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.