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