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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 21, issue 2
Hydrol. Earth Syst. Sci., 21, 1063–1076, 2017
https://doi.org/10.5194/hess-21-1063-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Observations and modeling of land surface water and energy...

Hydrol. Earth Syst. Sci., 21, 1063–1076, 2017
https://doi.org/10.5194/hess-21-1063-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 20 Feb 2017

Research article | 20 Feb 2017

On the consistency of scale among experiments, theory, and simulation

James E. McClure1, Amanda L. Dye2, Cass T. Miller2, and William G. Gray3 James E. McClure et al.
  • 1Advanced Research Computing, Virginia Tech, Blacksburg, Virginia 24601-0123, USA
  • 2Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, North Carolina 27599-7431, USA
  • 3Curriculum for the Environment and Ecology, University of North Carolina, Chapel Hill, North Carolina 27599-3135, USA

Abstract. As a tool for addressing problems of scale, we consider an evolving approach known as the thermodynamically constrained averaging theory (TCAT), which has broad applicability to hydrology. We consider the case of modeling of two-fluid-phase flow in porous media, and we focus on issues of scale as they relate to various measures of pressure, capillary pressure, and state equations needed to produce solvable models. We apply TCAT to perform physics-based data assimilation to understand how the internal behavior influences the macroscale state of two-fluid porous medium systems. A microfluidic experimental method and a lattice Boltzmann simulation method are used to examine a key deficiency associated with standard approaches. In a hydrologic process such as evaporation, the water content will ultimately be reduced below the irreducible wetting-phase saturation determined from experiments. This is problematic since the derived closure relationships cannot predict the associated capillary pressures for these states. We demonstrate that the irreducible wetting-phase saturation is an artifact of the experimental design, caused by the fact that the boundary pressure difference does not approximate the true capillary pressure. Using averaging methods, we compute the true capillary pressure for fluid configurations at and below the irreducible wetting-phase saturation. Results of our analysis include a state function for the capillary pressure expressed as a function of fluid saturation and interfacial area.

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A complicating factor in describing the flow of two immiscible fluids in a porous medium is ensuring that experiments, theory, and simulation are all formulated at the same length scale. We have quantitatively analyzed the internal structure of a two-fluid system including the distribution of phases and the location of interfaces between phases. The data we have obtained allow for a clearer definition of capillary pressure at the averaged scale as a state function that describes the system.
A complicating factor in describing the flow of two immiscible fluids in a porous medium is...
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