A mathematical model of ethanol fermentation from cheese whey (original) (raw)
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Bioresource Technology, 2011
Anaerobic batch fermentations of ricotta cheese whey (i.e. containing lactose) were performed under different operating conditions. Ethanol concentrations of ca. 22 g L À1 were found from whey containing ca. 44 g L À1 lactose, which corresponded to up to 95% of the theoretical ethanol yield within 15 h. The experimental data could be explained by means of a simple knowledge-driven biochemically structured model that was built on bioenergetics principles applied to the metabolic pathways through which lactose is converted into major products. Use of the model showed that the observed concentrations of ethanol, lactose, biomass and glycerol during batch fermentation could be described within a ca. 6% deviation, as could the yield coefficients for biomass and ethanol produced on lactose. The model structure confirmed that the thermodynamics considerations on the stoichiometry of the system constrain the metabolic coefficients within a physically meaningful range thereby providing valuable and reliable insight into fermentation processes.
An unstructured kinetic model was developed in this study for the batch production of bioethanol by the yeast Kluyveromyces marxianus DSM 5422 from the renewable sources of agricultural and food processing origin, such as whey permeate or inulin, which include the terms of both substrate and product inhibitions. Experimental data collected from multiple fermentations in bioreactors with three different initial concentrations for each substrate were used to estimate the parameters and to validate the proposed model. The growth of K.marxianus can be expressed by the Haldane-type extended Monod model in combination with the Jerusalimsky term for the non-competitive product inhibition and the Luedeking-Piret equation was adequate to describe the growth-associated formation of ethanol as the target product. The parameters in the models were estimated by minimizing mean-squared errors between the predictions of the models and the experimental data using the differential evolution (DE) algorithm and the L-BFGS-B nonlinear optimization code. In all cases, the model simulation matched well with the fermentation data being confirmed by the high R-squared values (0.984, 0.992 and 0.965 for WP, lactose and inulin, respectively). The kinetic models proposed here can be employed for the development and optimization of the bioethanol production processes from renewable resources.
A growth kinetic model of Kluyveromyces marxianus cultures on cheese whey as substrate
Journal of Industrial Microbiology and Biotechnology, 2004
This work presents a multi-route, non-structured kinetic model for determination of microbial growth and substrate consumption in an experimental batch bioreactor in which b-galactosidase is produced by Kluyveromyces marxianus growing on cheese whey. The main metabolic routes for lactose, and oxygen consumption, cell growth, and ethanol production are derived based on experimental data. When these individual rates are combined into a single growth rate, by rewriting the model equations, the model re-interpretation has a complexity similar to that of the usual variations of the Monod kinetic model, available in the literature. Furthermore, the proposed model is in good agreement with the experimental data for different growth temperatures, being acceptable for dynamic simulations, processes optimization, and implementations of model-based control technologies.
Batch kinetics and modelling of ethanolic fermentation of whey
International Journal of Food Science and Technology, 2005
The fermentation of whey by Kluyveromyces marxianus strain MTCC 1288 was studied using varying lactose concentrations at constant temperature and pH. The increase in substrate concentration up to a certain limit was accompanied by an increase in ethanol formation, for example, at a substrate concentration of 10 g L−1, the production of ethanol was 0.618 g L−1 whereas at 50 g L−1 it was 3.98 g L−1. However, an increase in lactose concentration to 100 g L−1 led to a drastic decrease in product formation and substrate utilization. The maximum ethanol yield was obtained with an initial lactose concentration of 50 g L−1. A method of batch kinetics was utilized to formulate a mathematical model using substrate and product inhibition constants. The model successfully simulated the batch kinetics observed at S0 = 10 and 50 g L−1 but failed in case of S0 = 100 g L−1 because of strong substrate inhibition.
Bulletin of Chemical Reaction Engineering & Catalysis, 2013
Whey is the liquid remaining after milk has been curdled and strained. It is a by-product of the manufacture of cheese or casein and has several commercial uses. In environmental point of view, whey is kind of waste which has high pollution level due to it's contain high organic compound with BOD and COD value 50 and 80 g/L respectively. On the other side, whey also contain an amount of lactose (4.5%-5%); lactose can be used as carbon source and raw material for producing ethanol via fermentation using yeast strain Kluyveromyces marxianus. The objective of this research is to investigate the kinetics of ethanol production from crude whey through fermentation using Kluyveromyces marxianus and to estimate the kinetics parameter using available model. The yeast was able to metabolize most of the lactose within 16 h to give 8.64 g/L ethanol, 4.43 g/L biomass, and remain the 3.122 g/L residual lactose. From the results presented it also can be concluded that common kinetic model for microbial growth, substrate consumption, and product formation is a good alternative to describe an experimental batch fermentation of Kluyveromyces marxianus grown on a medium composed of whey. The model was found to be capable of reflecting all batch culture phases to a certain degree of accuracy, giving the parameter value: µmax, Ks, YX/S, α, β : 0.32, 10.52, 0.095, 1.52, and 0.11 respectively.
