Available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/watres Mathematical modelling of autothermal thermophilic aerobic digesters J. Gomez a,b,Ã , M. de Gracia a , E. Ayesa a , J.L. Garcia-Heras a a CEIT and Tecnun (University of Navarra), Manuel Lardizabal 15, 20018 San Sebastian, Spain b Navarra de Infraestructuras Locales, S.A. (NILSA), Avda. Baran ˜ ain, 22, 31008 Pamplona, Spain article info Article history: Received 23 June 2006 Received in revised form 20 October 2006 Accepted 28 November 2006 Available online 29 January 2007 Keywords: Autothermal thermophilic aerobic digestion (ATAD) Calibration Energy model Influent characterization Modelling Specific heat yield abstract This paper presents a new mathematical model for Autothermal Thermophilic Aerobic Digesters. The reactor has been modelled as two completely mixed volumes to separately predict the behaviour of the liquid and gaseous phases as well as the interrelation between them. The model includes biochemical transformations based on the standard Activated Sludge Models of IWA, as well as physico-chemical transformations associated with the chemical equilibria and the mass transfer between the liquid and the gaseous phases similar to those proposed in the ADM1 of IWA. An energy balance has also been included in the model in order to predict the temperature of the system. This thermal balance takes into account all those biochemical and physico-chemical transformations that entail the most relevant heat interchanges. Reactor performance has been explored by simulation in two different scenarios: in the first where it acts as the initial stage in a Dual system, and in the second where it acts as a single-stage treatment. Each scenario enabled the identification of the relevance of the different parameters. & 2007 Elsevier Ltd. All rights reserved. 1. Introduction Autothermal thermophilic aerobic digestion (ATAD) is an advanced sewage sludge treatment that provides hygieniza- tion. The process has a self-heating ability and removes pathogens when working at a temperature of at least 55 1C for 20 h as a batch (European Commission, 2000). This operation pattern complies with the regulations for obtaining Class A biosolids (US EPA, 2003). Many experimental studies have been carried out to analyse the ATAD technology in particular cases (Messenger et al., 1993; Kelly and Warren, 1995; Gomez et al., 2007) leading to very helpful process guidelines. However, experiments have limitations concerning time and feasibility. These limitations, combined with the very long time-response of many of the involved process transformations, suggest the usefulnessof a simulator based on a dynamic model of ATAD. Using the model certain significant aspects of this technology could thus be explored in a fast and easy way and the performance of ATAD reactors in different scenarios could be predicted. In view of the fact that the temperature in the process is one of the most important aspects to take into account, a thermal model could help develop a more realistic overall model. Previous works on modelling the heat balance can be found in Vismara (1985), Messenger et al. (1990, 1993) and Gillot and Vanrolleghem (2003). This paper presents a mathematical model to predict the main biodegradation transformations, physico-chemical reactions and energy interchange occurring in an ATAD reactor. The overall model is made up of two sub-models, namely, that of mass balance and that of energy balance. The biochemical transformations are presented in matrix ARTICLE IN PRESS 0043-1354/$ - see front matter & 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2006.11.042 Ã Corresponding author. Navarra de Infraestructuras Locales, S.A. (NILSA), Avda. Baran ˜ ain, 22, 31008 Pamplona, Spain. Tel.: +34 948176928; fax: +34 948174960. E-mail address: jgomez@nilsa.com (J. Gomez). WATER RESEARCH 41 (2007) 959– 968