Conservation Law? Or Mass Conservation Equation?
1. In a petroleum reservoir, whether the change of the mass in the reservoir domain can only be caused by the mass flux through the boundaries and by mass sources or sinks within the reservoir?
Fluid phase saturation is just an additional fluid property to be considered for an immiscible multi-phase fluid flow in the absence of mass exchange between the fluids?
2. In the presence of external forces; or, in the absence of sources or sinks, whether, the mass will remain to be preserved locally in a petroleum reservoir in order to get it associated with a ‘conservation law’?
OR
Will it just be a ‘mass balance equation’ as the external forces would also include the internal changes such as chemical reactions associated with a chemical EOR?
In such cases, how easy would it remain to relate the ‘mass flux vector’ [associated with the outer normal vector] – as a function of ‘volumetric flux vector’ (and fluid density)?
3. Feasible to obtain the simplified ‘differential form’ of ‘mass conservation equation’ in the absence of sufficient smoothness of the involved functions; and when the Leibniz rule and the Gauss theorem remain applied for a ‘time-variant domain’?
4. If density gets associated with source or sink of mass term, then, is it not an incompressible fluid flow?
How could we address it as a compressible fluid in the absence of fluid density’s dependence on reservoir pressure, reservoir temperature and time?
5. Even if we consider phase fluid density, volumetric flux of the fluid phase and fluid phase saturation to be varying for each fluid phase, how could we treat porosity to remain as a constant assuming that the reservoir porosity does not change with time?
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