# ORC Optimal Design through Clusterization for Waste Heat Recovery in Anaerobic Digestion Plants
## 1 Introduction
proposed the optimization at nominal conditions for an ORC powered by the exhaust gases of a biogas fueled mGT. Several designs were proposed for different mGT operating conditions. In [25], [PERSON] et al. studied an ORC for biogas engine WHR by optimizing the evaporator geometry. All the studies above-mentioned considered fixed conditions as boundary conditions for the ORC design, and they neglected any variations in the anaerobic digestion plant operation. However, anaerobic digesters may change their thermal requirements daily, with significant seasonal variations [26], thus profoundly influencing ORC performance. Moreover, ambient temperature variation during the day influences the exhaust gas temperature of a mGT cogeneration unit and therefore the ORC evaporation temperature [11]. These phenomena should be considered during the ORC design to assess its actual performance. In [27], [PERSON] et al. partly considered this issue by proposing different sizes for an ORC + mGT system by considering the actual plant off-design in twelve different average conditions, one for each month of the year. The system was optimized, and the off-design of both mGT and ORC was analyzed to determine the best configuration. The analysis considered the seasonal modification of the digester thermal load, but did not consider the daily variations of cogenerator performance. This study proposed a methodology to fill the literature gap regarding the design of an ORC as a WHR unit for a biogas-fueled cogeneration unit. The design was performed by considering the digester load, the varying ambient conditions, and cogeneration unit operation. As a case study, the operating data presented in [11] for an anaerobic digestion plant near Pisa (central Italy) were considered. The ORC design was performed by clustering the plant data in four representative clusters and by defining four different designs, one for each cluster centroid. The ORC designs were compared among each other and with the designs related to the year average, winter average, and summer average operating conditions. The objective of the comparison was to select the design with the highest annual production. The comparison purpose was to demonstrate that careful choice of boundary conditions leads to an improved ORC design by maximizing the energy produced in the year. In particular, the energy production increase in comparison to the choice of annual average operating conditions was assessed to quantify the advantage of using the proposed design strategy based on a clusterization procedure. In theory, ORC design and off-design performance may be jointly considered, and they could be optimized together to maximize the annual production. In practice, this may result in a complex problem from an optimization point of view. The optimization would directly search for a trade-off between ORC power rating and operating hours since both parameters should be maximized. The reason for this trade-off is that a too-large power rating may yield a low production due to part-load operation. However, the search for the optimal configuration from both design and off-design operating conditions may be approximated by carefully choosing the design boundary conditions. The design can be divided into two steps:  
* a set of representative boundary conditions is selected for the design optimization problem through clusterization. * The design optimization problem is solved with a standard approach: the ORC power output is maximized for the given set of boundary conditions. As a previous study demonstrated, this may be efficiently and reliably done with general-purpose solvers [28]. After this, the ORC off-design performance was simulated, and the yearly production was calculated to verify the proposed methodology. A detailed off-design model was created to do this by using Aspen HYSYS, a state-of-the-art software for off-design system simulations.