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