Bottomhole flowing pressure during infinite-acting pseudoradial flow

Input(s)

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

$Q_{o}$: Well Flow Rate (STB/day)

$B_{o}$: Oil Formation Volume Factor (bbl/STB)

$\mu_{o}$: Oil Viscosity $(\mathrm{cP})$

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

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

$\mathrm{t}$: Flowing Time (h)

$\emptyset$: Porosity (fraction)

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

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

$\mathrm{S}$: Skin (dimensionless)

Output(s)

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

Formula(s)

$$ \begin{gathered} P_{w f}=p_{i}-\left(\frac{162.6 * Q_{o} * \mu_{o} * B_{o}}{k * h}\right) *\left(\log (t)+\log \left(\frac{k}{\emptyset * \mu_{o} * c_{t} * r_{w}^{2}}\right)-3.23+0.87 * S\right) \\ p_{i}-p_{w f}=\Delta p=a+m \log (t) \end{gathered} $$

Reference(s)

Ahmed, T., McKinney, P.D. 2005. Advanced Reservoir Engineering, Gulf Publishing of Elsevier, Chapter: 1, Page: 98.