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| along-hole geothermal temperature profile |
Inputs
Pipeline trajectory TVDss Regional (usually | LaTeX Math Inline |
|---|
| body | --uriencoded--j_z = 25 \div 55 \ mW/m%5e2 |
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|
) |
...
where
...
| Annual average surface temperature based on weather reports |
| Annual average surface temperature variation based on weather reports |
| Period of annual temperature variation cycle: | LaTeX Math Inline |
|---|
| body | --uriencoded--A_T = 1 \, %7B\rm year%7D |
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|
|
| Time moment of seasonal highest temperature with respect to January 1 |
| Rock thermal diffusivity |
Assumptions
Equations
| Below Neutral Temperature Layer | Above Neutral Temperature Layer |
| 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 |
| 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) |
| LaTeX Math Block |
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|
G_T(z) =\frac{d T_g}{d z}= \frac{j_z}{\lambda_e} |
| LaTeX Math Block |
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| T_Ag(t,zl) = \delta T_An + \, \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]int_{z_n}^z G_T(z) dz |
|
| LaTeX Math Block |
|---|
| T(t, z) = T_s + \frac{j_z}{\lambda_e} (z-z_s) + T_Y(t, z) + T_D(t, z) |
|
| LaTeX Math Block |
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| G_T(z) =\frac{d T_g}{d z}= \frac{j_z}{\lambda_e} |
|
| LaTeX Math Block |
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| T_DA(t,z) = \delta T_DA \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_e \, A_DT}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - \delta t_DA}{DA_T} + (z_s -z) \sqrt {\frac{\pi}{a_e \, DA_T}} \, \right] |
|
...
где
| 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] |
|
where
| TVDss of the Earth's surface in a given location. In case the Earth's surface is at sea level then |
| TVDss of the Earth's surface |
| Annual average surface temperature based on weather reports |
| Annual average surface temperature variation based on weather reports |
| Period of annual temperature variation cycle: | LaTeX Math Inline |
|---|
| body | --uriencoded--A_T = 1 \, %7B\rm year%7D |
|---|
|
) |
| Temperature variation cycle shift (time moment of minimal temperature with respect to astronomic midnight 0:00) |
| LaTeX Math Inline |
|---|
| body | a_e = \frac{\lambda_e}{\rho_e \, c_e} |
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|
| Rock temperature conductivity |
| Rock density |
| Rock specific volumetric heat capacity at constant pressureSee Also
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Geology / Geothermal Temperature Profile
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