## 2 Materials and Methods
### Calculations
#### 2.4.2 Acidogenic Fermentation  
The degree of fermentation (DF, gCOD-FP gCOD\({}^{-1}\)) was calculated by dividing the concentration of fermentation products (FP; HOrgs + EtOH) produced (difference between the amount of total detected outlet fermentation products, FP\({}_{\text{out}}\) (gCOD L\({}^{-1}\)), and the total inlet fermentation products, FP\({}_{\text{in}}\) (gCOD L\({}^{-1}\)), converted to COD units) by the influent COD (COD\({}_{\text{in}}\), gCOD L\({}^{-1}\)):  
\[DF= \frac{FP_{out}-FP_{in}}{COD_{in}} \tag{2}\]  
For the batch tests, FP produced (gCOD L\({}^{-1}\)) was calculated as the maximum FP concentration minus the initial FP concentration.  
The fermentation products yield on substrate (YFP/S, gCOD-FP gCOD\({}^{-1}\)) was calculated as follows:  
\[Y_{FP/S}\ =\ \frac{FP_{out}-FP_{in}}{(COD_{in}\text{-}FP_{in})-(COD_{out} \text{-}FP_{out})} \tag{3}\]  
where, COOD\({}_{\text{out}}\) is the outlet effluent COD (gCOD L\({}^{-1}\)). For the batch assays, the fermentation products yield was calculated from the linear regression of the experimental data of fermentation products (HOrgs + EtOH) concentration converted to COD units plotted over influent COD (COD\({}_{\text{in}}\)).  
Volumetric FP productivity (rFP, mgCOD-FP L\({}^{-1}\) h\({}^{-1}\)), volumetric substrate uptake rate (-rS, mgCOD L\({}^{-1}\) h\({}^{-1}\)), specific substrate uptake (-qS, mgCOD gVSS\({}^{-1}\) h\({}^{-1}\)) and specific FP production rates (qFP, mgCOD-FP gVSS\({}^{-1}\) h\({}^{-1}\)) were calculated as described by [PERSON] et al. [19].  
Considering the batch assays, maximum volumetric FP fermentation rate (rFPmax, mgCOD-FP L\({}^{-1}\) h\({}^{-1}\)) and maximum volumetric substrate uptake rate (-rSmax, mgCOD L\({}^{-1}\) h\({}^{-1}\)) were calculated from the linear regression of the fermentation products (HOrgs + EtOH) and substrate concentrations, respectively, over time (t in hours). Maximum specific substrate uptake (-qSmax, mgCOD gVSS\({}^{-1}\) h\({}^{-1}\)) and specific production rates (qFPmax, mgCOD-FP gVSS\({}^{-1}\) h\({}^{-1}\)) were calculated by dividing the respective maximum volumetric rates by the biomass concentration. Global FP volumetric productivity (rFP, mgCOD-FP L\({}^{-1}\) h\({}^{-1}\)) and volumetric substrate uptake rate (-rS, mgCOD L\({}^{-1}\) h\({}^{-1}\)) were calculated by dividing the FP produced, and substrate consumed, respectively, converted to COD units, by the length of each batch assay. Global specific substrate uptake (-qS, mgCOD gVSS\({}^{-1}\) h\({}^{-1}\)) and production rates (qFP, mgCOD-FP gVSS\({}^{-1}\) h\({}^{-1}\)) were calculated by dividing the respective volumetric rates by the volatile suspended solids (VSS) concentration.  
HLac, HAC and HBut were considered as hydroxybutyrate (HB) precursors whereas HProp, EtOH, HVal and HIsow were used as hydroxyvalerate (HV) precursors. HB and HV monomers concentrations (C-mol L\({}^{-1}\)) were estimated from the respective precursors based on stoichiometry. HB and HV monomers fractions were calculated by dividing the estimated HB or HV monomers concentrations by the sum of both estimated HB and HV monomers concentrations (%C-mol basis).  
For the batch assays, all kinetic parameters were calculated during the exponential phase of the acidogenic fermentation. Considering the EGSB, all the stoichiometric and kinetic parameters were calculated for the last 10 days of operation (between days 20 and 29). The standard deviations associated to all the determined stoichiometric and kinetic parameters were estimated using simple average errors formulas.