sCO2 Brayton Cycle Research Articles

Characterization of PCM-PCHE and its effect on the suppression of temperature fluctuations in the SCO2 Brayton cycle

Supercritical CO2 Brayton cycles are now widely used in industrial power generation systems based on various energy sources. In order to solve the temperature problem that is prone to occur at the outlet of the turbine, a printed circuit heat exchanger (PCHE) with phase change materials (PCM) incorporated in it is intended to minimize system temperature fluctuations at the cost of extremely low heat exchange loss.. In this paper, a numerical simulation method is used to study this PCM-embedded PCHE to investigate the overall heat exchanger performance. It is found that when the phase shift between the inlet fluctuations of the hot and cold sides is 180°, this PCHE with embedded PCM has the best reduction of the outlet temperature fluctuation amplitude. Then it was put into an overall supercritical CO2 Brayton cycle, and it was found that PCM-PCHE could reduce the amplitude of efficiency fluctuations by roughly 40.8 %, the overall stability of the system was significantly improved, average power generation was increased by about 1.6 kW based on the reduced power consumption of the two-stage compressor.

Integrated Performance of a Modular Biomass Boiler With a Combined Heat and Power Industrial Rankine Cycle and Supplementary sCO2 Brayton Cycle

Abstract In this paper, the integrated performance of a modular biomass boiler with an existing industrial Rankine steam heat and power cycle and a supplementary supercritical-carbon dioxide (sCO2) Brayton cycle is analyzed. The aim is to leverage the high efficiency supplementary sCO2 cycle to increase net generation and energy efficiency from the existing biomass boiler. Two sCO2 heater configurations situated within the flue gas flow path are investigated, namely a single convective-dominant heater, and a dual heater configuration with a radiative and a convective heater. A quasi-steady-state 1D model was developed to simulate the integrated cycle, including detailed component characteristics for the Rankine and Brayton cycles. The model solves the mass, energy, momentum, and species balance equations. The system is analyzed for three cases: (i) the existing Rankine cycle without the sCO2 integration, (ii) with the single convective-dominant sCO2 heater configuration, and (iii) the dual sCO2 heater configuration. The results show the required rate of overfiring for the sCO2 configurations, with a 15.3% increase in fuel flowrate resulting in an additional 21.2% in net power output. The model quantifies the impact of the sCO2 heaters, with reduced heat uptakes for downstream boiler heat exchangers. Furnace water wall heat uptake increased due to overfiring, offsetting the reduced heat uptakes at downstream evaporative heat exchangers. The dual configuration has more impact on Rankine cycle operation due to the radiative sCO2 heater placement in front of the second superheater, absorbing some of the direct radiation from the furnace.

Thermodynamic Analysis and Optimization of Binary CO2-Organic Rankine Power Cycles for Small Modular Reactors

Small nuclear power plants are a promising direction of research for the development of carbon-free energy in isolated power systems and in remote regions with undeveloped infrastructure. Improving the efficiency of power units integrated with small modular reactors will improve the prospects for the commercialization of such projects. Power cycles based on supercritical carbon dioxide are an effective solution for nuclear power plants that use reactor facilities with an initial coolant temperature above 550 °C. However, the presence of low temperature rejected heat sources in closed Bryton cycles indicates a potential for energy saving. This paper presents a comprehensive thermodynamic analysis of the integration of an additional low-temperature organic Rankine cycle for heat recovery to supercritical carbon dioxide cycles. A scheme for sequential heat recovery from several sources in S-CO2 cycles is proposed. It was found that the use of R134a improved the power of the low-temperature circuit. It was revealed that in the S-CO2 Brayton cycle with a recuperator, the ORC add-on increased the net efficiency by an average of 2.98%, and in the recompression cycle by 1.7–2.2%. With sequential heat recovery in the recuperative cycle from the intercooling of the compressor and the main cooler, the increase in efficiency from the ORC superstructure will be 1.8%.

