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LaTeX Math Inline
bodyl

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

LaTeX Math Inline
bodyl=0
)


Assumptions


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

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

LaTeX Math Inline
body\theta(l) = \rm const

LaTeX Math Inline
body--uriencoded--\rho_e = %7B\rm const%7D

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

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



Equations


LaTeX Math Block
anchorTf_Ramey
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T(t, l) = T_{0e} + G_T \, z - R(t) \, G_T \, \sin \theta  +  \big( T_s - T_{0e} + R(t) \, G_T \, \sin \theta \big)  \, e^{ - l/R(t)}



LaTeX Math Block
anchorRelaxationRamey
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R(t) = \frac{q_s}{2 \pi \, a_e} \, \bigg( T_D(t) + \frac{\lambda_e}{r_f \, U} \bigg)



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



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


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