Asymptotic reduction of a porous electrode model for lithium-ion batteries

Iain R. Moyles; Matthew G. Hennessy; Timothy G. Myers; Brian R. Wetton

doi:10.1137/18M1189579

Asymptotic reduction of a porous electrode model for lithium-ion batteries

Iain R. Moyles
, Matthew G. Hennessy
, Timothy G. Myers
, Brian R. Wetton

Research output: Contribution to journal › Article (Academic Journal) › peer-review

20 Citations (Scopus)

Abstract

We present a porous electrode model for lithium-ion batteries using Butler-Volmer reaction kinetics. We model lithium concentration in both the solid and fluid phase, along with solid and liquid electric potential. Through asymptotic reduction, we show that the electric potentials are spatially homogeneous, which decouples the problem into a series of time-dependent problems. These problems can be solved on three distinguished time scales: An early time scale where capacitance effects in the electrode dominate, a mid-range time scale where a spatial concentration gradient forms in the electrolyte, and a long-time scale where each of the electrodes saturate and deplete with lithium, respectively. The solid-phase concentration profiles are linear functions of time and the electrolyte potential is everywhere zero, which allows the model to be reduced to a system of two uncoupled ordinary differential equations. Analytic and numerical results are compared with full numerical simulations and experimental discharge curves, demonstrating excellent agreement.

Original language	English
Pages (from-to)	1528-1549
Number of pages	22
Journal	SIAM Journal on Applied Mathematics
Volume	79
Issue number	4
DOIs	https://doi.org/10.1137/18M1189579
Publication status	Published - 2019

Bibliographical note

Funding Information:
\ast Received by the editors May 24, 2018; accepted for publication (in revised form) May 24, 2019; published electronically August 21, 2019. https://doi.org/10.1137/18M1189579 Funding: This work was supported by an Irish Research Council New Foundations grant. The work of the first author was supported by the Science Foundation Ireland under grant SFI/13/IA/1923. The work of the second author was supported by a travel grant from the Mathematics and Applications Consortium for Science and Industry from the University of Limerick. The work of the third author was supported by Ministerio de Ciencia e Innovaci\o'n grant MTM2017-82317-P. The work of the second and third authors was also partially supported by the CERCA Programme of the Generalitat de Catalunya and the European Union's Horizon 2020 research and innovation programme under Marie Sk\lodowska-Curie grant agreement 707658.

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics.

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 7 Affordable and Clean Energy

Research Groups and Themes

Engineering Mathematics Research Group

Keywords

Asymptotic analysis
Butler-Volmer kinetics
Electrochemistry
Lithium-ion battery
Mathematical modelling
Model reduction
Porous electrode model
Volume averaging

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10.1137/18M1189579

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Cite this

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title = "Asymptotic reduction of a porous electrode model for lithium-ion batteries",

abstract = "We present a porous electrode model for lithium-ion batteries using Butler-Volmer reaction kinetics. We model lithium concentration in both the solid and fluid phase, along with solid and liquid electric potential. Through asymptotic reduction, we show that the electric potentials are spatially homogeneous, which decouples the problem into a series of time-dependent problems. These problems can be solved on three distinguished time scales: An early time scale where capacitance effects in the electrode dominate, a mid-range time scale where a spatial concentration gradient forms in the electrolyte, and a long-time scale where each of the electrodes saturate and deplete with lithium, respectively. The solid-phase concentration profiles are linear functions of time and the electrolyte potential is everywhere zero, which allows the model to be reduced to a system of two uncoupled ordinary differential equations. Analytic and numerical results are compared with full numerical simulations and experimental discharge curves, demonstrating excellent agreement.",

keywords = "Asymptotic analysis, Butler-Volmer kinetics, Electrochemistry, Lithium-ion battery, Mathematical modelling, Model reduction, Porous electrode model, Volume averaging",

author = "Moyles, \{Iain R.\} and Hennessy, \{Matthew G.\} and Myers, \{Timothy G.\} and Wetton, \{Brian R.\}",

