Organic Supercritical Thermodynamic Cycles with Isothermal Turbine

Abstract

Organic Rankine cycles (ORC) are quite popular, but the overall efficiencies of these plants are rather very low. Numerous studies have been conducted in many scientific centers and research centers to improve the efficiency of such cycles. The research concerns both the modification of the cycle and the increase in the parameters of the medium at the inlet to the turbine. However, the efficiency of even these modified cycles rarely exceeds 20%. The plant modifications and the optimization of the working medium parameters, as a rule, lead to cycles with the high pressure and high temperature of live vapor and with a regenerator (heat exchanger) for the heating, vaporization and superheating of the medium. A new modified cycle with supercritical parameters of the working medium and with a new type of turbine has been described and calculated in the paper. For the first time, the isothermal turbine is proposed for supercritical organic cycles, though this solution is known as the Ericsson cycle for gas turbines. The innovative cycle and the usual ORC plants are characterized by almost identical block diagrams, while in the proposed cycle, the work of the turbine is obtained as a result of isothermal expansion and not in an adiabatic process. The analysis has been performed for 11 different working media and two cycles. The calculations have shown that power plants with isothermal expansion achieve better efficiency than cycles with adiabatic turbines. For example, the rise in efficiency changes from 8 percentage points for R245fa up to 10 percentage points for acetone. The calculations have proved that it is possible to obtain efficiency exceeding 50% for organic power plants. This is an outstanding result compared with modern steam and gas turbine units.

1. Introduction

The idea of ORC systems was born relatively long ago; the first systems were built in the 1960s. It is a variation of the steam cycle called the organic Rankine cycle (ORC). This name refers to steam cycles in which organic compounds are used as a working medium. They can be various fluids, ranging from short aliphatic hydrocarbons, through aromatic compounds, to complex synthetic freons. As for the components of ORC installations, they do not differ from standard steam systems (pump, steam generator, turbine, condenser). Initially, these power plants were installed mainly in the USA, Japan, Germany, Israel and Italy and reached power from several dozen kilowatts to several megawatts. Typical refrigerants used at the time were toluene, R11, R12, R113, R114 and Florinol [1]. A characteristic feature of these systems is the ability to operate at lower temperatures than is possible with water. They can also operate in a different pressure range, for example, condensing at atmospheric pressure. Very often, the top source of energy in ORC cycles is waste heat from various energy, agricultural or domestic processes [2,3]. You can find the use of waste heat from technological processes in industrial facilities (e.g., metallurgical, cement, etc.) [4,5]. In the literature on the subject, there are numerous cases of using the heat emitted by internal combustion engines [6] and gas turbines [7] in these power plants. Thanks to such applications, it is possible to increase the overall efficiency of the existing gyms by several percentage points. Some frequently analyzed heat sources for ORC systems are geothermal energy [8] and solar energy [9]. There are also examples of using the thermal energy of the oceans as a source of heat for ORC power plants [10]. Fluids working in ORC power plants should meet a number of requirements not related to thermodynamic properties. First of all, they should not be toxic substances and should be environmentally friendly. They should be cheap and easily accessible. They cannot react with the elements of the flow system. Often, not all of these conditions can be met while maintaining good thermodynamic properties. This results in the necessity to build better-secured and thus more expensive installations. This is the case, for example, when using combustible gases as working media. A big challenge for designers is choosing the right working medium. The literature on the subject contains a large number of fluids that can be used in ORC cycles. Saturated, unsaturated hydrocarbons, cyclic, heterocyclic, aromatic, various refrigerants, alcohols, siloxanes and others are considered. Many mixtures and their thermodynamic properties are not commercially available, and some of them are protected by patents. A well-matched organic medium should, above all, enable the system to operate with the highest possible efficiency and make it possible to significantly utilize the available heat source. In the literature on the subject, as a rule, several factors are analyzed as working fluids in ORC systems, incl. R245fa, R123, n-butane, n-pentane, R1234yf [11] ethanol [12], R134a, R152a, R236fa, R245fa, R404a SES36 [13], toluene, siloxanes [14], ammonia, cyclohexanes or acetone [15]. Power plants with organic Rankine cycles (ORC) differ significantly in efficiency from systems in which water is used, mainly due to the very low temperature in front of the turbine. As a result, these installations achieve an efficiency of about 10%, and only exceptionally can they reach about 20% thanks to the use of various modifications [16]. It is possible to increase the efficiency of the cycle by increasing the upper temperature [17] and modifying the installation structure, e.g., by adding an additional cycle [18] or by using an additional heater [19]. As in the case of steam turbines, efficiency can be increased by using an inter-stage superheater [20], regenerators [21,22] or by using a parallel evaporator [23]. Sometimes the efficiency of power plant components such as turbines, compressors, boilers, pumps and electric generators can also be improved. Although there are certain limitations (material strength, technology), the efficiency of some power plant components is very impressive, e.g., the internal efficiency of modern gas turbines [24] or the most advanced medium-pressure steam turbines can reach 93–94% [25]. There are intensive efforts to find better solutions in order to develop new types of power plants and new cycles. An important element determining and classifying ORC power plants, apart from the temperature of the source from which the heat is taken, is the operating pressure of the cycle. A review of the literature showed that the efficiency of even the most complex ORC systems is low compared to other solutions used in the power industry. Currently, very intensive works are underway to increase the efficiency of the ORC power plant by increasing the parameters of the working medium [26,27].

