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| Astronomic time | | Annual average surface temperature variation based on weather reports |
| wellbore trajectory Measured Depth with reference to Earth's surface ( ) | | Period of annual temperature variation cycle: LaTeX Math Inline |
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body | --uriencoded--A_T = 1 \, %7B\rm year%7D |
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| Wellbore trajectory. True Vertical Depth Sub-Sea (TVDss) | | Time moment of annual highest temperature with respect to January 1 |
| True vertical component of regional Earth's heat flux (usually LaTeX Math Inline |
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body | --uriencoded--j_z = 25 \div 55 \ mW/m%5e2 |
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) | | Daily average surface temperature variation based on weather reports |
| Annual average surface temperature based on weather reports | | Period of daily temperature variation cycle: LaTeX Math Inline |
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body | --uriencoded--A_D = 1 \, %7B\rm day%7D |
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| Average Thermal diffusivity of the soil between Earth's surface and neutral layer | | Time moment of daily highest temperature with respect to Midnight 00:00 |
| Rock Thermal Conductivity along-hole profile |
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Assumptions
Equations
Neutral Layer |
LaTeX Math Block |
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| z_N = z_s + H_N |
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LaTeX Math Block |
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| H_N = \sqrt{\frac{a_e \, \delta_T }{\pi}} \, \ln \frac{T_A }{\delta T_{cut} } |
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Below Neutral Temperature Layer | Above Neutral Temperature Layer |
LaTeX Math Block |
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| T_g(l) = T_n + \int_{z_n}^z G_T(z) dz |
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LaTeX Math Block |
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| T(t, z) = T_s + \frac{j_z}{\lambda_e} (z-z_s) + T_Y(t, z) + T_D(t, z) |
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LaTeX Math Block |
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| G_T(z) =\frac{d T_g}{d z}= \frac{j_z}{\lambda_r} |
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LaTeX Math Block |
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| T_A(t,z) = \delta T_A \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_e \, A_T}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - \delta t_A}{A_T} + (z_s -z) \sqrt {\frac{\pi}{a_e \, A_T}} \, \right] |
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LaTeX Math Block |
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| T_D(t,z) = \delta T_D \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_e \, A_D}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - \delta t_D}{D_T} + (z_s -z) \sqrt {\frac{\pi}{a_e \, D_T}} \, \right] |
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where
| TVDss of the Earth's surface in a given location. In case the Earth's surface is at sea level then |
See Also
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Geology / Geothermal Temperature Profile
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