*3.5. Validation Experiments*

To confirm that the CCD-RSM model can be used to make accurate process predictions, validation experiments were performed at lab-scale using 50 mL vials based on the results presented in the first part of this study. Two process scenarios called respectively "scenario A" and "scenario B" were designed to maximise the ethanol productivity while taking into consideration specific operational process constraints. For both scenarios, the initial sugar concentration was kept between 125 and 225 g/L at a specific concentration of

170 g/L to trigger high ethanol yield and productivity responses. In addition, scenario B was designed to minimise the quantity of initial yeast while still trying to maximise the ethanol productivity response. Finally, the nutrient content was predicted within the design space with 3.9 and 4.0 g/L of initial nutrient concentration for scenario A and B, respectively.

Isoresponses curves predicting the ethanol productivity give valuable information regarding the combinatory effect of nutrient and yeast concentration on the process output, at a specific sugar concentration of 170 g/L (Figure 5A). Ethanol productivity performances higher than 19 g/L/d could be achieved by using a minimum of 3.5 g/L of nutrient during the fermentation. Interestingly, the quantity of yeast initially introduced in the system could be significantly lower to 0.2 g/L while still generating ethanol at a high production rate.

Confirmation experiments showed that after a first lag phase of 24 h, both scenarios continuously produced ethanol before reaching more than 70 g/L of ethanol after 72 h of incubation (Figure 5B). By the end of the fermentation, scenario A and B reached final ethanol concentrations of 80.2 and 86.0 g/L, which represent theoretical ethanol yields of 88.5% and 94.9%, respectively (Table S1). In addition, high ethanol productivities were achieved during the confirmation experimental assays with 19.5 and 21 g/L/d obtained for scenario A and B, respectively.

**Figure 5.** (**A**)—Isoresponse curves predicting the ethanol productivity responses based on nutrient and yeast concentrations using non-treated sugar beet molasses diluted at 170 g/L of initial sugar. (**B**)—Experimental fermentation kinetics of the two investigated scenarios for an initial sugar concentration of 170 g/L. Both scenarios A and B were designed for maximizing ethanol productivity with a high (0.7 g/L) and low concentration (0.27) of yeast, respectively. In addition, 3.9 and 4.0 g/L of nutrient were respectively used for scenario A and B. The dashed line represents the theoretical maximum ethanol yield of both scenarios.

The mathematical model developed in this study was able to accurately predict the ethanol productivity response with an error lower than 12.9%, which we considered as statistically acceptable based on the challenges of reproducibility associated with the implementation of biotechnological processes such as the fermentation one. In addition, the confirmation experimental results highlighted the fact that the quantity of yeast can be considerably reduced while obtaining high ethanol productivity of 18.6 g/L/d (scenario B). This might have a major impact on the operating expenses of the fermentation process, reducing by 2.6-fold the cost related to the use of yeast.
