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.