Multi-objective performance analysis of different SCO2 Brayton cycles on hypersonic vehicles

To provide the continuous and stable power supply of hypersonic vehicles, this study investigates four candidate cycles on the basis of three critical parameters. Specifically, the effects of cycle pressure ratio (PR), recompression split ratio (x), and cycle intermediate pressure ratio (RPR) on the regenerative, recompression, precompression, and partial cooling supercritical carbon dioxide (SCO2) Brayton cycles (BCs) are emphasized. The analysis is carried on by using an established thermodynamic simulation platform. Using PR as the working condition parameter, the influence laws of x and RPR on each cycle at common working conditions are given. The Non-dominated Solution Genetic Algorithm-II (NSGA-II) performs multi-objective optimization for different cycle types. The performance of these cycles is then compared under optimal conditions. The results show that the regenerative SCO2 BC could maintain relatively high output power while keep the structure simple, compared with other three cycles. The optimum power generation in the study range and the common operating conditions of regenerative SCO2 BC is 203.49 kW and 154.03 kW, respectively. Therefore, the regenerative SCO2 BC preferably satisfies the requirements of the hypersonic vehicles.

Off-design operation of supercritical CO2 Brayton cycle arranged with single and multiple turbomachinery shafts for lead-cooled fast reactor

The lead-cooled fast reactor (LFR) engenders novel requisites for the energy conversion system when applied to maritime ships and distributed energy supply systems. The supercritical carbon dioxide (sCO2) Brayton cycle, with the advantages of high efficiency, space-saving, simplicity, and flexibility, is a promising candidate for LFR. Here, we present the first study on the off-design operation of the sCO2 cycle for LFR, with the turbine and compressor arranged on a single shaft (coaxial-shaft) or two shafts (split-shaft). The off-design performances of the system are investigated using four rotational speed (RS) control-based hybrid control strategies. We showed that the split-shaft system controlled by separate turbine speed and compressor speed has a wider operating space of power load than the coaxial-shaft system. Among the four investigated control strategies, the RS-inventory hybrid control can achieve the best thermal efficiency during load variation by operating at the turbine speed and mass flow rate corresponding to the optimal turbine isentropic efficiency. The maximum operating space of power load (0%–100 %) can be achieved by the RS-turbine inlet pressure hybrid control and the RS-bypass hybrid control. Our study can provide guidance for the flexible and safe part-load operation for small-scale modular Gen-IV nuclear reactors.

Combined Supercritical CO2 Brayton Cycle and Organic Rankine Cycle for Exhaust Heat Recovery

Abstract In order to reduce energy consumption and related CO2 emissions, waste heat recovery is considered a viable opportunity in several economic sectors, with a focus on industry and transportation. Among different proposed technologies, thermodynamic cycles using suitable organic working fluids seem to be promising options, and the possibility of combining two different cycles improves the final recovered energy. In this paper, a combination of Brayton and Rankine cycles is proposed: the upper cycle has supercritical carbon dioxide (sCO2) as its working fluid, while the bottomed Rankine section is realized by an organic fluid (organic Rankine cycle (ORC)). This combined unit is applied to recover the exhaust energy from the flue gases of an internal combustion engine (ICE) for the transportation sector. The sCO2 Brayton cycle is directly facing the exhaust gases, and it should dispose of a certain amount of energy at lower pressure, which can be further recovered by the ORC unit. A specific mathematical model has been developed, which uses experimental engine data to estimate a realistic final recoverable energy. The model is able to evaluate the performance of each recovery subsection, highlighting interactions and possible trade-offs between them. Hence, the combined system can be optimized from a global point of view, identifying the most influential operating parameters and also considering a regeneration stage in the ORC unit.

Numerical studies of sCO2 Brayton cycle

This work describes the one-dimensional, thermo-hydraulic model of the sCO2 cycle Sofia developed to investigate optimal control methods and the behaviour of the cycle during operation. This dynamic model includes all devices such as turbomachinery, heat exchangers, valves, and piping including heat loss, in line with concept of the 1 MWe sCO2 cycle, to be realised in the site of a fossil power plant in the Czech Republic.The model assembly and calculations were conducted using the commercial Modelica-based library ClaRa + using the simulation environment Dymola and in combination with another Modelica-based library, UserInteraction; the real-time simulations, with some parameter changes during the calculation, are made and described in this paper.Nominal parameters were achieved during the steady-state simulation, except for the lower mass flow of sCO2. Transient simulation of power turbine start-up from standby state and results are also presented in this paper. The nominal state is achieved with the semi-automatic procedure in approx. 3 h. The simulation results allow more detailed analyses of control methods and a better understanding of real device control and behaviour during start-up, shutdown, or other transients.Careful manipulation of turbine valves in coordination with the pressuriser operation was identified as crucial for optimal control of the system. Also, the initial amount of CO2 in the pressuriser affects its behaviour during transients.

