Mixing across fluid interfaces compressed by convective flow in porous media

We study the mixing in the presence of convective flow in a porous medium. Convection is characterized by the formation of vortices and stagnation points, where the fluid interface is stretched and compressed enhancing mixing. We analyze the behavior of the mixing dynamics in different scenarios using an interface deformation model. We show that the scalar dissipation rate, which is related to the dissolution fluxes, is controlled by interfacial processes, specifically the equilibrium between interface compression and diffusion, which depends on the flow field configuration. We consider different scenarios of increasing complexity. First, we analyze a double-gyre synthetic velocity field. Second, a Rayleigh-B\'enard instability (the Horton-Rogers-Lapwood problem), in which stagnation points are located at a fixed interface. This system experiences a transition from a diffusion controlled mixing to a chaotic convection as the Rayleigh number increases. Finally, a Rayleigh-Taylor instability with a moving interface, in which mixing undergoes three different regimes: diffusive, convection dominated, and convection shutdown. The interface compression model correctly predicts the behavior of the systems. It shows how the dependency of the compression rate on diffusion explains the change in the scaling behavior of the scalar dissipation rate. The model indicates that the interaction between stagnation points and the correlation structure of the velocity field is also responsible for the transition between regimes. We also show the difference in behavior between the dissolution fluxes and the mixing state of the systems. We observe that while the dissolution flux decreases with the Rayleigh number, the system becomes more homogeneous. That is, mixing is enhanced by reducing diffusion. This observation is explained by the effect of the instability patterns

Reaction-diffusion with stochastic decay rates

Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by fluctuations in both transitions times and decay rates. We introduce and analyze a model framework that explicitly connects microscopic fluctuations with the mescoscopic description. For broad distributions of transport and reaction time scales we compute the particle density and derive the equations governing its evolution, finding power-law decay of the survival probability, and spatially heterogeneous decay that leads to subdiffusion and an asymptotically stationary surviving-particle density. These anomalies are clearly attributable to non-Markovian effects that couple transport and chemical properties in both reaction and diffusion terms.Comment: Explain model and applications in more detail. 19 pages, 6 figure

Transport under advective trapping

Advective trapping occurs when solute enters low velocity zones in heterogeneous porous media. Classical local modelling approaches combine the impact of slow advection and diffusion into a hydrodynamic dispersion coefficient and many temporally non-local approaches lump these mechanisms into a single memory function. This joint treatment makes parameterization difficult and thus prediction of large-scale transport a challenge. Here, we investigate the mechanisms of advective trapping and their impact on transport in media composed of a high conductivity background and isolated low permeability inclusions. Breakthrough curves show that effective transport changes from a streamtube-like behaviour to genuine random trapping as the degree of disorder of the inclusion arrangement increases. We upscale this behaviour using a Lagrangian view point, in which idealized solute particles transition over a fixed distance at random advection times combined with Poissonian advective trapping events. We discuss the mathematical formulation of the upscaled model in the continuous time random walk and mobile-immobile mass transfer frameworks, and derive a model for large-scale solute non-Fickian dispersion. These findings give new insight into transport in highly heterogeneous media. © 2020 BMJ Publishing Group. All rights reserved

Mixing-scale dependent dispersion for transport in heterogeneous flows

Dispersion quantifies the impact of subscale velocity fluctuations on the effective movement of particles and the evolution of scalar distributions in heterogeneous flows. Which fluctuation scales are represented by dispersion, and the very meaning of dispersion, depends on the definition of the subscale, or the corresponding coarse-graining scale. We study here the dispersion effect due to velocity fluctuations that are sampled on the homogenization scale of the scalar distribution. This homogenization scale is identified with the mixing scale, the characteristic length below which the scalar is well mixed. It evolves in time as a result of local-scale dispersion and the deformation of material fluid elements in the heterogeneous flow. The fluctuation scales below the mixing scale are equally accessible to all scalar particles, and thus contribute to enhanced scalar dispersion and mixing. We focus here on transport in steady spatially heterogeneous flow fields such as porous media flows. The dispersion effect is measured by mixing-scale dependent dispersion coefficients, which are defined through a filtering operation based on the evolving mixing scale. This renders the coarse-grained velocity as a function of time, which evolves as velocity fluctuation scales are assimilated by the expanding scalar. We study the behaviour of the mixing-scale dependent dispersion coefficients for transport in a random shear flow and in heterogeneous porous media. Using a stochastic modelling framework, we derive explicit expressions for their time behaviour. The dispersion coefficients evolve as the mixing scale scans through the pertinent velocity fluctuation scales, which reflects the fundamental role of the interaction of scalar and velocity fluctuation scales in solute mixing and dispersion. © © 2015 Cambridge University Press.The authors thank three anonymous reviewers for their insightful comments. M.D. acknowledges the support of the European Research Council (ERC) through the project MHetScale (617511).Peer reviewe

Spreading due to heterogeneity in two-phase flow

Postprint (published version

Building America Expert Meeting Report: Hydronic Heating in Multifamily Buildings

The topic of this expert meeting was cost-effective controls and distribution retrofit options for hot water and steam space heating systems in multi-family buildings with the goals of reducing energy waste and improving occupant comfort. The U.S. Department of Energy's Building America program develops technologies with the goal of reducing energy use by 30% to 50% in residential buildings. Toward this goal, the program sponsors 'Expert Meetings' focused on specific building technology topics. The meetings are intended to sharpen Building America research priorities, create a forum for sharing information among industry leaders and build partnerships with professionals and others that can help support the program's research needs and objectives. The topic of this expert meeting was cost-effective controls and distribution retrofit options for hot water and steam space heating systems in multifamily buildings with the goals of reducing energy waste and improving occupant comfort. The objectives of the meeting were to: (1) Share knowledge and experience on new and existing solutions: what works, what doesn't and why, and what's new; (2) Understand the market barriers to currently offered solutions: what disconnects exist in the market and what is needed to overcome or bridge these gaps; and (3) Identify research needs

Enhanced mixing in heterogeneous Buckley Leverett flow due to temporal fluctuations

Peer ReviewedPostprint (published version

Evolution of dissolution patterns by mixing corrosion in karst systems

Póster presentado en la European Geosciences Union General Assembly, celebrada en Viena del 27 de abril al 2 de mayo de 2014.Conduit enlargement in a karst system is usually assumed to be controlled by non-linear kinetics that allow aggressive water to penetrate along fractures (Gabrovšek and Dreybrodt, 2000, Water. Resour. Res.). However, other mechanism known as mixing corrosion may be decisive for the geometry of the resulting dissolution patterns, at least at depth. Mixing corrosion is caused by the renovation of the dissolution capacity that happens when two waters saturated with respect to calcite but with different CO2 partial pressure mix. In this case, the reaction rate is mixing-controlled and can be quantified in terms of the mixing proportion of the conservative components of the chemical system (De Simoni et al. 2005, Water. Resour. Res.). Therefore, the porosity creation governed by the reaction rate will depend on the chemical differences between the end members and by the degree of mixing. The aim of this work is to study the evolution of the porosity and permeability within a carbonate matrix by mixing-driven dissolution under different diffusion regimes. The speciation of the chemical system is calculated using CHEPROO. Flow and transport are modeled using an ad hoc code that accounts for feedback between reactions, porosity creation and permeability changes. The effects of the initial porosity field, water chemistry and the resulting geometry of the dissolution patterns are explored for different scenarios.Peer reviewe