Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems

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On the dynamics and kinematics of two‐fluid‐phase flow in porous media (2015, methodology): “For the more general case, it might be reasonable to break equation (39) into a component related to the average macroscale geometric orientation of the interface and an approximation of the interface velocity based upon a linearization of the phase velocities [Gray and Miller, 2014].”
Macroscopic model for unsteady flow in porous media (2019, methodology): “Among techniques like homogenization (Auriault, Boutin & Geindreau 2009) or the thermodynamically constrained averaging technique (Gray & Miller 2014) and many others (Cushman, Bennethum & Hu 2002), the method of volume averaging (Whitaker 1999) is retained in this work.”
Modeling Turbulent Flows in Porous Media (2020, methodology): “…theory (Bennethum & Giorgi 1997), homogenization methods (Mei & Auriault 1991, Panfilov & Fourar 2006), thermodynamically constrained averaging theory (Gray & Miller 2014), and VAT (Breugem & Boersma 2005; de Lemos 2006; Finnigan 2000; Lasseux et al. 2011, 2019; Rosti et al. 2018; Travkin 2001).”