SE0107ZZO
TERM-01/1 Projektrapporter
Biomass fueled closed cycle gas turbine with water injection Master of Science Thesis 1998/1999 SBardi
Rapporterna kan bestallas (ran Studsvikbiblioteket, 611 82 Nykdping. Tel 0155-22 10 84. Fax 0155-26 30 44 e-post [email protected] e Statens energimyndighet Box 310, 631 04 Eskilstuna Energimyndigheten 01-01-31
Energimyndigheten
Titel: Biomass fueled closed cycle gas turbine with water injection Master of Science Thesis 1998/1999
Forfattare: Silvia Bardi Inst, for kemiteknik, KTH
RAPPORT INOM OMRAdET TERMISK ELPRODUKTION
Rapportnummer: TERM 01/1
Projektledare: Yan Jinyue
Proj ektnummer: P7012-3
Projekthandlaggare pa Statens Energimyndighet: Jorgen Held
Box 310 • 631 04 Eskilstuna • Besoksadress Kungsgatan 43 Telefon 016-544 20 00 • Telefax 016-544 20 99 [email protected] • www.stem.se DISCLAIMER
Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. Abstract.
Abstract
Direct water injection has been studied for a small scale (~ 8 MW fuel input) closed cycle gas turbine coupled to a biomass fueled CFB furnace. Two different working fluids have been considered (helium-water mixture and nitrogen-water mixture). The water injection could take place between the compressor stages, as an intercooler, or after the high pressure compressor, as an aftercooler. Both this options have been studied, varying the relative humidity levels after the injection and the temperatures of the injected water. The effect of water injection on thermodynamic properties of the working fluids has been studied, together with its effect on turbomachinery isentropic efficiency. A sensitivity analysis on turbomachinery efficiency and cycle base pressure has been included. The results from this study have been compared to the performance of a dry closed cycle without water injection. The wet cycle shows an electric efficiency in the range 29-32% with helium water mixture as working fluid and 30-32% with nitrogen-water mixture as working fluid, while the total efficiency (referring to the fuel LHV) is always higher than 100%. In the non-injected cycle the electric efficiency is 30-35 % with helium and 32-36% with nitrogen. The total efficiency in the dry case with two level intercooling and postcooling is 87-89%, while is higher than 100 % when only one stage inter- and postcooling is present.
Aside from this, the study also includes a sizing of the heat exchangers for the different cycle variations. The heat transfer area is very sensible to the working fluid and to the amount of injected water and it's always higher when a nitrogen- water mixture is used. Compared to the cycle without water injection, by the way, the number of heat exchanger is reduced. This will bring to a lower pressure drop and a simpler plant layout. The total heat transfer area, however, is higher in the wet cycle than in the dry cycle. Index
Chapter 1...... 1.1
Chapter 2...... 2.1
Chapter 3...... 3.1
Chapter 4...... 4.1 4.1- Gas turbine power plants ...... 4.1 4.2- GT improvements ...... 4.4 4.3- Closed Cycle Gas Turbine ...... 4.8 4.3.1- Closed-cycle gas turbine working fluid ...... 4.9 4.4- Steam injection in gas turbine cycle ...... 4.12 4.4.1- Effect of water/steam injection on pollutant emissions ...... 4.12 4.4.2- Basic schemes of water/steam injection ...... 4.13
Chapter 5...... 5.1 5.1 - Cycle overall description. 5.1 5.2 - ASPEN Simulation ...... 5.4 5.5.1 - Cycle base pressure and pressure drops ...... 5.4 5.5.3 - Heat exchangers ...... 5.7 5.5.4 -Turbomachinery ...... 5.10
Chapter 6...... 6.1 6.1- Amount of injected water in helium/ nitrogen-water mixture ...... 6.1 6.2- Total Mass Flow rate behaviour and thermodynamic properties modifications with helium-water mixture and nitrogen-water mixture as a working fluid compared to pure helium and pure nitrogen ...... 6.7 6.3- Effect of water injection on turbomachinery work and efficiency ...... 6.10 6.4- lsentropic efficiency in wet and dry cycles ...... 6.15
Chapter 7 ...... 7.1 7.1 - Dry scheme with one stage intercooling and one stage postcooling.... 7.1 7.2- Dry cycle with two stage intercooling and two stage postcooling ...... 7.4 7.3- Water injection as 1 stage intercooling ...... 7.6 7.3.1 - Efficiencies ...... 7.10 7.3.2- Reasons for high electric efficiency in wet cycle: ...... 7.12 7.4- Water injection as 1 stage intercooling and 1 stage aftercooling ...... 7.15 7.5- Additional intercooling stage using district heating cooling water ...... 7.17 7.6- Water injection as intercooling and aftercooling: relative humidity cj) = 95% after both injections ...... 7.18 7.7- Comparison between the various configurations ...... 7.20 Chapter 8 ...... 8.1 8.1 - Dry scheme with one stage intercooling and one stage postcooling.... 8.1 8.2-Dry cycle with two level inter- and postcooling ...... 8.2 8.3 - Water injection as first stage intercooling ...... 8.4 8.4- Water injection as one stage intercooling - one stage aftercooling ...... 8.8 8.5- Water injection as intercooling, after cooling and two stage post cooling with external cooling water ...... 8.10 8.6 - Comparison between the various configurations ...... 8.13
Chapter 9...... 9.1 9.1- Sensitivity analysis on turbomachinery efficiency ...... 9.1 9.1.1 - Sensitivity analysis on LP/HP compressor efficiency ...... 9.1 9.1.2- Sensitivity analysis on turbine efficiency ...... 9.3 9.2- Sensitivity analysis on base pressure ...... 9.6 9.2.1- Effect of increasing cycle base pressure ...... 9.6 9.2.2- Influence of base pressure on dew point temperature ...... 9.9
Chapter 10...... 10.1 10.1- Heat Exchanger variables: dimensional and non dimensional ...... 10.1 10.2 - Flue Gas Heat Exchanger (FGHX)...... 10.4 10.3-External Bed Heat Exchanger ...... 10.6 10.5 - Postcooler ...... 10.15 10.5.1- Non-condensing postcooler ...... 10.16 10.5.2- Condensing postcooler ...... 10.16 10.5.3 - Pressure drops in condensers ...... 10.19 10.5.4 - Design of a condenser for partial condensation of water from a helium/ nitrogen - water vapour mixture ...... 10.20 10.6- lnfluence of base pressure on heat transfer area ...... 10.22 10.7- Comparison between dry cycle and wet cycle ...... 10.24 10.8- Conclusions ...... 10.26
Chapter 11 11.1 - Results and discussion ...... 11.1 11.2 - Conclusions ...... 11.5 Nomenclature
DRY 1 _IC Dry cycle with one level intercooling, one level postcooling DRY 2_IC_AC Dry cycle with two level intercooling, two level postcooling WET 1 _IC Wet cycle with water injection as intercooling WET 2_IC_AC Wet cycle with water injection as intercooling and aftercooling FGHX Flue gas heat exchanger EBHX External bed heat exchanger CFB Circulating fluidised bed HP High pressure LP Low pressure CHP Combined heat and power P Pressure [bar] T Temperature rc] AT Temperature difference [°C] ATml Mean logharitmic temperature difference [°C] CO Humidity ratio Relative humidity pv Vapour pressure [bar] P,S Vapour pressure at saturation [bar] y Molar fraction X Mass fraction M Molecular weight [kgLo, p Pressure ratio x e Recuperator effectiveness rj Efficiency % c Specific heat at constant pressure on mass basis &// cp Specific heat at constant pressure on molar basis kj/ /kmol, K cv Specific heat at constant volume on mass basis &// L /W cv Specific heat at constant volume on molar basis kj/ 'kmol, K k Specific heat ratio R Gas constant
r Universal gas constant
W Rate of work, or power
n Heat transfer rate m Mass flow rate X Re Reynolds number Pr Prandtl number Nu Nusselt number hi Inner heat transfer coefficient _/k,m 2 K Outer heat transfer coefficient _/k,m 2 u Overall heat transfer coefficient _/k,m
p Density [%] 1 K Conductivity ?rX
1 1 ____ P Viscosity 03 1 Subscripts
W water
V vapour h hot side c cold side mix mixture avg average pol polytropic is isentropic Chapter 1-Introduction.
Chapter 1. Introduction.
In the last decades the concern for the environment has grown, and with it the effort to increase the efficiency of the conversion from chemical energy to electrical power. The consciousness of the decreasing availability of fossil fuels has turned the attention to renewable fuels, such as biomass, solar energy, wind energy. The use of poor, “dirty “ fuels, for instance solid biomass fuels, compared to natural gas or oil, requires choosing a different power generation system. Closed-Cycle Gas Turbine (CCGT) plant has proved to be suitable to dirty fuels like biomass and coals, because the combustion is external, thus preventing the turbine blades to get in touch with the dirty corrosive combustion products. Use of this fuels results in a saving of clean fuels like natural gas or oil and in a zero net production of C02 in case of biomass combustion. Moreover, the high rejection temperature of the waste heat makes the closed cycle a good candidate for cogenerative applications like district heating or to generate steam for a bottoming cycle or process steam.
1-1 Chapter 2-Background.
Chapter 2.
Background.
In a project supported by the Swedish National Board for Industrial and Economical Development, a Biomass Fired CHP Closed Cycle Gas Turbine with a CFB Furnace was studied at the Department of Chemical Engineering and Technology/Energy Processes at KTH (Kungliga Tekniska Hogskolan), Stockholm, (Anheden, M., Ahlroth, M., 1998). In this study, a small biomass fired closed cycle gas turbine plant producing both power and heat is evaluated. The working fluid temperature is raised to 800 C degree by a 7.7 MWth CFB (Circulating Fluidised Bed) furnace, using pine sawdust as fuel. Three different working fluids (helium, nitrogen and a He/COa mixture) have been used. The working fluid is first heated in a flue gas heat exchanger (FGHX) and then in an external, combustion free bed, where the working fluid is heated by the fluidised sand and ashes. The flue gases pass the trough a flue gas condenser, and the condensation heat is used to warm up water for the district heating network. The hot working fluid is then expanded in a turbine. The heat remaining in the turbine exhaust is used for preheating the working fluid at the exit of the HP compressor, in a recuperator, and then the working fluid is cooled in a postcooler using district heating water as coolant, before entering the LP compressor. The compression is divided in two stages with intercooling. The heat removed in the intercooling is transferred to the district heating network.
2-1 Chapter 2-Background.
Flue gas
CFB-Fuma M ~ M ~ Recuperator Biomass Air preheater Turbine expander Low pressure High pressure compressor compressor 1. Flue gas condenser 5. Cooling water (optional) 2. District heating 6. Postcooler 3. External bed heat exchanger EXBHX 7. Intercooler 4. Flue gas heat exchanger FGHX 8. Flue gas condensate 9. Water Injection Figure 2.1-Schematic representation of a dosed cycle with two level post/intercooling. This cycle gives an electric efficiency in the range 30-32 in the cycle with one level intercooling/postcooling and 35-36 % in the cycle with two level intercooling/postcooling. The total efficiency is 106-107% in the first case and it drops down to 87-89% in the second one. 2-2 Chapter 3-Aim of the study. Chapter 3. Aim of the study. The aim of the present study is to examine the effect of introducing water injection into the CHP biomass fueled closed cycle gas turbine previously investigated by Anheden, Ahlroth, 1998. The water could be injected between the two compressor stages and replace the intercooler and therefore reducing the number of heat exchangers in the cycle. This reduces the pressure drops between compressor and turbine and thereby the loss of power in the system. It is also considered to be easier to insert a water injection between the two compressor stages than an intercooler heat exchanger. By injecting water into the working fluid, the working fluid, the gases are cooled down as sensible heat is used to evaporate the liquid water. Cooling the working fluid reduces the compressor power. Flue gas CFB-Furna< e Working fluid Recuperator Biomass Air preheater Turbine expander Low pressure High pressure compressor compressor 1. Flue gas condenser 6. Postcooler 2. District heating 8. Flue gas condensate 3. External bed heat exchanger EXBHX 9. Water Injection 4. Flue gas heat exchanger FGHX Figure 3.1-Schematic representation of closed cycle with water injection as intercooling. It is also possible to have a second water injection following the HP compressor, to act as an after cooler. By using this configuration, the recuperator inlet temperature goes down and it’s then possible to increase the recuperator heat duty. The injected water is fully condensed in the post 3-1 Chapter 3-Aim of the study. cooler and then returned to the injection point. By this procedure, no water will theoretically be consumed. Fluegas CFB-Fumace Working fluid Recuperator Air preheater Turbine expander Low pressure High pressure compressor compressor 1. Flue gas condenser 6. Postcooler Z District heating 8. Flue gas condensate 3. External bed heat exchanger EXBHX 9. Water Injection 4 Flue gas heat exchanger FGHX Figure 3.2-Schematic representation of closed cycle with water injection as intercooling and aftercooling. Different working fluids are used in the simulation, together with variations of different design parameters, to see the effect of water injection in combination with different working fluid properties. Finally, the heat transfer areas of the different heat exchangers in the cycle are calculated and compared to the required heat transfer areas in the non injected system. Design parameters like relative humidity, compressor and turbine polytropic efficiency are varied to investigate the sensitivity of the system. The system is simulated with the software ASPEN PLUS™. Heat exchangers areas are calculated using CHED (Compact Heat Exchangers Design) or code developed by myself. 3-2 Chapter 4-Literature report. Chapter 4. Literature report. In this chapter the basic theory of open and closed cycle gas turbine will be described, together with a review of different cycle configurations. Special attention will be given to cycles with a mixture of water-steam and gas as working fluid. 4.1 -Gas turbine power plants. A gas turbine power plants is basically an engine in which a gaseous working fluid is continuously drawn into the compressor, where it is compressed to high pressure, heated to high temperature and then expanded trough a turbine to generate power. Part of the turbine work is used to drive the compressor; the remainder is available to generate electricity, to propel a vehicle or for other purposes. If the gas turbine is an open cycle gas turbine (Figure 4. 1), atmospheric air is drawn into the compressor. The heating of the working fluid takes place trough combustion of a fuel with the pressurised air. The combustion products and the excess air expand trough the turbine and are subsequently discharged to the surroundings. Fuel Combustion chamber Net work out Products Figure 4. 1-Open Cycle Gas Turbine. If the gas turbine is a closed cycle gas turbine (Figure 4. 2), the working fluid is contained in a closed circuit which makes it possible to use any gas as working fluid. 4-1 Chapter 4-Literature report. Q* Heat exchanger — Net work out Heat exchanger Figure 4. 2-Closed Cycle Gas Turbine. The heat is supplied by an external source, via an heat exchanger, so that there is no contact between the working fluid and the combustion products. The working fluid exiting the turbine is cooled in an heat exchanger before entering the compressor. 4.1.1 Ideal Brayton Cycle. Considering an ideal gas as working fluid, and referring to a standard gas turbine the cycle can described by the ideal standard Brayton cycle: Figure 4. 3-Standard ideal Brayton Cycle. 4-2 Chapter 4-Literature report. Assuming the turbine operates adiabatically and with negligible effects of kinetic and potential energy, the work developed per unit of mass is: - = 4-4 m With the same assumption, the compressor work per unit of mass is: W„ = h~hi m The heat added to the cycle per unit of mass is: a, = A3 -A2 m The heat rejected per mass unit is: 2, - = A,-A, m The thermal efficiency of the cycle is: /rh /m _ fe ^4) (^2 K) lih = m h3 -h2 The thermal efficiency increases with increasing pressure ratio across the compressor. This increase is brought out simply by the following development: cM-Tj-cM-T,) (T,-T,) t______1 Cp(^3 ^2) ~(pjpr K where 7^=7; A P± If we consider a real gas instead of an ideal and introduce irreversibilities within the compressor and the turbine, the entropy generation within the cycle will increase. There will also be irreversibility caused by pressure drop due to friction. 4-3 Chapter 4-Literature report. In presence of irreversibilities the work of the compressor increases and the work of the turbine decreases, resulting in a marked decrease of the net work of the plant. 4.2-GT improvements. • Regeneration The turbine exhaust temperature of a gas turbine is normally well above the ambient temperature. If the gases were discharged directly to the surroundings a great potential for use would be lost. One way to use this potential is to use the exhaust to generate steam in a heat recovery steam generator (HRSG) connected to a steam cycle. One other way is by using an heat exchanger called a recuperator that allows the air entering the compressor to be preheated by the turbine exhaust, therefore reducing the amount of fuel needed in the combustor. This solution is normally employed for small plants or in cases where space or weight are limiting like in propulsion application or on board oil platforms. Recuperator Combustor Figure 4.4- Schematic of a gas turbine cycle with regeneration. 4-4 Chapter 4-Literature report. Figure 4. 5- Regenerative air-standard gas turbine cycle. The recuperator is a counterflow heat exchanger. The turbine exhaust is cooled from point 4 to point y while the air exiting the compressor is heated from state 2 to state x. Hence, an external heat source is required to increase the temperature only from x to 3, instead than from 1 to 3 (Moran, Shapiro 1998). • Intercooling By looking at a p-v diagram representing an internally reversible compression process between two fixed pressures, it is easy to see that for an adiabatic compression the work per unit mass is higher than for compression with heat transfer to the surroundings. Figure 4. 6-In ternally reversible compression processes between two fixed pressures. 4-5 Chapter 4-Literature report. This suggests that cooling a gas during compression is advantageous in terms of the work input requirement In practice, cooling the gas as it is compressed is very difficult. This is due to the difficulties in achieving a high enough heat transfer rate to significantly reduce the work input. A practical alternative is to separate the work and heat interactions into separate processes by letting compression take place in stages with heat exchangers, called intercoolers, cooling the gases between the stages, see Figure 4. 7. Compressor Compressor stage 1 stage 2 intercooler Figure 4. 7-Schematic of a gas turbine cycle with intercooling. PI 2 s' » Figure 4. 8-Two-stage compression with intercooling: P-v diagram. The crosshatched area in Figure 4. 8 represents the reduction in compressor work due to the intercooler. Some large compressors have several stages of compression with intercooling between stages. The use of multistage compression with intercooling in a gas turbine power plant increases the net work developed by reducing the compression work. By itself, though, 4-6 Chapter 4-Literature report. compression with intercooling would not necessarily increase the thermal efficiency of a gas turbine, because the inlet temperature of the combustor would be reduced. This requires additional heat to be transferred to the working fluid to achieve the desired turbine inlet temperature. However, the lower temperature at the compressor exit enhances the possibility of regeneration, so, by using intercooling in association with regeneration, it is possible to have an appreciable increase in thermal efficiency. 4-7 Chapter 4-Literature report. 4.3-Closed Cycle Gas Turbine. The first closed cycle gas turbine plant was built in 1939 in Switzerland, based on the idea registered by J. Ackeret and C. Keller. Since then, more than 20 plants have been built in Europe, Russia, Japan, for a total operation time of more than 100 000 hours, showing a great reliability. In the past years, the abundance of natural gas and oil has caused a loss of interest in closed cycle in favour of open cycle. In fact the closed cycle gas turbine, having an external heat source, requires multiple heat exchangers and a much more complex design than a simple open cycle. However, the progress in developing high temperature heat exchangers and the possibility to use working fluids different from air and with better thermal and transport properties will make it possible to reduce the size of the heat exchangers and therefore the cost of the plants. One of the main characteristic of a closed cycle turbine is that it is externally fired. This means that the working fluid, after being compressed by a compressor, goes trough a heat exchanger, where energy is added from the external heat source. The cycle being externally fired allows use different heat sources, like coal, biomass, nuclear energy or solar energy. The use of this heat sources would be beneficial in saving clean fuel and reducing the production of CO2. Solar energy and nuclear energy do not release any CO2, and the net release of CO2 from the combustion of biomass is zero, since biomass consume CO2 in its life cycle. Of course there are still problems connected to other gaseous pollutants resulting from combustion. The main problem is the production of particulate matters, HC (uncombusted hydrocarbons) and SOx (especially if coal is used). However, since the working fluid is not the combusted gases, there is no need to go trough a deep removal of particulate matters to prevent erosion of the turbine blades. The expanded working fluid is not released to the atmosphere as in a simple open cycle, but instead is recycled to the compressor, after being cooled in a second heat exchanger. In this way it is possible to use a 4-8 Chapter 4-Literature report. working fluid different than air, with better thermodynamic and transport properties. The high rejection temperature of the exhausted working fluid makes the closed cycle highly suitable for a cogenerative utilisation for a steam bottoming cycle. A possible way to improve the closed cycle gas turbine efficiency is by adding a recuperator to transfer heat from the turbine exhaust to the working fluid after the compressor. By doing this, in fact, less heat has to be supplied to the working fluid by the external heat source. A further improvement is the use of an intercooler between the stages of the compressor. This improvement can be up to 2-3 percentage points. Moreover, more heat can be extracted from the exhausts coming out the turbine, since the working fluid exiting the compressor is cooler. The rejected heat after the recuperator will therefore be at a lower temperature and therefore better to use for district heating than for power generation in a bottoming steam cycle. 4.3.1 -Closed-cycle gas turbine working fluid. As mentioned earlier, one of the most interesting characteristics of a closed cycle is the possibility to use working fluids different than air. Theoretically any other gas could be used, with the only requirement of the gas being above its critical temperature during the entire cycle. Other requirements of the working fluid are: • Suitable thermodynamic properties; • Effect on the design of the turbomachinery and heat exchangers; • Compatibility with materials; • Thermal and chemical stability; • Safety; • Cost and availability; 4-9 Chapter 4-Literature report. The choice of working fluids is narrowed down to some inorganic gases and mixture of inorganic gases Almost all of the organic gases do not fulfil the requirements, especially those concerning safety. Air has been used in most of the plants actually built. In order to optimise size and weight in space power system, monatomic gases with medium molecular weight, such as neon, argon and mixture of helium and xenon have been used. Helium has proved to be one of the most suitable gases to work as a working fluid for nuclear reactor cooling. Helium has also been used in fossil-fueled CCGT power plants. Carbon dioxide and nitrogen, or mixtures of gases has also been suggested. • Helium as working fluid: Helium has been proposed as the ideal working fluid due to its excellent heat transfer characteristics, safety and chemical stability, making it possible to reduce the weight and size of the heat exchangers. Its main disadvantage is that it is a low molecular weight gas, requiring compressors and turbines with a large number of stages. Helium has a specific heat cp, higher than air. The number of stages in a turbine or in a compressor is directly proportional to cp, where: AT = gas temperature difference across the turbine or compressor; AH = design enthalpy change between each stage; It follows that the number of stage is higher when a gas with a high cp is used, instead of a gas with a low cp, when a constant AT and AH is applied over the turbine or compressor stage. For monatomic gases, on a molar basis, we have that so " 2 2-M 4-10 Chapter 4-Literature report. being M the molecular weight. It is easy to see that a lower molecular weight gives a higher cp. One difficulty of helium as a working fluid is to keep it from leaking. However according to Lee et a!., 1980, the cost of the yearly refill due to leakage will be only 3 % of the coal saving made by using a CCGT relative to a steam cycle. • Nitrogen working fluid: Nitrogen, together with being a safe and non oxidative gas, has a molecular weight similar to that of air. This make it possible to use ordinary turbomachinery without major modifications. However its heat transfer characteristics are not as good as those of helium. » Helium/Carbon Dioxide as working fluid. The use of a mixture of a low molecular weight gas and a medium molecular weight gas shows some advantages. In fact the thermal characteristics are those of the low molecular gas, while the presence of a gas such as nitrogen or CO2 reduces significantly the required number of stages. Helium and carbon dioxide have both been used separately as working fluids in nuclear plants (Magnox plant for C02, HTGR for He). A mixture of 60 % He and 40 % CO2 on molar basis has a heat transfer coefficient of 80% of that of pure Helium, but the cp is lower, so fewer turbo-compressor stages are required (Lee et al., 1981). The cost of the working fluid is also are reduced in comparison to pure He, C02 being a quite cheap and easily available gas. * Hydrogen as working fluid: Other studies have considered hydrogen as a candidate working fluid for CCGTs. However, being hazardous and requiring a too large number of 4-11 Chapter 4-Literature report. turbine and compressor stages due to its a low molecular weight, it has never been used. 4.4-Steam injection in gas turbine cycle. The practice of steam/water injection in gas turbine was first applied in aeronautic turbines, previously to the application of turbofan propeller or re-heating. Steam injection for ground application was first introduced by the Swedish firm STAL-LAVAL (Nicolin, 1951), but the first commercial applications came about 30 years later in the U.S.A, namely: • Steam-injected simple open cycle or cogenerative cycle (Cheng); • Steam-injected cycle (STIC, Steam-Injected Gas Turbine) from General Electric. The main effect of steam injection is to increase the mass flow rate at the turbine inlet. If the working fluid has a molecular weight lower than the one of water it could also be used to increase the molecular weight of expanding gases . Steam injection increases the heat input, so that the efficiency might not increase, but the power output is boosted. The turbine work is increased while the compressor work, since the injection takes place after the compressor, does not change. The injected water can be up to 6 % of air mass flow rate, without causing relevant problems to combustion. To let an increased mass flow rate expand trough the turbine, the turbine inlet pressure has to increase as well. In ground application turbines it is often necessary to increase the number of stages or to modify the blades to accommodate for the increased mass flow rate. 4.4.1 -Effect of water/steam injection on pollutant emissions. Water injection has a very positive effect on pollutant emissions, especially NOx emissions. As known, NOx production is very high in oxidant, high temperature environment. It is possible to lower the 4-12 Chapter 4-Literature report. production of the so called thermal NOx by reaching homogeneous temperature in the combustion chamber. It is not possible to bring the NOx production to zero since the formation of fuel NOx and prompt NOx, do not depend on temperature but mainly on N2 already present in fuel. Water injection as a way for keeping NOx low is mainly suitable for rather old gas turbines. The presence of water in the combustion chamber can reduce combustion efficiency and a greater production of CO and HC has to be expected. From operating experience on LM 1600 gas turbine it has been found out that the optimum water to fuel ratio to keep both NOx and CO levels below the permitted values is 0.6 at all load levels, see Figure 4. 9 (Robinson, T.,1994). Waw/tuel teiio Figure 4. 9-Effect of water injection on NO x production. If a closed cycle gas turbine is considered, water injection in the compressor outlet stream does not affect combustion or pollutant emissions since the combustion products and gas turbine working fluid are never in contact. 4.4.2-Basic schemes of water/steam injection. The basic schemes of water/steam injection in can be divided in two main categories, evaporative cycles and directly injected cycle. • Evaporative cycle or Humid Air Turbine (HAT). HAT Cycle can be used in open or closed configuration (Rao, 1991). 4-13 Chapter 4-Literature report. In the open cycle, the liquid water is injected into the air after the air compressor in a so called multi-step humidifier with a counterflow flow arrangement. It consists on a plate column or packed column in which the water is brought in contact with the hot water and vaporised. An air-water vapour mixture exits at the top of the column while liquid water exits at the bottom. The air-water vapour mixture is then expanded in the gas turbine, while the liquid water is reheated and fed back to the column, together with make-up water. water in water out Figure 4. 