Thermodynamic Analysis on an Integrated Liquefied Air Energy

energies

Article Thermodynamic Analysis on an Integrated Liqueﬁed Air Energy Storage and Electricity Generation System

Yingbai Xie and Xiaodong Xue *

Department of Power Engineering, North China Electric Power University, Baoding 071003, China; [email protected] * Correspondence: [email protected]

Received: 22 August 2018; Accepted: 20 September 2018; Published: 23 September 2018

Abstract: For an integrated liquefied air energy storage and electricity generation system, mathematical models of the liquefied air energy storage and electricity generation process are established using a thermodynamic theory. The effects of the outlet pressure of the compressor unit, the outlet pressure of the cryogenic pump, the heat exchanger effectiveness, the initial air temperature and pressure before throttling on the performances of the integrated liquefied air energy storage, and the electricity generation system are investigated, using the cycle efficiency and liquid air yield ratio as the evaluation indexes. The results show that if the compressor outlet pressure is raised, both the compression work and the expansion work increase, but because the expansion work increases more slowly, the cycle efficiency of the system gradually decreases. Increasing the cryogenic pump outlet pressure and heat exchanger effectiveness can significantly increase the cycle efficiency of the system; the higher the air pressure and the lower the air temperature before throttling, the greater the liquid air yield after expansion, and the higher the cycle efficiency. The theoretical analysis models and research results can provide a reference for the development of an integrated system of liquefied air energy storage and electricity production, as well as for the development of medium-capacity energy storage technology.

Keywords: liqueﬁed air energy storage; cycle efﬁciency; liquid air yield ratio; electricity generation

1. Introduction Solar, wind, and other renewable energies are widely used to generate electricity in the world [1–5]. For these energy forms, because of their characteristics of instability and intermittence [6,7], efficient energy storage technologies are required in order for a sustained and stable output [8–12]. Energy storage technologies, such as bulk power management, compressed air energy storage (CAES), and pumped hydroelectricity storage (PHS) [13–16], are presently relatively mature and reliable. However, these two technical schemes [17] are limited by geographical or hydrogeological conditions. PHS technology needs abundant water resources for support, while CAES requires high-performance natural underground reservoirs. According to the Electric Power Research Institute (EPRI), the total cost for CAES is around 1000 $/kW. It may be double this for PHS. As a result, there is a demand to develop a general, cost-effective energy storage technology, regardless of local conditions. Liquid air energy storage (LAES) is an innovative and leading universal industrial energy storage technology [18–21]. The idea of LAES began in 1977 at the University of Newcastle, and was tested by Mitsubishi Industries Ltd. (Tokyo, Japan) in 1998 [1]. Researchers at the University of Leeds together with the Highview Power Storage Company developed the first 350 kW/2.5 MWh pilot demonstration plant at the University of Birmingham in 2010. The data gathered from this pilot plant showed that the efficiency of the total cycle is in the range of 50–60%.

Energies 2018, 11, 2540; doi:10.3390/en11102540 www.mdpi.com/journal/energies Energies 2018, 11, 2540 2 of 12

Since 2014, Viridor has selected Highview to design MW level pre-commercial, multi-MW, and conceptual Giga-Plant LAES. However the round-trip efficiency is still approximately 60%. Some literature has contributed to this topic. The process can be divided into two parts, namely air liquefied and electric generation. As the air liquefied process needs a lower temperature, while the electric generation process needs a higher temperature, internal heat exchangers, such as regenerators, are needed to connect these two processes in order to improve the cycle efficiency. An integrated system was put forward so as to investigate the operational parameters of the major devices effecting the cycle efficiency. Chino and Araki [22] also proposed an air liquefaction plant integrated with a conventional combined cycle power plant. Li et al. studied a LAES system integrated with a nuclear power plant [23]. The overall system efficiency is improved, owing to the reheating arrangement. In this paper, more detailed effects will be discussed regarding the outlet pressure of the compressor and cryogenic pump, the efficiency of the heat exchanger, the air temperature and pressure before the throttle on the cycle efficiency, and the liquid air yield.

2. System Description Figure1 shows the layout of an integrated liqueﬁed air energy storage and electricity generation system, referring to the literature [8]. The system adopts a two-stage compression and two-stage expansion.

