Pressure drop across perforations in gas wells

Input(s)

$q_{g}$ : Gas Flow Rate through Perforation $(\mathrm{bbl} / \mathrm{d})$

$n$ : Number of Perforations (dimensionless)

$\mu_{g}$ : Gas Viscosity (cP)

$Z$ : Gas Supercompressibility Factor (dimensionless)

T: Formation Temperature $\left(\mathrm{R}^{\circ}\right)$

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

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

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

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

$\gamma_{g}$ : Gas Specific Gravity $($ air $=1.0)$

$p_{s f}$ : Pressure at the Sandface (psi)

$p_{w b}$ : Pressure in the Wellbore (psi)

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

\begin{gathered} p_{s f}^{2}-p_{w b}^{2}=\left(A \cdot\left(\frac{q_{g}}{n}\right)\right)+\left(B \cdot\left(\frac{q_{g}}{n}\right)^{2}\right) \\ A=\frac{1.424 \cdot 10^{3} \cdot \mu_{g}(Z)(T)}{L_{p} k_{p d}} \operatorname{In}\left(\frac{r_{p d}}{r_{p}}\right) \\ B=\frac{(3.16)\left(10^{-12}\right) \beta_{p d} \gamma_{g}(Z)(T)}{L_{p}^{2}}\left(\frac{1}{r_{p}}-\frac{1}{r_{p d}}\right) \\ \beta_{p d}=(2.33)\left(10^{10}\right) k^{-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: 62.