Heat loss over an incremental length of a well (two-phase flow)
Input(s)
\(T_{s}\): Temperature in the Well (Saturation Temperature) \(\left({ }^{\circ} \mathrm{F}\right)\)
\(T_{e}\): Undisturbed Formation Temperature \(\left({ }^{\circ} \mathrm{F}\right)\)
y: Distance from the Bottom of the Well (ft)
\(k\): Thermal Conductivity of Earth \(\left(=33.6 \mathrm{BTU} /\left(\mathrm{ft} \mathrm{d}^{\circ} \mathrm{F}\right)\right)\)
\(f(t)\): Dimensionless Time Function that Represents the Transient Heat Transfer to the formation (dimensionless)
Output(s)
\(d q:\) Heat Loss over an Incremental Length of the Wellbore (BTU/h)
Formula(s)
\[
\mathrm{dq}=\frac{2 \pi \mathrm{k}\left(\mathrm{T}_{\mathrm{s}}-\mathrm{T}_{\mathrm{e}}\right)}{\mathrm{f}(\mathrm{t})} \mathrm{dy}
\]
Reference(s)
Ramey Jr, H. J. (1981). Reservoir Engineering Assessment of Geothermal Systems. Department of Petroleum Engineering, Stanford University. Page: 6.12.