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.