## 2 Materials and Methods
### Preliminary Assessment of the Alternative One-Step Digestate Processing Approach
It is also important to note that different energy carriers (i.e., electrical and thermal)will have different qualities (i.e., useful work obtainable reflective of the 2 nd law of thermodynamics), and thus, must be converted to equivalent energetic forms prior to employing the proposed NER methodology. Therefore, the values of the heat (thermal) energy required for maintaining the ACD process and the HTL process at 37 \({}^{\circ}\)C and 300 \({}^{\circ}\)C, respectively, were converted to their chemical energy forms. The electrical energy required to pressurize the digestate to 13.5 MPa within the HTL reactor was also converted to its chemical energy equivalent [52]. Therefore, the environmental performance of the integrated HTL and ACD processes, in terms of the NER metric, was determined by calculating the NER of the process as follows:  
\[\text{NER}=\frac{\sum\limits_{j}^{N}{HHV_{j}\times P_{j}}}{\left(\frac{E_{E} }{\eta_{H-E}+\frac{1}{\int\limits_{C-H}^{n}{\gamma_{C-H}}}}\right)} \tag{11}\]  
where \(HHV_{j}\) represents the higher heating value of the \(j\)th energy dense product of biogas (\(HHV_{m}\)) and biocrude (\(HHV_{b}\)), \(P_{j}\) represents the production capacity of the biogas and biocrude in kg/h, \(E_{H\_{f}i}\) represents input heat energy in kJ/h for the \(i\)th unit operation, from fossil based sources, \(E_{E}\) represents the electrical energy consumed by a high pressure pump, \(\eta_{C-H}\) represents the thermal efficiency of energy conversion from fuel to heat using boilers and \(\eta_{H-E}\) represent the thermal efficiency of energy conversion from fuel to electrical energy. \(N\) and \(n\) represent the number of energy dense product streams and the number of heat energy demanding unit operations, respectively. In this study, \(\eta_{C-H}\) and \(\eta_{H-E}\) were specified as 0.9 and 0.472 [52; 53; 54]. In this study it was recognized that the moisture content of the digestate will be largely influenced by the mass of the buffer solutions introduced to the ACD mixture, with a small (large) mass of the buffer solution leading to a small (large) overall moisture content of the digestate. Moreover, the dependence of the environmental performance (NER) of the integrated system on the moisture content of the digestate residue was assessed. In addition, it was assumed that the compositions of the ACD substrate mixture and the digestate were uniform, and the integrated system was operating at steady-state. Considering Equation (11), it was necessary to determine the HHVs of the energy dense biocrude and energy dense biogas products generated from the integrated system. Therefore, the HHV of the biocrude product (\(HHV_{b}\)) in MJ/kg was estimated as follows [45]:  
\[HHV_{b}=30.74-8.52 AOS_{c}+0.024X_{p} \tag{12}\]  
where \(X_{p}\) is the mass percentage protein content of digestate on a dry basis and \(AOS_{c}\) denotes the average oxidation state of feedstock-carbon which is calculated as follows [45]:  
\[AOS_{c}=\frac{3N_{mol}\%_{0}+2O_{mol}\%_{0}-H_{mol}\%_{0}}{C_{mol}\%_{0}} \tag{13}\]  
where \(C_{mol}\%\), \(H_{mol}\%\), \(N_{mol}\%\) and \(O_{mol}\%\) represent the percentage molar contents of corresponding elements in digestate. The HHV of the biogas product (\(HHV_{m}\)) in MJ/kg was estimated based on the experimentally determined mass fractions of the biomethane and carbon dioxide components, and methane HHV of 55 MJ/kg [55]. Due to the large range of the temperature change (from 298.15 K to 573.15 K) imposed during the HTL process, a change in the specific heat capacity of the digestate was anticipated during the HTL process.