| (1) | P_{\Psi}(p) = \frac{p_{ref} \cdot \Psi(p)}{\Psi(p_{ref})} = p_{ref} \cdot \int_0^p \frac{p \, dp}{\mu(p) \, Z(p)} \Bigg/ \int_0^{p_{ref}} \frac{p \, dp}{\mu(p) \, Z(p)} |
where
p_{ref} | reference pressure |
\Psi(p_{ref}) | Pseudo-Pressure at reference pressure p_{ref} |
\Psi(p) | Pseudo-Pressure at pressure p |
\mu(p) | dynamic fluid viscosity |
Z(p) | fluid compressibility factor |
It is widely used in Pressure Diffusion @model and transient data analysis (PTA / RTA ) of strongly compressible fluids.
The choice of reference pressure p_{ref} is made by engineer depending on common sense and objectives of the study.
The usual practise is to select p_{ref} = p(t=0) as the bottom-hole pressure at initial time moment.
In case the Normalized Pseudo-Pressure is used to linearize the Pressure Diffusion equation the choice of reference pressure is not going to affect the solution.
Normalized Pseudo-Pressure does represent a pressure in terms of physical property and has the same dimension unlike Pseudo-Pressure.
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-Pressure ]