Analysis of Two-Fluid-Phase Porous Medium Systems Using Microscale Experiments and Lattice Boltzmann Modeling

Modeling two-fluid-phase flow in porous medium systems requires the specification of closure relations to produce a solvable system. The thermodynamically constrained averaging theory (TCAT) has been used to formulate a closed model and to yield insights about the underlying microscale processes that must be represented at the macroscale. In this work we evaluate these TCAT developments using a two-dimensional microfluidic cell and an advanced lattice Boltzmann model (LBM). Microfluidic experiments were performed in which the external fluid pressures were varied and the system was allowed to equilibrate for a period of time before the next step change in fluid pressures. LBM simulations of drainage and imbibition were performed to mimic the experiments. Using imaging techniques the fluid distributions, interfacial areas, and interfacial curvatures of the experimental data were compared to the numerical results and analyzed. LBM simulations showed good agreement with the experimental data. The validated LBM was used to investigate the closure relations of the TCAT model. LBM simulations provided support for the existence of a unique relationship between capillary pressure, fluid saturation, and fluid-fluid interfacial area. The simulations also revealed that the approach to an equilibrium state involves a relatively slow process in which fluid interfaces relax to their equilibrium state. Motivated by this physical process, a temporally adaptive domain decomposition algorithm was developed using a level-set method to locate interfaces and estimate their rate of advancement. The proposed adaptive algorithm was shown to reduce computational effort by an order of magnitude, while yielding essentially identical solutions to a conventional fully coupled approach. Furthermore, the microfluidic experiments were modified to study the dynamics of a two-fluid-phase flow. Viscous fingering and Haines jumps were visualized. The validated LBM was used to model the experimental data and showed good agreement for certain aspects of the dynamics. Overall, the results show that the developed experimental and computational techniques can be used to evaluate multiscale theoretical models of porous medium systems accurately.