| (1) | t^*(t) = \mu_(p_{ref}) \cdot c_t(p_{ref}) \cdot \tau(t) = \mu_(p_{ref}) \cdot c_t(p_{ref}) \cdot \int_0^t \frac{dt}{\mu(p) \, c_t(p)} |
where
p_{ref} | reference pressure |
\tau(t) | pseudo-time at time moment t |
\mu(p) | dynamic fluid viscosity |
c_t(p) | total compressibility |
It is widely used in Pressure Diffusion @model and transient data analysis (PTA / RTA ) of strongly compressible fluids.
The choice of reference pressure is made by engineer depending on common sense. The popular choice is to select p_{ref} = p(t=0) as the pressure at initial time moment.
In case the Normalized Pseudo-Time is used to linearize the Pressure Diffusion equation the choice of reference pressure is not going to affect the solution.
Normalized Pseudo-Time does represent a time in terms of physical property and has the same dimension unlike Pseudo-Time.
See also
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Pressure Diffusion / Pressure Diffusion @model
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing
[ Pseudo-Time ]