Motivation

Outputs

$\begin{array}{l}T_e(t, l)\end{array}$

along-hole geothermal temperature profile

Inputs

$\begin{array}{l}t\end{array}$	Astronomic time	$\begin{array}{l}z(l)\end{array}$	Pipeline trajectory TVDss
$\begin{array}{l}j_z\end{array}$	True vertical component of Regional Earth's heat flux (usually $\begin{array}{l}j_z = 25 \div 55 \ mW/m^2\end{array}$ )

Assumptions

Equations

Below Neutral Temperature Layer

Above Neutral Temperature Layer

(1)	$\begin{array}{l}\displaystyle T_g(l) = T_n + \int_{z_n}^z G_T(z) dz\end{array}$

(2)	$\begin{array}{l}\displaystyle T(t, z) = T_s + \frac{j_z}{\lambda_e} (z-z_s) + T_Y(t, z) + T_D(t, z)\end{array}$

(3)	$\begin{array}{l}\displaystyle G_T(z) =\frac{d T_g}{d z}= \frac{j_z}{\lambda_e}\end{array}$

(4)	$\begin{array}{l}\displaystyle T_A(t,z) = \delta T_A \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_e \, A_T}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - \delta t_A}{A_T} + (z_s -z) \sqrt {\frac{\pi}{a_e \, A_T}} \, \right]\end{array}$

(5)	$\begin{array}{l}\displaystyle T_D(t,z) = T_A \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_e \, \delta_T}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - t_{min}}{\delta_T} + (z_{srf} -z) \sqrt {\frac{\pi}{a_e \, \delta_T}} \, \right]\end{array}$

where

где

$\begin{array}{l}z_s\end{array}$	TVDss of the Earth's surface
$\begin{array}{l}T_{srf}\end{array}$	Annual average surface temperature based on weather reports
$\begin{array}{l}T_A\end{array}$	Annual average surface temperature variation based on weather reports
$\begin{array}{l}A_T\end{array}$	Period of annual temperature variation cycle: $\begin{array}{l}A_T = 1 \, {\rm year}\end{array}$ )
$\begin{array}{l}\delta t_A\end{array}$	Temperature variation cycle shift (time moment of minimal temperature with respect to astronomic midnight 0:00)
$\begin{array}{l}a_e = \frac{\lambda_e}{\rho_e \, c_e}\end{array}$	Rock temperature conductivity
$\begin{array}{l}\rho_e\end{array}$	Rock density
$\begin{array}{l}\mathrm{c_e}\end{array}$	Rock specific volumetric heat capacity at constant pressure

References

Kasuda, T., and Archenbach, P.R. "Earth Temperature and Thermal Diffusivity at Selected Stations in the United States", ASHRAE Transactions, Vol. 71, Part 1, 1965.

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Motivation

Outputs

Inputs

Assumptions

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See Also

References

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Geothermal Temperature Profile @model

Motivation

Outputs

Inputs

Assumptions

Equations

See Also

References