GLOSSARY

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LaTeX Math Inline
bodyT_s

Intake temperature

LaTeX Math Inline
bodyT_e(l)

Background temperature of the surroundings

LaTeX Math Inline
bodyq_s\dot m

mass Intake flowrate

LaTeX Math Inline
bodyU

Heat Transfer Coefficient (HTC) between pipe fluid and surroundings

LaTeX Math Inline
bodya_e

Thermal Diffusivity of the surroundings

LaTeX Math Inline
bodyr_f

Flowing pipe radius

LaTeX Math Inline
body\lambda_e

Thermal Conductivity of the surroundings

LaTeX Math Inline
bodyr_w

Wellbore radius

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LaTeX Math Block
anchorTf_Ramey
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T(t, l) = T_e(l) - R(t) \, G_e(l)  +  \Big[ T_s - T_e(0) + R(t) \, G_e(l) \Big]  \cdot e^{ - l/R(t)}



LaTeX Math Block
anchorGb
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G_e = \frac{dT_e}{dl}




LaTeX Math Block
anchort_D
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t_D(t) = \frac{a_e \, t}{r_w^2}



LaTeX Math Block
anchorRelaxationRamey
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R(t) = \frac{q_s\dot m \, c_p}{2 \pi \, a\lambda_e} \,cdot \left( T_D(t) + \frac{\lambda_e}{r_f \, U} \right)



LaTeX Math Block
anchorT_D
alignmentleft
T_D(t) = \ln \Big[ e^{-0.2 \, t_D} + (1.5 - 0.3719 \, e^{-t_D}) \, \sqrt{t_D} \Big]


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