Theory and Applications of Macroscale Models in Porous Media

Toward a New Generation of Two-Fluid Flow Models Based on the Thermodynamically-Constrained Averaging Theory

“…The TCAT approach has been applied to derive a hierarchy of models for two-fluid-phase flow in a porous media [22,27,36,43]. The approach taken will be summarized and compared to the traditional approach, and a specific model instance from the general hierarchy of models available will be formulated to focus on the novel aspects of this work.…”

“…Despite these several limitations, resolving these issues has not received much attention in the literature.The overall goal of this work is to report advances to a new generation of two-fluid-flow models that responds to the limitations associated with traditional approaches. Alternatives to this new generation of models exist and are reviewed elsewhere [25][26][27]. The specific objectives of this work are: (1) to summarize the previously developed thermodynamically constrained averaging theory (TCAT) approach for building models that are both scale and thermodynamically consistent; (2) to summarize the application of the TCAT procedure for two-fluid flow; (3) to examine an example instance of a TCAT model for two-fluid flow; (4) to demonstrate how hysteresis can be removed using a state equation involving capillary pressure and how the parameters for this state equation can be determined; (5) to explore the existence of a state equation to approximate the conservation of momentum at the macroscale; and (6) to summarize the challenges that must be overcome to complete the formulation of this new class of two-fluid flow model.…”

“…Thermodynamically constrained averaging theory (TCAT) framework for model building, closure, evaluation, and validation[27].…”

Editorial for Special Issue in Honor of InterPore’s 10th Anniversary

“…The articles within this issue are here to help provide a "big picture" of many aspects of porous material research. Some of the articles address modeling: at the macroscale, where the multiple phases are indistinguishable (Battiato et al 2019), to the pore scale or microscale (Ramstad et al 2019); modeling of diffusion/dispersion of particles on the order of 10 microns and larger (Tartakovsky and Dentz 2019) and of colloids on the order of a micrometer to nanometers (Molnar et al 2019); modeling of reactions within porous materials that are limited by lack of mixing of the components (diffusion limited) (Valocchi et al 2018;Tartakovsky and Dentz 2019); modeling charged porous materials (Joekar-Niasar et al 2019), fractures (Berre et al 2018), and heat transfer (Nield and Simmons 2018). Other articles address experimental issues-at the macroscale (Falzone et al 2018) and fluid displacement at the pore scale (Gerami et al 2018), while Armstrong et al (2018) demonstrates how one can go from X-ray microcomputed tomography to characterizing porous media for modeling.…”

Intersection between engineering mechanics and supervised learning for modelling clogging dynamics in depth filters

“…) between the microscale and macroscale domains associated with the problem. The proposed hybrid technique derives average homogenized representations which quantify the macroscale behavior with a sufficiently small periodic microstructure (Papanicolau and Bensoussan, 1978;Sánchez-Palencia, 1980;Hornung, 2012;Battiato et al, 2019), which is again linked to the same defined perturbation parameter. While the periodic cell problem is not a realistic assumption, and may not be entirely correct mathematically, the hybrid approach is useful to garner first approximations of the complex macroscale behavior relating to the analysed problem.…”