# Pseudo-skin factor due to partial penetration (Yeh and Reynolds correlation)

## Input(s)

\(h_{p}\): Perforation Interval \((\mathrm{ft})\)

\(\mathrm{h}\) : Total pay thickness \((\mathrm{ft})\)

\(C_{d}\) : Location of open interval from graphical co-relation by Yeh and Ronald (dimensionless)

\(k_{v}\) : Horizontal Permeability \((\mathrm{mD})\)

\(k_{h}\) : Vertical Permeability (mD)

\(r_{w}\): Wellbore Dia (ft)

## Output(s)

b: Penetration ratio (dimensionless)

\(C_{1}\) : Location of open interval from graphical co-relation by Yeh and Ronald (dimensionless)

\(h_{d}\) : Dimensionless payzone thickness (dimensionless)

\(h_{\{w d\}}\) : Effective Wellbore depth (ft)

\(s_{p}\): Skin due to partial penetration (dimensionless)

## Formula(s)

\[
\begin{gathered}
b=\frac{h_{p}}{h} \\
C_{1}=\frac{h}{r_{w}} * \operatorname{sqrt}\left(\frac{k_{h}}{k_{v}}\right) \\
h_{d}=0.481+1.01 * b-0.838 * b^{2}
\end{gathered}
\]

\[
\begin{gathered}
h_{w d}=C_{d} * b *(1-b) * \frac{h_{d}}{2.71_{1}^{C}} \\
s_{p}=\frac{1-b}{b} * \ln \left(h_{\{w d\}}\right)
\end{gathered}
\]

## Reference(s)

Horizontal Well Technology, Joshi, Page: 496.