## 3 Results and Discussion
### Engine Energy Balance  
Figure 6a shows the energy balance of the engines at the operating point (see Table 1). Supplementary Material contains the thermodynamics diagram of the turbocharger as a function of specific entropy (Figure S1). Figure S2 represents mass and energy balance of one cylinder in biogas engines. Heat capacity and specific enthalpy of the fluid flowing through the compressor, intercooler and turbine are shown in Table S1. Table S2 contains energy parameters of these same elements. A loading of 86.9% was assumed for each engine (two units coupled). A fraction of the thermal power from the main cooling circuit, 19.9%, is used to raise the temperature of the boiler feed water from 15 to 80 \({}^{\circ}\)C. This boiler produces the steam needed in the thermal pre-treatment unit. The remaining thermal power of this circuit is dissipated in the cooling towers, 80.1%, and there is no possibility of using this heat in the sludge recirculation exchanger. However, when the digesters operated without hydrolysis pre-treatment, this heat was used to keep the mesophilic temperature of digesters. Introducing a thermal pre-treatment unit into the digestion section creates different heat demands. Therefore, sludge is heated up during thermal pre-treatment and subsequently cooled down to the desired temperature to cover for any thermal losses associated with digester conditions and sludge piping line, being no longer necessary to adjust the temperature by the heat sludge recirculation exchanger. This waste heat has a negative impact on the energy efficiency of the process. The demand of the thermal pre-treatment unit is covered by the boiler and engine exhaust gases, giving rise to a different heating circuit where no other use is given to that of the engine main cooling circuit.  
Figure 6b shows the energy balance represented as a percentage. Biogas consumption was used as base (expressed as thermal power). The available thermal energy of the main cooling circuit represents a significant share of the thermal distribution. Therefore, the gain associated with the higher efficiency of the turbocharged engine should translate into full use of the available thermal energy to take full advantage of the energy contained in biogas. In this graph, about 31% of the energy is in exhaust gases and about 23% in the cooling circuits. Thus, finding full use of this energy in the WWTP is imperative for increasing the efficiency of the global process.  
Table 7 shows the values obtained for the useful thermal power associated with engine operation, broken down into different efficiencies. Absolute and relative values are reported. The values obtained from nominal engine operation were used as base. Excess air at 59.4% is observed, which gives an indication of the operating performance of these engines under lean-burn conditions. This condition allows increasing the mass flow of gases and, as a consequence, their energy. The useful thermal power represents the power  
Figure 6: Energy balance of the biogas engines. (**a**) Parameters in absolute value; (**b**) Parameters expressed as percentage.  
capable of finding use in different equipment. Therefore, mechanical losses and radiation losses are discarded, and it is considered for calculation heat transfer from exhaust gases until a minimum temperature of 142 \({}^{\circ}\)C is reached. A value for _UTEF_ of 84.4% indicates that this type of engine achieves a high level of energy recovery.