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

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bodyp_{wf}(t)
and a reservoir pressure
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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 
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bodyp_{\rm ref}(t,r)
  estimated at wellbore radius:

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

where

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bodyr_w

wellbore radius


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

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bodyr > r_s
.

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