10-Open Evaporative Cycle In the HAT (Humid Air Turbine) closed cycle gas turbine, the working fluid is compressed in a multistage compressor with intercooling and aftercooling followed by direct contact of the pressurised gas with liquid water in a countercorrent humidifier. The humidified gas is preheated in a recuperator against the turbine exhaust and then with the external source. The hot humidified gas is then expanded in the turbine. The heat for the humidification operation is obtained by passing the liquid water leaving the saturator trough the intercooler and after cooler and the exhaust recuperator. The heated water is then sent to the humidifier. In order to avoid corrosion of the turbine blade, big water droplets should be prevented by using moisture separators (Rao, 1991). The proposed cycle recovers heat of compression for the useful purpose of evaporating water into the gases leaving the compressor, thus increasing the net amount of power developed by the cycle. In humid cycle like the one described 4-14 Chapter 4-Literature report. above, the equipments generally proposed for evaporating water into an air stream are a packed tower-a large structure in which the air contacts the water at low speeds, or a saturation chamber in which the air flow is slowed and water is sprayed. Both methods require a large piece of plant equipment and cause a pressure drop. By injecting water or steam directly into the fast moving air stream the cost and pressure drop associated with the two methods above should be avoided. This is a very valuable aspect of direct water injection. • Direct injection before entering the combustion chamber. This is the simplest of all water injected schemes. The electric efficiency is reduced because the turbine inlet temperature is lower than without injection, even if the turbine produces more work due to the increase of mass flow rate. The main advantage in injecting water or steam in a open cycle gas turbine is then connected to the reduction of pollutant emissions (see § 4.4.1 )up to 80 % (Brent, 1989). Steam/Water Figure 4. 11-Simple water/steam injected cycle This basic scheme above described can be improved by adding a thermal recovery from the turbine exhausts (Figure 4. 12). The water/steam, after raising its temperature against the turbine exhausts, is injected before the combustion chamber. In this way the temperature at the inlet of the recuperator is lower, and is therefor possible to cool the exhaust to a lower temperature. The maximum amount of injectable water corresponds to the one capable of saturating the stream exiting the compressor, and it depends on the atmospheric conditions (El-Wakil, 1985). 4-15 Chapter 4-Literature report. Water injection Water in Exhaust Figure 4. 12-Water/steam injected cycle with thermal recovery Direct water injection can be used both for compressor intercooling and aftercooling. • Direct water injection for compressor aftercooling. In the regenerative cycle, the compressor outlet stream is cooled down by injecting water in it, (aftercooling), making possible to recover more heat from the exhaust gases, Figure 4. 13. The heat required to evaporate the water is taken indirectly from exhaust gases not otherwise recoverable. The fuel consumption increases only slightly so that the increased mass flow in the turbine not only raises the power output of the plant but also improves the efficiency. It has been found that compared to plants without water injection, an improvement in efficiency of 10% and an increase in power output of about 35 % are possible (Gasparovic, N., Hellemans, G., 1970-1971). HzO (liquid) To combustor or <£> recuperator Figure 4. 13-Water injection for compressor aftercooling: schematic representation. 4-16 Chapter 4-Literature report. • Direct water injection with intercooling for compressor aftercooling. The previous scheme can be modified to add the positive effect of compressor intercooling to that of aftercooling. Water is the cooling fluid in a heat exchanger that works as an intercooler between the low pressure compressor and the high pressure compressor. The warmed-up water is then directly sprayed in the high pressure compressor outlet stream, working as an aftercooler, see Figure 4. 14 H=0 (liquid) To combustor ‘ or recuperator Figure 4. 14-Direct water injection for compressor aftercooling with one stage intercooling: schematic representation. » Direct water injection as compressor intercooling. Direct water injection can also be used for intercooling between two compressor stages, Figure 4. 15. By cooling down the gases while compressing, the compressor work is lowered and the net power increased. Liquid water is sprayed between the LP compressor and the HP compressor. The water takes sensible heat out of the hot gases while evaporating, cooling the hot gases. The air at the outlet of the HP compressor is cooler than without intercooling. HaO (liquid) To combustor or recuperator Figure 4. 15-Water injection as a compressor intercooler. Chapter 4-Literature report. • Direct water injection in compressor (MAT cycle), in MAT (Moisture Air Turbine) open cycle (Utamura, M., 1997), water can be sprayed directly in the oncoming air of a compressor, reducing the compressor work, Figure 4. 16. The MAT cycle aims to enter fine water droplets into the incoming air in the compressors, thus increasing the output of the gas turbine, and minimising at the same time erosion and corrosion of compressor blades. Injected water is not completely evaporate at the injection point at the inlet of the compressor, but the evaporative process goes on during the compression process, taking sensible evaporative heat from the hot gases, thus cooling the gases throughout the compression. By lowering the work of the compressor and increasing the one of the turbine, as in classical water injection, the net power output is increased. HzO( liquid ) air+H 20(liquid)+H20(gas) Figure 4. 16-Water injection in M.A.T. Cycle In a research carried on by L. Rogers, and E. Liese (1997), it was investigated how much water could be evaporated into the air stream. The results show that in cold water injection tests (10 °C), 25 to 35 % of the water remained in droplet form, while using hot water injection (304°C), 90 to 95 % of the water was evaporated. No significant air pressure drops through the test section was observed in either the hot or cold water tests. The conclusion is that direct water injection is an attractive alternative to an humidified power cycle if complete saturation is not required. 4-18 Chapter 5- System description. Chapter 5 System description. 5.1-Cycle overall description. The system studied in this report is a closed cycle gas turbine coupled to a circulating fluidised bed furnace. The fuel consists of pine sawdust with 50 % of humidity and a Lower Heating Value of 8,175 MJ/kg. The composition of the fuel is found in Appendix XVII. Combustion occurs at atmospheric conditions with a temperature of 850 °C (excess air = 1.2). The combustion air enters the fluidised bed furnace with a maximum temperature of 550 °C. This temperature is reached in the air preheater, using the heat contained in the flue gases leaving the FGHX. The maximum temperature allowable in the CFB as been fixed to 850 °C to prevent sintering of the bed. The combustion section of the CFB and the cyclone are completely refractory lined, to allow heat to be supplied to the externally fired closed cycle via the external bed heat exchanger and the flue gas heat exchanger. The fluidisation velocity in the furnace is 6.1 m/s. As mentioned, the heat is transferred to the cycle working fluid in two heat exchangers, the flue gas heat exchanger (FGHX) and the external bed heat exchanger (EBHX). The FGHX is composed of a bank of cross flow tubes, resembling the convection section of a typical furnace. Since the working fluid temperature exiting the FGHX is limited to 550°C, potential corrosion problems such as alkali deposit should be minimised. The EBHX is a bubbling bed heat exchanger, with a fluidisation velocity lower than 1 m/s. The tubes are immersed horizontally into the bubbling bed to ensure high bed-side heat transfer coefficients. About 70% of the total bed solids flows is passed through the EBHX. The maximum temperature reached by the working fluid is 800 °C. After the FGHX, the heat in the flue gases is first used to preheat the combustion air. The remaining heat is transferred to district heating network 5-1 Chapter 5- System description. in a condensing flue gas heat exchanger, where a part of the water content in the flue gases is condensed. The total efficiency reachable based on the fuel LHV will then be higher than 100 % since the latent heat of vaporisation of water will partially be recovered (See Appendix XVII). Condensation of the flue gases also acts as a valid particle removal from the flue gases. The flue gases exit the stack at around 60 °C (at the design point). The diffusion of the flue gas puff is not a problem since the outer temperature is very low, so that the AT is high enough. The stack is made of stainless steel, to avoid corrosion due to acid condensation of the gases. The hot working fluid leaving the EBHX is expanded in a turbine to the cycle base pressure. The exhaust leaving the turbine is used to warm up the working fluid after the HP compressor in a recuperator. After the recuperator the working fluid is cooled down to the LP compressor inlet temperature in a postcooler. The compression process takes place in two stages with intercooling. The optimum pressure ratio for the LP compressor is found in a sensitivity analysis where the pressure ratio throughout the LP compressor is varied, see chapters 7 and 8. The turbomachinery is taken to have a polytropic efficiency ?ipoi = 0.90 and a mechanical efficiency rjmec = 0.99 . The cycle can include one or two stages of intercooling and one or two stages of postcooling. The heat removed in the first stage intercooling and postcooling is transferred to the district heating network. The intercooler/postcooler using district heating water as coolant can not cool the working fluid to a temperature lower than 65°C, because the extreme temperatures of the district heating water are fixed to a 50 °C return temperature and 80 °C supply temperature. The minimum pinch point AT in the postcooler with district heating water is 5 °C when condensation occurs in the postcooler. The choice of such a narrow temperature difference is based on operational conditions in real plants. The second stage intercooling/ postcooling uses external cooling water as a coolant. In the dry cycle the intercooler/postcooler is a shell and tube heat 5-2 Chapter 5- System description. exchanger with district heating water on the tube side and working fluid on the shell side. Flue gas Working fluid Recuperator Biomass Air preheater Turbine expander Low pressure High pressure Ash compressor compressor 1. Flue gas condenser 5. Cooling water (optional) 2. District heating 6. Postcooler 3. External bed heat exchanger EXBHX 7. Intercooler 4. Flue gas heat exchanger FGHX 8. Flue gas condensate 9. Water Injection Figure 5. 1-Schematic representation of dosed cycle with two level intercooling and two level postcooling. The cycle will be then modified to include water injection as intercooling and aftercooling. Water will be directly sprayed in the stream, using an atomiser to reduce the size of the water droplets and prevent the entering of liquid water in the compressor, with the danger of erosion of the compressor ’s blades. The working fluids considered in this study are helium, nitrogen, helium-water vapour mixture and nitrogen-water vapour mixture. The relevant design parameters are summarised in Table 5.1. Parameter Value Parameter Value Fuel Flow [kg/s] 0.9395 AT gas/liquid f°C] 15 5-3 Chapter 5- System description. LHV 8,175 AT condensate/liquid [°C] 5 Fuel input to the cycle [kg/s] 7.68 SrecuD 0,93 Excess air factor 1.2 riooiv turbomachinery 0,9 Furnace bed T [°C] 850 Generator efficiency 0,99 Solid flow trough EBHX 70% Turbomachinery mechanic 0,99 efficiency Air inlet temperature [°C] 15 Cycle base pressure [bar] 2 T air oreheater [°C] <550 Ap postcooler 4% Working fluid T after FGHX 550 Ap intercooler 2% [°C] Working fluid T after EBHX 800 Ap recuperator cold side 1.5% [°C] District heating water inlet 50 Ap recuperator hot side 4% temperature [°C] District heating water outlet 80 Ap EBHX+FGHX 1.3% temperature [°C] AT gas/gas [°C] 25 Table 5.1 - Input parameters for CFB furnace and EFGT cycle 5-4 Chapter 5- System description. 5.2 - ASPEN Simulation. The cycle has been simulated using the commercial software ASPEN PLUS. This software is a simulator used in chemical engineering and energy industry with predefined components and numerous databases of chemical and thermophysical properties for ideal and non-ideal components. The various predefined blocks can be connected by streams to simulate different process configurations. In addition to supplying data to the simulation ni the different blocks, it is also possible to provide in-house calculation routines in user-defined FORTRAN blocks. The cycle flowsheet, referring to the dry case, is the following: 5-5 Chapter 5- System description. 5-6 Chapter 5- System description. In § 5.2.1 to § 5.2.4, the ASPEN model built up to simulate the dry CCGT is described in detail. 5.2.1 - Cycle base pressure and pressure drops. The pressure in different sections of the cycle, together with the pressure drops in the equipment pieces, is fixed by the FORTAN block P-RATIO found in Appendix XIX. For the heat exchangers the pressure drop as been taken as a fixed percentage of the inlet pressure, not regarding of the working fluid thermal properties. 5.5.2 - Air preheater and combustion zone. • Air preheater. The air preheater, Figure 5. 2, is represented as two heater blocks (AIRPRHOT and AIRPRCOLD), joined by the heat - duty stream QPREHEAT. Figure 5. 2- Air preheater ASPEN flowsheet 5-7 Chapter 5- System description. Heat is transferred from the flue gas in AIRPRHOT to the combustion air entering AIRPRCOL. The temperature in stream PRAIR is limited to 550 °C and the minimum AT between EXH1 and PRAIR is limited to 25 °C. • Circulating Fluidised Bed Furnace. The Circulating Fluidised Furnace is represented by 3 blocks (DECOMP, COMF1, COMP2) to simulate the combustion zone, a SSPLIT labelled CYCLON to simulate the cyclone and a SEPARATOR for the ASH- SEPARATOR, see Figure 5. 3. Figure 5. 3- Fluidised bed furnace ASPEN flowsheet. The combustion air is divided in two streams, primary air and secondary air, in the fsplit block SPLIT. The fuel enters the furnace with the stream FUEL to 5-8 Chapter 5- System description. a block labelled DECOMP. The combustion takes place in two stages, a primary combustion with the primary air in block COMB1 and a secondary combustion in block COMB2 where the secondary air is injected. The flue gases leaving the furnace go to a cyclone where the ashes and sand are separated from the flue gases and sent to the external bed heat exchanger. After that, the ashes are separated from the sand in a SEP2 block called ASH-SEP. The sand is recycled to the furnace with the stream RECY-BED. 5-9 Chapter 5- System description. 5.5.3 - Heat exchangers. The heat exchangers are specified using a shortcut method instead of a rigorous one. For shortcut rating no heat exchanger geometry information is required. The pressure drops used for the heat exchanger have been found in literature and are specified in Table 5.1. • Flue Gas Heat Exchanger. The flue gas heat exchanger is given by two HEATER blocks, one for the cold side and one for the hot side. The two blocks are connected by a heat - duty stream Q-GAS, as shown in Figure 5. 4. EXHCOOL GASHEAT2 Figure 5. 4- Flue Gas Heat Exchanger ASPEN flowsheet The temperature of the flue gases in stream CYC-GAS stream is always 850 °C. The temperature of the working fluid stream exiting the GASHEAT2, (stream 5A) is always 550 °C. The minimum temperature difference between working fluid and flue gas is set to 25 °C. • External Bed Heat Exchanger. The EBHX is simulated by two heater blocks, EX-FBED and HEATBED, (cold and hot side respectively).The two blocks are connected by a heat - 5-10 Chapter 5- System description. duty stream, Q-EXT, Figure 5. 5. The mass flow rate of the working fluid is adjusted so that a temperature of 800 °C is always obtained at the exit of EBHX. Figure 5. 5-External Bed Heat Exchanger ASPEN flowsheet. * Flue gas condenser. In the ASPEN simulation the flue gas condenser is represented by two heat exchanger blocks (DISTHOT and DiSTLOW),. The first one (DISTHOT) brings the flue gas to its dew point, the second one ( DISTLOW) condenses and cools it. In the flue gas condenser, the minimum pinch point AT allowed for district heating is 5 °C. The specification for the condenser can vary between a Atcoid =5 °C, Figure 5. 6 or a AW =5 °C, Figure 5. 7, being AtCOid the temperature approach at the cold stream outlet and AW the temperature approach at the hot stream outlet. Tout = 80 C Tin = 50 C O- Tdew = 75 C --- Tin ------Q------Tout = 55 C 4=^!- Figure 5. 6 - Schematic representation of the Flue Gas condenser when an approach on the hot side is fixed. AThoi - 5 C 5-11 Chapter 5- System description. Tout = 80 C Tin = 50 C Tout = 55 C Figure 5. 7-Schematic representation of the Flue Gas condenser when an approach on the cold side is fixed: ATcoid = 5 C. • Intercooler/aftercooler. The block used for the intercooler and the aftercooler are heaters. The design specification is the outlet temperature on the cold side. The coolant is not represented in the simulation of the intercooler/postcooler. • Recuperator. Figure 5. 8 - Recuperator ASPEN flowsheet The recuperator is a HE ATX block labelled RECUP, Figure 5. 8. Stream 4A exiting the HP compressor or the aftercooler (depending on the simulation) is warmed up by the turbine exhausts in stream 7. Stream 5 will then enter GASHEAT2 while stream 8 will be cooled in the postcooler. 5-12 Chapter 5- System description. The recuperator outlet temperature on the cold side is given by FORTAN block EPSILON, (Appendix XIX) 5.5.4 -Turbomachinery. The turbomachinery is modelled accordingly to the ASME method. This method allows modelling a polytropic compressor or an isentropic turbine. The compressors are simulated by a COMPR block. They are labelled HPCOMP and LPCOMP, Figure 5. 9. The pressure ratio across the two compressor is the same in the dry cycle, while in the wet cycle it is varied. The mechanic efficiency of the compressors is ri=0.99, while the polytropic efficiency is r|po l = 0.9. The compressor work (Appendix I) is given as an output in stream LPW and HPW. Figure 5. 9- LP and HP compressors ASPEN flowsheet. The turbine is simulated by the COMPR. block labelled TURBIN, Figure 5. 10. "TURBIN Figure 5. 10- Turbine ASPEN flowsheet. 5-13 Chapter 5- System description. Since the ASME method used for modelling the turbomachinery does not allow a polytropic efficiency for turbines, the isentropic efficiency corresponding to a polytropic efficiency equal to 0.9 is calculated in a FORTRAN block named EFF - T. (see Appendix XIX) The turbine work (see Appendix I) is given as an output in stream TW. • Water injection. The dry cycle is modified to include water injection. The intercooler heat exchanger is replaced by water injection, a MIXER block INJ is insert in stream 2, dividing it in two streams, 2 and 2A. The third stream entering the MIXER is the water stream 1A. A design specification makes a feed-back control on mass flow rate in stream 1A to reach the required relative humidity in stream 2A. The same scheme is used for the water injection as aftercooling, with mixer block INJ5. In the wet cycle, The FORTAN block P- RATIO is modified (Appendix XIX) so to allow a larger part of the compression process to take place in one of the two compressors. 5-14 Chapter 6-Effect of water injection into the closed cycle gas turbine. Chapter 6. Effect of water injection into the closed cycle gas turbine. The aim of the present study is to examine the effect of introducing water injection into the closed cycle gas turbine. The water could be injected between the two compressor stages and replace the intercooler heat exchanger. By using sensible heat to evaporate the injected water the working fluid is cooled down before being compressed in the HP compressor. It is also possible to have a second water injection after the HP compressor, to act as an aftercooler. By using an aftercooler the temperature of the working fluid entering the cold side of the recuperator is reduced and it is then possible to increase the recuperation. The injected water is fully condensed in the post cooler and then returned to the injection point. This way, no water will theoretically be consumed. 6.1-Amount of injected water in helium/ nitrogen-water mixture. As a first step, it is relevant to determine the amount of water that can be injected in helium or nitrogen to saturate it and how much cooling is provided. The intercooling process shown in Figure 6.1 has been simulated in E.E.S. (Engineering Equations Solver), to determine the amount of water to be injected to reach the required relative humidity after the water injection and the temperature reached in stream 3. The theory on which it is based can be seen in Appendix IV The inlet temperature in stream 1 is 65 C and the stream is saturated with water at this temperature at pressure P=2 bar. The pressure after the compressor is P=3.63 bar for the case with helium working fluid and P=4.52 bar for the case with nitrogen working fluid. More input data together with the results are found in Appendix IV. 6-1 Chapter 6-Effect of water injection into the closed cycle gas turbine. Figure 6.1-Schematic of water injection after compression. • Helium as a working fluid The results of the sensitivity analysis on relative humidity 1 0.12 RELATIVE HUMIDITY Figure 6.2-lnjected water mass flow rate vs. relative humidity. 6-2 Chapter 6-Effect of water injection into the closed cycle gas turbine. k 100 RELATIVE HUMIDITY Figure 6.3-Temperature in stream 3 vs. relative humidity. • Nitrogen (N2) as a working fluid. The same analysis for nitrogen as working fluid gives the results plotted in Figure 6.4 and Figure 6.5. The results are in Appendix IV, Table IV.2. 0.035 0.025 2 0.02 0.015 RELATIVE HUMIDITY Figure 6.4-lnjected water mass flow rate vs. relative humidity. Nitrogen as working fluid. 6-3 Chapter 6-Effect of water injection into the closed cycle gas turbine. 0.2 0.3 0.4 0.5 0.6 0.7 0,6 0.9 1 RELATIVE HUMIDITY Figure 6.5-Temperature in stream 3 vs. relative humidity. Nitrogen as working fluid. The results clearly show that at constant relative humidity, less water is injected in nitrogen than in helium. The reason why the amount of water that can be added to reach a certain relative humidity of the mixture is different when using nitrogen instead of helium is that the molar mass is different for the two gases. The amount of injected water is given by the difference between inlet humidity ratio and outlet humidity ratio, multiplied with the mass flow rate of non condensable working fluid. The saturation temperature for a moist stream can be iteratively calculated from equation 111-1, m co = wf knowing that MHi0 _ f0,642 N2 ^Tl4,5 and a heat balance of the adiabatic saturation process, given the working fluid conditions (the working fluid is assumed to be a non condensing gas). +m,A =("V +(mA +/%A,)L 6-4 Chapter 6-Effect of water injection into the closed cycle gas turbine. The unknowns are the outlet temperature and the amount of water that must be evaporated in the working fluid to reach the desired relative humidity. Assuming a outlet temperature, (and the corresponding vapour pressure and enthalpies), the heat balance can be solved for mw, the amount of water added to reach the desired relative humidity., and for the humidity ratio. Using equation 111-1 and inserting the saturation pressure for the vapour partial pressure, the humidity ratio for the assumed saturation temperature can be compared with the humidity ratio determined from the heat balance. If they differ, then a new saturation temperature is assumed and the process is repeated until the solution converge. The injected water will evaporate until saturated conditions are reached. If the injected water is not at the adiabatic saturation temperature, heat will be subtracted from the inlet mixture to raise the water temperature, so the mixture temperature will decrease. The total heat supplied from the working fluid to the injected water can be considered as the sum of heat for reaching the evaporation temperature, Q', and the evaporation heat, Q". Q' = rhHio-cp{AT) Q = ™h2o ' khfe The evaporation rate depends primarily on the temperature difference between the working fluid and water, the surface area of the water droplets and the mass concentration gradient (Lefebvre, 1983). It is increased with higher working fluid temperature, smaller droplets size and drier working fluid. In reality, particular care should be used when cold water is injected. In fact the inlet duct to the compressor should be long enough to allow sufficient residence time a complete evaporation of the water. An E.E.S. simulation has been developed to explore the effect of inlet stream temperature on the injected water mass flow rate, at a constant relative humidity level in the outlet stream. The input data, results and program are in Appendix V, Table V-1. The working fluid is a nitrogen-water mixture. The relative humidity after the injection is 6-5 Chapter 6-Effect of water injection into the closed cycle gas turbine. INLET TEMPERATURE Figure 6.6-lnjected Water Mass Flow Rate [kg/s] vs. Inlet Temperature [°CJ. Nitrogen-water mixture as working fluid. A second E.E.S. simulation explores how the injected water temperature affect the saturation process. The input data and results can be seen in Appendix V. The working fluid is nitrogen-water mixture. The results are plotted in Figure 6.7 and show that the injected water mass flow rate increases with increasing temperature. 0.375 u- 0.36 0.355 5 0,35 0.345 0.335 INJECTED WATER TEMPERATURE Figure 6.7-lnjected water mass flow rate [kg/s] vs injected water temperature [°C] 6-6 Chapter 6-Effect of water injection into the closed cycle gas turbine. 6.2-Total Mass Flow rate behaviour and thermodynamic properties modifications with helium-water mixture and nitrogen-water mixture as a working fluid compared to pure helium and pure nitrogen. As mentioned in §5.2.3, the total mass flow rate in the cycle is fixed by the E:BHX heat duty which is the same at the design point for all simulations. The working fluid mass flow rate is adjusted to raise its temperature from 550 °C to 800 °C. e = *-w(r2-r,) that can be rewritten as ™= —-fc-r,) c pavg where povg 2 Q = heat flow rate in the EBHX [KJ/s] T2 = 880 °C Ti = 550 °C AT=T 2~T 1 In the dry cycle QEBHX ™He = AT - Cp,He Qebhx AT • cpMe Qebhx AT • Cp y2 Qebhx A T-cpMi with cpHe =5,\9[kJ/kg,K] = 20.79 6-7 Chapter 6-Effect of water injection into the closed cycle gas turbine. S", -1041 =29.15 Kmol.K- If the working fluid composition is varied, its thermal characteristics vary as well, and the total mass flow rate needed to pick up a constant amount of heat should vary too. Q.EBHX = Qe EBHX A T-cpmix If a helium-water vapour mixture is used instead of dry helium, an increase in cycle mass flow rate has to be expected. Cp,Hemix ~ XHe ' CpHe + XH10 ' C pH20 cw=2,17 [kJIkg.K] CpHe > CpH2C) ^ Cpavg - CpHe It follows that mHemix > mHc On a molar basis Cp,He mix ~ ‘ Cp,He + 7H20 ' Cp,HxO ' CpH-p =39.13 [kJ / kmol,K] CpHe < CpH20 ^ CpHemix - CpHe and it follows that nHemix Using the same equations, a decrease in total mass flow rate and molar flow rate has to be expected when a nitrogen-water mixture is used instead of pure nitrogen, since. On a mass basis ^pN2mix > ^pN2 On a molar basis ^ pN2mix > CpN2 nN2mix < nN2 6-8 Chapter 6-Effect of water injection into the closed cycle gas turbine. If more water is added to the nitrogen-water mixture, the molar fraction of water increases and the total mass flow rate decreases even more. This means that the working fluid flow rate is lowered as the relative humidity at injection point is increased in the simulations of the wet cycle with N2/H20 mixture as working fluid. However, in the case of helium-water mixture working fluid, the mass flow rate is increased with increasing relatives humidity and the mass flow rate decreases. The pressure ratio has also an influence on the working fluid flow rate at constant relative humidity. An increases in pressure ratio at constant relative humidity level is responsible for a decrease in mass flow rate when nitrogen- water mixture is considered as working fluid. First, an increase in pressure ratio leads to an increase in pressure and temperature at the injection point. The saturation pressure increases at higher temperature. The water molar fraction is defined as ^ p The ratio curve for nitrogen shows that the saturation pressure grows more than the pressure, so the water molar fraction increases at increasing pressure ratios. A higher water molar fraction results in a decrease in mass flow rate. Secondly, the molar specific heat of water vapour increases with pressure, causing the c of the mixture to increase. To summarize, the mass flow rate is expected to have the following behavior, for nitrogen-water mixture: • Decreases when a wet mixture is used instead of pure nitrogen; • Decreases as the relative humidity increases; • Decreases with increasing pressure ratio at constant humidity level; While, for helium-water mixture, the total mass flow rate: • Increases when a wet mixture is used instead of pure helium; • Increases as the relative humidity increases; 6-9 Chapter 6-Effect of water injection into the closed cycle gas turbine. 6.3-Effect of water injection on turbomachinery work and efficiency. Turbomachinery performance is strongly dependant on the thermodynamic properties of the working fluid. The effect of a change in working fluid has been studied for expansion and compression process. • Expansion process. A sensitivity analysis varying the injected water mass flow rate in an helium/water mixture stream being expanded in a turbine has been developed using the software Engineering Equation Solver (E.E.S.). The aim of this simulation is to show how the change in composition of the working fluid, and therefore the change in thermodynamic properties affects the turbine work between the same pressure levels. When a mixture is used as working fluid the turbine outlet temperature is given by equation 1-1. The mixture k-value is defined as in equation I-6. The turbine work is given by equation I-4. A polytropic efficiency qp0i = 0.9 has been considered. The working fluid is helium-water mixture. The input and results are in Appendix VI, Table VI-1 and the results are plotted in Figure 6.8 and Figure 6.9. 6-10 Chapter 6-Effect of water injection into the closed cycle gas turbine. Figure 6.8-Total mass flowrate versus water molar fraction. Helium- water mixture as working fluid. 5 -1,15 5 -1,25 Figure 6.9-Turbine work/ EBHX heat input versus water molar fraction.. Helium-water mixture as working fluid. The expanded mass flow rate increases as the water molar fraction increases, but the turbine work decreases. 6-11 Chapter 6-Effect of water injection into the closed cycle gas turbine. • Compression process. A similar analysis has been performed for a compression process, taking place in a compressor with a polytropic efficiency ijpol= 0,90 In a compression process, the compressor outlet temperature is given by equation 1-5, in Appendix I. Since lcavg Cpavg X// c pavg — xM x mix • cpavg 1% R = R' M „Sv Kmol ■ K it follows f \ g'tfpol Tout - T,n W \P*J and therefore, from equation 1-6 R \ Cpavgr ‘Vpol compressor vg • xT in • -1 \ Tin J if the mass flow rate, the cp and the pressure ratio are constant, the compressor work increases proportionally to the inlet temperature. If the cp varies, as when the water molar fraction varies, the compressor work varies too, at the same inlet temperature. The cycle to which the E.E.S. simulation is referring to is a closed cycle with water injection as intercooling and aftercooling, see Figure 6.10. The working fluid is helium-water mixture. 