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 \(\left(\mathrm{lbm} / \mathrm{ft}^{3}\right)\)

Output(s)

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

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

Formula(s)

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

Reference(s)

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

Related

Pressure drop across perforations in gas wells

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