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.

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Pressure drop across perforations in oil wells

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