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.