Ilenia Battiato

Applicability regimes for macroscopic models of reactive transport in porous media

We consider transport of a solute that undergoes a nonlinear heterogeneous reaction: after reaching a threshold concentration value, it precipitates on the solid matrix to form a crystalline solid. The relative importance of three key pore-scale transport mechanisms (advection, molecular diffusion, and reaction) is quantified by the Péclet (Pe) and Damköhler (Da) numbers. We use multiple-scale expansions to upscale a pore-scale advection-diffusion equation with reactions entering through a boundary condition on the fluid-solid interface, and to establish sufficient conditions under which macroscopic advection-dispersion-reaction equations provide an accurate description of the pore-scale processes. These conditions are summarized by a phase diagram in the (Pe, Da)-space, parameterized with a scale-separation parameter that is defined as the ratio of characteristic lengths associated with the pore- and macro-scales.

An Analysis Platform for Multiscale Hydrogeologic Modeling with Emphasis on Hybrid Multiscale Methods

One of the most significant challenges faced by hydrogeologic modelers is the disparity between the spatial and temporal scales at which fundamental flow, transport, and reaction processes can best be understood and quantified (e.g., microscopic to pore scales and seconds to days) and at which practical model predictions are needed (e.g., plume to aquifer scales and years to centuries). While the multiscale nature of hydrogeologic problems is widely recognized, technological limitations in computation and characterization restrict most practical modeling efforts to fairly coarse representations of heterogeneous properties and processes. For some modern problems, the necessary level of simplification is such that model parameters may lose physical meaning and model predictive ability is questionable for any conditions other than those to which the model was calibrated. Recently, there has been broad interest across a wide range of scientific and engineering disciplines in simulation approaches that more rigorously account for the multiscale nature of systems of interest. In this article, we review a number of such approaches and propose a classification scheme for defining different types of multiscale simulation methods and those classes of problems to which they are most applicable. Our classification scheme is presented in terms of a flowchart (Multiscale Analysis Platform), and defines several different motifs of multiscale simulation. Within each motif, the member methods are reviewed and example applications are discussed. We focus attention on hybrid multiscale methods, in which two or more models with different physics described at fundamentally different scales are directly coupled within a single simulation. Very recently these methods have begun to be applied to groundwater flow and transport simulations, and we discuss these applications in the context of our classification scheme. As computational and characterization capabilities continue to improve, we envision that hybrid multiscale modeling will become more common and also a viable alternative to conventional single-scale models in the near future.

Single-parameter model of vegetated aquatic flows

Coupled flows through and over permeable layers occur in a variety of natural phenomena including turbulent flows over submerged vegetation. In this work, we employ a two-domain approach to model flow through and over submerged canopies. The model, amenable of a closed-form solution, couples the log-law and the Darcy-Brinkman equation, and is characterized by a novel representation of the drag force which does not rely on a parametrization through an unknown drag coefficient. This approach limits to one, i.e., the obstruction permeability, the number of free parameters. Analytical expressions for the average velocity profile through and above the canopies, volumetric flow rate, penetration length, and canopy shear layer parameter are obtained in terms of the canopy layer effective permeability. The model suggests that appropriately rescaled velocities in the canopy and surface layers follow two different scaling laws. The analytical predictions match with the experimental data collected by Ghisalberti and Nepf (2004) and Nepf et al. (2007).

Vertical dispersion in vegetated shear flows

Canopy layers control momentum and solute transport to and from the overlying water surface layer. These transfer mechanisms strongly dependent on canopy geometry, affect the amount of solute in the river, the hydrological retention and availability of dissolved solutes to organisms located in the vegetated layers, and are critical to improve water quality. In this work, we consider steady state transport in a vegetated channel under fully developed flow conditions. Under the hypothesis that the canopy layer can be described as an effective porous medium with prescribed properties, i.e., porosity and permeability, we model solute transport above and within the vegetated layer with an advection-dispersion equation with a spatially variable dispersion coefficient (diffusivity). By means of the Generalized Integral Transform Technique, we derive a semianalytical solution for the concentration field in submerged vegetated aquatic systems. We show that canopy layers permeability affects the asymmetry of the concentration profile, the effective vertical spreading behavior, and the magnitude of the peak concentration. Due to its analytical features, the model has a low computational cost. The proposed solution successfully reproduces previously published experimental data.

