Abstract
Several mathematical models have been developed in anaerobic digestion systems and a variety of methods have been used for parameter estimation and model validation. However, structural and parametric identifiability questions are relatively seldom addressed in the reported AD modeling studies. This paper presents a 3-step procedure for the reliable estimation of a set of kinetic and stoichiometric parameters in a simplified model of the anaerobic digestion process. This procedure includes the application of global sensitivity analysis, which allows to evaluate the interaction among the identified parameters, multi-start strategy that gives a picture of the possible local minima and the selection of optimization criteria or cost functions. This procedure is applied to the experimental data collected from a lab-scale sequencing batch reactor. Two kinetic parameters and two stoichiometric coefficients are estimated and their accuracy was also determined. The classical least-squares cost function appears to be the best choice in this case study.
Similar content being viewed by others
References
Batstone DJ, Keller J, Angelidaki I, Kalyuzhnyi SV, Pavlostathis SG, Rozzi A, Sanders WTM, Siegrist H, Vavilin VA (2002) The IWA anaerobic digestion model no. 1 (ADM1). Water Sci Technol 45(10):65–73
Siegrist H, Vogt D, Garcia-Heras J, Gujer W (2002) Mathematical model for meso- and thermophilic anaerobic sewage sludge digestion. Environ Sci Technol 36(5):1113–1123
Haag JE, Vande Wouwer A, Queinnec I (2003) Macroscopic modelling and identification of an anaerobic waste treatment process. Chem Eng Sci 58:4307–4316
Noykova N, Muller TG, Gyllenberg M, Timmer J (2002) Quantitative analyses of anaerobic wastewater treatment processes: identifiability and parameter estimation. Biotechnol Bioeng 78(1):89–103
Bernard O, Hadj-Sadok Z, Dochain D, Genovesi A, Steyer JP (2001) Dynamical model development and parameter identification for an anaerobic wastewater treatment process. Biotechnol Bioeng 75(4):424–438
Jeong HS, Suh CW, Lim JL, Lee SH, Shin HS (2005) Analysis and application of ADM1 for anaerobic methane production. Bioprocess Biosys Eng 27(2):81–89
Noykova N, Gyllenberg M (2000) Sensitivity analysis and parameter estimation in a model of anaerobic wastewater treatment processes with substrate inhibition. Bioprocess Eng 23:343–349
Saltelli A, Tarantola S, Campolongo F, Ratto M (2004) Sensitivity analysis in practice. A guide to assessing scientific models. Probability and Statistics series, Wiley, New York
Mailier J, Delmotte A, Cloutier M, Jolicoeur M, Wouwer AV (2011) Parametric sensitivity analysis and reduction of a detailed nutritional model of plant cell cultures. Biotechnol Bioeng 108(5):1108–1118
Sin G, Gernaey KV, Neumann MB, Van Loosdrecht MCM, Gujer W (2011) Global sensitivity analysis in wastewater treatment plant model applications: prioritizing sources of uncertainty. Water Res 45(2):639–651
Walter E, Pronzato L (1997) Identification of parametric models from experimental data. Springer-Verlag, Berlin
Lopez I, Borzacconi L (2009) Modelling a full scale UASB reactor using a COD global balance approach and state observers. Chem Eng J 146:1–5
Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simulat 55(1–3):271–280
Schmidt H, Jirstrand M (2006) Systems Biology Toolbox for MATLAB: a computational platform for research in systems biology. Bioinformatics 22(4):514–515. http://www.sbtoolbox2.org
Machado VC, Tapia G, Gabriel D, Lafuente J, Baeza JA (2009) Systematic identifiability study based on the Fisher information matrix for reducing the number of parameters calibration of an activated sludge model. Environ Model Software 24(11):1274–1284
D’Errico J (2005) Bound constrained optimization using fminsearch: fminsearchbnd. Matlab® Central. Available at http://www.mathworks.com/matlabcentral/fileexchange/8277
Sanchez JM, Arijo S, Muñoz MA, Morinigo MA, Borrego JJ (1994) Microbial colonization of different support materials used to enhance the methanogenic process. Appl Microbiol Biotechnol 41(4):480–486
Lokshina L, Vavilin V, Kettunen H, Rintala J, Holliger C, Nozhevnikova A (2001) Evaluation of kinetic coefficients using integrated Monod and Haldane models for low-temperature acetoclastic methanogenesis. Water Res 35(12):2913–2922
Kesavan P, Law VJ (2005) Practical identifiability of parameters in Monod kinetics and statistical analysis of residuals. Biochem Eng J 24(2):95–104
Palatsi J, Illa J, Prenafeta-Boldu FX, Laureni M, Fernandez B, Angelidaki I, Flotats X (2010) Long-chain fatty acids inhibition and adaptation process in anaerobic thermophilic digestion: Batch tests, microbial community structure and mathematical modelling. Bioresour Technol 101(7):2243–2251
Flotats X, Palatsi J, Ahring BK, Angelidaki I (2006) Identifiability study of the proteins degradation model, based on ADM1, using simultaneous batch experiments. Water Sci Technol 54(4):31–39
Batstone DJ, Torrijos M, Ruiz C, Schmidt JE (2004) Use of an anaerobic sequencing batch reactor for parameter estimation in modelling of anaerobic digestion. Water Sci Technol 50(10):295–303
Acknowledgments
This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its author(s).This study is also supported by a grant from Belspo (Belgian Science Policy) through its Postdoc fellowships to non-EU researchers program.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Donoso-Bravo, A., Mailier, J., Ruiz-Filippi, G. et al. Identification in an anaerobic batch system: global sensitivity analysis, multi-start strategy and optimization criterion selection. Bioprocess Biosyst Eng 36, 35–43 (2013). https://doi.org/10.1007/s00449-012-0758-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00449-012-0758-5