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Normalised Normalized dimensionless difference between the drawdown survey wellbore pressure the sandface bottomhole pressure (BHP) 

LaTeX Math Inline
bodyp_{wf}(t)
and a reservoir pressure
LaTeX Math Inline
bodyp_{\rm ref}(t,r)
 of a reference model of a full-entry vertical well with homogeneous reservoir and non-damaged near-well reservoir zone  estimated at wellbore radius 
LaTeX Math Inline
bodyp^*_{wf}(t)r_w
:

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alignmentleft
S = \frac{p_{\rm ref}(t, r_w) - p_{wf}(t)}{ \left[ r \cdot \frac{2\partial p_{\pirm \sigma}{q_t} \cdotref}}{\partial r} \right]_{r=r_w} }

It can be interpreted as the dimensionless ratio of linear-average pressure gradient between wellbore axis and wellbore radius to the actual pressure gradient at wellbore radius:

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S = \left[  \frac{p_{wf\rm ref}(t, r_w) - p^*p_{wf}(t)}{ r_w  } \right]

where

LaTeX Math Inline
bodyq_t
 – total sandface rate

LaTeX Math Inline
body\sigma

...



\Big/

{ \left[ \frac{ \partial p_{\rm ref}}{\partial r}  \right]_{r=r_w}}


By definition the skin-factor is a pressure adjustment at the well-reservoir contact and does not affect pressure distribution in reservoir away from wellbore

LaTeX Math Inline
bodyr > r_sw
.

This means that skin-based pressure calculations in the damaged or in non-homogenous and non-radial-flow area around a well may become a bit inaccurate.

Nevertheless the size of a damaged area is usually much smaller than a drainage area during the well testing () the skin-factor concept works just fine for the most practical well tests applications.


The total skin is usually decomposed into a sum of two components:

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S_T = S_G + \frac{A_w}{A_{wrc}} \cdot S_M

where

LaTeX Math Inline
bodyS_G

Geometrical skin, related to deviation of the well-reservoir contact from the simplest model

LaTeX Math Inline
bodyS_M

Mechanical skin, related to pressure drop caused by the near-reservoir zone formation damage

LaTeX Math Inline
bodyA_w

borehole flow area

LaTeX Math Inline
bodyA_{wrc}

well-reservoir contact area


Based on definition the wellbore pressure dynamics 

LaTeX Math Inline
bodyp_{wf}(t)
of the well with skin-factor can be writen as:

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alignmentleft
p_{wf}(t) = - \frac{q_t}{2 \pi \sigma} \, S +  p^*p_{wf\rm ref}(t,r_w)

...

where

LaTeX Math Inline
bodyq_t

total sandface rate

LaTeX Math Inline
body\sigma

formation transmissibility outside the damaged reservoir zone 

LaTeX Math Inline
bodyA_s

LaTeX Math Inline
body

...

p_{

...

\rm ref}(t,r)

...

a reference model of a full-entry vertical well with homogeneous reservoir and non-damaged near-reservoir zone

...


See Also

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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing

Well & Reservoir Surveillance ]

Skin-factor (geometrical) ][ Skin-factor (mechanical) ]