Temperature of a single-phase liquid or gas injected geothermal well
Input(s)
\(T_{\text {surf: }}\) Surface Temperature of the Earth \(\left({ }^{\circ} \mathrm{F}\right)\)
\(T_{i n j}\): Temperature of the Injected Fluid \(\left({ }^{\circ} \mathrm{F}\right)\)
a: Geothermal Gradient \(\left({ }^{\circ} \mathrm{F} / \mathrm{ft}\right)\)
A: Diffusion Depth (ft)
\(z\): Distance from the Bottom of the Well (ft)
Output(s)
T: Temperature of a Single-Phase Liquid or Gas Injected Geothermal Well \(\left({ }^{\circ} \mathrm{F}\right)\)
Formula(s)
\[
\mathrm{T}=\mathrm{T}_{\text {surf }}+\mathrm{az}-\mathrm{aA}+\left(\mathrm{T}_{\text {inj }}-\mathrm{T}_{\text {surf }}+\mathrm{aA}\right) \mathrm{e}^{-\mathrm{z} / \mathrm{A}}
\]
Reference(s)
Ramey Jr, H. J. (1981). Reservoir Engineering Assessment of Geothermal Systems. Department of Petroleum Engineering, Stanford University. Page: 6.6.