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A proxy model of watercut YW in producing well with reservoir saturation 

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bodys=\{ s_w, \, s_o, \, s_g \}
 and reservoir pressure
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bodyp_e
:

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

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anchorepsilon
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\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

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bodyB_w(p_e)

Water formation volume factor

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bodyB_o(p_e)

Oil formation volume factor

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bodys

Reservoir saturation

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body\{ s_w, \, s_o, \, s_g \}

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bodyM_{rw}(s)

Relative water mobility

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bodyM_{ro}(s)

Relative oil mobility

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bodyp_e

Current formation pressure

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body\rho_w

Water density

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body\rho_o

Oil density

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bodyg

Standard gravity constant

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bodyq_t

Total sandface flowrate 

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bodyA

Cross-sectional flow area

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body\alpha

Deviation of flow from horizontal plane

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bodyP_c(s)

capillary pressure



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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing (WT) / Flowrate Testing / Flowrate  / Production Water cut (Yw)

WORWatercut Diagnostics / Watercut Fractional Flow plot Watercut DiagnosticsCorrelation @model ] 

Watercut (Yw) Fractional Flow @modelWOR ]