Mathematical models are a means of representing essential aspects of reality (process, phenomenon, object, element, system, etc.) with the help of mathematical constructs. Mathematical models typically offer convenience and cost advantages over other means of obtaining the required information on reality. In the last decades, continuing progress has been observed in applications of mathematical modeling in biological growth. This research developed a mathematical model that illustrated the kinetics of ethanol production, incorporating both fermentation time and temperature from the batch fermentation of glucose with Kluveromyces Maxianus. Glucose biomass was found to decrease linearly with temperature rise and the modified Gompertz model was used to describe the ethanol production. The arhenious plot was used to illustrate the temperature dependence rate of the reaction. Matlab 9.0 and Microsoft Excel 2007 were the statistical software used for the iteration and the estimation of the biological parameters. The derived mathematical model could be adapted to illustrate the kinetics of ethanol production to the stationary phase during the fermentation of glucose as influenced by temperature and fermentation time using Kluveromyces Maxianus.
DOI 10.1007/s12257-012-0477-4, 2013
Lactococcus lactis species have been and still are extensively investigated due to their significant commercial importance. Current scientific research focuses on strains utilized in food industry, due to their multiple uses in food and beverages fabrication. Biomass of Lactococcus lactis is of great interest as well as the end products of its metabolism such as lactic acid and nisin. However their production is constantly challenged due to end product inhibition occurring during intensive propagation of the coccus in reactor systems. To successfully predict the behavior of the culture, the approach of combining mathematics with biology, ergo the development of an unstructured mathematical model, was taken. Although Luedeking and Piret is the model that has been extensively used to demonstrate growth in end-product inhibition cultures, its applicability is limited due to its dependance on the specific growth and product coefficients, particularly related to the culturing conditions used. To overcome these hurdles, a combination of the non competitive single product end inhibition Taylor and Hinselwood models was used, with the significance of this model laying in the fact that it offers a feasible alternative to the commonly used model of Luedeking and Piret for describing fermentation kinetics governed by end-product inhibitions. The fitting with the experimental values, in batch mode, was tested in terms of the coefficient of determination (R²), having values 0.97 to 0.99 and suggesting a very good fitting with the experimental data. The model was further developed to achieve theoretical predictions of volumetric cell productivity in continuous and fed-batch mode of substrate feed in different culturring systems.
Entropy, 2023
This paper presents results concerning mechanistic modeling to describe the dynamics and interactions between biomass growth, glucose consumption and ethanol production in batch culture fermentation by Kluyveromyces marxianus (K. marxianus). The mathematical model was formulated based on the biological assumptions underlying each variable and is given by a set of three coupled nonlinear first-order Ordinary Differential Equations. The model has ten parameters, and their values were fitted from the experimental data of 17 K. marxianus strains by means of a computational algorithm design in Matlab. The latter allowed us to determine that seven of these parameters share the same value among all the strains, while three parameters concerning biomass maximum growth rate, and ethanol production due to biomass and glucose had specific values for each strain. These values are presented with their corresponding standard error and 95% confidence interval. The goodness of fit of our system was evaluated both qualitatively by in silico experimentation and quantitative by means of the coefficient of determination and the Akaike Information Criterion. Results regarding the fitting capabilities were compared with the classic model given by the logistic, Pirt, and Luedeking–Piret Equations. Further, nonlinear theories were applied to investigate local and global dynamics of the system, the Localization of Compact Invariant Sets Method was applied to determine the so-called localizing domain, i.e., lower and upper bounds for each variable; whilst Lyapunov’s stability theories allowed to establish sufficient conditions to ensure asymptotic stability in the nonnegative octant, i.e., R3 +,0. Finally, the predictive ability of our mechanistic model was explored through several numerical simulations with expected results according to microbiology literature on batch fermentation. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Kinetics of Bioethanol Production from Lactose Converted by Kluyveromyces Marxianus
Chemical engineering transactions, 2013
A kinetic model for ethanol fermentation of lactose using yeast Kluyveromyces marxianus DSMZ 5422 is proposed. The model consists of a set of differential equations which account for substrate consumption, ethanol production and biomass production. In the model, it is assumed that alcoholic fermentation is inhibited by ethanol itself and that a different metabolic pathway is set at certain ethanol concentrations. Furthermore, lactose consumption is hypothesized to be associated to biomass growth. The model proposed is able to correctly describe lactose consumption and ethanol production. Also the main trend of biomass variation is satisfactorily correlated. The model with the set of the regression parameters is validated for its predictive ability in a larger scale batch reactor experiment.
A simultaneous saccharification and fermentation model for dynamic growth environments
Bioprocess and Biosystems Engineering, 2012
Many mathematical models by researchers have been formulated for Saccharomyces cerevisiae which is the common yeast strain used in modern distilleries. A cybernetic model that can account for varying concentrations of glucose, ethanol and organic acids on yeast cell growth dynamics does not exist. A cybernetic model, consisting of 4 reactions and 11 metabolites simulating yeast metabolism, was developed. The effects of variables such as temperature, pH, organic acids, initial inoculum levels and initial glucose concentration were incorporated into the model. Further, substrate and product inhibitions were included. The model simulations over a range of variables agreed with hypothesized trends and to observations from other researchers. Simulations converged to expected results and exhibited continuity in predictions for all ranges of variables simulated. The cybernetic model did not exhibit instability under any conditions simulated.