note = "Funding Information: \textbackslash{}ast Received by the editors May 24, 2018; accepted for publication (in revised form) May 24, 2019; published electronically August 21, 2019. https://doi.org/10.1137/18M1189579 Funding: This work was supported by an Irish Research Council New Foundations grant. The work of the first author was supported by the Science Foundation Ireland under grant SFI/13/IA/1923. The work of the second author was supported by a travel grant from the Mathematics and Applications Consortium for Science and Industry from the University of Limerick. The work of the third author was supported by Ministerio de Ciencia e Innovaci\textbackslash{}o'n grant MTM2017-82317-P. The work of the second and third authors was also partially supported by the CERCA Programme of the Generalitat de Catalunya and the European Union's Horizon 2020 research and innovation programme under Marie Sk\textbackslash{}lodowska-Curie grant agreement 707658. Publisher Copyright: {\textcopyright} 2019 Society for Industrial and Applied Mathematics.",

year = "2019",

doi = "10.1137/18M1189579",

language = "English",

volume = "79",

pages = "1528--1549",

journal = "SIAM Journal on Applied Mathematics",

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publisher = "Society for Industrial and Applied Mathematics",

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T1 - Asymptotic reduction of a porous electrode model for lithium-ion batteries

AU - Moyles, Iain R.

AU - Hennessy, Matthew G.

AU - Myers, Timothy G.

AU - Wetton, Brian R.

N1 - Funding Information: \ast Received by the editors May 24, 2018; accepted for publication (in revised form) May 24, 2019; published electronically August 21, 2019. https://doi.org/10.1137/18M1189579 Funding: This work was supported by an Irish Research Council New Foundations grant. The work of the first author was supported by the Science Foundation Ireland under grant SFI/13/IA/1923. The work of the second author was supported by a travel grant from the Mathematics and Applications Consortium for Science and Industry from the University of Limerick. The work of the third author was supported by Ministerio de Ciencia e Innovaci\o'n grant MTM2017-82317-P. The work of the second and third authors was also partially supported by the CERCA Programme of the Generalitat de Catalunya and the European Union's Horizon 2020 research and innovation programme under Marie Sk\lodowska-Curie grant agreement 707658. Publisher Copyright: © 2019 Society for Industrial and Applied Mathematics.

PY - 2019

Y1 - 2019

N2 - We present a porous electrode model for lithium-ion batteries using Butler-Volmer reaction kinetics. We model lithium concentration in both the solid and fluid phase, along with solid and liquid electric potential. Through asymptotic reduction, we show that the electric potentials are spatially homogeneous, which decouples the problem into a series of time-dependent problems. These problems can be solved on three distinguished time scales: An early time scale where capacitance effects in the electrode dominate, a mid-range time scale where a spatial concentration gradient forms in the electrolyte, and a long-time scale where each of the electrodes saturate and deplete with lithium, respectively. The solid-phase concentration profiles are linear functions of time and the electrolyte potential is everywhere zero, which allows the model to be reduced to a system of two uncoupled ordinary differential equations. Analytic and numerical results are compared with full numerical simulations and experimental discharge curves, demonstrating excellent agreement.

AB - We present a porous electrode model for lithium-ion batteries using Butler-Volmer reaction kinetics. We model lithium concentration in both the solid and fluid phase, along with solid and liquid electric potential. Through asymptotic reduction, we show that the electric potentials are spatially homogeneous, which decouples the problem into a series of time-dependent problems. These problems can be solved on three distinguished time scales: An early time scale where capacitance effects in the electrode dominate, a mid-range time scale where a spatial concentration gradient forms in the electrolyte, and a long-time scale where each of the electrodes saturate and deplete with lithium, respectively. The solid-phase concentration profiles are linear functions of time and the electrolyte potential is everywhere zero, which allows the model to be reduced to a system of two uncoupled ordinary differential equations. Analytic and numerical results are compared with full numerical simulations and experimental discharge curves, demonstrating excellent agreement.

KW - Asymptotic analysis

KW - Butler-Volmer kinetics

KW - Electrochemistry

KW - Lithium-ion battery

KW - Mathematical modelling

KW - Model reduction

KW - Porous electrode model

KW - Volume averaging

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DO - 10.1137/18M1189579

M3 - Article (Academic Journal)

AN - SCOPUS:85072055696

SN - 0036-1399

VL - 79

SP - 1528

EP - 1549

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 4

ER -

Asymptotic reduction of a porous electrode model for lithium-ion batteries

Abstract

Bibliographical note

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Keywords

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