# ORC Optimal Design through Clusterization for Waste Heat Recovery in Anaerobic Digestion Plants
## 3 Methodology
### Off-Design  
Once the design conditions were known, an off-design model was developed in Aspen HYSYS. Aspen HYSYS is a simulator used to model chemical reactive and non-reactive processes from unit operations to full plants. For a given design condition, the software can design and simulate the behavior of various typologies of commercial heat exchangers such as shell and tube, plate multi-stream heat, and air coolers.  
The off-design model of the ORC was implemented by considering design data from MATLAB optimization. The model considered the main components of the ORC, thus including heat transfer fluid loop and digesters. Shell and tube heat exchangers were considered for the evaporator, regenerator, and water-cooled condenser. Each heat exchanger was designed in Aspen Exchanger Design and Rating (Aspen EDR) and then imported in Aspen HYSYS. Starting from the geometry and the flow conditions in the heat exchanger, the model created an internal mesh to solve the heat transfer problem (finite volume approach). In each volume, the code estimated the actual value of the overall heat transfer coefficient (U) by adopting Aspen heat transfer and fluid service (HTFS) correlations [43]. By repeating the calculation in each finite volume, the heat transfer process was solved, and the flow conditions at the heat exchanger outlet were determined.  
The solver determined the oil pump and the ORC pump off-design behavior by considering the design conditions and the expected head in three operating points. Commercially available data were adopted to determine the operative curves. Centrifugal pumps were supposed for both the ORC and the heat transfer loop. Regarding the turbine, a more complex criterion based on [PERSON]'s law was applied to determine off-design behavior, since the software did not provide any curve for commercial turbines. The approach followed to derive the turbine off-design curves is detailed in the next subsection.  
Digesters were simulated as a heat sink due to the lower operating temperature, which did not provide any critical issue in the heat transfer process.  
As for ORC management, a sliding-pressure control strategy was assumed by optimizing the evaporation pressure, superheating grade, and mass flow rate for each operative point. Optimization was performed in Aspen HYSYS by maximizing the system net power output.  
The result of the ORC module off-design analysis was an operating map, which is function of the mass flow rate, the temperature of the flue gas, and the heat requested by  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Description** & **Value** \\ \hline \(T_{ce,enc}\) & ORC evaporation temperature [\({}^{\circ}\)C] & 143.9 \\ \(T_{cd,enc}\) & ORC condensation temperature [\({}^{\circ}\)C] & 34.3 \\ \(\Delta T_{sh,enc}\) & ORC superheating degree [\({}^{\circ}\)C] & 18.0 \\ \(T_{loop,1}\) & Thermal oil temperature entering the ORC evaporator [\({}^{\circ}\)C] & 197.3 \\ \(T_{loop,2}\) & Thermal oil temperature exiting the ORC evaporator [\({}^{\circ}\)C] & 106.7 \\ \(\dot{n}_{loop}\) & Thermal oil mass flow rate [kg/s] & 2.0 \\ \(\dot{W}_{net,enc}\) & ORC net power output [KW] & 57.8 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Organic ranking cycle (ORC) and thermal oil loop variables and ORC net power output for the design corresponding to the most populated cluster (Cluster 3).  
the digesters. From the annual turbine and digester behavior, the actual energy produced by the ORC module was estimated by interpolating the obtained maps.