6-12 Chapter 6-Effect of water injection into the closed cycle gas turbine. INTERCOOLER AFTERCOOLER HP COMPRESSOR TURBINE H20c m=m. POSTCOOLER Figure 6.10-Schematic representation of water injection as intercooling and aftercooiing. The water molar fraction in the turbine inlet stream has been varied, varying the relative humidity after the aftercooler. The total mass flow rate being expanded in the turbine increases when adding more water. The helium mass flow rate is constant in the cycle, at a relative humidity in the intercooler and aftercooler. The helium mass flow rate when the relative humidity is increased (§6.2). In the condenser the injected water is condensed and the stream entering the LP compressor is at saturated condition at P = 2 bar and T = 65 °C. The water molar fraction At the LP compressor inlet is given by: v - ^HlOc J H20c - . nHe + nH20c where the subscript c stands for LP compressor. The mass flow rate in the LP compressor is: K = fhffe + MfflOc ft* H20c= y H20c " M H20 'if1 He + ^HlOc ) y H2Oc y H20,sat [Te ’ ) The thermodynamic properties of the helium-water mixture stream entering the LP compressor are not affected by an increasing amount of injected water in the cycle. Since the composition of the LP compressor inlet stream is constant at constant temperature and pressure, the decrease in 6-13 Chapter 6-Effect of water injection into the closed cycle gas turbine. compressor work is only due to the decreasing mass flow rate being compressed. The results of the analysis are in Table VI-2. They show that for an increase of water molar fraction after the aftercooler of about 30%, the mass flow rate being compressed in the LP compressor decreases about 10 %. • HP compressor work. With the same hypothesis, the decrease in HP compressor work is due only to the decreasing mass flow rate going trough it, as shown in Figure 6.11 since the composition of the mixture entering the HP compressor is constant on a molar basis and therefore the k-value is constant. The results for HP compressor are shown in Table VI-3. □ Total mass flow rate ■ Helium Mass flo □ Compressor mass flow rate WATER MOLAR FRACTION Figure 6.11-Total mass flow rate, helium mass flow rate, HP compressor mass flow rate vs. water molar fraction. The mass flow rate being compressed in the HP compressor decreases about 4% when the water molar fraction increases around 10 %. On the contrary, If the water molar fraction at the inlet of a compressor is varied, i.e. a different relative humidity level is required in the stream after the intercooler, the work input for the compression process varies accordingly. 6-14 Chapter 6-Effect of water injection into the closed cycle gas turbine. The following results consider only one water injection, acting as intercooling, before the HP, so that: ^lH20c~1^lH20 where mlot is the mass flow rate expanded in the turbine and c stands for compressor. The compressor inlet temperature is considered constant, to show only the effect of k-value reduction on compressor work, without considering the benefit of a further inlet temperature decreasing. The results are in Appendix V, Table VI-5 W»t*r molar fraction Figure 6.12-Compressor work versus water molar fraction in the compressor inlet stream. The increase in water molar fraction at the compressor inlet has a positive effect on the compression work, reducing it. 6.4-lsentropic efficiency in wet and dry cycles. Isentropic efficiency shows how distant the real compression and expansion process is from the ideal one. The higher the efficiency is, the less irreversibilities are in the real compression and expansion process In the 6-15 Chapter 6-Effect of water injection into the closed cycle gas turbine. ideal process the entropy does not vary, while is increasing in the real, thanks mainly to friction. The isentropic efficiency is defined as the ratio between ideal expansion or compression work and real expansion or compression work. The equations for isentropic efficiency are available in Appendix I. The isentropic efficiencies corresponding to a polytropic efficiency of 0.9 have been calculated, both for turbine and compressor, first versus the pressure ratio then versus the water molar fraction in the stream entering the turbomachinery. • Expansion process Accordingly to the equation for turbine isentropic efficiency, in Appendix II, the expansion isentropic efficiency is higher than the polytropic one, at the same pressure ratio. In fact Ywr=wr because the isobaric curves have an increasing derivative. When a water-helium mixture is used as working fluid, the turbine isentropic efficiency is lower than the one in the dry cycle, with the same polytropic efficiency The k-value, as shown in § 6.2 is lower for a helium-water mixture than for pure helium. kmix "I pm tx R —1 '■He C pm ix ~ C pHe > '■He From equation 11-9 follows that the isentropic efficiency in the wet cycle is lower than in the dry one. This is shown for a cycle with water injection as intercooling and aftercooling, having the following requirements: 6-16 Chapter 6-Effectof water injection into the closed cycle gas turbine. %oi = 0,90 The resulting isentropic efficiency for the expansion process has been calculated at different pressure ratios and compared to the isentropic effciencies of expansion with pure helium at hpol=0.90, see Figure 6.13. The results are in Appendix VIII. 92,5 - 2.9 2,8 PRESSURE RATIO Figure 6.13-Expansion isentropic efficiency vs. pressure ratio. Helium and helium-water mixture as working fluid. The isentropic efficiency in the wet cycle is about 0.3 percentage point higher in the wet case than in the dry one. When nitrogen-water mixture is considered instead of helium-water mixture, the qualitative behaviour of the isentropic expansion efficiency is the same, since the mixture k-value is lower than the pure gas one. The resulting efficiency for wet and dry working fluid at different pressure ratios are plotted in Figure 6.14. The increase in the wet cycle compared to the dry one is about 0.05 % in this case. This is lower than for helium, however the absolute value of the isentropic efficiency is higher. 6-17 Chapter 6-Effect of water injection into the closed cycle gas turbine. PRESSURE RATIO Figure 6.14-Expansion isentropic efficiency vs. pressure ratio. Nitrogen and nitrogen-water mixture as working fluid. • Compression process. From equations II-2 and II-3 for the compression polytropic expansion comes that the isentropic compression efficiency is lower than the polytropic one at the same pressure ratio. In fact: 2X=r, The compressor isentropic efficiency is higher for a gas-water mixture than for dry gas with a constant polytropic efficiency . Considering a cycle with water injection intercooling and aftercooling, having (j>= 60 % after the intercooler; <(>= 95 % after the aftercooler; r|poi = 0.90 and helium-water mixture as working fluid, the isentropic efficiency versus pressure ratio is the following: 6-18 Chapter 6-Effect of water injection into the closed cycle gas turbine. -—WET -—DRY PRESSURE RATIO Figure 6.15- Compression isentropic efficiency vs. pressure ratio. Helium and helium-water mixture as working fluid. The results are in Appendix VI When nitrogen-water mixture is considered instead of helium-water mixture, the qualitative behaviour of the isentropic compression efficiency is the same, since the mixture k-value is lower than the pure gas one (§6.2) 89,4 - WET 89,2 - PRESSURE RATIO Figure 6.16-Compression isentropic efficiency vs. pressure ratio. Nitrogen and nitrogen-water mixture as working fluid. 6-19 Chapter 6-Effect of water injection into the closed cycle gas turbine. • Effect of relative humidity level. if the amount of injected water in the intercooler is varied, the composition of the working fluid and the k value of the gas-water mixture varies as well, affecting the isentropic efficiency of the turbomachinery. Cpmix ~ y He ’ C pHe + T H-fi ' C pH 20 kmix "I pmix R as the water molar fraction increases, yH20(2) > >tf20(l) kmixl 1 _ kmjx i c > c pmixl pmixl If If Kmixl Kmix 1 A change in water molar fraction in the turbine inlet at a fixed pressure ratio (in this simulation (3= 3.3) results in the following isentropic efficiencies, Figure 6.17 and Figure 6.18. The results are also found in Appendix VII, Table VII.5. 0,1922 WATER MOLAR FRACTION Figure 6.17-Turbine isentropic efficiency vs. water molar fraction. As clearly seen, the expansion isentropic efficiency decreases as the relative humidity increases. On the other hand, if a compression process is taking place, the decrease in k-value (Equation ll-9).is responsible for a higher compressor isentropic efficiency, as shown in Table VII-6 and Figure 6.18. 6-20 Chapter 6-Effect of water injection into the closed cycle gas turbine. 68.62 0,1246 Figure 6.18-Compressor isentropic efficiency vs. water molar fraction. The effect of water injection on turbomachinery isentropic efficiency seems to be a second hand effect. The percentage increase or decrease of isentropic efficiency as more water is injected is very small and it has an opposite behaviour for turbine and compressors. 6-21 Chapter 7-Helium and helium/water mixture as working fluid. Chapter 7. Simulations with helium or helium/water vapour mixture as working fluid. In this chapter the results from ASPEN simulations on closed cycle gas turbines with helium and helium/water mixture as working fluid will be described. At first the dry cycle will be studied as a starting point for the simulations including water injection(s). The effect of water injection on thermodynamic characteristics of the working fluid and cycle performance has been first predicted by means of theory only in Chapter 5 and will now be checked with the results from the ASPEN simulations. At the end of the chapter the results from all the studied simulations will be compared, to point out the design point, depending on the parameter to optimise. 7.1 - Dry scheme with one stage intercooling and one stage postcooling Flue gas 9 3 1. Flue gas condenser 6. Postcooler 2. District heating 8. Flue gas condensate 3. External bed heat exchanger EXBHX 4. Flue gas heat exchanger FGHX Figure 7. 1-Schematic representation of system configuration: dosed cycle with one level inter/postcooling. 7-1 Chapter 7-Helium and helium/water mixture as working fluid. In this cycle configuration there is no intercooling between LP and HP compressor and there ’s only one postcooler that cools down the recuperator outlet stream to 65 °C. The heat removed in the postcooler is used to warm up district heating water from 50°C to 80 °C. The base pressure, as for all the simulation with dry helium or water-helium mixture, is 2 bar. The simulations are ran varying the overall pressure ratio in order to determine the cycle design pressure ratio. The cycle performance will be described by efficiencies, as defined in Appendix VIII. The results of the sensitivity analysis on pressure ratio are in Appendix VIII, Table VIII-1. The design point for the cycle can be fixed at two pressure ratio values, depending on what we want to optimise. The first choice can be the pressure ratio when the air preheater reaches a temperature of 550 °C (this pressure ratio corresponds to point A, as defined in Appendix XVIII). This temperature is the maximum allowed to prevent the melting of alkali salts. At this point the electric efficiency has its maximum. The second choice can be the pressure ratio when the district heating flue gas heat exchanger changes its design specification from an approach AT = 5 °C on the cold side to an approach AT = 5 °C on the hot side. In this case, more heat is recovered from the hot gases exiting the stack at a lower temperature than before, so the total efficiency is increased, while the electric efficiency is still high. The choice of design pressure ratio depends on the main aim of the plant. If district heating is more valuable than electricity production, than a pressure ratios that guarantee an higher total efficiency is to be preferred, otherwise the logical choice would be to choose a pressure ratio that gives a high electric efficiency. In this paper, the electricity has always been considered the main product of the plant, with district heating as a valuable but second order by-product, therefore the optimum has always been fixed with the intent of a high power output. The design pressure ratio for the dry cycle with no intercooling is fixed at 2.8. This value is the one corresponding to a air preheater outlet temperature equal to 550 °C (point A). At the pressure ratios considered in this analysis, point B (see Appendix XVIII) is reached at pressure ratio 2.0. At this point in fact Ts=550 °C, therefore the heat duty in the flue gas heat exchanger is 7-2 Chapter 7-Helium and helium/water mixture as working fluid. fixed to zero (Appendix XVIII). The results of the sensitivity analysis are in Appendix VIII, Table VIII-1 and are plotted in Figure 7.2. -M-CYCLE EFFICIENCY FURNACE EFFICIENCY ELECTRIC EFFICIENCY PRESSURE RATIO Figure 7.2- Efficiency vs. Pressure Ratio. The efficiencies at design pressure ratio are in Table 7.1 Working fluid He Design 3 2.8 Net electric efficiency % 25.509 Furnace efficiency % 87.13 Thermal cycle efficiency % 30.99 Total efficiency % 107.74 Table 7. 1- Cycle performance at design pressure ratio. 7-3 Chapter 7-Helium and helium/water mixture as working fluid. 7.2-Dry cycle with two stage intercooling and two stage postcooling. F-igure 7.3 shows the process layout of the dry closed cycle gas turbine with two level inter- and postcooling. Flue gas Working fluid Recuperator Biomass Air preheater Turbine expander Low pressure High pressure compressor compressor 1. Flue gas condenser 5. Cooling water (optional) 2. District heating 6. Postcooler 3. External bed beat exchanger EXBHX 7. Intercooler 4. Flue gas heat exchanger FGHX 8. Flue gas condensate 9. Water Injection Figure 7.3-Schematic of system configuration: closed cycle with two level intercooling, two level postcooling. The first intercooler, labelled ICi, reduces the temperature of the LP compressor outlet stream to 65 °C. Removed heat is used to heat up district water supply from 50°C to 80 °C; A second intercooler, IC2, cools the stream to 30 °C. Cooling water is used as coolant. After the recuperator, a first postcooler PC1 cools the recuperator outlet stream to 65 °C. As for the intercooler IC1, the removed heat is used to heat up district water supply from 50°C to 80 °C. An additional postcooler PC2 brings down the temperature to 30 °C using external cooling water as a coolant. The same pressure ratio has been used for LP and HP compressor, to minimise the cycle compression work. (Moran, Shapiro, 1998 ). The results of the sensitivity analysis on pressure ratio are in Appendix VIII, Table VIII-2. 7-4 Chapter 7-Helium and helium/water mixture as working fluid. The cycle thermal efficiency, net electric efficiency and furnace efficiency are plotted in Figure 7.4: —»—C ycle therm a I e fficie n cy F u rn a c fficiency -■*— N et electric efficiency Figure 7.4-Efficiencies vs. Pressure Ratio. The design pressure ratio is identified at (3=2.8. The results at design pressure ratio are in Table 7.2. Working fluid He Pressure ratio 2.8 Net electric efficiency % 35.3 Furnace efficiency % Thermal cycle efficiency % 41.3 Total efficiency 87.7 Table 7. 2- Cycle performance at design pressure ratio. 7-5 Chapter 7-Helium and helium/water mixture as working fluid. 7.3-Water injection as 1 stage intercooling. The closed cycle gas turbine system with water injection for intercooling is found in Figure 7.3. Flue gas Working fluid Recuperator Biomass Air preheater Turbine expander Low pressure High pressure compressor compressor 1. Flue gas condenser 6. Postcooler 2. District heating 8. Flue gas condensate 3. External bed beat exchanger EXBHX 9. Water Injection 4. Flue gas heat exchanger FGHX Figure 7.5-Schematic of closed cycle with one water injection as intercooler and one-level postcooler. In this new cycle configuration the intercooler ICi has been replaced by water injection, while the intercooler IC2 and the postcooler PC2 have been removed. The water injection takes place between the IP and HP compressors; the injected water is at the same pressure as the stream where it is injected, Pw = Pbase*Pup- and at a temperature of 65 °C (same as at the postcooler exit). The temperature at the postcooler exit is fixed to 65°C to keep at least a AT of 15 °C between the hot outlet stream and the cold inlet stream. The coolant in fact is water used for district heating, entering at 50 °C and exiting at 80 °C. The condensed water exits at 65 °C. Extra cooling water is used to bring down the temperature of the stream exiting the postcooler if the pinch difference inside the postcooler should be less than 4 °C. The helium-water vapour mixture exiting the postcooler(s) is at saturated condition at 65 °C. A 7-6 Chapter 7-Helium and helium/water mixture as working fluid. relative humidity of 25 %, 60 % and 95 % has been used in the spray intercooler In the dry cycle the same pressure ratio has been used across the LP and HP compressor, to minimise the total work input required (Moran, Shapiro, 1998 ). However, with water injection as intercooling, the cycle efficiency is sensitive to the pressure ratio in the compressors. A different pressure ratio leads to a different LP compressor outlet temperature and therefore a different saturation temperature in the spray intercooler and a different amount of injected water to reach the designed relative humidity (§ 6.3). A sensitivity analysis has been performed in ASPEN on the ratio A TOT where (3 stands for pressure ratio to identify an optimum. The parameter to optimise is the electric efficiency. The FORTRAN block P-Ratio (see Appendix XIX) has been modified, making possible to vary the low pressure compressor pressure ratio. First of all, the overall design pressure ratio is fixed at the pressure ratio corresponding to point A (Appendix XVIII). The design pressure ratio depends on the cycle terminal temperatures and working fluid k-value, so it will be constant while varying the pressure ratio throughout the LP compressor. The results of the sensitivity analysis on overall pressure ratio (keeping the same pressure ratio across LP an HP compressors) are in Table IX. A more refined analysis is then pursued at the design pressure ratio, in order to identify the optimum Plp/Ptot- The optimum for electric efficiency in the case of Plp/|3tot =0.61, i.e. at a higher LP pressure than in the dry case. The results from the sensitivity analysis are in Appendix VIII, Table VIII-1. As to be expected, the injected water mass flow rate increases as the pressure ratio throughout the LP pressure compressor increases (Appendix VIII, Figure VIII.2), because a higher outlet pressure leads to a higher temperature. Therefore more water has to be injected to reach the same relative humidity. Since the mixture cp is smaller than cp for dry helium, when the cycle heat input is fixed to a constant value(§6.2) the total mass flow rate increases. 7-7 Chapter 7-Helium and helium/water mixture as working fluid. The cycle performance at design overall pressure ratio {3= 3.3 and optimum pLp/proT =0.61 is described by the efficiencies defined as in Appendix III. The results can be seen in Appendix IX, Table IX—3, and they are plotted in Figure 7.6. —•—ELECTRIC EFFICIENCY -—TOTAL EFFICIENCY -—CYCLE EFFICIENCY -—FURNACE EFFICIENCY PRESSURE RATIO Figure 7.6-Efficiencies vs. Pressure Ratio, at {3lp//3tot -0.61. The cycle performance at design point overall pressure ratio and optimum Plr/Ptot are in summarized in Table 7. 3. Working fluid He/HzO Design 0 3.3 Net electric efficiency % 32.03 Furnace efficiency % 86.56 Thermal cycle efficiency % 37.38 Total efficiency 104.4 Table 7. 3 - Cycle efficiency at the design pressure ratio p= 3.3 and optimum Plp^Ptot =0.61. Cycle with water injection as intercooling,, relative humidity after the injection 0=0.95. As shown in Figure 7.7, a higher LP pressure leads to a higher electric efficiency. 7-8 Chapter 7-Helium and helium/water mixture as working fluid. □OPTIMUM LP P R. ■ EQUAL P.R. FOR BOTH COMPRESSORS 18 2.9 3.0 3.1 X2 3.3 3.4 PRESSURE RATIO Figure 7.7- Electric efficiencies vs overall pressure ratio for different LP compressor pressure ratio. The same analysis has been repeated for relative humidity 0.6. The optima Plr /Ptot are different for each relative humidity level. All the results and charts are in Appendix VIII. • Relative humidity =0.6. The design pressure ratio is still found at (3=3.3. A sensitivity analysis on LP compressor pressure ratio shows that the optimum is found at (3lp/(3tot =0.65. The pressure ratio throughout the LP compressor is higher than the one throughout the HP compressor.The efficiencies for a relative humidity cj> =0,6 and a (3Lp/Plp = 0,65 are in Appendix IX, Table IX-5.The efficiencies at the design pressure ratio and optimum (3lp/(3tot are summed up in the following table: Working fluid He/HzO Design (3 3.3 Net electric efficiency % 31.34 Furnace efficiency % 36.81 Thermal cycle efficiency % 81.28 Total efficiency 105.25 Table 7. 4- Efficiency at the design pressure ratio and Plp/Plp - 0,65. Cycle with water injection as intercooling, relative humidity after the injection 0=0.60. 7-9 Chapter 7-Helium and helium/water mixture as working fluid. • Relative humidity = 0.25. The overall design pressure ratio is still found at p = 3.3. The optimum Plp/Ptot ratio is found for a Plp/Ptot = 0.72. The efficiencies at different design pressure ratio can be seen in Appendix IX, Table IX-4.at the results at design point are summed up in the following table. Working fluid He/HzO Design P 3.3 Net electric efficiency % 30.02 Furnace efficiency % 35.06 Thermal cycle efficiency % 86.50 Total efficiency 105.25 Table 7. 5-Cycle efficiency at the design pressure ratio and optimum Plp/Ptot -0.72. Water injection as intercooling, relative humidity after the injection 0=0.25. The behaviour of the cycle while varying the Plp/Ptot can be explained by noticing that the mass flow rate being compressed in the LP compressor is less than the total one since the injected water is condensed before entering the LP and then brought to the required pressure level by a pump. If a highest fraction of the total compression process interests only a part of the total mass flow rate the total compression work is reduced. When increasing Plp/Ptot, the injected water mass flow rate increases and the flowrate decreases. This results in a decrease in LP cm pressor total mass flow rate. A counterworking effect with a high bIP is that the average temperature ot the compressed fluid increases, thereby increasing the specific entropy generation. A optimum Plp/Ptot is finally found balancing these two effect. 7-10 Chapter 7-Helium and helium/water mixture as working fluid. 7.3.1-Efficiencies. The three different configurations performances have been compared by comparing the efficiencies. Each configuration is considered at its optimum Plp/Ptot • Total efficiency: In all cases, the total efficiency is decreasing for high overall pressure ratios while is more or less constant for low pressure ratios. This is due to the fact that for high pressure ratios, instead of fixing a AThot = 5 °C (approach on the hot side) in the flue gas condenser a ATCOid = 5 °C (approach on the cold side) is used to avoid a temperature cross-over. The flue gases entering the flue gas condenser are colder at higher pressure ratios because more heat is subtracted in the FGHX, since the recuperation is quite low. If a ATCOid = 5°C is used, more heat is lost with the flue gases and this causes a sensible decrease in total efficiency. When the pinch temperature difference in the district heating postcooler falls below 4 °C, as for pressure ratios below 2.8, extra cooling with external cooling water is needed to keep the compressor inlet temperature at 65 °C. This results in a loss of heat that causes a decrease in total efficiency. • • Cycle efficiency: The cycle efficiency shows a very flat behaviour and it decreases slightly but constantly with pressure ratio. By reaching a high relative humidity level (95 %) it is possible to gain as much as 3 percentages point more than in the 25 % relative humidity configuration, because the recuperation is more effective and the cooling effect in the compressor is larger.. 7-11 Chapter 7-Helium and helium/water mixture as working fluid. S 38.5 — relative humidity ■ 60 -—relative humldity=25% — relative humidity =95% PRESSURE RATIO Figure 7. 8-Cycle efficiency vs Pressure ratios. * Electric efficiency: the electric efficiency increases as the pressure ratio increases and then shows a flat maximum for pressure ratios of 3.3-3.4 and after that decreases slightly. Electric efficiency increases with increasing <)>, mainly because the total compression work is reduced (see following paragraph), while the expansion work is almost constant. A decrease in working fluid specific heat, as shown in 6.2, causes an increase in total mass flow rate, with a constant cycle heat input. The mass flow rate being compressed in the LP compressor decreases with increasing UJ 29 O 28 RELATIVE HUMIOUTY=0.25 RELATIVE HUMI0ITY=0.6 RELATIVE HUMIDITY=0.95 PRESSURE RATIO 7-12 Chapter 7-Helium and helium/water mixture as working fluid. Figure 7. 9- Electric efficiency vs Pressure ratio. 7.3.2-Reasons for high electric efficiency in wet cycle: Turbomachinery work. Since the electric efficiency is defined as the ratio of cycle power output and fuel input, the reason for an increase in electric efficiency must be seeked in a variations in turbomachinery work. The turbomachinery work for the various configurations versus the pressure ratio can be found in Appendix IX, and are plotted in Figure 7. 10, Figure 7. 11 and Figure 7. 12. • Low pressure compressor work: The low pressure compressor work decreases as the relative humidity level increases. Since the LP compressor inlet stream is at saturated condition at a pressure of 2 bars and a temperature of 65 °C, the water molar fraction is constant. The average k-value of the working fluid is constant for all humidity levels. The decrease in compressor work is due to the lower mass flow rate entering the LP compressor at increasing relative humidity levels (§ 6.3). 2700 relative humidity =95% relative humidity = 60% Figure 7. 10 - Low pressure compressor work vs. pressure ratio. • High pressure compressor work: A decrease in HP compressor work with increasing 7-13 Chapter 7-Helium and helium/water mixture as working fluid. paragraph 6.3, a lower k-value results in a lower compressor outlet temperature and work. Moreover, as more water is injected in the intercooler, the inlet temperature decreases, reducing the compression work. However for lower relative humidity level the optimum performance is obtained for a higher pressure ratio in the low pressure compressor in relations to the overall compressor pressure ratio. This decreases the HP compressor work for the low humidity ratios compared to the high humidity levels. This effect dominates as can be seen in Figure 7.11. -♦-relative humidity =95 —♦—relative humidity = 60% —♦—relative humidity=25% PRESSURE RATIO Figure 7.11- High pressure compressor work vs. pressure ratio. » Turbine work. The turbine work decreases slightly with increasing relative humidity <|> even though the total mass flow rate being expanded increases with higher relative humidity levels. The average k-value of the working fluid being expanded decreases and that results in a higher outlet temperature, as shown in § 6.3. 7-14 Chapter 7-Helium and helium/water mixture as working fluid. relative humidity =*95% relative humidity = 60% relative humidity=25% -6100 PRESSURE RATIO Figure 7. 12- Turbine work vs. Pressure Ratio. However the overall effect of water injection on the net power generation is that the power generation increases with increasing water injection as seen in Figure_7.9. 7.4-Water injection as 1 stage intercooling and 1 stage aftercooling. Flue gas CFB-Furna< e Working fluid Recuperator Biomass Air preheater Turbine expander Low pressure High pressure compressor compressor 1. Flue gas condenser 6. Postcooler 2. District heating 8. Flue gas condensate 3. External bed heat exchanger EXBHX 9. Water Injection 4. Flue gas heat exchanger FGHX Figure 7. 13 - Schematic representation of dosed cycie gas turbine with water injection as intercooling and aftercooling- 7-15 Chapter 7-Helium and helium/water mixture as working fluid. In this configuration a second water injection is added after the HP compressor: The temperature of the injected water in the aftercooler is 65°C (temperature of the condensed water in the postcooler) and the pressure is the same as the one of the stream where the injection takes place. The main effect of the aftercooling is to reduce the temperature of the stream entering the recuperator, making possible to recover more heat from the turbine exhausts. With injected water at 65 °C in both intercooler and aftercooler the optimum fVPtot is found at Plp/Ptot = 0.58. The results from the simulation are found in Table 7.7. The possibility of warming up the water to be injected in the aftercooler to a temperature of 150 °C, to enhance the positive effect of aftercooling by injecting more water has been also considered. When adding water at 150 °C, the analysis is run for pressure ratios higher than 3. In fact for lower pressure ratios water is already in vapour phase at a temperature of 150 °C. With injected water at 65 °C in the intercooler and 150 °C in the aftercooler the optimum Plp/Ptoti is found at Plp/Ptot = 0.56. The results are in and Table VIII-8 and are plotted in Figure 7.14. By warming up the water to be injected in the aftercooler, the gain in electric efficiency is not relevant, about 0.2 percentage points.The increase in expanded mass flow rate is probably counterbalanced by a decrease in the mixture k-value. The results at design pressure ratio and optimum Plp/Ptot are reported inTable 7. 6 and Table 7. 7 and compared in Figure 7. 14. Working fluid He/H 20 Optimum 3 3.3 Net electric efficiency % 32,58 Furnace efficiency % 86,28 Thermal cycle efficiency % 38,14 Total efficiency 105,54 Table 7. 6- Efficiencies at design pressure ratio for cycle with water injection as intercooling and aftercooling. Injected water temperature T= 65 °C. Working fluid He/HgO Optimum 6 3.3 Net electric efficiency % 32,81 7-16 Chapter 7-Helium and helium/water mixture as working fluid. Furnace efficiency % 85,97 Thermal cycle efficiency % 38,54 Total efficiency 106,52 Table 7. 7-Efficiencies at design pressure ratio for cycle with water injection as intercooling and aftercooling. Injected water temperature T=150 °C. 3.0 3.1 3.2 3.3 3.4 PRESSURE RATIO Figure 7. 14- Comparison between cycle with water injection as aftercooler at T=65 °C and cycle with water injection as aftercooler at T=150 °C. The electric efficiency is increased around one percentage point compared to the configuration without aftercooling, Figure 7.15, because the total compression work is significantly reduced, for the reasons already described in previous paragraphs. 7-17 Chapter 7-Helium and helium/water mixture as working fluid. BCYCLE WITH WATER INJECTION AS INTERCOOLING AND AFTERCOOUNG ■ CYCLE WITH WATER INJECTION AS INTERCOOLING. RELATIVE HUMIDITY * 95% OCYCLE WITH WATER INJECTION AS INTERCOOLING. RELATIVE HUMIDITY » 60% 2.8 2,9 3,0 3.1 3,2 3.3 3,4 PRESSURE RATIO Figure 7.15- Comparison between cycle with water injection as intercooling (at two different relative humidity levels) and cycle with water injection as intercooling and aftercooling: Electric efficiency. 