Transcritical cycle

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A transcritical cycle is a closed thermodynamic cycle where the working fluid goes through both subcritical and supercritical states. In particular, for power cycles the working fluid is kept in the liquid region during the compression phase and in vapour and/or supercritical conditions during the expansion phase. The ultrasupercritical steam Rankine cycle represents a widespread transcritical cycle in the electricity generation field from fossil fuels, where water is used as working fluid. [1] Other typical applications of transcritical cycles to the purpose of power generation are represented by organic Rankine cycles, [2] which are especially suitable to exploit low temperature heat sources, such as geothermal energy, [3] heat recovery applications [4] or waste to energy plants. [5] With respect to subcritical cycles, the transcritical cycle exploits by definition higher pressure ratios, a feature that ultimately yields higher efficiencies for the majority of the working fluids. Considering then also supercritical cycles as a valid alternative to the transcritical ones, the latter cycles are capable of achieving higher specific works due to the limited relative importance of the work of compression work. [6] This evidences the extreme potential of transcritical cycles to the purpose of producing the most power (measurable in terms of the cycle specific work) with the least expenditure (measurable in terms of spent energy to compress the working fluid).

Contents

While in single level supercritical cycles both pressure levels are above the critical pressure of the working fluid, in transcritical cycles one pressure level is above the critical pressure and the other is below. In the refrigeration field carbon dioxide, CO2, is increasingly considered of interest as refrigerant. [7] [8] [9] [10]

Transcritical conditions of the working fluid

Phase diagram of a generic fluid Image Phase-diag2.svg
Phase diagram of a generic fluid
TQ diagram of heat introduction to a subcritical and transcritical cold source TQ diagram of heat injection to a subcritical and transcritical cold source.png
TQ diagram of heat introduction to a subcritical and transcritical cold source

In transcritical cycles, the pressure of the working fluid at the outlet of the pump is higher than the critical pressure, while the inlet conditions are close to the saturated liquid pressure at the given minimum temperature.

During the heating phase, which is typically considered an isobaric process, the working fluid overcomes the critical temperature, moving thus from the liquid to the supercritical phase without the occurrence of any evaporation process, a significant difference between subcritical and transcritical cycles. [11] Due to this significant difference in the heating phase, the heat injection into the cycle is significantly more efficient from a second law perspective, since the average temperature difference between the hot source and the working fluid is reduced. [12]

As a consequence, the maximum temperatures reached by the cold source can be higher at fixed hot source characteristics. Therefore, the expansion process can be accomplished exploiting higher pressure ratios, which yields higher power production. Modern ultrasupercritical Rankine cycles can reach maximum temperatures up to 620°C exploiting the optimized heat introduction process. [13]

Characterization of the power cycle

Ts diagrams of subcritical (yellow), transcritical (blue) and supercritical (red) power cycles Ts diagrams of sub trans super cycles.png
Ts diagrams of subcritical (yellow), transcritical (blue) and supercritical (red) power cycles
Plant layouts of transcritical power cycles (top left), supercritical power cycles (top right), subcritical power cycles (bottom) Plant layout of transcritical cycles supercritical cycles and subcritical cycles.png
Plant layouts of transcritical power cycles (top left), supercritical power cycles (top right), subcritical power cycles (bottom)

As in any power cycle, the most important indicator of its performance is the thermal efficiency. The thermal efficiency of a transcritical cycle is computed as:

where is the thermal input of the cycle, provided by either combustion or with a heat exchanger, and is the power produced by the cycle.

The power produced is considered comprehensive of the produced power during the expansion process of the working fluid and the one consumed during the compression step.

The typical conceptual configuration of a transcritical cycle employs a single heater, [14] [15] thanks to the absence of drastic phase change from one state to another, being the pressure above the critical one. In subcritical cycles, instead, the heating process of the working fluid occurs in three different heat exchangers: [16] in economizers the working fluid is heated (while remaining in the liquid phase) up to a condition approaching the saturated liquid conditions. Evaporators accomplish fluid evaporation process (typically up to the saturated vapour conditions) and in superheaters the working fluid is heated form the saturated vapour conditions to a superheated vapor. Moreover, using Rankine cycles as bottoming cycles in the context of combined gas-steam cycles keeps the configuration of the former ones as always subcritical. Therefore, there will be multiple pressure levels and hence multiple evaporators, economizers and superheaters, which introduces a significant complication to the heat injection process in the cycle. [17]

Characterization of the compression process

Pump diagram Pump diagram.PNG
Pump diagram
Compressor Stage GE J79 Compressor Stage GE J79.jpg
Compressor Stage GE J79

Along adiabatic and isentropic processes, such as those theoretically associated with pumping processes in transcritical cycles, the enthalpy difference across both a compression and an expansion is computed as:

Consequently, a working fluid with a lower specific volume (hence higher density) can inevitably be compressed spending a lower mechanical work than one with low density (more gas like).