However, we suggest an innovative cycle of significantly better efficiency. The proposed cycle and the ORC are represented by the same block diagram, Figure 1a. In the case of a typical ORC, an adiabatic turbine is in use, Figure 1b. In the new cycle, an isothermal turbine is applied. The interpretation of this cycle in the temperature−entropy diagram is shown in Figure 1c. In this cycle, heat is added during the vapor generation (q_1a) and during the isothermal expansion (q_1b) while heat is rejected in the condenser (q₂). Work is generated in the isothermal turbine, and only a relatively small amount of it is used for the pump. In the regenerator, the superheat of the steam coming from the turbine after the isothermal expansion is used for the heating, evaporation and superheating of the medium. In turn, heat is supplied to the steam generator to further superheat the medium at the turbine inlet. In order to reach the final live vapor temperature, some heat q_1a from external sources is added. In the turbine, heat q_1b is introduced to realize the isothermal expansion. In this way, the proposed cycle is very similar to the Ericsson cycle known as the generalized Carnot cycle. The authors propose a new organic cycle which leads to a rise in efficiency up to 10 percentage points in the calculated variants (in the same temperature range). A new isothermal turbine is applied in the power plants which may be treated as the most important innovation.

The calculations showed that thanks to the use of an isothermal turbine and increasing the parameters of the working medium, it is possible to design an ORC power plant with efficiency comparable to modern steam turbines. In addition, at the end of the work, there is an example showing how to carry out isothermal expansion for one of the fluids analyzed in the study (Appendix A). These types of power plants seem to be a new approach that has not been considered and described so far. However, in the bibliography, some thermodynamic cycles with near-isothermal expansion have been described, both for turbines [28] as well as piston machinery [29]. Those methods consisted of injecting streams of hot medium into the main flow, but the effectiveness of this approach is uncertain. There are also no other mentions in the literature on this subject.

2. Modelling

The cycle diagram is the same for all the analyzed variants, but the plants vary in the type of expansion in the turbine. In both, the cycles live vapor is obtained in a vapor generator in which the heat of superheating is used for the heating, vaporization and superheating of the medium as well as the heat from an external resource.

The analysis includes two variants of power plants with different turbines:

Variant 1: cycle with adiabatic expansion in the turbine (AD);

Variant 2: cycle with the isothermal turbine (IZT).

Each cycle has been analyzed with the adiabatic (AD) and isothermal (IZT) turbines, so two variants of the cycle have been considered for each fluid.

