{r_c}{r_{ci}} + \frac{1}{\lambda_{cem}} \ln \frac{r_w}{r_c}

where

	outer radius of tubing
	inner radius of the tubing
	tubing wall thickness
	outer radius of casing
	inner radius of the casing
	casing wall thickness
	thermal conductivity of tubing material
	thermal conductivity of fluid moving through the tubing
	effective thermal conductivity of the annulus
	Natural Convection Heat Transfer Multiplier
	thermal conductivity of fluid in the annulus
	Pipe Flow Heat Transfer Coefficient
	Annular Flow Heat Transfer Coefficient

See also