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In the most general case (both reservoir and pipelines) the fluid velocity is proportional to pressure gradient and can be written as:
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{\bf u}(t, {\bf r})= - M({\bf r}, p, \nabla p) \nabla p |
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In case of linear correlation:
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| body | M({\bf r}, p, \nabla p) = M({\bf r}) |
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the
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{\bf u}(t, {\bf r}) = {\bf u}({\bf r}) |
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In the most general case (both reservoir and pipelines) the fluid velocity is proportional to pressure gradient and can be written as:
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{\bf u}(t, {\bf r})= - M({\bf r}, p, \nabla p) \nabla p |
with right side not dependent on time in stationary flow:
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\frac{\partial {\bf u}(t, {\bf r})}{\partial t}= 0 |
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PSS flow velocity will be stationary as the right side of
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is not dependant on time.
and velocity
are not changing in time:| LaTeX Math Block |
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{\bf u}(t, {\bf r}) = {\bf u}({\bf r}) |
The fluid temperature
is supposed to vary slowly enough to provide
quasistatic equilibrium.
In terms of Well flow regime with constant rate and constant delta pressure between wellbore and formation does not change in timeFlow Performance the PSS flow means:
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q_t(t) = \rm const |
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During the PSS regime the formation pressure declines also declines linearly with time:
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