The Heat Transfer Coefficient (HTC) of dual-barrier well completionIn case of dual-barrier single-string completion with flowing fluid in the annulus (see Fig. 3) 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}{\lambdar_t{ti} \, \ln \frac{rU_t}{r_{ti}} +
+ \frac{1}{\lambdad_{a, \rm eff}}ann} \ln \frac{r, U_{ciann}}{r_t} +
\frac{1}{\lambdar_c{ci} \ln \frac{r, U_c}{r_{ci}} + \frac{1}{\lambdar_c \, U_{cem}} \ln \frac{r_w}{r_c} |
where
| outer radius of the tubing |
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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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| tubing wall thickness |
| outer radius of the casing |
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| body | --uriencoded--r_%7Bci%7D |
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| inner radius of the casing |
| casing wall thickness |
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\lambda_t | thermal conductivity of tubing material| wellbore radius by drilling bit |
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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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| body | --uriencoded--\displaystyle U_t = \frac%7B\lambda |
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thermal conductivity of fluid moving through the tubing |
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| body | --uriencoded--\displaystyle U_%7Bann%7D = \frac%7B\lambda_%7Bann%7D%7D%7Bd_ |
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%7Ba eff%7D = \lambda_a \cdot \epsilon_aeffective thermal conductivity of the annulus \epsilon_a | Natural Convection Heat Transfer Multiplieradisplaystyle U_%7Bti%7D = \frac%7B\lambda%7D%7B2 \, r_%7Bti%7D%7D \, %7B\rm Nu%7D_%7Bti%7Dheat transfer coefficient (HTC)
between inner surface of tubing and moving fluid |
The equation
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can be written explicitly as:| LaTeX Math Block |
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\frac{1}{ r_{ti} \, U} = \frac{2}{\lambda \, {\rm Nu}_{ti}} + \frac{1}{\lambda_t} \, \ln \frac{r_t}{r_{ti}}
+ \frac{1}{\lambda_{ann} \, {\rm Nu}_{ann}} +
\frac{1}{\lambda_c} \ln \frac{r_c}{r_{ci}} + \frac{1}{\lambda_{cem}} \ln \frac{r_w}{r_c} |
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 ]
