## 2 Materials and Methods
### Detailed Plant Description
The digestate is subsequently sent for dewatering prior to HTC treatment. A value of 30% TS was assumed for this process. The HTC unit worked under batch conditions with loading, reaction and unloading operations carried out in a single day in two consecutive cycles. The process conditions were set at 200 \({}^{\circ}\)C (15.5 bar) for 1 h duration. The energy balance for this system was estimated considering the enthalpy of the sludge stream and steam injection and that of the final conditions under adiabatic approximation [56]. The energy demand of the boiler was calculated using an efficiency value of 85.7% for energy conversion [57]. Thermal energy recovery after the HTC system was achieved by considering the use of flash steam equipment. The amount of energy contained in the flash gas was obtained from the flash steam calculator available at [58]. The energy demand for heating the reactor unit was calculated based on assumptions found in [PERSON] et al. [59], where a 1.5 m\({}^{3}\) tank volume requires 1550 kJ/K. The resulting slurry from HTC was dewatered at 40% solid content. The HTC process water was sent back to the digestion process for further treatment. Assumptions for the HTC process were based on data reported in the literature, described as follows. Methane yield from the process water was 105.5 mL CH\({}_{4}\)/g COD added using average values reported by [PERSON] et al. [60] and [PERSON] et al. [39], considering a chemical oxygen demand (COD) concentration for HTC process water of 98.7 g COD/L. These values were considered for the case of HTC liquid fraction derived from manure digestate, keeping this assumption also for the co-digestion case with cheese whey. Data derived by [PERSON] et al. [61] from processing cow manure under HTC, gives higher values for the methane yield (246.5 mL CH\({}_{4}\)/g VS; average data from the two experimental set-ups) of the liquid fraction but a much lower VS content for the process water (23.8 g VS/L, average data), therefore, leading to similar results. Performance of the HTC process was obtained from data reported by [PERSON] and [PERSON] [62], [PERSON] et al. [39] and [PERSON] et al. [63]. A hydrocarbon yield of 78.7% was considered. Liquid and gas yields were 15.1 and 6.2%, respectively. This high hydrochar value was justified based on the high mineral content of the digested material and the high solid content of the digestate submitted to the thermal treatment. Other authors reported lower yields of char, but these values were derived from fresh material, a higher HTC process temperature and lower solid content of the waste slurry [64; 65; 66]. The energy demand for hydrochar drying was calculated using a value of 2296 kJ/kg for water heat vaporization at 85 \({}^{\circ}\)C and assuming an efficiency of 80% in drying operation. The higher heating value (HHV) of hydrochar was supposed to be 15.7 MJ/kg based on data reported by [PERSON] and [PERSON] [62]. The lower heating value (LHV) was estimated considering the ultimate analysis also reported by these authors leading to a value of 14.8 MJ/kg. LHV of digested material was estimated using elemental composition data reported by [PERSON] et al. [48], considering ash content to be equivalent to that of inorganic solids contained in the original feed and using the equation proposed by [PERSON] et al. [67] for estimating HHV of biomass from elemental analysis. Composting degradation rate was calculated based on the mineralization rate reported by [PERSON] and [PERSON] [68] with values of 0.06 d\({}^{-1}\) for the first-order kinetic constant. The initial organic matter was estimated, assuming VS to be equivalent to OM content and estimating the total amount of solids present in the stream to be composed of char, TS from digestate and wood chips. The addition of wood chips was assumed at a weight ratio of 1:1 (TS content of 50%) and degradation of this material was disregarded. A recovery rate of 90% for wood chips was used for calculating the final amount of compost.