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.