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.