Final Report Summary - MHETSCALE (Mixing in Heterogeneous Media Across Spatial and Temporal Scales: From Local Non-Equilibrium to Anomalous Chemical Transport and Dynamic Uncertainty)
The main objective of MHetScale was the quest for a new quantitative understanding of transport, mixing, and reaction of solutes and particles in natural and engineered porous media from the pore to the reservoir scale. Spatial heterogeneity together with small scale mass transfer processes lead to large scale (anomalous) transport phenomena that cannot be explained by advection-dispersion approaches characterized by constant effective transport parameters. The main challenges are the identification of the (collective) disorder, flow and mass transfer mechanisms that lead to anomalous large scale behaviors, and their quantification in physics-based predictive large scale models. MHetScale was organized along three interrelated scientific work packages in order to tackle these challenges, and develop an integrated approach to analyze, link and predict hydrodynamic mixing, transport, and reaction in heterogeneous media. We took a Lagrangian, particle based perspective in order to analyze and upscale the impact of heterogeneity and flow structure on large scale process dynamics from pore to regional scale. Changing from the classical isochrone to an equidistant view on processes along particle trajectories, we derived new Lagrangian data analysis strategies that allowed identifying the salient disorder mechanisms behind the complex (isochrone) stochastic dynamics of particle motion, mixing and reaction in disordered media.
Through the analysis of extensive data from pore and Darcy scale transport simulations and experiments in porous and fractured media, we discovered a universal principle that explains complex intermittent transport processes in porous media at all scales. It is based on the fact that particle velocities persist over characteristic length scales that are imprinted in the medium and flow structures. The resulting (equidistant) stochastic particle dynamics are directly related to (transport independent) Eulerian flow properties, which is a milestone for the prediction and upscaling of transport in disordered media. These dynamics have been cast in novel non-equilibrium Boltzmann-type transport models based on the continuous time random walk approach. This framework has been used to shed light on and predict scale-dependent intermittent and anomalous transport behaviors at the pore, Darcy and regional scale in strongly heterogeneous porous and fractured media.
The mechanisms of mixing have been quantified in terms of a general theory for the impact of fluid deformation and aggregation dynamics of lamellar structures on the evolution of concentration and concentration increments, which captures the salient mixing dynamics at all scales. We discovered that the evolution of Lagrangian deformation in porous media is due to intermittent shear and stretching events which are based on the same dynamic principle that governs the stochastic evolution of the Lagrangian velocities. Thus, the stochastic dynamics of Lagrangian deformations are quantified by a novel correlated continuous time random walk which provides the link to Eulerian flow properties. The fundamental nature of the fluctuation-induced mixing mechanisms and the universal character of the developed approaches and methods allowed to shed light on mixing and reaction phenomena in heterogeneous porous media from the pore to the Darcy scale under stable and unstable flow conditions.
Along these lines, we unravelled the fundamental role of flow and medium heterogeneity in reactant segregation and the formation of reaction and mixing hotspots for pore and Darcy scale porous media. We developed new agent-based approaches to account for the impact of stochastic particle dynamics, and lamellar stretching and coalescence on mixing-limited chemical reactions. We find that segregation leads non-local large scale reaction dynamics, which are caused by broad distributions of mass transfer time scales intrinsic to heterogeneous porous media at all scales. These behaviors were formalized within a novel kinetic Monte-Carlo approach that accounts for heterogeneity-induced random delay times between reaction events. These insights and new methodologies were used to provide new understanding for the modeling and prediction of reaction dynamics in pore and Darcy scale porous media across scales.
MHetScale has demonstrated that it is possible to relate medium and flow structure, as well as microscale mass transfer dynamics to large scale mixing, transport and reaction behaviors in a predictive, physics-based way, identified and quantified the salient disorder mechanisms across scales, and established a predictive large scale modeling framework.
Through the analysis of extensive data from pore and Darcy scale transport simulations and experiments in porous and fractured media, we discovered a universal principle that explains complex intermittent transport processes in porous media at all scales. It is based on the fact that particle velocities persist over characteristic length scales that are imprinted in the medium and flow structures. The resulting (equidistant) stochastic particle dynamics are directly related to (transport independent) Eulerian flow properties, which is a milestone for the prediction and upscaling of transport in disordered media. These dynamics have been cast in novel non-equilibrium Boltzmann-type transport models based on the continuous time random walk approach. This framework has been used to shed light on and predict scale-dependent intermittent and anomalous transport behaviors at the pore, Darcy and regional scale in strongly heterogeneous porous and fractured media.
The mechanisms of mixing have been quantified in terms of a general theory for the impact of fluid deformation and aggregation dynamics of lamellar structures on the evolution of concentration and concentration increments, which captures the salient mixing dynamics at all scales. We discovered that the evolution of Lagrangian deformation in porous media is due to intermittent shear and stretching events which are based on the same dynamic principle that governs the stochastic evolution of the Lagrangian velocities. Thus, the stochastic dynamics of Lagrangian deformations are quantified by a novel correlated continuous time random walk which provides the link to Eulerian flow properties. The fundamental nature of the fluctuation-induced mixing mechanisms and the universal character of the developed approaches and methods allowed to shed light on mixing and reaction phenomena in heterogeneous porous media from the pore to the Darcy scale under stable and unstable flow conditions.
Along these lines, we unravelled the fundamental role of flow and medium heterogeneity in reactant segregation and the formation of reaction and mixing hotspots for pore and Darcy scale porous media. We developed new agent-based approaches to account for the impact of stochastic particle dynamics, and lamellar stretching and coalescence on mixing-limited chemical reactions. We find that segregation leads non-local large scale reaction dynamics, which are caused by broad distributions of mass transfer time scales intrinsic to heterogeneous porous media at all scales. These behaviors were formalized within a novel kinetic Monte-Carlo approach that accounts for heterogeneity-induced random delay times between reaction events. These insights and new methodologies were used to provide new understanding for the modeling and prediction of reaction dynamics in pore and Darcy scale porous media across scales.
MHetScale has demonstrated that it is possible to relate medium and flow structure, as well as microscale mass transfer dynamics to large scale mixing, transport and reaction behaviors in a predictive, physics-based way, identified and quantified the salient disorder mechanisms across scales, and established a predictive large scale modeling framework.