7.5-Additional intercooling stage using district heating cooling water. Flue gas Working fluid Recuperator Biomass Air preheater Turbine expander Low [pressure ■5 compressor 2 1. Flue gas condenser 5. Cooling water (optional) L 2. District heating 6. Postcooler 3. External bed heat exchanger EXBHX 7. Intercooler 4. Flue gas heat exchanger FGHX 8. Flue gas condensate 9. Water Injection Figure 7. 16-Schematic of closed cycle: water injection as intercooling and after cooling, two level intercooling and preheating of the injected water. A different configuration has been studied. A new heat exchanger is inserted after the first water injection, as a second stage intercooler. The coolant (district heating return water) enters the heat exchanger at a temperature of 7-18 Chapter 7-Helium and helium/water mixture as working fluid. 50 °C. The outlet temperature of the hot stream is such that no condensation occurs, but exits at saturated condition. The cold outlet stream enters then the second postcooler and warms up to 80 °C and is then used for district heating purpose. The hot outlet stream of the second postcooler exits at 65 °C. No extra cooling water is needed. Condensation of the injected water takes place, as before, in the first postcooler, and therefore the condense has a temperature of 65 °C. Part of the condensed water is pumped up to the required pressure level and reinjected at the intercooler, while the remaining is warmed up to 100 °C in the first postcooler and then, reinjected at the aftercooler The heat exchanger ICi pressure drop is estimated to be 1 %. The additional pressure drop increases the high pressure compressor work thus lowering the power output, but the increased intercooling should more than compensate for that. However, The electric efficiency for a pressure ratio of 3.1 is only 0.2 % more than in the configuration without additional intercooling. This small increase in electric efficiency is not considered as being worth the additional equipment and the complications to the original plant scheme. Anyway it’s clear that additional intercooling might be more positive than an increase in the injected water mass flow rate in the aftercooler. This suggests to try to cool down the HP compressor inlet stream as much as possible without introducing an additional heat exchanger and without using external cooling water, to maintain a high total efficiency. 7.6-Water injection as intercooling and aftercooling: relative humidity The cycle scheme is the one already seen in § 7.5 with water injection as intercooling and aftercooling. To magnify the positive effect of water injection as intercooling, a relative humidity of 95 % (instead of 60%) is reached before the HP compressor. 7-19 Chapter 7-Helium and helium/water mixture as working fluid. Flue gas Working fluid Recuperator Biomass Air preheater Turbine expander Low pressure High pressure compressor compressor 1. Flue gas condenser 6. Postcooler 2. District heating 8. Flue gas condensate 3. External bed heat exchanger EXBHX 9. Water Injection 4. Flue gas heat exchanger FGHX Figure 7. 17-Schematic of closed cycle with water injection as intercooling and aftercooling. After the aftercooler a relative humidity level of 95% is still required. The injected water temperature is 65 °C, the same temperature as at the exit from the condenser. No additional cooling water is used. The total efficiency is quite high if a pinch point temperature difference of 4 °C in the condenser is allowed. The design point is fixed at a pressure ratio (3=3.3. Additional cooling water is needed for pressure ratios lower than 2.8. The optimum |3lp/Ptot is found at a 0.55. The efficiencies are plotted in Figure The electric efficiency in this configuration is 31.9%, which is slightly higher than in the one with the additional heat exchanger for intercooling purposes (Table IX-7 and Table IX-8), while the plant configuration is simpler. 7-20 Chapter 7-Helium and helium/water mixture as working fluid. ELECTRIC -X-TOTAL | PRESSURE RATIO Figure 7. 18-Efficiencies vs. Pressure Ratio 7.7-Comparison between the various configurations. To better explain the reason of such design pressure ratio choice the various configuration have been compared at pressure ratio J3=3.1 and (3=3.3. At pressure ratio 3.1 the electric efficiency is rather high and no external cooling water is needed. The heat recovery from the flue gases is high, making possible to reach a total efficiency high above 100 %. This pressure ratio can be considered a good compromise between district heating and electricity production. Furnace % Cycle Electric Total % % % WET 1JC; relative humidity 25 % 83,07 35,34 29,07 108,66 WET 1 IC; relative humidity 60 % 83,114 36,81 30,28 108,64 WET 1 IC; relative humidity 95 % 83,15 37,38 30,92 108,62 WET 2JC_AC; relative humidities 60% -95 82,89 38,228 31,374 108,89 %; injected water temperature 65 C WET 2_IC_AC; relative humidities 60% -95 82,61 38,57 31,55 %; injected water temperature 150 C ic2 83,107 38,414 31,616 WET 2_IC_AC; relative humidities 95% -95 82,95 38,832 31,88 108,84 %; injected water temperature 65 C Table 7. 8-Efficiencies at pressure ratio fi-3.1 7-21 Chapter 7-Helium and helium/water mixture as working fluid. B FURNACE ■ CYCLE D ELECTRIC DTOTAL Figure 7. 19 - Efficiencies vs amount of injected water at pressure ratio 3.1. If the aim is to maximise power production, the optimum can be fixed at pressure ratio 3.3. The total efficiency is still higher than 100%, even if about 3 percentage points are lost, while 1 point is gained in electric efficiency. Furnace % Cycle Electric Total % % % 1 IC; relative humidity 25 % 86,648 34,139 29,28 105,09 1 IC; relative humidity 60 % 86,609 36,229 31,064 105,18 1 IC; relative humidity 95 % 86,635 37,195 31,902 105,16 WET 2_IC_AC; relative humidities 60% - 86,284 38,146 32,585 105,54 95 %; injected water temperature 65 C WET 2_IC_AC; relative humidities 60% - 85,971 38,543 32,804 106,32 95 %; injected water temperature 150 C ic2 86,492 38,38627 32,869 106,4451 WET 2_IC_AC; relative humidities 95% - 86,336 38,77243 33,140 106,5438 95 %; injected water temperature 65 C 7-22 Chapter 7-Helium and helium/water mixture as working fluid. Table 7. 9-Efficiencies at pressure ratio p = 3.3. 1JC: relative 1JC: relative 1JC: relative 2JC_AC:relati\e 2JC_AC:relative 1C2 2_IC_AC:relative humtity25% hum*tiy60% humidity 95% humtities60%- humidities 60% - humidities 95%- 95 %; injected 95 %; injected 95 %; injected water water water temperature 65 temperature 150 temperature 65 C C C Figure 7. 20 - Efficiencies vs amount of injected water at pressure ratio 3.3. As shown in paragraph 6.3, water injection affects the total cycle mass flow rate. According to equations described in Chapter 6.2, the mass flow rate is expected to increase as more water is injected, as a consequence to a decrease in working fluid cp. The total mass flow rate expanding in the turbine in the different simulations is plotted against the cycle configuration in Figure 7. 21. 1 JC: relative 1JC:retative 1JC: relative 2JC_AC:relative 2JC_AC: relative Two stage 2JC_ACrelative humidity 25 % humidity 60% humidity 95% humidities 60% - humidities 60% - intercooling with humidities 95% - 95%; injected 95%; injected external cooling 95%; injected water temperature water temperature water temperature 65C 150C 65 C Figure 7. 21-Mass flow rate vs. amount of injected water. Pressure Ratio 3.3 7-23 Chapter 7-Helium and helium/water mixture as working fluid. The total mass flow rate increases as more water is added, which agrees with what has been predicted by theory. The marginal increase in electric efficiency as more water is added is decreasing. Total mass Helium mass flow rate flow rate Dry 1 JC 1 JC; relative humidity 25 % 5,1052 2,9433 1 JC; relative humidity 60 % 5,1918 2,8769 1 JC; relative humidity 95 % 5,2299 2,8477 2JC_AC; relative humidities 60% -95 %; 5,4727 2,6616 injected water temperature 65 C 2JC_AC; relative humidities 60% -95 %; 5,5141 2,629911 injected water temperature 150 C 2 IC AC, two stages postcooling 5,46459 2,66687 2_IC_AC; relative humidities 95% -95 %; 5,44 2,6867 injected water temperature 65 C Table 7.10- Mass flow rater at pressure ratio j3 = 3.3. The simulations results follow the trend predicted by theory. The main advantage of water injection seems connected to the intercooling effect and the reduction in compression work, more than in an increased expansion work. The value of turbomachinery work for different plant configurations can be seen in Appendix XI 7-24 Chapter 8-Nitrogen-water mixture as working fluid. Chapter 8 Nitrogen-water mixture as working fluid. In this chapter the results of the simulation on closed cycle with nitrogen and nitrogen-water mixture as working fluid will be described. At first the dry cycle will be studied as a starting point for the simulations including water injection. The results from ASPEN simulations will be checked against what predicted from theory in Chapter 6. At the end of the chapter the results from all the studied simulations will be compared, to point out the design point depending on the parameter to optimise. 8.1-Dry scheme with one stage intercooling and one stage postcooling. Flue gas CFB-Furnai e Working fluid Recuperator Biomass Air preheater Turbine expander Low pressure High pressure Ash compressor compressor 1. Flue gas condenser 5. Cooling water (optional) 2. District heating 6. Postcooler 3. External bed heat exchanger EXBHX 8. Flue gas condensate 4. Flue gas heat exchanger FGHX 9. Water Injection Figure 8. 1-Schematic of dry system configuration: closed cycle with one level intercooling, one level postcooling. The same basic layout of the system as in the case of helium has been used in simulating the system with nitrogen (Fig. 8.1). Postcooler PCi brings down the temperature to 65°C at the inlet of the low pressure compressor. Water for district heating is used as a coolant, entering at 50 °C and exiting at 80°C. 8-1 Chapter 8-Nitrogen-water mixture as working fluid. The intercooler IC1 brings down the temperature to 65°C at the inlet of the high pressure compressor. Water for district heating is used as a coolant, with the same terminal temperatures as previously said. The cycle base pressure is 2 bar. The cycle overall pressure ratio has been varied and the cycle performances analysed, using the efficiencies defined in Appendix VIII. The design point pressure ratio has been chosen as 4.8, using the criteria described in § 7.2. The results are in Appendix X, Table X.1 —♦—FURNACE CYCLE ELECTRIC -*-T0TAL Figure 8. 2-Efficiencies vs. Pressure ratio The cycle performance at the design pressure ratio are summarised in Table 8 .1. Working fluid n2 Design |3 8.8 Net electric efficiency % 32,30 Furnace efficiency % 85,37 Thermal cycle efficiency % 38,21 Total efficiency % 106,08 Table 8. 1-Cycle performance at design pressure ratio. 8.2-Dry cycle with two level inter- and postcooling. 8-2 Chapter 8-Nitrogen-water mixture as working fluid. Flue gas Ash compressor 1. Flue gas condenser 5. Cooling water (optional) 2. District heating 6. Postcooler 3. External bed heat exchanger EXBHX 7. Intercooler 4. Flue gas heat exchanger FGHX 8. Flue gas condensate 9. Water Injection Figure 8. 3- Schematic of dry system configuration: closed cycle with two level intercooling, two level postcooling.. The cycle is the same as in the helium case, see chapter 7.2. The design point has been fixed to a pressure ratio (3=4.7, referring to the work from Anheden e al., The efficiencies at the design point are summed up in Table 8.2. Fluido di lavoro n2 0 di progetto 4.7 Efficienza elettrica % 36.6 Efficienza termica del ciclo % 41.8 Efficienza totale % 92.9 Table 8. 2- Summary table of cycle performance at d esign pressure ratio. Chapter 8-Nitrogen-water mixture as working fluid. 8.3 - Water injection as first stage intercooling. Fluegas Harass Turtine expander Lav pressure Hgh pressure 1. Hue gas condenser Figure 8. 4-Schematic of system configuration: closed cycle with one water injection as intercooling and one level postcooling. In this configuration the intercooler ICi has been removed, and replaced by a water injection taking place after the low pressure compressor. The injected water is then condensed in the postcooler PC-i, compressed and recirculated to the injection point. As in the helium-water cycle, three level of relative humidity at the inlet of the high pressure compressor have been tried. With the same assumption as in chapter 7.3 the optimum Plp/Ptot, ratio of low pressure compressor over total compressor pressure, has been identified with a sensitivity analysis in ASPEN. The pressure ratio across LP and HP compressor is constant in the first sensitivity analysis to determine the design pressure ratio that is fixed at p=5.2. The pressure ratio ratio decides the pressure after the LP compressor and therefore at what pressure the water should be injected. A change in |3lp/|3tot is therefore responsible for a change in injected water mass flow rate, as explained in chapter 6.3. The results from the sensitivity analysis on Plp/Ptot at the 8-4 Chapter 8-Nitrogen-water mixture as working fluid. design pressure ratio can be seen in Appendix VIII for ail relative humidity levels, together with the charts. 8-5 Chapter 8-Nitrogen-water mixture as working fluid. • Relative humidity <|>=25 %. The optimum is found at Plp/Ptot =0.71. A larger part of the total compression process will take place in the LP compressor. The results of the sensitivity analysis on overall pressure ratio can be seen in Appendix X, Table X.2. As expected, the design point is still fixed at pressure ratio p = 5.2. The results at design pressure ratio and optimum Plp/Ptot are in Table 8 .2. Working fluid n2/h2o Design p 5.2 Net electric efficiency % 30,69 Furnace efficiency % 85,43 Thermal cycle efficiency % 36,28 Total efficiency % 104,95 Table 8. 3-Cycle performance at design pressure ratio, relative humidity 0=25 %. The same simulation described above has been repeated for a relative humidity • Relative humidity § =60 %. The optimum is found at Plp/Ptot =0.65. The cycle performance at design pressure ratio and optimum Plp/Ptot are summed up in Table 8.3. Working fluid n2/h2o Design 8 5.2 Net electric efficiency % 32,055 Furnace efficiency % 85,66 Thermal cycle efficiency % 37,79 Total efficiency % 104,74 Table 8. 4-Cycle performance at design pressure ratio, 0 =60 %. 8-6 Chapter 8-Nitrogen-water mixture as working fluid. • Relative humidity 95 % The optimum is at Plp/Ptot =0.59. The cycle performance at design pressure ratio and optimum (Wp-roT are summed up in Table 8.4. Working fluid N2/H20 Design (3 5.2 Net electric efficiency % 32,76 Furnace efficiency % 85,74 Thermal cycle efficiency % 38,59 Total efficiency % 104,66 Table 8. 5-Cycle performance at design pressure ratio. The efficiencies at every relative humidity level vs. the overall pressure ratio have been compared. Each different cycle configuration has been considered at its optimum Plp/Ptot. The results are in Appendix X. • Total efficiency: The total efficiency doesn't vary significantly for different relative humidity levels. It is about 104,7-105 % for the three humiidty levels considered. At the pressure ratios considered in the simulations, the approach temperature on the cold side ATCOid on the flue gas condenser is fixed. Less heat is then recovered from the flue gases for district heating purposes than when the approach temperature on the hot side, AThot ,is fixed, since the flue gases are sent to the stack at a higher temperature. The total efficiency increases at lower pressure ratios, because a higher recuperator outlet temperature leads to a lower heat input in the FGHX. More heat is left in the flue gases and is available for district heating. • • Cycle efficiency: 8-7 Chapter 8-Nitrogen-water mixture as working fluid. The cycle efficiency improves when more water is added, see Figure 8.4. The temperature after the intercooler is lower, so that the temperature after the HP compressor is lower. The recuperation in the recuperator is more effective. CYCLE EFFICIENCY Figure 8. 5-Cycle Efficiency vs. Pressure Ratio. • Electric efficiency: Relative humidity =0.95 Relative humidity =0.6 Relative humidity =0.25 PRESSURE RATIO Figure 8. 6- Electric Efficiency vs. Pressure Ratio. The electric efficiency increases steadily for pressure ratios up to 5.3. Thereafter the electric efficiency is almost constant or decreases slightly. Chapter 8-Nitrogen-water mixture as working fluid. The design point is fixed at slightly different pressure ratios for different relative humidity levels (when the air preheater temperature is fixed at 550 °C and Armin = 25°C), but always for pressure ratio very near to 5.2. As clearly shown from Figure 8.5, the electric efficiency for pressure ratios higher than the chosen pressure ratio, is almost constant. As in the water-helium cycle, the gain in electric efficiency while increasing the relative humidity to 60% from 25 % than while going from 60 % to 95 %. 8.4-Water injection as one stage intercooling - one stage aftercooling. Fluegas Working fluid Biomass Air preheater Turbine expander Low pressure High pressure compressor compressor 1. Flue gas condenser 6. Postcooler 2. District heating 8. Flue gas condensate 3. External bed heat exchanger EXBHX 9. Water Injection 4 Flue gas heat exchanger FGHX Figure 8. 7-Schematic of system configuration: dosed cycle with one water injection as intercooling, one water injection as aftercooling and one level postcooling. To further increase the electric efficiency and the recuperation, a water injection working as an aftercooler has been placed after the high pressure compressor, in addition to the intercooler with water injection. This reduces the temperature of the working fluid on the recuperator cold side and make possible to recover more heat from the turbine exhaust. A relative humidity level of 0.95 has been used both after the intercooler and the aftercooler. A postcooler PCi cools down the working fluid to 65 °C before the low pressure compressor. District heating water is used as a coolant. The temperature after the intercooler belongs to the interval 91; 8-9 Chapter 8-Nitrogen-water mixture as working fluid. 98.5°C, depending on the pressure ratio. The temperature after the aftercooler belongs to the interval 119; 127°C. The design pressure ratio has been fixed to (3=5.1. The optimum (3lp/|3tot is then found at (3lp/Ptot = 0 44. The efficiencies are plotted in Figure 8.7 and the results at design point and optimum Plp/Ptot are summarised in Table 8.5. -♦-FURNACE -e-CYCLE -^-ELECTRIC -*-TOTAL PRESSURE RATIO Figure 8. 8-Efficiencies vs. pressure ratio. Working fluid Ng Design (3 5,2 Net electric efficiency % 34,35 Furnace efficiency % 86,13 Thermal cycle efficiency % 40,29 Total efficiency % 104,47 Table 8. 6- Cycle performance at design pressure ratio and optimum Plp/Ptot- It is interesting to note that it is possible to get the same electric efficiency than in the dry cycle 2_IC_AC using a much simpler cycle. The number of heat exchangers (including the recuperator) is reduced from seven, in the dry case with two level intercooling and postcooling, to four. Comparing these efficiency values with those in the dry cycle with one stage intercooling, an increase in electric efficiency up to 2 percentage points is gained. The gain is around 2 percentage points relative to the cycle with only one water injection too. The reduction in compressor work due to a smaller mass flow rate should be regarded as the main reason for such results. 8-10 Chapter 8-Nitrogen-water mixture as working fluid. 8.5-Water injection as intercooling, after cooling and two stage post cooling with external cooling water. Flue gas Working fluid Recuperator Biomass Air preheater Turbine expander Low pressure High pressure compressor compressor 1. Flue gas condenser 6. Postcooler 2. District heating 8. Flue gas condensate 3. Externalbed heat exchanger EXBHX 9. Water Injection 4. Flue gas heat exchanger FGHX Figure 8. 9- Schematic of system configuration: closed cycle with one water injection as intercooling, one water injection as aftercooling and two level postcooling. In order to even further increase the power production and electric efficiency, a second stage of postcooling is added after the district heating postcooler. This results in a lower temperature at the compressor inlet and therefore a reduction in compression work. The injected water will also have a lower temperature (if not heated between condenser and injection) and a lower temperature after the intercooler and aftercooler could be obtained. By using a second stage of postcooling, less water is injected, both because the temperature of the stream where injection takes place is lower and the water injected temperature is lower (see § 6.3). This is expected to cause an increase in total mass flow rate and therefore an increase in turbine expansion work. At the same time the LP compressor work will be reduced due to the lower inlet temperature (at the same pressure ratio). The results from the sensitivity analysis on pressure ratio, for the cycle with water injection as intercooling and aftercooling and a second level postcooling to 20 °C. (cooling water at 15°C) can be found in Appendix X, Table X—6. 8-11 Chapter 8-Nitrogen-water mixture as working fluid. The gain in electric efficiency of this configuration compared to the one with only one level postcooling with district heating water (temperature after the postcooler T=65 °C) is clearly shown by Figure 8.9. 4.6 4.7 4.8 4.9 5 5.1 PRESSURE RATIO Figure 8. 10-EIectric Efficiency vs. Pressure Ratio: comparison between configuration with two level postcooling and configuration with one level postcooling. The reason for such behaviour lies in the fact that for Tjnj =20 °C, the mass flow rate expanded in turbine is higher than in the other configurations, therefore the turbine work is slightly increased, while the compressors work is lower due to the lower inlet temperature, The resulting power output is higher and the electric efficiency gains around 5%. 8-12 Chapter 8-Nitrogen-water mixture as working fluid. Figure 8. 11-Compression Work vs. Pressure Ratio: comparison between configuration with two level intercooling and configuration with one level intercooling. □ INJCTED WATER TEMPERATURE » 6S C QINJECTgD WATER TEMPERATURE-20 p PRESSURE Figure 8. 12-Turbine Power vs. Pressure Ratio: comparison between configuration with two level intercooling and configuration with one level intercooling. On the other hand the total efficiency is significantly reduced (around 30 %) by using a second postcooler. A huge amount of condensing heat has to be removed from the system with the external water as coolant. ■INJECTED WATER TEMPERATURE = 20C □INJECTED WATER TEMPERATURE * 65 C f ^ ^ g l Jj: 8E 4.6 4.7 4.6 4.9 5.0 5.1 PRESSURE RATIO 8-13 Chapter 8-Nitrogen-water mixture as working fluid. Figure 8. 13-Total Efficiency vs. Pressure Ratio: comparison between configuration with two level intercooling and configuration with one level intercooling. 8.6 - Comparison between the various configurations. The cycle configurations using nitrogen or nitrogen/water mixture as working fluid have been compared, to point out the one who best fits the performance requirements, such as high electric efficiency and/or high total efficiency. In the following plot, figure 8.14, the electric efficiency for the various configurations is shown: 0RY2JC V\ET 1JC relative WET 1JC relate VNET1JC relate W£T2JC_AC V\ET2JC_AC- humidity *25% humidfy *60% humidity *95% retatwe humidity two stage *95% postcooBng 20 C Figure 8. 14-Optimum Electric Efficiency for the various configura tions. The injected water mass flow rate for the different configurations has the following behaviour: 8-14 Chapter 8-Nitrogen-water mixture as working fluid. D INJECTED WATER MASS FLOW RATE IJC relative humidty 1JC relative humidty 1JC relative humidty 2JC_AC relative humidty 2JC_AC-tsvo stage •25% ” -60% *95% -95% postcooling 20 C Figure 8. 15-lnjected Water Mass Flow Rate for the various configurations. From Figure 8. 14 and Figure 8. 15 follows that the electric efficiency increases as the injected water mass flow rate increases. The only exception is for the cycle with two level postcooling to T=20 °C. In this case, the electric efficiency is higher than when only one level postcooling is used, even if less water is present. A reduced LP compressor temperature and a more efficient intercooling prove to be more effective than plain water injection. The total efficiencies are plotted in Figure 8.16: 1JC relative humdrty 1JC relative hurridty 2JC_AC relative 2JC.A0 relative 2JC_AC two stage =25% =60% huhdity=95% hurricfty =95% postcooling 20 C. Inj. water tenrperature=20 C Figure 8. 16-Optimum Total Efficiency for the various configurations. 8-15 Chapter 8-Nitrogen-water mixture as working fluid. The total efficiency does not seem to be influenced by the amount of injected water, while an additional postcooler reduces the total efficiency with around 30 %. In fact the dew temperature in the stream entering the condenser is lower for a lower water mass flow rate, as to be expected from theory, se Figure 8.15. Since the outlet temperature on the cold side in the district heating postcooler is fixed to 65 °C, in the configuration with two level postcooler the condensation will not start in the district heating postcooling, but will take place in the second postcooler. The condensation heat will then be lost, since external water is used as coolant. 1JC relative humidity 1JC relative humidity one stage intercooling 2_IC_AC relative 2_IC_AC two stage =25% =60% relative humidity =95% humidty =95% postcooling 20 C Figure 8. 17-Dew Temperature in the condenser for the various configurations. As expected, the total mass flow rate varies accordingly to the total water mass flow rate: ■ TOTAL WATER MASS FLOW RATE 1JC relative humidity 1JC relative humidity 1JC relative humidity 2JC_AC relative 2_tC_AC two stage =25% =60% =95% humidity =95% postcooiing 20 C 8-16 Chapter 8-Nitrogen-water mixture as working fluid. Figure 8. 18-Total Water Mass Flow Rate and Total Mass Flow Rate for the various configurations. The choice of one configuration instead of another depends mainly on the main aim of the cycle. If district heat is valuable, like in Nordic countries or in winter season, then a configuration with only one stage post cooling seems by far the best solution. On the other hand, if the primary goal of the plant is to produce electricity, then a second level of postcooling seems to be the best solution. The plant can be shifted from one configuration to the other to face peakloads. 8-17 Chapter 9-Sensitivity analysis on turbomachinery rj and cycle base pressure. Chapter 9. Sensitivity analysis on turbomachinery polytropic r\ and cycle base pressure. In this chapter the effect of a decrease in the compressor and turbine efficiency on the cycle electric and total efficiency is studied. The effect of an increase in cycle base pressure on electric and total efficiency is also studied. 9.1-Sensitivityanalysis on turbomachinery efficiency Throughout all the previous simulations, the LP/HP compressor polytropic efficiency has been assumed equal to 0.9. The cycle performance is strictly connected with the turbomachinery efficiency therefore the effect of a decrease in efficiency for the LP compressor, HP compressor and turbine, separately, has been simulated in an ASPEN sensitivity analysis. 9.1.1 - Sensitivityanalysis on LP/HP compressor efficiency. The polytropic efficiency is defined as in II-3: The compressor work is given by equation I-5. The electric efficiency is defined as: Net Electric Efficiency = ^ge " P— P being the cycle total power output. Z3 ^compressor ^lmech,comp ^ l ^turbine Vmech,turb ^ : air fan The polytropic efficiency has been varied between 0.85-0.90 for the LP and HP compressor independently. That means that only one efficiency is varied while the others are constant at a value of 0.9. The analysis is carried out for the cycle configuration with water injection as intercooling and aftercooling and one stage postcooling with district heating water as coolant, 9-1 Chapter 9-Sensitivity analysis on turbomachinery r| and cycle base pressure. water vapour mixture. The electric efficiency values at different LP and HP compressor polytropic efficiency are in Table Xil-1 and Table Xll-2 and are plotted in Figure 9.1 and Figure 9.2. LP COMPRESSOR LP COMPRESSOR LP COMPRESSOR LP COMPRESSOR LP COMPRESSOR LP COMPRESSOR POLYTROPIC POLYTROPIC POLYTROPIC POLYTROPIC POLYTROPIC POLYTROPIC EFFICIENCY'!).* EFFICIENCY-0.68 EFFICIENCY-0.87 EFFICIENCY-!)# EFFICIENCY-0,83 EFFICIENCY-0,90 Figure 9.1-Comparison between electric efficiency for different LP compressor polytropic efficiency level at design pressure ratio. COMPRESSOR COMPRESSOR COMPRESSOR COMPRESSOR COMPRESSOR COMPRESSOR POLYTROPIC POLYTROPIC POLYTROPIC POLYTROPIC POLYTROPIC POLYTROPIC EFFICIENCY • 0.85 EFFICIENCY-0.86 EFFICIENCY » 0* EFFICIENCY- 0.66 EFFICIENCY « 0,89 EFFICIENCY » 0.90 Figure 9.2-Comparison between electric efficiency for different HP compressor polytropic efficiency level at design pressure ratio. As can be seen from Figure 9.3, the cycle is slightly more sensitive to a decrease in high pressure compressor efficiency since it affects a higher fraction of the total mass flow rate. 9-2 Chapter 9-Sensitivity analysis on turbomachinery rj and cycle base pressure. Figure 9.3-Comparison between electric efficiency for a LP compressor and HP compressor at design overall pressure ratio. 9.1.2-Sensitivity analysis on turbine efficiency. The turbine polytropic efficiency has been taken equal to 0.9 in all the previous simulations. The expansion polytropic efficiency is defined in equation 11-1 .The expansion work is given by equation I-4. The values of electric efficiency at different values of turbine polytropic efficiency can be found in Table IV-3 and are plotted in Figure 9.4. TURBINE TURBINE TURBINE TURBINE TURBINE TURBINE POLYTROPIC POLYTROPIC POLYTROPIC POLYTROPIC POLYTROPIC POLYTROPIC EFFICIENCY ■ EFFICIENCY* EFFICIENCY * EFFICIENCY * EFFICIENCY - EFFICIENCY* 0.85 0,86 0,87 0,88 0,89 0,90 Figure 9.4-Comparison between electric efficiency for different turbine polytropic efficiency level at design overall pressure ratio. 9-3 Chapter 9-Sensitivity analysis on turbomachinery r\ and cycle base pressure. In a second simulation, both compressors have been taken to have a lower polytropic efficiency ?jpol =0.85. The results of both simulations are in Table 9.1. p Compressors tj = Compressors t) = Compressors rj = 0,9; 0,85; 0,9; Turbine rj =0,9 Turbine n =0,9 Turbine n =0,85 3 28,62 27,74 31,2 3,1 29,02 28,35 31,84 3,2 29,799 28,92 32,54 3,3 30,32 29,45 33,14 3,4 30,31 29,96 33,17 Table 9.1-Comparison at different polytropic efficiency: electric efficiency. The results of these sensitivity analysis are compared in Figure 9.4 TURBOMACHINERY ' EFFICIENCY®}. LP/HP COMPRESSOR TURBINE EFFICIENCY®).* EFFICIENCY®),85 EFFICIENCY®).# Figure 9. 5-Comparison between electric efficiency when the turbomachinery polytropic efficiency is varied at optimum overall pressure ratio. As to be expected, the decrease in turbine efficiency has a stronger influence on the electric efficiency, since it affects all the mass flow rate being expanded, while a decrease in one of the two compressor affects only 9-4 Chapter 9-Sensitivity analysis on turbomachinery r\ and cycle base pressure. a fraction of the total mass flow rate and only a part of the total pressure ratio. A decrease in turbine efficiency has also a stronger effect on the cycle performance than a decrease in both compressors efficiency. The total mass flow rate expanded in the turbine is given by the dry helium and the total injected water mass flow rate, while both compressor work on a smaller mass flow rate, since the water injection as intercooling takes place after the L.P compressor, the water injection as aftercooling take place after the HP compressor, and the water is condensed before the LP compressor. 