## 3 Results and Discussion
### Micro-Oxygenation  
The first biogas purification step was carried out by insufflating into the digester headspace a low quantity of oxygen with a purity \(>\) 95%, produced by a PSA-based O\({}_{2}\) generator. It is known that micro-aeration and micro-oxygenation allow for the bio-oxidation of biogas H\({}_{2}\)S to elemental sulfur using the biological reactions of sulfide-oxidizing bacteria in the digester headspace [36]. The choice not to insufflate air was mainly attributable to the high quantity of N\({}_{2}\), which would have been introduced in the reactor without any possibility of being separated by the membrane-based upgrading system. Consequently, N\({}_{2}\) would have diluted biogas, decreasing CH\({}_{4}\) concentration and lowering the higher heating value (HHV) and the Wobbe index (WI), bringing them in the final biomethane below the minimum limits established by the national legislation (HHV: 34.95-45.28 MJ/Sm\({}^{3}\); WI: 47.31-52.33 MJ/Sm\({}^{3}\)). It is known that introducing O\({}_{2}\) into the headspace and not into the liquid phase of the digester minimizes biogas dilution, limits the need for O\({}_{2}\) overdose due to the co-oxidation of organic compounds, avoids methanogenic inhibition, and reduces operating costs [25]. It was also demonstrated [37] that using 95% O\({}_{2}\) produced by a PSA generator, despite the higher fixed costs of the initial equipment, was more profitable than using pure O\({}_{2}\), air, or FeCl\({}_{3}\) thanks to both lower operating costs and long-term profitability. In order to evaluate the efficiency of H\({}_{2}\)S oxidation and to optimize O\({}_{2}\) volume to be blown into the headspace of an anaerobic digester, some tests were performed. Since O\({}_{2}\) cannot be removed by membrane-based upgrading systems, a test range between 0.1 and 0.6% (vol) of O\({}_{2}\) was chosen based on the maximum O\({}_{2}\) concentration allowed in the final biomethane according to national legislation (O\({}_{2}\leq\) 0.6%). The tests were performed over 5 weeks, in which biogas production and H\({}_{2}\)S concentration remained almost constant, equal to 468 \(\pm\) 19 Sm\({}^{3}\)/h and 860 \(\pm\) 24 ppm\({}_{v}\), respectively. The results of O\({}_{2}\) insufflation tests are reported in Table 3.  
The extent of biogas H\({}_{2}\)S oxidation rose with an increasing O\({}_{2}\) concentration up to 0.3 %vol (entries 1-4), after which it remained constant reaching a plateau level (entries 4-7). In fact, the maximum oxidation yield of H\({}_{2}\)S was about 69% and did not vary significantly with percentages of insufflated O\({}_{2}\) volume between 0.3% and 0.6% (entries 4-7). A direct comparison with the desulfurization efficiency obtained by similar FW AD industrial plants was not possible due to a lack of published data. The H\({}_{2}\)S removal efficiency varies from 68.2% up to 99.5% if full-scale AD plants treating manure and sewage sludge are taken into account [21; 25]. The abatement efficiency of 69.3% achieved in this study is comparable to the minimum value reached by other full-scale AD plants treating manure as reported by [PERSON] et al. [25]. Further tests (entries 8-10) were carried out by lowering the operational volume of the digester in order to increase its headspace volume by 20%, maintaining the same operating conditions of the AD process. Insufflating an O\({}_{2}\) volume of 0.3%, a higher percentage of H\({}_{2}\)S oxidation was measured (81.3%, entry 8) than that observed with a smaller headspace volume (69.3%, entry 4). By increasing the amount of insufflated O\({}_{2}\) to 0.4-0.5% vol (entries