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S = \frac{Big[ \frac{p_{wf}(t) - p_{\rm ref}(t, r_w)}{ r_w } }{\Big] \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
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