Machine-Learning Modeling of Sulfuric-Acid Leaching of Metalliferous Oil-Shale Ash: Predictive Performance, Feature Importance, and Confounding in an Unbalanced Experimental Design

Abstract

A dataset of 28 sulfuric-acid leaching experiments on metalliferous oil-shale ash was analyzed using multiple linear regression, second-order polynomial regression, and random forest models to predict the recovery of uranium, thorium, vanadium, molybdenum, scandium, and rhenium. The input variables were liquid-to-solid ratio, temperature, leaching time, and H₂SO₄ concentration. Because of the small sample size, model performance was evaluated by leave-one-out cross-validation (LOO-CV). Random forest provided the highest predictive performance for all six elements, with LOO-CV R² values of 0.823-0.906, whereas multiple linear regression gave 0.515-0.784. Polynomial regression performed similarly to random forest for most elements, confirming a substantial nonlinear component in the response surface. Random-forest feature importance attributed approximately 89-98% of total model importance to sulfuric-acid concentration. In the full linear model, the H₂SO₄ coefficient was significant for all elements (p < 0.001). In contrast, the temperature coefficient was negative in the pooled regression but statistically non-significant for five of the six elements. A controlled comparison at 50 g L⁻¹ H₂SO₄ reversed the apparent temperature effect; for uranium, mean recovery increased from 48.0% at 30 °C to 51.2% at 75 °C. The sign reversal is consistent with confounding caused by an unbalanced experimental design rather than a physically adverse temperature effect. The study shows that nonlinear machinelearning models can improve prediction for small hydrometallurgical datasets, but interpretable process conclusions require explicit diagnosis of experimental-design structure, confounding, and uncertainty