초록
<P><B>Summary</B></P><P>The aim of this paper was to estimate fermentation kinetic parameters to develop a mathematical model of the bioethanol production under magnetic field effect. Thus, a non‐structured mathematical model was developed considering three non‐lineal kinetic models typically known as Levenspiel, Aiba, Jerusalimsky, which take into account inhibitory effects of the high product concentration on yeasts. The non‐lineal differential equations system solution was carried out by MatLab software using the Runge–Kutta fourth‐order multivariable method. This method was improved through a replication scheme coupled with Newton–Raphson method modified with a damping Broyden parameter. Experimental data on substrate consumption, biomass formation and ethanol production were collected at magnetic field intensities (H) of 414, 796 and 1216 A/cm during 16 h of fermentation. Consequently, the adjusted model for biomass, consumed substrate and bioethanol produced allowed us to correlate fermentation kinetic parameters with the magnetic field. The best result was observed when Jerusalimsky model modified with a magnetic field parameter was considered, because the RMSD order and R‐square correlation coefficient were around 10<SUP>−3</SUP> and higher than 0.95, respectively. These results are important to understand the phenomenological behavior of this unconventional bioprocess and be helpful to further sensibility analysis and scale up of the bioethanol production assisted by electromagnetic field. Copyright © 2016 John Wiley & Sons, Ltd.</P>