Regression based state space adaptive model of two-phase anaerobic reactor Antonius Yudi Sendjaja a , Youming Tan a,b,⇑ , Santosh Pathak a , Yan Zhou a , Maszenan bin Abdul Majid c , Jian Lin Liu d , Wun Jern Ng a,c,e,⇑ a Advanced Environmental Biotechnology Center, Nanyang Environment and Water Research Institute, Nanyang Technological University, Singapore b School of Public Health, Shanghai Jiaotong University, Shanghai, PR China c Nanyang Environment and Water Research Institute, Nanyang Technological University, Singapore d Sembcorp Industries Ltd., Jurong Island, Singapore e School of Civil and Environmental Engineering, Nanyang Technological University, Singapore highlights  The discrete state space correlation among parameters in anaerobic reactor.  The relation is updated at every time point, giving it an adaptive feature.  The proposed algorithm to estimate methane generation from industrial waste. article info Article history: Received 21 January 2014 Received in revised form 3 November 2014 Accepted 9 November 2014 Available online 23 December 2014 Keywords: Adaptive model Anaerobic reactor Process control Biogas Volatile fatty acids (VFAs) abstract In this paper, a linear state space model for the two-phase anaerobic reactor system was developed based on historical data. Subsequently, the model was used to predict its future behavior. The state space model developed involved correlation analysis and model development. The model would be updated at every time point when a new data set became available, giving it an ‘‘adaptive’’ feature. The model was then applied to monitor two-phase anaerobic co-digestion of a feed comprising 2 industrial secondary sludges and 2 industrial wastewaters. The case study showed the proposed model was able to provide good pre- dictions of various process parameters. In addition, it also predicted impending process failure and this would have allowed the operator to take necessary measures to prevent or reduce impact of such failure during plant operation. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction The anaerobic process converts organic carbon into methane gas and is attractive as it has the potential to address two main issues simultaneously, organic wastes treatment and energy recov- ery via the biogas generated. Various types of organic wastes, such as industrial and municipal wastes, livestock manure, and food wastes, can be utilized as organic carbon sources (Gunaseelan, 1997; Van Starkenburg, 1997; Molino et al., 2012). The anaerobic process can be divided into two parts: acidogen- esis, which converts complex organic substrates into acetic acid, mediated by the Eubacteria consortium, and methanogenesis, which generates methane gas from acetic acid or from carbon dioxide and hydrogen by the methanogens (Gujer and Zehnder, 1983). Acidogenesis and methanogenesis can be performed either in a single reactor or in separate reactors. They are usually referred to then as the single stage and two-phase anaerobic process, respectively. As compared to the single stage process, the two- phase anaerobic process allows optimization of each individual process with the intention to increase conversion (Azbar and Speece, 2001). Moreover, as later shown in this work, the first phase can act as an early warning of a failing process. In order to gain better understanding and control of the anaer- obic process, mathematical models of the anaerobic reaction have been developed. These models were typically developed from empirical equations involving several constants. These constants were subsequently sought using experimental data and statistical analysis. One of the most commonly used empirical model is anaerobic digestion model number 1 (ADM1) (Batstone et al., http://dx.doi.org/10.1016/j.chemosphere.2014.11.027 0045-6535/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding authors at: Advanced Environmental Biotechnology Center, Nanyang Environment and Water Research Institute, Nanyang Technological University, Singapore. Tel.: +65 6592 1833 (Y. Tan), +65 6790 6813 (W.J. Ng). E-mail addresses: youmingtan@ntu.edu.sg (Y. Tan), wjng@ntu.edu.sg (W.J. Ng). Chemosphere 140 (2015) 159–166 Contents lists available at ScienceDirect Chemosphere journal homepage: www.elsevier.com/locate/chemosphere