## 2 Materials and Methods
### Organic Rankine Cycle (ORC) Unit  
Transcritical organic Rankine cycles (ORCs) were selected for the investigation, owing to their high performance, low payback period and efficient heat exchange with low and medium-temperature heat sources [60,81, 81, 82, 83, 84]. In fact, organic fluids present usually low critical pressures and, as a consequence, transcritical configurations are very attractive, owing to the possibility to guarantee proper performance without operating into extreme and dangerous conditions [16]. The main components of an ORC are a pump, an evaporator, a turbine, and a condenser (Figure 2a) [85,86]. The pump increases the pressure of the organic working fluid to the maximum value (1-2 process) then the evaporator is adopted to obtain the superheated vapour (2-3) that expands in the turbine (3-4) to provide the mechanical work that is converted into electricity by an alternator. Finally, the working fluid is condensed (4-1). An internal heat exchanger (IHE) is often used to improve the system efficiency [87]. To this purpose, the energy content of the organic fluid at the exit of the turbine is exploited (4-4*) to preheat the liquid before the entrance in the evaporator (2-2*). Specifically,  
Figure 1: Simplified scheme of the integrated geothermal-driven CHP system. centrifugal pumps, radial turbine and shell and tube heat exchangers were selected, according to the literature [19; 88; 89; 90]. Figure 2b depicts the different processes in the T-s diagram. The performances of the geothermal-driven ORC were characterised by adopting a thermodynamic model developed by the authors in the last years [16; 29; 91]. The model is general and refers to the ORC unit alone (pump, evaporator, turbine, regenerator and condenser). It is capable of characterising the behaviour of ORC systems in both nominal and partial load operations independently of the energy source. The model includes an intermediate thermal oil circuit when high-temperature sources are adopted. Since this component is not necessary for geothermal application, the algorithm considers only a single heat exchanger that transfers the heat input from the geofluid to the organic fluid directly. The model integrates the Refprop database to define the working fluid properties [92], whereas steady state conditions were imposed [93] and pressure losses in the ORC components were neglected [94], in line with the literature. The behaviour of the geothermal organic Rankine cycle system at full and part loads has been defined in terms of electric power and efficiency. The electric power \(P_{el}\) is evaluated as:  
\[P_{el}=\eta_{em,t}\ P_{t}-P_{p}/\eta_{em,p}-\ P_{p,g\alpha}/\eta_{em,geo}-P_{ p,coal}/\eta_{em,coal} \tag{4}\]  
where \(P_{t}\) and \(P_{p}\) represent the ORC turbine and pump power, respectively, while \(\eta_{em,t}\) and \(\eta_{em,p}\) are the corresponding electro-mechanical efficiencies. \(P_{p,g}\) and \(P_{p,coal}\) denote the power request of the pumps used to drive the geofluid and the cooling water, whereas \(\eta_{em,g}\) and \(\eta_{em,coal}\) are the corresponding electro-mechanical efficiencies. The electric efficiency of the ORC system \(\eta_{el,ORC}\) is:  
\[\eta_{el,ORC}=\frac{P_{el}}{\dot{m}_{g,\ ORC}\left(h_{g,ORC\ in}-h_{g,ORC\ out}\right)} \tag{5}\]  
where \(\dot{m}_{g,\ ORC}\) is the mass flow rate of the geothermal source exploited in the ORC unit while \(h_{g,ORC\ out}\) represents the enthalpy of the geofluid at the exit (\(out\)) of the ORC evaporator. An iterative procedure has been implemented to take into account the variation of temperature and pressure at the turbine inlet when the system operates at partial loads, by using the [PERSON]'s ellipse approach. The algorithm evaluates the off-design variation of the turbine, pump and heat exchanger performance. More details on ORC partial load operations are available in a previous  
Figure 2: Typical system layout (**a**) and T\({}_{s}\) diagram (**b**) of an organic Rankine cycle (ORC) with internal regenerator (IHE) and transcritical conditions.