GLOSSARY

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LaTeX Math Inline
bodyT_e(t, l)

along-hole geothermal temperature profile

Inputs

LaTeX Math Inline
bodyt

Astronomic time



LaTeX Math Inline
bodyl

wellbore trajectory Measured Depth with reference to Earth's surface (

LaTeX Math Inline
bodyl=0
)



LaTeX Math Inline
bodyz(l)

wellbore trajectory True Vertical Depth Sub-Sea (TVDss)

LaTeX Math Inline
bodyj_z

True vertical component of regional Earth's heat flux (usually 

LaTeX Math Inline
body--uriencoded--j_z = 25 \div 55 \ mW/m%5e2
)

where



LaTeX Math Inline
bodyT_

{srf}

s

Annual average surface temperature based on weather reports

LaTeX Math Inline
bodya_e

Average Thermal diffusivity of the soil between Earth's surface and neutral layer



where


Rock thermal diffusivity



LaTeX Math Inline
bodyT_A

Annual average surface temperature variation based on weather reports

LaTeX Math Inline
bodyA_T

Period of annual temperature variation cycle:

LaTeX Math Inline
body--uriencoded--A_T = 1 \, %7B\rm year%7D

LaTeX Math Inline
body\delta t_A

Time moment of seasonal highest temperature with respect to January 1

LaTeX Math Inline
bodya_e





Assumptions




Equations

Below Neutral Temperature LayerAbove Neutral Temperature Layer


LaTeX Math Block
anchorT_g
alignmentleft
T_g(l) = T_n + \int_{z_n}^z G_T(z) dz



LaTeX Math Block
anchorT_z
alignmentleft
T(t, z) = T_s + \frac{j_z}{\lambda_e} (z-z_s) + T_Y(t, z) + T_D(t, z)



LaTeX Math Block
anchorG_T
alignmentleft
G_T(z) =\frac{d T_g}{d z}= \frac{j_z}{\lambda_e}



LaTeX Math Block
anchorT_z
alignmentleft
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]




LaTeX Math Block
anchorT_z
alignmentleft
T_D(t,z) = \delta T_D \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_e \, A_D}} \, \right] \, \cos \left[  \, 2 \pi \frac{t - \delta t_D}{D_T} + (z_s -z) \sqrt {\frac{\pi}{a_e \, D_T}} \, \right]


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