MHetScale

Mixing in Heterogeneous Media Across Spatial and Temporal Scales: From Local Non-Equilibrium to Anomalous Chemical Transport and Dynamic Uncertainty

The MHetScale team investigates mixing, transport and reaction processes under heterogeneity from the pore to the field scale. Natural and engineered media are inherently heterogeneous, which gives rise to scale effects and process laws that can be very different from what is expected for homogeneous media. Heterogeneity increases the dispersion and thus global segregation of dissolved substances, while it enhances solute mixing locally, as illustrated in Figure 1. Heterogeneity induces a broad spectrum of mass transfer times, which leads to history-dependent transport and reaction dynamics. Our research focuses on the upscaling of transport, mixing and reaction phenomena from pore to Darcy to regional scale.

Figure 1: Concentration distribution in a steady heterogeneous flow (after Dentz and de Barros, J. Fluid. Mech., 2015).

Research lines

Transport dynamics

Large scale transport is in general non-Fickian or anomalous.  This means, first passage time distributions show heavy tails, the centered mean square displacement evolve non-linearly, and spatial solute distributions are non-Gaussian. These non-equilibrium transport phenomena cannot be described by advection-dispersion equations based on constant average transport parameters. We investigate the transport dynamics induced by the interaction of small scale mass transfer mechanisms and flow and medium heterogeneity and their quantification in large scale transport equations. Our take on this challenge is to characterize and understand small scale fluctuations of particle motion in a stochastic framework and derive large scale equations by stochastic averaging. This strategy is similar to the quantification of Brownian motion through a stochastic process, which leads to the diffusion equation. We consider transport processes in heterogeneous porous and fractured media from the pore to the regional scale.

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Mixing

Intuitively mixing can be understood as the process that increases the volume occupied by a dissolved substance, decreases maximum concentrations, and increases the entropy of systems. It is a process that smoothes out concentration gradients, leads to dilution and brings segregated constituents into contact. In analogy to Fick’s law, it was believed that large scale mixing in porous media can be quantified by dispersion coefficients that characterize the spreading of an average solute plume. As can be clearly seen from Figure 1, this concept is not able to describe the mixing dynamic and mixing state of a solute distribution in a heterogeneous flow field. In this case, a dispersion coefficient quantifies the spread of the solute distribution caused by advective heterogeneity. The flow fluctuations and the creation of a complex lamellar organization can be seen in analogy to a stirring process in a free fluid, with the difference that here the stirring is done by the porous medium driven by a pressure gradient. The creation of concentration gradients due to stirring and their attenuation by small scale mass transfer mechanisms on the fine structure of the lamellar concentration field are the fundamental mechanisms of mixing.  We quantify these mechanisms for flows in heterogeneous porous media from pore to Darcy to field scale based on stochastic representations for motion and deformation of fluid elements.

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Reaction

Reactive transport processes in heterogeneous media are specifically affected by microscale mass transfer processes because chemical reac- tions are intrinsically local phenomena: reactions occur when the reacting species get into contact. Therefore, microscale heterogeneity and mass transfer phenomena play a crucial role for the correct quantification of reactive transport across scales. Mass transfer limitations that are present in any natural medium can lead to reduced reaction efficiency, localization of chemical reactions (hotspots) and in general to reaction rate laws that are very different from the ones obtained in a well-mixed laboratory environment. We investigate the impact of spatial heterogeneity and hydrodynamic fluctuations on reaction phenomena in porous media and their systematic quantification.

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Numerics and data

Detailed numerical simulations and experimental data from pore to regional scale provide process understanding, guide theory development, and serve for model validation. Large scale transport, mixing and reaction models are implemented in numerical toolboxes.

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