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This study aims to bridge length scales in immiscible multiphase flow simulation by connecting two published governing equations at the pore-scale and continuum-scale through a novel validation framework. We employ Niessner and Hassnaizadeh's [“A model for two-phase flow in porous media including fluid-fluid interfacial area,” Water Resour. Res. 44(8), W08439 (2008)] continuum-scale model for multiphase flow in porous media, combined with the geometric equation of state of McClure et al. [“Modeling geometric state for fluids in porous media: Evolution of the Euler characteristic,” Transp. Porous Med. 133(2), 229–250 (2020)]. Pore-scale fluid configurations simulated with the lattice-Boltzmann method are used to validate the continuum-scale results. We propose a mapping from the continuum-scale to pore-scale utilizing a generalized additive model to predict non-wetting phase Euler characteristics during imbibition, effectively bridging the continuum-to-pore length scale gap. Continuum-scale simulated measures of specific interfacial area, saturation, and capillary pressure are directly compared to up-scaled pore-scale simulation results. This research develops a numerical framework capable of capturing multiscale flow equations establishing a connection between pore-scale and continuum-scale simulations. 

Flow fluctuations that are commonly associated with multiphase flow in porous media are studied using concepts from non-equilibrium thermodynamic and statistical mechanics. We investigate how the Green–Kubo formulation of the fluctuation dissipation theorem can be used to predict the transport coefficient from the two-phase extension of Darcy's law. Flow rate-time series data are recorded at the millisecond timescale using a novel experimental setup that allows for the determination of flow fluctuation statistics. By using Green–Kubo relations, a transport coefficient is predicted based on the integrated autocorrelation function. Notably, this coefficient aligned closely with the total effective phase mobility computed using Darcy's equation for multiphase flow, particularly in scenarios where a linear relationship between flow rate and pressure gradient was observed. Our results open a new field of coefficient explorations where microscale fluctuations during multiphase flow are directly linked to macroscale parameters.