Vertical well critical rate correlations - Meyer, Gardner, and Pirson - Water coning

Input(s)

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

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

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

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

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

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

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

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

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

Output(s)

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

Formula(s)

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

Reference(s)

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