Well flow regime with constant rate and constant delta pressure between wellbore and formation does not change in time:
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q_t(t) = \rm const |
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\Delta p(t) = | p_e(t) - p_{wf}(t) | = \Delta p = \rm const |
The exact solution of diffusion equation for PSS:
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p_{wf}(t) = p_e(t) + J^{-1} q_t |
where
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| J = \frac{q_t}{2 \pi \sigma} \left[ \ln \left ( \frac{r_e}{r_w} \right) +S + 0.75 \right] |
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constant productivity index |
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| p_e(t) = p_i + \frac{q_t}{ V_{\phi} \, c_t} \ t |
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varying formation pressure at the external reservoir boundary |
and is shown as unit slope on PTA diagnostic plot and Material Balance diagnostic plot.
During the PSS regime the formation pressure linearly declines
