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Normalised dimensionless difference between the sandface bottomhole pressure (BHP) 

LaTeX Math Inline
bodyp_{wf}(t)
  and the sandface reservoir pressure 
LaTeX Math Inline
body\displaystyle p({\bf r}, t) |_{{\bf r} \in \Gamma_s}
 at the boundary
LaTeX Math Inline
body\Gamma_s
 of damaged reservoir zone
LaTeX Math Inline
bodyA_s

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.

It contributes to the total skin estimated in transient well testing


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

LaTeX Math Block
anchorTI84W
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


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
    .


The most popular practical range of skin-factor variation is 

LaTeX Math Inline
body-5 < S < 8
.


Formula 

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