Permeability and reservoir pressure from buildup tests

Input(s)

$\mathrm{t}_{\mathrm{p}}$: Time till which drawdown was done (h)

$d t_{a}$: Time of shut in 1 from given values or trendline (h)

$d t_{b}$: Time of shut in 2 from given values or trendline (h)

$p w s_{a}$: Well flowing Pressure at shut in point 2 from given values or trendline (psi)

$p w s_{b}$: Well flowing Pressure at shut in point 1 from given values or trendline (psi)

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

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

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

$\mathrm{p}_{\mathrm{wf}}$: Pressure flowing well $(\mathrm{psi})$

Ø: Porosity (fraction)

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

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

Output(s)

s: Skin Factor (dimensionless)

Formula(s)

$$ s=1.151 *\left((p h r-p w f)-\log \left(\frac{\frac{p w s_a-p w s_b}{\log \left(\frac{t p+d t_b}{d t_b}\right)-\log \left(\frac{t p+d t_a}{d t_a}\right)}}{\emptyset * \mu * c_t * r_w^2}\right)+3.23\right) $$

Reference(s)

Pressure Buildup and Flow Tests in Wells, Matthews \& Russell, Page: 21.