Motivation
In many subsurface applications which require the knowledge of subsurface temperature distributions the land area of the study is small enough to consider the subsurface heat flux
{ \bf j}(x,y,z) = \{ j_x, \, j_y, \, j_z \} to be independent on areal location:
{ \bf j}(x,y,z) ={ \bf j}(z).
Further admitting that lateral inhomogeneity with the study area is not high the Thermal Conductivity is going to be a function of true vertical depth only \lambda_r(x,y,z) = \lambda_r(z) which leads to vanishing lateral components of the heat flux: { \bf j}(x,y,z) = \{ j_x = 0, \, j_y = 0 , \, j_z(z) \}.
Normally there are no heat sources within a subsurface volume under study other than upward Earth's Heat Flux which means that true vertical component j_z(z) = j_z = \rm const is constant along true vertical direction. It varies across the Earth but local value is usually well known.
This simplifies the procedure of modelling the Geothermal Temperature Field { \bf j}(x,y,z) = \{ 0, \, 0 , \, j_z \} along a given wellbore trajectory.
Outputs
T_G(t, l) | |
G_T(z) | Geothermal Temperature Gradient |
H_n | Neutral Temperature Layer (NTL) |
Inputs
t | Local Calendar Time | \delta T_A | Annual average surface temperature variation based on weather reports |
z(l) | A_T | Period of annual temperature variation cycle: A_T = 1 \, {\rm year} | |
j_z | True vertical component of regional Earth's Heat Flux | \delta t_A | Time shift of annual highest temperature with respect to January 1 |
T_0 | Local annual average surface temperature based on weather reports | \delta T_D | Daily average surface temperature variation based on weather reports |
a_e | Local average Thermal diffusivity of the soil between Earth's surface and NTL | D_T | Period of daily temperature variation cycle: A_D = 1 \, {\rm day} |
\lambda_r(z) | Subsurface Thermal Conductivity profile as function of TVDss | \delta t_D | Time shift of daily highest temperature with respect to Midnight 00:00 |
\delta T_{\rm cut} | Temperature measurement threshold (usually \delta T_{\rm cut} = 0.01 \, {\rm °C}) |
where
l | wellbore trajectory Measured Depth with reference to Earth's surface ( l=0) |
Assumptions
{ \bf j}(x,y,z) = \{ 0, \, 0 , \, j_z = {\rm const} \} | \lambda_r(x,y,z) = \lambda_r(z) |
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Equations
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Neutral Layer | |||||
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where
z_s = z(l=0) |
See Also
Geology / Geothermal Temperature Field / Geothermal Temperature Profile
Geothermal Temperature Field @model
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.
GeothermalTemperatureProfile.xlsx