**1. Introduction**

Organic Rankine cycle-based processes are popular and effective methods to utilize heat sources with a wide range of temperature to utilize for electricity production. Most of the heat sources (like geothermal heat, industrial heat) are localized. Sometimes, there is a possibility to use an additional, non-localized heat source (like solar heat) to increase the maximal cycle temperature. For the basic thermodynamic cycle (Carnot-cycle), the first law efficiency is increasing by increasing the maximal cycle temperature while minimal cycle temperature is constant [1]. For other cycles, a similar law can be used, only in that case, maximal and minimal cycle temperatures have to be replaced by mean temperatures of heat addition and removal [2]. Using the assumption, that mean temperature of heat addition is increased when maximal cycle temperature is increased [2], a thumb-rule can be deducted, that by increasing the maximal cycle temperature, the cycle efficiency is always increased. Therefore, the increase of the temperature is always desirable in simple thermodynamic cycles, when the goal is the better performance, although other constraints (like the cost of the utilization of this added heal source) can overshadow the gain caused by the efficiency increase.

The design of an ORC-based power plant has at least four different layers [3]. The first one is about the thermodynamic cycle itself; one can design and optimize the Rankine-

cycle using various working fluids and various constraints (like defining the "ideality" or "reality" of the cycle by defining the irreversibility-induced entropy-production during expansion). The second layer is the technical/engineering layer; the designed Rankinecycle should be realized, the constraints of the previous steps have to be associated with various hardware components or process properties (like expander internal efficiency, pressure loss within the heat exchanger, etc.). An optimal second layer design might require several successive approximation steps, where the first step design has to be recalculate due to various points (for example inaccessibility of expander with the desired internal efficiency), and the new result has to be used for the next iteration. The third layer is the economical one. One should realize that investors built power plants not to generate electricity but to generate profit. Therefore, even the most brilliant thermodynamic cycle or ORC layout might be rejected upon financial points. The fourth layer is the environmental one; it is strongly connected to the third one [4].

With a bit of oversimplification, one can say that in the first layer, the thermodynamic properties of the working fluids, especially the shape of their *T-s* diagram are the most important factor [5,6], involving even molecular properties [7,8], while in the second layer already having the working fluid, the proper choice of technological components (most often the expander) plays the leading role [9,10]. However, sometimes these two steps are very much interlocked [11]. Obviously, the final vote is always for the economic side [4].

To have successful optimization in the second layer, one should clarify the problems raised in the first layer. Although most people assume that thermodynamics already solved all related problem and no further study is necessary concerning basic cycles, it is not a valid assumption. Here, we are going to show a clear example to disprove this assumption.

ORCs are supposed to be used to utilize heat sources not utilizable with traditional steam Rankine cycle; these heat sources are most often low-enthalpy ones with relatively low temperature and sometimes with low heat flow. For this reason, ORC-based power plants have limited financial viability; investment, operational and maintenance cost should be kept as low as possible. One of the ways to do that is the use of the basic ORC layout, namely one with a heater (liquid heater plus evaporator), an expander, a condenser and a pump, without using superheater or regenerative/recuperative heat exchanges [12]. Addition of any extra component can increase investment cost and decrease the "robustness" of the design. Therefore, our goal is to solve the thermodynamic problems without the involvement of any new part, i.e., using only the basic ORC design.

In this paper, we would like to show, that using the simplest ORC (or even traditional, water/steam-based RC) layout, a thermodynamic efficiency maximum should be found in all ideal cycles using wet and in several ideal cycles using dry working fluids. To prove this statement, the efficiencies of simple ideal ORC and TFC (Trilateral Flash Cycles) processes will be studied, using working fluids from various classes. The exact location of these maxima depends on the working fluid, as well as on the minimal cycle temperature. The existence of this kind of maximum shows that the increase of the maximum cycle temperature is not always a proper tool to increase cycle efficiency; sometimes it can be contra-productive.

## **2. Hybrid Systems**

The temperature of the heat source is an important factor for ORC applications, even though this technology can utilize sources with relatively low temperature. Geothermal energy is often considered as a low-grade energy-source; therefore, it cannot independently support high load applications. This is true even for countries with quite good geothermal potentials (like Hungary), where the well-head temperature of most of the existing geothermal wells are below 90 ◦C [13]. These kinds of sources are usually excluded from the pool of potential sources for electricity generation, although they can be numerous and some of them have very impressive heat-flux. In this case, one might apply hybrid systems (using secondary heat sources with a smaller heat flux but with higher temperature) to overcome the inherent weakness of the low-temperature sources.

Probably the most frequently used double-source design is the hybrid solar-geothermal installation [14–16]. For interested readers, a short overview of these kinds of systems is given in Appendix A. In hybrid solar-geothermal systems, the initial heating can be done by the low-temperature geothermal source, and then the solar heat is used to increase the maximal temperature. This can be done in two different ways. In the first solution, the solar heat can be used to "superheat" the already evaporated vapor [17]; this solution can be easily applied in retrofitted systems because only minor modifications of the existing geothermal power plant are required. In the second solution, the geothermal heat is used to preheat the compressed liquid, while the solar heat would be used to reach the maximal temperature and for evaporation. In this case, the pressure in the evaporator, as well as the input pressure of the expander, will be higher than for the same systems without solar heat; therefore, this method is not ideal for retrofitting of existing systems, but might be better for novel units [18]. The choice between the two options depends not only on the temperature values of the two sources but also on the available heat flows; in case of very small secondary heat flow, only the first case could be a plausible choice. Here, we prefer the second method, because our simple layouts would not consist of superheating units, i.e., the ORC design would remain simple.

Maximal cycle temperature, which is an important factor of the efficiency, can be increased in three ways in solar or hybrid solar systems:


One might expect, that just like for the ideal Carnot-cycle [1]; increasing the maximal cycle temperature for ORC or similar cycles would increase the thermal efficiency at least up to the critical point and therefore the application of an additional heat source would be limited only by technical or economic constraints [3]. Here, we are going to show that by using a basic ORC cycle, thermodynamic efficiency can have a maximum, associated with a sub-critical temperature, which depends on the material and the minimal cycle temperature.