Compressor #1 Expander #2 5S 6S 1L 7E

12S Hot Storage 2L Tank 6E

11S Heat Cooler #1 Exchanger #2

Compressor #23L 5E Expander #1

4L 4E 7S Heat Cooler #2 Cold Storage Exchanger #1 Tank #1 10S 9S 8S 5L 3E

10L 1S 3S

Cold Cold Storage Gasification Heat Box Tank #2 Exchanger

6L 2S 4S 9L J-T Valve 2E Cryogenic 7L Pump Separator Liquid 1E 8L Air Tank

Figure 1. 1. SchematicSchematic diagram diagram of of an a integratedn integrated liquid liquid air energy air energy storage storage and electricity and electricity generation generation system. system. The left side is the air liquefying process. It contains two air compressors, a J–T valve (It is 3.a throttleMathematical valve), M aodels separator, for Processes a liquid air tank, and some heat exchangers. When there is surplus electricity from the renewable energy sources or from the grid, the outer air is compressed by the two 3.1.air compressors,Air Liquefying andProcess itstemperature and pressure are raised. Then, the gaseous air is cooled down and throttled in the J–T valve. The liqueﬁed air is then collected in the separator and stored in the The outlet pressure and inlet pressure of the air compressors are as follows: liquid air tank.

ppac,, out= ac in ac (1) where pac,out is the outlet pressure of the air compressor, Pa; pac,in is the inlet pressure of the air compressor, Pa; and πac is the compression ratio. The relationship between the inlet and outlet temperature of the air compressor is as follows:

nc −1 nc (2) TTac,, out= ac in ac where Tac,out is the outlet temperature of the air compressor, K; Tac,in is the inlet temperature of the air compressor, K; and nc is the polytropic index of the compression process. The efficiency of the compressor ƞac can be expressed as follows:

 −1 nc ac = (3)  nc −1 where κ is the adiabatic index. The specific work, wac, done to the compress air is as follows:

2 wac= c air()()() T ac, out , i − T ac , in , i = h 2 L − h 1 L + h 4 L − h 3 L (4) i=1 where cair is the specific heat capacity of air, J/(kg·K). After the two air compressors, two internal heat exchangers are used. The high-temperature and high-pressure air is cooled down to heat the low temperature cold fluid within the internal heat

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When there is an insufﬁcient supply of electricity available to meet the consumers’ demands, the cryogenic pump is activated. The liquid air in the liquid air tank increases its temperature through the heat exchangers, and recovers to a gaseous state. When it reaches the set-points for the temperature and pressure, the air enters the two-stage expander in order to generate electricity. This is the electricity generation process. There are some regenerators between the two processes. To decrease the system ﬂuctuation, the large capacity storage method is used. The above integrated system is modeled with the following assumptions:

• Ignoring other components, it is assumed that the air is a mixture of 21% oxygen and 79% nitrogen. The thermodynamic properties of nitrogen and oxygen are evaluated in REFPROP (Reference Fluid Thermodynamic and Transport Properties Database), according to the authors of [24,25], respectively. • According to thermodynamics, it is assumed that the compression and expansion processes are polytropic processes. • The pressure losses along the cycle have been ignored, in order to have a solution that compares different cycles under the same conditions. In the analysis, the system is assumed to be in a steady state condition, and the thermal losses in the heat exchangers are ignored [26].

3. Mathematical Models for Processes

3.1. Air Liquefying Process The outlet pressure and inlet pressure of the air compressors are as follows:

pac,out = pac,inπac (1) where pac,out is the outlet pressure of the air compressor, Pa; pac,in is the inlet pressure of the air compressor, Pa; and πac is the compression ratio. The relationship between the inlet and outlet temperature of the air compressor is as follows:

nc−1 Tac,out = Tac,inπac nc (2) where Tac,out is the outlet temperature of the air compressor, K; Tac,in is the inlet temperature of the air compressor, K; and nc is the polytropic index of the compression process. The efﬁciency of the compressor ηac can be expressed as follows:

κ − 1 nc ηac = × (3) κ nc − 1 where κ is the adiabatic index. The speciﬁc work, wac, done to the compress air is as follows:

2 wac = ∑ cair(Tac,out,i − Tac,in,i) = (h2L − h1L) + (h4L − h3L) (4) i=1 where cair is the speciﬁc heat capacity of air, J/(kg·K). After the two air compressors, two internal heat exchangers are used. The high-temperature and high-pressure air is cooled down to heat the low temperature cold ﬂuid within the internal heat exchanger. Ignoring the heat dissipated to the surroundings, the outlet air temperature of the cold side, Thex,cold,out, is as follows:

Thex,cold,out = (1 − ε)Tac,out + εThex,cold,in (5) Energies 2018, 11, 2540 4 of 12

where ε is the efficiency of the heat exchanger, and Thex,cold,in is the inlet air temperature of the internal heat exchanger on the cold side, K. The lower the temperature of the air entering the second compressor, the smaller the power consumption needed for compressing the air. Therefore, the cold side air from these two heat exchangers is introduced from cold storage tank #1. When leaving the heat exchanger, the cold side air discharges the absorbed heat into the hot storage tank. The heat stored in the hot storage tank per unit mass is as follows: qhst = h6S − h5S (6) The hot side air continues cooling down in the cold box. The parameters of point 6L (in Figure1) must be controlled to be below certain values. In the cold box, the energy balance equation must include the mass flow rate of the three working fluid streams. Then, the air passes the J–T valve and is throttled into the two-phase region. The gaseous air is recovered to be reused. The liquefied air flows out from the bottom of the separator and is stored in the liquid air tank. The ratio of liquid air yield is as follows: m Y = 8L (7) m1L where m8L is the mass flow rate of the liquid air that enters the liquid air tank, kg/s, and m1L is the mass flow rate of the gaseous air being suctioned at air compressor #1, kg/s.

