_Applied_  
_sciences_  
_Article_  
**Optimization of the Acetification Stage in the Production of Wine Vinegar by Use of Two Serial Bioreactors**  
**[PERSON] 1, [PERSON] 1,*+**, [PERSON] 2 and [PERSON] 1  
1 Department of Chemical Engineering, University of Cordoba, Campus de Rabanales, 14071 Cordoba, Spain; q42 alcae@yahooes (C.M.A.-C.); [EMAIL_ADDRESS] (I.G.-G.)  
2 Department of Electrical Engineering and Automatic Control, University of Cordoba, Campus de Rabanales, 14071 Cordoba, Spain; [EMAIL_ADDRESS]  
* Correspondence: [EMAIL_ADDRESS]; Tel. : +34-957-218-658  
**Abstract**: In the scope of a broader study about wine acidification, 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 acidification of \(0.11\leq(r_{A})_{global}\leq 0.27\) g acetic acid-(100 mL h)\({}^{-1}\) and acetic acid production of \(14.7\leq P_{m}\leq 36.6\) g acetic acid h\({}^{-1}\) were identified; the results show that simultaneously maximizing \((r_{A})_{global}\) and \(P_{m}\) 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 (\(34.6\leq P_{m}\leq 35.5\) g acetic acid-h\({}^{-1}\)) with an almost complete substrate use [0.2% \(\leq E_{u2}\leq 1.5\%\) (\(\
icefrac{{\gamma}}{{\upsilon}}\))]. Finally, comparing the performance of the bioreactors operating in series and in parallel revealed that the former choice resulted in greater production. vinegar; wine; acidification; bioreactor systems; bioprocesses; optimization  
**1. Introduction**  
Bioprocesses, in general, and acidification as an example, are especially complex owing to the large number of variables involved and their mutual interactions. When a bioprocess is microbially driven--which is the case with acidification--most of the complexity arises from the biological activity of a cell population that is usually highly diverse and capable of adjusting to a variety of environments--and hence of behaving in rather different manners. The problem is even greater when the microbial population comprises not a single species but rather a mixture of species or even genera. Although omics techniques have considerably increased the available knowledge on industrial bioprocesses, there is still a long way to go before they can be elucidated at the molecular scale, so their modelling is an invaluable tool to design them as efficiently as possible. Because such systems are normally industrially or economically significant, developed models are frequently used to identify the operating conditions that will optimize the output in terms of specific performance indicators or variables. The scientific literature abounds with very recent references to modelled bioprocesses: the xanthan biosynthesis by _Xanthomonas campestris_ ATCC 13951 using winery wastewater [1], the uricase production by _Aspergillus wewlischiae_ strain 1-4 [2], the use of polyethylene terephthalalate (PET) for the cultivation of _Pseudomonas_ sp. GO16 [3], the extracellular protease production by a native _Bacillus argabhattai_ Ab15-ES [4] and many other examples could be found. Usually, however, the large number of variables involved in a process, and their mutual interactions, require careful analysis and specific optimization methods with a view to establishing their optimum values for the intended purpose. The acidification process, which involves a bio-oxidative transformation effected by a mixture of acetic acid bacteria (AAB) [5], leads to the biological conversion of ethanol into acetic acid.