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 \(=1.0)\)

Output(s)

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

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

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

Formula(s)

\[ \begin{gathered} p_{s f}^{2}-p_{w b}^{2}=\left(A \cdot\left(\frac{q_{g}}{n}\right)\right)+\left(B \cdot\left(\frac{q_{g}}{n}\right)^{2}\right) \\ A=\frac{1.424 \cdot 10^{3} \cdot \mu_{g}(Z)(T)}{L_{p} k_{p d}} \operatorname{In}\left(\frac{r_{p d}}{r_{p}}\right) \\ B=\frac{(3.16)\left(10^{-12}\right) \beta_{p d} \gamma_{g}(Z)(T)}{L_{p}^{2}}\left(\frac{1}{r_{p}}-\frac{1}{r_{p d}}\right) \\ \beta_{p d}=(2.33)\left(10^{10}\right) k^{-1.201} \end{gathered} \]

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: 62.

Pressure drop across perforations in gas wells

Input(s)

Output(s)

Formula(s)

Reference(s)

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Pressure drop across perforations in oil wells

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