GLOSSARY

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LaTeX Math Inline
bodyT_s

Intake temperature

LaTeX Math Inline
bodyT_be(l)

Background temperature of the surroundings

LaTeX Math Inline
bodyq_s

Intake flowrate

LaTeX Math Inline
bodyU

Heat Transfer Coefficient (HTC) between pipe fluid and surroundings

LaTeX Math Inline
bodya_be

Thermal Diffusivity of the surroundings

LaTeX Math Inline
bodyr_f

Flowing pipe radius

LaTeX Math Inline
body\lambda_be

Thermal Conductivity of the surroundings

LaTeX Math Inline
bodyr_w

Wellbore radius

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



LaTeX Math Block
anchorGb
alignmentleft
G_be = \frac{dT_b}{dl}




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



LaTeX Math Block
anchorRelaxationRamey
alignmentleft
R(t) = \frac{q_s}{2 \pi \, a_be} \, \left( T_D(t) + \frac{\lambda_be}{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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Intake Flowrate is constant in time

Intake Temperature is constant in time

LaTeX Math Inline
body--uriencoded--q_s(t) = q_s = %7B\rm const%7D

LaTeX Math Inline
bodyT_s(t) = T_s = \rm const

Thermal diffusivity of the surroundings is constant along-hole

Thermal Conductivity of the surroundings is constant along-hole

LaTeX Math Inline
bodya_be(l) = a_b e = \rm const

LaTeX Math Inline
body\lambda_be(l) = \lambda_b e = \rm const

Flowing pipe radius is constant along-holeWellbore radius is constant along-hole

LaTeX Math Inline
bodyr_f(l) = r_f = \rm const

LaTeX Math Inline
bodyr_w(l) = r_w = \rm const

Heat Transfer Coefficient (HTC) between pipe fluid and surroundings is constant along-hole

LaTeX Math Inline
bodyU(l) = U = \rm const

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