Horizontal well critical rate correlation - Chaperon

Input(s)

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

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

$x_{A}$: Location of a Constant Pressure Boundary $(\mathrm{ft})$

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

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

F$: \quad \mathrm{F}=5.48$ for $\mathrm{k}_{\mathrm{v}} / \mathrm{k}_{\mathrm{h}}=1, \mathrm{~F}=4.8$ for $\mathrm{k}_{\mathrm{v}} / \mathrm{k}_{\mathrm{h}}=0.01$ and $\mathrm{F}=4.16$ for $\mathrm{k}_{\mathrm{v}} / \mathrm{k}_{\mathrm{h}}=0.01(\mathrm{mD})$

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

L: Horizontal Well Length $(\mathrm{m})$

Output(s)

$Q_{c}$: Critical Oil Rate $\left(\mathrm{m}^{3} / \mathrm{h}\right)$

Formula(s)

$$ Q_{c}=\left(3.486 * 10^{-5}\right) * \frac{L}{x_{A}} * h^{2} *\left(\rho_{w}-\rho_{o}\right) * \frac{F}{k_{h} * \mu_{o}} $$

Reference(s)

Chaperon, I. 1986. Theoretical Study of Coning Toward Horizontal and Vertical in Anisotropic Formations: Subcritical and Critical Rates. SPE ATCE, New Orleans, Louisiana.