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).