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| along-hole geothermal temperature profile |
Inputs
| 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 sAnnual | Daily average surface temperature variation based on weather reports |
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a_e | Average Thermal diffusivity of the soil between Earth's surface and neutral layer | where
| LaTeX Math Inline |
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body | T_A | Annual average surface temperature |
variation A annual daily temperature variation cycle: |
T year%7DA seasonal | daily highest temperature with respect to |
January 1
Assumptions
Equations
| 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_er} |
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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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