## 2 Hybrid System Components
### BG Production
#### 2.1.2 BG Plant  
BG production varies with the methanogenic capacity of the organic matter, which depends on the type of anaerobic fermentation process. A mesophilic process will be used, for which it will be necessary to maintain a temperature in the digester between 25 \({}^{\circ}\)C and 45 \({}^{\circ}\)C, with an average value of 35 \({}^{\circ}\)C.  
The average daily amount of waste available is 27.07 t/day. With a retention time of 30 days and a density of approximately 1000 kg/Nm\({}^{3}\), the useful volume required for the reactor is 812 m\({}^{3}\). A cylindrical reactor with a diameter of 14.38 m and a useful height of 5 m (6 m total height), which is covered with a double membrane (polyester and PVC), is used to obtain a gasometer, with a volume of 400 m\({}^{3}\).  
The production of biomethane (\(Q\)) in Nm\({}^{3}\)/day will be  
\[Q=q\cdot m \tag{1}\]  
where \(q\) is the methanogenic capacity, which depends on the substrate temperature, composition, pH (should be close to 7), and retention time, mainly. Its value in the conditions of this installation can range between 0.19 and 0.25. A value of 0.228 will be taken. The factor \(m\) is the feed rate of volatile solids (\(m=3800\) kg/day), resulting in a production of 867 Nm\({}^{3}\) (methane)/day.  
Although BG production varies with ambient temperature, a relationship of Q = Q(T) cannot be established, due to the large thermal inertia of the substrate volume in the digester, so a stable gas production will be assumed.  
The methane produced is part of the mixture called BG in a variable proportion between 45% and 70%. As an average value, 60% can be taken. The lower calorific value of the BG is 5.6 kWh/Nm\({}^{3}\), so that the total available energy will be \(E=8094\) kWh/day.  
With an internal combustion engine coupled with a generator, with an efficiency of 29%, the electrical energy will be \(E_{e}=2509\) kWh/day and the useful thermal energy will be \(E_{t}=3909\) kWh/day.  
In cold weather (outside temperature of 0 \({}^{\circ}\)C), to maintain a substrate temperature of 35 \({}^{\circ}\)C a heat input is required which will be estimated using Equation (2):  
\[P_{c}=\gamma_{h}\cdot(T_{i}-T_{0})\cdot\frac{S}{e}, \tag{2}\]  
where \(P_{c}\) is the flow of heat losses in W; \(\gamma_{h}\) is the thermal conductivity of concrete (1.63 W\(\cdot\)K\({}^{-1}\cdot\)m\({}^{-1}\)); \(T_{i}\) is the internal surface temperature (35 \({}^{\circ}\)C); \(T_{0}\) is the external surface temperature (0 \({}^{\circ}\)C); \(S\) is the surface (1 m\({}^{2}\)); and \(e\) is the wall thickness (0.15 m), which results in \(P_{c}=380\) W/m\({}^{2}\).  
For the average temperature of the municipality (14 \({}^{\circ}\)C), the heat required is 228 W/m\({}^{2}\)  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Animal Type** & **Residues (mt/Year)** & **Volatile Solids (mt/Year)** & **Volatile Solids (\%)** \\ \hline Chicken & 1920.00 & 518.40 & 27.00 \\ Rabbit & 810.00 & 243.00 & 30.00 \\ Pig & 6400.00 & 512.00 & 8.00 \\ Calf & 750.00 & 112.50 & 15.00 \\
**Total** & **9880.00** & **1385.90** & **14.02** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Estimated yearly residues in the municipality.  
Although it is a cylindrical digester, due to its large diameter and small wall thickness, the calculation has been approximated as if it were a flat wall.  
The wetted surface of the digester wall is 225.9 m\({}^{2}\), resulting in a heat input requirement of 2060 kWh/day, which can be provided by the useful thermal energy of the internal combustion engine. The excess thermal energy will be used for drying wood waste from the area.  
Figure 1 shows the flow diagram that will follow the BG generation process, for its subsequent use as fuel in a BG generator.