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.