The calculations have been performed assuming the upper and lower parameters of the working medium. The properties of the working fluids have been determined using the REFPROP [30] media library. Standard thermodynamics formulae have been used, occasionally applying the iteration method (when values of specific heat, which depend on other thermodynamic parameters, have been calculated). The basic equations are presented below:

-

heat delivered to the working media between the regenerator and the turbine nozzles:

$$q_{1a}=\left(i_1-i_6\right),$$

(1)

where:

q−heat,

i−enthalpy,

indexes refer to points marked in the diagram (Figure 1),

-

heat of the isothermal expansion

$$q_{1b}=T_1·\Delta s=T_1·(s_2-s_1),$$

(2)

T−temperature,

s−entropy,

Δ−gradient,

-

heat rejected in the condenser:

$$q_2=\left(i_3-i_4\right),$$

(3)

-

adiabatic turbine work:

$$l_{T\_AD}=\left(i_1-i_2\right),$$

(4)

l−work,

-

isothermal turbine work:

$$l_{T\_IZT}=T_1·\Delta s+\Delta i=T_1·(s_2-s_1)+(i_1-i_2),$$

(5)

-

pump work:

$$l_{PG}=\left(i_5-i_4\right).$$

(6)

Energy efficiency is understood as the relation between the net electric power and the heat flux supplied to the plant, given by the equation:

$${\eta }_{el}=\frac{N_{el}}{\stackrel{•}{Q_D}},$$

(7)

N−power,

$\stackrel{•}{Q_D}$−heat flux.

Depending on the variant, the net electric power is the power obtained in the turbine N_T, diminished by the power N_PG, used to drive the pump and by the losses in the system (generator efficiency η_G, mechanical efficiency η_m, external glands losses ζ_n:

$$N_{el}={\eta }_G·{\eta }_m·(1-{\zeta }_n)·N_T-N_{PG}.$$

(8)

The effectiveness of the regenerator (σ_R) is calculated as the relation between the actual temperature increase in the exchanger and the maximum possible increase and is determined by the formula:

$${\sigma }_R=\frac{\Delta T_{real}}{\Delta T_{\max }}=\frac{T_6-T_5}{T_2-T_5}.$$

(9)

The cycle analyses have been performed for 11 different media. The values of the initial vapor parameters have been determined, taking into account the media stability and the maximum cycle efficiency. Although the latest literature provides information about the research of the media at high parameters, e.g., for MDM [31], MM [32], c1cc6 [33], ndodecane [34], R134a [35], n-decane [36], R152, R236fa [37], R245fa [38], HFO-1234ze(E) [39] or titanium tetrachloride [40], the problem of the chemical decomposition of the organic media has not been sufficiently explained. In practice, the plant installation is refilled from time to time with some fresh media. However, to be on the safe side, a margin of 50 °C below the maximum temperature has been assumed while the initial pressure has been limited to 35 MPa (the maximum value for advanced ultra-supercritical steam turbines).

For all the calculated examples of variant 1, the initial parameters (temperature and pressure) and outlet pressure (in the condenser) are presented in

Table 1. Initial temperatures, pressures and condenser pressures for different working media for cycles with saturated live vapor and a regenerator for warming up the working fluid.

No.	Fluid	Chemical Formula	Name	Initial Temperature (AD and IZT) T0 [°C]	Initial Pressure (AD) p0 [MPa]	Initial Pressure (IZT) p0 [MPa]	Condenser Pressure (AD and IZT) pcond [MPa]
1	MDM	C8H24O2Si3	Octamethyltrisiloxane	686.00	16.00	30.00	0.003
2	D6	C12H36O6Si6	Dodecamethylcyclohexasiloxane	686.00	9.00	15.00	0.003
3	D4	C8H24O4Si4	Octamethylcyclotetrasiloxane	686.00	11.00	21.00	0.003
4	MM	C6H18OSi2	Hexamethyldisiloxane	686.00	13.00	24.00	0.006
5	R245fa	C3H3F5	1,1,1,3,3-pentafluoropropane	335.00	11.00	35.00	0.161
6	Acetone	C3H6O	2-propanone	501.00	12.00	35.00	0.034
7	R365mfc	C4H5F5	1,1,1,3,3-pentafluorobutane	420.00	13.00	35.00	0.062
8	c1cc6	C7H14	Methylcyclohexane	570.00	12.00	32.00	0.007
9	c3cc6	C9H18	N-propylcyclohexane	650.00	12.00	29.00	0.003
10	R1233zd	C11H24	Undecane	500.00	17.00	35.00	0.140
11	C11	C3H2ClF3	1-chloro-3,3,3-trifluoroprop-1-ene	700.00	13.00	27.00	0.003

[41,42,43]. The pressure in the condenser has been estimated, taking into account the temperature of cooling water equal to 15 °C, but not lower than 3 kPa. The increase in the temperature of the cooling water and the final difference in temperature in the condenser were assumed. Thus, the temperature of the vapor condensation was equal to about 28 °C or more (higher values for the limit of the minimum pressure in the condenser). The efficiencies of particular elements are presented in

Table 2. Assumed values of the efficiencies of particular cycle elements.

