Structural identifiability of a model for the acetic acid fermentation process

Modelling has proved an essential tool for addressing research into biotechnological processes, particularly with a view to their optimization and control. Parameter estimation via optimization approaches is among the major steps in the development of biotechnology models. In fact, one of the first tasks in the development process is to determine whether the parameters concerned can be unambiguously determined and provide meaningful physical conclusions as a result. The analysis process is known as ‘identifiability’ and presents two different aspects: structural or theoretical identifiability and practical identifiability. While structural identifiability is concerned with model structure alone, practical identifiability takes into account both the quantity and quality of experimental data. In this work, we discuss the theoretical identifiability of a new model for the acetic acid fermentation process and review existing methods for this purpose

Modelling of wine vinegar acetification bioreactor: Global sensitivity analysis and simplification of the model

First-principles models of any process usually describe its complex underlying mechanisms using differential and algebraic equations including several unknown parameters, whose values must be normally estimated from experimental data. In this context, assessment of the influence of each parameter on model outputs, also known as sensitivity analysis, is an invaluable tool to, for example, simplify the structure of such model. In this work, variance-based Global Sensitivity Analysis (GSA) using Sobol’ main and total effects was carried out on a previously proposed acetification process first-principles model. Three parameters (KSE, KIA and KSO) showed less influence than the remaining nine considering their stated value ranges; KSE presented no influence in all the analysed experimental conditions, value variation of KIA exhibited a slightly greater effect on experiments with higher mean acetic acid concentrations and KSO showed the strongest impact by varying its value in all the experiments. According to these results, the model was simplified and its simulation compared with the initially proposed model and the experimental data. The analysis performed, by way of example, can be of crucial importance for any other process

Modelling Acetification with Artificial Neural Networks and Comparison with Alternative Procedures

Modelling techniques allow certain processes to be characterized and optimized without the need for experimentation. One of the crucial steps in vinegar production is the biotransformation of ethanol into acetic acid by acetic bacteria. This step has been extensively studied by using two predictive models: first-principles models and black-box models. The fact that first-principles models are less accurate than black-box models under extreme bacterial growth conditions suggests that the kinetic equations used by the former, and hence their goodness of fit, can be further improved. By contrast, black-box models predict acetic acid production accurately enough under virtually any operating conditions. In this work, we trained black-box models based on Artificial Neural Networks (ANNs) of the multilayer perceptron (MLP) type and containing a single hidden layer to model acetification. The small number of data typically available for a bioprocess makes it rather difficult to identify the most suitable type of ANN architecture in terms of indices such as the mean square error (MSE). This places ANN methodology at a disadvantage against alternative techniques and, especially, polynomial modelling

Optimization of biotechnological processes. The acetic acid fermentation. Part I: The proposed model

Vinegar is a food product of increasing significance by virtue of its widely variable origin and uses (particularly as a condiment or food preservative). The gastronomic value of vinegar has been appreciated for thousands of years. The growing social and economic significance of these products has fostered research into the most salient aspects of their production processes. The widespread use of submerged cultures in such processes has aroused an obvious interest in their modelling with a view to facilitating their design, control and optimization. Also, the availability of increasingly powerful utility and dedicated software tools has enabled a much rigorous approach to devising and application of more complex and accurate models for these purposes. This paper (Part I) reviews previous attempts at modelling acetic acid fermentation and proposes a new mathematical model for the process based on extensive experimental testing. The model introduces newequations and considers cell lysis during the process. Part II is devoted to study the key subject of parameter estimation and finally Part III deals with the optimization task. Though the wine vinegar process is being considered, many of the studied issues could be applied to other fermentations

Optimization of biotechnological processes. The acetic acid fermentation. Part II: Practical identifiability analysis and parameter estimation

In part I of this series a mathematical model for acetic acid fermentation was reported. However, no kinetic model can be complete until its equation parameters are estimated. This inevitably entails a practical identifiability analysis intended to ascertain whether the parameters can be estimated in an unambiguous manner based not only on the sensitivity of the model to them, but also on the amount and quality of available experimental data for this purpose. Also, estimating the model parameters entails optimizing a specific objective function subject to the model equations as major constraints and to additional, minor constraints on variables and parameters. This approach usually leads to the formulation of a non-linear programming problem involving differential and algebraic constraints where the decision variables constitute the parameter set to be estimated. In the scope of modelling biotechnological processes, this problem is not usually dealt with in a proper way. This second paper reviews available models for practical identifiability assessment and parameter estimation with a viewto their prospective application to the proposed model and its validation

