Total skin in partially depleted wells for a buildup test

Input(s)

$r_{e w}$: Dimensionless Parameter in terms of Perforated Length and Wellbore Radius (dimensionless)

$\emptyset$ : Porosity (fraction)

$\mu$ : Viscosity $(\mathrm{cP})$

$c_{t}$: Total Compressibility $(1 / \mathrm{psi})$

k: Permeability $(\mathrm{mD})$

$p_{s}$: Shut-in Pressure at any Shut-in Time (psi)

$p_{w}$ : Well Flowing Pressure at the Instant of Shut-in (psi)

$\Delta t$: Shut-in Time (day)

$\mathrm{m}$ : Slope of Cartesian Pressure Build-up Plot (psi/cycle)

Output(s)

S: Skin (dimensionless)

Formula(s)

$$ S=34.7 * r_{e w} *\left(\left(\left(\emptyset * \mu * \frac{c_{t}}{k}\right)\right)^{0.5}\right) *\left(\left(\frac{p_{s}-p_{w}}{m}\right)+\left(\frac{1}{(\Delta t)^{0.5}}\right)\right)-1 $$

Reference(s)

Ahmed, T., McKinney, P.D. 2005. Advanced Reservoir Engineering, Gulf Publishing of Elsevier, Chapter: 1, Page: 81 .