## 2 Materials and Methods
### Preliminary Assessment of the Alternative One-Step Digestate Processing Approach  
To initially assess the viability of the one-step HTL digestate processing pathway proposed, the yields of the possible products were predicted and assessed. This is because the theoretical product yields from the HTL processing of the digestate can be estimated if the digestate's carbohydrate, lipid, proteins and ash content are known [44; 45]. The digestate residue investigated as a feedstock for the HTL was obtained from the ACD bioreactor that presented the highest biomethane potential. The yields of the products, namely biocrude, insoluble solid residue (also called biochar), soluble solids dissolved in the post-HTL water and the gas phase products, obtained after the HTL processing of the wet digestate, were estimated using predictive models [44; 45; 46]. According to the recent work of [PERSON] et al. [46], the optimal yield of the biocrude product (\(y_{bio}\)) on a dry basis (wt.%, percentage of kg product/kg of dry digestate) can be estimated as follows:  
\[ \begin{array}{ll}y_{bio}&=0.9X_{l}+0.385X_{p}+0.025X_{c}+0.052\bigg{[}\frac{ X_{l}X_{p}}{\big{|}X_{l}-X_{p}\big{|}}\bigg{]}+0.093\Big{[}\frac{X_{l}X_{c}}{ \big{|}X_{l}-X_{c}\big{|}}\Big{]}\\ &+0.003\bigg{[}\frac{X_{p}X_{c}}{\big{|}X_{p}-X_{c}\big{|}}\bigg{]}\end{array}  \tag{7}\]  
where \(X_{l}\), \(X_{p}\) and \(X_{c}\) represent the lipid, protein and carbohydrate mass content, in wt.%, in feedstock, respectively. The optimal yield on a dry basis (wt.%, percentage of kg product/kg of dry digestate) of other useful products, such as the yield of soluble solids(\(y_{ss}\)) and the yield of the gaseous products (\(y_{g}\)), were estimated by applying the additive models proposed by [PERSON] et al. [45] as follows:  
\[y_{ss}=0.24X_{p}+0.86X_{a} \tag{8}\]  
\[y_{g}=0.07X_{p}+0.46X_{c} \tag{9}\]  
In the two equations, \(X_{p}\), \(X_{c}\) and \(X_{a}\) represents the protein, carbohydrate and ash content in wt.%, in the digestate on a dry basis, respectively. The theoretical yield of the biochar product (\(y_{char}\)) was estimated by mass balance as follows:  
\[y_{char}=100\%-\big{(}y_{g}+y_{aq}+y_{bio}\big{)} \tag{10}\]  
The theoretical model equations of Equations (8)-(10) were determined for the HTL process occurring at a reaction temperature and reaction time of 300 \({}^{\circ}\)C and 30 min [45], respectively. In the present study the reactor pressure has been specified as 13.5 MPa, since HTL processes typically occur at pressures conditions ranging from 5-20 MPa. To characterize the digestate residue, the ash content, specific gravity and elemental content were measured using the methods highlighted in Section 2.2 above. The residual lipid content, was determined gravimetrically [47] using a BST/SXM-1 after Soxhlet extraction unit (FOSS Ind., Denmark). The protein content was determined according to the AOCS (American Oil Chemists' Society) official method Ba4e-93 [48]. The total carbohydrate content was determined by subtracting the fractional ash content, crude fat content and protein content from the value of unity [49]. To further test the viability of introducing a HTL processing step for enhanced resource recovery, the environmental performance of an integrated system of HTL and ACD technologies was initially assessed. In this study, the environmental performance of the integrated system was analyzed using the net energy ratio (NER), because NER is widely regarded as a surrogate measure of renewability, and thus, is considered a sufficient metric in most initial sustainability assessments [50]. Generally speaking, if the NER ratio is greater than one, the NER of the overall system presents a favorable energetic performance and is environmentally sustainable [50; 51]. This is because a NER ratio that is greater than one constitutes the minimum requirement necessary to indicate if a given system results in reduced dependency on fossil energy [51].