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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 Modified
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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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body | --uriencoded--h_t = r_t - r_%7Bti%7D |
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| tubing wall thickness |
| outer radius of casing (with outer radius ) |
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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 |
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 |
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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
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outer radius of tubing (with outer radius
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Image Removed
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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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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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)...
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LaTeX Math Inline |
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body | --uriencoded--\lambda_%7Ba, \rm eff%7D = \lambda_a \cdot \epsilon_a |
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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:See also
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Physics / Thermodynamics / Heat Transfer / Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model
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