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Normalised dimensionless difference between the sandface bottomhole pressure (BHP) and sandface reservoir pressure 

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bodyp_{wf}(t)
and a model of a full-entry vertical well with homogeneous reservoir and non-damaged near-well reservoir zone 
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bodyp^*_{wf}(t)
:

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S = \frac{2 \pi \sigma}{q_t} \cdot \left[ p_{wf}(t)  - p({\bf r}, t) |_{{bf r} \nin A_sp^*_{wf}(t)} \right]

where

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bodyq_t

total sandface rate

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body\sigma

formation transmissibility outside the damaged reservoir zone 

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bodyA_s

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bodyA_s

damaged reservoir zone


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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