## 3 System Configurations and Modelling
### Modelling  
The modelling of the single-effect AHT and AHP and double-lift AHP are based on the usual mass and energy balances and assumptions used for the modelling of absorption cycles [3]. On the other hand, the model of the double-absorption AHT is based on the work of [PERSON] et al. [29]. All models were developed in engineering equation solver (EES) [20].  
The general expression for the mass balance in each system component is written as follows:  
\[\sum m_{in,i}\cdot x_{in,i}=\sum m_{out,i}\cdot x_{out,i}, \tag{1}\]  
and the general expression for the energy balance in each component is given by the following expression:  
\[\sum m_{in,i}\cdot h_{in,i}-\sum m_{out,i}\cdot h_{out,i}=Q-W. \tag{2}\]  
Table 2 summarizes the main modelling assumptions for the temperature and temperature differences between the internal and external streams involved in the main heat exchangers of the absorption machines operating both at the SUS and SDS and for all the configurations presented in Figure 5.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multicolumn{2}{c}{**Absorption Heat Transformer (SUS)**} & \multicolumn{6}{c}{**Absorption Heat Pump (SDS)**} \\ \cline{2-7}  & **Single-Effect** & **Double AHT Type 3** & **Single-Effect** & **Double-Lift** & **Double-Effect** \\  & **[Figure 4a]** & **[Figure 4b]** & **[Figure 5a]** & **[Figure 5b]** & **[Figure 5c]** \\ \hline \multirow{4}{*}{Generator(s)} & \(T_{13}/T_{12}=\frac{20}{30}\,^{\circ}\)C & \(T_{23}/T_{24}=\frac{20}{30}\,^{\circ}\)C & \(T_{11}-T_{24}=5\,^{\circ}\)C & \(T_{21}-T_{14}=5\,^{\circ}\)C & \(T_{21}-T_{14}=5\,^{\circ}\)C & \(T_{21}-T_{14}=5\,^{\circ}\)C \\  & \(T_{14}-T_{6}=1\,^{\circ}\)C & \(T_{24}-T_{6}=1\,^{\circ}\)C & \(T_{11}-T_{21}=10\,^{\circ}\)C & \(T_{22}-T_{22}=10\,^{\circ}\)C & \(T_{21}-T_{22}=10\,^{\circ}\)C \\  & \(T_{7}=T_{1}\) & \(T_{7}=T_{1}\) & \(T_{7}=T_{1}\) & \(T_{7}=T_{14}(\text{\emph{pv}}_{7},\text{\emph{x}}_{13})\) & \(T_{17}=T_{14k}(\text{\emph{pv}}_{7},\text{\emph{x}}_{13})\) \\ \hline \multirow{4}{*}{Absorber(s)} & \(T_{30}-T_{12}=5\,^{\circ}\)C & \(T_{30}-T_{22}=5\,^{\circ}\)C & \(T_{11}-T_{14}+1\,^{\circ}\)C & \(T_{4}-T_{31}=10\,^{\circ}\)C & \(T_{4}-T_{30}+1\,^{\circ}\)C & \(T_{1}-T_{24}+1\,^{\circ}\)C \\  & \(T_{3}-T_{12}=1\,^{\circ}\)C & \(T_{13}-T_{22}=1\,^{\circ}\)C & \([\text{\emph{pc}}](\text{\emph{dh}}]\) & \(T_{1}-T_{8}=5\,^{\circ}\)C & \(T_{24}/T_{23}=\frac{20}{30}\,^{\circ}\)C \\ \hline \multirow{4}{*}{Condenser(s)} & \(T_{18}/T_{17}=\frac{20}{30}\,^{\circ}\)C & & & & & \\  & \([\text{\emph{pc}}](\text{\emph{dh}}]\) & \(On the other hand, solution heat exchangers are modelled using the effectiveness NTU method. The effectiveness (\(\varepsilon\)) for the solution heat exchangers is defined as follows:  
\[\varepsilon_{\text{{SHE}}}=\frac{Q}{{(m\text{-}Cp)}_{min}\ \Delta\text{T}_{max}}. \tag{3}\]  
The common assumptions for all the absorption systems modelled in this work are listed below:  
* Simulations were performed under steady-state conditions.
* Heat and pressure losses were not considered.
* The only pressure drop considered was in the throttle valves and assumed as isenthalpic.
* Saturated conditions at the outlet of absorbers, generators, condensers, and evaporators.
* The effectiveness of solution heat-exchangers was 50%.
* The heat transport line was pressurized at 600 kPa.