Abstract
The complexity of copper-cobalt-bearing ores has prompted continuous research and development projects. The prediction and modelling of the dissolution behaviour would add value of the metal recovery and process efficiency. This work dealt with the optimization and prediction of metallurgical results of ores subjected to leaching by means of three approaches, the first is based on case-based reasoning (CBR), the second is response surface methodology (RSM) and the last is based on artificial neural network (ANN). The ores studied come from 6 different deposits of the Congolese copperbelt including Kamfundwa, Kamatanda, Mukondo, Kimpe, Luiswishi and Tilwizembe. All these ores are oxidized (average grades of 2.0 %Cu and 0.8 %Co) to siliceous gangue (Si2O > 45%).
Taking into account the specificities of a design of experiments (DOE), 6 DOEs were used to generate the data necessary for modelling the leaching process. The data obtained were grouped into 4 series of results: (1) Principal Components Analysis (PCA) - Expert system (CBR), (2) Response surface methodology (RSM), (3) Case-based reasoning approch (CBR) and (4) Artificial neural network (ANN).
Multivariate analysis based on the principal component analysis (PCA) approach was the tool to assist in the interpretation of the results. Four ores were leached under the very same operating conditions using four different cobalt reducing agents (Fe2+, Fe, Cu, Na2S2O5). The PCA approach made it possible to highlight the leaching behaviour of the ores from copperbelt deposits by detecting the main variables of the process and identifying the ore/reducer groups with similar metallurgical performance.
The data and results of the principal component analysis were formalized to generate a new database that served as the basis of facts for the expert system whose code was written in Python language implemented in the Jupyter environment. The basis of the rules was drawn up on the basis of the results obtained in this study and on the industrial results. This expert system was based on the case-based reasoning principle, the request focused mainly on the amount of reducing agent. The inferences made were satisfactory, with the overall similarity values close to 1 (0.93). Box-Behenken design (BBD) L27(34) using the RSM gave equations modelling the leaching yields of Co and Cu. Initially, 7 parameters were modeled by a multiple linear regression according to the Plackett-Burman screening design L12(27). From the analysis of the main effects, 4 parameters were found to be statistically significant: the solid percentage (15, 27.5 and 40%), time (45, 90 and 135 h), particle size (53, 75 and 105 μm) and concentration of the Fe2+ ion (2, 4 and 6 g/L). Quadratic models developed according to the RSM made it possible to simultaneously optimize the leaching yields of Cu and Co by means of the desirability function available in the Minitab 18 software. With a composite desirability of 0.94, the optimal parameters (pourcentsolide = 15%, time = 58.5 minutes, particle size = - 95.12 μm, Fe2+ = 6 g/L) gave respective yields of Cu and Co of 93, 46 and 89, 43%.
The case-based reasoning (CBR) approach focused on defining a function measuring the level of similarity between a current case and a previously known and optimized case, a metric was interpolated and implemented in the myCBR 3.1 software. The results obtained from the BBD and the Central Composite Design (CCD) are well suited to be used with confidence as a database because higher similarity values (0.98 and 0.97 close to 1) were obtained. The second CBR model relied on 17 attributes and 20 cases to form the knowledge database. The leaching data were modelled by an overall similarity function which gave the value of 0.86 and the predictions were made. These results showed a fairly good fit with the model validation results.
The artificial neural network (ANN) approach has adapted to the results of experimental designs based on the RSM. ANN was used for the prediction of Cu and Co leaching yields. The MLP {4-7-1} (Multilayer Perceptron 4-7-1) neural structure gave the best results (R2= 0.96) due to the hyperbolic tangent activation function used in the hidden layer and the gradient backpropagation algorithm.
Keywords: Leaching, Modelling, Case-based reasoning, Artificial neural network, Response surface methodology, Expert system, Hydrometallurgy, Copperbelt Cu-Co ores.