The Heat Transfer Coefficient (HTC) of dual-barrier well completionIn 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:
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\frac{1}{ r_{ti} \, U} = \frac{1}{r_{ti} \, U_{ti}} + \frac{1}{r_{ti} \, U_t} +
\frac{1}{rd_t{ann} \, U_{ann}} +
\frac{1}{r_{ci} \, U_c} + \frac{1}{r_c \, U_{cem}} |
where
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| body | --uriencoded--r_%7Bti%7D |
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| body | --uriencoded--h_t = r_t - r_%7Bti%7D |
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| tubing wall thickness |
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| body | --uriencoded--r_%7Bci%7D |
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\lambdat | wellbore radius by drilling bit |
thermal conductivity of tubing material\lambda | thermal conductivity of fluid moving through the tubinglambda%7Bann%7D a | t%7D%7Br_%7Bti%7D \cdot \ |
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epsilon_aeffective thermal conductivity of the annulus \epsilon_a | Natural Convection Heat Transfer Multiplier| --uriencoded--\displaystyle U_%7Bann%7D = \frac%7B\lambda_%7Bann%7D%7D%7Bd_%7Bann%7D%7D \, %7B\rm Nu%7D_%7Bann%7D |
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| Annular Flow Heat Transfer Coefficient |
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| body | --uriencoded--\displaystyle U_c = \frac%7B\lambda |
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_athermal conductivity of fluid in the annulus |
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| body | --uriencoded--\displaystyle U_ |
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%7Bti%7D \lambda%7D%7B2 \, r_%7Bti%7D%7D \, %7B\rm Nu%7D_%7Bti%7DPipe Flow \displaystyle U \frac%7B\lambda%7D%7B2 \, r_t%7D \, %7B\rm Nu%7D_%7Bann%7DAnnular Flow Heat Transfer Coefficient
The equation
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can be written explicitly as:| LaTeX Math Block |
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\frac{1}{ r_{ti} \, U} = \frac{12}{r_{ti}\lambda \, U{\rm Nu}_{ti}} + \frac{1}{\lambda_t} \, \ln \frac{r_t}{r_{ti}} +
+ \frac{1}{r_t\lambda_{ann} \, U {\rm Nu}_{ann}} +
\frac{1}{\lambda_c} \ln \frac{r_c}{r_{ci}} + \frac{1}{\lambda_{cem}} \ln \frac{r_w}{r_c} |
where
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| body | --uriencoded--r_%7Bti%7D |
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inner radius of the tubing
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| body | --uriencoded--h_t = r_t - r_%7Bti%7D |
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| body | --uriencoded--r_%7Bci%7D |
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inner radius of the casing
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| body | --uriencoded--\lambda_%7Bann%7D = \lambda_a \cdot \epsilon_a |
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| body | --uriencoded--\displaystyle U_%7Bti%7D = \frac%7B\lambda%7D%7B2 \, r_%7Bti%7D%7D \, %7B\rm Nu%7D_%7Bti%7D |
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Pipe Flow Heat Transfer Coefficient
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See also
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Physics / Thermodynamics / Heat Transfer / Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model
[ Single-barrier well completion Heat Transfer Coefficient @model ]
[ Thermal conductivity ] [ Nusselt number (Nu) ] [ Natural Convection Heat Transfer Multiplier ]