A comparative performance analysis of sensible thermal energy storage (with concentrated solar field and sCO2 Brayton Cycle) and hydrogen energy storage (with solar PV field)

Utility scale energy storage is an integral part of renewable energy installations to achieve sustainable and reliable transition to a net zero energy economy. There exists a myriad of such storage solutions each having unique characteristics. This paper attempts at a systems level quantitative study and comparison between two different energy storage technologies, Thermal Energy Storage System (TESS) which is already mature, and Hydrogen Energy Storage System (HESS) which gained a lot of momentum recently, with the former coupled with a concentrated parabolic trough solar field using molten salt as heat transfer fluid and a power block running on high efficiency sCO2 Brayton cycle while the latter is coupled with a solar photovoltaic (PV) field. So that comparisons can be made on similar scale, both the systems are normalized on the total equipment area used for capturing incident solar irradiation, i.e., total aperture area for the PTC field and total flat surface area of PV modules. Both the systems are subjected to year-long variations of ambient conditions and solar irradiance and off-design performances are simulated over various seasons. The results show superior performance of TESS in terms of roundtrip efficiency (96% as opposed to 32% with HESS) which also results in superior capacity utilization factor (CUF of 64.5% and 48% for TESS and HESS respectively) and better specific energy and energy density. However, HESS offers virtually infinite idling time where TESS has a shorter self-discharge time (17 h), and better power performance (specific power and power density) in 10MWe output range.

Parameters analysis and techno-economic comparison of various ORCs and sCO2 cycles as the power cycle of Lead–Bismuth molten nuclear micro-reactor

Organic Rankine cycle (ORC) and supercritical CO2 (sCO2) Brayton cycle are two key and competition technology routes as the power cycle of Lead–Bismuth micro-reactor (LBMR). However, few studies focus on the comparison of thermodynamic and economic performance between ORCs and sCO2 cycles in nuclear micro-reactor. The objectives in this study are to perform parameters analysis and techno-economic comparison in ORCs and sCO2 cycles with various configurations as the power cycle of LBMR, so as to provide the technical support for the selection of power cycle and its operating conditions in different scenarios. Several high/low-temperature working fluids are screened for ORCs in view to achieve high net efficiency (ηth) and low electricity production cost (EPC). Multi-objective optimization is performed to solve the trade-off between ηth and EPC, and then to compare the comprehensive performance of various cycles from thermodynamic, compact and economic aspects. Results show that, the ηth and EPC of ORCs are comparable or superior to that in sCO2 cycles when the two cycles have similar structures (simple/regenerative). Among the ORCs, the cascade ORC with two-side regeneration using N-Dodecane/Pentane as working fluid pair has the best performance. In all cycles, recompression sCO2 cycle performs best, but only when the heat source temperature is higher than 460 °C, the performance of the recompression sCO2 cycle are overall better than the cascade ORC.

Numerical study on the flow and heat transfer performance of SCO2/molten salt in Z-type printed circuit heat exchangers

The utilization of a PCHE in conjunction with a SCO2 Brayton cycle and molten salt thermal storage demonstrates a high efficiency. Investigating the flow and heat transfer characteristics of SCO2 and molten salt within a Z-type PCHE is essential. However, this particular aspect has not been explored by previous researches. This study employs a Z-type PCHE to analyze the heat transfer and flow characteristics of SCO2 and molten salt under different inlet temperatures, mass fluxes, and outlet pressures. Furthermore, the heat transfer efficiency of a Z-type PCHE is evaluated and compared to that of a conventional straight-type PCHE. The results indicate that the flow pattern of SCO2 exhibits periodic behavior due to the periodic bending structure of Z-type PCHE, while the flow of molten salt is minimally affected. Furthermore, different SCO2 conditions lead to divergent patterns in flow and heat transfer efficiency compared to molten salt. Z-type channels help alleviate the decline in heat transfer that typically happens in the inlet section of straight channels. Nu for a dual working fluid in a straight-type PCHE is only 1.1 times greater than that of a single working fluid. In Z-type PCHE configuration, the ratio of the dual working fluid to the single working fluid Nu is 1.4. The sensitivity of SCO2/molten salt dual working fluid to the heat exchanger structure is significant, with Z-type PCHE demonstrating superior heat transfer capabilities. The results outlined in this study offer the prospect of improving the design and deployment of Z-type PCHE in molten salt energy storage systems that operate within SCO2 Brayton cycle.

