The nation's water supply, subsurface energy extraction, storage of greenhouse gases, global climate change, biological tissues, concrete materials, and fuel cell design are all examples of critical areas involving natural and engineered porous medium systems. Despite the widespread occurrence and importance of porous medium processes, the basic approach to modeling them, although well-established and nearly universally used, is seriously flawed. The flaws have become more consequential with the need for reliable simulators of increasingly complex problems. These flaws include: (a) a disconnect between well-understood microscale physics of multiphase flow and transport and the modeling of these processes at the macroscale; (b) reliance upon quasi-static assumptions to describe quantities such as relative permeability and capillary pressure even for systems where dynamic effects are important; (c) lack of a methodical, rigorous, theoretical framework within which conservation equations and thermodynamic relations can be established for general and specialized applications; and (d) a lack of physical realism in closure schemes for energy transport, dispersion, and phase interactions. The end result is that the study of porous medium systems requires transformational research combining theory, computation, and mathematical analysis to produce the rigorous, multiscale, physics-based models needed to advance understanding and reliability of simulations in applications across a broad and important range of scientific disciplines.
This project will combine theory, computation, mathematical analysis, and high-resolution experimental observation to formulate, solve, and validate models that capture the physics of multiphase flow and transport phenomena in porous media across a range of length scales. The multi-pronged approach will produce the foundational underpinnings of a new generation of porous medium models that will apply across a wide range of scientific fields involving both natural and engineered systems. The general foundational work will be illustrated by specific study of three important problems: non-dilute density dependent transport, two-fluidphase flow, and three-fluid-phase flow. The tools integrated in this work will include high-resolution imaging of pore structure and fluid distributions, image analysis and data extraction, continuum mechanics of fluids and solids, classical and extended thermodynamics, multiscale analysis, high-resolution lattice-Boltzmann algorithm development and simulation, mathematical analysis of new models, time and space adaptive numerical methods, and advanced integral methods for solving systems of nonlinear partial differential algebraic equations.
This project will contribute to education through short courses, student research, and science outreach. It will enhance the infrastructure for fundamental porous media research across disciplines through the production of a monograph and the distribution of tools for modeling and analysis of porous media. The project will encourage the participation of underrepresented researchers and has linkages to minority recruitment programs. It will help improve our to manage natural resources and engineer porous systems for a variety of applications.