In transcritical cycles, the very high maximum pressures and the liquid conditions along the whole compression phase ensure a higher density and a lower specific volume with respect to supercritical counterparts. Considering the different physical phases though which compression processes occur, transcritical and supercritical cycles employ pumps (for liquids) and compressors (for gases), respectively, during the compression step.

Characterization of the expansion process

Traditional classification of expansions with pure working fluids Traditional classification of pure working fluids.svg
Traditional classification of expansions with pure working fluids
TurbineBlades TurbineBlades.jpg
TurbineBlades

In the expansion step of the working fluid in transcritical cycles, as in subcritical ones, the working fluid can be discharged either in wet or dry conditions.

Typical dry expansions are those involving organic or other unconventional working fluids, which are characterized by non-negligible molecular complexities and high molecular weights.

The expansion step occurs in turbines: depending on the application and on the nameplate power produced by the power plant, both axial turbines and radial turbines can be exploited during fluid expansion. Axial turbines favour lower rotational speed and higher power production, while radial turbines are suitable for limited powers produced and high rotational speed.

Organic cycles are appropriate choices for low enthalpy applications and are characterized by higher average densities across the expanders than those occurring in transcritical steam cycles: for this reason a low blade height is normally designed [18] and the volumetric flow rate is kept limited to relatively small values. On the other hand in large scale application scenarios the expander blades typically show heights that exceed one meter and that are exploited in the steam cycles. Here, in fact, the fluid density at the outlet of the last expansion stage is significantly low.

In general, the specific work of the cycle is expressed as:

Even though the specific work of any cycle is strongly dependent on the actual working fluid considered in the cycle, transcritical cycles are expected to exhibit higher specific works than the corresponding subcritical and supercritical counterparts (i.e., that exploit the same working fluid). For this reason, at fixed boundary conditions, power produced and working fluid, a lower mass flow rate is expected in transcritical cycles than in other configurations.

Applications in power cycles

Ultrasupercritical Rankine cycles

Simplified layout of a coal fired power plant Figure 1- Sample Layout of Emissions Controls at a Coal Power Plant (7315637538).jpg
Simplified layout of a coal fired power plant

In the last decades, the thermal efficiency of Rankine cycles increased drastically, especially for large scale applications fueled by coal: for these power plants, the application of ultrasupercritical layouts was the main factor to achieve the goal, since the higher pressure ratio ensures higher cycle efficiencies.

The increment in thermal efficiency of power plants fueled by dirty fuels became crucial also in the reduction of the specific emissions of the plants, both in therms of greenhouse gas and for pollutant such as sulfur dioxide or NOx. In large scale applications, ultrasupercritical Rankine cycles employ up to 10 feedwater heaters, five on the high pressure side and five on the low pressure side, including the deaerator, helping in the increment of the temperature at the inlet of the boiler up to 300°C, allowing a significant regenerative air preheating, thus reducing the fuel consumption. Studies on the best performant configurations of supercritical rankine cycles (300 bar of maximum pressure, 600°C of maximum temperature and two reheats) show that such layouts can achieve a cycle efficiency higher than 50%, about 6% higher than subcritical configurations. [19]

Organic Rankine cycles

Internal view of Plug-and-Play Micro-ORC Internal view of Plug-and-Play Micro-ORC.jpg
Internal view of Plug-and-Play Micro-ORC
Ts Diagram of subcritical and transcritical R134a cycles Ts Diagram of subcritical and transcritical R134a cycles.png
Ts Diagram of subcritical and transcritical R134a cycles

Organic Rankine cycles are innovative power cycles which allow good performances for low enthalpy thermal sources [20] and ensure condensation above the atmospheric pressure, thus avoiding deaerators and large cross sectional area in the heat rejection units. Moreover, with respect to steam Rankine cycles, ORC have a higher flexibility in handling low power sizes, allowing significant compactness. Typical applications of ORC cover: waste heat recovery plants, geothermal plants, biomass plants and waste to energy power plants.

