Homogenizability conditions for multicomponent reactive transport

Boso, Francesca; Battiato, Ilenia

doi:10.1016/j.advwatres.2013.07.014

Cited by 59 publications

(70 citation statements)

References 31 publications

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“…where K is defined by (23). Combining (A19) with (A17) to eliminate the temporal derivative, we obtain …”

Section: Terms Of Order O(ε −2mentioning

confidence: 98%

“…Diffusion, migration, and reaction are of the same order of magnitude at the point (α, β) = (0, 0). [27] for x ∈ , provided the additional conditions (26) and (27), the dimensionless parameter K is defined by (23) and the effective diffusion and conductivity tensors are given by…”

Section: B(x)mentioning

confidence: 99%

“…cell-scale). [21][22][23] For example, pore-scale molecular diffusion fundamentally affects lithium-ion mixing and heat generation at the electrode scale, 9 and z E-mail: harunac@clemson.edu localized SEI-growth in the pores (over time scales spanning many orders of magnitude) can lead to drastic porosity changes and long term impairment (e.g. aging and capacity fade) of battery systems.…”

mentioning

confidence: 99%

“…Following the approach introduced by, 22,23 we use multiple-scale expansions technique to upscale the dimensionless PNP equations describing lithium dynamics and to derive physics-based conditions under which classical porous-electrode continuum models, or dualcontinua diffusion-migration-reaction (DMR) equations, accurately describe lithium-ion pore-scale dynamics.…”

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confidence: 99%

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On Veracity of Macroscopic Lithium-Ion Battery Models

Arunachalam¹,

Onori²,

Battiato³

2015

J. Electrochem. Soc.

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Batteries are electrochemical energy storage devices that exhibit physico-chemical heterogeneity on a continuity of scales. As such, battery systems are amenable to mathematical descriptions on a multiplicity of scales that range from atomic to continuum. In this paper we present a new method to assess the veracity of macroscopic models of lithium-ion batteries. Macroscopic models treat the electrode as a continuum and are often employed to describe the mass and charge transfer of lithium since they are computational tractable and practical to model the system at the cell scale. Yet, they rely on a number of simplifications and assumptions that may be violated under given operating conditions. We use multiple-scale expansions to upscale the pore-scale Poisson-Nerst-Planck (PNP) equations and establish sufficient conditions under which macroscopic dual-continua mass and charge transport equations accurately represent pore-scale dynamics. We propose a new method to quantify the relative importance of three key pore-scale transport mechanisms (electromigration, diffusion and heterogenous reaction) by means of the electric Péclet (Pe) and Damköhler (Da) numbers in the electrolyte and the electrode phases. For the first time, applicability conditions of macroscopic models through a phase diagram in the (Da-Pe)-space are defined. Finally, we discuss how the new proposed tool can be used to assess the validity of macroscopic models across different battery chemistry and conditions of operation. In particular, a case study analysis is presented using commercial lithium-ion batteries that investigates the validity of Newman-type macroscopic models under temperature and current rate of charge/discharge variation. Predictive understanding of battery dynamical behavior still remains a major bottleneck in achieving diagnostic capabilities, safety, optimization and control of battery systems under different operating conditions. Such a difficulty arises from two main factors: i) nonlinearity of lithium-ion transport processes 1 and ii) battery systems multiscale structure that exhibits physicochemical heterogeneity on a continuity of scales (from the nanometer to the meter).2-5 Since the seminal work by Newman and Tiedemann, 6 where macroscopic ion transport equations were first formulated, a plethora of models have spurred in the past decades. They range from fully empirical approaches to generalizations of electrochemical models based on the porous electrode theory to account for concentrated solutions, 7,8 thermal effects 9 and capacity fade due to Solid-Electrolyte Interphase (SEI)-growth, [10][11][12] just to mention a few. In the past decade, ever increasing computational capabilities have fuelled the development of fully molecular/atomistic models and multiscale/multiphysics approaches. 13 For a thorough review on the topic, we refer the reader to Ref. 4. Microscale models 14,15 (e.g. molecular dynamics, kinetic Monte Carlo and pore-scale models) are theoretically robust, but are impractical as a predictive tool at t...

