@wikipedia
Stationary Fluid flow when with fluid pressure and temperature across reservoir do not change pressure
is not changing in time:| LaTeX Math Block |
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p(t, {\bf r}) = p({\rm const
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Tbf r}) |
This immediately leads to stationary fluid velocity
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This automatically implies that fluid density also stay constant as soon as the flow is in thermodynamic quasistatic equilibrium:
:
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{\rhobf u}(t, {\bf r}) = {\bf u}({\rm const |
Well production or injection resulting in steady state flow is characterized by
constant rate:
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| In the most general case (both reservoir and pipelines) the fluid velocity is a function of pressure and pressure gradient and can be written as: |
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mathblock| q= q = \rm const |
constant formation pressure
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p_e(t) = p_e = \rm const |
and constant bottom-hole pressure:
with right side not dependent on time in stationary flow: | LaTeX Math Block |
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| \frac{\partial {\bf u}(t, {\bf r})}{\partial t}= 0 |
which leads to | LaTeX Math Block Reference |
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The fluid temperature
is supposed to vary slowly enough to provide quasistatic equilibrium.
This flow regime is often observed in pipeline fluid flow and reservoir fluid flows.
See also
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Physics / Fluid Dynamics
[ Steady State Well Flow Regime (SS) ]
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