Physics-based hybrid method for multiscale transport in porous media

Despite advancements in the development of multiscale models for flow and reactive transport in porous media, the accurate, efficient and physics-based coupling of multiple scales in hybrid models remains a major theoretical and computational challenge. Improving the predictivity of macroscale predictions by means of multiscale algorithms relative to classical at-scale models is the primary motivation for the development of multiscale simulators. Yet, very few are the quantitative studies that explicitly address the predictive capability of multiscale coupling algorithms as it is still generally not possible to have a priori estimates of the errors that are present when complex flow processes are modeled. We develop a nonintrusive pore-/continuum-scale hybrid model whose coupling error is bounded by the upscaling error, i.e. we build a predictive tightly coupled multiscale scheme. This is accomplished by slightly enlarging the subdomain where continuum-scale equations are locally invalid and analytically defining physics-based coupling conditions at the interfaces separating the two computational sub-domains, while enforcing state variable and flux continuity. The proposed multiscale coupling approach retains the advantages of domain decomposition approaches, including the use of existing solvers for each subdomain, while it gains flexibility in the choice of the numerical discretization method and maintains the coupling errors bounded by the upscaling error. We implement the coupling in finite volumes and test the proposed method by modeling flow and transport through a reactive channel and past an array of heterogeneously reactive cylinders.

Sequential Homogenization of Reactive Transport in Polydisperse Porous Media

Direct numerical simulations of flow and transport in porous media are computationally prohibitive due to the disparity between the typical scale at which processes are well understood (e.g., the pore-scale) and the scale of interest (the system- or field-scale). Homogenization approaches overcome some of the difficulties of full pore-scale simulations by providing an upscaled representation of fine-scale processes. Real porous systems, e.g., rocks, pose additional challenges since they usually exhibit multimodal distributions in physical and chemical properties. Perforated domains, i.e., domains with impermeable inclusions embedded in a porous matrix, represent one such example. These hierarchical media cannot be approached by a single continuum formulation. Sequential homogenization techniques build a hierarchy of effective equations that sequentially carry the smallest scale information through the intermediate scales up to the macroscale. The advantage of sequential upscaling in handling multimodal distribution in physical and chemical properties lies in its computational efficiency compared to one-step homogenization: the information about smaller-scale heterogeneity is incorporated in the subsequent scales in terms of effective media properties. Yet, existence of one or multiple intermediate scales can significantly decrease the accuracy of multiscale formulations. We show that the accuracy of multiscale methods based on sequential upscaling is strongly influenced by a combination of geometric and dynamical scale separation conditions. In particular, we investigate under which conditions sequential homogenization of reactive solute transport in geometrically and chemically heterogeneous porous domains composed of bidisperse cylinders can accurately describe pore-scale processes. We show that under appropriate conditions, expressed in terms of Peźclet and Damkoźhler numbers and a scales separation parameter, the sequential upscaling method has second-order accuracy. We compare sequential upscaling results with the direct solution of the fully resolved pore-scale problem.

Universal scaling-law for flow resistance over canopies with complex morphology

Flow resistance caused by vegetation is a key parameter to properly assess flood management and river restoration. However, quantifying the friction factor or any of its alternative metrics, e.g. the drag coefficient, in canopies with complex geometry has proven elusive. We explore the effect of canopy morphology on vegetated channels flow structure and resistance by treating the canopy as a porous medium characterized by an effective permeability, a property that describes the ease with which water can flow through the canopy layer. We employ a two-domain model for flow over and within the canopy, which couples the log-law in the free layer to the Darcy-Brinkman equation in the vegetated layer. We validate the model analytical solutions for the average velocity profile within and above the canopy, the volumetric discharge and the friction factor against data collected across a wide range of canopy morphologies encountered in riverine systems. Results indicate agreement between model predictions and data for both simple and complex plant morphologies. For low submergence canopies, we find a universal scaling law that relates friction factor with canopy permeability and a rescaled bulk Reynolds number. This provides a valuable tool to assess habitats sustainability associated with hydro-dynamical conditions.

