...
Fluid flow with fluid pressure gradient
and velocity | LaTeX Math Inline |
|---|
body | linearly changing in time:| LaTeX Math Block |
|---|
|
p(t, {\bf |
...
...
+ 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 motion equation is of fluid pressure and pressure gradient:
| LaTeX Math Block |
|---|
|
\nabla p(t, {\bf r}) = \nabla p({\bf r}) |
| LaTeX Math Block |
|---|
|
|
{\bf u}(t, {\bf r}) = F({\bf u}({\bf r})r}, p, \nabla p) |
with right side dependent on time through the pressure variation.
In case of the flow with velocity dependent on pressure gradient only The fluid temperature
| LaTeX Math Inline |
|---|
| body | T(t, {\bf u} = {\bf u}({\bf r}, \nabla p) |
|---|
|
) the PSS flow velocity will be stationary as the right side of is supposed to vary slowly enough to provide quasistatic equilibrium.| LaTeX Math Block Reference |
|---|
|
is not dependant on time.
In terms of Well Flow Performance the PSS flow meansWell flow regime with constant rate and constant delta pressure between wellbore and formation does not change in time:
| LaTeX Math Block |
|---|
|
q_t(t) = \rm const |
...
During the PSS regime the formation pressure declines also declines linearly with time:
.
...
See Also
...
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / PSS Diagnostics
[ Steady State (SS) well fluid flow regime ]