Investigation into the predicted performance of a cooling fan for an sCO2 concentrated solar power plant

An axial flow fan is designed for dry cooling of a sCO2 Brayton cycle for a CSP plant, and a scaled model of the fan is manufactured and tested experimentally in an ISO 5801:2017 Type A fan test facility. While the design procedure’s estimate of the total-to-static efficiency at the design flow rate is relatively high, at 74.4%, the experimental fan efficiency was found to be only 50.6%. This paper details an investigation into the causes of fan performance degradation, using both experimental and numerical methods. The investigation finds that the hub configuration, tip clearance size, and scale of the test fan is responsible for the reduced performance. Two alternative hub and casing configurations are identified which improve the fan’s performance significantly.

Performance of a supercritical carbon dioxide compressor using a streamline curvature based throughflow method

Supercritical carbon dioxide (sCO2) has emerged as a promising working fluid for the Brayton power cycle, offering enhanced efficiency due to its high density and low viscosity near the critical point. A critical component of the sCO2 Brayton cycle is the turbomachinery, namely the compressor. The pronounced sensitivity of the thermophysical properties of sCO2 in the vicinity of the critical point where the compressor operates can significantly impact the performance characteristics of sCO2 compressors. This study presents a two-dimensional (2D) streamline curvature-based throughflow method, considering real gas thermophysical properties, to analyze a centrifugal compressor operating with sCO2 at near-critical inlet conditions. The method’s validity is established through comparisons of the predicted performance characteristics with those of the Sandia National Laboratories compressor and by comparing the predicted flow field with the pitch-averaged flow field obtained from computational fluid dynamic (CFD) analysis. Moreover, various compressor intake conditions including subcritical vapor, supercritical vapor, supercritical liquid, and near-critical conditions are investigated to explore their impact on compressor performance. The streamline curvature-based throughflow method demonstrates its effectiveness by achieving significant agreement between the flow field and performance characteristics, both at design and off-design conditions where efficiency predictions were within 5.84% near the best efficiency point compared to CFD simulations. At near critical conditions, a maximum of 3201% increase the computational run-time required for CFD based computation was observed compared to superheated conditions while only a maximum of 164% increase in run-time was observed in the throughflow based computations as a result of the numerical under-relaxation required.

Evaluation of coated steels in supercritical CO2

AbstractThe carburizing supercritical CO2 (sCO2) environment limits the use of lower cost steels in the lower temperature (450–650°C) portions of the sCO2 Brayton cycle because of concerns about internal carburization and embrittlement. Results on a ferritic–martensitic steel and conventional and advanced austenitic steels at 450–650°C in 30 MPa sCO2 with and without 1% O2 and 0.1% H2O additions have indicated that sCO2 environments will have lower maximum operating temperatures compared to steam plants. Pack Al and Cr coatings were evaluated at 650°C on T91 and 316H substrates and showed some benefit for up to 2000 h at 650°C, especially without impurities. However, characterization indicated Al2O3 was not formed and Cr‐rich carbides formed in the Cr coatings. With the addition of impurities in the sCO2, the coatings were less protective at 650°C. Subsequent exposures at 600°C in sCO2 showed similar behavior. Postexposure evaluations included measuring the bulk C content and room temperature tensile properties. Improvements were indicated but the tensile results were complicated by the high temperature pack coating process affecting the substrate properties.

Structural optimization of S-CO2 Brayton cycle compressor impeller based on evolutionary algorithm

As the critical components for marine low-speed diesel engine flue gas waste heat recovery (WHR) supercritical carbon dioxide (S-CO2) Brayton cycle system, the structure of the compressor impeller is optimized by the evolutionary algorithm (EA) based on the co-simulation of the CAESES, ANSYS CFX and Opti Slang. The law of impeller pressure ratio, efficiency and power consumption in S-CO2 Brayton cycle (SCBC) as a function of rotational speed, inlet temperature, pressure and impeller structural parameters are revealed, and the method of improving SCBC efficiency for marine low-speed diesel engine flue gas waste heat recovery is studied. The optimized impeller structure is greatly enhanced in aerodynamic performance and safety, and the isentropic efficiency is increased by 2.54%, the pressure ratio is increased by 35.64%, and the temperature rise is increased by only 4.6%. A 100kW S-CO2 compression cycle test bench was set up to verify the simulation-optimized impeller results. The final results show that the optimized impeller structure, aerodynamic performance and safety are greatly improved. It provides theoretical support for selecting and optimising compressor impellers for marine low-speed diesel engine flue gas waste heat recovery S-CO2 Brayton cycle.

