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Abstract This study evaluates the main effects of including 'non-ideal' bio-physical-chemical corrections in high-solids anaerobic digestion (HS-AD) of the organic fraction of municipal solid waste (OFMSW), at total solid (TS) between 10 and 40%. As a novel approach, a simple 'non-ideal' module, accounting for the effects of ionic strength (I) on the main acid-base equilibriums, was coupled to a HS-AD model, to jointly evaluate the effects of 'non-ideality' and the TS content dynamics on the HS-AD bio-physical-chemistry. 'Non-ideality' influenced the pH, concentration of inhibitors (i.e. NH 3), and liquid-gas transfer (i.e. CO 2), particularly at higher TS (i.e. ≥ 20%). Meanwhile, fitting the experimental data for batch assays at 15% TS showed that HS-AD of OFMSW might be operated at I ≥ 0.5 M. Therefore, all HS-AD simulations should account for 'non-ideal' corrections, when assessing the main inhibitory mechanisms (i.e. NH 3 buildup and acidification) potentially occurring in HS-AD of OFMSW. Graphical abstract Image 1 Highlights • Ionic strength can be higher than 0.5 M in high-solids anaerobic digestion. • Non-ideality strongly affects NH 3 inhibition and CO 2 liquid-gas transfer. • Non-ideal effects on anaerobic digestion are exacerbated at total solids ≥20%. • High-solids simulations jointly require non-ideality and reactor mass/volume dynamics. • Non-ideality is interrelated to NH 3 inhibition parameters and the model structure. [ABSTRACT FROM AUTHOR]