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  • Periodic Report Summary 2 - MHETSCALE (Mixing in Heterogeneous Media Across Spatial and Temporal Scales: From Local Non-Equilibrium to Anomalous Chemical Transport and Dynamic Uncertainty)

MHETSCALE Report Summary

Project ID: 617511
Funded under: FP7-IDEAS-ERC
Country: Spain

Periodic Report Summary 2 - MHETSCALE (Mixing in Heterogeneous Media Across Spatial and Temporal Scales: From Local Non-Equilibrium to Anomalous Chemical Transport and Dynamic Uncertainty)

Natural and engineered media are in general heterogeneous across scales ranging from the pore to regional and global scales. Spatial heterogeneity and temporal fluctuations are key players for the understanding and quantification of the dynamics of flow, transport, and reaction processes. The heterogeneity impact on transport has traditionally been quantified in terms of dispersion coefficients. From the pore to the Darcy scale, this refers to hydrodynamic dispersion, from Darcy to regional scale, macrodispersion. Dispersion quantifies the impact of sub-scale velocity fluctuations on solute transport, in analogy to Brownian motion, in which micro scale thermal fluctuations of particle velocities are quantified through a diffusion coefficient. However, it has been ubiquitously found that the dispersion paradigm does not provide a realistic description for transport, mixing and reaction processes in heterogeneous media. Transport and reaction phenomena across scales are anomalous in the sense that they cannot be described by advection-dispersion-reaction dynamics which are characterized by equivalent transport and reaction parameters. These phenomena can be linked to the notion of incomplete mixing or physical non-equilibrium, which give rise to anomalous transport behaviors that are characterized by history-dependent dynamics, multivaluedness of concentration at the support scale, and inequality between transported particles. The main objective of MHetScale is to establish a global predictive framework that quantifies mixing across scales, anomalous transport and reaction, and dynamic uncertainty for heterogeneous media. Anomalous chemical transport is studied in terms of the characteristic mixing and homogenisation length and time scales and the statistics of Lagrangian particle transitions at pore and Darcy scales. Observed intermittent behaviors of particle velocities and accelerations are traced back to velocity persistence along characteristic length scales. The resulting stochastic particle dynamics have been cast in novel non-equilibrium transport frameworks based on the continuous time random walk (CTRW) which quantify the space-time evolution of particle velocities and positions. The new framework provides a link between the Eulerian velocity statistics and medium characteristics, and the large scale mixing and transport dynamics. 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. We discovered that the dynamics of sub-exponential and non-linear fluid stretching in heterogeneous media are due to intermittent shear events and obey a coupled CTRW (Lévy walks) that links particle transition times to elongation increments. These findings link the mechanisms of fluid deformation and mixing to the Eulerian flow statistics and ultimately the medium heterogeneity. This framework has been used to quantify the interaction of flow field heterogeneity and chemical reaction in a lamellar approach that systematically integrates information on fluid deformation for the prediction of the large scale reaction efficiency. We find that the impact of small scale reactant segregation due to medium heterogeneity gives rise to non-local effective reaction kinetics. The impact of intermittent particle and mixing dynamics on large scale transport and chemical reactions is quantified by reactive (continuous time) random walk models that allow to integrate the derived stochastic particle dynamics into large scale reactive transport modelling and the derivation of effective large scale reaction kinetics and transport behaviors.

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