Permeability and skin factor from a constant-rate flow test

Input(s)

$t_{a}$: Time at Pwf1 from given values or trendline (h)

$t_{b}$: Time at Pwf 2 from given values or trendline (h)

$p_{w}$: Well flowing Pressure at point 2 from given values or trend line (psi)

$p_{w f}$: Well flowing Pressure at point 1 from given values or trendline (psi)

$p_{i}$: Initial Pressure (psi)

$\mathrm{p}_{\mathrm{hr}}$: Pressure Value at $t=1 \mathrm{~h}(\mathrm{psi})$

q: Flow Rate (STB/day)

B: Volume factor $(\mathrm{RB} / \mathrm{STB})$

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

$\mu$: Viscosity of Oil (cP)

$\varnothing$: Porosity (fraction)

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

$r_{w}$: Wellbore Radius (ft)

Output(s)

s: Skin Factor (dimensionless)

Formula(s)

$$ s=1.151 *\left(\frac{p_{i}-p h r}{\frac{p_{w f}-p_{w}}{\log \left(t_{b}\right)-\log \left(t_{a}\right)}}-\log \left(\frac{162.6 * q * B * \frac{\mu}{\left(\frac{p_{w f}-p_{w}}{\log \left(t_{b}\right)-\log \left(t_{a}\right)}\right) * h}}{\varnothing * \mu * c_{t} * r_{w}^{2}}\right)+3.23\right) $$

Reference(s)

Pressure Buildup and Flow Tests in Wells, Matthews & Russell, Page: 57.