*2.2. Statistical Experimental Design Methodology*

The first part of this study aimed to optimise the ethanol fermentation of sugar beet molasses using a CCD-RSM. This statistical approach allows investigating specific operational parameters together with their related effects on the fermentation process with a limited number of experiments. Therefore, a CCD-RSM was implemented for three process variables: initial sugar concentration (Factor A) as well as yeast (Factor B) and nutrient (Factor C) concentrations. These investigated factors were studied at low, middle and high levels, coded −1, 0 and +1, respectively (Table 2). In addition, two centre points were added to check for curvature and verify the repeatability of the fermentation process. Finally, confirmation experiments were performed to verify the accuracy of the developed mathematical model and its capacity to predict process responses within the design space. The CCD-RSM was designed and analysed using the Design-Expert 12 software (Stat-Ease Inc., Minneapolis, MN, USA).


**Table 2.** Experimental factors and their associated levels used during the development of the CCD-RSM for the fermentation of diluted sugar beet molasses using *Saccharomyces cerevisiae* yeast.

The ethanol productivity was used as the main experimental process response (Y1) for the CCD-RSM and calculated using Equation (1).

$$\text{Ethanol productivity} \left(\text{g/L/d}\right) = \text{EtOH}\_{\text{max}} / \text{ t}\_{\text{formation}} \tag{1}$$

where EtOHmax represents the maximum ethanol concentration (g/L) and tfermentation represents the time of incubation (d) required to achieve the EtOHmax.

In addition, ethanol yields were calculated based on the maximum theoretical ethanol concentration calculated for the three initial sugar concentrations. Using Equation (2), it can be assumed that 1 g of glucose produces 0.51 g of ethanol and 0.49 g of carbon dioxide (CO2).

$$\rm{C}\_6\rm{H}\_{12}\rm{O}\_6 \rightarrow 2\rm{C}\_2\rm{H}\_6\rm{O} + 2\rm{CO}\_2\tag{2}$$

Ethanol yields were expressed as % of the maximum theoretical ethanol concentration.
