The "Anaerobic Digestion Model No. 1'' (ADM1) was modified in the study by improving the bio-chemical framework and integrating a more detailed physico-chemical framework. Inorganic carbon and nitrogen balance terms were introduced to resolve the discrepancies in the original bio-chemical framework between the carbon and nitrogen contents in the degraders and substrates. More inorganic components and solids precipitation processes were included in the physico-chemical framework of ADM1. The modified ADM1 was validated with the experimental data and used to investigate the effects of calcium ions, magnesium ions, inorganic phosphorus and inorganic nitrogen on anaerobic digestion in batch reactor. It was found that the entire anaerobic digestion process might exist an optimal initial concentration of inorganic nitrogen for methane gas production in the presence of calcium ions, magnesium ions and inorganic phosphorus. (C) 2015 Elsevier Ltd. All rights reserved.