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“…where K is defined by (23). Combining (A19) with (A17) to eliminate the temporal derivative, we obtain …”

Section: Terms Of Order O(ε −2mentioning

confidence: 98%

Section: B(x)mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

On Veracity of Macroscopic Lithium-Ion Battery Models

Arunachalam¹,

Onori²,

Battiato³

2015

J. Electrochem. Soc.

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“…A brief review of mixing, spreading and reaction in heterogeneous media has been given in [46]. Battiato et al [67][68][69] developed a multiscale analysis of a mixing-controlled precipitation reaction that identified sufficient conditions (in terms of ranges of dimensionless Pé-clet (Pe) and Damköhler (Da) numbers) under which macroscopic advection-dispersion-reaction equations provided an accurate description of the pore-scale processes. Outside of these ranges, it was postulated that pore-scale processes must be explicitly simulated to obtain an accurate solution.…”

Section: Introductionmentioning

confidence: 99%

Hybrid multiscale simulation of a mixing-controlled reaction

Scheibe

Schuchardt

Agarwal

et al. 2015

Advances in Water Resources

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a b s t r a c tContinuum-scale models, which employ a porous medium conceptualization to represent properties and processes averaged over a large number of solid grains and pore spaces, are widely used to study subsurface flow and reactive transport. Recently, pore-scale models, which explicitly resolve individual soil grains and pores, have been developed to more accurately model and study pore-scale phenomena, such as mineral precipitation and dissolution reactions, microbially-mediated surface reactions, and other complex processes. However, these highly-resolved models are prohibitively expensive for modeling domains of sizes relevant to practical problems. To broaden the utility of pore-scale models for larger domains, we developed a hybrid multiscale model that initially simulates the full domain at the continuum scale and applies a pore-scale model only to areas of high reactivity. Since the location and number of pore-scale model regions in the model varies as the reactions proceed, an adaptive script defines the number and location of pore regions within each continuum iteration and initializes pore-scale simulations from macroscale information. Another script communicates information from the pore-scale simulation results back to the continuum scale. These components provide loose coupling between the pore-and continuum-scale codes into a single hybrid multiscale model implemented within the SWIFT workflow environment. In this paper, we consider an irreversible homogeneous bimolecular reaction (two solutes reacting to form a third solute) in a 2D test problem. This paper is focused on the approach used for multiscale coupling between pore-and continuumscale models, application to a realistic test problem, and implications of the results for predictive simulation of mixing-controlled reactions in porous media. Our results and analysis demonstrate that the hybrid multiscale method provides a feasible approach for increasing the accuracy of subsurface reactive transport simulations.

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Hybrid modeling of heterogeneous geochemical reactions in fractured porous media

Roubinet

Tartakovsky

2013

Water Resour. Res.

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[1] Quantitative modeling of geochemical reactions at the Darcy scale is challenging due to their dependence on pore-scale characteristics that often cannot be averaged out. We propose a hybrid pore-scale/continuum-scale algorithm to bridge the gap between the porescale mechanisms of reactive transport and the Darcy-scale observations of their impact. These two scales are coupled by introducing extra nodes at the pore/continuum interfaces, in which the continuity of both concentrations and mass fluxes is enforced. Our algorithm is applicable to highly localized transport phenomena that can be adequately described by Darcy-scale equations in most of a computational domain except for small regions (e.g., reaction fronts) wherein pore-scale simulations are necessary. We employ the proposed hybrid algorithm to model transient reactive solute transport involving fracture cementation.

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Homogenizability conditions for multicomponent reactive transport

Cited by 59 publications

References 31 publications

On Veracity of Macroscopic Lithium-Ion Battery Models

On Veracity of Macroscopic Lithium-Ion Battery Models

Hybrid multiscale simulation of a mixing-controlled reaction

Hybrid modeling of heterogeneous geochemical reactions in fractured porous media

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