Characterization of Two-Phase Fluid Flow: Feasible @ Pore-Scale?

1. In continuum mechanics, where field theories remain constructed on integral balances of mass, momentum and energy, are the (dependent) variables (pressure and saturation) in the region of interest remain to be ‘continuously differentiable’ in a petroleum reservoir having an oil-brine system (with a finite presence of an interface in a two-phase fluid flow)?

If not, how could a Jacobian transformation would remain to exist between oil/brine and spatial coordinates?

If not, then, how could Eulerian differential balance equations be obtained by using Leibnitz rule (i.e., by using Reynolds Transport Theorem), which allows interchanging differential and integral operations?

2. If two-phase fluid flow is considered as a field, which remains to be subdivided into single-phase regions, with moving boundaries separating the constituent phases, then, (even, if the differential balance holds for each sub-region), can it be applied to ‘the set of sub-regions’ in the absence of violating the conditions of continuity?

If so, then, two-phase fluid flow @ pore-scale remains to be ruled out – as it requires to be represented by macroscopic field equations and closure relations using a continuum formulation?

3. If the transport mechanisms in a two-phase fluid flow involve (a) existence of a phase interface; (b) motion of a phase interface; and (c) existence of both internal and external scales (scale effects); then, how do we develop closure relations for the macroscopic two-phase flow formulation?

Is this the reason why closure relations for two-phase flow forced to be strongly empirical?

If we cannot extend the existing correlations, then, prediction of two-phase flow in a new situation remains to be not only difficult, but also, unreliable?

4. When the concept of flow regime itself is no more a mathematical entity in a two-phase formulation, then, how would closure relations becoming dependent on flow regime (while, flow regimes being sensitive to initial and BCs) would remain to be reliable?

In other words, can we afford to get rid-off the fundamental concept of ‘interfacial area concentration’, which actually characterizes the interfacial geometry associated with a two-phase fluid regime, particularly, in Chemical EOR (involving the estimation of IFT)?

5. If the two-phase fluid flow remains formulated by considering each phase separately in terms of two sets of macroscopic field equations for mass, momentum and energy for each phase in the averaged fields; and, if the interaction terms (which, represent the transfer of mass, momentum and energy at a phase interface and satisfy the macroscopic jump conditions as additional balance equations at the interface; and which, couple the transport of mass, momentum and energy of each phase) appear, only after, proper averaging, then, where exactly, ‘the IFT measurements and the contact-angle measurements from experimental investigations’ would fit in the macroscopic field equations?

Suresh Kumar Govindarajan

09-Dec-2024