SHORT COMMUNICATION An autocatalytic kinetic model for describing microbial growth during fermentation Albert Ibarz • Pedro E. D. Augusto Received: 22 April 2014 / Accepted: 7 July 2014 / Published online: 22 July 2014 Ó Springer-Verlag Berlin Heidelberg 2014 Abstract The mathematical modelling of the behaviour of microbial growth is widely desired in order to control, predict and design food and bioproduct processing, stabil- ity and safety. This work develops and proposes a new semi-empirical mathematical model, based on an autocat- alytic kinetic, to describe the microbial growth through its biomass concentration. The proposed model was success- fully validated using 15 microbial growth patterns, cover- ing the three most important types of microorganisms in food and biotechnological processing (bacteria, yeasts and moulds). Its main advantages and limitations are discussed, as well as the interpretation of its parameters. It is shown that the new model can be used to describe the behaviour of microbial growth. Keywords Biochemical engineering  Bioprocessing  Kinetics  Modelling List of symbols a, b Parameters of model fit evaluation (Eq. 27) [different units] A, B Parameters for the partial fractions integration (Eq. 8) [different units] k Kinetic parameter of the reaction (Eq. 1) [g L -1 h -1 ] K 1 ,K 2 ,K 3 Parameters of the new model (Eq. 20) [g L -1 ,h -1 , dimensionless, respectively] M Microorganism biomass concentration [g L -1 ] M 0 Initial microorganism biomass concentration [g L -1 ] M ? Maximum microorganism biomass concentration [g L -1 ] MRSS Residual sum-of-squares values (Eq. 26) [(g L -1 ) 2 ] Q Fractional yield (Eqs. 3, 4) [dimensionless] S Substrate concentration [g L -1 ] S 0 Initial substrate concentration [g L -1 ] t Time [h] Introduction A mathematical model of the behaviour of microbial growth is widely desired in order to control, predict and design food and bioproduct processing, stability and safety. The modelling of microbial growth through its biomass is especially interesting for fermentation processes. In fact, there are many mathematical models in the lit- erature for describing microbial growth behaviour. The most widely applied models are those by Gompertz, gen- eralized Verhulst (logistic) and Baranyi-Roberts, although many others are described, such as Richards, Stannard and Schnute [7, 11, 15]. Although those models fit the micro- bial growth data well, they are based on the microbial cell concentration count, which can be awkward in some A. Ibarz Department of Food Technology (DTA), School of Agricultural and Forestry Engineering (ETSEA), University of Lleida (UdL), Lleida, Spain e-mail: aibarz@tecal.udl.cat P. E. D. Augusto (&) Department of Agri-food Industry, Food and Nutrition (LAN), Luiz de Queiroz College of Agriculture (ESALQ), University of Sa ˜o Paulo (USP), Piracicaba, SP, Brazil e-mail: pedro.ed.augusto@usp.br 123 Bioprocess Biosyst Eng (2015) 38:199–205 DOI 10.1007/s00449-014-1256-8