Diffusion depth in a geothermal well
Input(s)
w: Mass Flow Rate \((\mathrm{lb} / \mathrm{h})\)
c: Thermal Heat Capacity of the Fluid \(\left(\mathrm{BTU} / \mathrm{lbm}{ }^{\circ} \mathrm{F}\right)\)
\(k\): Thermal Conductivity of Earth (= \(33.6 \mathrm{BTU} /\left(\mathrm{ft} \cdot\right.\) day \(\left.\left.{ }^{\circ} \mathrm{F}\right)\right)\)
\(f(t)\): Dimensionless Time Function that Represents the Transient Heat Transfer to the formation (dimensionless)
Output(s)
\(A(t)\): Diffusion Depth as a Function of Time (ft)
Formula(s)
\[
A(t)=\frac{w c f(t)}{2 \pi k}
\]
Reference(s)
Ramey Jr, H. J. (1981). Reservoir Engineering Assessment of Geothermal Systems. Department of Petroleum Engineering, Stanford University. Equation (6-2).