Organic Rankine cycles use organic fluids (such as hydrocarbons, perfluorocarbons, chlorofluorocarbon, and many others) as working fluids. [21] Most of them have a critical temperature in the range of 100-200°C, [22] for this reason perfectly adaptable to transcritical cycles in low temperature applications. [23] Considering organic fluids, having a maximum pressure above the critical one can more than double the temperature difference across the turbine, with respect to the subcritical counterpart, and significantly increase both the cycle specific work and cycle efficiency.

Applications in refrigeration cycles

A refrigeration cycle, also known as heat pump, is a thermodynamic cycle that allows the removal of heat from a low temperature heat source and the rejection of heat into a high temperature heat source, thanks to mechanical power consumption. [24] Traditional refrigeration cycles are subcritical, with the high pressure side (where heat rejection occurs) below the critical pressure. [25]

Innovative transcritical refrigeration cycles, instead, should use a working fluid whose critical temperature is around the ambient temperature. For this reason, carbon dioxide is chosen due to its favourable critical conditions. In fact, the critical point of carbon dioxide is 31°C, reasonably in between the hot source and cold source of traditional refrigeration applications, thus suitable for a transcritical applications.

In transcritical refrigeration cycles the heat is dissipated through a gas cooler instead of a desuperheater and a condenser [26] like in subcritical cycles. This limits the plant components, plant complexity and costs of the power block.

The advantages of using supercritical carbon dioxide as working fluid, instead of traditional refrigerant fluids (like HFC of HFO), in refrigeration cycles is represented both by economic aspects and environmental ones. The cost of carbon dioxide is two order of magnitude lower than the ones of the average refrigerant working fluid and the environmental impact of carbon dioxide is very limited (with a GWP of 1 and an ODP of 0), the fluid is not reactive nor significantly toxic. No other working fluids for refrigeration is able to reach the same environmental favourable characteristics of carbon dioxide. [27]

Related Research Articles

<span class="mw-page-title-main">Heat engine</span> System that converts heat or thermal energy to mechanical work

In thermodynamics and engineering, a heat engine is a system that converts heat to usable energy, particularly mechanical energy, which can then be used to do mechanical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, particularly electrical, since at least the late 19th century. The heat engine does this by bringing a working substance from a higher state temperature to a lower state temperature. A heat source generates thermal energy that brings the working substance to the higher temperature state. The working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a lower temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid. During this process, some heat is normally lost to the surroundings and is not converted to work. Also, some energy is unusable because of friction and drag.

<span class="mw-page-title-main">Rankine cycle</span> Model that is used to predict the performance of steam turbine systems

The Rankine cycle is an idealized thermodynamic cycle describing the process by which certain heat engines, such as steam turbines or reciprocating steam engines, allow mechanical work to be extracted from a fluid as it moves between a heat source and heat sink. The Rankine cycle is named after William John Macquorn Rankine, a Scottish polymath professor at Glasgow University.

For fluid power, a working fluid is a gas or liquid that primarily transfers force, motion, or mechanical energy. In hydraulics, water or hydraulic fluid transfers force between hydraulic components such as hydraulic pumps, hydraulic cylinders, and hydraulic motors that are assembled into hydraulic machinery, hydraulic drive systems, etc. In pneumatics, the working fluid is air or another gas which transfers force between pneumatic components such as compressors, vacuum pumps, pneumatic cylinders, and pneumatic motors. In pneumatic systems, the working gas also stores energy because it is compressible.

A supercritical fluid (SCF) is any substance at a temperature and pressure above its critical point, where distinct liquid and gas phases do not exist, but below the pressure required to compress it into a solid. It can effuse through porous solids like a gas, overcoming the mass transfer limitations that slow liquid transport through such materials. SCF are superior to gases in their ability to dissolve materials like liquids or solids. Also, near the critical point, small changes in pressure or temperature result in large changes in density, allowing many properties of a supercritical fluid to be "fine-tuned".

