## 3 A Novel Model of the Reversible Rankine-Based Thermodynamic Cycle (RRTC)
### A Proposed Design of the Reversible Rankine-Based Thermodynamic Cycle (RRTC)
Figure 1 illustrates that the RRTC in ORC mode indicates red process lines, whereas heat pump mode refers to blue process lines. The control valve must be installed as a  
Figure 1: The proposed design of a novel reversible Rankine-based thermodynamic cycle (RRTC): the operating scheme for (**a**) the organic Rankine cycle (ORC), (**b**) the heat pump, and (**c**) its processes in a \(T\)-s diagram with the same temperature range (blue lines represent heat pump mode and red lines represent ORC mode, referring to the stream of working fluid through each component). regulator to switch between the processes from ORC to heat pump modes. These regulators have to be placed at the inlet and outlet of the pump or compressor, which increase the pressure of the working fluid in the liquid phase (for the ORC), and the superheated gas or two-phase (\(0<x<1\)) mixture (for the heat pump). Figure 1 illustrates that the liquid pump and compressor act to increase the pressure for ORC and heat pump modes. In this case, the pump is operating for the liquid phase while the compressor is operating for the vapor phase of the working fluids. In addition to a machine to transfer and pressurize the inlet and outlet working fluid, regulators must also be applied for the heat exchangers because the RRTC requires a single apparatus (see the heat exchanger side for the RRTC illustrated in Figure 1a,b). This regulator helps to regulate the working fluid flow rate through the heat exchanger; therefore, it can successfully change the phase of working fluids. Environmental impacts are often assessed based on ozone depletion potential (ODP) and global warming potential (GWP), and require that suitable and pro-ecological working fluids are used in further applications. Moreover, some working fluids have been phased out or are forbidden by the Montreal and Kyoto Protocols, or the Kigali Amendment [27]. Therefore, the use of a natural working fluid, which has a relatively low impact on the environment, seems to be promising. Propane is a natural working fluid that appears to be a good candidate because it has low toxicity, zero ODP, and relatively low GWP, and is environmentally friendly. Therefore, this study used propane as the working fluid for the RRTC. The thermal properties and other parameters of propane are listed in Table 1.  
A literature review shows that propane has been investigated as a suitable candidate as a working fluid [30] and applied to the ORC [31, 32], cascaded cycle [33], and transcritical cycle [34]. It is also used for the Joule-Thompson refrigeration cycle [35] and air conditioning/refrigeration [36, 37]. Moreover, because propane is a well-known and widely used substance, the development of novel parts (such as lubricant, etc.) may be unnecessary. Because it is an A3 working fluid, the hermetic seal needs to be considered. In modeling, the process can be calculated using thermophysical properties such as REFPROP [28] and CoolProp [29] using enthalpy changes. The mathematical description for each mode is discussed in the following sections: Section 3.2 for ORC mode and Section 3.3 for heat pump mode. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Name & Propane \\ CAS number & 74-98-6 \\ Formula & C\({}_{3}\)H\({}_{8}\) \\ R name & R-290 \\ Working fluid type [9] & ACZ (or wet working fluid) \\ Molar mass (g/mol) & 44.09562 \\ ODP & 0 \\ GWP & 3.3 \\ Safety based on ASHRAE designation & A3 \\ Critical temperature (K) & 369.89 \\ Critical pressure (MPa) & 4.2512 \\ Critical density (mol/dm\({}^{3}\)) & 5 \\ Triple point temperature (K) & 85.525 \\ Normal boiling temperature (K) & 231.036 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Thermal properties and other parameters of propane [28, 29].