# 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 .

## Related

### Horizontal well critical rate correlations - Joshi method for gas coning

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