Incorporating bubble evolution and transport in constitutive relationships for quasi- and non-equilibrium two-phase flows in porous media

There is a need to better understand the presence and transport of bubbles in multi-phase subsurface porous media so that these processes can be accurately described, and more efficient engineered solutions can be developed. To this end, constitutive relationships between geometric state variables (fluid-fluid curvature, Jnw; non-wetting phase volume, Vn; fluid-fluid interfacial area, anw; and Euler characteristic, χn) have become increasingly more common in efforts to uniquely predict the state of a two-fluid flow system. Both lattice Boltzmann simulations and fast X-ray microtomography (μCT) imaging experiments have shown that a geometric state function using the non-dimensionalized invariant properties of saturation, specific interfacial area, and Euler characteristic can uniquely predict the mean curvature of the system for both quasi- and non-equilibrium conditions, however, the presence of bubble evolution and the subsequent transport phenomena have not been explored. This study investigates whether the geometric state function remains unique with the inclusion of bubble generation and transport under quasi- and non-equilibrium two-fluid flow. The data presented here suggests that bubble formation and entrapment occur in a manner that cannot be predicted by the more traditional capillary pressure-saturation-interfacial area, Pc(Sw, anw), relationship, and further extensions to the constitutive relationship are needed to fully capture these mechanisms.