3.2. Electricity Generation Process During the peak electricity demand period or in the case of a power failure, the electricity generation process is activated. The liquid air in the liquid air tank is extracted by the cryogenic pump, and the power consumption is as follows:

p2E wcp = Rair,gasT1E ln (8) p1E where T1E is the liquid air temperature at the outlet of the liquid air tank, K; p1E is the pressure of liquid air at the outlet of the liquid air tank, Pa; and p2E is the pressure of air at the outlet of the cryogenic pump, Pa. The air then absorbs heat from cold storage tank #2, turning into a gaseous state in the gasiﬁcation heat exchanger. The air temperature at the outlet of the heat exchanger is as follows:

T3E = (1 − ε)T2E + εT4S (9)

In heater #1, the air heats to T4E, and enters expander #1 to produce work. The expansion process is also a polytropic process, where the temperature at the outlet of each expander is as follows:

− (ne−1) ne Tae,out = Tae,inπe (10) where ne is the polytropic index of the expansion process, and πe is the expansion ratio. The polytropic efﬁciency and the polytropic index of the expander is as follows:

(ne − 1) κ ηe = × (11) ne κ − 1

The work produced for the unit mass working ﬂuid expansion in the expanders is as follows:

we = (h5E − h4E) + (h7E − h6E) (12) Energies 2018, 11, 2540 5 of 12

3.3. Cyclic Performance A complete cycle of the liquefied air energy storage system includes two stages, the liquefied energy storage and the energy released to power generation. The main parameter used to measure the system performance is the system cycle efficiency, also called the round-trip efficiency, which can be expressed as follows: we − wcp ηRT = Y (13) wac

4. Performance Analysis of an Integrated System of Liqueﬁed Air Energy Storage and Power Generation MATLAB software is used to program the established models. Referring to the literature [27], the basic operating parameters of the liqueﬁed air energy storage and power generation system are shown in Table1.

Table 1. Basic operating parameters of the system.

Parameters Value Units

Ambient temperature (T0) 293 K Ambient pressure (p0) 100 kPa Outlet pressure of cryogenic pump (p2E) 7000 kPa Liquid air storage pressure (p1E) 100 kPa Minimum temperature of cold storage tank #2 93 K Maximum temperature of cold storage tank #2 300 K Pinch point temperature of cold box (cold side) 5 K Pinch point temperature of cold box (hot side) 10 K Gross compression ratio of compressors 80 - Isentropic efficiency of compressors 0.92 - Isentropic efficiency of expanders 0.9 - Heat exchanger effectiveness 0.92 - Isentropic efficiency of cryogenic pump 0.9 -

REFPROP (Reference Fluid Thermodynamic and Transport Properties Database) is an internationally recognized physical property calculation software developed by the National Institute of Standards and Technology (NIST). The properties of the working ﬂuid at each point labeled in the system are generated by the NIST REFPROP database. For the air liqueﬁed process and the electric generation process, the values of these points are shown in Tables2 and3, respectively.

Table 2. Parameters of the points in the air liqueﬁed process.

Point p/kPa T/K h/kJ·kg−1 ρ/kg·m−3 1L 100.00 293.00 293.27 1.16 2L 894.43 578.60 584.91 7.35 3L 894.43 315.85 314.67 16.21 4L 8000.00 623.72 632.65 85.10 5L 8000.00 319.46 305.60 191.42 6L 8000.00 98.00 −84.42 769.30 7L 100.00 79.11 −84.42 29.13 8L 100.00 79.11 −125.95 812.26 Energies 2018, 11, 2540 6 of 12

Table 3. Parameters of the points in the electric generation process.

