Machine learning-guided rare-earth recovery from morupule B coal fly ash: XRD-informed mineralogy, mass-balanced HCl leaching and sparse-data optimization

Abstract Morupule B coal fly ash was evaluated as a secondary rare-earth-element (REE) resource by integrating the complete experimental record with X-ray diffraction (XRD), ICP-OES mass balance, machine learning, and uncertainty-guided experimental design. The source XRD pattern identifies a refractory mullite–quartz assemblage with trace iron oxides. All nine ICP-OES digestion records were retained, including four non-detects, and the recorded triplicates were recalculated before use. The dysprosium digest mean is $$0.04168\,\textrm{mg~L}^{-1}$$ from the three raw replicates rather than the inconsistent tabulated value, whereas the high erbium signal is retained but treated as requiring independent confirmation. After carrying the documented digestion dilution and leaching mass/volume through the balance, direct HCl extraction at $$25^{\circ}\textrm{C}$$ is in the single- to low-double-digit range rather than above 100%. The strongest experimental feature is a common maximum at $$1.2\,\textrm{mol L}^{-1}$$ HCl: 6.44% Ce, 16.91% Dy, 1.16% Er, 6.56% La, and 9.12% Nd. Nested leave-one-concentration-out validation was used for analysing a complete set of 16 observations for Ce, Dy, La and Nd. Support vector regression (SVR) performed best among the tested machine-learning models under nested concentration-grouped validation (MAE 2.72 and RMSE 3.47 percentage points; $$R^2=0.134$$ ), but its RMSE was 15.2% higher than the element-mean baseline. The fitted concentration response indicates a maximum at $$1.258\,\textrm{mol L}^{-1}$$ , and the response-seeking follow up point determined by Gaussian-process regression (GPR) is: $$1.248\,\textrm{mol L}^{-1}$$ , the largest unresolved region determined by GPR is approximately: $$1.35\,\textrm{mol L}^{-1}$$ . The measured extraction results at 1.2 M are uncorrelated with standard-state oxide enthalpies or entropies (Spearman correlations ρ = 0.10 for the five quantified REEs), meaning that they cannot be described by oxide standard-state energetics alone. The outcome is a linkage between the actual XRD, raw analytical data, mass balance and machine learning, without synthetic observations and a narrowed experimental trajectory for Morupule B ash.