## 2 Methodology
### Off-Design Model  
The operating conditions of the system are influenced by the performance of the heat exchangers and turbine [33; 34]. In this regard, the different steps of off-design calculation are indicated in Figure 2. As shown, the first step in off-design process calculation is related to obtain the heat transfer capacity (UA) of heat exchangers in the design mode which is outlined in Table 1. The heat transfer rate (\(\dot{Q}\)) in the heat exchangers is expressed as [35]:  
\[\dot{Q}=\textit{UA}\ \Delta T_{\textit{LMTD}} \tag{1}\]  
where \(U\) is the overall heat transfer coefficient, the area of the heat exchanger is \(A\) and \(\Delta T_{\textit{LMTD}}\) represents the logarithmic mean temperature difference between the hot and cold streams in the heat exchanger. In the next step, the off-design behavior of the heat exchangers is considered according to the method presented by [PERSON] [34]. In off-design conditions, the variations in mass flow rates from the design conditions bring about a change in the UA. The heat exchange capacity is modified considering the actual mass flow rate:  
\[\frac{(\textit{UA})_{\textit{off-design}}}{(\textit{UA})_{\textit{design}}}= \left(\frac{\dot{m}_{\textit{off-design}}}{\dot{m}_{\textit{design}}}\right)^{m} \tag{2}\]  
The heat exchanger configuration determines the exponent \(m\). The exponent m is set to 0.44 for the air-cooled condenser, 0.66 for the generator, solution heat exchanger and evaporators, 0.15 for the boiler [36]. After obtaining the off-design characteristics such as UA for the considered heat exchangers, calculation of the turbine isentropic efficiency is the next step. The isentropic efficiency of the turbine is considered as a function of enthalpy drop and volumetric flow rate at the outlet of the turbine. The off-design behavior of the isentropic efficiency of the turbine depends on two coefficients \(r_{h}\) and \(r_{v}\) according to [37]. The coefficients depend on the outlet volume flow rate and the enthalpy drop in the turbine:  
\[r_{T}=\sqrt{\frac{h_{\textit{Turbine inlet}}-h_{\textit{Turbine outlet}}}{\left(h_{ \textit{Turbine inlet}}-h_{\textit{Turbine outlet}}\right)^{design}}} \tag{3}\]  
\[r_{h}=\left(\left[\left(1.39r_{T}-5.425\right)\times r_{T}+6.274\right]\times r _{T}-1.866\right)\times r_{T}+0.619 \tag{4}\]  
where \(h\) is the enthalpy and exponents design means the calculated value at design [37]:  
\[r_{VT}=\frac{\left(\dot{V}\right)}{\left(\dot{V}\right)^{design}} \tag{5}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Dead state pressure (\(\textit{bar}\)) & P\({}_{0}\) & 1 \\ Dead state temperature (\({}^{\circ}\)C) & T\({}_{0}\) & \(T_{0}+5\) \\ Geothermal hot water temperature (\({}^{\circ}\)C) [24] & T\({}_{\text{in,geo}}\) & 138 \\ Geothermal hot water mass flow rate (kg/s) [24] & m\({}_{\text{geo}}\) & 120 \\ Ambient temperature (\({}^{\circ}\)C) [24] & T\({}_{\text{amb}}\) & \(-5.68\) \\ Heating demand (\(M\)W) [24] & \(\dot{\text{Q}}_{\text{heating}}\) & 11.8 \\ Evaporator temperature (\({}^{\circ}\)C) [24] & T\({}_{\text{eva}}\) & 5 \\ Turbine inlet pressure (bar) [31] & TIP & 20 \\ Ammonia concentration in the boiler (\(\%\)) [32] & \(\dot{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text  
\[r_{v}=([(-0.21r_{VT}+1.117)\times r_{VT}-2.533]\times r_{VT}+2,588)\times r_{VT}+0.038 \tag{6}\]  
where \(\dot{V}\) shows the volumetric flow rate at the outlet of the turbine. Therefore, the isentropic efficiency of the turbine in off-design can be calculated as [32]:  
\[\eta_{s,tur}=\eta_{tur}\times r_{v}\times r_{h} \tag{7}\]  
It is important to note that the off-design values of \(\eta_{s,tur}\) and \(r_{VT}\) can take a value higher than the design mode values. In addition, the UA value and turbine isentropic efficiency, the thermodynamic properties of different states have been calculated. The whole off-design case is calculated in an iterative process which ends when the simulation shows convergence.