Point p/kPa T/K h/kJ·kg−1 ρ/kg·m−3 4E 7000.00 534.49 537.19 18.14 1E 100.00 79.11 −125.95 812.26 5E 836.66 309.54 308.36 8.89 2E 7000.00 79.11 −121.22 813.12 6E 836.663E 7000.00536.06 290.00 274.45540.48 81.53 2.28 7E 100.004E 7000.00310.44 534.49 537.19310.83 18.14 1.21 5E 836.66 309.54 308.36 8.89 6E 836.66 536.06 540.48 2.28 4.1. Outlet Pressure of Compressor (p4L) 7E 100.00 310.44 310.83 1.21 The work consumption of the compressor is associated with the number of compression stages and the4.1. compression Outlet Pressure mode of Compressor at the identical (p4L) rated isentropic efficiency of compressor, and the same heat exchangerThe work effectiveness consumption. Theoretically, of the compressor the isothermal is associated compression with the number process of compressionhas a minimum stages work consumption,and the compression while the modeadiabatic at the compression identical rated process isentropic has efficiency a maximum of compressor, work consumption and the same. The isothermalheat exchanger compression effectiveness. process can Theoretically, be approached the isothermal if the number compression of compression process hasstage as minimum is increased infinitely,work an consumption,d if internal whilecoolers the are adiabatic put between compression the stages. process has a maximum work consumption. InThe fact, isothermal the number compression of compression process stage can bes are approached limited, as if increasing the number the of number compression will cause stages a more is complicatedincreased system infinitely, configuration and if internal and coolers will areresult put in between greater the irreversible stages. losses, such as mechanical friction andIn flow fact, theresistance. number ofAccording compression to the stages thermodynamic are limited, as increasing theory, for the the number multi will-stage cause compression a more complicated system configuration and will result in greater irreversible losses, such as mechanical process, the compression work consumption will be at a minimum if the compressors of the different friction and flow resistance. According to the thermodynamic theory, for the multi-stage compression stages adopt identical pressure ratios. process, the compression work consumption will be at a minimum if the compressors of the different Forstages the adopt afore identicalmentioned, pressure two- ratios.stage compression and intermediate cooling is adopted. Figure 2 shows theFor relationship the aforementioned, between two-stage the outle compressiont pressure and of the intermediate compressor cooling unit is ( adopted.p4L) to the Figure work2 of compression,shows the work relationship of expansion between, and the cycle outlet efficiency. pressure of the compressor unit (p4L) to the work of compression, work of expansion, and cycle efficiency.

0.56 800 Work of compression 0.54 750 Work of expansion Cycle efficiency 0.52 700

0.50 650

0.48 600

0.46 550 Work/kJ/kg Cycle efficiency Cycle 0.44 500

0.42 450

0.40 400 2 4 6 8 10 12 14 16 18 20 22

Compressor outlet pressure p4 /MPa

Figure 2. Influence of the compressor outlet pressure (p4L) on the work of compression, work of Figureexpansion, 2. Influence and cycle of the efficiency. compressor outlet pressure (p4L) on the work of compression, work of expansion, and cycle efficiency. In Figure2, with the increasing compressor outlet pressure ( p4L), the compression work and the Inexpansion Figure 2, work with both the increase,increasing but, compressor the expansion outlet work pressure increases (p more4L), the slowly. compression However, work thecycle and the expansionefficiency work of theboth system increase gradually, but, the decreases. expansion work increases more slowly. However, the cycle efficiency Theof the increment system of gradually the compression decreases. work because of the increase in the compression pressure ratio. TheEquations increment (2) and of (4) the indicate compression that the greater work the because compression of the pressure increase ratio, in thethe higher compression the compressor pressure outlet temperature. This means that the specific compression work increases. The elevation of the ratio. Equations (2) and (4) indicate that the greater the compression pressure ratio, the higher the compressor outlet temperature results in a higher temperature of the heat storage medium, which also compressor outlet temperature. This means that the specific compression work increases. The increases the heating temperature of the air in the electric power generation process. elevation Accordingof the compressor to Equation outlet (12), temperature a higher inlet results air temperature in a higher of temperature the expander of means the heat a higher storage medium,specific which work also output. increases However, the theheating air cannot temperature be liquefied of completely, the air in thereforethe electric the liquefactionpower generation rate process. According to Equation (12), a higher inlet air temperature of the expander means a higher specific work output. However, the air cannot be liquefied completely, therefore the liquefaction rate cannot reach 100%. It can be seen from the conservation of energy, that the heat collected during the compression process is not fully used in the release phase, so the increase of the expansion work is slower than that of the compression work, resulting in a decrease in the cycle efficiency. Therefore, the outlet pressure of the compressor unit (p4L) should not be too high.

