Pseudo-skin factor due to partial penetration (Papatzacos correlation)
Input(s)
\(h_{p}\): Perforation interval \((\mathrm{ft})\)
\(\mathrm{h}\) : Total pay thickness \((\mathrm{ft})\)
\(h_{1}\) : Distance from top of reservoir to top of open interval (ft) \(k_{v}\): Horizontal permeability \((\mathrm{mD})\)
\(k_{h}\) : Vertical permeability \((\mathrm{mD})\)
\(r_{w}\): Wellbore dia \((\mathrm{ft})\)
Output(s)
b: Penetration ratio (dimensionless)
A: Constant for calc (dimensionless)
B: Constant for calc (dimensionless)
\(h_{d}\) : Dimensionless payzone thickness (dimensionless)
\(s_{p}\) : Skin due to partial penetration (dimensionless)
Formula(s)
\[
\begin{gathered}
b=\frac{h_{p}}{h} \\
A=\frac{h}{r_{w}} * \operatorname{sqrt}\left(\frac{k_{h}}{k_{v}}\right) \\
B=\frac{h}{h_{1}+0.25 * h_{p}} \\
h_{d}=\frac{h}{h_{1}+0.75 * h_{p}} \\
s_{p}=\frac{1-b}{b} * \ln \left(\pi * \frac{h_{d}}{2}\right)+\frac{1}{b} * \ln \left(\frac{b}{b+2} * \operatorname{sqrt}\left(\frac{A-1}{B-1}\right)\right)
\end{gathered}
\]
Reference(s)
Horizontal Well Technology, Joshi, Page: 498.