A proxy model of watercut Y_W in producing well with reservoir saturation and reservoir pressure :

{\rm Y_{Wm}} = \frac{1  - \epsilon_g}{1 + \frac{M_{ro}}{M_{rw}}  \cdot \frac{B_w}{B_o} }

\epsilon_g = \frac{A}{q_t} \cdot M_{ro} \cdot \left[ \frac{\partial P_c}{\partial r}  +  (\rho_w-\rho_o) \cdot g \cdot \sin \alpha \right]

where

Water formation volume factor	Oil formation volume factor	Reservoir saturation
Relative water mobility	Relative oil mobility	Current formation pressure
Water density	Oil density	Standard gravity constant
Total sandface flowrate	Cross-sectional flow area	Deviation of flow from horizontal plane
capillary pressure

If capillary effects are not high or saturation does not vary along the streamline substantially , then .

If flow is close to horizontal then gravity effects are vanishing too: .

In these cases simplifies to:

{\rm Y_{Wm}} = \frac{1}{1 + \frac{M_{ro}}{M_{rw}}  \cdot \frac{B_w}{B_o} } = \frac{1}{1 + \frac{k_{ro}}{k_{rw}}  \cdot \frac{\mu_w }{\mu_o } \cdot \frac{B_w}{B_o}}

The models and can also be used in production analysis assuming homogeneous reservoir water saturation :

s_w(t) = s_{wi} + (1-s_{wi}) \cdot \rm E_{Dow}(t) = s_{wi} + (1-s_{wi}) \cdot \rm RFO(t)/E_S

where

	current oil recover factor
	cumulative oil production
	STOIIP
	sweep efficiency
	initial water saturation
	residual oil saturation to water sweep

See Also