Dimensionless time function (transient heat transfer to the formation)
Input(s)
\(\alpha\): Thermal Diffusivity of the Formation \(\left(\mathrm{ft}^{2} /\right.\) day \()\)
\(r\): Diffusion Depth \((\mathrm{ft})\)
\(t\): Production Time (day)
Output(s)
\(f(t)\): Dimensionless Time Function that Represents the Transient Heat Transfer to the formation (dimensionless)
Formula(s)
\[
f(t)=-\ln \frac{r}{2 \sqrt{\alpha t}}-0.290
\]
Reference(s)
Ramey Jr, H. J. (1981). Reservoir Engineering Assessment of Geothermal Systems. Department of Petroleum Engineering, Stanford University, Equation no (6.3).