Geometric state function for two-fluid flow in porous media

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

doi:10.1103/PhysRevFluids.3.084306

Geometric state function for two-fluid flow in porous media

Journal Article · Thu Aug 30 00:00:00 EDT 2018 · Physical Review Fluids

DOI:https://doi.org/10.1103/PhysRevFluids.3.084306· OSTI ID:1515702

McClure, James E. ^[1]; Armstrong, Ryan T. ^[2]; ^[3]; Schlüter, Steffen ^[4]; Berg, Steffen ^[5]; Gray, William G. ^[6]; Miller, Cass T. ^[6]

Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
Univ. of New South Wales, Sydney, NSW (Australia)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Helmholtz-Centre for Environmental Research–UFZ, Halle (Germany)
Shell Global Solutions International B.V., Amsterdam (The Netherlands)
Univ. of North Carolina at Chapel Hill, Chapel Hill, NC (United States)

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 nonunique, thus requiring a hysteretic description. As an alternative to the traditional perspective, we consider a geometric 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 microcomputed tomography 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. As a result, this provides a critical missing component needed to enable a new generation of higher fidelity models to describe two-fluid flow in porous media.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: DOE Office of Science; USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1515702

Alternate ID(s):: OSTI ID: 1467953

Journal Information:: Physical Review Fluids, Journal Name: Physical Review Fluids Journal Issue: 8 Vol. 3; ISSN 2469-990X

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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