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).