<span class="mw-page-title-main">Chiller</span> Machine that removes heat from a liquid coolant via vapor compression

A chiller is a machine that removes heat from a liquid coolant via a vapor-compression, adsorption refrigeration, or absorption refrigeration cycles. This liquid can then be circulated through a heat exchanger to cool equipment, or another process stream. As a necessary by-product, refrigeration creates waste heat that must be exhausted to ambience, or for greater efficiency, recovered for heating purposes. Vapor compression chillers may use any of a number of different types of compressors. Most common today are the hermetic scroll, semi-hermetic screw, or centrifugal compressors. The condensing side of the chiller can be either air or water cooled. Even when liquid cooled, the chiller is often cooled by an induced or forced draft cooling tower. Absorption and adsorption chillers require a heat source to function.

<span class="mw-page-title-main">Supercritical carbon dioxide</span> Carbon dioxide above its critical point

Supercritical carbon dioxide is a fluid state of carbon dioxide where it is held at or above its critical temperature and critical pressure.

A binary cycle is a method for generating electrical power from geothermal resources and employs two separate fluid cycles, hence binary cycle. The primary cycle extracts the geothermal energy from the reservoir, and secondary cycle converts the heat into work to drive the generator and generate electricity.

<span class="mw-page-title-main">Steam-electric power station</span>

The steam-electric power station is a power station in which the electric generator is steam driven. Water is heated, turns into steam and spins a steam turbine which drives an electrical generator. After it passes through the turbine, the steam is condensed in a condenser. The greatest variation in the design of steam-electric power plants is due to the different fuel sources.

A zeotropicmixture, or non-azeotropic mixture, is a mixture with liquid components that have different boiling points. For example, nitrogen, methane, ethane, propane, and isobutane constitute a zeotropic mixture. Individual substances within the mixture do not evaporate or condense at the same temperature as one substance. In other words, the mixture has a temperature glide, as the phase change occurs in a temperature range of about four to seven degrees Celsius, rather than at a constant temperature. On temperature-composition graphs, this temperature glide can be seen as the temperature difference between the bubble point and dew point. For zeotropic mixtures, the temperatures on the bubble (boiling) curve are between the individual component's boiling temperatures. When a zeotropic mixture is boiled or condensed, the composition of the liquid and the vapor changes according to the mixtures's temperature-composition diagram.

<span class="mw-page-title-main">Vapor-compression refrigeration</span> Refrigeration process

Vapour-compression refrigeration or vapor-compression refrigeration system (VCRS), in which the refrigerant undergoes phase changes, is one of the many refrigeration cycles and is the most widely used method for air conditioning of buildings and automobiles. It is also used in domestic and commercial refrigerators, large-scale warehouses for chilled or frozen storage of foods and meats, refrigerated trucks and railroad cars, and a host of other commercial and industrial services. Oil refineries, petrochemical and chemical processing plants, and natural gas processing plants are among the many types of industrial plants that often utilize large vapor-compression refrigeration systems. Cascade refrigeration systems may also be implemented using two compressors.

<span class="mw-page-title-main">Turboexpander</span>

A turboexpander, also referred to as a turbo-expander or an expansion turbine, is a centrifugal or axial-flow turbine, through which a high-pressure gas is expanded to produce work that is often used to drive a compressor or generator.

<span class="mw-page-title-main">Heat pump and refrigeration cycle</span> Mathematical models of heat pumps and refrigeration

Thermodynamic heat pump cycles or refrigeration cycles are the conceptual and mathematical models for heat pump, air conditioning and refrigeration systems. A heat pump is a mechanical system that allows for the transmission of heat from one location at a lower temperature to another location at a higher temperature. Thus a heat pump may be thought of as a "heater" if the objective is to warm the heat sink, or a "refrigerator" or “cooler” if the objective is to cool the heat source. In either case, the operating principles are similar. Heat is moved from a cold place to a warm place.

Natural refrigerants are considered substances that serve as refrigerants in refrigeration systems. They are alternatives to synthetic refrigerants such as chlorofluorocarbon (CFC), hydrochlorofluorocarbon (HCFC), and hydrofluorocarbon (HFC) based refrigerants. Unlike other refrigerants, natural refrigerants can be found in nature and are commercially available thanks to physical industrial processes like fractional distillation, chemical reactions such as Haber process and spin-off gases. The most prominent of these include various natural hydrocarbons, carbon dioxide, ammonia, and water. Natural refrigerants are preferred actually in new equipment to their synthetic counterparts for their presumption of higher degrees of sustainability. With the current technologies available, almost 75 percent of the refrigeration and air conditioning sector has the potential to be converted to natural refrigerants.

