Operating Range for a Combined, Building-Scale Liquid Air Energy Storage and Expansion System: Energy and Exergy Analysis

Article Operating Range for a Combined, Building-Scale Liquid Air Energy Storage and Expansion System: Energy and Exergy Analysis

Todd A. Howe *, Anthony G. Pollman and Anthony J. Gannon

Graduate School of Engineering and Applied Sciences, Naval Postgraduate School, Monterey, CA 93943, USA; [email protected] (A.G.P.); [email protected] (A.J.G.) * Correspondence: [email protected]; Tel.: +1-813-943-1120

Received: 15 September 2018; Accepted: 5 October 2018; Published: 8 October 2018

Abstract: This paper presents the results of an ideal theoretical energy and exergy analysis for a combined, building scale Liquid Air Energy Storage (LAES) and expansion turbine system. This work identifies the upper bounds of energy and exergy efficiency for the combined LAES-expansion system which has not been investigated. The system uses the simple Linde-Hampson and pre-cooled Linde-Hampson cycles for the liquefaction subsystem and direct expansion method, with and without heating above ambient temperature, for the energy production subsystem. In addition, the paper highlights the effectiveness of precooling air for liquefaction and heating air beyond ambient temperature for energy production. Finally, analysis of the system components is presented with an aim toward identifying components that have the greatest impact on energy and exergy efficiencies in an ideal environment. This work highlights the engineering trade-space and serves as a prescription for determining the merit or measures of effectiveness for an engineered LAES system in terms of energy and exergy. The analytical approach presented in this paper may be applied to other LAES configurations in order to identify optimal operating points in terms of energy and exergy efficiencies.

Keywords: liquid air energy storage; energy analysis; exergy analysis; cryogenic system

1. Introduction Liquid air energy storage (LAES) is a developing thermal electrical energy storage technology and is a promising addition to other long-term storage technologies like pumped hydroelectric storage (PHS) and compressed air energy storage (CAES) [1,2]. LAES has a higher energy density than PHS and four to six times the energy density of CAES at 200 bar [1,3]. Studies have shown LAES is capable of higher round trip efficiency than CAES [4]. In addition, LAES has an advantage over CAES and PHS due to not being constrained to geographical features [5]. Although, micro-CAES systems are not constrained to geographic features and are effective in distributed power networks [6,7]. Highview Power Storage developed a 300 kW LAES pilot plant in Slough, Scotland and have a 10 MW commercial demonstration plant planned [8]. LAES has two main subsystems, the air liquefaction subsystem and energy production subsystem. In the liquefaction subsystem, air is compressed, cooled, and expanded which produces liquid air. Multiple configurations like Linde-Hampson cycle, Claude cycle, Heylandt cycle, Collins cycle, and more, liquefy and store air [9]. The energy production system has multiple configurations like direct expansion method, indirect Rankine cycle, indirect Brayton cycle, and other variations that may be implemented [10]. Storage is commonly included as a third subsystem, although this paper includes liquid air storage in the liquefaction subsystem.

Entropy 2018, 20, 770; doi:10.3390/e20100770 www.mdpi.com/journal/entropy Entropy 2018, 20, 770 2 of 17 Entropy 2018, 20, x FOR PEER REVIEW 2 of 17