9-5 Chapter 9-Sensitivity analysis on turbomachinery t| and cycle base pressure. 9.2-Sensitivityanalysis on base pressure. A base pressure of 2 bars has been used for all the previous simulations. Such a choice was made in order to reduce the strain in the external bed heat exchanger tubes on the gas side. On the other hand, the choice of an higher base pressure can affect the required heat exchange surfaces. The effect of an increase in base pressure on the postcooler has been studied in Chapter 10. 9.2.1-Effect of increasing cycle base pressure. The vapour pressure at saturated condition, Pv s ,is constant at constant temperature If the relative humidity .defined in Eq. III-2, is constant, the vapour pressure Pv is independent of the total pressure. The water molar fraction is defined as From the two equations follows that the water molar fraction needed to reach a certain relative humidity is reduced at an higher base pressure, at the same pressure ratio than with base pressure P=2 bar. • Helium-water vapour mixture as working fluid. The effect of an increase in base pressure for the wet helium cycle has been studied for the cycle configuration with water injection as intercooling and aftercooling, both with a required relative humidity level of 95% in the stream after the injection. The new base pressure is P=5 bar. The results for different pressure ratios can be seen in Table IX-10. The cycle performance at design base pressure is summarised in Table 9.2. Working fluid He/water mixture Design 6 3.1 9-6 Chapter 9-Sensitivity analysis on turbomachinery rj and cycle base pressure. Net electric efficiency % 32,39 Furnace efficiency % 86,25 Thermal cycle efficiency % 37,829 Total efficiency % 105,34 Table 9.2-Cycle performance at design pressure ratio: The design overall pressure ratio has moved to J3 = 3.1, compared to a pressure ratio (3= 3.3 in the case with base pressure P=2 bar. The electric and total efficiency for the cycle with base pressure P=2 bar and the one with base pressure P=5 bar, are compared in Figure 9.6 and Figure 9.7. 2.8 2.9 3.0 3,1 3.2 3.3 3.4 PRESSURE RATIO Figure 9. 6-Comparison between He-H 20 cycle with base pressure = 2 bar and cycle with base pressure = 5 bar: electric efficiency. ■ BASE PRESSURE *5 BAR B BASE PRESSURE » 2 BAR n *1 rfi d I I fl in I I LI Jll I I 3.1 3.2 BASE PRESSURE 9-7 Chapter 9-Sensitivity analysis on turbomachinery rj and cycle base pressure. Figure 9. 7-Comparison between He-HiO cycle with base pressure = 2 bar and cycle with base pressure = 5 bar: total efficiency. From chapter 6.2, the average specific heat of the helium-water mixture working fluid on mass basis is higher at a pressure higher than P = 2 bar, since the water mass fraction is lower. This decreases the total mass flow rate. As can be seen, there is not any improvement in electric and total efficiency by simply increasing the base pressure. The electric efficiency of the cycle with base pressure P=5 bar is actually slightly lower than the one of the cycle with base pressure = 2 bars. The cycle design pressure ratio shifts to a lower pressure ratio. • Nitrogen-water vapour mixture as working fluid. When a nitrogen-water mixture is considered as working fluid, the total mass flow rate is expected to increase as less water is injected compared to the same cycle (water injection as intercooling and aftercooling , relative humidity (j>=95% after both injections) at base pressure 2 bar, since the mixture k-value is lower than the pure nitrogen. The optimum overall pressure ratio is found at (3 = 5 compared to (3= 5.1 in the cycle with base pressure P= 2 bar. At the design pressure ratio the cycle shows the following efficiencies, Table 9.3. Working fluid N2/water mixture Design 0 5 Net electric efficiency % 33,40 Furnace efficiency % 85,51 Thermal cycle efficiency % 39,46 Total efficiency % 104,88 Table 9.3-Cycle performance at design pressure ratio. The electric efficiency in the cycle with base pressure P=5 bar is significantly reduced with respect to the electric efficiency in the cycle with base pressure 9-8 Chapter 9-Sensitivity analysis on turbomachinery t\ and cycle base pressure. P=2 bar. As less water is injected, the total mass flow rate increases. This means that the mass flow rate expanded in the turbine increases but, at the same time, the mass flow rate to be compressed also increases, since a smaller fraction of the total mass flow rate (the condensed water) will reach the required pressure level by means of a pump. 4.7 4,8 4,9 5.0 5,1 5,2 5,3 PRESSURE RATIO Figure 9. 8-Comparison between cycle with base pressure = 2 bar and cycle with base pressure = 5 bar: electric efficiency. ■ BASE PRESSURE *5 BAR Q8ASE PRESSURE - 2 BAR PRESSURE RATIO Figure 9. 9-Comparison between cycle with base pressure = 2 bar and cycle with base pressure = 5 bar: total efficiency. The total efficiency at design point is more or less constant. The values shift together with the pressure ratio. 9-9 Chapter 9-Sensitivity analysis on turbomachinery ti and cycle base pressure. 9.2.2-lnfluence of base pressure on dew point temperature. The base pressure has a strong influence on dew temperature. By increasing the pressure, condensation will start at higher temperature. It follows that the vapour pressure in the stream is higher at constant temperature, so the saturation temperature will be higher too. The configuration with a second postcooler using external water as coolant (nitrogen-water mixture as working fluid) has been simulated with a base pressure of 5 bar, without varying any of the design input for the postcoolers. The total mass flow rate decreases, as to be expected from theory. No improvement seems to be found in increasing the base pressure regarding electric efficiency, in fact it actually decreases about one percentage point. 4.6 4.7 4,6 4.9 5.0 8AS6 PRESSURE Figure 9. 10-Electric efficiency for cycle with water injection for intercooling and aftercooling, two stage postcooling: base pressure 2 bar and 5 bar. With base pressure P=5 bar, as said before, the dew point will be at a higher temperature, (Tdew = 86 °C) than with base pressure P=2 bar (Tdew = 55 °C), so a second and better option would be to start condensing in the district heating postcooler by cooling down the stream to 65 °C, using district heating water as coolant, so that a big fraction of injected water will condense, and then cool down to 20 °C in the second postcooler, condensing some more water. By doing so, a higher fraction of the latent 9-10 Chapter 9-Sensitivity analysis on turbomachinery t\ and cycle base pressure. heat will be recovered for district heating purposes, reducing the mass flow rate of external coolant. In the case with base pressure P=2 bar it was not possible to start condensing in the district heating postcooler, because the dew point temperature is lower than 65 °C, minimum outlet temperature allowed. It is not possible to cool further down in the postcooler with district heating because the inlet and outlet temperature of the district heating water are fixed to 50 °C and 80 °C respectively and the minimum pinch point AT is 5 °C. PRESSURE RATIO Figure 9. 11-Comparison between cycle with base pressure -2 bar and cycle with base pressure = 5 bar: Total efficiency. The gain in total efficiency by starting the condensation in the district heating postcooler is around four percentage points, as can be seen in Figure 9.11. 9-11 Chapter 10- Heat Exchangers. Chapter 10 Heat Exchangers. The objective of this chapter is to study how water injection affects the performance and dimension of the heat exchangers. The heat transfer coefficient is one of the main parameter when comparing different plant configurations. It affects not only the total heat transfer area and therefore the overall cost of the plant, but also the pressure drops in the cycle. In the ASPEN simulations the pressure drops have always been assumed as a fixed fraction of the inlet pressure and therefore not depending on the working fluid. A working fluid with high friction characteristic can cause a higher pressure drop in the cycle and this will turn out in an increase in compressor pressure ratio compared to the one experienced in the turbine. This means that the total power output will be lower. The heat exchangers have been sized trying to obtain the assumed pressure drops ( see Table 5.1). Some heat exchangers have been sized using the commercial software CHED (Compact Heat Exchanger Design, by Intercept Software Co.), based on “ Compact Heat Exchangers", (W. M. Kays, A. L. London, 1998). The program can both determine the size based on the heat exchanger performance or the performance based on the heat exchanger dimension. Other heat exchangers like the external bed heat exchanger and the postcooler have been sized by hand calculations. 10.1-Heat Exchanger variables: dimensional and non dimensional. The parameters relating to heat transfer performance are the following: U = overall conductance for heat transfer [W/m2 Kj; A = surface area on which U is based [m2]; = hot - fluid terminal temperatures [°C]; 10-1 Chapter 10- Heat Exchangers. = cold - fluid terminal temperatures [°C]; Ch = (m ■ cp)h =hot - fluid capacity rate [W/K]; Ce =(m-cp)c- cold - fluid capacity rate [W/K]; Flow arrangement = counterflow, parallelflow, crossflow, parallel counterflow, or combinations of these basic arrangements; The term U comes from an overall heat transfer rate equation which combines the convective and conductive mechanism responsible for the heat transfer from the hot to the cold fluid in a single equation: where — is the heat flux per unit transfer area at a section in the exchanger where the temperature difference is (Th -Tc). This equation must be combined with an energy equation, equating the loss of enthalpy in the hot fluid to the gain of enthalpy in the cold fluid, in order to relate the heat exchanger variables listed at the beginning of the paragraph. These variables are grouped in the following non dimensional parameters: • • Exchanger heat transfer effectiveness: The effectiveness compares the actual heat transfer rate, 7 = CA- (rA> - TKoul )=Cc- (tcM - TCfiUt) to the thermodynamically limited, maximum possible heat transfer rate as would be realised only in a counterflow heat exchanger of infinite heat transfer area, namely 10-2 Chapter 10- Heat Exchangers. • Number of exchanger heat transfer units: The number of heat transfer units Nju is a non dimensional expression of the heat transfer size of the heat exchanger. When the NTu is small the effectiveness is low and when the Ntu is large, s approaches asymptotically the limit imposed by flow arrangement and thermodynamics considerations. min min 0 • Capacity - rate ratio: Cm The capacity ratio is simply the ratio of mass flow rate times specific c heat capacity for the two streams. Cmjn and Cmax are, respectively, the smaller and the larger of the two magnitudes Ch and Cc • Heat exchanger sizing. The parameters required for sizing an heat exchanger are: • Density p at inlet and outlet condition for both fluid [ kg/m 3]; • Viscosity p for both fluids [kg/m,s]; • Cp for both fluids [J/kg,K]; C ’ }l • Prandtl number Pr =——, a non dimensional number, where k is the K conductivity of the fluid. • Wall conductivity [W/m,K]; • rp fouling factor [m2,K/W]; • Flow arrangement; The heat exchanger for which sizing will be performed are: Flue Gas Heat Exchanger, External Bed Heat Exchanger, Recuperator, Postcooler for 10-3 Chapter 10- Heat Exchangers. configurations DRY1 _IC, WET 1_IC WET 2_IC_AC with nitrogen and helium as working fluid. 10.2 - Flue Gas Heat Exchanger (FGHX). The flue gas heat exchanger raises the working fluid temperature to 550 °C subtracting heat from the flue gases leaving the CFB furnace. The FGHX is a single pass, staggered array tube bank. The working fluid is on the tube side. The tubes have a length of 1.7 m and there are 37 transverse row. § -— = 1.5 Spacing to diameter ratio; D, D0 = 25 mm outer diameter; D, = 20 mm inner diameter; k = 25 W/m,K = tube wall conductivity Rf = 0.001 m2/W,K = fouling factor; The flue gas heat exchanger sizing is performed using the commercial software CHED (Compact Heat Exchanger Design, by Intercept Software Co.). Since CHED does not allow to include a fouling resistance explicitly, an effective wall conductivity has been utilised instead. The wall resistance is given by: Ao = tzD0L An effective wall conductivity k' is defined, such as R 2*t% 2 D. 2k With the design value 10-4 Chapter 10- Heat Exchangers. k- = 2.5 W/m.K The chosen surface is S1.50-1.50 (Kays and London, 1998), staggered array with a spacing to diameter ratio of 1.5. The outlet diameter is 3/8 ”, therefore a scaling factor of 2.62 is used. The Flue gas Heat Exchanger has been sized for the different cycle configurations at the design overall pressure ratio. The input data for each heat exchanger are in appendix XIII, together with the results. The total area and overall heat transfer coefficient for the various configuration can be seen in Table 10.1 and Figure 10.1. for helium and helium-water mixture and in Table 10.2 and Figure 10.2 for nitrogen and nitrogen-water mixtures. • Helium-water mixture as working fluid. Dry IC Wet 1 IC Wet 2 IC AC Overall heat transfer coefficient 78.7 74.5 73.6 Total heat transfer area fm2j 108 118 123 Table 10. 1- Summary table for Flue Gas Heat Exchanger. Helium-water mixture as working fluid. DRY, 1JC WET 1JC WET 2JC.AC Figure 10. 1-FGHX heat transfer area. Helium-water mixture as working fluid. Water injection is responsible of a decrease in the overall heat transfer coefficient and consequentially of an increase in the total heat transfer area. 10-5 Chapter 10- Heat Exchangers. The heat transfer area is increased about 10 % comparing the dry case with one stage intercooling to the case with water injection as intercooling and aftercooling. Dry IC Wet 1 IC Wet 2 IC AC Overall heat transfer coefficient 60 59.7 59.5 Total heat transfer area [m2j 138 143 148 Table 10.2-Summary table for Flue Gas Heat Exchanger. Nitrogen-water mixture as working fluid. DRY 1JC WET 1JC WET 2JC.AC Figure 10. 2 - FGHX heat transfer area. Nitrogen-water mixture as working fluid. The effect of water injection on the flue gas heat exchanger dimension seems to be almost negligible. The heat transfer area in increased in about 7 % comparing the dry case with one stage intercooling to the case with water injection as intercooling and aftercooling. 10.3-External Bed Heat Exchanger. The external bed heat exchanger is a bubbling bed with immersed tubes in a staggered array, single pass. The fluidisation velocity is lower than 1 m/s. The working fluid is on the tube side. The working fluid raises its temperature 10-6 Chapter 10- Heat Exchangers. from 550 °C (temperature at the outlet of the FGHX) to 800 °C (temperature at turbine inlet). The heat transfer coefficient on the fluidised bed side is assumed equal to: h„ = 500 W/ The geometry of the heat exchanger is the following: Din =0.025 [m] D^=0.02 [m] St/ = 1.5 The heat transfer coefficient on the tube side is calculated as Nu • k h, =■ Nu =0.0215-Re0 8-Pr053 (7.8) This equation is valid when 0.2 rw = = wall resistance The pressure drop on the tube side is < 1%. The total maximum pressure drop on the flue gas side in the FGHX and EBHX sa been assumend as 1.3%, (Agazzani et al.). The terminal temperatures are: 7^ = 850°C 7,,^ = 736°C 3%,=550°C =800°C The results for each configuration can be found in Appendix XV, and are summarized in Table 10.3-4 and Figure 10.3-4. 10-7 Chapter 10- Heat Exchangers. DRY 1 IC WET 1 IC WET 2 IC AC Total heat transfer area [m2] 144.05 138.9 137.8 Overall heat transfer coefficient 249.4 254.71 260 Table 10. 3 - EBHX heat transfer area. Helium-water mixture as working fluid. Figure 10. 3 - Overall heat transfer coefficient and total heat transfer area. Helium-water mixture as working fluid. DRY 1 IC WET 1 IC WET 2 IC AC Total heat transfer areafm 2] 302.47 307.7 307.7 Overall heat transfer coefficient 110.25 109,45 109.41 Table 10. 4 - EBHX heat transfer area. Nitrogen-water mixture as working fluid. 10-8 Chapter 10- Heat Exchangers. Q Overall heat transfer coefficient (W/m,kj ■ heat transfer area (m21 Dry cycle Water injection as intercoo&ng Water injection as interceding and aftercooling Figure 10. 4 - Overall heat transfer coefficient and total heat transfer area. Nitrogen-water mixture as working fluid. The results show that water injection does not seem to have a significant effect on the heat transfer area of the external bed heat exchanger. 10.4 - Recuperator. In the recuperator heat is recovered from the turbine exhaust to raise the working fluid temperature before entering the FGHX. The recuperator is a plate-fin heat exvchanger. The chosen surface is a strip-fin, plate-fin double sandwich surface, (1/8 — 20.06 (D)), 10-9 Chapter 10- Heat Exchangers. Fig, 10-70 Stnp-fin plate-fin surface 1/8-19.82(0). .0505 BEST INTERPRETATION .015 -- .010 -- 4 .5 6 4 5 6 Fin pitch » 19.82 per in - 780 per m Plate spacing, b » 0.205 in - 5.21 x 10"3 m Splitter symmetricallY located Fin length flow direction - 0.125 in = 3.175 x 10*3 m Flow panage hydraulic diameter. 4r„ » 0.005049 ft - 1.537 x 10"3 m Fin metal thickness - 0.004 in. nickel - 0.102 x 10'3 m Splitter metal thickness « 0.006 in » 0.152 x 10*3 m Total heat transfer area/volume between plates, 8 * 680 ft^/ft3 - 2,231 m3 /m3 Fin area (including splitter)/total area - 0,841 Figure 10. 5 - Heat transfer and flow friction design data. tp = plate thickness 0.003= m; b = plate spacing = 0.00521 m |3= Total heat transfer area / volume between plates = 2231 m3/m2 Fin area / Total area = 0.841; k - Wall conductivity = 20 W/m,K; Li= Fluid 1 (cold) flow length; l_2= Fluid 2 (hot) flow length; l-3= Non - flow length; The number of plates is given by N plates = (Ls/(tp + b)) The volume between plates is V = L1*L2*b*(Np,ate s -1) 10-10 Chapter 10- Heat Exchangers. Total heat transfer area = V*j3 The thermal capacity ratio is almost equal to 1, since the same working fluid is used on both side of the heat exchanger, and the cp varies only slightly with temperature. When the efficiency is almost 1, the Ntu goes asimptotically to the maximum allowed by thermodynamical characteristics and flow arrangement. A numerical method has been used to calculate the Ntu corresponding to an effectiveness e = 0.93. The required Ntu is equal to 56. The design pressure drops are: AP hot - 4 % AP cold = 1.5 % The recuperator sizing is performed using the commercial software CHED ( Compact Heat Exchanger Design, by Intercept Software Co.). The input data for each heat exchangers are in Appendix XIV, together with the results. The dimensions of the recuperators are compared in table 10.5 for helium and helium-water mixture and in table 10.6 for nitrogen and nitrogen-water mixture. The heat transfer areas and overall heat transfer coefficients are plotted in Figure 10.6, figure 10.7 and Figure 10.8. • Helium-water vapour as working fluid. Dry 1 IC Wet 1JC Wet 2 IC AC Volumefm 3! 3,056 3,899 4,265 Li fml 1,238 1,615 1,858 L2 fml 0,679 0,785 0,852 L3 fml 3,95 3,073 2,696 Plate area [m2l 0,840602 1,267775 1,583016 Plates number 661 559 490 Total plates area fm2] 603 708 776 Table 10. 5 - Dimensions and total plate area. 10-11 Chapter 10- Heat Exchangers. TOTAL PLATE AREA HEAT TRANSFER COEFFICIENT COLO HEAT TRANSFER COEFFICIENT HOT Figure 10. 6 - Total heat transfer area c Heat transfer coefficient cold side fW/m2,k], Heat transfer coefficient hot side [W/m2,k] vs. configuration. The results for the cycle using nitrogen/water mixture as working fluid are compiled in the next table. Dry 1 IC Wet 1 IC Wet 2 IC AC Volume[m 3] 9,706 9,213 9,406 Li [m] 3,954 4,167 4,351 L.2 [m] 1,638 1,601 1,701 L3 [m] 1,499 1,381 1,271 Plate area [m2] 6,47 6,67 7,40 Plates number 272 252 246 Total plates area [m2] 1762 1679 1782 Table 10. 6 - Dimensions and total plate area. Nitrogen-water mixture as working fluid 10-12 Chapter 10- Heat Exchangers. Figure 10. 7 - Total plate heat transfer area [m2]. MEAT TRANSFER COEFFICIENT HOT HEAT TRANSFER COEFFICIENT COLO Figure 10. 8 -Heat transfer coefficient on cold/hot side [W/m2,k]. The heat transfer coefficient is function of Reynolds, Prandtl, and Stanton numbers and the flow stream mass velocity. A = /(Re,Pr,A,G) BY R= = 4r‘G- Pr = St= h G-cr 10-13 Chapter 10- Heat Exchangers. G = Exchanger flow stream mass velocity; If the diameter and the flow characteristics are constant, the heat transfer coefficient depends on conductivity, Reynolds and Pr1/3. A = A - Re" Pr^ d where A, a are constant depending on the flow characteristics. As working fluid composition varies, it is possible to point out these behaviour for k and Pr: • The thermal conductivity of gases increases with temperature in the range of low pressures. The ratio of thermal conductivity for dry helium and dry nitrogen is roughly one third and it reflects on the ratio of required heat transfer area. Regarding to water injections, the behaviour is different between helium/water mixture and nitrogen/water mixture. In the first case the conductivity decreases, while in the second one it increases slightly with increasing water. • The cp of the working fluid varies as the water content varies. For an helium-water mixture the cp is lower compared to pure helium, while for a nitrogen-water mixture the cp is higher than for pure nitrogen. The heat transfer coefficient depends on cp from the Prandtl number. • The viscosity in gases increases with temperature. In the region of low pressure (0.1-10 bar) the viscosity of gases and vapours is nearly independent of pressure. « The Prandtl number of the mixture increases compared to the one of pure helium or nitrogen. » The overall effect of water injection on h is a decrease when water in injected in helium and an increase when water is injected in nitrogen. The total heat transfer area does not depend only on the overall heat transfer coefficient but also on the total transferred heat and in the mean logarithmic temperature difference defined as 10-14 Chapter 10- Heat Exchangers. fafitt ~~ Th,m )“ (rc,m - Th,ou: ) A7L = ~Th,inl In (Tcjn ~ Th,ou, ) The heat transfer area is given by A = - [/ATml where Q is the total heat transfer duty and U is the overall heat transfer coefficient. The heat transfer area is larger for those configuration having a second water injection as aftercooler, even if the mean logarithmic temperature difference is higher than in the case without, since the cold side inlet temperature is lower, and the effectiveness is constant. The heat transfer coefficient does not vary too much for the different configuration, so that the heat duty is the most important parameter. As shown in Appendix XIV, the heat duty is much higher than in the cycle with only intercooling, and, from the definition of heat transfer area and the considerations above mentioned follows that a larger area is required. 10.5 - Postcooler. The postcooler is represented as the series of two heat exchangers. In the first one no condensation occurs and the working fluid is cooled down to the dew temperature, while in the second one part of the water vapour is condensed as the working fluid is further cooled by the district heating water. Non-condensing Condensing Postcooler Postcooler Figure 10. 9 - Schematic of the postcooier. In reality, the two parts can be joined into one unit. 10-15 Chapter 10- Heat Exchangers. 10.5.1 -Non-condensing postcooler. The non condensing postcooler is a shell and tube heat exchanger with working fluid on shell side and water on the tube side. The geometry of the non condensing postcooler is the following: D„ =0.025 [m] A-=0-02 M Nu -k The heat transfer coefficient on the working fluid side is given by ha = The water side transfer coefficient is assumed equal to hr 3000 W/m12 ,k,3 4to have a fair comparison with the dry cases studied by Anheden et al. ( 1998). 10.5.2-Condensing postcooler. While sizing the condensing postcooler the following features must be considered: 1. The condensation will not be isothermal. As the condensable component condenses out the composition of the vapour, and therefore its dew point changes. 2. Because the condensation is not isothermal there will be a transfer of sensible heat from the vapour to cool the gas to its dew point. There will also be a transfer of sensible heat from the condensate, as it must be cooled down from the temperature at which is condensed to the outlet temperature. 3. As the composition of the vapour and liquid change throughout the condenser, their physical properties vary. 4. The condensable component must diffuse trough the non-condensable components to reach the condensing surface. The rate of condensation will be governed by the rate of diffusion, as well as the rate of heat transfer, 10-16 Chapter 10- Heat Exchangers. To evaluate the true temperature difference in a mixed vapour condenser, a condensation curve (temperature vs. enthalpy) must be calculated, showing the change in vapour temperature versus heat transferred throughout the condenser. There are two limiting conditions of condensate-vapour flow: 1. Differential condensation: in which the liquid separates from the vapour from which it has condensed; 2. Integral condensation: in which the liquid remains in equilibrium with the uncondensed vapour. It is normal practice to assume that integral condensation occurs. The conditions for integral condensation will be approached if condensation is carried out in one pass, so that the liquid and vapour follow the same path, as in vertical condenser with condensation inside or outside the tubes. The methods developed for partial condensation and condensation from a non condensable gas can be divided in approximate methods and analytical methods. An approximate method developed by Gilmore will be used here to calculate the heat transfer coefficient on the working fluid side ( Sinnot, 1994). The local coefficient for heat transfer, hcg, can be expressed in terms of the local condensate film coefficient A'and the local coefficient for the sensible heat transfer from the vapour (the gas film coefficient) hg .Gilmore (1963) K, K Qi K where hcg = mean effective coefficient, hc - mean condensate film coefficient, evaluated from the single component correlations, at the average condensate composition, and total condensate loading. 10-17 Chapter 10- Heat Exchangers. hg = mean gas film coefficient, evaluated using the average vapour flow rate; arithmetic mean of the inlet and outlet vapour ( gas) flow rates Qg = total sensible heat transfer from vapour (gas) Qt = total heat transferred: latent heat of condensation + sensible heat from cooling the vapour (gas) and condensate. In partial condensation it is usually better to put the condensing stream on the shell side, and to select a baffle spacing that will maintain high vapour velocities, and there fore high sensible heat transfer coefficients. The steps to undergo to calculate the required heat transfer area are the following: 1. Calculate a mean condensation film coefficient for the condensing part, at the average condensate composition. and L.= tube length Wc = total condensate flow. Nt = total number of tubes in the bundle 10-18 Chapter 10- Heat Exchangers. 2. Calculate a mean gas coefficient considering the total incondensable gas and the average between the condensable mass flow rate at inlet and outlet, considered as incondensable. The design methods will be that of Kerns (1950) jh = heat transfer factor; PF / As = ——K _ Spec ijic area P, de = 4 (pf - n • d] / 4)/ it dl - hydraulic diameter Ws = mass flowrate p, = pitch d0 = outlet diameter lB = baffle spacing Ds = shell inside diameter Mw ~ fluid vis cos ity at the wall 3. The water side transfer coefficient is assumed equal to hr 3000 to have a fair comparison with the dry cases studied by Anheden, Ahlroth (1998) 10.5.3 - Pressure drops in condensers. The pressure drops on the condensing side is difficult to predict as two phases are present and the vapour mass velocity is changing throughout the condenser. A common practice is to calculate the pressure drop using the methods for single phase flow and then apply a factor to allow for the change in vapour velocity. An alternative method, which can also be used to estimate the pressure drop in a partial condenser, is given by Glover (1970). The pressure drop is 10-19 Chapter 10- Heat Exchangers. calculated using an average vapour flow -rate in the shell (or tubes), and the temperature profile Ws (average) = Ws (inlet )*Kg l<2 is plotted against the ratio between mass flow rate of vapour in and out and is available in literature. The tube side pressure drop is due mainly to the friction losses in the tube and the losses due to the sudden contractions and expansion and flow reversal that the fluid experiences in flowing trough the tube arrangement. The tube friction loss can be calculated using the equations for pressure drops losses in pipes. The basic equation for isothermal flow in pipes is Where jf is the dimensionless friction factor and L' is the effective pipe length. The flow in a heat exchanger will clearly not be isothermal, and this is allowed for by including an empirical correction factor to account for the change in physical properties with temperature. Normally only the change in viscosity is considered m=0.25 for laminar flow, Re < 2100 rn= 0.14 for turbulent flow, Re >2100. 10.5.4 - Design of a condenser for partial condensation of water from a helium/ nitrogen - water vapour mixture. The design choice is a shell and tube vertical postcooler, one pass, with condensation on the shell side and cooling water on the tube side. □out = 25 mm Din = 20 mm Tube thickness = 2.5 mm Squared pitch pt = 1,25*Dou t L = tube length = 3.66 m 10-20 Chapter 10- Heat Exchangers. The results from the calculations from the postcooler for each configurations at its optimum pressure ratio are In Appendix XVI. The resulting area for helium and helium-water mixture are summarised in Table 10.7 and Table 10.8 . Area of non Area of Total area of condensing condensing Postcooler Postcooler [m2] Postcooler [m2] [m2l DRY 1 IC 122,4 122,4 WET 1 IC 114 193 307 WET 2 IC AC 70,15 592 662,5 Table 10. 7 - Postcooler Heat transfer area for helium and helium-water mixture. 700 600 500 300 200 100 DRY 1JC WET 1JC WET 2JC>C WET 2JC.AC P=5 BAR Figure 10. 10 - Postcooler heat transfer area. Helium/water mixture as working fluid. As can be seen, the area for the condensing part of the heat exchanger increases quite dramatically when the water content of the working fluid increases. As more water is injected (i.e., with an aftercooler), the dew point temperature of the mixture will be higher. A higher dew temperature leads to a lower mean temperature in the condensing postcooler. Since the slope of the T-Q curve on the condensing side is flatter than on the district heating water side, the approach temperature difference on the hot side is narrowing with increasing dew point. The mean logarithmic temperature difference will 10-21 Chapter 10- Heat Exchangers. then decrease, since the approach on the cold side is fixed to AT=15 °C. The overall effect is that the heat transfer area in the condensing postcooler is significantly increased at high water molar fractions. As in the helium-water mixture case, the presence of an aftercooling stage Heads to a higher heat transfer area in the condensing postcooler. The negative effect is not so strong as in the helium case because a nitrogen- water mixture shows better thermal properties than pure nitrogen and the water molar fraction is lower than in the helium case. The conductivity of the mixture increases slightly at same temperature and pressure compared to the one of pure dry gas. The heat transfer coefficient on the non condensable side is then higher for a mixture, opposite to helium-water mixture. Non-condensing Condensing Total Area [m2] Area [m2] Area [m2] DRY 1 IC 166,8 166,8 WET 1 IC 146,1 390 536,1 Wet 2 IC AC 183,78 521 704,78 Table 10. 