A novel predictive model for estimation of cobalt leaching from waste Li-ion batteries: Application of genetic programming for design
Graphical abstract
Introduction
Increasing the applications of lithium-ion secondary batteries in the world has required intensive studies for the recycling of main components from waste LIBs in a beneficial way to prevent from environmental pollution as well as alternative resources for precious metals [1]. LIBs are widely used as electrochemical power sources in electronic devices and contain as cobalt, lithium, copper and an organic electrolyte. Extensive studies have been carried out for development of the hydrometallurgical processes to recycle the valuable metals from the LIBs waste batteries [2], [3], [4], [5], [6], [7]. On the other hand, the optimum recovery of the main metals (e.g., Co, Li) by leaching of LIBs is one of the most important factors that determine whether the recycling of LIBs can be carried out in a time frame applicable for the industrial applications. Therefore, to facilitate the process optimization and to control the design of leaching processes, to the best of our knowledge, accurate modeling of the reactions has considerable significance.
The leaching reactions are complex with strong non-linearity, which cannot be reflected accurately by a simple modeling approach such as regression analysis. Considering the importance and complexity of leaching reactions in the recycling of LIBs, it was necessary to apply the modern techniques for comprehensive study and determination of optimum recovery of the metals present in the electrode active material of waste LIBs.
Recently, gene expression programming (GEP) is one of the modern and efficient tools to obtain a mathematical description of the physicochemical process. GEP is the modified form of the conventional genetic programming [8] approaches which has been developed by Ferreira [9]. A notable advantage of GEP is its capability to specify accurately the phenotype given the sequence of a gene, and vice versa which is assigned as Karva language [10]. The GEP method has been applied to recognize the manner of non-linear systems such as modeling of composite material fatigue behavior [11], prediction and scoring of human protein-protein interactions [12], prediction of discharge coefficient in rectangular side weirs [13], modeling of alumino silicate compressive damage [14], modeling and optimization of As(III) and As(V) adsorption on the tannin-formaldehyde (TFA) and tannin-aniline-formaldehyde (TAFA) resins [15] and the acidolysis behavior modeling of triolein and palmitic acid under the catalysis of immobilized sn-1, 3 lipase [16]. Evolutionary soft computing methods were also applied in the field of lithium-ion battery optimization and leaching reaction analysis. For instance, Zhang et al. [17] employed a multi-objective genetic algorithm for identifying the multi-physics structural model of lithium-ion batteries. Also, Hoseinian et al., [18] applied a hybrid of genetic algorithm and artificial neural network (GA-ANN) to predict the optimized conditions of copper oxide ore column leaching and concluded that the model can be used to predict the Cu recovery with a reasonable error. Xie et al. [19] using a state transition algorithm and kernel extreme learning machine methods modeled the leaching rate of alumina and leaching kinetics of diaspore with relative prediction errors within ±2%. The prediction accuracy of new evolutionary techniques, especially GEP for quantitative analysis in non-lınear problems is acceptable [20], [21], [22], [23], [24] and therefore, the method can be used to better understand and prediction of leaching reactions.
In the present study, the leached percentage of cobalt from waste lithium ion-batteries using H2SO4 in the presence of H2O2 is simulated with a new approach based on the GEP method. To the best of our knowledge, there is no relevant publication in the literature that model the recovery of cobalt from waste LIBs by means of GEP technique. To find the dependency of the leached percentage of cobalt on the operational parameters, i.e., sulfuric acid and hydrogen peroxide concentration, solid-liquid ratio, reaction temperature and leaching time, 42 reliable various experiments are carried out using leaching of waste LIBs cathode active materials. The experimental data employed to train and test of 8 models with various architectures. Finally, to demonstrate its predictive accuracy, the three best models were analyzed.
Section snippets
Materials and experimental procedure
Different types of waste LIBs were first discharged and dismantled manually to separate out into the cathodes, anodes, plastic separators and metal cases [25], [26]. Then, the cathode active material was collected and treated with N-Methyl-2-pyrrolidone (NMP; Merck, 99.5%) for an hour at 60 °C. After filtration, the resulted powder dried for 24 h at 50 °C and sieved with the screen of 0.5 mm. Thermal pretreatment of the resulting powder carried out at 700 °C for 5 h in a muffle to eliminate
Results and discussion
Fig. 3 shows the variation of statistical measures in training and testing of GEP models. Accordingly, R-square (Fig. 3a) and errors (Fig. 3b, c, and d) increased and decreased with the number of mathematical functions used in the training and test phases of models, respectively. Moreover, the R-square value of all models is higher than 0.95 and consequently, the proposed models are suitable for the prediction of the leached cobalt percentage. Based on Fig. 3a, the GEP-2, GEP-3 and GEP-8 models
Conclusion
The gene expression programming (GEP) was proposed to predict the leached cobalt percentage from the waste LIBs using H2SO4 in the presence of H2O2. The leaching reaction parameters affecting the leached percentage of cobalt were presented by introducing the concentration of the leaching species, reaction temperature, leaching time and solid-liquid ratio for training and testing of GEP models. Our proposed approach provides accurate predictions on the base of statistical measures of GEP model
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