Line-source solution for damaged or stimulated wells

Input(s)

$P_{i}$: Initial Pressure $(\mathrm{psi})$

$\mathrm{t}$: Time of production $(\mathrm{h})$

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

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

Ø: Porosity (fraction)

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

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

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

$\mathrm{r}$: Radius of wellbore $(\mathrm{ft})$

q: Flow Rate (STB/day)

s: Skin Factor (dimensionless)

Output(s)

$P_{w f}$: Line-Source Solution for Damaged or Stimulated Wells (psi)

Formula(s)

$$ P_{w f}=P_{i}+70.6 * q * B * \mu * \frac{\left(\ln \left(\frac{1688 * \emptyset * \mu * c_{t} * r^{2}}{k * t}\right)\right)-2 * s}{k * h} $$

Reference(s)

Pressure Transient Testing, Lee, Rollins \& Spivey, Page: 11.