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Leaching kinetics of valuable metals from waste Li-ion batteries using neural network approach

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A Correction to this article was published on 08 December 2022

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Abstract

The kinetic study of valuable metals recovery from waste lithium-ion batteries (LIBs) using the artificial neural network (ANN) was investigated. A multilayer feed-forward artificial neural network with back-propagation learning algorithm was used for kinetic analysis of Co, Mn, Ni, and Li leaching from waste LIBs using H2SO4 in the presence of H2O2. Required data for ANNs learning were generated using various random combinations of kinetic parameters in their extended ranges (i.e., activation energy and Arrhenius equation constant) as well as the most common solid–liquid reaction model. The predictive accuracy of the model was comparable with the correlation coefficient of the model fitting method (R2). Results showed that the model developed in this study can be a useful tool in accurately predicting the kinetics of leaching reactions. The activation energy of Co, Mn, Ni, and Li recovery from waste LIBs using the proposed method calculated to be 40.83, 43.35, 39.06, and 27.30 kJmol−1, respectively, and leaching reaction for metals found to follow the surface chemical reaction model.

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Fig. 1

This figure is reproduced with permission from [42], Copyright Elsevier (2016)

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Author information

Authors and Affiliations

  1. New Sciences and Technologies, Shahid Bahonar University of Kerman, P. O. Box No. 76135-133, Kerman, Iran

    Hossein Ebrahimzade

  2. Department of Materials Science and Engineering, Shahid Bahonar University of Kerman, P. O. Box No. 76135-133, Kerman, Iran

    Gholam Reza Khayati

  3. Department of Chemical Engineering, Shahid Bahonar University of Kerman, P. O. Box No. 76135-133, Kerman, Iran

    Mahin Schaffie

Authors
  1. Hossein Ebrahimzade
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  2. Gholam Reza Khayati
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  3. Mahin Schaffie
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Corresponding author

Correspondence to Gholam Reza Khayati.

Appendix

Appendix

The present example illustrates how to calculate the activation energy and the reaction mechanism using input and output data with ANN models #1 and #2, respectively. Input variables 1–35 are the reaction fraction values for the reaction times 10, 15, …, 80 min in the corresponding temperature of 25, 35, …, 60 °C. Simulated reaction model with ANN#2 is the M3 type (Table 1).

Input 1

Input 2

Input 3

Input 4

Input 5

Input 6

Input 7

Input 8

0.0370

0.0774

0.1047

0.1386

0.1808

0.0648

0.0949

0.1505

Input 9

Input 10

Input 11

Input 12

Input 13

Input 14

Input 15

Input 16

0.1967

0.2459

0.0972

0.1191

0.1990

0.2807

0.3684

0.1644

Input 17

Input 18

Input 19

Input 20

Input 21

Input 22

Input 23

Input 24

0.2057

0.2654

0.3815

0.4506

0.1923

0.3185

0.3966

0.5088

Input 25

Input 26

Input 27

Input 28

Input 29

Input 30

Input 31

Input 32

0.5882

0.2632

0.4178

0.5815

0.6856

0.7117

0.3347

0.6938

Input 33

Input 34

Input 35

     

0.7185

0.7210

0.7392

     

The output of the ANN model #2 shows that reaction type is third in the following row (Table 1: M1, M2, M3, …, M11, M12), i.e., the model corresponding to the output 3: two-third-order kinetics (shrinking core with chemical reaction-controlled process).

Output 1

Output 2

Output 3

Output 4

Output 5

Output 6

Output 7

Output 8

Output 9

Output 10

Output 11

Output 12

0.000057

0.000088

0.984007

0.000006

0.000000

0.000000

0.000004

0.000000

0.000000

0.000001

0.000000

0.000017

The numerical values of the other models output are zero or close to zero and are not chosen as the correct reaction model. This result can be confirmed further using the complementary analyzes. However, by developing the ANN kinetic analysis method for multi-stage reactions, one can probably determine the contribution of each model to the overall reaction mechanism.

The ANN model #1 calculated activation energy value is:

Output 1

 

40,8260

 

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Ebrahimzade, H., Khayati, G.R. & Schaffie, M. Leaching kinetics of valuable metals from waste Li-ion batteries using neural network approach. J Mater Cycles Waste Manag 20, 2117–2129 (2018). https://doi.org/10.1007/s10163-018-0766-x

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  • DOI: https://doi.org/10.1007/s10163-018-0766-x

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