# Influences of Temperature and Substrate Particle Content on Granular Sludge Bed Anaerobic Digestion
## 2 Materials and Methods
### ADM1 Simulation  
The modeling was based on the standard ADM1 implemented in Aquasim software [5; 26], only modified by splitting substrate particulates into two fractions, one fast and one slow disintegrating, and making first-order disintegration of these particle fractions temperature-dependent. Rate expressions for the disintegration of fast and slow fractions of the composite substrates are given as follows:  
\[\frac{\mathrm{d}\mathrm{X}\mathrm{c}\mathrm{1}}{\mathrm{dt}}=\mathrm{K}_{ \mathrm{dis}\mathrm{1}}\mathrm{X}\mathrm{c}\mathrm{1}, \tag{2}\]  
\[\frac{\mathrm{d}\mathrm{X}\mathrm{c}\mathrm{2}}{\mathrm{dt}}=\mathrm{K}_{ \mathrm{dis}\mathrm{2}}\mathrm{X}\mathrm{c}\mathrm{2}, \tag{3}\]  
where \(\frac{\mathrm{d}\mathrm{X}\mathrm{c}\mathrm{1}}{\mathrm{dt}}\) and \(\frac{\mathrm{d}\mathrm{X}\mathrm{c}\mathrm{2}}{\mathrm{dt}}\) are disintegration rates for fast and slow fractions in kg COD-m-3-day-1, Xc1 and Xc2 are fast and slow disintegrating fractions of the complex particulate, respectively, and Kdis1 and Kdis2 are rate constants for fast and slow disintegrating fractions, respectively. The dependency of Kdis values on temperature was based on Equation (4). \[\mathrm{K}_{\mathrm{dis}}=\mathrm{K}_{\mathrm{dis,ref}}\mathrm{e}^{[\frac{- \mathrm{E}_{\mathrm{a}}}{\mathrm{R}}][\frac{1}{\mathrm{T}}-\frac{1}{\mathrm{T} \mathrm{ref}}]}, \tag{4}\]  
where E\({}_{\mathrm{a}}\) is the activation energy in J-mol-1, R is the gas constant in J-mol-1.K-1, and Tref is the reference temperature in K. Activation energy was estimated from literature data on energy requirements for mechanical disintegration of solid substrates such as straw. According to [PERSON] and [PERSON] [22], the energy required to disintegrate straw to sizes less than 10 mm is 29 kWh/t (104.4 kJ/kg). In addition, [PERSON] et al. [27] showed that the activation energy of cellulose hydrolysis is \(96.4\pm 4.1\) kJ/mol. Since straw, which is composed of up to 50% cellulose, is one of the main sources of particulates in manure substrates, it is reasonable to base the estimate of E\({}_{\mathrm{a}}\) on these data. We used an E\({}_{\mathrm{a}}\) of 90 kJ/mol for fast disintegrating and 130 kJ/mol for slow disintegrating particles (corresponding to Kdis of 0.03-0.05 and 0.17 at 25 and 35 \({}^{\circ}\)C, respectively). [PERSON] et al. [28] showed that Kdis for swine \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiment** & **Time (days)** & **Temperature (\({}^{\circ}\)C)** & **Substrate** \\ \hline Phase 1 & 0–11 & 35 & RF \\ Phase 2 & 11–26 & 25 & RF \\ Phase 3 & 26–45 & 25 & CF \\ Phase 4 & 45–60 & 35 & CF \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Time, temperature, and feed types used during the experiment. RF—raw feed; CF—centrifuged feed. Figure 1: Schematic diagram of applied up-flow anaerobic sludge bed reactor (UASB) reactor set-up. manure samples at 35 \({}^{\circ}\)C is around 0.17 day\({}^{-1}\), which we used as reference K\({}_{\rm dis}\) and T values. Input composite materials (Xc1 and Xc2) were determined based on the ratio between total and soluble COD values COD\({}_{\rm total}\) and COD\({}_{\rm soluble}\) as shown in Equations (5)-(7). Yields for the disintegration of complex materials for swine manure ADM1 modeling by [PERSON] et al. [28] were used with modification to account for fast and slow disintegrating components (Tables 2-4). \[\rm{Xc}=\ Xc1+Xc2. \tag{5}\]  
\[\rm{Xc1}=\ \frac{COD_{\rm soluble}}{COD_{\rm total}}Xc. \tag{6}\]  
\[\rm{Xc2}=1-\frac{COD_{\rm soluble}}{COD_{\rm total}}Xc. \tag{7}\]