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During the PSS regime the formation pressure declines  declines linearly with time: 

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bodyp_e(t) \sim t
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anchorpe
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p_e(t) = p_i + \frac{q_t}{ V_{\phi} \, c_t} \ t



varying formation pressure at the external reservoir boundary



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anchorpwf
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p_{wf}(t) = p_e(t) + J^{-1} q_t



varying bottom-hole pressure



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anchorJ
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J = \frac{q_t}{2 \pi \sigma} \left[ \ln \left ( \frac{r_e}{r_w} \right)  +S + 0.75 \right]



constant productivity index

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