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

**Carmen M. Álvarez-Cáliz 1, Inés María Santos-Dueñas 1,\*, Jorge E. Jiménez-Hornero <sup>2</sup> and Isidoro García-García <sup>1</sup>**


Received: 28 November 2020; Accepted: 16 December 2020; Published: 18 December 2020

**Abstract:** 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.

**Keywords:** vinegar; wine; acetification; bioprocesses; experimental design; polynomial modelling; black-box models

### **1. Introduction**

Vinegar production is a biotechnological process essentially involving the biological conversion of ethanol from a given source into acetic acid. Vinegar can be obtained from alcohol, wine, cereals or fruits, among other sources [1–4]. The key step of the process is possibly that by which a complex microbiota of acetic acid bacteria (AAB) convert ethanol into acetic acid in a bioreactor. The bacterial mixture affecting the conversion arises from the natural microbial selection in the acetification medium. In practice, only AAB can exist in an environment containing medium concentrations of ethanol and acetic acid at the beginning but low levels of the former and high levels of the latter at the end [5]. These conditions make it unnecessary to sterilize containers or keep aseptic conditions during operation.

Acetification bioreactors usually operate in a semi-continuous mode. Thus, once the reactors are in full operation, the ethanol concentration is allowed to decrease to a preset level and then an also preset fraction of the reactor contents is unloaded, the remainder being allowed to stand in it in order to act as an inoculum in the next conversion cycle [6–10]. After the bioreactor is unloaded, it is slowly replenished with a fresh alcoholic substrate to start a new ethanol depletion cycle.

Because the temperature and airflow rate are usually fixed, the operational variables that can be altered include the ethanol concentration at the time the reactor is unloaded, the proportion of broth that is unloaded, the loading mode and/or rate, and the total concentration of the culture medium—which is the combination of the ethanol concentration in % *v*/*v* and the acidity in % *w*/*v* [11–16]. These variables influence the mean ethanol concentration and acidity in each cycle [8–10], which in turn affect the AAB concentration and cell activity [17,18]. As a result, the acetification conditions will be more or less stressful for the bacteria affecting the process (AAB).

Usually, an acetification bioreactor is operated in an automated manner in order to not alter the spontaneous dynamics of the system. In practice, this allows repeated cycling to be easily and rapidly achieved [19]. Also, the characteristics of AAB [20–23] make cultivation and selection outside their typical natural or industrial environment rather difficult. In addition, their complex identification, behaviour, and interactions, and their potential synergistic effects, require determining their optimum conditions of operation in an empirical manner.

Notwithstanding the previous difficulties, there is a wealth of technical experience and knowledge about the most suitable working methods and operating conditions for acetification. The use of non-segregated non-structured models [24] could be appropriated to model this kind of system; working with this type of approach allowed us to reach most of the knowledge on this particular process, which has allowed quantitative relations between operational variables and diverse industrial objective functions such as productivity to be established [8–10,25–30].

The advent of massive methods of analysis, such as several omic techniques, has considerably expanded available knowledge about the acetification process at the molecular level, and is bound to help improve the stability and food safety of the end-product [31]. There is, however, an ongoing search for more or less structured modelling approaches to relating the variables of the overall process.

Previous modelling studies [7,10,30] led to proposing the use of two serially arranged bioreactors to optimize the outcome of the acetification process under operationally restricted conditions. Thus, vinegar production is most often subjected to strict regulations with regards to the properties of the end-product, which, for example, should contain very little or no ethanol. In practice, however, ethanol in the acetification medium should never be depleted before the reactor is unloaded since that would place AAB under extremely stressful conditions (viz., a high acidity and a lack of substrate) and render them virtually useless in subsequent biomass conversion cycles. As a result, many industrial acetification plants use additional bioreactors to deplete ethanol present in the vinegar following the unloading of the production bioreactors.

In this scenario, modelling of the two serial bioreactors system requires the use of an appropriate experimental design. Previous experience with modelling of the biotransformation stage in the vinegar production process suggests that black-box models based on second-order generalized polynomials [7,19,32–34] provide a more accurate depiction of the experimental results than do existing alternatives, allowing it to describe potential interactions between independent variables to be considered—and with added advantages like ease of development and statistical validation. The number of experiments needed for the accurate fitting of a polynomial equation depends on whether the polynomial is linear or non-linear [35]. In any case, the greater the number of polynomial terms is (increasing the accuracy of the model), the more experiments will be required to calculate their coefficients. All testing should be conducted in the framework of an experimental design using the minimum possible number of runs to identify interactions between variables and allowing representative equations for the target process to be established as possible.

Based on the previous comments, the main aim of this work was to obtain polynomial models for several key variables of the two serially arranged bioreactors system and to determine an appropriate experimental design for gathering the experimental data needed to estimate such models. A fractional factorial design with central points including the six major operational variables involved on the acetification process has been used, considering the fulfilment of several restrictions arising from the operation of the two bioreactors, which required identifying and examining the impact of such variables (specifically, establishing their lower and upper limits in the framework of the experimental design). Once the experiments were conducted, polynomial models of relevant target variables of the process such as productivity, acetification rate, etc. were fitted using the gathered experimental data. As far as we know, this thorough study where a detailed analysis considering the constraints for the operational variables, the so many experiments, as well as the replications carried out for each experimental set of variables' values has not been done before; additionally, the modelling approach for this acetification set-up has not been reported in any other previous work.
