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@wikipedia
Stationary flow with reservoir and fluid staying at quasistatic equilibrium and fluid pressure and temperature are not changing in time:
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p(t, {\bf r}) = p({\bf r}) |
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T(t, {\bf r}) = T({\bf r}) |
Well production or injection resulting in steady state flow is characterised by:
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constant flow rate |
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constant formation pressure |
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p_{wf}(t) = p_{wf} = \rm const |
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constant bottom-hole pressure |