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LaTeX Math Inline
bodyB_w(p_e)

Water formation volume factor

LaTeX Math Inline
bodyB_o(p_e)

Oil formation volume factor

LaTeX Math Inline
bodys

Reservoir saturation

LaTeX Math Inline
body\{ s_w, \, s_o, \, s_g \}

LaTeX Math Inline
bodyM_{rw}(s)

Relative water mobility

LaTeX Math Inline
bodyM_{ro}(s)

Relative oil mobility

LaTeX Math Inline
bodyp_e

Current formation pressure

LaTeX Math Inline
body\rho_w

Water density

LaTeX Math Inline
body\rho_o

Oil density

LaTeX Math Inline
bodyg

Standard gravity constant

LaTeX Math Inline
bodyq_t

Total sandface flowrate 

LaTeX Math Inline
bodyA

Cross-sectional flow area

LaTeX Math Inline
body\alpha

Deviation of flow from horizontal plane

LaTeX Math Inline
bodyP_c(s)

capillary pressure




If saturation does not vary along the flow substantially then capillary effects are vanishing 

LaTeX Math Inline
body\displaystyle \frac{\partial P_c}{\partial r} = \dot P_c \cdot \frac{\partial s_w}{\partial r} \approx 0
.

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

LaTeX Math Inline
body\sin \alpha \approx 0
.

In these cases  If drawdown is much higher than delta pressure from gravity and capillary effects then  

LaTeX Math Block Reference
anchorFF
 simplifies to:

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