Well flowing pressure under Pseudo-steady state flow for non-circular reservoirs

Input(s)

$p_{i}$ : Initial Reservoir Pressure (psi)

$\mathrm{k}$ : Permeability $(\mathrm{mD})$

$\mathrm{h}$ : Thickness (ft)

B: Formation Volume Factor (bbl/STB)

$\mu$ : Viscosity $(\mathrm{cP})$

$C_{A}$: Shape Factor (dimensionless)

$r_{w}$: Wellbore Radius (ft)

Q: Flow Rate (STB/day)

$c_{t}$ : Total Compressibility (1/psi)

$\emptyset$: Porosity (fraction)

$\mathrm{t}$ : Time (hour) A: Area $\left(\mathrm{ft}^{2}\right)$

Output(s)

$P_{w f}$: Well Flowing Pressure (psi)

Formula(s)

$$ P_{w f}=\left(p_{i}-\left(\frac{162.6 * Q * B * \mu}{k * h}\right) * \log \left(\frac{2.2458 * A}{C_{A} * r_{w}^{2}}\right)\right)-\left(\frac{0.23396 * Q * B * t}{A * h * \emptyset * c_{t}}\right) $$

Reference(s)

Ahmed, T., McKinney, P.D. 2005. Advanced Reservoir Engineering, Gulf Publishing of Elsevier, Chapter: 1, Page: 33