8 - Postcooler heat transfer area. Nitrogen and nitrogen- water mixture as working fluid. 0 NON-CONDENSING ■ CONDENSING QTOTAL DRY 1JC WET 1JC WET2_IC_AC WET2JCACP=5 BAR Figure 10. 11 -Postcooler heat transfer area. Nitrogen/water mixture as working fluid. 10-22 Chapter 10- Heat Exchangers. 10.6-Influence of base pressure on heat transfer area. The heat exchanger have been sized for the configuration with water injection as intercooling and aftercooling and base pressure P=5 bar, both for helium-water mixture working fluid and nitrogen-water working fluid. The resulting electrical and total efficiency with helium-water and nitrogen-water working fluid for the case with base pressure P=5 bar and the case with base pressure P=2 bar can be found in Chapter 9, Table 9.2 and Table 9.3. The heat transfer area for both base pressure are shown in Table 10. 9 and a re plotted in Figure 10. 10 for helium-water mixture and in Table 10. 10 and Figure 10.11 for nitrogen-water mixture. FGHX EBHX Recuperator Non Condensing Total Area Area plate area condensing postcoooler postcooler K] fm2l postcooler [m2] [m2] Area [m2] WET 2_IC_AC 123 260 776 70,15 592 662,5 P=2 bar WET 2_IC_AC 123,4 254.71 718 42,39 385 427,39 P-5 bar 4 Table 10.9- Helium-water as working fluid. a WET 2JC.AC P-2 bar ■WET 2JC.AC P=2 bar la a a B 1 ' 1 T 1 —H FGHX EBHX Recuperator Non-condensing Condensing Total postcooler postcoot er postcoooler Figure 10. 12 - Heat transfer area. Helium-water as working fluid. 10-23 Chapter 10- Heat Exchangers. FGHX EBHX Recuperator Non Condensing Total Area Area plate area condensing postcoooier postcooler [m2j [m2] [m2] postcooler Area fm2j Area [m2] WET 2_IC_AC 148 307,7 1782 183,78 521 704,78 P=2 bar WET 2_IC_AC 143.2 307 1318.8 108 330 438 P=5 bar Table 10. 10- Nitrogen-water as working fluid. FGHX EBHX Recuperator Non- Condensing Total condensing postcoooier postcooler postcooler Figure 10. 13 - Heat transfer area. Nitrogen-water mixture as working fluid A higher base pressure seems to be an effective way of reducing the condenser area. The heat transfer area reduces around 35 % in the helium- water case and about 37% in the nitrogen-water case. As shown in Chapter 6, less water is injected, so that a smaller condensing postcooler area is needed. Moreover the thermal characteristic of the working fluid improves, so that even the non-condensing heat exchanger heat transfer area will be smaller than in the corresponding configuration with a lower base pressure. The recuperator area decreases as well, because the heat transfer coefficient increases on both side, as can be seen in Appendix XIV, Table XIV.5 and Table XIV.10, The flue gas heat exchanger and the external bed heat exchanger are not relevantly affected by an increase in base pressure, because the limiting heat capacity is on the flue gas side. 10-24 Chapter 10- Heat Exchangers. The choice of an higher base pressure will increase the strains on the tubes on the working fluid side, so that the tube thickness will have to be increased, reducing the wall conductivity. In this analysis this factor has not been considered, and the same tube wall conductivity has been used for both base pressures. 10.7-Comparison between dry cycle and wet cycle. The dry cycle with two level intercooling and postcooling and the wet cycle with water injection as intercooling and aftercooling show similar electric efficiency. The wet cycle has the advantage of not requiring an heat exchanger for intercooling and only one unit for postcooling. Moreover, the total efficiency in the wet case is about 20 % point higher for any working fluid. The total heat transfer area becomes then a very important parameter in the choice of one cycle instead of the other. The heat transfer area for the two different cycle configurations have been compared in Figure 10.14 and Figure 10.15. The results for dry cycle with two level intercooling and two level postcooling refers to the work of Anheden at al., 1997. FGHX EBHX IC1 IC2 PC1 PC2 Recuperator Total riel r|tot Area [m2] Area Area Area Area [m2] Area Area [m2] Area [m2] [m2] [m2] [m2] [m2] DRY 113,5 249,5 102 63 114 63 558,5 126935.3 87.7 WET 2_IC_AC 123,4 254 427 718 1522 31,7 109 P=5 bar WET 123 260 662,5 776 1821 33.1 106. 2JC_AC. P=2 5 bar Table 10. 11-Heat transfer area and efficiencies of helium and helium water mixture as working fluid. 10-25 Chapter 10- Heat Exchangers. Figure 10.14-Heat transfer area: helium and helium-water mixture as working fluid. FGHX EBHX 1C1 IC2 PC1 PC2 Recuperator Total r|el T]t0t Area Area Area Area Area Area Area [m2] Area [m2] [m2] [m2]v [m2] [m2] [m2J iml DRY 138 302 236 140 311 170 1750 3047 36,6 89,4 WET 2_IC_AC 143.2 307 438 1318 2206 33 105 P=5 bar WET 2 IC AC 148 307,7 705 1782 2942 34,3 104,47 P=2 bar 5 Table 10. 12-Nitrogen and nitrogen-water mixture as working fluid. FGHX SBHX IC1 IC2 PC1 PC2 Recuperator Figure 10. 15 - Heat transfer area: nitrogen and nitrogen-water mixture as working fluid. 10-26 Chapter 10- Heat Exchangers. The heat transfer area for helium-water mixture increases significantly compared to the dry case, while for nitrogen-water mixture is almost constant. In both cases the postcooler heat transfer area is significantly increased with water injection, around 400% in the helium case and 200 % in the nitrogen case. With and without water injection, the heat transfer area for helium is smaller than for nitrogen. The recuperator area is also increased, with water injection, thanks to a more effective recuperation, around 30% in the helium case while it’s almost constant in the nitrogen one. If a base pressure of 5 bar is used instead of a base pressure of 2 bars in the wet cycle, more heat transfer area can be saved, (17% with helium, around 30 % with nitrogen) but there will be a loss in electric efficiency of about 2 points for each working fluid. 10.8-Conclusions. The heat transfer area in fired heat exchangers as the flue gas heat exchanger and the external bed heat exchanger is expected to be less affected by a change in working fluid compositions, because the controlling influence on the overall heat transfer coefficient is usually on the flue gas side. The results are summarised in Figure 10.16 and seems to go accordingly to theory. HELIUM HELIUM HELIUM HELIUM NITROGEN NITROGEN NITROGEN NITROGEN DRY 1 IC WET 1 IC WET WET DRY 1 IC WET 1 IC WET WET 2JC_AC 2JC_AC 2JC.AC 2_IC__AC P-5 BAR P-5 BAR Figure 10.16-FGHX and EBHX heat transfer area for different configurations. 10-27 Chapter 10- Heat Exchangers. In unfired heat exchanger, like the recuperator and the coolers, on the contrary, the limiting thermal resistance is on the working fluid side and a change in working fluid thermal properties can affect significantly the overall heat transfer coefficient and the total heat transfer area. In this study, the heat capacity, mM •cp, does not vary when water is added. Being the heat input to the cycle fixed, in fact, the total mass flow rate is adjusted so that mtot ■ cp = const ( § 6.2). This value is the thermal capacity of the working fluid. HELIUM DRY HELIUM WET HELIUM WET HELIUM WET NITROGEN NITROGEN NITROGEN NITROGEN 1 IC 1JC 2JC_AC 2 IC AC P=5 DRY 1 _IC WET 1 IC WET 2_IC_AC WET 2JC_AC EAR P=5 BAR Figure 10. 17-Postcooier heat transfer area for different configurations. 2000 1800 HEUUM DRY 1 IC HELIUM WET 1 JC HEUUM WET 2 IC AC NITROGEN DRY 1JC NITROGEN WET 1_IC NITROGEN WET 2JC.AC Figure 10.18-Recuperator total plate area for different configurations. 10-28 Chapter 10- Heat Exchangers. Helium-water mixture requires smaller area than nitrogen-water mixture in all the heat exchangers, although its performances deteriorate as more water is injected. Regarding condensation, nitrogen-water mixture seems to be less influenced by an increase in water mole fraction than helium-water mixture. The area of the condensing postcooler in the cycle with intercooling and aftercooling for helium-water mixture is almost three times the one for the cycle with only one water injection as intercooling. With nitrogen-water mixture, the increase in condensing postcooler area when adding a second water injection is around 25 %. 10-29 Chapter 11-Conclusions. Chapter 11. Conclusions. 11.1 - Results and discussion. The main parameters to consider when comparing different plant configurations are the plant thermodynamic performance and the plant cost. Although a detailed economic analysis is required for the latter point, the overall plant cost is mainly connected to the equipment size and, on second hand, to the working fluid cost and availability. » System configuration. Both with helium-water mixture and nitrogen-water mixture, the electric efficiency increases as more water is added to the cycle. The higher the relative humidity after the injection, the higher the electric efficiency. By adding a second water injection after the HP compressor, the cycle efficiency is further increased because more heat can be recovered in the recuperator from the expanded working fluid. The positive effect of water injection is mostly connected to the intercooling effect and its positive effect on compression work (Figure 6.12). The temperature at the inlet of the HP compressor is lower, so that the compression work is reduced, being the working fluid denser. Moreover the electric efficiency increases when water is added to the cycle because a smaller fraction of the total mass flow rate has to be compressed in the LP and HP compressor (see Table VI-2). The injected water is in fact condensed and then brought to the required pressure level with a pump. The pumping work is neglectable when calculating the power output. An increase in water molar fraction in the working fluid seems to effect the expansion process in a negative way causing the turbine outlet temperature to increase, reducing slightly the turbine isentropic efficiency due to a change in working fluid thermal properties compared to the dry working fluid, and therefore the expansion work (Figure 6.9). The efficiencies versus the cycle configuration are plotted in Figure 11.1 11-1 Chapter 11-Conclusions. 0FURNACE ■ CYCLE QELECTRIC DTOTAL 40 - r 1_IC: relative 1JC: relative 1JC: relative 2_IC_AC^elative 2JC_AC:relative humidity 25% humidity 60% humidity 95% humidities 60% - humidities 60% - humidities 95% - 95 %; injected 95 %; injected 95 %; injected water water water temperature 65 temperature 150 temperature 65 C C C Figure 11. 1- Efficiencies for different configurations. Helium and helium-water mixture as working fluid. The option with injected water at an higher temperature than the condensate is rejected, since it will possibly lead to a lower total efficiency (the heat to warm up the water will be subtracted from the cycle), a more complicated cycle layout (a new heat exchanger should be added, with additional pressure drop) while the gain in electric efficiency will be almost negligible. The configuration with water injection as intercooling and aftercooling and one stage postcooling using district heating water as coolant has a simple plant layout joined to high cycle performances, for both working fluid. The best compromise between electricity production and district heating seems to be found with a humidity level of 95% after each injection, and one level postcooling with district heating water. This configuration shows, both for helium-water mixture and nitrogen-water mixture, an electric efficiency higher than the dry case with one level intercooling, but still lower than in the dry case with two level intercooling. On the other hand, the total efficiency is always higher than 100 %, against a total efficiency in the dry case of around 90 %, since no external cooling water is used. One of the main advantage of intercooling and aftercooling by direct water injection instead of water-gas heat exchanger is connected to a reduction in the number of heat exchangers compared to the dry cycle. The heat to evaporate the liquid water atomised in the stream is directly subtracted from 11-2 Chapter 11-Conclusions. the gases, that reduce their temperature, without the need of any additional piece of equipment If the compressor inlet duct is not long enough to allow a complete evaporation of the water droplets, a droplets separator might be needed. The wet cycle with two water injection is then simpler than the dry one with two level intercooling and two level postcooling, and the total heat exchanger number is reduced to five (EBHX, FGHX, Recuperator, Flue Gas Condenser, Postcooler), while the electric efficiency is reduced only by two points. However, the total heat transfer area in the wet cycle increases as more water is injected in the cycle. This is connected mostly to an increase in the postcooler size. The other heat exchangers area does not vary significantly (see Figure 10.13 and Figure 10.14). The temperature after the postcooler can not be lower than 65 °C without the use of external cooling water since the district heating water terminal temperatures are fixed. The configuration with an additional postcooling stage, studied for nitrogen-water mixture, would be a good option when the electricity production is more valuable than district heating. However, due to the presence of an additional heat exchanger in the cycle using external water as cooler a huge portion of the cycle heat will be lost with the coolant, significantly lowering the total efficiency. » Working fluid. The choice of one working fluid instead of an other must be seen as a compromise between electric efficiency and equipment size. Nitrogen and helium are very different gases: helium has a higher cp, lower molecular weight and a higher conductivity than nitrogen. This effects the total mass flow rate, the heat transfer surface required and the turbomachinery dimension. As shown in the previous chapters, the addition of water to the dry gas modifies the thermodynamic properties of the working fluid. Every cycle configuration has a different working fluid, because the water molar fraction varies. A different water molar fraction, as shown in § 6.2, leads to a different total mass flow rate. The choice of one cycle design Chapter 11-Conclusions. instead of another is made more difficult by this, since different parameters vary at the same time. The main trend is: • The pressure ratio is lower when helium-water is used instead of nitrogen-water because of a higher k-value. • The nitrogen/water mixture cycle shows an higher electric efficiency than the helium/water mixture cycle for every cycle configuration. This behaviour agree with the results found by Lee, Campbell and Wright (1981), that show an higher electric efficiency for diatomic gases than monatomic gases, at a fixed cycle pressure drops. This difference levels out as more water is injected, (see Figure 11.2). B HELIUM ■NITROGEN E i» I ;31 DRY 1 1C WET 1JC WET 2_IC_AC Figure 11.2- Electric efficiency: comparison for different working fluid • The heat transfer area in the dry cycle is smaller when helium is used instead of nitrogen (Anheden et at., 1998). By adding water to helium its heat transfer characteristics get worse, while the opposite happens to nitrogen. Still, the heat transfer area for helium-water mixture is always smaller than the one for nitrogen-water mixture, as shown in Chapter 10. Detailed calculations on the effect of water injection on turbomachinery have not been performed in the present study, but the following observations have been made: 11-4 Chapter 11-Conclusions. • Helium, having an higher cp, requires a higher number of turbomachinery stages. The helium turbine has to be specially designed while nitrogen can be used in air turbine without major modifications. One positive aspect of using helium is that a gain in turbine polytropic efficiency is expected compared to other working fluid. The work of op het Veld, van Buijtenen (1998) shows in fact that the rotating components of the helium gas turbines will have an efficiency advantage over the rotating components of air cycles because of the low optimum pressure ratio. In case of the single shaft axial compressor the polytropic efficiency advantage will be 0.5 % over an air compressor with equal dimensions. When adding water to helium the number of turbomachinery stages is expected to be reduced while, when adding water to nitrogen the number of turbomachinery stages is expected to increase. At the same time the decrease in cp when adding water to helium, causes an increase in mass flow rate, while the increase in cp with a nitrogen-water mixture leads to a smaller mass flow rate (§ 2.3). On a volume basis, however, water injection leads to a reduction in volume mass flow rate to be expanded in the turbine in both cases, affecting the turbomachinery size. The closed cycle gas turbine with water injection shows rather good performances with both He/H 20 and N2/H20 mixture as working fluid. Compared to the dry cycle with two level intercooling and two level postcooling, the wet cycle with water injection as intercooling and aftercooling shows a higher total efficiency of about 20 percentage points, while the electric efficiency loses around 2 percentages point, for both working fluids. It is to be stressed the fact that in the simulations the relative pressure drops in the heat exchangers are considered constant for all the working fluids. The recuperator is defined by its effectiveness and a fictious pressure drop is specified. That means that all the ASPEN simulations shows the same percentage pressure drop, regardless of the working fluid. In the actual plant the choice of a working fluid with high transfer coefficient and low flow frictions will be desirable to keep the pressure loss low, since a decrease in cycle pressure drop has a strong influence on the electric efficiency. 11-5 Chapter 11-Conclusions. 11.2-Conclusions. The plant shows, for all configuration, quite good performances both regarding electricity production than district heating, despite the small fuel input. The results should be evaluated comparing on to performances of already existing cogeneration plants of the same size. A biomass fueled cogeneration plant has been active in Mala, Sweden, since 1991. With a fuel input (based on LHV) of 16.3 MW, a steam pressure of 41 bar and a steam temperature of 480 °C, this plant produces 2.95 MW of power, for an electric efficiency of 18 % and 11 MW of heat (total efficiency 86 %), used to dry wood. The furnace is a fluidised bed with an efficiency of 0.86. The externally fired gas turbine studied in this report is then competitive with currently existing Rankine cycle, both in total and electric efficiency. The cycle still offers various way of improving its performances. The cycle performance is bounded to the inlet turbine temperature, fixed to 800 °C. This temperature depends on the maximum temperature allowable in the CFB, and although being high enough to transfer heat at the working fluid at a high average temperature, it still makes possible to use conventional heat exchangers. The turbine inlet temperature can be raised by adding a stage of top firing after the external bed heat exchanger, using external fuel or hot syngas fuel that can be produced in the fluidised bed furnace working with very little oxygen. The cycle performance can be improved by using more advanced heat exchanger, to reduce pressure drops in the cycle. It could be of interest to estimate the additional work required for water injection, connected to the atomisation of water in fine droplets. 11-6 Appendix I - Turbomachinery work for a mixture as working fluid. Appendix I Turbomachinery work for a mixture as working fluid. When a mixture is considered as working fluid the turbine outlet temperature is given by (^avg l) ( D M ’lp"‘ xT out -T.x in (M) J where the temperature is expressed in Kelvin degrees and the pressure in bar. + k— kavg ~ in ' '''out (I-2) 2 [T0m Am) pmix Km “ c(TomA0m) (I-3) h = pmix Cvmix {Tm y P,„ ) The turbine work is f k-vr-1)) ^ (p A W. m-c T. • (1-4) turbine pavg J -if, y Accordingly, the compressor outlet temperature is given by (Aovg-l)^ / r, X Tom - Tin (1-5) V K ) and the compression work is out rTW compressor = fh* c pavg «xT in (1-6) V Tin J 1-1 Appendix II - Isentropic efficiency. Appendix II Isentropic efficiency. -or an expansion process the isentropic efficiency is defined as PF A# Vis (H-1) while for a compression process it is defined as Vis =■ (II—2) the polytropic efficiency considers the fact that the isentropic work required for going from a pressure level Pi to a pressure level P2 is higher if a multi stage compression is considered. IX (II—3) Vpol = Z ^ Z^ If a perfect gas is considered as a working fluid, in a compression process V - ^X.dT) (II-4) / v-p1-*-1 / RT V =------p (11-5) c p _ k — 1 i~~r integration gives (dp) >-!)" (11-6) U J Ip J (*-i) Tj_ k-Vpoi (H-7) Tx From the isentropic efficiency definition, in a compression process, 11-1 Appendix II - Isentropic efficiency. 11-2 Appendix III- Gas-water mixtures. Appendix ill Gas-water mixtures. Moist gas is defined as a mixture of dry gas and water vapour in which the gas is regarded as if it were a pure component. The composition of moist gas can be described by the humidity ratio, 00, which is the ratio of the mass of water vapour to the mass of dry gas. m CO - w/ where the pressure of the moist gas mixture is defined in terms of the partial pressures of the components, as p = pwf + pHiQ (Moran, M., Shapiro, H. 1988). The humidity ratio is sometimes referred to as specific humidity. Relative humidity Since p v = yvp and pv sat = yv satp , this can be expressed also as X Tv \p ) 0 = (HI-2) Tv ,sat 'Jr.p If/ The amount of water in the gas, relative to the maximum amount that can be held (the saturation condition), can also be described in terms of the difference between the actual gas temperature and the adiabatic saturation temperature. To define the adiabatic saturation temperature we first consider a device called adiabatic saturator. An adiabatic saturator is represented as a two inlet, one-exit device trough which moist air passes. The device is assumed to operate at steady state condition and without significant heat transfer with the surroundings. An air - 111-1 Appendix III- Gas-water mixtures. water vapour mixture of unknown humidity ratio co enters the saturator at a known pressure p and temperature T and come in contact with a pool of water. Moist air Saturated mixture P,T/ii Tas.P.o' X7 Makeup water mass flow rate = Figure ill-1: Adiabatic saturator- schematic representation. Each of the two moist air streams is modelled as an ideal gas mixture of dry air and water vapour. Heat transfer with the surroundings is assumed to be negligible. There is no work and changes in kinetic and potential energy are ignored. If the entering stream is not saturated (<|><100%), some of the water would evaporate The energy required to evaporate the water would come from the moist air, so the mixture temperature would decrease. Since a saturated mixture will be achieved without heat transfer with the surroundings, the temperature of the exiting mixture is called the adiabatic- saturation temperature (Tas ). State si list! water vapour in fie incoming moist air stream State of the water vgpout in ihe exiting most aw stream Figure 111-2: Adiabatic saturator: process representation. Appendix III- Gas-water mixtures. The saturation temperature for a moist air stream can be calculated from equation 111-1 and a energy balance of the adiabatic saturation process, given the air condition and the condition of the liquid water. The unknowns are the saturation temperature and the amount of water that must be evaporated into the air to reach saturation. Saturation can be also achieved with direct water or steam injection in the stream. 12 wet mixture Figure ill-3: Schematic representation of water injection module The temperature of the moist gas as it exits the humidifier depends on the conditions of the water introduced. When relatively high-temperature steam is injected both the humidity ratio and the temperature would be increased. If liquid water was injected instead of steam, the moist gas may exit the humidifier with a lower temperature than at the inlet. Referring to the schematic module of adiabatic mixing of liquid water and a generic gas mixture in fig. III-3 the balance looks like: m»-hu{Tn)+(mdg = (W’7 ) » mdg = cons tan t = mass flow rate of dry gases * mvx = cox • mdg = mass flow rate of vapors « mw = mdg ■ ( M. ( p ^ • a) = ; humidty ratio of the single component 1-1) M,wf Appendix IV- Amount of injected water in helium/nitrogen -water mixture Appendix IV Amount of injected water in helium/nitrogen-water mixture. The amount of water needed to saturate a stream at a certain temperature and pressure can be calculated by a mass and energy balance. Considering a closed system consisting of an ideal gas mixture, the extensive properties of the mixture, such as internal energy, enthalpy and entropy, can be found by adding the contribution of each component at the condition in which the component exists in the mixture. The specific internal enthalpy becomes: h = j = number of components j=i Since _ dh ^ " ar ' _ du c- —. the expressions for the specific heats of the mixture become: ZP = ZtT/v t=l C = 2>iC,, 1=1 >>,.= — = — = mole fraction of the component / n p From the value of cp is possible to get the value of cv, using the relation cp -cv = R [KJ/kg.K] and then the specific heat ratio of the mixture. An E.E.S. program calculates the amount of water needed to reach a fixed relative humidity. The schematic of the simulation can be seen in Figure 2.13. The stream entering the compressor is supposed to be at saturated condition. IV-1 Appendix IV- Amount of injected water in helium/nitrogen -water mixture The amount of injected water is given by the difference between the humidity ratio before entering the aftercooler and the one after the aftercooler: The humidity ratio at the exit of the intercooler depends on the temperature of the mixture, r3. To determine the temperature after the water injection, an iterative energy balance is carried out, giving the humidity ratio at the exit of the intercooler as a result. The stream is assumed to be saturated at temperature T3. The first guess temperature T'3 is taken as the average between the intercooler inlet temperature and the injected water temperature. T2 is calculated from equation I - 5, with a polytropic efficiency rjpol = 0.90 The mass balance and energy balance are then carried out: » Mass balance: m, = m m3= m2 +mw Energy balance: The partial pressure of water vapour at T = T\ comes from the equation 111-1 The relative humidity If IV-2 Appendix IV- Amount of injected water in helium/nitrogen -water mixture The results of a sensitivity analysis on relative humidity Table IV-1: Sensitivity analysis on relative humidity with helium / water mixture as working fluid. The cycle input were: Ti= temperature of the working fluid at the compressor inlet. Saturated condition at pressure = 65 °C Pi= 2 bar. J2 = temperature of the working fluid after the compressor = 147.1 °C P2 = 3.63 bar. Ts = temperature of the working fluid after the water injection. P3=3.63 bar. t3 Injected water r°ci [Kg/s] 0,1 154,7 0,004197 0,2 134.3 0,01385 0,3 122,8 0,01943 0,4 115 0,02332 0,5 110,1 0,02575 0,6 105,2 0,02824 0,7 101,2 0,03031 0,8 97,71 0,03208 0,9 94,73 0,03362 1 92,11 0,03498 Table V-2: Sensitivityanalysis on relative humidity with nitrogen / water mixture as working fluid. IV-3 Appendix V-Influence of temperature on injected water mass flow rate. Appendix V. Influence of temperature on injected water mass flow rate. The water injection takes place at a pressure of 4.4721 bar, after the low pressure compressor ( pressure ratio 5). The required relative humidity after the injection is 95%. The working fluid is helium-water mixture. Inlet temperature * Injected water [°C] mass flow rate [ kg/sl 100 0,951 0,2514 105 0,951 0,2765 110 0,951 0,3019 115 0,951 0,3274 120 0,951 0,3532 Table V-1: Sensitivity analysis on inlet stream temperature. Helium- water mixture as working fluid. The injected water temperature influences the amount of water needed to reach saturation. A second E.E.S. simulation calcualtes the water mass flow rate with the following asumptions: • The injection takes place at a pressure of 4.4721 bar, after the low pressure compressor ( pressure ratio 5). • The required relative humidity after the injection is 95%. The input are: =0.0212189 (L, = 0.95 P = 4.4721 5, y H-flm ~ p .PVto = 0.0948 bar P MHlo P = • = 0.0138 V-1 Appendix V-lnfluence of temperature on injected water mass flow rate. Temperature ©out 4) Injected water f°ci [kg/s] 20 0,03587 0,9501 0,3362 30 0,03618 0,951 0,3408 40 0,03648 0,951 0,3454 50 0,03679 0,951 0,3501 60 0,03711 0,951 0,355 70 0,03744 0,951 0,36 80 0,03778 0,951 0,3652 90 0,03813 0,951 0,3706 100 0,03849 0,951 0,3761 Table V-2: Sensitivity analysis on injected water temperature. Helium- water mixture as working fluid. V-2 Appendix Vl-Effect of water injection on turbomachinery work and efficiency. Appendix VI Effect of water injection on turbomachinery work and efficiency. « Expansion process. The influence of the humidity level has been investigated keeping the pressure ratio over the turbine constant at the design pressure ratio for the wet cycle with water injection as intercooling,. Pin= 6,416 bar Pout = 2,17 bar Yh20 Cpmixin Cpmixout Kavg Tout W bin W Hin 0 3,88 5,194 5,194 1,666 453,3 -6987 21630 -0,323 0,05 4,354 4,645 4.6 1,619 465,8 -6726 21704 -0,3099 0,1 4,786 4.239 4,163 1,578 477,6 -6483 21772 -0,2978 0,15 5,182 3,926 3,829 1,542 488,6 -6258 21833 -0,2866 0,1922 5,492 3,713 3,603 1,514 497,4 -6079 21880 -0,2778 0,25 5,883 3,475 3,353 1,481 508,7 -5851 21940 -0,2667 0,3 6,194 3,308 3,178 1,455 517,9 -5666 21987 -0,2577 0,35 6,483 3,167 3,032 1,431 526,6 -5493 22031 -0,2493 0,4 6,752 3,046 2,908 1,41 534,8 -5330 22071 -0,2415 0,45 7.002 2,942 2,801 1,391 542,6 -5176 22108 -0,2341 Table VI -1: Sensitivity analysis on expansion work vs water mass flow rate in the working fluid being expanded in a turbine. Helium-water mixture as working fluid. » Compression process. LP compressor work. Pin = 2 bar Pout = 3,633 bar Tin =65 °C VI-1 Appendix VI-Effect of water injection on turbomachinery work and efficiency. yHOc= Water molar fraction at saturated condition in the inlet stream=0,1245155 [kmolnao/kmoltot] Yh2o= Water molar fraction in the postcooler inlet stream. Q =5039 KJ/s Tout = 158.5 °C Kavg = 1.583 . Yh20 ^comp W W-HlOc ™-H20 Hin 0,13 5,028 3,006 4,93 1812 1,924 2,022 6556 0,135 5,067 2,976 4,881 1794 1,905 2,091 6491 0,138 5,09 2,959 4,852 1783 1,894 2,132 6452 0,139 5,098 2,953 4,843 1779 1,89 2,145 6440 0,14 5,106 2,947 4,833 1776 1,886 2,159 6427 0,15 5,182 2,888 4,737 1741 1,849 2,294 6299 0,175 5,368 2,746 4,504 1655 1,758 2,622 5990 0,18 5,405 2,719 4,459 1638 1,74 2,686 5929 0,185 5,441 2,691 4,414 1622 1,723 2,749 5869 0,19 5,476 2,664 4,369 1605 