Energies 2018, 11, 2540 7 of 12

cannot reach 100%. It can be seen from the conservation of energy, that the heat collected during the compression process is not fully used in the release phase, so the increase of the expansion work is 4.2. Outletslower Pressure than that of ofthe the Cryogenic compression Pump work, resulting in a decrease in the cycle efficiency. Therefore, the outlet pressure of the compressor unit (p4L) should not be too high. The cryogenic pump is a special pump that leads liquid air from the liquid air tank to the gasification4.2. Outlet heat Pressure exchanger of the Cryogenicfor gasification. Pump The outlet pressure of the cryogenic pump is treated as the inlet pressureThe cryogenic of the pumpexpander, is a ignoring special pump the flowing that leads pressure liquid airloss from of the the air liquid in the air heat tank exchangers to the and thegasification pipelines heat. The exchanger inlet forair gasification. pressure and The outletthe temperature pressure of the of cryogenic the expander pump is are treated the as primary the parametersinlet pressure that determine of the expander, the expansion ignoring thework flowing with pressurethe condition loss of of the the air constant in the heat air exchangers flow. Therefore, and the inletthe pipelines.air pressure The and inlet temperature air pressure and of the temperatureexpander should of the expander be increased are the as primary much as parameters possible, in orderthat to increase determine the the output expansion expansion work withwork. the condition of the constant air flow. Therefore, the inlet Accordingair pressure to and basic temperature thermodynamic of the expander principles should, be for increased the multi as- muchstage asexpansion possible, in process, order to the expansionincrease work the outputreaches expansion its maximum work. at the identical expansion ratio for each stage. Therefore, two- According to basic thermodynamic principles, for the multi-stage expansion process, stage expansion and inter-stage reheating expansion modes are adopted in this paper. The inter-stage the expansion work reaches its maximum at the identical expansion ratio for each stage. Therefore, reheater is used to elevate the inlet air temperature of the next stage expander and the efficiency of two-stage expansion and inter-stage reheating expansion modes are adopted in this paper. the expanderThe inter-stage unit. reheater is used to elevate the inlet air temperature of the next stage expander and the Figureefficiency 3 shows of the expanderthe expansion unit. work and cycle efficiency to the outlet pressure of the cryogenic pump. Figure3 shows the expansion work and cycle efficiency to the outlet pressure of the cryogenic pump.

0.50 500 0.48 Cycle efficiency 480 0.46 Work of expansion

460 /kJ/kg

0.44 440 0.42 420 0.40 400

Cycle efficiency Cycle 0.38 380

0.36 Workexpansion of 360 0.34 340 0.32 2 4 6 8 10 Cryogenic pump outlet pressure /MPa

Figure 3. Influence of the outlet pressure of the cryogenic pump on the expansion work and the Figurecycle 3. Influence efficiency. of the outlet pressure of the cryogenic pump on the expansion work and the cycle efficiency. As shown in Figure3, the cycle efficiency and the expansion work increase in a similar way to the Asincrease shown of in the Figure outlet pressure3, the cycle of the efficiency cryogenic and pump. the Forexpansion example, work when increase the outlet in pressure a similar of way the to the increasecryogenic of pumpthe outlet boosts pressure from 2 MPa of the to 5cryogenic MPa, the cycle pump. efficiency For example, increases when from 36%the outlet to 44%, pressure and the of the cryogenicexpansion pump work increasesboosts from from 2 345MPa kJ/kg to 5 toMP 425a, kJ/kg.the cycle efficiency increases from 36% to 44%, and the expansionAccording work toincreases the basic from principles 345 kJ/kg of thermodynamics, to 425 kJ/kg. the higher the pressure and temperature before the air enters the expander, the more work is output during the expansion process. Increasing According to the basic principles of thermodynamics, the higher the pressure and temperature the outlet pressure of the cryogenic pump is equivalent to increasing the pressure at the inlet of before the air enters the expander, the more work is output during the expansion process. Increasing the expander. Theoretically, augmenting the outlet pressure of the cryogenic pump is beneficial for the outletimproving pressure the cycleof the efficiency cryogenic of the pump system. is equivalent However, in to reality, increasing the outlet the pressure of at the the cryogenic inlet of the expander.pump Theoretically, is limited, considering augment theing harm the of outlet the high pressure pressure ofon the equipment. cryogenic pump is beneficial for improving the cycle efficiency of the system. However, in reality, the outlet pressure of the cryogenic pump4.3. is limited, Heat Exchanger considering Effectiveness the harm of the high pressure on the equipment. Heat storage and cold storage tanks, as well as other heat exchangers are used to guarantee 4.3. Heatthe E independentxchanger Effectiveness operation of the liquid air storage and electric power generation processes. Heat storage and cold storage tanks, as well as other heat exchangers are used to guarantee the independent operation of the liquid air storage and electric power generation processes. These heat exchangers have the capacity to provide cooling or heating at any time during single or two-phase processes. The heat exchanger effectiveness is the maximum actual heat transfer. Figure 4 shows the heat exchanger effectiveness compared to the compression work, expansion work, and the cycle efficiency, supposing that heater #1, heater #2, cooler #1, and cooler #2 have an identical heat exchanger effectiveness.

Energies 2018, 11, 2540 8 of 12

These heat exchangers have the capacity to provide cooling or heating at any time during single or two-phase processes. The heat exchanger effectiveness is the maximum actual heat transfer. Figure4 shows the

heat exchanger effectiveness compared to the compression work, expansion work, and the cycle efﬁciency,With supposing the constant that outlet heater pressure #1, heater of the #2,compressor cooler #1, unit and and cooler inlet pressure #2 have of an the identical expander heat unit, With the constant outlet pressure of the compressor unit and inlet pressure of the expander unit, exchangerincreasing effectiveness. the heat exchanger effectiveness will greatly decrease the compression work consumed, increasing the heat exchanger effectiveness will greatly decrease the compression work consumed, increaseWith thethe constantexpansion outlet work pressure, and the of cycle the compressorefficiency. unit and inlet pressure of the expander unit, increaseincreasing the expansion the heat work exchanger, and effectivenessthe cycle efficiency. will greatly decrease the compression work consumed, increase the expansion work, and the cycle efﬁciency. 0.54 650 0.54 0.52 650 600 0.52 0.50 0.50 0.48 Work of compression 600 Work of expansion 550 0.46 0.48 Work Cycleof compression efficiency 0.44 Work of expansion 550