Dynamic characteristic analysis of SCO2 Brayton cycle under different turbine back pressure modes

Closed supercritical carbon dioxide Brayton cycle has the advantages of high efficiency and high compactness. The response speed of SCO2 cycle is much faster than that of steam Rankine cycle since the compact system structure and small amounts of heat storage, but the complex mutual effect of multi facilities and closed loop iteration of operation parameters makes the system control difficult. In order to examine the iteration of pressure and temperature in the SCO2 closed cycle, the dynamic characters of SCO2 cycle and the related facilities were investigated with different turbine back pressure modes, such as normal operation mode (unconfined back pressure), fixed pressure mode and open loop mode. It has been shown that for different disturbances in the dynamic characteristics of the heat exchanger, the response time of the return heaters is about 4–5 times longer than the response time of the precoolers and heaters. For the dynamic characterization of the SCO2 cycle in different turbine backpressure modes, the effect of pressure iteration on the SCO2 system characteristics is less important than that of temperature iteration. In addition, the fixed turbine backpressure operation mode has the advantages of fast response and easy control for the SCO2 cycle.

Modelling and analysis of pre-cooler for a sCO2 Brayton cycle with different banking configurations using a stack-based model

A correctly designed pre-cooler improves the cycle efficiency in the sCO2 Brayton cycle. The sCO2 pre-cooler operates close to the critical point of CO2 where conventional design strategies may not be suitable due to substantial variation of the thermo-physical properties with small changes in temperature and pressure. Heat exchangers for sCO2 applications require a robust modelling tool to attain optimum cycle performance with the correct footprint. The tool for providing quick size optimization iterations and capturing the heat transfer in solid and fluid effectively with the capability to model different banking configurations is missing in the literature. The article implements a full-scale Thermal Resistance Network (TRN) framework relying on the electrical analogy of heat transfer processes to model a PCHE-based sCO2 pre-cooler with water as the cooling medium. The model helps in estimating the stack size/volume and analyzing different banking configurations (H-C, H-C-H, C-H-C, C-C-H-C-C, and H-H-C-H-H) for the pre-cooler within a range of Reynolds numbers for both sCO2 and water obtained by ensuring a temperature pinch of 3 °C at the cold inlet. Cooler volume and water pumping power with corresponding heat transfer area of air-cooled heat exchanger (for cooling water) are investigated. The order of banking configurations for channel length is H-H-C-H-H > H-C-H > H-C > C-H-C > C-C-H-C-C over the entire range of Reynolds numbers. The C-C-H-C-C and H-H-C-H-H bankings provided the highest and lowest pumping power as 2.95 kW and 0.42 kW, respectively for Reco2,in and Rewater,in of 3,000 and 800. Whereas C-C-H-C-C and H-C-H bankings provided the highest and lowest stack volumes as 1.66 m3 and 0.74 m3. Multi-objective optimizations using pre-cooler stack volume and water outlet temperature show that H-C-H banking results in a lower stack volume than H-C. Additionally, it impacts the water outlet temperature, which in turn affects the heat transfer area of the air-cooled heat exchanger.

Capacity-operation collaborative optimization of the system integrated with wind power/photovoltaic/concentrating solar power with S-CO2 Brayton cycle

Capacity-operation collaborative optimization of the system integrated with wind power/photovoltaic/concentrating solar power with S-CO2 Brayton cycle

Comparative study of steam, organic Rankine cycle and supercritical CO2 power plants integrated with residual municipal solid waste gasification for district heating and cooling

