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Synonym: Geothermal Temperature Profile @model = Constant Areal Geothermal Temperature Profile @model 

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  

LaTeX Math Inline
body--uriencoded--%7B \bf j%7D(x,y,z) = \%7B j_x, \, j_y, \, j_z \%7D
 and Thermal Conductivity 
LaTeX Math Inline
body--uriencoded--\lambda_e(%7B\bf r%7D)
 to be homogeneous across location area: 

LaTeX Math Block
anchor1
alignmentleft
{\bf j}({\bf r}) ={\bf j}(x,y,z)={ \bf j}(z)
LaTeX Math Block
anchor1
alignmentleft
\lambda_e({\bf r}) =\lambda_e(z)

where 

LaTeX Math Inline
bodyz
 is true vertical depth.

Since the  heat flux is conservative (see

LaTeX Math Block Reference
anchorrot_j
pageGeothermal Temperature Field @model
) then it immediately implies that:

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This simplifies the procedure of modelling the a Geothermal Temperature Field 

LaTeX Math Inline
body--uriencoded--%7B \bf j%7D(x,y,z) = \%7B 0, \, 0 , \, j_z \%7D
 along  to modelling of a Constant Areal Geothermal Temperature Profile along a given wellbore trajectory.

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[ Geothermal Temperature Field @model ] [ Geothermal Temperature Gradient ]

[ Neutral Temperature Layer @model ]

References

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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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