Pressure drop across perforations in oil wells

Input(s)

$q_{o}$ : Oil Flow Rate through Perforation (bbl/d)

$n$ : Number of Perforations (dimensionless)

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

$B_{o}$ : Oil Formation Volume Factor (dimensionless)

$L_{p}$ : Perforation Length (ft)

$k_{p d}$ : Perforation Damaged Zone Permeability $(\mathrm{mD})$

$r_{p}$ : Perforation Radius ( $\mathrm{ft}$ )

$r_{p d}$ : Perforation Damaged Zone Radius (ft)

$\rho_{o}$ : Oil Density $\left(\mathrm{lbm} / \mathrm{ft}^{3}\right)$

$\Delta p_{p}$ : Pressure Drop across Perforations (psi)

$\beta_{p d}$ : Velocity Coefficient of Turbulence Factor $(1 / \mathrm{ft})$

\begin{gathered} \Delta p_{p}=\left(A \cdot\left(\frac{q_{o}}{n}\right)\right)+\left(B \cdot\left(\frac{q_{o}}{n}\right)^{2}\right) \\ A=\frac{141.2 \cdot \mu_{o} B_{o}}{L_{p} k_{p d}} \operatorname{In}\left(\frac{r_{p d}}{r_{p}}\right) \\ B=\frac{2.3\left(10^{-14}\right) \beta_{p d} B_{o}^{2} \rho_{o}}{L_{p}^{2}}\left(\frac{1}{r_{p}}-\frac{1}{r_{p d}}\right) \\ \beta_{p d}=\frac{(2.33)\left(10^{10}\right)}{k_{p d}^{1.201}} \end{gathered}

Bell, W. T., Sukup, R. A., & Tariq, S. M. (1995). Perforating. Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers, Page: 61.