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In 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}{d_{ann} \, U_{ann}} +
\frac{1}{r_{ci} \, U_c} + \frac{1}{r_c \, U_{cem}} |
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where
| outer radius of tubing | ||||||||||||||||
| inner radius of the tubing | ||||||||||||||||
| tubing wall thickness | ||||||||||||||||
| outer radius of casing | ||||||||||||||||
| inner radius of the casing | ||||||||||||||||
| casing wall thickness | ||||||||||||||||
| \lambda
| t
| wellbore radius by drilling bit | thermal conductivity of tubing material |
| thermal conductivity of fluid moving through the tubing | |||||||||||
| effective thermal conductivity of the annulus | ||||||||||||||||
| Natural Convection Heat Transfer Multiplier | ||||||||||||||||
| annular hydraulic diameter |
| thermal conductivity of fluid in the annulus | ||||||||||||||
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| Tubing Wall Conductive Heat Transfer Coefficient | ||||||||||||||||
| Annular Flow Heat Transfer Coefficient | ||||||||||||||||
| Casing Wall Conductive Heat Transfer Coefficient | ||||||||||||||||
| Cement Conductive Heat Transfer Coefficient | Fig. 1. Dual-barrier well completion schematic |
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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} |
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| outer radius of tubing | |||||
| inner radius of the tubing | |||||
| tubing wall thickness | |||||
| outer radius of casing | |||||
| inner radius of the casing | |||||
| casing wall thickness | |||||
| thermal conductivity of tubing material | |||||
| thermal conductivity of casing material | |||||
| thermal conductivity of cement | |||||
| thermal conductivity of fluid moving through the tubing | |||||
| effective thermal conductivity of the annulus | |||||
| Natural Convection Heat Transfer Multiplier | |||||
| thermal conductivity of fluid in the annulus | |||||
| ||||||
| Annular Flow Heat Transfer Coefficient |
See also
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Physics / Thermodynamics / Heat Transfer / Heat Transfer Coefficient (HTC) / Heat Transfer Coefficient (HTC) @model
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