Pseudo Steady State (PSS)

Well flow regime with constant rate and constant delta pressure between wellbore and formation does not change in time:

(1)	$\begin{array}{l}\displaystyle q_t(t) = \rm const\end{array}$

(2)	$\begin{array}{l}\displaystyle \Delta p(t) = \| p_e(t) - p_{wf}(t) \| = \Delta p = \rm const\end{array}$

The exact solution of diffusion equation for PSS:

(3)	$\begin{array}{l}\displaystyle p_{wf}(t) = p_e(t) + J^{-1} q_t\end{array}$

where

(4)	$\begin{array}{l}\displaystyle J = \frac{q_t}{2 \pi \sigma} \left[ \ln \left ( \frac{r_e}{r_w} \right) +S + 0.75 \right]\end{array}$

constant productivity index

(5)	$\begin{array}{l}\displaystyle p_e(t) = p_i + \frac{q_t}{ V_{\phi} \, c_t} \ t\end{array}$

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

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