Compositional Data and Network Analysis Identify Statistically Inferred Domains of Critical Elements in Municipal Solid Waste Incineration Fly Ash

Municipal solid waste incineration (MSWI) fly ash is an environmentally challenging residue and a potential secondary source of critical raw materials. This study investigated the occurrence and geochemical relationships of 24 selected major, critical, and trace elements or element groups in 30 samples collected from a Polish MSWI facility. Left-censored concentrations were treated using Tobit regression, whereas compositional data analysis (CoDA), non-negative matrix factorization (NMF), consensus analysis, and bootstrap resampling were applied to identify and evaluate multielement associations. Three statistically inferred compositional domains were distinguished: an Sb-Tl-Be domain consistent with volatilization, gas-phase transport, condensation, and capture during flue-gas treatment; a mixed Fe-Zn-Cu-Co domain compatible with mineral, metallic, and thermochemical contributions; and a comparatively stable P-Mg-Sr-Li-Sc-REE assemblage associated with matrix-related constituents. Consensus and bootstrap analyses supported the reproducibility of the dominant associations within the investigated dataset, but the inferred domains should be treated as process hypotheses rather than as directly verified mineralogical phases. Comparison with published MSWI residue data showed that most concentrations fall within reported ranges, whereas volatile and technology-related elements display greater inter-facility variability than matrix-associated elements. The proposed workflow provides a reproducible framework for identifying statistically supported element associations and for prioritizing subsequent mineralogical, leaching, mass-balance, and recovery tests.