Description	Symbol	Value	Unit
Turbine efficiency	ηT	0.85	[−]
Pump efficiency	ηPG	0.80	[−]
Mechanical efficiency	ηm	0.98	[−]
External glands losses	ζn	0.02	[−]
Generator efficiency	ηG	0.90	[−]
Regenerator efficiency	ηR	0.95	[−]
Pressure drop in vapor generator/regenerator	pi/pi−1	0.98	[−]

[12,13,18].

3. Results and Discussion

The interpretations of the calculated cycles with the adiabatic and isothermal turbines are presented in Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7. As examples of working media, C₆H₁₈OSi₂ (MM), C₇H₁₄ (c1cc6), C₉H₁₈ (c3cc6), C₈H₂₄O₂Si₃ (MDM), C₁₁H₂₄ (C11) and C₃H₆O (acetone) have been chosen.

As can be seen in Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7, the type of factor has a very large impact on the initial and final values of the parameters at the turbine inlet. The saturation curves for the 11 analyzed factors are very diverse. This affects both the initial temperature (from 335 °C for R245fa to 700 °C for C11) but also the final pressure (from a minimum of 3kPa for MDM, D4, D6, c3cc6 and C11 to 161 kPa for just R245fa). However, in each of the analyzed cases, the application of isothermal expansion also causes, apart from greater work obtained in the turbine, an increase in the amount of heat (area under curves 2–3 in Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7) that can be recovered in the regenerator—marked as Vb in Figure 1a. Numerical values are presented in

Table 3. Overall efficiency, heat to be recovered in the regenerator and turbine work for adiabatic and isothermal expansions.

No.	Fluid	Adiabatic Expansion	Isothermal Expansion	Adiabatic Expansion	Isothermal Expansion	Adiabatic Expansion	Isothermal Expansion
		Overall Efficiency [−]		Heat [kJ/kg]		Turbine Work [kJ/kg]
1	MDM	0.4259	0.4837	1089.43	1346.03	224.22	312.92
2	D6	0.3584	0.4106	959.12	1105.07	115.76	156.68
3	D4	0.4047	0.4610	936.43	1140.12	175.67	244.01
4	MM	0.4557	0.5169	1108.86	1440.86	302.22	429.02
5	R245fa	0.2870	0.3728	186.12	329.95	109.61	191.84
6	Acetone	0.3679	0.4714	389.57	894.81	424.99	727.99
7	R365mfc	0.3403	0.4217	309.14	494.82	146.77	239.69
8	c1cc6	0.4286	0.4988	905.00	1369.11	387.34	578.33
9	c3cc6	0.4292	0.4937	1173.13	1624.15	372.95	538.03
10	R1233zd	0.3688	0.4588	289.45	493.89	167.97	272.31
11	C11	0.4067	0.4668	1392.12	1793.38	330.42	466.25

.

In the variant with the adiabatic turbine, the smallest efficiency was determined for R245fa (28.7%) and for R365mfc (34%), while the highest values of about 45.3% were found for MM. For isothermal expansion, the smallest efficiency was also found for R245fa (37.3%) and for D6 (41.1%) while the highest efficiency of about 51.7% was obtained for MM. In each case, the efficiency of the cycle with isothermal expansion is remarkably higher than the efficiency of the cycle with adiabatic expansion. The increase in efficiency varies from 8 points for R245fa up to 10 points for acetone. From the above considerations, it follows that the power plants with isothermal turbines (isothermal expansion) are characterized by significantly higher efficiency than the cycles with adiabatic expansion.

