Well flowing pressure (line-source solution by including skin factor)
Input(s)
\(P_{i}\): Initial Reservoir Pressure (psi)
q: Flow Rate \((\mathrm{bbl} / \mathrm{d})\)
\(\mu\) : Viscosity (cP)
B: Formation Volume Factor (bbl/STB)
k: Permeability \((\mathrm{mD})\)
h: Payzone Thickness \((\mathrm{ft})\)
\(\phi\) : Porosity (fraction)
\(c_{t}\) : Total Compressibility \((1 / \mathrm{psi})\)
\(\mathrm{r}\): Radius of Reservoir \((\mathrm{ft})\)
\(\mathrm{t}\) : Time (days)
S: S Variable (psi)
Output(s)
\(P_{w f}\): Well Flowing Pressure (psi)
Formula(s)
\[
P_{w f}=P_{i}+\left(70.6 * q * \mu * \frac{B}{k * h}\right) *\left(\ln \left(1688 * \emptyset * \mu * c_{t} * \frac{r^{2}}{k * t}\right)-2 * S\right)
\]
Reference(s)
Lee, J., Rollins, J. B., & Spivey, J. P. (2003). Pressure Transient Testing (Vol. 9). Richardson, Texas: Society of Petroleum Engineers, Page: 13.