MULTIBAT: Unified workflow for fast electrochemical 3D simulations of lithium-ion cells combining virtual stochastic microstructures, electrochemical degradation models and model order reduction

We present a simulation workflow for efficient investigations of the interplay between 3D lithium-ion electrode microstructures and electrochemical performance, with emphasis on lithium plating. Our approach addresses several challenges. First, the 3D microstructures of porous electrodes are generated by a parametric stochastic model, in order to significantly reduce the necessity of tomographic imaging. Secondly, we integrate a consistent microscopic, 3D spatially-resolved physical model for the electrochemical behavior of the lithium-ion cells taking lithium plating and stripping into account. This highly non-linear mathematical model is solved numerically on the complex 3D microstructures to compute the transient cell behavior. Due to the complexity of the model and the considerable size of realistic microstructures even a single charging cycle of the battery requires several hours computing time. This renders large scale parameter studies extremely time consuming. Hence, we develop a mathematical model order reduction scheme. We demonstrate how these aspects are integrated into one unified workflow, which is a step towards computer aided engineering for the development of more efficient lithium-ion cells.

[1]  Q. Horn,et al.  The Effect of Microstructure on the Galvanostatic Discharge of Graphite Anode Electrodes in LiCoO2-Based Rocking-Chair Rechargeable Batteries , 2009 .

[2]  J. Tarascon,et al.  Comparison of Modeling Predictions with Experimental Data from Plastic Lithium Ion Cells , 1996 .

[3]  Randolph E. Bank,et al.  A posteriori error estimates based on hierarchical bases , 1993 .

[4]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[5]  Ann Marie Sastry,et al.  Micro-Scale Modeling of Li-Ion Batteries: Parameterization and Validation , 2012 .

[6]  Volker Schmidt,et al.  A unified simulation framework for spatial stochastic models , 2004, Simul. Model. Pract. Theory.

[7]  Oliver Lass,et al.  Parameter identification for nonlinear elliptic-parabolic systems with application in lithium-ion battery modeling , 2015, Comput. Optim. Appl..

[8]  Mario Ohlberger,et al.  Localized Reduced Basis Approximation of a Nonlinear Finite Volume Battery Model with Resolved Electrode Geometry , 2016, 1606.05070.

[9]  D. Sauer,et al.  Parameterization of a Physico-Chemical Model of a Lithium-Ion Battery II. Model Validation , 2015 .

[10]  Jochen Zausch,et al.  On 2D Finite Element Simulation of a thermodynamically consistent Li Ion Battery Microscale Model , 2014 .

[11]  J. Hesthaven,et al.  Certified Reduced Basis Methods for Parametrized Partial Differential Equations , 2015 .

[12]  M. Wohlfahrt‐Mehrens,et al.  Ageing mechanisms in lithium-ion batteries , 2005 .

[13]  John Newman,et al.  Two-Dimensional Modeling of Lithium Deposition during Cell Charging , 2008 .

[14]  Jochen Zausch,et al.  Numerical simulation of phase separation in cathode materials of lithium ion batteries , 2016 .

[15]  Bernhard Wieland,et al.  Reduced basis methods for partial differential equations with stochastic influences , 2013 .

[16]  Sergei Zuyev,et al.  Random Laguerre tessellations , 2008, Advances in Applied Probability.

[17]  Shiquan Zhang,et al.  On some model reduction approaches for simulations of processes in Li-ion battery , 2015 .

[18]  J. Møller Random tessellations in ℝ d , 1989, Advances in Applied Probability.

[19]  N. Nguyen,et al.  An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations , 2004 .

[21]  René Milk,et al.  pyMOR - Generic Algorithms and Interfaces for Model Order Reduction , 2015, SIAM J. Sci. Comput..

[22]  R. Prim Shortest connection networks and some generalizations , 1957 .

[23]  Karsten Urban,et al.  A hierarchical a posteriori error estimator for the Reduced Basis Method , 2018, Adv. Comput. Math..

[24]  Marc Doyle,et al.  Mathematical Modeling of the Lithium Deposition Overcharge Reaction in Lithium‐Ion Batteries Using Carbon‐Based Negative Electrodes , 1999 .

[25]  Stefan Volkwein,et al.  The reduced basis method applied to transport equations of a lithium-ion battery , 2013 .

[26]  Sebastian Schmidt,et al.  A Model Reduction Framework for Efficient Simulation of Li-Ion Batteries , 2014, 1404.0972.

[27]  Volker Schmidt,et al.  Stochastic 3D modeling of La0.6Sr0.4CoO3−δ cathodes based on structural segmentation of FIB–SEM images , 2013 .

[28]  Volker Schmidt,et al.  Stochastic 3D modeling of complex three-phase microstructures in SOFC-electrodes with completely connected phases , 2016 .

[29]  LassOliver,et al.  Parameter identification for nonlinear elliptic-parabolic systems with application in lithium-ion battery modeling , 2015 .

[30]  S. Raël,et al.  Physical characterization of the charging process of a Li-ion battery and prediction of Li plating by electrochemical modelling , 2014 .

[31]  C. Schwab,et al.  Isotropic Gaussian random fields on the sphere: Regularity, fast simulation and stochastic partial differential equations , 2013, 1305.1170.

