Diagnostic Decomposition of Single-Scalar Severity Descriptors in Biomass Torrefaction: A SIC–CO Framework

Severity factors are widely used to compress torrefaction temperature–time history into a single scalar descriptor. However, whether such scalar representations are structurally sufficient to describe realised conversion across heterogeneous biomass samples remains unclear. In this study, we evaluated the adequacy of single-scalar severity descriptors using a literature-derived dry torrefaction dataset comprising 154 observations from 7 published studies, covering multiple biomass categories and operating conditions. A severity factor, SF(α), was formulated, and its scaling parameter α was optimised through a systematic α-sweep to maximise its relationship with the experimentally determined extent of conversion (EOC). Based on the optimised formulation, EOC was decomposed into severity-implied conversion (SIC) and conversion offset (CO), separating the dominant severity-controlled trajectory from sample-specific deviations. The optimised formulation (α* = 65.1) showed a strong global correlation with EOC (R2 = 0.8593), confirming that severity captures the main average conversion trend. However, nested model comparisons showed that including CO consistently improved explanatory power for both absolute fuel properties and enhancement ratios, with the greatest gains in enhancement space. SIC and CO accounted for 85.9% and 14.1% of the total variance, respectively, indicating that a non-negligible component of conversion variability was not captured by the single severity descriptor. These results show that, although a single severity scalar is useful for describing dataset-level trends, it does not fully resolve sample-level torrefaction behaviour within the analysed dataset. The SIC–CO framework is therefore proposed not as a new severity index or a pre-measurement predictive model, but as a post hoc diagnostic framework for identifying the explanatory limits of scalar severity representations in biomass torrefaction analysis.