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Fluid flow with fluid pressure
is linearly changing linearly changing in time:
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p(t, {\bf r}) = \psi({\bf r}) + A \cdot t, \quad A = \rm const |
The fluid temperature
is supposed to vary slowly enough to provide quasistatic equilibrium.
The fluid velocity
may not be stationary.In the most general case (both reservoir and pipelines) the fluid velocity is proportional to pressure gradient and can be written asmotion equation is of fluid pressure and pressure gradient:
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{\bf u}(t, {\bf r})= - MF({\bf r}, p, \nabla p) \nabla p |
with right side dependent on time through the pressure variation.
In case of linear correlation: the flow with velocity dependent on pressure gradient only
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| body | M({\bf r}, p, \nabla p) = M({\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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) the PSS flow velocity will be stationary as the right side of | LaTeX Math Block Reference |
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is not dependant on time.
In terms of Well Flow Performance the PSS flow means
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.Well flow regime with constant rate and constant delta pressure between wellbore and formation does not change in time:
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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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See Also
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Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / PSS Diagnostics
[ Steady State (SS) well fluid flow regime ]
