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2. A geometric state function for two-fluid flow in porous media

Author

McClure, James E., Armstrong, Ryan T., Berrill, Mark A., Schlüter, Steffen, Berg, Steffen, Gray, William G., and Miller, Cass T.

Subjects
Physics - Fluid Dynamics, Condensed Matter - Soft Condensed Matter
Abstract

Models that describe two-fluid flow in porous media suffer from a widely-recognized problem that the constitutive relationships used to predict capillary pressure as a function of the fluid saturation are non-unique, thus requiring a hysteretic description. As an alternative to the traditional perspec- tive, we consider a geometrical description of the capillary pressure, which relates the average mean curvature, the fluid saturation, the interfacial area between fluids, and the Euler characteristic. The state equation is formulated using notions from algebraic topology and cast in terms of measures of the macroscale state. Synchrotron-based X-ray micro-computed tomography ({\mu}CT) and high- resolution pore-scale simulation is applied to examine the uniqueness of the proposed relationship for six different porous media. We show that the geometric state function is able to characterize the microscopic fluid configurations that result from a wide range of simulated flow conditions in an averaged sense. The geometric state function can serve as a closure relationship within macroscale models to effectively remove hysteretic behavior attributed to the arrangement of fluids within a porous medium. This provides a critical missing component needed to enable a new generation of higher fidelity models to describe two-fluid flow in porous media.

Published
2018
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6. Applications

Author

Gray, William G., primary, Leijnse, Anton, additional, Kolar, Randall L., additional, and Blain, Cheryl A., additional

Published
2020
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7. Theorem Notation

Author

Gray, William G., primary, Leijnse, Anton, additional, Kolar, Randall L., additional, and Blain, Cheryl A., additional

Published
2020
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8. Integration Theorems

Author

Gray, William G., primary, Leijnse, Anton, additional, Kolar, Randall L., additional, and Blain, Cheryl A., additional

Published
2020
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10. Averaging Theorems

Author

Gray, William G., primary, Leijnse, Anton, additional, Kolar, Randall L., additional, and Blain, Cheryl A., additional

Published
2020
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16. Evolution Equations

Author

Gray, William G., Miller, Cass T., Hutter, Kolumban, Series editor, Gray, William G., and Miller, Cass T.

Published
2014
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21. Two-Phase Flow

Author

Gray, William G., Miller, Cass T., Hutter, Kolumban, Series editor, Gray, William G., and Miller, Cass T.

Published
2014
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28. Correction to: modelling sediment transport in three-phase surface water systems.

Author

Miller, Cass T., Gray, William G., Kees, Christopher E., Rybak, Iryna V., and Shepherd, Brittany J.

Subjects
*CONTINUUM mechanics, *SEDIMENT transport, *POROUS materials
Abstract

This note corrects an error made in Miller et al. (2019). Modelling sediment transport in three-phase surface water systems. Journal of Hydraulic Research, 57(4), 439–463, . [ABSTRACT FROM AUTHOR]

Published
2023
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40. Reading

Author

Gray, William G.

Published
1935

45. Hydrogeological research: just getting started. (Issue Paper)

Author

Miller, Cass T. and Gray, William G.

Subjects
Hydrogeology -- Research, Geology -- Research, Earth sciences, Research
Abstract

This paper comments on the current state of knowledge in the field of hydrogeology and claims that fundamental understandings must be developed if creative research is to have maximum impact. Problems of great importance to society include water development and quality, waste disposal, and global cycling of resources. These problems cannot be addressed effectively unless significant advances are made in understanding of a range of challenging scientific issues including fundamental physics, the importance of scale, modeling, and chemical and biological processes. Meaningful advances in hydrogeologic research will require an increased emphasis on fundamental understanding, interdisciplinary approaches, educational reforms, and the attraction of excellent researchers to the field., Introduction Our experiences as educators, researchers, editors, reviewers, and advisors active in water resources have provided us with a perspective on the general state of knowledge in hydrogeological research. Our [...]

Published
2002

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