Stationary flow when fluid pressure and temperature across reservoir do not change in time:
p(t, {\bf r}) = \rm const
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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
constant rate:
q(t) = q = \rm const |
constant formation pressure
p_e(t) = p_e = \rm const |
and constant bottom-hole pressure:
p_{wf}(t) = p_{wf} = \rm const |