# Optimized Analytical-Numerical Procedure for Ultrasonic Sludge Treatment for Agricultural Use
## 11 Comparison with Some Known Scenarios in Literature  
The following simplifications have been considered in our numerical implementation. First, we have not considered some microflows (polymer thickening and dehydration). On the contrary, we considered it appropriate to include both nitrogen dioxide and sulfur dioxide emissions in the combined heat and power production. expanded sludge by 1/3 with considerable water expenditure. Next, the sludge is subjected to anaerobic digestion, yielding two main products: 98.6% raw digestate and 1.4% biogas. The sludge output possesses the characteristics shown in Table 9.  
Classifying the treated sludge, as opposed to the incoming sludge, allows it to be used in the agricultural sector because it meets the parameters required by current regulations. The raw digestate undergoes further dewatering, and the resulting by-products are transported and spread on agricultural land. At the same time, the generated biogas is directed to a cogeneration plant for energy recovery [71]. The fusion of anaerobic digestion, land application, and biogas involves six processes, of which the first four mirror those of the second method presented. The unique feature lies in the treatment of biogas carried out by this method through the purification of biogas and the subsequent utilization of energy. About 41.3% of the biogas is transformed into biomethane, while 48.7% of the CO\({}_{2}\) is removed. The theoretically required amount of oxygen for the combustion of 41.3% biomethane is four times higher [72]. The disintegration process can be achieved thermally (at 170-190 \({}^{\circ}\)C for 30-60 min), resulting in substantial solubilization along with a transformation of the sludge characteristics. This leads to a significant improvement in filterability and a reduction in pathogens [73]. Literature methods indicate that the product of the former method boasts the highest relative nutrient recovery efficiency due to its small volume and low water content compared to digestate. However, composting is constrained by its inherent limitations in that it cannot harness the energy content of sludge, making its energy contribution negligible. This represents a significant disadvantage of composting. The performance of anaerobic digestion is more complete, although its relative nutrient recovery efficiency is lower than that of composting. Compared with composting technology, anaerobic digestion is more energy efficient and has less environmental impact. The latter methodology shares a similar energy recovery efficiency as the former but exceeds it in environmental impact. Therefore, from an overall perspective, the combination of anaerobic digestion, agricultural application, and cogeneration should be considered the most optimal. However, all methods presented require intensive electricity consumption. Contrary to the literature's findings, the research demonstrates both effective sludge weight reduction and reasonable energy consumption. Conventional systems suffer energy losses due to frictional heat, especially with high-pressure pumps and blade mixers that create turbulence during processing. These turbulences lead to friction between the liquid particles and the vibrating parts of the equipment, converting the input energy into frictional heating, which is lost and does not contribute to the dispersion effects. The stronger the cavitation forces that exert stress on the particles, the less energy is required for effective dispersion [74]. Finally, the sludge mixer, designed to reduce the water content in the sludge further, operates based on energy-harvesting techniques [75; 76]. It is worth noting that the results obtained meet all normative requirements (UNI EN 13657:2004+ UNI EN ISO 11885:2009 method; UNI 10802-04, UNI 12457-204, and UNI EN ISO 11885:09 methods; UNI EN 13657:2004 and UNI EN ISO 11885:2009 methods).