Temperature of a producing geothermal well

Input(s)

$T_{o}$: Inflowing Fluid Temperature $\left({ }^{\circ} \mathrm{F}\right)$

$T_{b h}$: Downhole Reservoir Temperature $\left({ }^{\circ} \mathrm{F}\right)$

a: Geothermal Gradient $\left({ }^{\circ} \mathrm{F} / \mathrm{ft}\right)$

A: Diffusion Depth (ft)

y: Distance from the Bottom of the Well ( $\mathrm{ft}$ )

$t$: Function of Time (d)

Output(s)

T: Temperature of a Producing Geothermal Well $\left({ }^{\circ} \mathrm{F}\right)$

Formula(s)

$$ \mathrm{T}=\left(\mathrm{T}_{\mathrm{bh}}-\mathrm{ay}\right)+\mathrm{aA}\left(1-\mathrm{e}^{-\mathrm{y} / \mathrm{A}}\right)+\left(\mathrm{T}_{\mathrm{o}}-\mathrm{T}_{\mathrm{bh}}\right) \mathrm{e}^{-\mathrm{y} / \mathrm{A}} $$

Reference(s)

Ramey Jr, H. J. (1981). Reservoir Engineering Assessment of Geothermal Systems. Department of Petroleum Engineering, Stanford University. Page: 6.2.