Phenomenological model‐based analysis of lithium batteries: Discharge, charge, relaxation times studies, and cycles analysis

Henquín, E. R.; Aguirre, Pío A.

doi:10.1002/aic.14618

Cited by 8 publications

(23 citation statements)

References 24 publications

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“…As previously stated, the mathematical model being used has its bases published in Ref. and is adjusted to a system of more than one particle. Thus, the salt balance in the electrolyte is

\frac{d C_{normale}^{normalA}}{d t} = \sum_{m} j_{normalm}^{normalA} true(1 - t_{+}^{normalo} true) \frac{a_{e / s, m}^{normalA}}{v_{normale}^{normalA}} n_{normalm}^{} - K_{normall}^{normalA} true(C_{normale}^{normalA} - C_{normale}^{normalS} true) \frac{a_{tr . e}^{normalA}}{v_{normale}^{normalA}}

\frac{d C_{normale}^{normalC}}{d t} = \sum_{m} - j_{normalm}^{normalC} true(1 - t_{+}^{normalo} true) \frac{a_{e / s, m}^{normalC}}{v_{normale}^{normalC}} n_{normalm} + K_{normall}^{normalC} true(C_{normale}^{normalS} - C_{normale}^{normalC} true) \frac{a_{tr . e}^{normalC}}{v_{normale}^{normalC}}

\frac{d C_{normale}^{normalS}}{d t} = K_{normall}^{normalA} true(C_{normale}^{normalA} - C_{normale}^{normalS} true) \frac{a_{tr . e}^{normalA}}{v_{normale}^{normalS}} - K_{normall}^{normalC} true(C_{normale}^{normalS}

…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…The heretofore defined equations involve the volume fraction of phase j in compartment i:

ɛ_{normalj}^{normali}

is defined in the same way as reported in Ref. . In this work, however, a study where batteries are made up of different particle sizes is performed.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…Other authors have worked on simplified mathematical models that are analogous to electric circuits, thus obtaining very fast models involving lesser phenomenological predictive capacity compared to the previously mentioned. In a previous paper, we presented a simplified mathematical model, based on mass and energy balance equations. The main advantages of our model compared with other models mentioned above are that (i) currents balances are used correctly and properly (Eq.…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, and as it was mentioned in Ref. , these models have multiple differential equations coupled with their contour conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, in this article, the mathematical model presented in Ref. is extended and adapted to calculate cell voltage, reaction rates, states of charge, equilibrium potentials, and other ohmic drops inside the battery, considering that electrodes are composed by particles of two different sizes. The model is validated by comparing theoretical predictions with experimental points of two batteries using different electrode materials.…”

Section: Introductionmentioning

confidence: 99%

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Model based analysis of lithium batteries considering particle‐size distribution

Henquín

Aguirre

2017

AIChE Journal

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Performance of lithium ion batteries whose electrodes are composed of particles of different sizes is studied. Simplified model developed in (Henquín and Aguirre, AIChE J. 2015; 61:90–102) is extended and the simulations are compared with experiments from the literature so as to validate this new model. The differences in current density observed in particles of different sizes, which are in contact, depend on particle size and state of charge. Internal particle to particle discharge currents are observed during relaxation times. A parametric study of the applied current and particle sizes of electrodes is performed to evaluate cell performance, with emphasis on cell voltage and final capacity measurement. The evolution of reaction rates on the surface of electrode particles and their corresponding states of charge are depicted. An analysis of relaxation times in terms of cell voltage, current density, equilibrium potentials, and overpotentials is included. © 2017 American Institute of Chemical Engineers AIChE J, 64: 904–915, 2018

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“…As previously stated, the mathematical model being used has its bases published in Ref. and is adjusted to a system of more than one particle. Thus, the salt balance in the electrolyte is

\frac{d C_{normale}^{normalA}}{d t} = \sum_{m} j_{normalm}^{normalA} true(1 - t_{+}^{normalo} true) \frac{a_{e / s, m}^{normalA}}{v_{normale}^{normalA}} n_{normalm}^{} - K_{normall}^{normalA} true(C_{normale}^{normalA} - C_{normale}^{normalS} true) \frac{a_{tr . e}^{normalA}}{v_{normale}^{normalA}}

\frac{d C_{normale}^{normalC}}{d t} = \sum_{m} - j_{normalm}^{normalC} true(1 - t_{+}^{normalo} true) \frac{a_{e / s, m}^{normalC}}{v_{normale}^{normalC}} n_{normalm} + K_{normall}^{normalC} true(C_{normale}^{normalS} - C_{normale}^{normalC} true) \frac{a_{tr . e}^{normalC}}{v_{normale}^{normalC}}

\frac{d C_{normale}^{normalS}}{d t} = K_{normall}^{normalA} true(C_{normale}^{normalA} - C_{normale}^{normalS} true) \frac{a_{tr . e}^{normalA}}{v_{normale}^{normalS}} - K_{normall}^{normalC} true(C_{normale}^{normalS}

…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…The heretofore defined equations involve the volume fraction of phase j in compartment i:

ɛ_{normalj}^{normali}

is defined in the same way as reported in Ref. . In this work, however, a study where batteries are made up of different particle sizes is performed.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, and as it was mentioned in Ref. , these models have multiple differential equations coupled with their contour conditions.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations