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
M_{ro}(s) | Relative oil mobility | B_o(p_e) | Oil formation volume factor | s | Reservoir saturation \{ s_w, \, s_o, \, s_g \} |
|---|---|---|---|---|---|
M_{rw}(s) | Relative water mobility | B_w(p_e) | Water formation volume factor | p_e | Current formation pressure |
A | cross-sectional flow area |
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 |