Here, the residence time is measured in hours, and the temperature is given in Kelvins. The rate constant k of the reaction is assumed to obey the Arrenhius equation with an activation energy of 125.6 kJ mol -1 . We employed a fixed liquid-to-solid ratio L : S = 1, motivated by our earlier investigation of the AqSO biorefinery that indicated this ratio to be favorable for the yield and structural properties of the lignin-containing products .