Motivation

Outputs

$\begin{array}{l}T(t, l)\end{array}$

Along-hole Temperature Profile

$\begin{array}{l}t\end{array}$	Flowing duration
$\begin{array}{l}T_b\end{array}$
	Local Calendar Time	$\begin{array}{l}\delta T_A\end{array}$	Annual average surface temperature variation based on weather reports
$\begin{array}{l}z(l)\end{array}$	Wellbore trajectory. True Vertical Depth Sub-Sea (TVDss)	$\begin{array}{l}A_T\end{array}$	Period of annual temperature variation cycle: $\begin{array}{l}A_T = 1 \, {\rm year}\end{array}$
$\begin{array}{l}j_z\end{array}$	True vertical component of regional Earth's Heat Flux	$\begin{array}{l}\delta t_A\end{array}$	Time shift of annual highest temperature with respect to January 1
$\begin{array}{l}T_0\end{array}$	Local annual average surface temperature based on weather reports	$\begin{array}{l}\delta T_D\end{array}$	Daily average surface temperature variation based on weather reports
$\begin{array}{l}a_e\end{array}$	Local average Thermal diffusivity of the soil between Earth's surface and NTL	$\begin{array}{l}D_T\end{array}$	Period of daily temperature variation cycle: $\begin{array}{l}A_D = 1 \, {\rm day}\end{array}$
$\begin{array}{l}\lambda_r(z)\end{array}$	Subsurface Thermal Conductivity profile as function of TVDss	$\begin{array}{l}\delta t_D\end{array}$	Time shift of daily highest temperature with respect to Midnight 00:00
		$\begin{array}{l}\delta T_{\rm cut}\end{array}$	Temperature measurement threshold (usually $\begin{array}{l}\delta T_{\rm cut} = 0.01 \, {\rm °C}\end{array}$ )

where

$\begin{array}{l}l\end{array}$

wellbore trajectory Measured Depth with reference to Earth's surface ( $\begin{array}{l}l=0\end{array}$ )

Equations

where

$\begin{array}{l}z_s = z(l=0)\end{array}$

TVDss of the Earth's surface in a given location. In case the Earth's surface is at sea level then $\begin{array}{l}z_s = 0\end{array}$