A mathematical model is developed in this study to simulate the performance and fates of carbon (C), nitrogen (N) and phosphorus (P) in wet and high-total solid (TS) anaerobic digestion (AD) processes. The "Anaerobic Digestion Model No.1" (ADM1) is improved by adding inorganic components and integrating the inhibition of high-TS and liquid-solid processes. The model's outputs are validated with experimental results obtained from a semi-continuous reactor, with pig manure as a single substrate at wet and high-TS operation stages. The predicted C (methane production and volatile fatty acid concentrations), N (ammonia nitrogen concentrations) and P (phosphorus concentrations) fates are reasonable and exhibit good accuracy. The model is subsequently applied to simulate CH4 production under different hydraulic retention times and organic loading rates. The simulation analysis demonstrates that pret-reatments, such as promoting the hydrolysis and biodegradility of substrate and immobilising strains, are necessary in the high-TS AD process for pig manure to enhance performance. This study provides guidance for the future optimisation of process and nutrient recycling in AD. (C) 2019 Elsevier Ltd. All rights reserved.