Pressure drop across perforations in oil wells

Input(s)

qoq_{o}: Oil Flow Rate through Perforation (bbl/d)

nn: Number of Perforations (dimensionless)

μo\mu_{o}: Oil Viscosity (cP)(\mathrm{cP})

BoB_{o}: Oil Formation Volume Factor (dimensionless)

LpL_{p}: Perforation Length (ft)

kpdk_{p d} : Perforation Damaged Zone Permeability (mD)(\mathrm{mD})

rpr_{p}: Perforation Radius ( ft\mathrm{ft} )

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

ρo\rho_{o}: Oil Density (lbm/ft3)\left(\mathrm{lbm} / \mathrm{ft}^{3}\right)

Output(s)

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

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

Formula(s)

Δpp=(A(qon))+(B(qon)2)A=141.2μoBoLpkpdIn(rpdrp)B=2.3(1014)βpdBo2ρoLp2(1rp1rpd)βpd=(2.33)(1010)kpd1.201\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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