Steady State Flow (SS)

Stationary flow when fluid pressure and temperature across reservoir do not change in time:

$\begin{array}{l}\displaystyle p(t, {\bf r}) = \rm const\end{array}$

$\begin{array}{l}\displaystyle T(t, {\bf r}) = \rm const\end{array}$

This automatically implies that fluid density also stay constant as soon as the flow is in thermodynamic quasistatic equilibrium:

$\begin{array}{l}\displaystyle \rho(t, {\bf r}) = \rm const\end{array}$

Well production or injection resulting in steady state flow is characterised by:

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

constant flow rate

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

constant formation pressure

$\begin{array}{l}\displaystyle p_{wf}(t) = p_{wf} = \rm const\end{array}$

constant bottom-hole pressure

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