*Article* **Optimization 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>**


**\*** Correspondence: ines.santos@uco.es; Tel.: +34-957-218-658

**Abstract:** 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)−<sup>1</sup> and acetic acid production of 14.7 <sup>≤</sup> *Pm* <sup>≤</sup> 36.6 g acetic acid·h−<sup>1</sup> 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 <sup>≤</sup> *Pm* <sup>≤</sup> 35.5 g acetic acid·h<sup>−</sup>1) with an almost complete substrate use [0.2% ≤ *Eu*<sup>2</sup> ≤ 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.

**Keywords:** vinegar; wine; acetification; bioreactor systems; bioprocesses; optimization
