Motivation

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

	Along-hole Geothermal Temperature Profile
	Geothermal Temperature Gradient

Inputs

	Local Calendar Time
	Position vector
	Wellbore trajectory True Vertical Depth Sub-Sea (TVDss)
	Earth's Heat Flux at some reference depth as function of
	Volumetric density of heat sources distributed throughout the subsurface rock volume
	Surface temperature based on weather reports
	Subsurface Thermal Conductivity profile as function of position vector
	Subsurface Thermal diffusivity profile as function of position vector

where

	Measured Depth of wellbore trajectory with reference to Earth's surface ()
	TVDss of the Earth's surface in a given location. In case the Earth's surface is at sea level then

Assumptions

Equations

\rho_e \, c_e \frac{\partial T_G}{\partial t} + \nabla \left( \lambda_e \nabla T_G \right) = q({\bf r})

 T_G(t, x, y, z = z_s) = T_s(t, x, y)

\Big[ \lambda_e \nabla T_G \Big]_{z=z_{ref}} = {\bf j}(x,y, z = z_{ref})

G_T({\bf r}) = \frac{j_z({\bf r})}{\lambda_e({\bf r})}

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.

J. H. Davis, D. R. Davis, Earth’s surface heat flux - London -2010.pdf

Georgios Florides, Soteris Kalogirou, Annual ground temperature measurements at various - Cyprus - 2014.pdf

Геотермическое поле земли

Outputs

Inputs

Assumptions

Equations

See Also

References