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

• Novel hybrid SCM-ANFIS-ANN modelling approach for improved copper(II) leaching. • Machine learning for enhanced prediction accuracy. • Advanced computational methods for soil remediation. • Diffusion-controlled kinetics. • Cost-effective solution for industrial soil remediation. 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.