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LaTeX Math Block
anchor3AIXS
alignmentleft
J_s = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon+ S}

where 

LaTeX Math Inline
body\sigma = \Big \langle \frac{k} {\mu} \Big \rangle \, h = k \, h\, \Big[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \Big]
 – water or water-oil transmissbility above bubble point   (see also 
LaTeX Math Block Reference
anchorPerrine2phase_alpha
pageLinear Perrine multi-phase diffusion model
),

 

LaTeX Math Inline
body\epsilon = 0.5
 for steady-state SS flow and 
LaTeX Math Inline
body\epsilon = 0.75
 for pseudo-steady state PSS flow.


For gas wells, condensate producers, light-oil producers, and oil producers below bubble point 

LaTeX Math Inline
bodyP_{wf} < P_b
  the fluid compressibility is high, formation flow in well vicinity becomes non-linear (deviating from Darcy) and free gas slippage effects inflict the downward trend on WFP – Well Flow Performance plot (Fig. 2).

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