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ERE Seminar: Cass Miller (UNC) - Toward a New Generation of Models to Simulate Two-Fluid Flow...

Monday, May 18, 2020 12:30 PM
Room 104, Green Earth Sciences Building, 367 Panama Street, Stanford
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ERE Seminar: Cass Miller (UNC) - Toward a New Generation of Models to Simulate …
Faculty/Staff, Students
Energy Resources Engineering

Cass Miller, PhD | University of North Carolina

Toward a New Generation of Models to Simulate Two-Fluid Flow in Porous Media


Two fluid flow in porous medium systems is an important application in many different areas of science and engineering.  Overwhelmingly, it is necessary to mathematically model the behavior of applications of concern at an averaged scale where the juxtaposed position of the phases is not resolved in detail.  This length scale is called the macroscale and the traditional model that is used nearly universally was formulated phenomenologically nearly 100 years ago. Since that time, considerable, and important, work has been done to close this model, advance more efficient numerical methods to solve the resultant equations, and analyze mathematical aspects of the model behavior.   This considerable work notwithstanding, many important open issues remain with this traditional model, including hysteretic behavior of the closure relations, lack of connection between the microscale and the macroscale, absence of explicit dependence upon variables well known to be important (contact angles, interfacial tensions, curvatures, etc), and the absence of thermodynamic constraints.  We report on a sustained effort to resolve these theoretical shortcomings and to formulate a new generation of models for this important class of applications.  A summary of the theoretical approach based upon the thermodynamically constrained averaging theory (TCAT) is discussed, a hierarchy of models is formulated, and an example model instance is examined in detail.   The problem of model closure and validation is considered.  Relying upon notions from integral geometry, we formulate a hysteretic-free state equation that applies under both equilibrium and dynamic conditions. We show that this equation is essentially exact by comparing to high-resolution simulations for a wide variety of systems.  We extend the notion of a state equation to resistance coefficients, and we show promising results for the removal of hysteresis from common relative permeability relations as well.  We summarize recent results to derive evolution equations for curvatures, and we assemble the various components to reveal a complete, closed model.

Professor Miller is educated as an environmental engineer earning his PhD from the University of Michigan in 1984 and beginning his academic career soon after that as an assistant professor in the department of environmental sciences and engineering at the University of North Carolina, where he has remained on the faculty ever since. He is currently the Okun Distinguished Professor of Environmental Engineering with involvement in multiple departments at UNC (Env Sci and Eng, Mathematics, and Applied Physical Sciences).  He has served as the primary advisor of about 100 post docs and graduate students and produced a total of more than 700 published works, including a recent book on the thermodynamically constrained averaging theory, which he coauthored with Bill Gray.  Professor Miller has served in a wide range of scientific leadership positions including more than two decades as an editor of leading journals in the field---Environmental Science & Technology, and Advances in Water Resources.  Professor Miller was an organizer of the bi-annual conference on Computational Methods in Water Resources for several years, which will convene at Stanford in June 2020.   A distinguishing feature of the research of Professor Miller is his joint, synergistic use of theory, computational methods, and experimental approaches to advance understanding of transport phenomena in complex systems.

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