# The Effect of Biogas Origin on the Electricity Production by Solid Oxide Fuel Cells
## 4 Results and Discussion  
To start with, we present typical results for an optimized system. The overall performance of the power plant can be defined in both energetic and energetic terms as the percentage ratio of the produced electricity over the chemical energy and exergy, respectively, that enter the system. The optimization was achieved by applying the parameters' values as follows:  
* \(\lambda\) = 2.5. * Pressure = 1 Atm (constant). * Air excess at inlet = 26.80% over the stoichiometric requirement. * Water excess at inlet = 6.93% over the stoichiometric requirement. * Extension of reforming reaction = 90%. * Extension of WGS reaction = 90%. * Extension of electrochemical oxidization of H\({}_{2}\) = 90%. * Extension of CO reaction in the SOFC = 15%. * Temperature of burner = 1043 K.
* Temperature of flue gases = 313.50 K.  
In compliance with the notation introduced by Figure 1, Table 2 presents the temperatures, the masses and the energy at any branch of the system, as well as the overall energy and exergy efficiencies and the thermal losses. The energetic efficiency reaches high levels (above 70%) due to the operational conditions: the reforming reaction is as extensive as 90%, corresponding to the large amount of hydrogen produced. In conjunction with the high utilization in the SOFC (90%) along with the high operational temperature for the reformer and the fuel cell, the efficiency of the system is estimated as very high. The minus sign during enthalpy's calculations (last column of Table 2) results from the heat of the formation method, which is used to meet the energy balance among the several branches of the simulated power plant (see Figure 1). As presented in Figure 2, the irreversibilities encountered by the optimized system are sufficiently low: 3.26% at the heat exchangers, 2.15% at the reformer, 5.25% at the fuel cell and 3.74% at the burner. These produce a total amount of 14.40%, which is more than acceptable to characterize the optimization process as successful. Figure 2: _Cont_. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Branch** & **Elements** & **Temperature (K)** & **Mass Flux (Kg/s)** & **Enthalpy (\(\times 10^{6}\) J)** \\ \hline
1 & Atmospheric Air (O\({}_{2}\) and N\({}_{2}\)) & 298.00 & 11.55 & +0.0044 \\
2 & Biogas (CH\({}_{4}\), CO\({}_{2}\) and H\({}_{2}\)O) & 298.00 & 1.00 & \(-6.0400\) \\
3 & Water (H\({}_{2}\)O) & 298.00 & 1.44 & \(-21.0000\) \\
4 & Biogas (CH\({}_{4}\), CO\({}_{2}\) and H\({}_{2}\)O) & 1100.00 & 1.00 & \(-3.7600\) \\
5 & CH\({}_{4}\), CO\({}_{2}\), H\({}_{2}\)O, H\({}_{2}\), CO & 1120.00 & 2.44 & \(-12.7000\) \\
6 & Steam (H\({}_{2}\)O) & 1100.00 & 1.44 & \(-16.9000\) \\
7 & CH\({}_{4}\), CO\({}_{2}\), H\({}_{2}\)O, H\({}_{2}\), CO, O\({}_{2}\) and N\({}_{2}\) & 1025.00 & 13.94 & \(-38.6000\) \\
8 & CH\({}_{4}\), CO\({}_{2}\), H\({}_{2}\)O, H\({}_{2}\), CO, O\({}_{2}\) and N\({}_{2}\) & 1043.50 & 13.94 & \(-46.9000\) \\
9 & CH\({}_{4}\), CO\({}_{2}\), H\({}_{2}\)O, H\({}_{2}\), CO, O\({}_{2}\) and N\({}_{2}\) & 921.50 & 13.94 & \(-49.2750\) \\
10 & CH\({}_{4}\), CO\({}_{2}\), H\({}_{2}\)O, H\({}_{2}\), CO, O\({}_{2}\) and N\({}_{2}\) & 803.00 & 13.94 & \(-51.5490\) \\
11 & CH\({}_{4}\), CO\({}_{2}\), H\({}_{2}\)O, H\({}_{2}\), CO, O\({}_{2}\) and N\({}_{2}\) & 313.50 & 13.94 & \(-60.2390\) \\
12 & Atmospheric Air (O\({}_{2}\) and N\({}_{2}\)) & 1000.00 & 13.94 & \(+8.6900\) \\ \hline  & Energy efficiency (\%) & & 74.98 & \\  & Energy efficiency (\%) & & 69.90 & \\  & Total Thermal Losses to the environment (\(\times 10^{6}\) J) & & 8.80 & \\  & Thermal Losses to the environment through devices (\% of energy entering & & 24.33 & \\  & the system) & & 24.33 & \\  & Thermal Losses to the environment through flue gases, see Branch 11, Figure 1 (\% & & 0.73 \\  & of energy entering the system) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Typical results for the optimized system, \(\lambda\)=2.5.