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In some specific subsurface applications which require the knowledge of subsurface temperature distributions the assumption of the Constant Areal Geothermal Temperature Profile is not valid and the problem requires a proper 3D modelling solution.


Outputs

LaTeX Math Inline
body--uriencoded--T_G(t, %7B\bf r%7D)

Along-hole Geothermal Temperature Profile

LaTeX Math Inline
body--uriencoded--G_T(%7B\bf r%7D)

Geothermal Temperature Gradient


Inputs

LaTeX Math Inline
bodyt

Local Calendar Time

LaTeX Math Inline
body--uriencoded-- %7B\bf r%7D

Positioning

LaTeX Math Inline
bodyz(l)

Wellbore trajectory True Vertical Depth Sub-Sea (TVDss)

LaTeX Math Inline
body--uriencoded--%7B
{
\bf
j}
j%7D(x,y, z = z_
{ref}
%7Bref%7D)

Earth's Heat Flux at some reference depth 

LaTeX Math Inline
body--uriencoded--z = z_%7Bref%7D
 as function of 
LaTeX Math Inline
body (x, \, y)

LaTeX Math Inline
body--uriencoded--q(%7B\bf r%7D)

volumetric density of heat sources

LaTeX Math Inline
bodyT_s(t, x, y)

Surface temperature based on weather reports

LaTeX Math Inline
body--uriencoded--\lambda_e(%7B\bf r%7D)

Subsurface Thermal Conductivity profile as function of position vector

LaTeX Math Inline
body--uriencoded--a_%7Be%7D(%7B\bf r%7D)

Subsurface Thermal diffusivity profile as function of position vector

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