Diffusivity equation for describing oil flow through a petroleum reservoir is deduced by coupling mass and momentum conservation equations. In many cases, the oil flow within the reservoir is characterized by assuming that the fluid of interest to be incompressible - as a simplified means.
It is to be noted that the "conservation of mass" will become equivalent to the "conservation of volume", when the fluid of interest is assumed to be incompressible.
Now, considering the compressibility of (crude) oil, the resultant density variation associated with a given pressure change - cannot be considered to be insignificant - and it may probably be significant.
This compressibility effect (the deviation from the incompressible fluid assumption) becomes very sensitive during oil production (unsteady-state) as it influences the volume of oil that the reservoir unit will expel from its storage per unit surface area per unit change in head.
Does this compressibility effect will still be significant - even - for an under-saturated oil reservoir? If so, are there any case studies?
Thanks in anticipation.