# 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.

## Related

### Skin factor due to partial penetration

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