1,705 2,812 5810 Table VI - 2; Sensitivity anlysis on LP compressor work vs water molar fraction after the injection point Helium-water mixture as working fluid. HP compressor work Pin = 3,633 bar Pout = 6,6 bar Tin =97,2 C Yh20c = Water molar fraction in the inlet stream = 0,1574 kmol H2o / kmol to t YH2o= Water molar fraction in the inlet turbine stream. Q =5039 KJ/s T out = 197 °C k= 1.561 VI-2 Appendix Vl-Effect of water injection on turbomachinery work and efficiency. Yh20 W ™H20c ^H20 Hin 0,18 5,182 2,719 5,004 1859 2,286 2,294 6918 0,185 5,368 2,691 4,954 1841 2,262 2,622 6848 0,19 5,405 2,664 4,903 1822 2,24 2,686 6778 0,192 5,441 2,652 4,881 1814 2,23 2,749 6748 0,2 5,476 2,61 4,804 1785 2,194 2,812 6641 Table VI.3- Sensitivity analysis on HP compressor work vs water molar fraction after the injection point Helium-water mixture as working fluid. k YH20c W Tout ™H2 Oc Hin 0,1 2053 201,6 1,595 4,786 3,19 1,597 7291 0,11 2034 200,8 1,74 4,868 3,128 1,591 7280 0,12 2015 200 1,882 4,948 3,066 1,584 7270 0,13 1996 199,2 2,022 5,028 3,006 1,578 7260 0,15 1960 197,6 2,294 5,182 2,888 1,565 7245 Table VI.4 - Sensitivity analysis on compression work while varying the water mass flow rate in the compressor inlet stream. VI-3 Appendix VII- Effect of water injection on polytropic efficiency. Appendix VII Effect of water injection on polytropic efficiency. (3 His P His 2 0,9102 2 0,912 2,2 0,9136 2,2 0,9116 2,4 2,4 0,915 0,9128 2,6 0,9139 2,6 0,9163 2,8 0,9175 2,8 0,915 3 0,9186 3 0,9159 0,9164 3,1 0,9191 3,1 3,2 0,9196 3,2 0,9168 3,3 0,9201 3,3 0,9173 3,6 0,9214 3,6 0,9184 Table VII-1 :isentropic Table VII - :isentropic efficiency vs efficiency vs pressure ratio. pressure ratio. Wet cycle expansion. Dry cycle expansion. (3 His P His 2 0,8929 2,1 0,893 2,1 0,8924 2,2 0,8926 2,4 0,891 2,4 0,8918 2,6 0,8902 2,6 0,891 2,8 0,8894 2,8 0,8903 3 0,8887 3 0,8896 3,1 0,8883 3,1 0,8893 3,2 0,888 3,2 0,889 3,3 0,8877 3,3 0,8887 3,4 0,8873 3,4 0,8884 Table VII-3:isentropic Table VIII -4:isentropic efficiency vs efficiency vs pressure ratio. pressure ratio. Wet cycle Dry cycle compression. compression VII-1 Appendix VII- Effect of water injection on polytropic efficiency. Water ms Water molar molar fraction r|is fraction 0,05 0,91927 0,04 0,88798 0,1 0,91852 0,05 0,88806 0,15 0,91781 0,06 0,88814 0,16 0,91768 0,07 0,88822 0,17 0,91754 0,08 0,8883 0,18 0,91741 0,09 0,88838 0,19 0,91728 0,1 0,88846 0,1922 0,91725 0,11 0,88854 0,2 0,91715 0,12 0,88862 0,21 0,91703 0,1246 0,88866 Table VII-5: Effect of water Table VII-6: Effect of water injection injection on isentropic on isentropic efficiency: efficiency: expansion. compression VI1-2 Appendix Vlil-Helium-water mixture as working fluid. Appendix VIII Helium-water mixture as working fluid. pLp/Pror electr Espansion Compression Injected Total LP mass flow rate ic r] work work water mass flow mass flow rate rate KW KW KG/SEC KG/SEC 0,55 31,06 -6188,2 3731,20 0,472505 5,191493 4,718988 0,56 31,12 -6183,70 3722,09 0,490448 5,199462 4,709014 0,57 31,17 -6179,19 3713,61 0,508196 5,207309 4,699113 0,58 31,21 -6174,76 3705,77 0,525682 5,215055 4,689372 0,59 31,25 -6170,39 3698,56 0,542924 5,222695 4,679771 0,6 31,28 -6166,10 3691,95 0,559923 5,230244 4,670321 0,61 31,30 -6161,85 3685,90 0,576688 5,237672 4,660984 0,62 31,32 -6157,65 3680,40 0,593226 5,244982 4,651755 0,63 31,33 -6153,52 3675,39 0,609540 5,252227 4,642686 0,64 31,34 -6149,44 3670,87 0,625640 5,259357 4,633717 0,65 31,34 -6145,40 3666,77 0,641441 5,266339 4,624898 0,66 31,33 -6141,41 3663,15 0,657224 5,273326 4,616102 0,67 31,32 -6137,41 3659,86 0,6729925,280301 4,607309 0,68 31,32 -6133,51 3656,49 0,688250 5,287103 4,598853 0,69 31,30 -6129,6 3654,09 0,703340 5,293788 4,590447 0,700 31,28 -6125,89 3652,01 0,718259 5,300398 4,582139 0,71 31,25 -6122,15 3650,28 0,732997 5,306929 4,573932 0,72 31,22 -6118,44 3648,88 0,747560 5,313381 4,565822 0,73 31,19 -6114,78 3647,79 0,761951 5,319757 4,557807 0,74 31,15 -6111,17 3646,99 0,776175 5,326060 4,549885 0,75 31,11 -6107,68 3646,97 0,789936 5,332133 4,542196 Table VIII.1 - Sensitivity analysissensitivita'on Plp/Ptot. Cycle with water injection come intercooling. Design pressure ratio p=3.3. Relative humidity 0=95%. “31,7 Figure VIII.1 - Electric efficiencyvs pip/pm VIII-1 Appendix VIII-Helium-water mixture as working fluid. Qinjeded water ■Total mass flow rate BLP compressor mass flow rate 1,00- 0,50 0,51 0,52 0,53 0,54 0,55 0,56 0,57 0.58 0,59 0,60 0,61 0,62 0,63 0,64 0,65 0,67 0,67 0,68 0,69 0,70 Figure VIII.2- Total mass flow rate , injected water mass flow rate and LP compressor mass flow rate vs. fiip/fitot- Design pressure ratio J3=3.3. Vlll-2 Appendix Vlll-Helium-water mixture as working fluid. Plp/Ptot Electric r| LP HP TB Injected Total mass water mass flow rate flow rate % KW KW KW KG/SEC KG/SEC 0,50 28,61 1487,46 2502,88 -6257,31 0,199010 5,070338 0,51 28,77 1549,46 2423,70 -6252,34 0,218716 5,079045 6,237492 0,52 28,92 1610,30 2346,76 -6247,61 5,087387 0,53 29,05 1670,38 2271,93 -6242,96 0,255900 5,095532 0,54 29,17 1729,50 2198,86 -6238,40 0,274033 5,103577 0,55 29,27 1787,89 2128,02 -6234,01 0,291365 5,111240 0,56 29,38 1845,08 2057,60 -6229,35 0,309896 5,119472 0,57 29,47 1901,66 1989,58 -6224,95 0,327264 5,127151 0,58 29,55 1957,44 1923,47 -6220,81 0,343613 5,134399 0,59 29,62 2012,71 1858,62 -6216,53 0,360683 5,141957 0,60 29,69 2066,77 1794,85 -6212,33 0,377242 5,149291 0,61 29,76 2120,05 1731,97 -6207,95 0,394580 5,156975 0,62 29,82 2172,74 1670,89 -6203,81 0,410948 5,164224 0,63 29,86 2224,84 1611,23 -6199,77 0,426928 5,171307 0,64 29,90 2276,29 1553,19 -6196,01 0,441728 5,177872 0,65 29,93 2327,08 1495,75 -6191,98 0,457714 5,184943 0,66 29,96 2376,94 1439,27 -6187,96 0,473623 5,191994 0,67 29,99 2426,36 1384,16 -6184,11 0,488802 5,198714 0,68 30,00 2475,50 1330,57 -6180,52 0,502959 5,204983 0,69 30,01 2523,73 1277,48 -6176,76 0,517873 5,211599 0,70 30,02 2571,35 1225,39 -6173,03 0,532504 5,218070 0,71 30,03 2618,53 1174,30 -6169,37 0,547000 5,224494 0,72 30,03 2665,10 1124,12 -6165,76 0,561284 5,230832 0,73 30,02 2711,10 1074,78 -6162,15 0,575459 5,237104 0,74 30,01 2756,64 1026,36 -6158,62 0,589405 5,243281 0,75 30,00 2801,63 978,75 -6155,11 0,603228 5,249405 Table VIH.2-Sensitivity analysis on Plp/Ptot- Cycle with water injection as intercooling. Design pressure ratio j3=3.3. Relative humidity Figure Vlll.3-Electric efficiencyvs pip/pior VI11-3 Appendix Vlll-Helium-water mixture as working fluid Plp/Ptot Electric LP HP TB Injected Total mass efficiency water flow rate mass flow rate % KW KW KW KG/SEC KG/SEC 0,55 31,06 1750,44 1980,76 -6188,23 0,47 5,19 0,56 31,12 1806,50 1915,59 -6183,71 0,49 5,20 0,57 31,17 1861,73 1851,89 -6179,20 0,51 5,21 0,58 31,22 1916,14 1789,63 -6174,77 0,53 5,22 0,59 31,25 1969,791728,77 -6170,40 0,54 5,22 0,60 31,28 2022,69 1669,26 -6166,11 0,56 5,23 0,61 31,31 2074,87 1611,04 -6161,86 0,58 5,24 0,62 31,32 2126,34 1554,07 -6157,65 0,59 5,24 0,63 31,34 2177,11 1498,29 -6153,53 0,61 5,25 0,64 31,34 2227,22 1443,66 -6149,44 0,63 5,26 0,65 31,34 2276,63 1390,14 -6145,40 0,64 5,27 0,66 31,34 2325,45 1337,71 -6141,42 0,66 5,27 0,67 31,33 2373,67 1286,20 -6137,42 0,67 5,28 0,68 31,32 2420,92 1235,58 -6133,52 0,69 5,29 0,69 31,30 2467,95 1186,15 -6129,69 0,70 5,29 0,70 31,28 2514,39 1137,63 -6125,90 0,72 5,30 0,71 31,25 2560,28 1090,01 -6122,15 0,73 5,31 0,72 31,23 2605,62 1043,26 -6118,45 0,75 5,31 0,73 31,19 2650,44 997,35 -6114,79 0,76 5,32 0,74 31,16 2694,74 952,26 -6111,17 0,78 5,33 0,75 31,11 2738,83 908,14 -6107,68 0,79 5,33 Table Vlll.3-Cycle with water injection as intercooling. Design pressure ratioJ3=3.3. Relative humidity 0=60%. Figure Vlll.4-Eiectric efficiency vs fo/froT VIM-4 Appendix VHI-Helium-water mixture as working fluid. Plr /Ptot Electric Total LP HP TB n work KW KW KW KW 0,50 32,41 -2513,9 1332,10 2132,16 -6025,47 0,51 32,46 -2517,7 1390,94 2069,92 -6025,87 0,52 32,50 -2521,2 1449,02 2008,67 -6026,19 0,53 32,54 -2523,9 1506,43 1948,76 -6026,42 0,54 32,56 -2526,2 1563,19 1889,98 -6026,63 0,55 32,59 -2528,00 1619,19 1832,31 -6026,74 0,56 32,60 -2528,83 1674,78 1775,99 -6026,84 0,57 32,61 -2529,57 1729,60 1720,42 -6026,83 0,58 32,61 -2529,82 1783,85 1666,02 -6026,95 0,59 32,61 -2529,43 1837,56 1612,71 -6026,95 0,60 32,59 -2528,50 1890,74 1560,33 -6026,81 0,61 32,58 -2527,13 1943,39 1508,97 -6026,75 Table VIII.4-Sensitivity analysis on Plp/Ptot- Cycle with water injection as intercooling and aftercooling. Injected water temperature T- 65 C. 32.60 Figure Vlll.5-Electric efficiency vs Plp/Ptot- VIII-5 Appendix VIII-Helium-water mixture as working fluid. Plp/pTOT H electric LP HP TB Total mass Injected flow rate water mass flow rate % KW KW KW KG/SEC KG/SEC 0,55 32,81 1600,02 1810,55 -6002,86 5,514 1,201 0,56 32,82 1655,16 1755,13 -6003,53 5,513 1,198 0,57 32,82 1710,11 1700,97 -6004,26 5.512 1,195 0,58 32,82 1764,15 1647,69 -6004,85 5,511 1,193 0,59 32,80 1817,93 1595,60 -6005,43 5,510 1,191 0,60 32,79 1871,08 1544,12 -6005,98 5,509 1,188 Table VIII.5 - Sensitivity analysis on Plp/Ptot ■ Cycle with water injection as intercooling and aftercooling. Injected water temperatureT= 150 C 0,57 Figure VIII.6 - Electric efficiency vs Pip/pror- VIII-6 Appendix IX- Nitrogen-water mixture as working fluid. Appendix IX Nitrogen-water mixture as working fluid. Plp/Pt Elect LP HP TB MFR 0,65 30,83 2674,86 1068,92-6182,37 15,56 OT ric h 0,66 30,84 2711,68 1030,34 -6181,38 15,55 KW KW KW KG/S 0,67 30,85 2747,62 992,17-6180,36 15,54 0,50 30,25 2059,691745,94 -6199,7115,69 0,68 30,86 2783,48 954,81 -6179,38 15,53 0,51 30,31 2105,36 1694,30 -6198,45 15,68 0,69 30,87 2818,44 917,80 -6178,36 15,53 0,52 30,38 2149,98 1643,33 -6197,18 15,67 0,70 30,87 2853,50 88193 -6177,54 15,52 0,53 30,43 2194,19 1593,75 -6195,9215,66 0,71 30,88 2887,60 845,85 -6176,42 15,51 0,54 30,49 2237,50 1544,78 -6194,62 15,65 0,72 30,88 2921,78 810,80 -6175,50 15,50 0,55 30,54 2280,12 1497,15 -6193,42 15,64 0,73 30,88 2955,42 776,36 -6174,63 15,50 0,56 30,58 2322,35 1450,68 -6192,26 15,63 0,74 30,88 2988,81 742,35 -6173,73 15,49 0,57 30,62 2363,68 1404,92 -6191,0915,62 0,75 30,88 3021,18 708,54 -6172,73 15,48 0,58 30,65 2404,72 1360,39 -6189,9815,62 0,76 30,88 3053,84 675,54 -6171,85 15,48 0,59 30,69 2444,81 1316,29 -6188,82 15,61 0,77 30,88 3085,62 642,83 -6170,92 15,47 0,60 30,71 2484,65 1273,46 -6187,77 15,60 0,78 30,87 3117,41 610,76 -6170,07 15,46 0,61 30,74 2523,83 1231,16 -6186,69 15,59 0,79 30,86 3148,75 579,13 -6169,23 15,46 0,62 30,76 2562,29 1189,53 -6185,62 15,58 0,80 30,85 3180,00 547,94 -6168,39 15,45 0,63 30,78 2600,46 1148,73 -6184,53 15,57 0,64 30,81 2637,95 1108,38 -6183,41 15,57 Table IX.5-Sensitivity analysis on Plp/Ptot . Cycle with water injection as intercooling. Relative humidity 25 Figure iX.7-Eiectric efficiency vs (Ilp/Ptot at the design pressure ratio P=5.2. IX-1 Appendix IX- Nitrogen-water mixture as working fluid. P.WP Electri LP HP TB MFR 0,6 32,04 2387,98 1186,43 -6107,39 15,46 c TOT 0,61 32,04 2426,03 1146,81 -6106,26 15,45 h 0,62 32,05 2463,39 1107,86 -6105,16 15,44 0,5 31,80 1975,06 1629,92 -6119,73 15,561 0,63 32,05 2500,44 1069,69-6104,04 15,43 0,51 31,84 2019,40 1581,21 -6118,39 15,55 0,64 32,05 2536,81 1032,13 -6102,97 15,43 0,52 31,88 2062,90 1533,50 -6117,11 15,54 0,65 32,05 2572,86 995,30 -6101,89 15,42 0,53 31,91 2105,85 1486,94 -6115,8 15,53 0,66 32,0 2608,29 -6100,83 15,41 0,54 31,94 2147,96 1441,27 -6114,57 15,52 959,05 0,67 32,04 2643,40 923,47 -6099,7915,40 0,55 31,96 2189,56 1396,72 -6113,31 15,51 0,68 32,03 2677,92 888,44 0,56 31,98 2230,39 1352,92 -6112,11 15,50 -6098,76 15,39 0,69 32,02 2712,15 854,03 -6097,75 15,39 0,57 32.00 2270,73 1310,10 -6110,89 15,49 0,7 32,0 2745,81 820,14 -6096,74 15,38 0,58 32,02 2310,34 1268,04 -6109,7 15/8 0,75 31,93 2908,52 658,63 -6091,9215,34 0,59 32,03 2349,50 1226,88 -6108,54 15/7 Table IX.5 - Sensitivity analysis on Plp/Ptot- Cycle with water injection as intercooling. Relative humidity 60 %. Error! Not a valid link. Figure IX.8 - Electric efficiency vs Plp^Ptot at the design pressure ratio P=5.2. Plp ! 0 POUT LP HP TB MFF ,60 32,76 -2541,67 2363,43 1146,30 -6098,6515,40 Ptot [,61 32,76 -2541,40 2400,95 1107,86 -6097,46 15,39 0,50 32,64 -2532,20 1955,53 1576,22 -6111,1915,5 [,62 32,75 -2540,992437,93 1070,19 -6096,37 15,38 0,51 32,67 -2534,34 1999,331528,89 -6109,8115/1 ,63 32,75 -2540,33 2474,43 1033,20 -6095,21 15,37 0,52 32,69 -2536,22 2042,35 1482,68 -6108,50 15/' ,64 32,74 -2539,62 2510,37 996,88 -6094,12 15,36 0,53 32,71 -2537,73 2084,72 1437,48 -6107,18 15/ ,65 32,73 -2538,71 2545,89 961,16 -6093,01 15,35 0,54 32,73 -2539,00 2126,40 1393,25 -6105,9015,4, [,66 32,71 -2537,65 2580,93 926,11 -6091,9315,35 0,55 32,74 -2540,02 2167,42 1349,95 -6104,64 15,41 ,67 32,70 -2536,46 2615,51 891,66 -6090,8715,34 0,56 32,75 -2540,79 2207,81 1307,54 -6103,40 15/ I: ,68 32,68 -2535,14 2649,64 857,79 -6089,8215,33 0,57 32,76 -2541,33 2247,59 1266,00 -6102,17 15,4 t,69 32,66 -2533,71 2683,35 824,49 -6088,7915,32 0,58 32,76 -2541,66 2286,77 1225,29 -6100,9715/ ,70 32,64 -2532,16 2716,63 791,73 -6087,77 15,31 0,59 32,77 -2541,77 2325,38 1185,38 -6099,7815/ ,75 32,52 -2522,93 2877,10 635,60 -6082,88 15,27 Table IX.5 - Sensitivity analysis on j3Lp/j3Tot ■ Cycle with water injection as intercooling. Relative humidity 95 %. IX-2 Appendix IX- Nitrogen-water mixture as working fluid. Figure IX.9- Electric efficiency vs J3lp/Ptot IX-3 Appendix X-Sensitlvityanalysis on overall p at optimum Plp/Ptot- Appendix X Sensitivity analysis on overall pressure ratio at optimum Plp/Ptot. Furnace Efficiency = ®FGHX -+ @EBffX p Cycle Thermal Efficiency = ------Qfghx + Qebhx Net Electric Efficiency = —— Total Efficiency = Table X.1- Dry Cycle, no intercooling. p n r|Fornace r| Elettrica Termica % % % 4 33,60 90,55 30,12 3,9 33,84 90,32 30,26 3,8 34,10 90 30,38 3,7 34,32 89,63 30,46 3,6 34,56 89,66 30,67 3,5 34,78 88,97 30,64 3,4 35,00 88,55 30,69 3,3 35,22 88,12 30,73 3,2 35,41 87,69 30,74 3,1 35,58 87,18 30,71 3 35,76 86,94 30,78 2,9 35,90 86,13 30,61 2,8 36,01 85,44 30,46 2,7 36,08 83,03 29,66 2,6 36,09 80,50781 28,77 2,4 35,97 75 26,70 2,2 35,52 68,84115 24,20 2 34,54 65,44271 22,37 1,8 32,65 65,44271 21,15 X-1 Appendix X-SensitSvity analysis on overall p at optimum Plp/Ptot- Table X.2 - Dry Cycle, two level intercooling, two level postcooling. p Furnace Net Electric Cycle t| n T| % % % 2 65,43 25,39 39,19 2,2 69,60 27,81 40,36 2,4 75,79 30,75 40,98 2,6 81,29 33,21 41,27 2,7 83,83 34.28 41,31 2,8 86,25 35,27 41,31 2,9 86,80 35,47 41,27 3,0 86,96 35,46 41,18 3,1 87,50 35,60 41,09 3,2 87,93 35,66 40,96 3,4 88,83 35,78 40,68 Table X.3 - Water injection as intercooling, relative humidity after injection 0=0.95. Plot Electric n Total ti Furnace n Cycle ti 2,8 28,86 109,31 77,36 37,68 2,9 29,61 109,26 79,38 37,67 3,0 30,30 109,23 81,31 37,64 3,1 30,92 108,62 83,15 37,57 3,2 31,50 106,88 84,89 37,48 3,3 32,03 105,14 86,56 37,38 3,4 31,94 104,40 86,61 37,25 Table X.4 - Water injection as intercooling, relative humidity after injection 0=0.95. 3tot Electric ti Total ti Furnace ti Cycle ri 3,5 29,90 104,00 87,06 34,69 3,4 29,91 104,38 86,61 34,88 3,3 30,02 105,25 86,50 35,06 3,1 29,07 108,66 83,07 35,34 3,0 28,52 109,20 81,24 35,46 2,9 27,71 108,70 78,75 35,54 2,8 27,25 109,28 77,29 35,61 X-2 Appendix X-Sensitivityanalysis on overall p at optimum Plp/PtqT' Table X.5 - Water injection as intercooling, relative humidity after injection 0=0.25. Ptot Electric r\ Total r| Furnace Cycle ti 3,5 29,90 104,00 87,06 34,69 3,4 29,91 104,38 86,61 34,88 3,3 30,02 105,25 86,50 35,06 3,1 29,07 108,66 83,07 35,34 3,0 28,52 109,20 81,24 35,46 2,9 27,71 108,70 78,75 35,54 2,8 27,25 109,28 77,29 35,61 Table X.6 - Water injection as intercooling, relative humidity after injection 0=0.60. PtOt Electric r] Total t) Furnace r| Cycle n 3,4 31,21 104,29 86,55 36,43 3,3 31,34 105,25 86,54 36,58 3,2 30,83 106,90 84,86 36,70 3,1 30,28 108,64 83,11 36,81 3,0 29,68 109,22 81,28 36,89 2,9 29,02 109,25 79,35 36,94 2,8 28,30 109,28 77,34 36,97 Table X.7-injection 0=0.60/0.95. Injected water temperature 7=65 °C. P Furnace r| Cycle Electric r\ Total r) n 3,8 87,97 37,70 32,84 103,28 3,6 87,33 37,89 32,76 103,69 3,4 86,74 38,08 32,70 104,62 3,3 86,28 38,14 32,58 105,54 3,2 84,63 38,18 31,99 107,17 3,1 82,89 38,22 31,37 108,89 3 81,10 38,22 30,69 109,25 2,9 79,20 38,20 29,95 109,29 2,8 77,22 38,17 29,18 109,33 2,7 75,11 38,10 28,33 104,97 2,6 72,91 37,96 27,40 104,97 2,4 68,12 37,55 25,32 104,94 2,2 65,60 36,87 23,94 105,52 X-3 Appendix X-Sensitivity analysis on overall ft at optimum Plp/Ptot- Table X.8-Water injection as intercooling and aftercooling. Relative humidity after injection 0=0.60/0.95. Injected water temperature T=150 °C. p Furnace % Cycle Electric rj Total rj T| 3,8 87,80 38,16 33,17 106,67 3,6 87,20 38,33 33,10 107,38 3,4 86,349 38,49 32,90 108,06 3,3 85,97 38,54 32,80 106,32 3,2 84,33 38,58 32,21 106,57 3,1 82,61 38,59 31,56 107,06 3 80,81 38,58 30,87 106,04 Table X.9: Water injection as intercooling and aftercooling. Relative humidity after injection 0=0.95/0.95. Injected water temperature 7=65 °C. (3 Furnace Cycle Electric Total 3,8 87,97 37,70 32,84 103,28 3,6 87,339 37,89 32,76 103,69 3,4 86,74 38,08 32,70 104,62 3,3 86,28 38,14 32,58 105,54 3,2 84,63 38,184 31,99 107,179 3,1 82,899 38,22 31,37 108,89 3 81,102 38,22 30,69 109,25 2,9 79,20 38,20 29,95 109,29 2,8 77,22 38,17 29,18 109,33 2,7 75,11 38,10 28,33 104,97 2,6 72,91 37,96 27,40 104,97 2,4 68,12 37,55 25,32 104,949 2,2 65,60 36,87 23,94 105,529 Table X.10 - Water injection as intercooling and aftercooling. Relative humidity after injection 0=0.95/0.95. Injected water temperature 7=65 °C. Base pressure P=5 bar. Electric Total Cycle Furnace 3,4 32,329 103,16 3,3 32,27 103,589 3,2 32,187 104,04 37,719 86,19 3,1 32,29 105,2511 37,70 86,49 3 31,71 109,199 37,85 84,62 2,9 30,98 109,23 37,869 82,64 2,8 30,19 109,27 37,84 80,58 2,7 29,32 109,309 37,78 78,40 X-4 Appendix X-Sensitivityanalysis on overall p at optimum Plp/Ptqt- Nitrogen and nitrogen water as working fluid Table X.11: Dry Cycle, one level intercooling, one level postcooling. p Furnace Cycle Electric Total 5,4 86,96 37,73 32,48 104,23 5,2 86,53 37,88 32,45 104,61 5 86,67 38,06 32,66 105,45 4,9 86,20 38,13 32,54 105,51 4,8 85,37 38,21 32,30 106,08 4,7 84,50 38,28 32,03 106,96 4,6 83,61 38,35 31,74 107,8458 4,5 82,69 38,41 31,45 108,77 4,4 81,75 38,46 31,12 110,31 4,2 79,78 38,56 30,45 110,35 4 77,69 38,62 29,71 110,38 Table X.12 - Water injection as intercooling, relative humidity after injection 0=0.25., P Electric Total Cycle Furnace 5,5 30,87 104,15 35,98 86,67 5,4 30,89 104,34 36,091 86,45 5,3 30,87 104,21 36,19 86,17 5,2 30,69 104,95 36,28 85,43 5,1 30,50 105,68 36,38 84,68 5,0 30,30 106,46 36,47 83,91 4,9 30,09 107,24 36,57 83,12 4,8 29,87 108,05 36,65 82,30 4,7 29,64 108,50 36,74 81,47 Table X.13 - Water injection as intercooling, relative humidity after injection P Electric Total Cycle Furnace 5,5 32,22 104,14 37,53 86,73 5,4 32,25 104,34 37,62 86,59 5,3 32,21 104,48 37,71 86,27 5,2 32,05 104,74 37,79 85,66 5,1 31,84 105,48 37,88 84,90 5,0 31,73 106,44 37,97 84,407 4,9 31,38 107,037 38,04 83,34 4,8 31,14 107,84 38,11 82,53 4,7 30,88 108,51 38,18 81,69 X-5 Appendix X-Sensitivity analysis on overall ft at optimum Plp/Ptot- Table X.14 - Water injection as intercooling, relative humidity after injection p Electric Total Cycle Furnace 5,4 32,95 104,32 38,43 86,62 5,3 32,92 104,46 38,51 86,33 5,2 32,76 104,66 38,59 85,74 5,1 32,54 105,40 38,67 84,99 5,0 32,30 106,17 38,74 84,22 4,9 32,06 106,96 38,81 83,42 4,8 31,80 107,77 38,88 82,61 4,7 31,53 108,52 38,95 81,78 Table X.15 - Water injection as intercooling and aftercooling. Relative humidity after injection 4=0.95/0.95. Injected water temperature 7=65 °C. Furnace Cycle Electric Total 5,6 87,1 40,09 34,57 103,88 5,4 86,61 40,2 34,47 104,16 5,3 86,43 40,24 34,43 104,2 5,2 86,13 40,29 34,35 104,47 5,1 85,43 40,31 34,09 105 5 84,66 40,34 33,81 105,74 4,9 83,89 40,37 33,53 106,48 4,8 83,06 40,43 33.24 107,36 4,7 82,22 40,44 32,92 108,19 4,6 81,36 40,47 32,6 108,56 Table X.16- Injected water as intercooling and aftercooling, two level postcooling. Injected water temperature T=20 C P Electric Furnace Cycle Total 5,1 38,28 73,82 44,66 86,58 5 38,24 74,23 44,71 86,40 4,9 38,22 74,67 44,74 86,27 4,8 37,88 75,53 45,53 84,04 4,7 37,52 76,80 44,80 84,60 4,6 37,16 78,09 44,82 83,73 X-6 Appendix Xl-Turbomachinery work. Appendix XI Turbomachinerywork. turbine output work dry 6470 One stage intercooling; relative humidity 25 % 6234 One stage intercooling; relative humidity 60 % 6188 One stage intercooling; relative humidity 95 % 6166 2JC_AC; relative humidities 60% -95 %; 6027 injected water temperature 65 C 2_IC_AC; relative humidities 60% -95 %; 6003 injected water temperature 150 C 2_IC_AC; relative humidities 95% -95 %; 6031 injected water temperature 65 C Table Xl.1-Turbine work. LP compressor work dry One stage intercooling; relative humidity 25 % 2665 One stage intercooling; relative humidity 60 % 2276 One stage intercooling; relative humidity 95 % 2053 2_IC_AC; relative humidities 60% -95 %; 1622 injected water temperature 65 C 2_iC_AC; relative humidities 60% -95 %; 1655 injected water temperature 150 C 2JC_AC; relative humidities 95% -95 %; injected water temperature 65 C Table XI.2- LP compressor work. HP compressor work dry One stage intercooling; relative humidity 25 % 1124 One stage intercooling; relative humidity 60 % 1390 One stage intercooling; relative humidity 95 % 1552 2_lC_AC; relative humidities 60% -95 %; 1830 injected water temperature 65 C 2_IC_AC; relative humidities 60% -95 %; 1755 injected water temperature 150 C 2_IC_AC; relative humidities 95% -95 %; injected water temperature 65 C Table Xl.2-.HP compressor work. XI-1 Appendix Xll-Sensitivityanalysis on turbomachinery r}p0|. Appendix XII Sensitivity analysis on turbomachinery r|poI. t] compressor = n t| compressor T\ 0,85 electric% = 0,88 electric% P P 3 29,92 3 30,71 3,1 30,58 3,1 31,39 3,2 31,18 3,2 32,01 3,3 31,749 3,3 32,6 3,4 31,77 3,4 32,64 r| compressor n r| compressor n = 0,86 electric% = 0,89 . electric% P P 3 30,19 3 30,95 3,1 30,85 3,1 31,64 3,2 31,47 3,2 32,28 3,3 32,04 3,3 32,87 3,4 32,06 3,4 32,869 r| compressor n r| compressor n = 0,87 electric% = 0,90 electric% P P 3 30,45 3 31,2 3,1 31,12 3,1 31,89 3,2 31.74 3,2 32,54 3,3 32,32 3,3 33,14 3,4 32,35 3,4 33,138 Table XII-1: Electric efficiency vs. LP compressor politropic efficiency. XII-1 Appendix Xll-Sensitivityanalysis on turbomachinery T|poi r| compressor = n ri compressor ,89 0,87 electric% 3 3 3 30,95 3 30,43 3,1 31,63 3,1 31,1 3,2 32,27 3,2 31,72 3,3 32,87 3,3 32,3 3,4 32,89 3,4 32,32 r| compressor = T| t] compressor n 0,90 electric% 0,88 electric% 3 3 3 31,2 3 30,69 3,1 31,84 3,1 31,37 3,2 32,54 3,2 32 3,3 33,14 3,3 32,58 3,4 33,17 3,4 32,61 Table XII-2: Electric efficiency vs. HP compressor politropic efficiency. Turbine n Turbine n efficiency= electric efficiency= electric 0,85 % 0,88 % 3 3 3 27,74 3 29,82 3,1 28,35 3,1 30,2 3,2 28,92 3,2 31,1 3,3 29,45 3,3 31,67 3,4 29,96 3,4 32,11 Turbine T] Turbine n efficiency= electric efficiency=0,89 electric 0,86 % 3 % 3 3 30,29 3 28,22 3,1 30,96 3,1 28,85 3,2 31,8 3,2 29,66 3,3 32,4 3,3 30,2 3,4 32,8 3,4 30,71 Turbine T| Turbine n efficiency=0,90 electric efficiency= electric % 0,87 % 3 3 3 30,97 3 28,91 3,1 31,66 3,1 29,56 3,2 32,53 3,2 30,37 3,3 33,16 3,3 30,93 3,4 33,13 3,4 31,46 Table XII-3: Electric efficiency vs. turbine politropic efficiency. XII-2 Appendix Xlll-Flue Gas Heat Exchanger sizing. Appendix XIII Flue Gas Heat Exchanger Sizing Helium and helium-water mixture as working fluid. • Dry cycle one level intercooling, one level postcooling. Mass Flow Rates (kg/s): (6) Side 2 (Exit)- .322 (1) Side 1 (outside tubes) Viscosity (kg/m-s): 4.3398 (7) Side 1-.000047 (2) Side 2 (inside tubes)-3.8534 (8) Side 2 -.000039 Specific Heat (J/kg-K): Fluid Properties (9) Side 1-1400 Fluid Density (kg/m3): (10) Side 2-5193 (3) Side 1 (Entrance) - Prandtl Number (dimensionless): .343244 (11) Side 1-.7862 (4) Side 1 (Exit)-.3892 (12) Side 2-.672 (5) Side 2 (Entrance) -.3552 The terminal temperatures are: ^ =850°C Q = 1553 W e = 0.69 Cmin/Cmax = 0.304 Ntu = 1.43. The dimensions are: Volume = 1.967 cu m Flue gases flow length = 0.8 m Helium flow length = 1.7 m Non-flow length = 1.4 m XIII-1 Appendix Xlll-Flue Gas Heat Exchanger sizing. outside inside heat transfer coefficients 120.8 365.6 fW/K-m2] overall heat transfer 78.7 coefficient, u1|W/K-m2] mass velocities [kg/s-m 2] 5.366 15.186 Reynolds numbers 2721.9 7787.5 resistance ratio, 2.42 side1/side2 percent pressure drop 0.34 0.23 Table XII. 1- Dry cycle one level intercooling, one level postcooling. for a total of 37 transverse rows and 22 vertical rows. Total heat transfer area = At*Nt =108 m2 • Wet cycle with water injection as intercooling. Mass Flow Rates (kg/s): Viscosity (kg/m-s): (1) Side 1 (outside tubes) -4.3398 (7) Side 1-.000047 (2) Side 2 (inside tubes)-5.2295 (8) Side 2-.000039 Specific Heat (J/kg-K): Fluid Properties (9) Side 1-1400 Fluid Density (kg/m3): (10) Side 2-3800 (3) Side 1 (Entrance )-.343244 Prandtl Number (4) Side 1 (Exit)- .3957 (dimensionless): (5) Side 2 (Entrance) -.653 (11) Side 1-.7862 (6) Side 2 (Exit) -.578 (12) Side 2-.69 The terminal temperatures are: ?L=850°C e = 0.69 Cmin/Cmax = 0.31 =572°C Ntu — 1.43. ?V,=468°C Volume = 2.086 cu m 7^ =550°C Flue gases flow length = 0.886 m Q=-1615 W Helium flow length = 1.677 m Design dimension: Non- flow length =1.404 m XIII-2 Appendix XIII-Flue Gas Heat Exchanger sizing. outside inside heat transfer coefficients 118.1 316.1 fW/K-m2l overall heat transfer 74.5 coefficient, u1[W/K-m2] mass velocities [kg/s-m 2] 5.522 18.773 Reynolds numbers 3090.1 8691.0 resistance ratio, 2.14 side1/side2 percent pressure drop 0.38 0.16 Table XII. 2- Wet cycle with water injection as intercooling. for a total of 37 transverse rows and 24 vertical rows. Total heat transfer area = A*Nt = 118 m2 • Wet cycle with water injection as intercooling and after cooling, and one stage postcooling. Mass Flow Rates (kg/s): (6) Side 2 (Exit) -.618 (1) Side 1 (outside tubes) - Viscosity (kg/m-s): 4.3398 (7) Side 1 -.0000426 (2) Side 2 (inside tubes)- (8) Side 2 -.000042 5.4703 Specific Heat (J/kg-K): Fluid Properties (9) Side 1-1400 Fluid Density (kg/m3): (10) Side 2-3620 (3) Side 1 (Entrance) - Prandtl Number (dimensionless): .343244 (11) Side 1-.7862 (4) Side 1 (Exit)-.3936 (12) Side 2-.69 (5) Side 2 (Entrance)-.? Q =1589 W Design dimension: = 850°C s = 0.7 Cmin/Cmax = 0.31 ^ =580°C Ntu = 1.43. TV =470°C Volume =2.112 cu m =S50°C Flue gases flow length = 0.892 m The transferred heat is: XI11-3 Appendix Xlll-Flue Gas Heat Exchanger sizing. Helium-Water vapour flow Non-flow length =1.406 m length = 1.684 m outside) inside) heat transfer coefficients [W/K-m2! 117.7 305.9 overall heat transfer coefficient, 73.6 u1 [W/K-m2! mass velocities [kg/s-m 2! 5.491 19.473 Reynolds numbers 3073.2 9273.0 resistance ratio, side1/side2 2.08 percent pressure drop 0.38 0.16 Table XII. 3- Wet cycle with water injection as intercooling and after cooling, and one stage postcooling for a total of 37 transverse rows and 25 vertical rows. Total heat transfer area = At*Nt = 123 m2 Wet cycle with water injection as intercooling and after cooling, and one stage postcooling. Helium as working fluid. Base pressure P=5 bar Mass Flow Rates (kg/s): (7) Side 1 -.0000426 (1) Side 1 (outside tubes)- 4.3398 (8) Side 2- .0000415 (2) Side 2 (inside tubes)- 4.8498 Specific Heat (J/kg-K): Fluid Density (kg/m3): (9) Side 1-1400 (3) Side 1 (Entrance)-.343244 (10) Side 2- 4084 (4) Side 1 (Exit)- .3938 Prandtl Number (5) Side 2 (Entrance)-1 .378 (dimensionless): (6) Side 2 (Exit)-1.2439 (11) Side 1- .7862 Viscosity (kg/m-s): (12) Side 2-.6S6 Th in = 850°C The transferred heat is: Th,out = 579°C 2 = 1592 W 7^=470°C ^ =550°C design dimensions: XI11-4 Appendix Xlll-Flue Gas Heat Exchanger sizing. volume = 2.128 cum fluid 1 (outside) flow length = 0.897 m fluid 2 (inside) flow length = 1.761 m non-flow length = 1.347 m outside) inside) heat transfer coefficients fW/K-m2! 117.6 325.6 overall heat transfer coefficient, 74.9 u1[W/K-m2l mass velocities [kg/s-m 2] 5.480 17.916 Reynolds numbers 3066.7 8634.2 resistance ratio, side1/side2 2.22 percent pressure drop 0.38 0.03 Table XII. 4- Wet cycle with water injection as intercooling and after cooling, and one stage postcooling. Helium as working fluid. Base pressure P-5 bar Xlll-5 Appendix Xlll-Flue Gas Heat Exchanger sizing. Nitrogen and nitrogen-water mixture as working fluid. • Dry cycle one level intercooling, one level postcooling. Mass Flow Rates (kg/s): (6) Side 2 (Exit)-3.8 (1) Side 1 (outside tubes)- Viscosity (kg/m-s): 4.33 (7) Side 1-.000042 (2) Side 2 (inside tubes)- (8) Side 2- .000035 17.22 Specific Heat (J/kg-K): (9) Side 1-1359 Fluid Properties (10) Side 2-1118 Fluid Density (kg/m3): Prandtl Number (dimensionless): (3) Side 1 (Entrance)-.34 (11) Side 1-.784 (4) Side 1 (Exit) -.39 (12) Side 2-.7065 (5) Side 2 (Entrance)-4.28 The terminal temperatures are: Cmin/Cmax = 0.31 = 850°C Ntu = 1.48. = 580°C 7V,=467°C =550«C Q = -1596 s = 0.7 Working fluid flow length = 1.699 volume = 2.507 m3 m flue gases flow length = 1.054 m non-flow length = 1.399 m (outside) (inside) heat transfer coefficients [W/K-m2! 113.2 182.8 overall heat transfer coefficient, 60.0 u1 [W/K-m2! mass velocities [kg/s-m 2! 