Vertical well critical rate correlations - Meyer, Gardner, and Pirson - Simultaneous gas and water coning

Input(s)

$\rho_{o}$: Oil Density $(\mathrm{g} / \mathrm{cc})$

$\rho_{w}$: Water Density $(\mathrm{g} / \mathrm{cc})$

$r_{e}$: Drainage Radius ( $\mathrm{ft}$ )

$r_{w}$: Radius of Wellbore (ft)

$h_{p}$: Thickness of Perforated Interval (ft)

$\mathrm{h}$: Oil Column Thickness (ft)

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

$B_{o}$: Oil Formation Volume Factor (RB/STB)

$k_{o}$: Effective Oil Permeability $(\mathrm{mD})$

Output(s)

$q_{o}$: Critical Rate (Maximum Oil Rate without Water Coning) (STB/day)

Formula(s)

$$ q_{o}=0.001535 * \frac{\rho_{w}-\rho_{o}}{\ln \left(\frac{r_{e}}{r_{w}}\right)} *\left(\frac{k_{o}}{\mu_{o} * B_{o}}\right) *\left(h^{2}-\left(h_{p}\right)^{2}\right) $$

Reference(s)

Joshi, S. D. 1991, Horizontal Well Technology. Tulsa, Oklahoma: PennWell Publishing Company. Chapter: 8, Page: 255.