A proxy model of watercut in producing well with reservoir saturation s=\{ s_w, \, s_o, \, s_g \} and reservoir pressure p_e:
| (1) | {\rm Y_{wm}} = \frac{1 +\epsilon_g}{1 - \frac{M_{ro}}{M_{rw}} \cdot \frac{B_w}{B_o} }, \quad \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
B_w(p_e) | Water formation volume factor | B_o(p_e) | Oil formation volume factor | s | Reservoir saturation \{ s_w, \, s_o, \, s_g \} |
|---|---|---|---|---|---|
M_{rw}(s) | Relative water mobility | M_{ro}(s) | Relative oil mobility | p_e | Current formation pressure |
\rho_w | Water density | \rho_o | Oil density | g | Standard gravity constant |
q_t | Total sandface flowrate | A | Cross-sectional flow area | \alpha | Deviation of flow from horizontal plane |
P_c(s) | capillary pressure |
It provides a good estimate when the drawdown is much higher than delta pressure from gravity and capillary effects.
The model (1) can also be used in gross field production analysis assuming homogeneous reservoir saturation:
| (2) | s_w(t) = s_{wi} + (1-s_{wi}-s_{or}) \cdot \rm RF(t)/E_S |