## 4 Conclusions  
The reciprocal impact of TAC and FOS on the determination of each other by the classical FOS/TAC method of [PERSON] (1977) was experimentally confirmed both in a synthetic water solution and in anaerobic media. High loading in FOS could greatly impact the determination of TAC and vice versa (relative errors up to 35% in moderate conditions and over 300% in extreme conditions). The present paper proposed two new formulas with which this reciprocal effect was taken into account in order to calibrate the concentration of each. With the help of new formulas, the mean absolute percentage errors between the estimated and the real values were significantly reduced to less than 6% in real anaerobic medium, with a moderate loading of VFAs or bicarbonate.  
Wrong FOS/TAC results may lead to an inappropriate operation and, thus, cause digestion failure. The question that arose is the interest and the importance of correcting FOS/TAC calculation formulas. In another word, if, in practice, the correction would be necessary. In Table S2 in the Supplementary Materials, two sets of literature FOS and TAC data of organic waste [16] were collected and recalculated using new formulas. Results showed that the calibration by new formulas could significantly change the judgement on the reactor state; thus, proving it is necessary. The newly proposed equations could allow a more accurate characterization of alkalinity and VFA content in anaerobic digesters, which contributes to a better monitoring of the reactor performance during anaerobic digestion.  
**Supplementary Materials:** The following are available online at [[https://www.mdpi.com/article/10.3390/app112411843/s1](https://www.mdpi.com/article/10.3390/app112411843/s1)]([https://www.mdpi.com/article/10.3390/app112411843/s1](https://www.mdpi.com/article/10.3390/app112411843/s1)), Figure S1: programming flowchart for the simulation of FOS/TAC titration curves, Table S1: pKa of main compounds in an anaerobic digester at 25 \({}^{\circ}\)C (data extracted from [PERSON] et al., 2016 [18]), Table S2: TAC and FOS values reported in literature and calculated using Nordmann method versus the respective corrected values using new formulas (raw data collected from [16]), Scilab code 1: Scilab code for calculation of the sodium bicarbonate contents at different acetic acid concentrations, Scilab code 2: Scilab code for calculation of the acetic acid contents at different sodium bicarbonate concentrations.  
**Author Contributions:** Conceptualization, X.L., A.P., L.A. and T.R.; methodology, X.L., A.P., L.A. and T.R.; software, A.P. and X.L.; validation, A.P. and T.R.; formal analysis, X.L.; investigation, X.L.; resources, M.M.-H. and J.-M.G.; writing--original draft preparation, X.L.; writing--review and editing, A.P., L.A. and T.R.; visualization, X.L. and A.P.; supervision, A.P. and T.R.; project administration, J.-M.G., A.P. and T.R.; funding acquisition, J.-M.G., A.P. and T.R. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the ANRT (Association Nationale de la Recherche et de la Technologie, France, CIFRE no. 2017/1298) and Cultimer France Producteurs Associes for the Ph.D. thesis of [PERSON].  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Acknowledgments:** The authors would like to extend their thanks to [PERSON] (TIMR, universite de technologie de Compiegne) for his valuable support on Scilab code realization.  
**Conflicts of Interest:** The authors declare no conflict of interest.