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.