0.46 Cycle efficiency 500 Work/kJ/kg

Cycle efficiency Cycle 0.42 0.44

0.40 500450 Work/kJ/kg

Cycle efficiency Cycle 0.42 0.38 0.40 0.36 450400 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.38 Efficiency of heat exchanger 0.36 400 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 Figure 4. Influence of heat exchanger Efficiencyeffectiveness of heat exchanger on the compression work, expansion work, and the cycle efficiency. Figure 4. Influence of heat exchanger effectiveness on the compression work, expansion work, and the Figurecycle 4. Influence efficiency. of heat exchanger effectiveness on the compression work, expansion work, and the cycleIn efficiency Figure 4,. when the heat exchanger effectiveness increases from 0.8 to 0.96, the compression workIn Figuredecrease4,s when from the630 heatkJ/kg exchanger to 585 kJ/kg effectiveness, the expansion increases work increases from 0.8 from to 0.96, 425 the kJ/kg compression to 500 kJ/kg, Inwork andFigure decreases the cycle4, when fromefficiency the 630 heat kJ/kg increase exchanger to 585s from kJ/kg, abouteffectiveness the 39% expansion to around increases work 52%. increases from from0.8 to 425 0.96, kJ/kg the to compression 500 kJ/kg, According to the above analysis data, as the heat exchanger effectiveness increases, the work anddecrease the cycles from efficiency 630 kJ/kg increases to 585 from kJ/kg about, the 39% expansion to around work 52%. increases from 425 kJ/kg to 500 kJ/kg, compression work decreases and the expansion work increases, so the cycle efficiency of the system and the cycleAccording efficiency to increase the aboves from analysis about data, 39% to as around the heat 52%. exchanger effectiveness increases, theincreases. compression This result work decreasesalso conforms and to the the expansion basic principles work increases, of thermodynamics. so the cycle Therefore, efficiency ofa larger the According to the above analysis data, as the heat exchanger effectiveness increases, the systemheat exchange increases.r Thiseffectiveness result also means conforms better to the heat basic transfer principles effect ofs. thermodynamics.Where possible, a Therefore, higher heat a compression work decreases and the expansion work increases, so the cycle efficiency of the system largerexchanger heat exchanger effectiveness effectiveness should be meansapplied. better heat transfer effects. Where possible, a higher heat increases.exchanger This effectivenessresult also conforms should be applied.to the basic principles of thermodynamics. Therefore, a larger heat exchange4.4. Temperaturer effectiveness and Pressure means before betterAir Throttling heat transfer effects. Where possible, a higher heat 4.4. Temperature and Pressure before Air Throttling exchanger effectivenessFigure 5 is the should inversion be curveapplied. of air . The regions of cooling and heating are clearly shown on theFigure temperature5 is the inversion pressure curve coordinates. of air. TheIf a regions maximum of cooling inversion and heating pressure are exists clearly with shown an initial on the air 4.4. Temperaturetemperaturepressure greater and pressure Pressure than coordinates. this before pressure Air If T a, hrottlingit maximum will raise inversionthe temperature pressure of exists the air. with an initial air pressure Figuregreater 5 than is the this inversion pressure, itcurve will raise of air the. The temperature regions ofof thecooling air. and heating are clearly shown on the temperature pressure coordinates.1000 If a maximum inversion pressure exists with an initial air pressure greater than this pressure,900 it will raise the temperature of the air. 800 700 600

1000 /K

T 500 900 400 800 300 700 200

600 100 /K

T 500 0 0 5 10 15 20 25 30 35 400 p/MPa 300 200 Figure 5. Air inversion curve. Figure 5. Air inversion curve. 100 0 Only if the initial pressure0 and5 temperature10 15 20 fall in25 to the30 cooling35 zone, will the air lower its temperature by throttling. The envelope of thep/MPa cooling zone is the inversion curve. In Figure 5, the pressure of the air before throttling should be smaller than the maximum inversion pressure, which is 34.16 MPa for air. Figure 5. Air inversion curve.

Only if the initial pressure and temperature fall into the cooling zone, will the air lower its temperature by throttling. The envelope of the cooling zone is the inversion curve. In Figure 5, the pressure of the air before throttling should be smaller than the maximum inversion pressure, which is 34.16 MPa for air.