[32]  Jochen Zausch,et al.  Thermodynamic consistent transport theory of Li-ion batteries , 2011 .

[33]  James B. Robinson,et al.  Investigating lithium-ion battery materials during overcharge-induced thermal runaway: an operando and multi-scale X-ray CT study. , 2016, Physical chemistry chemical physics : PCCP.

[34]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[35]  Jochen Zausch,et al.  Thermodynamic derivation of a Butler-Volmer model for intercalation in Li-ion batteries , 2013 .

[36]  Volker Schmidt,et al.  Stochastic microstructure modeling and electrochemical simulation of lithium-ion cell anodes in 3D , 2016 .

[37]  Jochen Zausch,et al.  Multiscale modeling of lithium ion batteries: thermal aspects , 2015, Beilstein journal of nanotechnology.

[38]  John Newman,et al.  Electrochemical Systems, 3rd Edition , 2004 .

[39]  Volker Schmidt,et al.  Stochastic 3D modeling of fiber-based materials , 2012 .

[40]  Leilei Yin,et al.  Simulation of heat generation in a reconstructed LiCoO2 cathode during galvanostatic discharge , 2013 .

[41]  Yavor Vutov,et al.  Finite Volume Discretization of Equations Describing Nonlinear Diffusion in Li-Ion Batteries , 2010, NMA.

[42]  J. Koenderink Q… , 2014, Les noms officiels des communes de Wallonie, de Bruxelles-Capitale et de la communaute germanophone.

[43]  Bernard Haasdonk,et al.  Chapter 2: Reduced Basis Methods for Parametrized PDEs—A Tutorial Introduction for Stationary and Instationary Problems , 2017 .

[44]  D. Wheeler,et al.  Modeling of lithium-ion batteries , 2003 .

[45]  W. Bessler,et al.  Low-temperature charging of lithium-ion cells part I: Electrochemical modeling and experimental investigation of degradation behavior , 2014 .

[46]  R. Stephenson A and V , 1962, The British journal of ophthalmology.

[47]  Roland Zengerle,et al.  Three-dimensional electrochemical Li-ion battery modelling featuring a focused ion-beam/scanning electron microscopy based three-phase reconstruction of a LiCoO2 cathode , 2014 .

[48]  Bernard Haasdonk,et al.  Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation , 2012, SIAM J. Sci. Comput..

[49]  Ralph E. White,et al.  Reduction of Model Order Based on Proper Orthogonal Decomposition for Lithium-Ion Battery Simulations , 2009 .

[50]  Ann Marie Sastry,et al.  Mesoscale Modeling of a Li-Ion Polymer Cell , 2007 .

[51]  Mario Ohlberger,et al.  Model Reduction for Multiscale Lithium-Ion Battery Simulation , 2016, ENUMATH.

[52]  Volker Schmidt,et al.  Parametric stochastic 3D model for the microstructure of anodes in lithium-ion power cells , 2017 .

[53]  Jochen Zausch,et al.  Modeling of Species and Charge Transport in Li-Ion Batteries Based on Non-equilibrium Thermodynamics , 2010, NMA.

[54]  M. Doyle,et al.  Simulation and Optimization of the Dual Lithium Ion Insertion Cell , 1994 .

[55]  S. Griffis EDITOR , 1997, Journal of Navigation.

[56]  Volker Schmidt,et al.  A New Approach to Model‐Based Simulation of Disordered Polymer Blend Solar Cells , 2012 .

[57]  Rohan Akolkar,et al.  Mathematical model of the dendritic growth during lithium electrodeposition , 2013 .

[58]  S. Torquato,et al.  Random Heterogeneous Materials: Microstructure and Macroscopic Properties , 2005 .

[59]  Charles W. Monroe,et al.  Dendrite Growth in Lithium/Polymer Systems A Propagation Model for Liquid Electrolytes under Galvanostatic Conditions , 2003 .

[60]  Michael Buchholz,et al.  Low-temperature charging of lithium-ion cells Part II: Model reduction and application , 2014 .

[61]  Volker Schmidt,et al.  Stochastic 3D modeling of the microstructure of lithium-ion battery anodes via Gaussian random fields on the sphere , 2015 .

[62]  Ralph E. White,et al.  Capacity Fade Mechanisms and Side Reactions in Lithium‐Ion Batteries , 1998 .

[63]  J. Newman,et al.  Porous‐electrode theory with battery applications , 1975 .

[64]  Arnulf Latz,et al.  Influence of local lithium metal deposition in 3D microstructures on local and global behavior of Lithium-ion batteries , 2016 .

[65]  M. Doyle,et al.  Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell , 1993 .

[66]  L. Sirovich TURBULENCE AND THE DYNAMICS OF COHERENT STRUCTURES PART I : COHERENT STRUCTURES , 2016 .

[67]  Volker Schmidt,et al.  Stochastic modeling and predictive simulations for the microstructure of organic semiconductor films processed with different spin coating velocities , 2015 .

[68]  Alessandro Ledda,et al.  Mathematische morfologie in de beeldverwerking Mathematical Morphology in Image Processing , 2007 .

[69]  Ralph E. White,et al.  Review of Models for Predicting the Cycling Performance of Lithium Ion Batteries , 2006 .

[70]  L. Sirovich Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .