REFPROP Software Research Articles

Exploratory study on low-GWP working fluid mixtures for industrial high temperature heat pump with 200 °C supply temperature

The development of an industrial high temperature heat pump (HTHP) using a subcritical vapor-compression cycle (VCC) for process heat delivery at 200 °C faces significant challenges due to the scarcity of suitable single-component working fluids. These challenges are further compounded by safety, environmental concerns, material and lubrication oil compatibility and cost considerations. In response, this study investigates the potential of various fluid mixtures to meet these stringent criteria. Using the REFPROP and Cantera software libraries, a Python code was developed to simulate a simplified HTHP VCC with an advanced cycle architecture and assess the flammability risks of the proposed mixtures. Ten single-component fluids of two different families of compounds, hydrocarbons (HCs) and hydro(chloro)fluoroolefins (H(C)FOs), were pre-selected as promising candidates as mixture components. From these, over 460,000 binary, ternary, and quaternary mixtures were generated and evaluated for cycle performance. Although no mixture perfectly met all the predefined criteria, a binary blend of cyclopentane and R1336mzz(Z) in a mole fraction of 0.68 and 0.32, respectively, emerged as the most promising candidate. This mixture demonstrated the best balance of performance and safety under the imposed constraints and is selected for further experimental investigation and validation in a specially designed test rig.

Investigating Internal Heat Exchanger Performance in a VCR System with a CO2 and LPG Refrigerant Mixture

In this study, an attempt was made to develop a cooling system with an internal heat exchanger using a mixture of carbon dioxide (CO2) and liquefied petroleum gas (LPG) as refrigerants to help eliminate the global warming potential and other harmful environmental effects caused by conventional refrigerants'. The CO2 and LPG refrigeration experimental setup was constructed with varying sizes of capillary tubes, a pressure controller, an evaporator, and a gas hob. The working ranges were initially confirmed through exploratory experiments with low-pressure and high-pressure flow circuits, using and without an internal heat exchanger (IHE). The evaporator temperature helped to determine the proportional changes in the coefficient of performance (COP). The REFPROP software design was used to conduct experiments and determine the important process parameters. A confirmation test was performed to validate the expected results of the REFPROP software technique. The results showed that the experiments conducted using IHE had a COP with greater performance levels as follows: mean of 1.398 and SD of 0.367 which is greater than the value of the experiments undertaken without IHE which had a COP performance levels as follows: mean of 0.67 and SD of 0.19. The Paired Samples T-test found these differences to be significant, at p-value < 0.033. The null hypothesis was rejected, hence there is evidence to suggest that the COP of the experiment with IHE is statistically greater than the COP of the experiment without IHE, with a 95% confidence interval of -1.357 and -0.099

Energy, exergy, exergoeconomic, economic, and environmental analyses and multi-objective optimization of a novel combined cooling and power system with dual-pressure Kalina cycle-absorption refrigeration

A novel combined cooling and power system, the dual-pressure Kalina cycle-absorption refrigeration (DPKC-AR-CCP), is proposed for the cascade utilization of waste heat from high-temperature flue gas and jacket water from internal combustion engines. A pneumatic booster pump unit is employed to increase the inlet pressure of the low-pressure expander, with heat generated during the compression process utilized for preheating the ammonia/water mixture, and exhaust gas from the low-pressure expander is combined with driving gas for absorption refrigeration. By integrating the first and second laws of thermodynamics with the SPECO Methodology, models for energy, exergy, exergoeconomy, economy, and environment of the DPKC-AR-CCP system are developed. A multi-objective optimization model is formulated with maximum exergy efficiency, minimum total exergy cost rate, and maximum annual equivalent carbon dioxide (CO2) emission reduction as objective functions. MATLAB software (combined with REFPROP software) is utilized for simulation and multi-objective optimization. The performance of each component under specific conditions is assessed, and a comparison with the simple absorption refrigeration/Kalina cogeneration system (AR/KC) highlights the advantages of the DPKC-AR-CCP system; an investigation into the effects of different operating parameters on performance is conducted. The results indicate that, under identical operational parameters, the DPKC-AR-CCP system exhibits a substantial increase in net output power (230.2 %), cooling capacity (98.7 %), and exergy efficiency (148.8 %) compared to the simple AR/KC system; payback period is reduced by 64.8 %; and annual equivalent CO2 emissions are decreased by 202.2 %. However, there is an increase in the total exergy cost rate by 90.5 %. The optimal concentration of ammonia/water is determined to be 0.816/0.184, with a heat exchanger outlet temperature of 341.07 K, driving pressure of 0.654 MPa, and low-pressure expander inlet pressure of 5.064 MPa. Correspondingly, the optimal exergy efficiency is 87.2 %, the annual reduction in CO2 emissions is 5.53 × 107 kg, and the total exergy cost rate is 288.48$/h.

Wet-to-dry transition description in the mixture of working fluids

The organic rankine cycle performance and some similar processes depend on many factors. One of them is the category of the working fluid, influencing the performance through the phase/phases during and at the end of the expansion process. Droplet formation for wet fluids and superheated for dry fluids motivated the researchers to seek isentropic working fluids, where expansion could proceed and terminate in a saturated vapour state. The shape of the T-s diagram is a material property; it cannot be changed for real pure fluids, but small jumps can be initiated by replacing one working fluid with a chemically very similar one, like Propane (a wet one) with Butane (a dry one). Our study presents a much smoother transition, using mixed working fluids prepared from chemically similar materials to obtain almost ideal zeotropic mixtures. The main point of our study is to show the wet-to-dry transition for mixtures and prove or disprove the existence of compositions where the fluid can show T-s diagram resembling the ones for ideal isentropic working fluids. For this purpose, Propane was mixed with other alkanes, such as Butane, Pentane, and Hexane, in various compositions, and the thermophysical properties of fluids were calculated by using the REFPROP software program. Wet-to-dry transitions were shown for the Propane/Hexane mixture at (0.6584 + 0.3416 mass fraction), while (0.5823 + 0.4177 mass fraction) and (0.6436 + 0.3564 mass fraction) was the transition mixture for Propane/Butane and Propane/Pentane respectively. Consequently, when exceeding the mentioned composition range, the fluids switch from wet to dry without forming a composition showing ideal isentropic properties. Therefore, isentropic working fluid (showing an infinite slope for the saturated vapour branch in a finite, nonzero temperature range) was not found during this transition.

Evaluating the techno-economic viability of different solar collectors integrated into an adsorption cooling system in tropical climate conditions

The technology and performance of solar adsorption cooling systems have reached maturity, enabling them to meet the growing demand for air conditioning. High upfront and operating costs have, however, hindered the commercial spread of solar adsorption cooling systems. Comparing the solar adsorption cooling system with commercial air conditioners, the solar thermal system offers superior efficiency. In order to enhance the techno-economic potential of solar adsorption cooling in Malaysia, this study developed a combination of analytical and conceptual frameworks in the form of a multilayer computational network to identify the most efficient solar thermal system. TRNSYS, MATLAB, and REFPROP software were used to model and simulate the solar adsorption cooling system. A Particle Swarm Optimization algorithm (PSO) implemented in MATLAB and linked to TRNSYS was then used to determine the optimal components and variables for each solar thermal system. To determine the most efficient solar thermal system, a techno-economic assessment was conducted to evaluate the solar adsorption cooling system incorporating optimized solar thermal systems. The findings reveal that among the various types of collectors investigated, the evacuated tube collectors demonstrated the highest efficiency in providing the necessary heat energy for the adsorption cooling system. In contrast, the linear Fresnel reflector collector and parabolic trough collectors display exceptional performance, mainly under clear sky conditions. Meanwhile, the photovoltaic-thermal collectors exhibit the greatest energy-saving and techno-economic potential. This advantage arises from their ability to simultaneously generate power and heat, taking advantage of the cost disparity between electricity and natural gas in Malaysia.

Energy and cooling performance of carbon-dioxide and hydrofluoroolefins blends as eco-friendly substitutes for R410A in air-conditioning systems

Air-conditioning and refrigeration systems are electrical appliances that use a huge amount of energy and contribute indirectly to global warming. Also, R410A which was initially developed as a substitute for ozone-depleting refrigerants in the air-conditioning systems has been phase-out due to its high global warming potential (GWP) and the resulting harmful effect on the climate. In addition to the issue of refrigerant high GWP, energy consumption is a significant issue. The energy efficiency of new refrigerants must then be considered in the search for alternative refrigerants to ensure that they do not lead to an increase in greenhouse gas generation at the power source. Therefore, this paper investigates the energy and cooling performance of four new multi-components and ecologically friendly refrigerant blends that contained carbon dioxide and hydrofluoroolefins in their compositions as substitutes for R410A in air-conditioning systems. Relevant thermodynamic equations and REFPROP software were employed for the computational analysis. The results indicated that the new blends (R445A, R455A, R470B and R470A) exhibited a desirable low compression ratio and high heat transfer for cooling applications. The blends also exhibited low compressor energy input and low specific cooling energy. R455A has an average coefficient of performance (COP) of 24.6% above that of the reference refrigerant (R410A). The cooling capacity per unit volume for R470B, R455A and R470A across a temperature range of 253 to 293 K are higher by 1.3, 6.0, and 12.6%, respectively than that of R410A. Generally, among all the four new substitute blends, the overall assessment revealed R455A as the best replacement for R410A in air-conditioning systems due to its superior performance in terms of its low compression ratio, compressor energy and specific cooling energy. R455A also has the highest COP and relatively high cooling capacity per unit volume.

Evaluation of Three Working Fluid on an Organic Rankine Cycle of a Waste Heat Recovery Electric Generator

The aim of this study is to evaluating an Organic Rankine Cycle (ORC) system from diesel engine waste heat recovery by selecting three different working fluids with different pressure and temperature condition. The working fluid include N-Pentane, R-245fa, and R-134a are conditioned on variations in pressure and evaporation temperature with a difference of 0.5 bar and 5 °C to achieve the best thermal efficiency. The proposed evaluation involved two phases, first is analysis of the working fluid with various condition is carried out using REFPROP software and then results of that analysis will be used as the basis of input in calculating the overall heat balance using the Cycle Tempo software. This study found that a diesel engine with a capacity of 1000 kVA wastes energy of 1177 kW which is released through exhaust pipe and engine radiator can produce a turbine power of 144,47 kW. The highest thermal efficiency of 13.48% was obtained by using the working fluid R-245fa at the evaporator pressure and temperature of 23.5 bar and 154 ⁰C, respectively.

Comparison and analysis of the performance of a spiral groove mechanical seal subjected to phase change with different sealing media

The goal of this research is to investigate the impact of four kinds of easily vaporized sealing media(liquid hydrogen, liquid oxygen, liquid nitrogen and water) on phase change and sealing characteristics of a spiral groove mechanical seal(SGMS). Based on homogeneous flow assumption, a dynamic continuous boiling model is developed taking into account phase change of fluid film. With fluid pressure and fluid enthalpy as primitive variables, the properties of single-phase fluid and mixture fluid can be obtained by REFPROP software. The influence of the sealing medium on phase state stability criterion, steady-state and dynamic performances, and geometric structure parameter optimization is investigated. The findings reveal that dynamic viscosity is the key physical parameter of the sealing medium, affecting the seal stability and the phenomenon of phase change of an SGMS. The sealing medium with a high dynamic viscosity may obviously block the phenomenon of vaporization, which is advantageous in delaying the process of phase change and shortening the temperature range of quasi-vapor phase state in which an SGMS is unstable. The trends of steady-state and dynamic performances of an SGMS undergoing phase transition are identical for any type of easily vaporized fluid indicated in this work as a sealing medium. Taking into account both steady-state and dynamic performances, and independent of the type of sealing medium used, the best range of groove-to-dam ratio of an SGMS undergoing phase change is 0.5 < γ < 1.5.

An Exploration of the Application to Buildings of an Organic Rankine Cycle Power Generation System Driven by Solar Evacuated Glass Tubes

Abstract Solar technologies are an efficient means of addressing environmental pollution and climate change challenges. In this study, an organic Rankine cycle (ORC) system driven by solar evacuated glass tubes named solar water power generation (SWPG) system was experimentally investigated to explore the performance of the SWPG system in powering buildings. For ORC, a new mixture called TD-3 was introduced for the experiment after comparing the thermodynamic characteristics of five working fluids using refprop software. The solar radiation intensity was simulated for solar collectors to determine the best installation angle of the evacuated glass tubes to be 30 deg in Tianjin, China. The power generating efficiency was tested as high as 4.5% at 1:00 pm on July 15. The optimization of operating parameters and the modification of generating equipment contributed to the increase in power generation. The SWPG system could achieve an optimal power output when the system guaranteed a small superheat and no more than 3 °C subcooling using the TD-3. The transmission ratio between the generator and expander also impacted power generation that the ratio of 2:1 helped optimize the power generation.

The NIST REFPROP Database for Highly Accurate Properties of Industrially Important Fluids.

The NIST REFPROP software program is a powerful tool for calculating thermophysical properties of industrially important fluids, and this manuscript describes the models implemented in, and features of, this software. REFPROP implements the most accurate models available for selected pure fluids and their mixtures that are valid over the entire fluid range including gas, liquid, and supercritical states, with the goal of uncertainties approaching the level of the underlying experimental data. The equations of state for thermodynamic properties are primarily of the Helmholtz energy form; a variety of models are implemented for the transport properties. We document the models for the 147 fluids included in the current version. A graphical user interface generates tables and provides extensive plotting capabilities. Properties can also be accessed through third-party apps or user-written code via the core property subroutines compiled into a shared library. REFPROP disseminates international standards in both the natural gas and refrigeration industries, as well as standards for water/steam.

Homogeneous condensation and thermophysical properties of R450A, R513A and R515A using molecular dynamics simulations

The selection of appropriate refrigerants concerning the environmental impact and system performance is a critical issue. Blends of hydrofluoroolefins and hydrofluorocarbons are an excellent choice of refrigerants to overcome environmental and systems performance issues. In this paper, molecular dynamics (MD) simulations was used to investigate the homogeneous condensation and thermophysical properties of R450A, R513A and R515A. Our MD results have a fair agreement with standard REFPROP software and previous available numerical data. The liquid densities and isobaric heat capacities of these refrigerants were obtained at lower condensation temperatures and higher condensation pressure. Condensation phenomena and diffusion motion were analyzed with variations of temperatures. The mean square displacement for different temperatures was investigated for dynamical analysis. The variations in potential energies, volume and condensation rate were obtained to get insight into the condensation process. The radial distribution function computed at the micro level for structural analysis that revealed the phase transition of R450A, R513A and R515A did not affect the intramolecular structure. The Molecular dynamics simulations outcome shows that the R515A has a lower condensation rate and excellent thermophysical properties compared with R450A and R513A.

Density and speed of sound in refrigerant vapor R-125 (31 wt. %) + R-134A (69 wt. %)

Using a constant volume piezometer and ultrasonic interferometer methods, the density and speed of sound in gaseous mixture R-125 (31 wt. %) + R-134a (69 wt. %) were measured within the temperature range from 293 to 393 K and at pressure from 0.18…0.47 to 2.5 MPa. The errors in the measuring temperature, pressure, density and speed of sound were ±20 mK, ±4 kPa, ± (0.15–0.3) %, ± (0.1–0.2) %, respectively. It was shown that the speed of sound values increase with temperature and decrease with pressure. The obtained results were compared with the calculations using the REFPROP software.

Modeling, analyses, and assessment of a liquid air energy storage (LAES) system

In this research paper, a comprehensive thermodynamic model of a LAES system is carried out. Exergy analysis as a potential tool to determine the location and magnitude of losses is applied. The proposed system is comprised of two sub-systems, one is used for air liquefaction which is considered as energy storage. This step is called the charging process. The liquid air is then stored in a cryo-tank. The liquid air is then directed to a series of turbo-expanders for the discharge process. For the system simulation, a code is developed which links the Refprop software to Matlab software where thermophysical properties are obtained. In order to have a better insight of the analyses, a parametric study is performed. The effect of several main parameters (i.e., the main pressure entering the cold box, compressor inlet temperature and the first compressor pressure) of the storage cycle on efficiency and cost are investigated. The results indicate that the outlet temperature of the final turbine is limited to the temperature that can enter the evaporator. This constrains limits the inlet temperature to the turbine, which reduces efficiency. In addition, the storage cycle pressure is low. An increase in the main pressure to the cold box can be useful in increasing efficiency. Besides, reducing the inlet temperature to the compressors can increase performance.

Analysis and optimization of a fuel cell integrated with series two-stage organic Rankine cycle with zeotropic mixtures

In this article, thermodynamic modeling of a cogeneration system consisting of a series two-stage organic Rankine cycle (STORC) and a proton exchange membrane (PEM) fuel cell is conducted. The fuel cell dissipated heat is utilized as STORC plant input. In order to gain a higher efficiency for the proposed cogeneration system, the condenser of the organic Rankin cycle is replaced by a thermoelectric generator (TEG) to minimize heat loss. Moreover, zeotropic mixtures have been employed due to their lower irreversibility compared to single working fluid. Simulation code is developed in MATLAB software linked with the REFPROP software to extract the thermodynamic properties. This simulation code calculates the exergy efficiency and system's total cost rate. Since the performance of the system is affected by the working fluid, three zeotropic mixtures are compared with R123. The parametric study shows that high pressure (HP) and low pressure (LP) evaporator temperature, current density, and PEM operating pressure significantly affect the total cost rate and the second law efficiency. The results indicate that Ipentane-cis Butane has better efficiency among the selected zeotropic mixtures. Furthermore, the genetic algorithm multi-objective optimization is applied to determine the optimal design parameters of the system in a scatter distribution schematic. Finally, the normalized Pareto frontier of Ipentane-cis Butane is given and the related best point of working as a higher exergy efficiency and lower cost rate are specified. Eventually, it is concluded that the integration of STORC with primary PEM fuel cell improves overall exergy efficiency by 1.9%. The total cost rate for optimum point can be in a range of 1.36–14.94 ($/h), depending on the hydrogen production process.

A simulation of R32 refrigerant mixing with R1270 to reduce GWP R410A on wall mounted air conditioning

Refrigerant R410A is a cooling barrier that is still widely used for air conditioning. This R410A contains the Fluoro element which can increase the value of GWP. In this research simulation, we used an AC unit using R410A with the aim of reducing GWP (Global Warming Potential) by mixing synthetic refrigerant with hydrocarbons. R410A still has content GWP: Mixing using R32 / R1270 refrigerant is predicted to reduce the GWP value because R1270 is one of the hydrocarbon refrigerants that has a GWP value of only: 3. By using Refprop software it can be simulated a mixture composition starting from 50/50, 40/60, 30/70, 20/80 and 10/90. From the results of the mixture simulation conducted, obtained a mixture approaching the characteristics of R410A, namely in the mixture: 20/80 with COP: 5.17 while R410A: 4.12. Compression ratio: R410A: 2.0 and for mixed refrigerants 20/80: 1.9. The refrigerant effect of mixed refrigerants is 20/80: 254,51, R410A: 162,77. Using this refrigerant mixture can reduce the GWP value and improve the performance of the AC cooling system. This refrigerant has considerable potential to replace the R410A.

Development and analysis of mathematical model of capillary for conventional refrigerants R22, R427A, R407C, R32, R410A

The Vapor Compression Refrigeration System (VCRS) uses a circulating refrigerant as the medium which absorbs and removes heat from the space to be cooled and subsequently rejects that heat elsewhere. Capillary tubes are commonly used as expansion device, serving almost all small refrigeration systems to reduce the pressure and temperature of the refrigerant and to regulate the flow of refrigerant to the evaporator. Objective of this research is to develop an analytical method for computing the length of capillary tube required for a specified reduction in temperature and to determine various thermodynamic and transport properties for refrigerant fluids and mixtures viz. R22, R427A, R407C, R32, R410A, available in REFPROP database and perform a comparative analysis. For achieving this objective, a mathematical model is developed using the integration of MATLAB and REFPROP software programs.

Evaluation of the coefficient of performance of an air source heat pump unit and an air to water heat pump

Air source heat pump (ASHP) water heaters are efficient devices for sanitary hot water heating. The coefficient of performance (COP) of the air to water heat pump (AWHP) is constantly lower than that of the corresponding ASHP unit. The study focused on determining the COP of both the ASHP unit and the AWHP. This was achieved by the implementation of both experimental and simulation methods, with the help of a data acquisition system and the REFPROP software. The system comprised of a 1.2 kW split type ASHP unit and a 150 L high pressure geyser. A power meter, flow meters, temperature sensors, pressure sensors, ambient temperature and relative humidity sensor were installed at precise locations on the split type AWHP. Controlled volumes of 150, 50 and 100 L were drawn off from the AWHP during the morning, afternoon and evening for a year. The average COP for the summer and winter, in terms of the input electrical and output thermal energies of the AWHP were 3.02 and 2.30. The COPs of the ASHP unit, in terms of the change in the enthalpies of the refrigerant at the inlet and the outlet of the condenser and the evaporator, were 3.52 and 2.65 respectively. The study showed that the difference between the COP of the ASHP unit and that of the AWHP could be ascribed to the electrical energy consumed by the fan and the water circulation pump during the vapour compression refrigeration cycles. The work provides an energy optimisation opportunity to the manufacturers of this technology, helping to enhance the efficiency and COP of ASHP water heaters.&#x0D; Highlights&#x0D; &#x0D; The COPt of the ASHP unit was higher than the COPe of the AWHP.&#x0D; The COPe of the AWHP was the ratio of the input electrical energy consumed and the output thermal energy gained by the stored water.&#x0D; The COPt of the ASHP unit was enthalpies-dependent and a function of inlet and outlet enthalpies of the evaporator and condenser.&#x0D; The inlet and outlet refrigerant temperatures profiles of the condenser confirmed thermal energy dissipation.&#x0D;

Simulation of Mixing Synthetic with hydrocarbons Refrigerant to Reduce the Value of Global Warming Potential with Refprop Software

The problem of global warming or called GWP (Global Warming Potential) that occurs in the earth’s atmosphere, one of which comes from synthetic refrigerants used in household air-conditioning refrigeration machines. R410A is a refrigerant that still contains GWP: 1942. Hydrocarbon refrigerant is a refrigerant that does not contain ODP (Ozone Depleting Potential) and a very small GWP. By using ref prop software, the mixing process can be simulated to obtain refrigerants that have characteristics similar to R410A. Mixing using R32 / R290 ingredients varied with percentage compositions ranging from 50/50, 40/60, 30/70, 20/80, and 10/90. From the simulation results, a mixture approaching R410A with 10/90 composition with COP: 3.85 for R410A and 5.76 for 10/90 mixture was obtained. Compression ratio: R410A: 2.8 and for mixed refrigerants 10/90: 1.8. The refrigerant effect of mixed refrigerants is 10/90: 264,13, R410A: 161,68. By using this refrigerant mixture can reduce the GWP and improve the performance of the Air Conditioning cooling system so that it has a reduced GWP value that can be obtained significantly and has a large enough potential to replace the R410A.

Performance of a Flat-Tube Louvered-Fin Automotive Condenser with R1234yf

Numerical simulation of a mini-channel, flat-tube, louvered fin, automotive condenser is performed to study the heat rejection rate, pressure drop and performance of the heat exchanger. The simulation study is carried out for the refrigerant R1234yf. The properties of R1234y are obtained from REFPROP software. The moist air properties are calculated from those of dry air and water vapor using suitable correlations. To select the input data, the cycle performance is carried out for a standard vapor compression refrigeration system working with R1234yf between the temperature limits of [Formula: see text]C on the low-pressure side and [Formula: see text]C on the high-pressure side. The condensation process is taken into account in three sections, namely, the superheated, two-phase and the subcooled regions. A custom code is prepared in MATLAB to solve the simultaneous equations of heat transfer from refrigerant to inside tube wall, inside tube wall to outside tube wall and outside tube wall to moist air. The simulation results show the sensible heat transfer during desuper heating to be very small compared to the condensing region. Results are reported for the pressure variation along the refrigerant flow passage in the desuper heating, two-phase and subcooling regions. The heat-transfer coefficient is found to be the highest in the two-phase region for higher dryness fractions. The effect of inlet air velocity is less compared to that of the inlet air temperature on the heat rejection rate.

Analysis of vapour compression refrigeration system with R-12, R-134a and R-22: An exergy approach

This article concerned with the exergy analysis of different components of vapour compression refrigeration system and investigates the losses occurred in overall cycle as well as different stages of processes due to exergy destruction in the system based on evaporator temperature variation. The present article explained the nature of three different refrigerants R-134a, R-12 and R-22 on the basis of exergetic efficiency and total irreversibility as the performance parameters with evaporator temperature variation. REFPROP software used for calculation of different specified points of state and others thermophysical properties of the given refrigerants. Based on the exergy analysis, exergy loss decreases as the evaporator temperature rises and second law efficiency decreases along with the evaporator temperature rise. Exergy loss for R-134a is maximum and R-12 shows minimum and R-22 is in between but closed to R-12. The second law efficiency for R-12 is maximum, followed by R-22 and minimum for R-134a.