Among the different waste-to-energy solutions, gasification is considered a promising option and an alternative to landfilling of residual municipal solid waste (RMSW). Therefore, the potential of RMSW air gasification in combination with three different power cycles for district cooling and heating applications is investigated. The model of a fluidized bed air gasifier developed in Aspen Plus is integrated with the models of steam turbine (ST), organic Rankine cycle (ORC), and supercritical CO2 (sCO2) Brayton cycle power plants for the combined cooling, heating, and power production in district networks.The results of the numerical study show that the ST power plant provides higher electrical power compared to the other systems, while sCO2 exhibits better thermal power and the maxima combined energy conversion efficiency. In between, ORCs prove to be a reliable and flexible solution for varying RMSW compositions and temperature levels of the district network. The size of the district network strongly varies with scenarios and in the best case, more than 1,400 residential buildings can be connected to the trigeneration plant considering 20 ktons/year of RMSW input to the gasifier.

Enhancing performance of multi-pressure evaporation organic Rankine Cycle/Supercritical Carbon Dioxide Brayton cycle through genetic algorithm and Machine learning optimization

The Supercritical Carbon Dioxide Brayton combined cycle is one of the most important ways to enhance the performance of the cycle. Since the considerable exergy loss resulting from large temperature differences in the heat exchangers of combined cycles, the multi-pressure evaporation concept was adopted from Organic Rankine cycle research. Two novel multi-pressure evaporation configurations, namely parallel evaporation Brayton combined cycle and series evaporation Brayton combined cycle, are designed with the purpose of enhancing SCO2 Brayton cycle performance. The performance of the two new cycles was compared with that of the baseline cycle. Moreover, Printed Circuit Heat Exchangers were employed to improve the overall compactness of the cycles. The results from model calculations were utilized to train an Artificial intelligence neural network model using machine learning techniques which allowed to simplify the cycle and improves the computational speed. Subsequently, genetic algorithm was employed to conduct multi-objective optimization on the three cycles. Finally, a detailed exploration was conducted from the perspective of thermal and exergy to elucidate the reasons for the advantages and differences between the two new cycles compared to the baseline cycle. The results indicate that the series Brayton combined cycle exhibits the highest performance, and the combined cycle of multi-pressure evaporation helps to improve the performance of the combined cycle. Compared to the baseline cycle, the combined cycle efficiency of both series and parallel combined cycles has increased from 45.54% to 46.18% and 46.29%, respectively, while the bottom cycle efficiency has improved from 3.81% to 4.93% and 5.03%. The ratio of heat exchange area to net output power increased from 0.6051 to 0.6614 and 0.6740 for the parallel and series cycles, respectively. Thermal analysis shows that, the fundamental purpose of changing the layout is to improve the specific power per unit of working medium in the cycle. Exergy analysis shows that, the two new combined cycles improve cycle efficiency by reducing exergy losses in the intermediate heat exchanger. Compared to the parallel version, the series version's staged compression allows for a lower temperature difference in intermediate heat exchanger 1, resulting in smaller exergy losses and higher cycle efficiency. This work will contribute to an enhanced understanding of Supercritical Carbon Dioxide combined cycles within the academic community and the introduction of multi-pressure evaporation will further improve the performance of these important cycles.

Supercritical CO2 power cycle

The article is focused on summarizing the issue of energy circuits working with supercritical carbon dioxide sCO2. Carbon dioxide is currently coming to the forefront of many research institutions with regard to its possible use in its supercritical conditions, thanks to which higher efficiency and compactness of equipment can be achieved compared to conventional steam-water cycles. The article describes the basic properties of this medium, including a description of sCO2 cycles (Brayton, Rankine, etc.). Furthermore, the possible use of energy cycles with sCO2 is discussed, especially in solar and nuclear power plants and in power plants burning fossil fuels. In the case of solar power plants, the sCO2 Brayton cycle can offer higher cycle efficiencies than using super-critical steam cycles. The use of sCO2 in nuclear or coal power plants in turn increases efficiency and reduces water consumption. In addition, the use of the sCO2 circuit in new nuclear reactors of the IV generation is currently being considered, in which the operating temperatures are in the range of 500 - 900 °C, i.e. they are generally higher than operating water-cooled reactors. Even though the use of CO2 refrigerant in power systems has been known for a long time (e.g. use in the first Czechoslovak power plant in Jaslovské Bohunice), they are still not used commercially in the energy industry. One of the reasons is the ongoing research into the behavior of materials at high temperatures in sCO2, corrosion protection, or the effect of carbon dioxide purity on behavior in the supercritical region.