Energies 2018, 11, 2540 9 of 12 The envelope temperature, which is larger than the corresponding temperature of the maximum inversion Onlypressure if the, is initial the upper pressure part and of the temperature inversion fall curve. into theThe cooling lower part zone, of will the the inversion air lower curve its is the boundarytemperature of bythe throttling. heating The and envelope cooling of region the coolings for zone temperature is the inversions below curve. the corresponding In Figure5, The envelope temperature, which is larger than the corresponding temperature of the maximum temperaturethe pressure of the of maximum the air before inversion throttling pressure. should beThe smaller temperature than the of maximum the air before inversion throttling pressure, must inversion pressure, is the upper part of the inversion curve. The lower part of the inversion curve is be in whichthe envelope is 34.16 MPaof the for upper air. as well as the in the lower inversion curve. the boundaryThe envelope of the temperature,heating and which cooling is larger region thans the for corresponding temperature temperatures below the of the corresponding maximum The end state of the air expansion always falls into the two-phase liquid–vapor region, which temperatureinversion of pressure, the maximum is the upper inversion part of thepressure. inversion The curve. temperature The lower partof the of theair inversionbefore throttling curve is the must means that only a fraction of the gas expanded in this region is liquefied. The liquid air yield ratio be in theboundary envelope of the of heating the upper and coolingas well regions as the forin t temperatureshe lower inversion below the curve. corresponding temperature of and the system cycle efficiency with respect to the temperature and pressure of the air before Thethe maximumend state inversionof the air pressure. expansion The temperaturealways falls of into the airthe before two-phase throttling liquid must–vapor be in the region envelope, which throttling, are shown in Figures 6 and 7, assuming that the air is throttled down to atmospheric meansof that the upperonly a as fraction well as theof inthe the gas lower expanded inversion in curve. this region is liquefied. The liquid air yield ratio pressure. The initial end state pressure of the and air temperature expansion always are 10 fallsMPa into and the140 two-phaseK, respectively liquid–vapor. region, and the system cycle efficiency with respect to the temperature and pressure of the air before which means that only a fraction of the gas expanded in this region is liqueﬁed. The liquid air throttling, are shown in Figures 6 and 7, assuming that the air is throttled down to atmospheric yield ratio and the system cycle efﬁciency with respect to the temperature and pressure of the air pressurebefore. The throttling, initial pressure are shown and in Figures temperature6 and7, assumingare 10 MPa that and the 140 air is K, throttled respectively down. to atmospheric 1.0 0.6 pressure. The initial pressure and temperature are 10 MPaLiquid air and yield 140 K, respectively. Cycle efficiency 0.8 0.5

1.0 0.6 0.6 Liquid air yield 0.4 Cycle efficiency 0.8 0.5

0.4 0.3

Liquidair yield Cycle efficiency Cycle 0.6 0.4 0.2 0.2

0.4 0.3 0.0

Liquidair yield 0.1 Cycle efficiency Cycle 0.2 70 80 90 100 110 120 130 140 150 160 0.2 Air temperature before the throttle /K 0.0 0.1 Figure 6. Influence of temperature70 before80 90 air100 throttling110 120 130on liquid140 150 air160 yield ratio and cycle efficiency. Air temperature before the throttle /K

In FigureFigure 6, 6.whenInfluence the pressure of temperature is under before 10 air MPa, throttling the on air liquid temperature air yield ratio before and cycle air throttling efficiency. is 75 K, the liquidFigure air 6. yield Influence ratio of is temperature close to 100%, before and air the throttling cycle efficiency on liquid isair close yield toratio 60%. and If cyclethe air efficiency temperature. In Figure6, when the pressure is under 10 MPa, the air temperature before air throttling is is increased from 75 K to 155 K, the liquid air yield ratio and the system cycle efficiency decrease In75 Figure K, the 6, liquid when air the yield pressure ratio is is close under to 100%,10 MPa, and the the air cycle temperature efficiency before is close air to 60%.throttling If the is air 75 K, monotonically. the liquidtemperature air yield is ratio increased is close from to 75 100%, K to 155and K, the the cycle liquid efficiency air yield is ratio close and to the 60%. system If the cycle air temperature efficiency Therefore, the lower the temperature before air throttling, the higher the liquid air yield ratio is increaseddecrease from monotonically. 75 K to 155 K, the liquid air yield ratio and the system cycle efficiency decrease and the cycle efficiency after expansion. In field conditions, the air temperature before the throttling monotonically.Therefore, the lower the temperature before air throttling, the higher the liquid air yield ratio and should be as low as possible. Therefore,the cycle efficiency the lower after the expansion. temperature In field before conditions, air throttling, the air temperature the higher before the the liquid throttling air yield should ratio be as low as possible. and the cycle efficiency after expansion. In field conditions, the air temperature before the throttling should be as low as possible. 0.40 0.25 0.35 0.20 0.30 0.40 0.25 0.25 0.15 0.35 Liquid air yield 0.20 Cycle efficiency 0.20 0.30 0.15 0.10

