Model calibration
The difference of each measured sampling point (ti)with the modelled data was made. This was done for every component and for every measured data point. All the obtained differences were squared and summed to obtained the sum of squared errors (SSE) as shown in equation A-2.
\begin{equation} \text{SS}E_{j}=\sum_{i=1}^{N}\left(n_{j}^{\text{measure}}\left(t_{i}\right)-n_{j}^{\text{model}}\left(t_{i}\right)\right)^{2}(A-2)\nonumber \\ \end{equation}
Subsequently the SSE of each component was summated to each other obtaining the total error of the model. The VSS was not taken into account for the SSE, as the SRT was significantly longer than the HRT the quantification of VSS was assumed not to be accurate within one cycle. The SSE was obtained as follows (eq. A-3):
\(Total\ error=\ \sum{\text{SS}E_{j}}\ (A-3)\)
The total error was minimized adjusting characteristic parameters e.g., qSmax, KSP, KLac, KGlu and the yields shown in table A.1, done by the solver tool of Microsoft Excel. The solver was used to obtain the minimal total error, and the solver was set at GRG non-linear method. No additional constraints were made for the model then the constraints mentioned before. The intial yields used were 0.5 gCOD·gCOD-1, KSP was initially 0.01 min-1 and an initial qSmax of 1 gCOD·gVSS-1·h-1.