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Fig. 1. Single-barrier well completion schematic


The Heat Transfer Coefficient (HTC) of dual-barrier well completion is defined by the following equation:

LaTeX Math Block
anchorU
alignmentleft
\frac{1}{ r_{ci} \, U} = \frac{1}{r_{ci} \, U_{ci}} + \frac{1}{r_{ci} \, U_c}  + \frac{1}{r_c \, U_{cem}}  

where

LaTeX Math Inline
bodyr_c

outer radius of the casing

LaTeX Math Inline
body--uriencoded--r_%7Bci%7D

inner radius of the casing

LaTeX Math Inline
bodyh_c = r_c - r_i

casing wall thickness

LaTeX Math Inline
bodyr_w

wellbore radius by drilling bit

LaTeX Math Inline
body--uriencoded--\displaystyle U_%7Bci%7D = \frac%7B\lambda%7D%7B2 \, r_%7Bci%7D%7D \, %7B\rm Nu%7D_%7Bci%7D

Pipe Flow Heat Transfer Coefficient

LaTeX Math Inline
body--uriencoded--\displaystyle U_c = \frac%7B\lambda_c%7D%7Br_%7Bci%7D \cdot \ln (r_c/r_%7Bci%7D)%7D

Casing Wall Conductive Heat Transfer Coefficient

LaTeX Math Inline
body--uriencoded--\displaystyle U_%7Bcem%7D = \frac%7B\lambda_%7Bcem%7D%7D%7Br_c \cdot \ln (r_w/r_c)%7D

Cement Conductive Heat Transfer Coefficient

LaTeX Math Inline
body\lambda

thermal conductivity of fluid moving through the tubing

LaTeX Math Inline
body\lambda_с

thermal conductivity of casing material

LaTeX Math Inline
body--uriencoded--\lambda_%7Bcem%7D

thermal conductivity of cement


The equation 

LaTeX Math Block Reference
anchorU
 can be written explicitly as:

LaTeX Math Block
anchorFZZ1H
alignmentleft
\frac{1}{ r_{ti} \, U} = \frac{2}{\lambda \, {\rm Nu}_{ci}} + \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

Dual-barrier well completion Heat Transfer Coefficient @model ]

Thermal conductivity ] [ Nusselt number (Nu) ]