0.25 Liquidair yield 0.10 0.15 efficiency Cycle Liquid air yield 0.20 0.05 0.05 Cycle efficiency 0.15 0.10

0.00 0.00 Liquidair yield 0.10 efficiency Cycle 4 6 8 10 12 0.05 0.05 Air pressure before the throttle /MPa 0.00 0.00 Figure 7. Inﬂuence of pressure before air throttling on liquid air yield ratio and cycle efﬁciency. Figure 7. Influence of pressure before4 air6 throttling8 on liquid10 air12 yield ratio and cycle efficiency. Air pressure before the throttle /MPa

From Figure 7, we can see that both the liquid air yield ratio and the system cycle efficiency are 0 in theFigure 5 MPa 7. and Influence 140 K o initialf pressure state. before When air raisthrottlinging the on pressure liquid air from yield 5ratio MPa and to cycle6 MPa efficiency while keeping. the temperature stable, the liquid air yield ratio and system cycle efficiency increase rapidly. From Figure 7, we can see that both the liquid air yield ratio and the system cycle efficiency are Then, the liquid air yield ratio and system cycle efficiency increase gradually from 6 MPa to 12 0 in the 5 MPa and 140 K initial state. When raising the pressure from 5 MPa to 6 MPa while keeping MPa. As shown in Figure 5, the maximum inversion pressure of the air is 34.16 MPa, so the pressure the temperature stable, the liquid air yield ratio and system cycle efficiency increase rapidly. Then, the liquid air yield ratio and system cycle efficiency increase gradually from 6 MPa to 12

MPa. As shown in Figure 5, the maximum inversion pressure of the air is 34.16 MPa, so the pressure

Energies 2018, 11, 2540 10 of 12

From Figure7, we can see that both the liquid air yield ratio and the system cycle efficiency are 0 in the 5 MPa and 140 K initial state. When raising the pressure from 5 MPa to 6 MPa while keeping the temperature stable, the liquid air yield ratio and system cycle efficiency increase rapidly. Then, the liquid air yield ratio and system cycle efficiency increase gradually from 6 MPa to 12 MPa. As shown in Figure5, the maximum inversion pressure of the air is 34.16 MPa, so the pressure before throttling must be less than the maximum inversion pressure, in order to ensure a cold effect after throttling. From Figures6 and7, for air at a temperature of 140 K, it is necessary to increase its pressure to at least 6 MPa in order for it to liquefy. According to the above analysis, the pressure before air throttling has a significant influence on the liquid air yield ratio and the system cycle efficiency. Higher pressures and lower temperatures before air throttling are beneficial for increasing the liquid air yield ratio and the system cycle efficiency.

5. Conclusions For an integrated system of liquefied air energy storage and electricity production, a mathematical model of the energy storage stage, energy release stage, and cycle parameter calculation has been established, based on thermodynamic principles. Using the cycle efficiency and the liquid air yield ratio as evaluation indexes, the influence of the outlet pressure of the compressor unit (p4L), the outlet pressure of the cryogenic pump, the heat exchanger effectiveness, the air temperature and pressure before throttling on the performance of integrated system of liquefied air energy storage, and electricity generation are discussed. The following conclusions have been obtained:

• When raising the outlet pressure of the compressor unit (p4L), both the compression work and the expansion work are increased. However, the air is not completely liquefied. The heat collected during the compression process is not fully used in the energy release phase, so the increase of the expansion work is slower than that of the compression work, resulting in a decrease in the cycle efficiency. • After the air is taken out of the liquid air tank, the pressure is increased by the cryogenic pump. The increased air pressure of the cryogenic pump is equivalent to an increase in the air pressure at the inlet of the expander, which increases the expansion work. In this process, the consumption work of the cryogenic pump is much less than the increase in the expansion work, so the system cycle efficiency increases. A larger heat exchanger effectiveness means a better heat transfer effect. Therefore, increasing the outlet pressure of the cryogenic pump and the heat exchanger effectiveness can significantly increase the cycle efficiency of the system. • According to the air inversion curve, the maximum inversion pressure of air is 34.16 MPa, so the pressure before throttling must be less than the maximum inversion pressure, in order to ensure the cold effect after throttling. Under the premise of not exceeding the maximum air inversion pressure, the higher the air pressure and the lower the air temperature before throttling, the greater the liquid air yield ratio after throttling, and the higher the system cycle efficiency.

Author Contributions: Y.X. proposed the research direction, the adaptive method, and the system model. X.X. completed the establishment of the mathematical model of the system, programming with MATLAB, mapping with Origin, and data analysis. X.X. wrote the paper. Funding: This research received no external funding. Acknowledgments: This paper was supported by the Natural Science Foundation of Hebei Province (E2014502085). Conﬂicts of Interest: The authors declare no conﬂicts of interest. Energies 2018, 11, 2540 11 of 12

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