*2.4. Experimental Design and Statistical Analysis*

In this study, 17 runs (experiments 1–17 collected in Table 2) were performed in accordance with a face-centered factorial design with three replicates at the central point [20] so as to investigate the effects of the variables: X1, cooking time (30–60 min), X2, formic acid (FA) concentration (80–95%) and X<sup>3</sup> hydrochloric acid (HA) concentration (0.05–0.10%). Following the normalization of the independent variables to the range (−1, 1), quadratic response surfaces were fitted by least-squares multiple regression (Equation (1)) using an excel statistical module (DOE PRO XL, SigmaZone):

$$\mathbf{D}\mathbf{V} = \mathbf{b}\_{\bullet} + \sum\_{\mathbf{l}=1}^{3} \mathbf{b}\_{\mathbf{j}} \mathbf{X}\_{\mathbf{j}} + \sum\_{\mathbf{l}=1,\mathbf{j}\le\mathbf{k}}^{3} \mathbf{b}\_{\mathbf{jk}} \mathbf{X}\_{\mathbf{j}} \mathbf{X}\_{\mathbf{k}} \mathbf{a} \tag{1}$$

where DV denotes each of the dependent variables (system responses) studied, and X<sup>j</sup> and X<sup>k</sup> are the previously defined normalized variables. The values of b0, b<sup>i</sup> , and bjk represent the fitting parameters calculated by multiple regression between the system responses (DV) and the normalized variables.


**Table 2.** Design of the experiments used to evaluate the delignification process by the formosolv of Paulownia wood and the main results (all data expressed in an oven dry basis).

**PY: Pulp yield KN: kappa number; VIS: viscosity; FA**: formic acid concentration; **HA**: hydrochloric acid concentration; **GnP**: glucan remaining in pulp; **FAP**: formic acid remaining in pulp; **AGP**: acetyl groups remaining in pulp; **Xyl**+**Gal**+**Man dis**: xylose, galactose, and mannose dissolved in liquor.; <sup>1</sup> kg pulp/100 kg raw material; <sup>2</sup> kg component/100 kg pulp; <sup>3</sup> percentage over content of component in Paulownia wood.
