Calculation of pressure beyond the wellbore (line-source solution)
Input(s)
\(P_{i}\): Initial Pressure \((\mathrm{psi})\)
\(\mathrm{t}\): Time of Production (h)
\(\mathrm{k}\): Permeability \((\mathrm{mD})\)
B: Volume Factor (RB/STB)
\(\emptyset\): 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)
Output(s)
P: Pressure \((\mathrm{psi})\)
Formula(s)
\[
P=P_{i}+70.6 * q * B * \mu * \frac{\ln \left(1.688 * \emptyset * \mu * c_{t} * \frac{r^{2}}{k * t}\right)}{k * h}
\]
Reference(s)
Lee, J., Rollins, J. B., & Spivey, J. P. (2003). Pressure Transient Testing (Vol. 9). Richardson, Texas: SPE, Page: 11