Skin factor due to partial penetration

Input(s)

hth_{t}: Total Formation Thickness (ft)(\mathrm{ft})

rw: Radius of Wellbore (ft)

kvk_{v}: Vertical Permeability (mD)(\mathrm{mD})

khk_{h} : Horizontal Permeability (mD)(\mathrm{mD})

hph_{p} : Height of Perforated interval (ft)

hah_{a} : Height (ft)

hpdh_{p d} : Dimensionless Perforated Thickness (fraction)

h\mathrm{h} : Thickness of reservoir ( ft\mathrm{ft} )

Output(s)

rdr_{d}: Permeability of altered zone (mD)(\mathrm{mD})

A: Dimensionless Constant A (dimensionless)

B: Dimensionless Constant B (dimensionless)

sps_{p} : Skin Factor from partial penetration (dimensionless)

Formula(s)

rd=(rwht)(kvkh)0.5r_{d}=\left(\frac{r w}{h_{t}}\right) *\left(\frac{k_{v}}{k_{h}}\right)^{0.5}A=hphtB=hahtsp=(1hpd1)2.303log(0.53.142(rwht)(kvkh)0.5)+1hpdln(hpd2+hpd(((hpht)1(haht)1)0.5))\begin{gathered} A=\frac{h_{p}}{h_{t}} \\ B=\frac{h_{a}}{h_{t}} \\ s_{p}=\left(\frac{1}{h_{p d}}-1\right) * 2.303 * \log \left(0.5 * \frac{3.142}{\left.\left(\frac{r w}{h_{t}}\right) *\left(\frac{k_{v}}{k_{h}}\right)^{0.5}\right)}+\frac{1}{h_{p d}} * \ln \left(\frac{h_{p d}}{2+h_{p d}} *\left(\left(\frac{\left(\frac{h_{p}}{h_{t}}\right)-1}{\left(\frac{h_{a}}{h_{t}}\right)-1}\right)^{0.5}\right)\right)\right. \end{gathered}

Reference(s)

Pressure Transient Testing, Lee, Rollins & Spivey, Page: 44.


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