Skin factor due to partial penetration

Input(s)

$h_{t}$: Total Formation Thickness $(\mathrm{ft})$

rw: Radius of Wellbore (ft)

$k_{v}$: Vertical Permeability $(\mathrm{mD})$

$k_{h}$ : Horizontal Permeability $(\mathrm{mD})$

$h_{p}$ : Height of Perforated interval (ft)

$h_{a}$ : Height (ft)

$h_{p d}$ : Dimensionless Perforated Thickness (fraction)

$\mathrm{h}$ : Thickness of reservoir ( $\mathrm{ft}$ )

Output(s)

$r_{d}$: Permeability of altered zone $(\mathrm{mD})$

A: Dimensionless Constant A (dimensionless)

B: Dimensionless Constant B (dimensionless)

$s_{p}$ : Skin Factor from partial penetration (dimensionless)

Formula(s)

$$ r_{d}=\left(\frac{r w}{h_{t}}\right) *\left(\frac{k_{v}}{k_{h}}\right)^{0.5} $$

$$ \begin{gathered} A=\frac{h_{p}}{h_{t}} \\ B=\frac{h_{a}}{h_{t}} \\ s_{p}=\left(\frac{1}{h_{p d}}-1\right) * 2.303 * \log \left(0.5 * \frac{3.142}{\left.\left(\frac{r w}{h_{t}}\right) *\left(\frac{k_{v}}{k_{h}}\right)^{0.5}\right)}+\frac{1}{h_{p d}} * \ln \left(\frac{h_{p d}}{2+h_{p d}} *\left(\left(\frac{\left(\frac{h_{p}}{h_{t}}\right)-1}{\left(\frac{h_{a}}{h_{t}}\right)-1}\right)^{0.5}\right)\right)\right. \end{gathered} $$

Reference(s)

Pressure Transient Testing, Lee, Rollins \& Spivey, Page: 44.