In case of dual-barrier well completion with flowing fluid in the annulus (see Fig. 3) the HTC is defined by the following equation:
| LaTeX Math Block |
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\frac{1}{ d_{ti} \, U} = \frac{1}{d_{ti} \, U_{ti}} + \frac{1}{\lambda_t} \, \ln \frac{d_t}{d_{ti}} +
+ \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_{cem}} \ln \frac{d_w}{d_c} |
where
| outer radius of tubing (with outer radius ) |  Image Added
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| body | --uriencoded--d_%7Bti%7D = 2 \cdot r_%7Bti%7D |
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| inner diameter of the tubing (with inner radius | LaTeX Math Inline |
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| body | --uriencoded--r_%7Bti%7D |
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) |
| LaTeX Math Inline |
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| body | --uriencoded--h_t = r_t - r_%7Bti%7D |
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| tubing wall thickness |
| outer radius of casing (with outer radius ) |
| LaTeX Math Inline |
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| body | --uriencoded--d_%7Bci%7D = 2 \cdot r_%7Bci%7D |
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| inner diameter of the casing (with inner radius | LaTeX Math Inline |
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| body | --uriencoded--r_%7Bci%7D |
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) |
| casing wall thickness |
| thermal conductivity of tubing material |
| thermal conductivity of fluid moving through the tubing |
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| body | --uriencoded--\lambda_%7Ba, \rm eff%7D = \lambda_a \cdot \epsilon_a |
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| effective thermal conductivity of the annulus |
| Natural Convection Heat Transfer Multiplier |
| thermal conductivity of fluid in the annulus |
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| body | --uriencoded--\displaystyle U_%7Bti%7D = \frac%7B\lambda%7D%7Bd_%7Bti%7D%7D \, %7B\rm Nu%7D_%7Bti%7D |
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| heat transfer coefficient (HTC)
between inner surface of tubing and moving fluid |
| Expand |
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| title | Dual-barrier Completion |
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In case of single-string well completion with flowing fluid in the annulus (see Fig. 3) the HTC is defined by the following equation: | LaTeX Math Block |
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| \frac{1}{ d_{ti} \, U} = \frac{1}{d_{ti} \, U_{ti}} + \frac{1}{\lambda_t} \, \ln \frac{d_t}{d_{ti}} +
+ \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_{cem}} \ln \frac{d_w}{d_c} |
where | outer radius of tubing (with outer radius ) | | | LaTeX Math Inline |
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| body | --uriencoded--d_%7Bti%7D = 2 \cdot r_%7Bti%7D |
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| inner diameter of the tubing (with inner radius | LaTeX Math Inline |
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| body | --uriencoded--r_%7Bti%7D |
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) | | LaTeX Math Inline |
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| body | --uriencoded--h_t = r_t - r_%7Bti%7D |
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|
| tubing wall thickness | | outer radius of casing (with outer radius ) | | LaTeX Math Inline |
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| body | --uriencoded--d_%7Bci%7D = 2 \cdot r_%7Bci%7D |
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| inner diameter of the casing (with inner radius | LaTeX Math Inline |
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| body | --uriencoded--r_%7Bci%7D |
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) | | casing wall thickness | | thermal conductivity of tubing material | | thermal conductivity of fluid moving through the tubing | | LaTeX Math Inline |
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| body | --uriencoded--\lambda_%7Ba, \rm eff%7D = \lambda_a \cdot \epsilon_a |
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| effective thermal conductivity of the annulus | | Natural Convection Heat Transfer Multiplier | | thermal conductivity of fluid in the annulus | | LaTeX Math Inline |
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| body | --uriencoded--\displaystyle U_%7Bti%7D = \frac%7B\lambda%7D%7Bd_%7Bti%7D%7D \, %7B\rm Nu%7D_%7Bti%7D |
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| heat transfer coefficient (HTC)
between inner surface of 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 is a function of Rayleigh number .In case the annulus fluid is moving the annulus fluid convection will be forced and the Convection Heat Transfer Multiplier can be approximated as:
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