*2.9. Calculation of Xylose Yield, Xylitol Yield, Xylitol Volumetric Productivity, Specific Xylitol Yield and Combined Severity Factor*

Xylose yield obtained during the hydrolysis of wheat bran and rice straw was expressed as percentage of theoretical. Theoretical xylose yield was calculated from the composition of the raw material used by assuming a complete hydrolysis of its xylan content into xylose.

Xylitol yield achieved in xylitol fermentation experiments was also expressed as percentage of theoretical. Theoretical xylitol yield was calculated from the initial xylose concentration by assuming a complete (stoichiometric) conversion into xylitol. Xylitol volumetric productivity (g/(L × h)) was calculated by dividing the xylitol concentration by the elapsed fermentation time. The specific xylitol yield was calculated as the amount of xylitol produced divided by the amount of xylose consumed and expressed as g/g.

In order to compare different pre-treatment methods, combined severity factor was calculated according to Wyman et al. [43].

### *2.10. Statistical Evaluations and Optimisation*

A full factorial, orthogonal design of experiments (3<sup>2</sup> ) with triplicates in the center point was performed in order to investigate the effects of two independent variables (OTR, initial xylose concentration) and their interactions on the maximum xylitol yield, maximum xylitol volumetric productivity and the xylitol yield after 24 h of fermentation. Maximum xylitol yield and maximum xylitol volumetric productivity refers to the highest values achieved during the given experiment. The results were evaluated by StatisticaTM v.13 (TIBCO Software, Palo Alto, USA) software. The settings of the two factors of initial xylose concentration and OTR value were the following: 30, 55, and 80 g/L initial xylose concentration and 1.1, 2.1, and 3.1 mmol O2/(L × h) OTR (Table 2). A quadratic polynomial model was fitted to the measured data. The adequacy of the model was tested with an F-test (*p* = 0.05). The fitted model is described by Equation (1).

$$\mathbf{Y} = \beta\_0 + \beta\_1 \mathbf{X}\_1 + \beta\_2 \mathbf{X}\_2 + \beta\_{12} \mathbf{X}\_1 \mathbf{X}\_2 + \beta\_{11} \mathbf{X}\_1^2 + \beta\_{22} \mathbf{X}\_2^2 \tag{1}$$

where Y represents the response variable, β<sup>0</sup> is the interception coefficient, b<sup>1</sup> and b<sup>2</sup> are the linear terms, β<sup>11</sup> and β<sup>22</sup> are the quadratic terms and X<sup>1</sup> and X<sup>2</sup> represent the independent variables studied [44]. The model was reduced by non-significant terms, where it was possible. In the model equations, the original numerical values of OTR and initial xylose concentration were used without their units, and initial xylose concentration was referred to as IXC. The Pareto chart was also used to investigate the effects of the terms and interactions of the independent variables. Critical values of the fitted models were determined within the experimental range in order to find the optimum condition of xylitol fermentation.

To investigate the effect of the particle size of rice straw on the acidic hydrolysis, a grinding process was applied prior to acidic treatment, and the results were evaluated by one-way ANOVA analysis at a significance level of 5%. It was performed by StatisticaTM v.13 (TIBCO Software, Palo Alto, USA) software.
