Heat loss over an incremental length of a well (two-phase flow)


\(T_{s}\): 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)


\(d q:\) Heat Loss over an Incremental Length of the Wellbore (BTU/h)


\[ \mathrm{dq}=\frac{2 \pi \mathrm{k}\left(\mathrm{T}_{\mathrm{s}}-\mathrm{T}_{\mathrm{e}}\right)}{\mathrm{f}(\mathrm{t})} \mathrm{dy} \]


Ramey Jr, H. J. (1981). Reservoir Engineering Assessment of Geothermal Systems. Department of Petroleum Engineering, Stanford University. Page: 6.12.

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