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LaTeX Math Block
alignmentleft
S = \frac{2 \pi \sigma}{q_t} \cdot \left[ p_{wf}(t) - p({\bf r}, t) |_{{\bf r} \in \Gamma_s} \right]

where

LaTeX Math Inline
bodyq_t

total sandface rate

LaTeX Math Inline
body\sigma

formation transmissibility at the boundary

LaTeX Math Inline
body\Gamma_s
of the damaged reservoir zone 
LaTeX Math Inline
bodyA_s

LaTeX Math Inline
bodyA_s

damaged reservoir zone

LaTeX Math Inline
body\Gamma_s


It quantitatively characterises permeability change in a thin layer around the well or fracture plane caused by stimulation or deterioration during production, injection or well intervention.

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For the radial-symmetric permeability change around the well it can be estimated from Hawkins equation:

LaTeX Math Block
anchorTI84WSM
alignmentleft
S_M = \left (  \frac{k}{k_s} - 1   \right ) \ \ln \left (  \frac{r_s}{r_w}   \right )

where 

LaTeX Math Inline
bodyr_w

well radius from drilling

LaTeX Math Inline
bodyr_s

damaged reservoir (

LaTeX Math Inline
bodyk_s \neq k
) radius:
LaTeX Math Inline
bodyr_s > r_w
( the most typical range is:
LaTeX Math Inline
bodyr_w < r_s < 1
m )

LaTeX Math Inline
bodyk

absolute formation permeability in the undamaged reservoir zone away from well location

LaTeX Math Inline
bodyk_s

absolute formation permeability in the damaged near-well reservoir zone


The definition 

LaTeX Math Block Reference
anchorSM
page1DR pressure diffusion of low-compressibility fluid
suggests Definition suggest that
 

  • deteriorated near-well reservoir zone 
    LaTeX Math Inline
    bodyk_s < k
     is characterized by a positive skin-factor 
    LaTeX Math Inline
    bodyS>0
    ,
     
  • improved near-well reservoir zone  
    LaTeX Math Inline
    bodyk_s > k
     is characterized by a negative skin-factor 
    LaTeX Math Inline
    bodyS<0
    .

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Formula 

LaTeX Math Block Reference
anchorpwf
page1DR pressure diffusion of low-compressibility fluid
 provides a good example how mechanical skin-factor affects pressure dynamics.