The working fluids are characterized by different values of the maximum applicable temperature; thus, it seems that the ratio of the total efficiency to the efficiency of the appropriate Carnot cycle (in the same temperature range) would be more suitable for the assessment of the cycle effectiveness (Figure 8). In this type of analysis, the most favorable fluids are acetone, c1cc6 and c3cc6, whose efficiency ratio is equal to 0.77. The use of isothermal expansion instead of adiabatic expansion allows the value of this ratio to increase from 9 percentage points for MDM, D6, D4 and MM to 17 percentage points for acetone.

The considerations show that it is possible to design organic power plants of relatively high efficiency even exceeding 50%, which is a very competitive value. It must also be underlined that the increase in initial pressure above the critical value leads to a significant rise in power plant efficiency (at the same upper temperature). In the case of ORC power plants (with a typical adiabatic turbine), the increase in efficiency varies from about two percentage points (acetone, c1cc6 c3cc6) to about six points for the medium R1233zd. For power plants with isothermal turbines, this growth is as high as 3.6 points for c3cc6 up to 10.1 percent points for R1233zd. The comparison of the efficiency for power plants with isothermal and adiabatic expansion is presented in Figure 9 for subcritical live vapor parameters [19] and in Figure 10 for supercritical parameters.

In the case of supercritical parameters, due to a higher value of the initial pressure, we observe higher cycle efficiency than for the power plants with subcritical parameters. The comparison of the optimum value of the initial pressure for subcritical and supercritical parameters is shown in Figure 11 for isothermal expansion and in Figure 12 for adiabatic turbines. The difference in the optimum initial pressure can reach several MPa and, sometimes, even more than 30 MPa (R365mfc).

The ratio of the total efficiency to the Carnot cycle efficiency for subcritical and supercritical parameters is shown in Figure 13 for adiabatic expansion and in Figure 14 for isothermal turbines. The increase in this ratio varies from 3 percentage points for c1cc6 and c3cc6 fluids and supercritical parameters up to 16 percentage points for R245fa and R1233zd fluids and subcritical parameters.

4. Conclusions

Nowadays, only simple ORC plants of small output are applied. As a rule, in these units, adiabatic turbines are used to drive an electric generator. The live vapor temperature in these cases is relatively low (<300 °C). The presented analyses have been performed for supercritical parameters of live vapor: high pressures and temperatures up to 700 °C. Furthermore, the thermodynamic cycles of power plants with organic media have been modified, and instead of typical organic Rankine cycles (ORC), organic cycles with isothermal expansion have been proposed and analyzed.

• It is possible to design organic power plants with relatively high efficiency even exceeding 50% (for MM as a working media at the temperature of 686 °C and pressure p₀ = 13 MPa). In the case of steam power plants, such high efficiencies can be achieved for ultra-supercritical steam parameters (pressures of the order of 30 MPa, temperatures of 600 °C, even above 700 °C, with double interstage superheating and an extensive system of regenerative heaters).
• The increase in initial pressure above the critical value leads to a significant rise in power plant efficiency (at the same upper temperature). The increase in initial pressure above the critical value causes the increase in efficiency of ORC power plant from about two percentage points (acetone, c1cc6 c3cc6) to about six points for the medium R1233zd for power plants with adiabatic turbines, and for power plants with isothermal turbines, this growth is as high as 3.6 points for c3cc6 up to 10.1 percent points for R1233zd. The values depend on the working media and on their parameters.
• The efficiency of the cycle with isothermal expansion is visibly higher than the efficiency of the cycle with the adiabatic turbine. The increase in efficiency varies from 8 points for R245fa up to 10 points for acetone.
• The isothermal expansion and the supercritical parameters of working media can significantly increase the efficiency of ORC power plants by up to 47−51%, which are competitive values characteristic of modern advanced power plants with ultra-supercritical parameters.

Isothermal expansion can be considered as a very effective and significant method of increasing power plant efficiency. Thus, the most important innovation is that instead of a typical adiabatic turbine, an isothermal turbine is applied. These types of power plants with organic media have not been described in the literature so far.

Our team has successfully designed, built and tested an experimental isothermal turbine. The photo of its model and the experimental stand is presented in [19]. Therefore, the obtained results can be of great relevance in future designs.