Horizontal well critical rate correlations - Joshi method for gas coning

Input(s)

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

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

$r_{e}$: Effective Radius of drainage (ft)

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

$l_{v}$: Distance between Gas/Oil interphase and perforated top of Vertical Well (ft)

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

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

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

$k_{h}$: Horizontal Permeability $(\mathrm{mD})$

Output(s)

$q_{o}$: Critical Oil Rate (STB/day)

Formula(s)

$$ q_{o}=1.535 * 10^{-3} *\left(\rho_{o}-\rho_{g}\right) * k_{h} * \frac{h^{2}-\left(h-l_{v}\right)^{2}}{B_{o} * \mu_{o} * \ln \left(\frac{r_{e}}{r_{w}}\right)} $$

Reference(s)

Horizontal Well Technology, Joshi, Page: 286-295.