<span class="mw-page-title-main">Organic Rankine cycle</span> Variation on the Rankine thermodynamic cycle

In thermal engineering, the organic Rankine cycle (ORC) is a type of thermodynamic cycle. It is a variation of the Rankine cycle named for its use of an organic, high-molecular-mass fluid whose vaporization temperature is lower than that of water. The fluid allows heat recovery from lower-temperature sources such as biomass combustion, industrial waste heat, geothermal heat, solar ponds etc. The low-temperature heat is converted into useful work, that can itself be converted into electricity.

The term subcooling refers to a liquid existing at a temperature below its normal boiling point. For example, water boils at 373 K; at room temperature (293 K) liquid water is termed "subcooled". A subcooled liquid is the convenient state in which, say, refrigerants may undergo the remaining stages of a refrigeration cycle. Normally, a refrigeration system has a subcooling stage, allowing technicians to be certain that the quality, in which the refrigerant reaches the next step on the cycle, is the desired one. Subcooling may take place in heat exchangers and outside them. Being both similar and inverse processes, subcooling and superheating are important to determine stability and well-functioning of a refrigeration system.

<span class="mw-page-title-main">Hygroscopic cycle</span> Thermodynamic cycle converting thermal energy into mechanical power

The Hygroscopic cycle is a thermodynamic cycle converting thermal energy into mechanical power by the means of a steam turbine. It is similar to the Rankine cycle using water as the motive fluid but with the novelty of introducing salts and their hygroscopic properties for the condensation. The salts are desorbed in the boiler or steam generator, where clean steam is released and superheated in order to be expanded and generate power through the steam turbine. Boiler blowdown with the concentrated hygroscopic compounds is used thermally to pre-heat the steam turbine condensate, and as reflux in the steam-absorber.

<span class="mw-page-title-main">Non ideal compressible fluid dynamics</span>

Non ideal compressible fluid dynamics (NICFD), or non ideal gas dynamics, is a branch of fluid mechanics studying the dynamic behavior of fluids not obeying ideal-gas thermodynamics. It is for example the case of dense vapors, supercritical flows and compressible two-phase flows. With the term dense vapors, we indicate all fluids in the gaseous state characterized by thermodynamic conditions close to saturation and the critical point. Supercritical fluids feature instead values of pressure and temperature larger than their critical values, whereas two-phase flows are characterized by the simultaneous presence of both liquid and gas phases.

The Allam Cycle or Allam-Fetvedt Cycle is a process for converting carbonaceous fuels into thermal energy, while capturing the generated carbon dioxide and water. This zero emissions cycle was validated at a 50 MWth natural gas fed test facility in La Porte, Texas in May 2018. This industrial plant is owned and operated by NET Power LLC, a privately held technology licensing company. NET Power is owned by Constellation Energy Corporation, Occidental Petroleum Corporation (Oxy) Low Carbon Ventures, Baker Hughes Company and 8 Rivers Capital, the company holding the patents for the technology. The key inventors behind the process are English engineer Rodney John Allam, American engineer Jeremy Eron Fetvedt, American scientist Dr. Miles R Palmer, and American businessperson and innovator G. William Brown, Jr. The Allam-Fetvedt Cycle was recognized by MIT Technology Review on the 2018 list of 10 Breakthrough Technologies.

Heat engines, refrigeration cycles and heat pumps usually involve a fluid to and from which heat is transferred while undergoing a thermodynamic cycle. This fluid is called the working fluid. Refrigeration and heat pump technologies often refer to working fluids as refrigerants. Most thermodynamic cycles make use of the latent heat of the working fluid. In case of other cycles the working fluid remains in gaseous phase while undergoing all the processes of the cycle. When it comes to heat engines, working fluid generally undergoes a combustion process as well, for example in internal combustion engines or gas turbines. There are also technologies in heat pump and refrigeration, where working fluid does not change phase, such as reverse Brayton or Stirling cycle.

<span class="mw-page-title-main">Supercritical carbon dioxide blend</span> Homogeneous mixture of CO2

Supercritical carbon dioxide blend (sCO2 blend) is an homogeneous mixture of CO2 with one or more fluids (dopant fluid) where it is held at or above its critical temperature and critical pressure.

References

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