## 3 Results  
### Reactors' Operation Overview  
Data cleaning was performed according to the set criteria in Section 2.3. The two-substrate mixture of PM+CWM (pellets 1) had a BMP\({}_{\infty}\) of 342.83 L\({}_{\rm CH4}\)/kg\({}_{\rm SVS}\). Meanwhile, the BMP\({}_{\infty}\) values for the three-substrate mixtures of pellets 2 and 3 were 534.21 and 530.28 L\({}_{\rm CH4}\)/kg\({}_{\rm SVS}\), respectively [24; 47]. After data cleaning, the resulting data sets have sizes of 162, 181, and 203 instances for reactors 1, 2, and 3 respectively. To accurately characterize the performance of a reactor, four employed output variables, including MPR (L\({}_{\rm CH4}\)/L\({}_{\rm reactor}\)/d), MY (L\({}_{\rm CH4}\)/kg\({}_{\rm VS}\)), \({}^{\sf D}\)\({}_{\rm COD}\), and \({}^{\sf D}\)\({}_{\rm BOD5}\) (%), were used [28; 48]. The overview of reactor 1 is shown in Figure 2. The MPR suffered a sudden drop at the operating point of 5 d. This interrupted the upward trend that was observed from HRT of 15 to 7 d. From 3 to 1 d, a sustained increase in the MPR was observed, with a value that was almost 2\(\times\) the second-highest average value observed at 7 d. This suggested that a punctual failure occurred at 5 d, which was not due to reaching an operational HRT limit. MY had the highest mean value of 272 L\({}_{\rm CH4}\)/kg\({}_{\rm SVS}\) at 15 d. After 15 d, the values significantly decreased and a similar sudden drop in MPR was observed at a HRT of 5 d. However, MY did not experience a significant recovery after the inhibition, unlike MPR. Thus, by considering both variables of MPR and MY simultaneously, the operation can be divided into two main stages: before and after inhibition. There is a noteworthy difference between these two stages. The former reached considerably higher yields than the latter; however, similar values of MPR were found in both stages. The removal efficiencies in these two stages were not as evident. BOD\({}_{5}\) removal efficiency values noticeably dropped at 10 and 1 d. The low BOD\({}_{5}\) removal values may explain the drop in MY at 10 and 1 d in the previous operation point. This was most likely due to low reaction completions [49]. A minimum average value for the chemical oxygen demand (COD) removal efficiency was observed at 5 d. However, the trend followed by the average \({}^{\sf D}\)\({}_{\rm COD}\) values had a smaller variation compared to both MPR and MY. Furthermore, both BOD\({}_{5}\) and removal efficiencies behaved differently since the calculated BOD\({}_{5}\)/COD ratios were fluctuating. Figure 2: Summary of the main response variables for reactor 1. \(\bullet\): averaga values; \(\blacklozenge\): outliers. To identify the potential causes of inhibition, the control variables of OLR and VOA/TIC were employed. The results are summarized in Figure 3. The high OLR values observed were not an indicative cause of inhibition. In particular, the OLR value was not very high at 5 d. Moreover, the system did not run at very high OLR values despite a constant decrease in the HRT values. Therefore, the COD values in the inflow suffered sizable fluctuations, as shown in Figure 4.  
OLR fluctuations were not strongly correlated with the VOA/TIC, which implies that a failure was not due to a system overload caused by overfeeding. Instead, they seemed to be more connected to the quality of the feed (Figure 4). However, the VOA/TIC results showed that an acid accumulation occurred at 10 d. In these results, the values decreased sharply and approached zero at the operating point of 5 d. Hence, two possibilities were weighted, such as the non-failure of a system due to OAs accumulation and a system delayed response due to VOA accumulation at 10 d. In the former, there was no sign of strong inhibition before 5 d and a lack of VOAs in the system. This were supported by the close to zero VOA/TIC values. In the latter, the system had a delayed response to VOA accumulation at 10 d, which seemed more unlikely, given how large the delay had to be.