5.456 52.120 Reynolds numbers 3097.1 29783.1 resistance ratio, sidei/side 2 1.29 percent pressure drop 0.45 0.11 Table XII. 5- Dry cycle one level intercooling , one level postcooling. XIII-6 Appendix Xlil-Flue Gas Heat Exchanger sizing. for a total of 37 transverse rows and 28vertical rows. • Wet cycle with water injection as intercooling, one stage postcooling. Mass Flow Rates (kg/s): (6) Side 2 (Exit)- 3.85 (1) Side 1 (outside tubes)- Viscosity (kg/m-s): 4.339 (7) Side 1-4.273E-05 (2) Side 2 (inside tubes)- (8) Side 2- .0000368 15.27 Specific Heat (J/kg-K): (9) Side 1- 1358 Fluid Properties (10) Side 2-1258 Fluid Density (kg/m3): Prandtl Number (dimensionless): (3) Side 1 (Entrance) -.3431 (11) Side 1- .787 (4) Side 1 (Exit)- .393 (12) Side 2-.778 (5) Side 2 (Entrance)- 4.34 The terminal temperatures are: s = 0.701 ^ =850°C Cmin/Cmax = 0.307 = 572*C Ntu — 1.49 7L»=464°C ^ =550°C The transferred heat is: Q=1643 W Flue gases flow length = 1.1 m non-flow length = 1.4 m Working fluid flow length = 1.7 m outside inside heat transfer coefficients [W/K-rn^] 114.0 179.0 overall heat transfer coefficient, u1 [W/K-m2] 59.7 mass velocities [kg/s-nn*| 5.462 44.305 Reynolds numbers 3042.1 24025.5 resistance ratio, side 1/side 2 1.26 percent pressure drop 0.47 0.07 Table XII. 6- Wet cycle with water injection as intercooling, one stage postcooling. XIII-7 Appendix Xlll-Flue Gas Heat Exchanger sizing. for a total of 37 transverse rows and 30 vertical rows. • Wet cycle with water injection as intercooling and aftercooling, one stage postcooling. Mass Flow Rates (kg/s): (6) Side 2 (Exit)- 3.809 (1) Side 1 (outside tubes)- Viscosity (kg/m-s): 4.339 (7) Side 1-4.276E-05 (2) Side 2 (inside tubes)- (8) Side 2- .0000358 15.18 Specific Heat (J/kg-K): (9) Side 1-1359 Fluid Properties (10) Side 2-1261 Fluid Density (kg/m3): Prandtl Number (dimensionless): (3) Side 1 (Entrance)- .3431 (11) Side 1- .787 (4) Side 1 (Exit)-3930 (12) Side 2- .781 (5) Side 2 (Entrance)-4.23 The terminal temperatures are: = 850°C e = 0.699 Cmin/Cmax = 0.308 ^ =578°C Ntu = 1.48 TV =466°C ^ =S50°C flue gases flow length = 1.106 m The transferred heat is: Working fluid flow length = 1.699 m Q= 1610 KJ/s non-flow length = 1.403 m XIII-8 Appendix Xlll-Flue Gas Heat Exchanger sizing. outside inside heat transfer coefficients 114.1 177.2 W/K-m2 overall heat transfer coefficient, u1 59.5 W/K-m2 mass velocities 5.462 44.044 kg/s-m 2 reynolds numbers 3040.0 24551.0 resistance ratio, side 1/side 2 1.24 percent pressure drop 0.47 0.08 Table XII. 7- Wet cycle with water injection as intercooling and aftercooling, one stage postcooling. for a total of 37 transverse rows and 31 vertical rows. XIII-9 Appendix Xlll-Flue Gas Heat Exchanger sizing. • Wet cycle with water injection as intercooling and aftercooling, one stage postcooling.. Base pressure P=5 bar The terminal temperatures are: s = 0.696 Cmin/Cmax - 0.308 = 850°C Ntu = 1.46 = 580°c ^ = 467 °C flue gases flow length = 1.08 m ^ =550°C Working fluid flow length = 1.7 m The transferred heat is: non-flow length = 1.4 m Q= 1610 KJ/s outside inside heat transfer coefficients 114.1 180.0 W/K-m2 overall heat transfer coefficient, u1 59.8 W/K-m2 mass velocities 5.462 47.224 kg/s-m 2 reynolds numbers 3040.0 26323.5 resistance ratio, side 1/side 2 1.26 percent pressure drop 0.46 0.02 Table XII. 8- Wet cycle with water injection as intercooling and aftercooling, one stage postcooling.. Base pressure P=5 bar for a total of 37 transverse rows and 29 vertical rows. XIII-10 Appendix XIV- Recuperator sizing. Appendix XIV Recuperator sizing. Helium as working fluid. • Dry cycle with intercooling and one stage postcooling. Mass Flow Rates (kg/s): (1) Side 1-3.8513 Viscosity (kg/m-s): (2) Side 2- 3.8513 (7) Side. 1 - .0000297 (8) Side 2 - 3.847E-05 Fluid Properties Specific Heat (J/kg-K): Fluid Density (kg/m3): (9) Side 1-5193 (3) Side 1 (Entrance) - .6273 (10) Side 2- 5193 (4) Side 1 (Exit)- .3552 Prandtl Number (dimensionless): (5) Side 2 (Entrance) - .1355 (11) Side 1 - .6723 (6) Side 2 (Exit) - .221 (12) Side 2- .672 The cold/hot side inlet/outlet temperatures are: W =156 °C = iso °c Tcold,out - 474 °C Q= 6372 W AT,,, = 23.84°C 7L, =498°C The design dimensions needed to fulfil the design performance are: Volume = 3.056 m3 Fluid 1 (hot side) flow length = 1.238 m Fluid 2 (cold side) flow length = 0.679 m Non-flow length = 3.635 m XIV-1 Appendix XIV- Recuperator sizing. side 1 side 2 heat transfer coefficients 1367.1 2200.3 fW/K-m2! fin effectiveness 0.336 0.266 overall heat transfer coefficient, u1 338.9 W/K-m2! mass velocities 3.869 2.124 fkg/s-m 2] Reynolds numbers 194.3 82.3 resistance ratio, side 1/side 2 1.39 percent pressure drop 1.50 4.00 Table XIV. 1- Dry cycle with intercooling and one stage postcooling. The number of plates is Npiates = L3/(tp + b) = 716; Plate heat transfer area = 602.6 • Dry cycle two stage intercooling, two stage postcooling. Helium as working fluid. Mass Flow Rates (kg/s): (7) Side 1 - 0.0000297 (1) Side 1-3.87 (8) Side 2 - 0 3.847E-05 (2) Side 2 - 3.87 Specific Heat (J/kg-K): (9) Side 1-5193 Fluid Properties (10) Side 2-5193 Fluid Density (kg/m3): Prandtl Number (dimensionless): (3) Side 1 (Entrance) - 0 .699 (11) Side 1 - .6723 (4) Side 1 (Exit) - 0.356 (12) Side 2 - .672 (5) Side 2 (Entrance) - 0.1355 • Dry cycle two stage (6) Side 2 (Exit) - 0.243 intercooling, two stage Viscosity (kg/m-s): postcooling. The cold/hot side inlet/outlet temperatures are: W = 111 "C n«.,= 498 °C W, =470°C 138 “C XIV-2 Appendix XIV- Recuperator sizing. Q =7220 kJ/s A Tlm =27.01 °C Design dimensions: volume = 3.079 m3 fluid 1 flow length = 1.263 m fluid 2 flow length = 0.692 m non-flow length = 3.521 m side 1 side 2 heat transfer coefficients 1362.3 2190.7 [W/K-m2] fin effectiveness 0.336 0.266 overall heat transfer coefficient, u1 338.0 W/K-m2] mass velocities 3.938 2.159 [kg/s-m 2] Reynolds numbers 197.7 83.7 resistance ratio, side 1/side 2 1.39 percent pressure drop 1.50 4.00 Table XIV. 2- Dry cycle two stage intercooling, two stage postcooling. Helium as working fluid. The number of plates is N plates —639, Total plate area = 558.5 m2 • • Wet cycle with water injection as intercooling and one stage postcooling. Helium/water vapour mixture as working fluid. Mass Flow Rates (kg/s): (4) Side 1 (Exit) - .653 (1) Side 1-5.22 (5) Side 2 (Entrance) - .2119 (2) Side 2- 5.22 (6) Side 2 (Exit) - .3244 Viscosity (kg/m-s): Fluid Properties (7) Side 1 - .0000283 Fluid Density (kg/m3): (8) Side 2-.0000415 (3) Side 1 (Entrance) -1.07 Specific Heat (J/kg-K): XIV-3 Appendix XIV- Recuperatorsizing. (9) Side 1 - 3740 (11) Side 1 - .708 (10) Side 2 - 3760 (12) Side 2 - .69 Prandtl Number (dimensionless): The cold/hot side inlet/outlet temperatures are: TaUt. =184 °C = 469 °C ATm, = 21.69 °C = 498 °C Q = 5586 KJ/S The resulting dimensions are: Fluid 1 flow length = 1.615 m Fluid 2 flow length = 0.785 m Volume = 3.899 m3 Non-flow length = 3.073 m side 1 side 2 heat transfer coefficients 856.6 1630.6 fW/K-m2! fin effectiveness 0.419 0.308 overall heat transfer coefficient, u1 259.3 W/K-m2! mass velocities 5.364 2.609 fkg/s-m 2l Reynolds numbers 282.6 93.7 resistance ratio, side 1/side 2 1.56 percent pressure drop 1.51 4.01 Table XIV. 3- Wet cycle with water injection as intercooling and one stage postcooling. Helium/water vapour mixture as working fluid. The number of plates is Npiates — 559, Total plate area = 708.3 m2 • Wet cycle with water injection as intercooling and aftercooling and 1 stage postcooling. Helium/water vapour mixture as working fluid. Mass Flow Rates (kg/s): (2) Side 2- 5.46 (1) Side 1-5.46 XIV-4 Appendix XIV- Recuperatorsizing. Fluid Properties (8) Side 2 - .0000415 Fluid Density (kg/m3): Specific Heat (J/kg-K): (3) Side 1 (Entrance) -1.387 (9) Side 1 - 3550 (4) Side 1 (Exit) - .7 (10) Side 2 - 3555 (5) Side 2 (Entrance) -.225 Prandtl Number (dimei (6) Side 2 (Exit) - .4 (11) Side 1 - .7 Viscosity (kg/m-s): (12) Side 2- .69 (7) Side 1 - .0000246 The cold/hot side inlet/outlet temperatures are: =107 °c r^„=470°c ATml = 27.62 °C r.„> = 498 °c Q = 7019 KJ/s Design dimension: Fluid 2 flow length = 0.852 m Volume = 4.265 cu m Non-Flow length = 2.696 m Fluid 1 Flow Length = 1.858 m side 1 side 2 heat transfer coefficients 706.2 1526.8 rW/K-m2] fin effectiveness 0.457 0.318 overall heat transfer coefficient, u1 235.3 W/K-m2! mass velocities 5.899 2.705 fkq/s-m2! Reynolds numbers 357.6 97.2 resistance ratio, side 1/side 2 1.70 percent pressure drop 1.50 4.01 Table XIV. 4- Wet cycle with water injection as intercoofing and aftercooiing and 1 stage postcooling. Helium/water vapour mixture as working fluid. The number of plates is Npiates — 490,’ Total plate area =776.14 XIV-5 Appendix XIV- Recuperatorsizing. • Wet cycle with water injection as intercooling and aftercooling and 1 stage postcooling. Base pressure P=5 bar Mass Flow Rates (kg/s): Specific Heat (J/kg-K): (1) Side 1 - 4.8498 (9) Side 1 - 4035 (2) Side 2 - 4.8498 (10) Side 2 - 4041 Prandtl Number (dimensionless): Fluid Density (kg/m3): (11) Side 1-.69 (3) Side 1 (Entrance) - 2.66 (12) Side 2-.694 (4) Side 1 (Exit) - 1.378 (5) Side 2 (Entrance) -.4729 design dimensions: (6) Side 2 (Exit) - .836 volume = 3.928 cu m Viscosity (kg/m-s): fluid 1 flow length = 3.570 m (7) Side 1 - .000035 fluid 2 flow length = 2.164 m (8) Side 2- .000033 non-flow length = 0.508 m side 1 side 2 heat transfer coefficients 1180.7 1089.0 [W/K-m2] fin effectiveness 0.360 0.374 overall heat transfer coefficient, u1 257.9 W/K-m2] mass velocities 10.931 6.627 [kg/s-m 2] Reynolds numbers 465.7 299.5 resistance ratio, side 1/side 2 0.95 percent pressure drop 1.50 4.05 Table XIV. 5- Wet cycle with water injection as intercooling and aftercooling and 1 stage postcooling. Base pressure P=5 bar XIV-6 Appendix XIV- Recuperator sizing. Nitrogen. • Dry cycle one level intercooling, one level postcooling. Nitrogen as working fluid. =163 °c 7L^=186°C %L,^=468°C ATm,=23.18°C 7L,„=491°C Q =5647 kJ/s Mass Flow Rates (kg/s): Viscosity (kg/m-s): (1) Side 1 (cold) -17.22 (7) Side 1 - .0000287 (2) Side 2 (hot) -17.22 (8) Side 2 - .0000295 Specific Heat (J/kg-K): Fluid Properties (9) Side 1-1081 Fluid Density (kg/m3): (10) Side 2-1082 (3) Side 1 (Entrance) - 7.38 Prandtl Number (dimensionless): (4) Side 1 (Exit) - 4.28 (11) Side 1 - .707 (5) Side 2 (Entrance) - .955 (12) Side 2- .706 (6) Side 2 (Exit)-1.52 Fluid 1 flow length = 3.954 m Design dimension: Fluid 2 flow length = 1.638 m Non-flow length = 1.499 m Volume = 9.706 cu m side 1 (cold) side 2 (hot) heat transfer coefficients 321.7 256.8 fW/K-m2] fin effectiveness 0.621 0.668 overall heat transfer coefficient, ui 99.3 W/K-m2] mass velocities 17.401 7.209 [kg/s-m 2] Reynolds numbers 904.0 364.4 resistance ratio, side 1/side 2 0.84 percent pressure drop 1.50 3.98 Table XIV. 6- Dry cycle one level intercooling, one level postcooling. Nitrogen as working fluid. XIV-7 Appendix XIV- Recuperator sizing. The number of plates is Nplates =;272 Total plate area = 1761 m2 • Wet cycle with one water injection as intercooling and one level postcooling. Nitrogen - water vapourmixture as working fluid. The relative humidity after the intercooling is =198 °c =220°C 7^=467*0 ATmr20.82°C r^=487°C Q = 4948 kJ/s Mass Flow Rates (kg/s): (7) Side 1 - .0000296 (1) Side 1 - 15.56 (8) Side 2 - .0000303 (2) Side 2- 15.56 Specific Heat (J/kg-K): Fluid Density (kg/m3): (9) Side 1 - 1185 (3) Side 1 (Entrance) - 6.99 (10) Side 2- 1190 (4) Side 1 (Exit)- 4.38 Prandtl Number (dimensionless): (5) Side 2 (Entrance) - .9 (11) Side 1 - .77 (6) Side 2 (Exit)- 1.33 (12) Side 2- .772 Viscosity (kg/m-s): Volume = 9.213 cu m Fluid 2 Flow length = 1.601 m Fluid 1 Flow length = 4.167 m Non- Flow length = 1.381 m Appendix XIV- Recuperator sizing. side 1 side 2 heat transfer coefficients 338.8 273.1 [W/K-m2] fin effectiveness 0.611 0.655 overall heat transfer coefficient, u1 103 6 W/K-m2l mass velocities 17.457 6.705 [kg/s-m 2] Reynolds numbers 879.4 330.0 resistance ratio, side 1/side 2 0.85 percent pressure drop 1.50 3.98 Table XIV. 7- Wet cycle with one water injection as intercooling and one level postcooling. Nitrogen - water vapour mixture as working fluid. The number of plates is Nplates ",251.6 Total plate area = 1678.7 m2 Wet cycle with water injection as intercooling and aftercooling, one level postcooling. Nitrogen - water vapour mixture as working fluid. Mass Flow Rates (kg/s): Viscosity (kg/m-s): (1) Side 1-15.1831 (7) Side 1 - .000028 (2) Side 2-15.1831 (8) Side 2 - .000029 Specific Heat (J/kg-K): Fluid Properties (9) Side 1 - 1207 Fluid Density (kg/m3): (10) Side 2- 1213 (3) Side 1 (Entrance) - 8.03 Prandtl Number (dimensionless): (4) Side 1 (Exit) -4.237 (11) Side 1 - .794 (5) Side 2 (Entrance) - .8844 (12) Side 2- .791 (6) Side 2 (Exit) - 1.534 The terminal temperatures on the cold and hot side are: Cw, = 123 -C 7Lm,=151°C = 467 °C Q = 6284 r„,>=493°C ATm, = 26.86 °C Design dimension: Volume = 9.406 m3 X1V-9 Appendix XIV- Recuperator sizing. Fluid 1 Flow Length = 4.351 m Non- Flow Length = 1.271 m Fluid 2 Flow Length = 1.701 m side 1 side 2 heat transfer coefficients 328.8 262.1 fW/K-m2] fin effectiveness 0.617 0.664 overall heat transfer coefficient, u1 100.9 W/K-m2] mass velocities 17.420 6.810 rkq/s-m2l Reynolds numbers 927.7 350.2 resistance ratio, side 1/side 2 0.84 percent pressure drop 1.50 3.98 Table XIV. 8- Wet cycle with water injection as intercooling and aftercooling, one level postcooling. Nitrogen - water vapour mixture as working fluid. Plates number = 231.6 Total plate area = 1714.6 m2 • Wet cycle with two water injection as intercooling and after cooling and two level postcooling with cooling water at 20 °C. Nitrogen - water vapour mixture as working fluid. = 92 »c Fluid Density (kg/m3): (3) Side 1 (Entrance) - 8.63 W = 467 °C (4) Side 1 (Exit) - 4.18 r = 497°c ± hot,in ' (5) Side 2 (Entrance) - 0.925 ^ =122°C (6) Side 2 (Exit) - 1.73 ATmi=29.28 °C Viscosity (kg/m-s): (7) Side 1 - 0 .0000274 Q =6098 kJ/s (8) Side 2 - 0.0000284 Specific Heat (J/kg-K): Mass Flow Rates (kg/s): (9) Side 1-1119 (1) Side 1 16.46 (10) Side 2-1124 (2) Side 2-16.46 Prandtl Number (dimensionless) (11) Side 1-0.741 Fluid Properties (12) Side 2 - 0.74 XIV-10 Appendix XIV- Recuperatorsizing. Fluid 1 Flow Length = 4.185 m Design dimension: Fluid 2 Flow Length = 1.730 m Non - Flow Length = 1.351 m Volume = 9.775 m3 side 1 side 2 heat transfer coefficients 316.5 249.2 [W/K-m2] fin effectiveness 0.625 0.674 overall heat transfer coefficient, u1 97.6 W/K-m2] mass velocities 17.480 7.224 fkq/s-m2] Reynolds numbers 951.2 379.3 resistance ratio, side 1/side 2 0.84 percent pressure drop 1.51 3.98 Table XIV. 9- Wet cycle with two water injection as intercooling and after cooling and two level postcooling with cooling water at 20 °C. Nitrogen - water vapour mixture as working fluid. The number of plates is N plates = 246; Total plate area = 1782 m2 • Wet cycle with two water injection as intercooling and after cooling. Base pressure P=5 bar. Nitrogen - water vapourmixture as working fluid. Mass Flow Rates (kg/s): Viscosity (kg/m-s): (1) Side 1 - 15.93 (7) Side 1 -.000028 (2) Side 2- 15.93 (8) Side 2 - .000028 Fluid Properties Specific Heat (J/kg-K): Fluid Density (kg/m3): (9) Side 1-1156 (3) Side 1 (Entrance) - 19.9 (10) Side 2- 1161 (4) Side 1 (Exit) - 10.95 Prandtl Number (dimensionless): (5) Side 2 (Entrance) - 2.28 (11) Side 1 - .76 (6) Side 2 (Exit) - 3.82 (12) Side 2- .755 -139 °C 7L.„=488°C = 464 °C 7L,,., = 165 °C XIV-11 Appendix XIV- Recuperator sizing. ATm,=25.3°C volume = 7.446 cu m 6=5976 kJ/s fluid 1 flow length = 7.480 m fluid 2 flow length design dimensions: = 3.181 m non-flow length = 0.313 m side 1 side 2 heat transfer coefficients 539.8 321.8 [W/K-m2! fin effectiveness 0.512 0.621 overall heat transfer coefficient, u1 128.1 W/K-m2] mass velocities 39.696 16.883 fkg/s-m 2! Reynolds numbers 2113.9 899.1 resistance ratio, side 1/side 2 0.69 percent pressure drop 1.50 3.99 Table XIV. 10- Wet cycle with two water injection as intercooling and after cooling. Base pressure P-5 bar. Nitrogen - water vapour mixture as working fluid. XIV-12 Appendix XV-EBHX sizing. Appendix XV EBHX sizing. Helium and helium-water mixture as working fluid. * Dry cycle one level intercooling, one level postcooling. Helium as working fluid. W = 0.975= 26 rows H = 26 rows = 0.975 m h0 = 500 ht — 404.7 [7 = 144.05 [W/m2,K] L= 4.7 m Single tube area = n-d0-L Total heat transfer area = 7t-d0-L-Nt = 249.4 m2 • Wet cycle with water injection as intercooling. Relative humidity 95 %. W = 0.975= 26 rows H = 26 rows = 0.975 m ha = 500 ^ = 384.73 U = 138.9 [W/m2,K] L=4.8 m Single tube area = n-d0-L Total heat transfer area = n-d0-L-Nt - 254.71 m2 XV-1 Appendix XV-EBHX sizing. • Wet cycle with water injection as intercooling and after cooling, and one stage postcooling. Helium - water vapour mixture as working fluid. W = 0.975= 26 rows H = 26 rows = 0.975 m A. = 500 A. — 380.6 [/ = 137.8 [W/m=,K] L=4.9 m Single tube area = n-d0-L Total heat transfer area = n-d0-L-Nt = 260,023 m2 * Wet cycle with water injection as intercooling and after cooling, and one stage postcooling. Helium - water vapour mixture as working fluid. Base pressure = 5 bar W = 0.975= 26 rows H = 26 rows = 0.975 m A, = 500 A, =388.19 U = [W/m2,K] L.=4.9 m Single tube area = n-d0-L Total heat transfer area = n-d0-L-Nt = 218.5 m2 XV-2 Appendix XV-EBHX sizing. Nitrogen and nitrogen-water mixture as working fluid. • Dry cycle one level intercooling, one level postcooling. Nitrogen as working fluid. W = 0.975= 26 rows H = 26 rows = 0.975 m ha = 500 A, = 282.9 U = 110.25 [W/m2, K] L= 5.7 m Single tube area - n-d0-L Total heat transfer area = rc-d0-L-Nt = 302.47 m2 • Wet cycle with water injection as intercooling. Relative humidity 95 %. W = 0.975= 26 rows H = 26 rows = 0.975 m h0 = 500 ht = 280.26 U = 109.45 [W/m2, K] L=5.8 m Single tube area = n-d0-L Total heat transfer area = n-da-L-Nt = 307.7 m2 • Wet cycle with water injection as intercooling and after cooling, and one stage postcooling. W = 0.975= 26 rows H = 26 rows = 0.975 m h0 = 500 h.t = 280.26 U = 109.41 [W/m2,K] L=5,8 m XV-3 Appendix XV-EBHX sizing. Single tube area = n-d0-L Total heat transfer area = tc ■ dg ■ L - Nt = 307,7 m2 * Wet cycle with water injection as intercooling and after cooling, and one stage postcooling. Base pressure P=5 bar. W = 0.975= 26 rows H = 26 rows = 0.975 m h0 = 500 h, = 281 .7 U = 110 [W/m 2,K] L=5.8 m Single tube area = n-d0-L Total heat transfer area = n-d0-L-Nt - 307 m2 XV-4 Appendix XVI- Postcooler sizing. Appendice XVI. Postcooler sizing. Helium-water mixture as working fluid. Water inlet temperature f°C] 50 Water outlet temperature [°C| 80 Working fluid inlet temperature [°C] 206 Working fluid outlet temperature [°C] 65 Logarithmic mean temperature [°C] 52.15 Total heat transferred 4024 Total heat transfer area [m2] 307 Pressure drop on the shell side 3.3 Table XVI. 1- Water injection as intercooling. Water inlet temperature [°C] 50 Water outlet temperature f°C] 80 Working fluid inlet temperature [°C] 136 Working fluid outlet temperature f°C] 65 Logarithmic mean temperature r°Cl 31.12 Total heat transferred 3943 Total heat transfer area [rn^l 662.5 Pressure drop on the shell side 2% Table XVI. 2-Water injection as intercooling and aftercooling, one level postcooling. Water inlet temperature f°C] 50 Water outlet temperature f°C] 80 Working fluid inlet temperature f°C1 145 Working fluid outlet temperature [°C1 65 Logarithmic mean temperature [°C] 34.09 Total heat transferred 3959 Total heat transfer area [m^l 428 Pressure drop on the shell side 4% Table XVI. 3-Water injection as intercooling and aftercooling, one level postcooling. Base pressure P= 5 bars. XVI-1 Appendix XVI- Postcooler sizing. Nitrogen-water mixture as working fluid. Water inlet temperature [°C1 50 Water outlet temperature [°C] 80 Working fluid inlet temperature [°C] 220 Working fluid outlet temperature [°C] 65 Logarithmic mean temperature [°C| 55.9 Total heat transferred 3911 Total heat transfer area [m^] 390 Pressure drop on the shell side 1.87 Table XVI. 4- Water injection as intercooling. Water inlet temperature [°C] 50 Water outlet temperature [°C] 80 Working fluid inlet temperature [°C] 151 Working fluid outlet temperature [°C1 65 Logarithmic mean temperature f°Cl 36.02 Total heat transferred 3774 Total heat transfer area [m2] 566 Pressure drop on the shell side 2.4 Table XVI. 5- Water injection as intercooling and aftercooling, one level postcooling. Water inlet temperature f°C] 50 Water outlet temperature [°C] 80 Working fluid inlet temperature f°Cl 164 Working fluid outlet temperature [°C] 65 Logarithmic mean temperature [°C] 40.05 Total heat transferred 3847 Total heat transfer area [m^l 438 Pressure drop on the shell side 2.4 Table XVI. 6-Water injection as intercooling and aftercooling, one level postcooling. Base pressure P= 5 bars. XVI-2 Appendix XVIl-Fuel composition. Appendix XVII. Fuel composition. Proximate analysis (wt.%,d.b.) Volatile matter 83.0 Fixed carbon 16.8 Ash 0.2 Ultimate analysis (wt.%,d.b.) C 50.2 H 6.1 N 0.1 S 0 Ash 0,2 0 (difference) 43,4 Na content ppm-wt(d.b-) 40 K content, ppm-wt(d.b.) 500 Cl content, ppm-wt(d.b.) <15 Table XVII - Fuel composition. The fuel has an heating value LHV = 8,175 MJ/kg The maximum total efficiency ( see Appendix I) in the cycle is the one achievable if all the water vapour in the flue gas would be condensed in the flue gas condenser. Fuel mass flow rate = 0.9395 kg/s Hydrogen in the fuel = 6.1 % Humidity in the fuel = 50% Fuel input = 7,680 MJ/s HHV-LLV = 2400*(H20-9*H) kj'/kg Fuel input (HHV) = 10.54 Mj'/s n = 137,2% The Low Heating Value (LHV) considers the combustion products in vapour phase, while the High Heating Value (HHV) considers the combustion products in liquid phase. The difference between the two values is the heat released by the water during the condensation process. XVII-1 Appendix XVIII-Design specification for Flue Gas Heat Exchanger. Appendix XVIII. Design specification for Flue Gas Heat Exchanger. The design specification of the flue Gas Heat Exchanger are strictly connected to the overall pressure ratio and air preheater temperature. Depending on pressure ratio value we can identify 3 regions: TO THE FLUE GAS CONDENSER oaveusnoNAiR TO THE FRO TURBINE MHP TO LP TURBINE FROM THE CFB FGHXIHHOT 7) FEOHar.our FGWKJT.OJT AIRPFO€AT.CaniN 2)"*" air pRBEATjor.our ^ AHFeBHEAT.CCU3.CUr T AIRPR&EAT.CCLD.OUT = ^ REC.CCLD.IN RBc.cciB.our RECIN.HCT Figure XVIII. 1- Schematic representation of air preheater and flue gas heat exchanger 1. T9 < 550 °C, T5<550 °C and Ti0 = 550 °C. In this region the pressure ratio is high, the turbine outlet stream has a low temperature, so the temperature on the outlet stream from recuperator on the cold side (Tin , FGHX.coid) is low. The heat input in FGHX and air pre heather is high and so is the furnace efficiency (see appendix ??). Appendix XVIII-Design specification for Flue Gas Heat Exchanger. Point A: At this point, the T air preheater,cold,out is fixed at its maximum temperature of 550 °C (to prevent melting of alkali salts in the flue gas) 2. T 9 = 550 °C, Ts<550 °C. As the pressure ratio decreases, the turbine outlet temperature increases, so the temperature of the working fluid exiting the recuperator on the cold side is higher and the heat input to be supplied in the FGHX is decreasing. More heat is therefore available to increase the Tg. However since the Tg is fixed at 550 °C, more heat is instead used for district heating. Point B: the inlet temperature on the cold side of FGHX is equal to 550 °C, so there is no heat input trough FGHX. 3. T 9= 550 °C, Ts>550 °C. The temperature at the compressor outlet is sufficiently high so that the FGHX is not required, hence the cycle heat input is limited. Since there is no heat transfer trough FGHX, all the heath in flue gases goes to district heating. The heat transfer in the cycle is only in EBHX. Figure ?? and ?? show the temperature profile along the flue gas path for the different design points. Figure ?? depicts the temperature profile for the case PR>PR(B) When considering a pressure ratio between point A and point B, both the FGHX and the air preheater are removing heat from the flue gases. XVI11-2 Appendix XVIII-Design specification for Flue Gas Heat Exchanger. —•—FLUE GAS •-*- FGHX COLO AIR PREHEATER COLD -w-FLUE GAS CONDENSER PART 1 FLUE GAS CONDENSER PART 2 0 1000 2000 3000 4000 SQ00 6000 [KJ/sJ Figure XVIII. 2- Temperature profile along the flue gas path for a pressure ratio higher than point B. For pressure ratios lower than point B, only the air preheater and flue gas condenser are subtracting heat from the flue gases, as depicted in figure ??. -*-AIRPREt-EATER FLUE GAS CCNCeGER PART 1 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 3300 3600 3900 4200 4500 4800 5100 5400 5700 600 M's] Figure XVIII. 3- Temperature profile along the flue gas path for a pressure ratio lower than point B. XVIll-3 Appendix XVIII-Design specification for Flue Gas Heat Exchanger. Depending on pressure ratio value, the simulations will undergo some slight modifications: • When pressure ratio value is lower than the pressure ratio at point B, the temperature of the working fluid exiting the recuperator is higher than the maximum temperature of the working fluid exiting the FGHX. A Fortran block checks the temperature of the stream exiting the recuperator and sets the heat duty of the FGHX equal to zero. Fortran block F - 1. if (Ts.gt.550) then Qheat2 = 0 endif • Varname t5 T5a Qheat2 Vartype stream-var stream-var block-var Block gasheat 2 Stream 5 5a Substream mixed mixed Component Paramno Attribute Variable temp temp duty Sentence parameter Prop-Set Table XVIII.1- Sampled block and stream variables. • For pressure ratio higher than point A, a design specification is created for the air preheater. The difference between the cold side and the hot side of the air preheater has to be 25 °C and the preheated air temperature can vary between 300 °C and 700 °C. To keep the amount of the total bed flow passed trough the EBHX at 70%, the outlet temperature of the EBHX is varied. XVIII-4 Appendix XVIH-Design specification for Flue Gas Heat Exchanger. 1. Set bed outlet temperature to Tbo = 736°C; 2. Run ASPEN and note the solid flow rate mb; 3. Target solids flow rate is 54.6 Kg/s ( 70 %of total solids flow), so calculate updated bed outlet temperature which correspond to this: ^(850-^ = 54.6(850-^) 4. Set outlet bed temperature to T'bo and run ASPEN. XVI11-5 Appendix XIX-Fortran Blocks. Appendix XIX. Fortran Blocks. • FORTAN block P-Ratio. p2=pi*sqrt(pr) p3=p2-0.02*p2 P4 =Pi*pr p5=p4-0.015*p4 P6=p5-0.013*p5 ps=pi/(1-0.04) P7=Ps/( 1-0.04) P1C=P1 Varname P4 Pi P2 Py Pe Vartype block-var stream-var block-var block-var block-var Block hpcomp Ipcomp turbin heatbed Stream 1 Substream mixed Component Paramno Attribute Variable pres pres pres pres pres Sentence param param param param Varname P5 Ps Pic PR P3 Vartype block-var block-var block-var stream-var block-var Block recup recup heatsink intercoo Stream in Substream mixed Component Paramno Attribute Variable pres-cold pres-hot pres pres pres Sentence param param param param Table XIX.1 - Sampled block and stream variables. The FORTAN block P-ratio will be later modified as: X = Pw TOT P2=Pi*(pr*X) P4 =Pi*pr XIX-1 Appendix XlX-Fortran Blocks. p5=P4-0.015*P4 Pe=P5-0.013*p5 p8 =Pi/(1-0.04) p7 =p8 /( 1-0.04) P1C=P1 • FORTAN block EPSILON. Epsilon = 0.93 T5 = T4 +epsilon*( T7-T4) Varname T4 T7 T5 Vartype stream-var stream-var block-var Block recup Stream 4 7 Substream mixed mixed Component Paramno Attribute Variable temp temp t-cold Sentence param Prop-Set Table XIX.2 - Sampled block and stream variables . T4 = temperature of the stream exiting the HP compressor; T7 = temperature of the stream exiting the turbine; • FORTRAN block EFF - T effp= 0.9 kavg=0.5*(kin+kout) write(*,*)'kavg-,kavg if(kavg.gt. 10) goto 101 effis= 1.0-(pout/pin)**(effp*(kavg- 1,0)/kavg) effis=effis/( 1.0-(pout/pin)**((kavg- 1.0)/kavg)) write(*,*)'effis-,effis 101 continue XIX-2 Appendix XIX-Fortran Blocks. Varname Pin Pout Kin Kqut EFF1S Vartype stream-var stream-var stream-prop stream-prop block-var Block turbin Stream 6 7 6 7 Substream mixed mixed Component Paramno Attribute Variable pres pres seff Sentence param Prop-Set kratio kratio Table XIX. 3 - Sampled block and stream variables. Appendix XX-T-s diagrams. Appendix XX. T-s diagrams. » Cycle with two level intercooling, two level postcooling. Helium as working fluid. The T-s diagram for this cycle at pressure ratio 2.8 is entropy [ kj/kmoi,k} Figure XX. 1 - T-s diagram of dry cycle with two level intercooling. 1. LP compressor inlet stream; 7. FGHX cold outlet stream; 2. LP compressor outlet stream; 8. EBHX cold outlet stream; 3. IC1 outlet stream; 9. Turbine outlet stream; 4. IC2 outlet stream; 10. Recuperator hot outlet stream 5. HP compressor outlet stream; 11. PC1 hot outlet stream; 6. Recuperator cold outlet stream; 12.PC2 hot outlet stream; XX-1 Appendix XX-T-s diagrams. • T - s diagram of the closed cycle with water injection as intercooling and aftercooling is: entropy kj/kmol.k Figure XX.2-T -s diagram of the cycle with water injection as intercooling and aftercooling 1. LP compressor inlet stream; 7. FGHX cold outlet stream; 2. LP compressor outlet stream; 8. EBHX cold outlet stream; 3. After water injection; 9. Turbine outlet stream; 4. HP compressor outlet stream; 10. Recuperator hot outlet stream; 5. After water injection; 11. PC1 hot outlet stream; 6. Recuperator cold outlet stream; XX-5 Appendix XX-T-s diagrams. • Water injection as one stage intercooling. The T - s diagram for the cycle is: entropy {KJ/Kmoi,K] Figure XX.2- T -s diagram of the cycle with water injection as intercooling and aftercooling 1. LP compressor inlet stream; 6. FGHX cold outlet stream; 2. LP compressor outlet stream; 7. EBHX cold outlet stream; 3. After water injection; 8. Turbine outlet stream; 4. HP compressor outlet stream; 9. Recuperator hot outlet stream; 5. Recuperator cold outlet stream; 10. PC1 hot outlet stream; XX-7 References. References. Agazzani, Massardo, Korakianitis An assesment of the performance of closed cycle with and without heat rejection at criogenic temperatures ASME TURBO-EXPO' 96 Anheden, M.,Ahlroth, M. Aspects on closed cycle gas turbines 1997 Dept, of Chemical Engineering and Technology Energy Processes KTH Stockholm Anheden, M.,Ahlroth, M. System Studies on a Biomass Fired CHP Closed Cycle gas Turbine with a CFB Furnace ECOS 98 Nancy Anheden, M.,Ahlroth, M., Martin, A. Externally Fired Gas Turbine cylce for small scale biomass cogeneration To be presented at International Joint Power Generation Conference 1999 Bollard, O. J. Comparative Evaluation of Closed Cycle and Gas Turbines Systems with water injection, steam injection and recuperation 1995, Journal of Engineering for gas turbines and Power, vol. 117 Camporeale, S.,Fortunate, B. Design and off - design performance of advanced mixed gas steam cycle power plants 1994 1 References. Cohen, H., Rogers, G. F., Saravanamuttoo H.I.H. Gas Turbine theory 1997, Flowers 97 Colin F. Me Donald Large closed - Cycle Gas Turbine Plants Corti,A.,Failli,L.,Fiaschi,D.,Manfrida,G. Exergy analysis of two second generation SGCT plant proposals 1998 Couldson, Richardson Chemical Engineering Pergamon Ed. Facchini,B.,Fiaschi,D.,Manfrida,G. Semi-Closed gas turbine/combined cycle with water recovery and extensive exhaust gas recirculation 1996, ASME IGTI Gas Turbine Conference and Exhibition Facchini,B.,Fiaschi,D.,Manfrida,G. SCGT/CC:An innovative cycle with advanced environmental and peakload shaving features ECOS 96 Stockholm Fiaschi,D.,Manfrida,G. A new semiclosed gas turbine cycle with C02 separation Gasparovic, N., Stapersma.D. Gas Turbines with heat exchangers and water injections in the compressed air 1973 2 References. Griepentrog, H. First Closed - Cycle Helium Turbine 1975, Diesel and gas turbine progress Hewitt, G.F. Hemisphere Handbook of Heat Exchanger Design 1990, Hemisphere Publishing Corporation Horlock, J.H. The Effect of heat exchanger effectiveness and exergy loss in the estimation of cycle efficiency 1998, International Gas Turbine and Aeroengine Congress and Exhibition, Stockholm, Sweden Horlock, J.H. The Evaporative Gas Turbine ( EGT) Cycle 1998, Journal of Engineering for gas turbines and Power, vol. 120 Horlock, J.H. Heat exchanger performance with water injection (with relevance to evaporative gas turbine(EGT) cycles) Flowers'97 Kays, W.M., Crawford, M.E. Convective Heat and Mass Transfer 1998 Kays,W.M.,London,A.L. Compact Heat Exchangers Krieger Publishing Company Lee J.C., J. Campbell, D.E. Wrigth Closed - Cycle gas turbine Working Fluids 1981, Journal of Engineering for gas turbines and Power, vol. 103 3 References. Macchi, E., Chiesa, P. et Al. An assessment of the thermodynamic performance of mixed gas - steam Cycles: part A:!ntercooled and steam - injected Cycles. 1994, International Gas Turbine and Aeroengine Congress and Exposition The Hague Netherlands op het Veld, R.P., van Buijtenen, J.P. Am empirical approach to the preliminary design of a closed cycle gas turbine 1998, International Gas Turbine and Aeroengine Congress and Exhibition, Stockholm, Sweden Rao, A.,Tanner, A. et al. Closed Cycle Gas Turbine with humidification of the working fluid 1991, 26th Intersociety Energy Conversion Conference Rice I. J. Steam Injected Gas Turbines Analysis: Steam Rate 1995 Journal of Engineering for gas turbines and Power, vol. 117 Robinson, T. Water injected LM 1600 installation and operating experience International Gas Turbine and Aeroengine Congress and Exposition, The Hague, Netherlands Rogers, L, Liese, E. Humidification of a high pressure air stream by direct water injection 1997, Joint power Generation Conference Sandberg, C. On the partial condensation of water vapour - air mixtures 1994 Dept, of Chemical Engineering and Technology Energy Processes KTH Stockholm 4 References. Xiao,Y.,Lin,R., Cai,R. System Optimization of Humid Air Turbine Cycle 1993, International Gas Turbine and Aeroengine Congress and Exposition, The Hague, Netherlands 5