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alignmentleft
S = \frac{p_{wf}(t)  - p(t, r_w)}{ \bigg[ r_w \cdot \frac{\partial p}{\partial r} \Bigg|_bigg]{r=r_w} }

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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