Total heat loss of a geothermal well
Input(s)
\(T_{o}\): Inflowing Fluid Temperature \(\left({ }^{\circ} \mathrm{F}\right)\)
w: Mass Flow Rate \((\mathrm{lb} / \mathrm{h})\)
\(c\): Thermal Heat Capacity of the Fluid \(\left(\mathrm{BTU} / \mathrm{lbm}^{\circ} \mathrm{F}\right)\)
a: Geothermal Gradient \(\left({ }^{\circ} \mathrm{F} / \mathrm{ft}\right)\)
A: Diffusion Depth (ft)
\(H\): Total Well Depth \((\mathrm{ft})\)
\(b\): Surface Temperature \(\left({ }^{\circ} \mathrm{F}\right)\)
Output(s)
q: Total Heat Loss of a Geothermal Well (BTU/h)
Formula(s)
\[
q=-w c\left[a H-\left(T_{o}+a A-b\right)\left(1-e^{\frac{-H}{A}}\right)\right]
\]
Reference(s)
Horne, R. N., & Shinohara, K. (1979). Wellbore Heat Loss in Production and Injection Wells. Journal of Petroleum Technology, 31(01), Page: 117.