Application of shrinking core and soft computing models (ANFIS and ANN) for the leaching of copper (II) from artificially contaminated soil

Abstract

This leaching experiment optimises copper (II) leaching using sulfuric acid by integrating the shrinking core kinetic model with machine learning techniques, adaptive neuro-fuzzy inference systems (ANFIS), and artificial neural networks (ANN), providing a hybrid computational framework that significantly enhances predictive accuracy and leaching efficiency compared to conventional empirical approaches. The factors in the leaching process, such as acid concentration, leaching time, temperature, soil-to-solution ratio, and stirring speed, were investigated for the removal of copper (II). Experimental and computational analyses revealed that leaching efficiency is governed by diffusion through insoluble sulfate/oxide layers, with agitation speed (reducing boundary layers) and acid concentration (enhancing H⁺ access) as key drivers. Under optimal conditions (pH 5.96, 0.88 M H₂SO₄, 274 rpm, 12.5 g/200 mL solid-liquid ratio), ANFIS predicted 99.8 % Cu(II) recovery, validated experimentally. Kinetic analysis confirmed product-layer diffusion control (R² > 0.99), supported by a low activation energy (17.96 kJ/mol) and rate suppression at high pH/solid ratios. The ANN (10 hidden layers, 4 inputs) outperformed ANFIS, achieving superior predictive accuracy (R² = 0.995 vs. 0.986) and lower error (RMSE: 0.061 vs. 0.129). Among the performance metrics, R² is the most critical, indicating that both models explain >98.6 % of variance in leaching behaviour well above the acceptable threshold (R² > 0.9) for reliable industrial prediction. The exceptionally low RMSE values (<0.13) further confirm minimal deviation between experimental and predicted results. This hybrid framework bridges mechanistic insight with AI-driven optimisation, offering a 15–20 % efficiency gain over conventional methods while diagnosing rate-limiting steps for scalable applications.