@wikipedia

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

p(t, {\bf r}) = \rm const

T(t, {\bf r}) = \rm const

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

\rho(t, {\bf r}) = \rm const

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

q(t) = q = \rm const

p_e(t) = p_e = \rm const

p_{wf}(t) = p_{wf} = \rm const