## 6 Off Design Analysis of the ORC Regenerated Cycle  
Once the geometry of the heat exchangers has been defined, it was possible to switch to the off-design analysis of the bottoming cycle. The simulations have been done at different engine loads, taking into account the actual size of the heat exchangers obtained by the detailed design. A simplified turbine model has been considered, taking into account the isentropic efficiency reduction vs. mass flow rate [6]. It should be emphasized that, by using exchangers with fixed characteristics, the performance of the cycle is usually lower compared to those derived from the preliminary analysis of the different possible configurations, presented in Section 3. The main differences lie in a reduction in the mass flow rate of toluene (3.3 instead of 3.8 kg/s) because the ORC is operated keeping the condenser pressure constant, and controlling the working fluid mass flow rate by changing the speed of the pump, or with a throttle valve placed after the pump itself [46; 47]. A reduced mass flow rate limits the effectiveness \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Regenerated Cycle Heat Exchangers**} & \\  & **Gas/Oil** & **Evaporator** & **Regenerator** & **Condenser** \\ \hline Shell kg/s & 9.1 (Gas) & 5.5 (Oil) & 3.36 (Tol.) & 3.36 (Tol.) \\ Tubes kg/s & 5.5 (Oil) & 3.36 (Tol.) & 3.36 (Tol.) & 80 (Water) \\ T\({}_{\text{HOT-IN }}^{\circ}\)C & 400 & 340 & 145 & 68 \\ T\({}_{\text{HOT-OUT }}^{\circ}\)C & 209 & 164 & 68 & 41 \\ T\({}_{\text{COD-IN }}^{\circ}\)C & 163 & 101 & 42 & 38 \\ T\({}_{\text{COD-OUT }}^{\circ}\)C & 340 & 262 & 101 & 42 \\ Configuration & / & CFU (parallel) & DFU & BIM \\ \(\Delta\)P\({}_{\text{shell}}\) bar & 0.008 & 0.027 & 0.019 & 0.013 \\ \(\Delta\)P\({}_{\text{thues bar}}\) & 0.28 & 0.017 & 0.025 & 0.04 \\ Q exchanged kW & 2064 & 2097 & 367 & 1472 \\ U\({}_{\text{0}}\) W/m\({}^{2}\)-K & 263 & 174 & 39 & 751 \\ Total cost \(\epsilon\) & 34,740 & 124,800 & 60,720 & 47,740 \\ Exchangers area m\({}^{2}\) & 152 & 791 & 266 & 395 \\ Tube length mm & 2700 & 6000 & 3000 & 3500 \\ Ext. diameter mm & 1300 & 800 & 1400 & 1200 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main exchangers sized. of the heat exchangers, therefore, superheated conditions may not be always reached at turbine inlet. Furthermore, the pressure losses in the heat exchangers reduce the turbine enthalpy drop, with a consequent lower power of about 50 kW at maximum load. Finally, the heat transfer coefficients calculated through the libraries of Aspen Tasc(r) have been almost always lower than the default value used in Aspen Plus(r), increasing the area of heat exchangers. This last aspect significantly affects their costs and overall dimensions. The actual performance obtained by the bottom regenerative Rankine cycle is presented in Table 5. The gross power gain reaches 520 kW and it is constant for medium and high engine loads, until the organic fluid flow rate can be kept constant. Knowing the real off-design performances of the energy recovery system, it is possible to calculate the real power of the combined engine and ORC system at each load, in order to evaluate the annual achievable fuel saving. By considering the engine average operation duty equal to 6960 h per year, the fuel saved can be calculated taking the engine load distribution into account, like in [48; 49]:  
* 100% load is typically used 1.5% of the time for maximum operating speed;
* 85% load is used to obtain the cruising speed, with the minimum specific consumption of the engine, and is usually kept for 85% of the time;
* 75% load is used for 5% of the time;
* 50% load is used in ancillary services, when the ship stops in port, for 7% of the time;
* 25% load is used for 1.5% of the time in port operation.