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) + J^{-1} q_t

where

J = \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 develops a unit slope on PTA diagnostic plot  and Material Balance diagnostic plot.

During the PSS regime the formation pressure linearly declines

See also

Steady State (SS) well flow regime