## 4 Materials and Methodology
### Model Inputs, Assumptions, and Limitations  
Biogas production estimates were based on the latest available data on GCC wastewater and sludge generation rates. Estimation of the expected growth of biogas production, based on future wastewater and sludge generation rates, was beyond the scope of this study due to the lack of such data. The COD loading rates for each country are presented in Table 2. The COD removal efficacy was, in its near entirety, based on the influent and effluent COD concentration. The BOD/COD ratio served as the biodegradable fraction of wastewater (\(f_{d}\)). The fraction of substrate that was used for cell synthesis (\(f_{s}\)) ranged between 5-25%, a midpoint value of 15% was used in the model [40]. For Kuwait's reference case, 158,000 tonnes of dry sludge are produced annually. The AD was assumed to operate at the conventional temperatures range of 30-40 \({}^{\circ}\)C (mesophilic temperatures range) with an optimal pH range (6.5-8) [28,47]. The biodegradability of sludge was not analyzed in this study, though it was assumed to be 20.2% [48]. The total volume of biogas was impacted by the partitioning CO\({}_{2}\) in the aqueous and gas phase (biogas). Although CH\({}_{4}\) has low water solubility, a significant portion of CO\({}_{2}\) typically remains in solution [40]. The partitioning of CO\({}_{2}\) (i.e., composition of biogas) is also affected by temperature and pH of the final solution. It is worth noting that biomethane estimates, which are based on COD loading data, were expected to be overestimated since the COD method does not account for energy expenditure on cell synthesis, and this model consequently assumed that all carbon is converted to CH\({}_{4}\) and CO\({}_{2}\). The model also assumed the COD of CH\({}_{4}\) to be 64 g of O\({}_{2}\)/mole of CH\({}_{4}\), regardless of substrate. Additionally, the C/N ratio of the sludge was 6.48:1 which \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Mean** &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & **Unit** \\ \hline pH & 6.42 & 0.4 & \\ Moisture & 7.1 & 0.5 & \% \\ Ash & 51.5 & 3.7 & \% \\ Conductance & 10,277 & 15.2 & \(\mu\)mho/cm \\ Alkalinity & 818 & 43.1 & mg/L \\ T.O.C & 201,719 & 14,666 & \(\mu\)g/g \\ T.C & 236,096 & 36,938 & \(\mu\)g/g \\ Carbon & 24.2 & 3 & \% d.m. \\ Hydrogen & 4.6 & 0.9 & \% d.m. \\ Oxygen & 14.8 & 2.4 & \% d.m \\ Nitrogen & 4.2 & 0.5 & \% d.m. \\ Sulfur & 0.9 & 0.08 & \% d.m. \\ C/N & 6.5 & & \\ Calcium & 27,560 & 210 & mg/Kg \\ Copper & 389 & 15 & mg/Kg \\ Iron & 14,600 & 511 & mg/Kg \\ Manganese & 9694 & 377 & mg/Kg \\ Zinc & 826 & 20 & mg/Kg \\ C.O.D & 6695 & 203.9 & mg/Kg \\ H.H.V & 9.4 & 0.8 & MJ/Kg \\ Empirical formula \({}^{\star}\) & C\({}_{7}\)H\({}_{15}\)O\({}_{3}\)N & & \\ Mass & 158 \(\times\) 10\({}^{3}\) & & Tonne/year \\ \hline \hline \end{tabular} \({}^{\star}\)The empirical formula was calculated using a mass composition (C,H,O,N) data approach.  
\end{table} 
Table 3: Dry wastewater sludge characteristics for Kuwait. is sub-optimal for AD as the optimal range of C/N ratio for gas production is 20-35:1 [36]. Consequently, the biomethane production rates (which are based on COD loadings) are considered as the theoretical upper limits for biomethane production. Estimation of electrical power was based on a CHP engine with 45% efficiency and a biomethane energy content of 11.04 kwh/m\({}^{3}\). The reverse osmosis (RO) energy requirement was 5.5 kwh/m\({}^{3}\) for desalinating seawater and was calculated using Kuwait's RO performance data and applied to the other GCC states. The estimated biomethane production level for the region is based on the assumption that all the produced sludge from the wastewater plants is collected and anaerobically digested and does not take into account other waste streams such as municipal and agricultural wastes, the economic feasibility--which varies by location, plant size, and market conditions within each member state.