Optimization of biotechnological processes. The acetic acid fermentation. Part III: Dynamic optimization

Wine vinegar is obtained in a biotechnological process one of the crucial steps in which is the biological oxidation of the starting wine. Such a step is usually performed in a semi-continuous operation mode where a preset fraction of the culture medium is unloaded from the fermenter as product and the remainder left in it as inoculum to facilitate expeditious fermentation of the wine subsequently added to replenish the amount withdrawn. The overall performance of the fermenter can vary markedly depending on the particular operating conditions, and so can the quality of the product and the economy of the process as a result. Identifying the most suitable operating conditions therefore poses a typical optimization problem named as dynamic optimization or open-loop optimal control, which is solved by determining the time profiles for the control variables of the system in order to optimize a given cost function. Such a function represents the goal to be achieved as regards the specific needs of the problem. In Part III of this series the previously proposed model in Parts I and II has been used for addressing the dynamic optimization of the acetic fermentation process in terms of various objective functions, with special emphasis on productivity

Optimization of the Acetification Stage in the Production of Wine Vinegar by Use of Two Serial Bioreactors

In the scope of a broader study about wine acetification, previous works concluded that using a single bioreactor hindered simultaneously reaching high productivities with high substrate consumption and the use of two serially arranged bioreactors (TSAB) could achieve such goal. Then, the aim of this work is the optimization, using Karush–Kuhn–Tucker (KKT) conditions, of this TSAB using polynomial models previously obtained. The ranges for the operational variables leading to either maximum and minimum mean rate of acetification of 0.11 ≤ (rA)global ≤ 0.27 g acetic acid·(100 mL·h)−1 and acetic acid production of 14.7 ≤ Pm ≤ 36.6 g acetic acid·h−1 were identified; the results show that simultaneously maximizing (rA)global and Pm is not possible so, depending on the specific objective, different operational ranges must be used. Additionally, it is possible to reach a productivity close to the maximum one (34.6 ≤ Pm ≤ 35.5 g acetic acid·h−1) with an almost complete substrate use [0.2% ≤ Eu2 ≤ 1.5% (v/v)]. Finally, comparing the performance of the bioreactors operating in series and in parallel revealed that the former choice resulted in greater production

Modeling and optimization of acetic acid fermentation: A polynomial-based approach

Vinegar production is a typical bioprocess in the scope of the agrifood industry. Its optimization requirescareful modeling which has so far been addressed by using mainly unstructured first principles models. Because of the difficulties in obtaining these models, black box models, such as those used here, are becoming more frequently used. The polynomial models developed in this work, accurately reflect theeffect of the major and typical operational variables used in industry for this process. Also, responsesurfaces were used to identify the optimum operating conditions with a view to maximizing the meanfermentation rate and productivity. The followed strategy has a huge industrial interest since yields a tool that does not only allow finding the best operational conditions depending on different criteria but also is useful for process control. As far as we know this is the first time that these variables have been correlated in this way

Modelling of the Acetification Stage in the Production of Wine Vinegar by Use of Two Serial Bioreactors

In the scope of a broader study about modelling wine acetification, the use of polynomial black-box models seems to be the best choice. Additionally, the use of two serially arranged bioreactors was expected to result in increased overall acetic acid productivity. This paper describes the experiments needed to obtain enough data for modelling the process and the use of second-order polynomials for this task. A fractional experimental design with central points was used with the ethanol concentrations during loading of the bioreactors, their operation temperatures, the ethanol concentrations at unloading time, and the unloaded volume in the first one as factors. Because using two serial reactors imposed some constraints on the operating ranges for the process, an exhaustive combinatorial analysis was used to identify a working combination of such ranges. The obtained models provided highly accurate predictions of the mean overall rate of acetic acid formation, the mean total production of acetic acid of the two-reactor system, and ethanol concentration at the time the second reactor is unloaded. The operational variables associated with the first bioreactor were the more strongly influential to the process, particularly the ethanol concentration at the time the first reactor was unloaded, the unloaded volume, and the ethanol concentration when loading

Aplicaciones y concentraciones de plaguicidas en la zona regable de La Violada tras la modernización

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