## 1 Introduction
### Characteristics and Benefits of Supercritical Energy Conversion  
A working fluid achieves a supercritical state (i.e., becomes a supercritical fluid) when the pressure and temperature is at or above its critical pressure and temperature. In the vapor generator of an ORC the working fluid at critical pressure is heated from subcooled conditions through the critical point ending in a supercritical state. During this process the temperature of the working fluid increases and during the subcooling phase it closely follows the saturation liquid curve. This property is exploited when recovering energy from sensible heat streams. It is known that closely matching heat profiles (see Figure 1) are beneficial to increase the thermal efficiency (higher mean temperature of the working fluid) and to increase the energy recovered (waste heat stream cooled to a lower temperature) [6]. For water,both the critical temperature (647.096 K) and the critical pressure (22.064 MPa) are high while for CO\({}_{2}\) the critical temperature (304.36 K) is low and the critical pressure (7.38 MPa) is moderate. These high pressures result in technical challenges and additional material cost [12]. Furthermore, complex multistage pumps are required to reach those pressures. If the efficiencies of the pumps are low, their used power will amount to a large share of the gross power produced [13]. Many studies theoretically investigate the performance benefit of supercritical ORCs. [PERSON] et al. [14] investigated the use of supercritical ORCs applied to the desalination of seawater using low grade heat sources. They concluded that for applications like waste heat recovery, a supercritical cycle is much more efficient and is capable of operating in a wider range when compared to a conventional ORC. [PERSON] et al. [15] carried out an exergy analysis with the aim of comparing the performance of a sub and supercritical ORC for the recovery of waste heat from the exhaust of a biogas fueled combined heat and power (CHP) system. [PERSON] et al. [5] found that the second law efficiency of supercritical cycles was up to 10% higher compared to subcritical ORCs depending on the waste heat temperature. For lower heat source temperatures the performance gain was higher. For the generation of power, where condensation takes place at constant temperature, while liquid to vapor transition phase occurs at a continuously varying temperature the supercritical cycle is sometimes referred as a transcritical cycle. If such a transcritical cycle is reversed, heat supply results in isothermal vaporization and condensation occurs at variable temperature with the heat rejected being used for heating applications. Such applications do not always require heat at a constant temperature. Examples are found in district heating and sensible heat storage systems. Because in the phase change region, pressure and temperature are directly linked, an increase in the cycle temperature inevitably increases the overall pressure ratio. Supercritical vapor compression cycles are inherently free from this limitation. Supercritical heat pumps for application in industry are mostly studied on a theoretical basis in the literature. [PERSON] et al. [16] proposed a supercritical heat pump with two evaporators with CO\({}_{2}\) as working fluid for drying application. [PERSON] et al. [17] performed a comparison between the performances of a supercritical CO\({}_{2}\) heat pump with an electric heating system and found that savings in energy of up to 65% can be achieved on using an optimized supercritical heat pump. [PERSON] et al. [18] used a transcritical CO\({}_{2}\) heat pump cycle to evaluate the performance of two heat pumps in (i) heating, cooling and domestic hot water and (ii) simultaneous cooling and desalination applications, achieving a coefficient of performance (COP) between two and three. After the curtailment of fluorinated fluids in the refrigeration sector in Europe interest in CO\({}_{2}\) as refrigerant has grown.