Flow-induced shear instabilities of cohesive granulates

In this work we use a multiscale framework to calculate the fluidization threshold of three-dimensional cohesive granulates under shear forces exerted by a creeping flow. A continuum model of flow through porous media provides an analytical expression for the average drag force on a single grain. The balance equation for the forces and a force propagation model are then used to investigate the effects of porosity and packing structure on the stability of the pile. We obtain a closed-form expression for the instability threshold of a regular packing of monodisperse frictionless cohesive spherical grains in a planar fracture. Our result quantifies the compound effect of structural (packing orientation and porosity) and dynamical properties of the system on its stability.

Multiscale modeling approach to determine effective lithium-ion transport properties

This paper elaborates upon the limitations of using volume-averaged macroscale electrochemical models for lithium-ion batteries, such as the Pseudo-two-Dimensional (P2D) model [1]. To address some of these limitations, an enhanced electrochemical modeling framework that is developed using the homogenization technique is presented in this work. The mass and charge transport equations of the new modeling framework are derived by multiple-scale asymptotic expansion of the pore-scale Poisson-Nernst-Planck (PNP) equations [2]. The effective diffusion and conductivity coefficients of the homogenized model are determined by formulating and solving a closure variable in the electrode microstructure. This paper demonstrates the methodology to calculate the effective transport parameters using the closure approach. We compare the closure-based effective parameters with the effective parameters obtained by using the Bruggeman theory. The Bruggeman approach relies on a simplified approximation of the pore-scale parameters to determine effective values using only porosity. Results indicate that the Bruggeman approach underpredicts the effective transport parameters. This could critically influence model predictive ability, particularly for high C-rates and temperatures of battery operation.

Hydrodynamic dispersion in thin channels with micro-structured porous walls

Flow and transport within porous- and microtextured-walled channels is relevant to a number of natural and industrial processes. Designing and optimizing the topology of the pores and/or microstructure to achieve target performance at the system scale (or macroscale) is still an open question. In this work, we study whether hydrodynamic dispersion in microfluidic channels with walls structured by obstacles can be modeled by dispersion in channels with porous walls described as continuous porous media of zero or finite permeability. We perform single phase microfluidic non-reactive flow experiments in channels embedded in micropatterns with different topologies. Specifically, we focus on transverse riblets and arrays of pillars as examples of impermeable and permeable obstructions, respectively. We compare the experimental results with three models: 3D pore-scale simulations which resolve the micropattern geometry explicitly and two upscaled models which treat the micropattern as a continuum of zero or finite permeability. This study demonstrates that polydimethylsiloxane micromodels with appropriately patterned surfaces can be successfully employed to validate various continuum-scale modeling approximations in different physical regimes, identified by the order of magnitude of the Peclet number and the obstruction permeability.Flow and transport within porous- and microtextured-walled channels is relevant to a number of natural and industrial processes. Designing and optimizing the topology of the pores and/or microstructure to achieve target performance at the system scale (or macroscale) is still an open question. In this work, we study whether hydrodynamic dispersion in microfluidic channels with walls structured by obstacles can be modeled by dispersion in channels with porous walls described as continuous porous media of zero or finite permeability. We perform single phase microfluidic non-reactive flow experiments in channels embedded in micropatterns with different topologies. Specifically, we focus on transverse riblets and arrays of pillars as examples of impermeable and permeable obstructions, respectively. We compare the experimental results with three models: 3D pore-scale simulations which resolve the micropattern geometry explicitly and two upscaled models which treat the micropattern as a continuum of zero or fin...