A proxy model of watercut YW in a given producing well with reservoir saturation
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body | s=\{ s_w, \, s_o, \, s_g \} |
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and reservoir pressure :
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Wm}} = \frac{1 - \epsilon_g}{1 + \frac{M_{ro}}{M_{rw}} \cdot \frac{B_w}{B_o} } |
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where
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anchor | epsilon |
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alignment | left |
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| \epsilon_g = \frac{A}{q_t} \cdot |
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body | (s)relative oil mobility | | relative water mobility \cdot \left[ \frac{\partial P_c}{\partial r} + (\rho_w-\rho_o) \cdot g \cdot \sin \alpha \right] |
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where
oOil (Bo)wWater (Bw)reservoir It provides a good estimate when the drawdown is much higher than delta pressure from gravity and capillary effects.
If capillary effects are not high
or saturation does not vary along the streamline substantially LaTeX Math Inline |
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body | \displaystyle \frac{\partial s_w}{\partial r} \rightarrow 0 |
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, then LaTeX Math Inline |
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body | \displaystyle \frac{\partial P_c}{\partial r} = \dot P_c \cdot \frac{\partial s_w}{\partial r} \approx 0 |
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.If flow is close to horizontal
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body | \sin \alpha \rightarrow 0 |
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then gravity effects are vanishing too: LaTeX Math Inline |
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body | (\rho_w-\rho_o) \cdot g \cdot \sin \alpha \approx 0 |
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.In these cases
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simplifies to: LaTeX Math Block |
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anchor | Ywsimple |
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alignment | left |
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{\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 The model
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can and LaTeX Math Block Reference |
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can also be used in
gross field production analysis and in this case the average reservoir saturation can be assumed homogeneous assuming homogeneous reservoir water saturation :
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s_w(t) = s_{wi} + (1-s_{wi}) \cdot \rm E_{Dow}(t) = s_{wi} + (1-s_{orwi}) \cdot \rm RFRFO(t)/E_S |
See also
where
See Also
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing (WT) / Flowrate Testing / Flowrate / Production Water cut (Yw)
[ Watercut Diagnostics / Watercut Fractional Flow plot ] [ Watercut Correlation @model ]
[ WOR ]