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titleSingleDual-barrier Completion

In case of flow in a simple one-casing well completion (see Fig. 1) the HTC is single-string well completion with flowing fluid in the annulus (see Fig. 3) the HTC is defined by the following equation:

LaTeX Math Block
anchorU
alignmentleft
\frac{1}{ d_{citi} \, U} = \frac{1}{d_{ti} \, U_{ti}} + \frac{1}{\lambda_t} \, \ln \frac{d_t}{d_{ci} \, Uti}} +
+ \frac{1}{\lambda_{a, \rm eff}} \ln \frac{d_{ci}}{d_t} + 
\frac{1}{\lambda_c} \ln \frac{d_c}{d_{ci}} + \frac{1}{\lambda_{\rm cem}} \ln \frac{d_w}{d_c}

where

LaTeX Math Inline
bodyd

_w

_t = 2 \cdot r_t

outer radius of tubing (with outer radius

LaTeX Math Inline
bodyr_t
)

Image Added

LaTeX Math Inline
body--uriencoded--d_%7Bti%7D = 2 \cdot r_

w

%7Bti%7D

wellbore

inner diameter of the tubing (with inner radius

LaTeX Math Inline
body--uriencoded--r_

w

%7Bti%7D
)

Image Removed

LaTeX Math Inline
body--uriencoded--h_t = r_t - r_%7Bti%7D

tubing wall thickness

LaTeX Math Inline
bodyd_c = 2 \cdot r_c

outer

diameter

radius of

the

casing (with outer radius

LaTeX Math Inline
bodyr_c
)

LaTeX Math Inline
body--uriencoded--d_%7Bci%7D = 2 \cdot r_%7Bci%7D

inner diameter of the casing (with inner radius

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

LaTeX Math Inline
bodyh_c = r_c - r_i

casing wall thickness

LaTeX Math Inline
body\lambda_

c

t

thermal conductivity of tubing material

LaTeX Math Inline
body\lambda

thermal conductivity of fluid moving through the
casing material
tubing

LaTeX Math Inline
body--uriencoded--\lambda_

{cem}

%7Ba, \rm eff%7D = \lambda_a \cdot \epsilon_a

effective thermal conductivity of the annulus 

LaTeX Math Inline
body\epsilon_a

Natural Convection Heat Transfer Multiplier
thermal conductivity of cement

LaTeX Math Inline
body\lambda_a

thermal conductivity of
wellbore 
fluid
 
in the annulus

LaTeX Math Inline
body--uriencoded--\displaystyle U_

%7Bci%7D

%7Bti%7D = \frac%7B\lambda%7D%7Bd_

%7Bci%7D%7D

%7Bti%7D%7D \, %7B\rm Nu%7D_

%7Bci%7D

%7Bti%7D

heat transfer coefficient (HTC)
between inner surface of

the casing and moving fluid

tubing and moving fluid


In case the annulus is filled with stagnant fluid the annulus fluid convection will be natural and the Convection Heat Transfer Multiplier 

LaTeX Math Inline
body

{

\epsilon_a(\rm

Nu}_{ci}

Nusselt number for the moving wellbore fluid with account of its contact with inner surface of the casing

Ra)
  is a function of Rayleigh number 
LaTeX Math Inline
body\rm Ra
.

In case the annulus fluid is moving the annulus fluid convection will be forced and the Convection Heat Transfer Multiplier 

LaTeX Math Inline
body\epsilon_a
 can be approximated as:

Fig. 1. Schematic of a typical multi-layer structure around single-barrier (casing) well completion




See also

...

Physics / Thermodynamics / Heat Transfer /  Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model

...