The valorisation of waste generated during orange juice manufacturing (OPW) by anaerobic digestion is gaining attention due to the several economic, social and environmental advantages of the process. Given that anaerobic digestion is a process that requires rigorous control to improve the biodegradability of the waste and methane production, this paper highlights the importance of modelling for adequate process monitoring. Specifically, this study fitted three sigmoidal models (Logistic, Gompertz, and Sigmoid models) to methane production from OPW. At laboratory scale, two thermophilic continuously stirred-tank reactors working in semi-continuous mode was used. D-limonene removal of 70% was previously reached by applying a pre-treatment on OPW. The results showed a biodegradability of the pre-treated waste of up to 96.7% in COD. The Logistic, Gompertz and Sigmoid models fitted adequately to cumulative methane production (R-2 was 0.9691; 0.9492 and 0.9511, respectively). However, the Logistic model showed the best fit to the experimental data even under critical conditions. Specifically, the Logistic model predicted the maximum methane production rate within loads of 2.5-5.0g COD/L. Therefore, this model might be very useful in predicting the maximum methane production rate and the maximum load that could be added without the inhibition of anaerobic digestion at real scale. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.