Average permeability in radial systems

Input(s)

$k_{a}$: Permeability between $r_{w}$ and $r_{a}(\mathrm{mD})$

$k_{e}$: Permeability between $r_{e}$ and $r_{a}(\mathrm{mD})$

$r_{e}$: Drainage radius (ft)

$r_{w}$: Well bore radius (ft)

$r_{a}$: Radius lesser than $r_{e}(\mathrm{ft})$

Output(s)

$k_{\text {avg }}$: Average Permeability in Radial Systems Series (mD)

Formula(s)

$$ k_{a v g}=\frac{k_{a} * k_{e} * \ln \left(\frac{r_{e}}{r_{w}}\right)}{k_{a} * \ln \left(\frac{r_{e}}{r_{a}}\right)+k_{e} * \ln \left(\frac{r_{a}}{r_{w}}\right)} $$

Reference(s)

Applied Reservoir Engineering Vol. 1, Smith, Tracy \& Farrar, Equation 7-7.