# 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.

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### Pressure drop across perforations in gas wells

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