There areare multiplemultiple thermodynamicthermodynamic studies on liquid air energy storage available in literature. Early researchresearch inin 19771977 compressedcompressed air toto 77 atm,atm, dehumidifieddehumidified airair andand compressedcompressed further to 49 atmatm and cooledcooled for storage; then repressurized liquid air to 80 atm before expanding through a turbine, whichwhich gavegave anan efficiencyefficiency upup toto 72%72% [[11].11]. GuizziGuizzi etet al.al. [[12]12] conductedconducted aa thermodynamicthermodynamic analysisanalysis ofof aa LAES systemsystem withwith aa multi-stagemulti-stagecompressor compressor and and turbine, turbine, and and a a storage storage subsystem, subsystem, which which resulted resulted in in a round-tripa round-trip efficiency efficiency of 54–55%.of 54–55%. A similarA similar system system and and analysis analysis conducted conducted by [by13] [13] showed showed round round trip efficienciestrip efficiencies from 45–57% from 45 when–57% adjusting when adjusting the inlet pressure the inlet to pressure a JT valve. to Another a JT valve. analysis Another demonstrated analysis thedemonstrated effects on LAES the effects energy onefficiency LAES when energy adjusting efficiency the when compressor adjusting efficiency, the compressor compressor effi dischargeciency, pressure,compressor and discharge cryogenic pressure, pump discharge and cryogenic pressure pump [14]. Additional discharge workpressure has focused[14]. Additional on the liquefaction work has subsystem.focused on Abdo the liquefaction et al. conducted subsystem. a thermodynamic Abdo et al. analysisconducted on thea thermodynamic Linde-Hampson analysis cycle, Claude on the cycle,Linde- andHampson Collins cycle, cycle andClaude showed cycle, Claude and Collins and Collins cycle and cycles sho bothwed having Claude higher and Collins overall cycles efficiencies both thanhaving the higher Linde-Hampson overall efficiencies cycle [15 ].than Yu etthe al. Linde conducted-Hampson an exergy cycle [15]. analysis Yu et of al. a Linde-Hampson conducted an exergy cycle withanalysis an ejectorof a Linde and-Hampson showed the cycle addition with an of ejector the ejector and reducedshowed the addition total exergy of the destruction ejector reduced in the cyclethe total [16 ].exergy destruction in the cycle [16]. This paper presents the the results results of of an an ideal ideal theoretical theoretical energy energy and and exergy exergy analysis analysis for for a liquid a liquid air airenergy energy storage storage system. system. Energy Energy is conserved is conserved through through all processes all processes and systems, and systems,but this is butuntrue this for is untrueexergy [17]. for exergy Unlike [ 17exergy]. Unlike analysis, exergy energy analysis, analysis energy does analysisnot account does for not the account quality forof energy; the quality this ofmakes energy; exergy this analysis makes useful exergy when analysis searching useful for when areas searching of improvement for areas within of improvement a system [18,19 within]. The a systemquality [of18 ,energy,19]. The or quality exergy, of energy,is the “maximum or exergy, is work the “maximum which can workbe obtained which can from be a obtained given form from of a givenenergy form using of energythe environmental using the environmental parameters as parameters the reference as the state” reference [20]. state”The importance [20]. The importance of exergy ofanalysis, exergy opposed analysis, toopposed only energy to only analysis, energy analysis, is analyzing is analyzing the irreversibilities the irreversibilities in the system in the systemand its andcomponents. its components. The analysis The in analysis this paper in thisexplores paper the explores upper bounds the upper of energy bounds efficiency of energy and efficiency exergetic andefficiency exergetic of the efficiency combined of the LAES combined-expansion LAES-expansion system, highlights system, the highlights effectiveness the of effectiveness precooling for of precoolingliquefaction, for liquefaction,heating air heating beyond air ambient beyond ambient temperature temperature for expansion, for expansion, and and analysis analysis of of the systemsystem components.components.

2.2. System Description The liquid liquid air air energy energy storage storage system system analyzed analyzed in this this paper paper investigates investigates the two different different liquefactionliquefaction subsystems,subsystems, thethe simple Linde-HampsonLinde-Hampson cycle and the pre pre-cooled-cooled Linde Linde-Hampson-Hampson cycle; and two different energy production subsystems,subsystems, aa direct expansion methodmethod andand the direct expansion method with additionaladditional heatheat added.added. Figure1 1 displays displays thethe completecomplete LAESLAES systemsystem withwith alternative alternative options toto useuse eithereither typetype ofof liquefactionliquefaction subsystemsubsystem oror energyenergy productionproduction subsystem.subsystem.

Makeup Air

1 Qin Compressor d c 2’ 3 2 JT Valve 7 8 5’ 5 HX-2 HX-1 4

Qout 6 Pump b a Turbine Liquid Reservoir Generator 9 HX-1'

Figure 1. System diagramdiagram of a liquidliquid airair energyenergy storagestorage system.system.

The simple Linde-Hampson cycle consists of a compressor, heat exchanger (HX-1), Joule-Thomson (JT) valve, and liquid reservoir. At steady state, mixing of makeup air and return air occurs prior to entering the compressor at state 1. Air is compressed to state 2 and then cooled in HX-

Entropy 2018, 20, 770 3 of 17

EntropyThe 2018 simple, 20, x FOR Linde-Hampson PEER REVIEW cycle consists of a compressor, heat exchanger (HX-1), Joule-Thomson3 of 17 (JT) valve, and liquid reservoir. At steady state, mixing of makeup air and return air occurs prior to 1entering to state the3. The compressor cooled high at state-pressure 1. Air air is is compressed expanded through to state the 2 and JT thenvalve cooled to state in 4 HX-1where to it stateis a 2 3.- Thephase cooled mixture. high-pressure The liquid air reservoir is expanded stores through liquid air the at JT state valve 6 for to statelater 4use where by the it is energy a 2-phase production mixture. Thesubsystem liquid reservoirand the gas stores returns liquid to air HX at-1 state at state 6 for 5 later providing use by the the cooling energy from production states 2 subsystem to 3. The preand-cooled the gas Linde returns-Hampson to HX-1 system at state adds 5 providing an additional the cooling heat from exchanger, states 2 HX to-1 3.′. The pre-cooled subsystem 0 providingLinde-Hampson the additional system adds cooling an additionalin HX-1′ is heat treated exchanger, as a black HX-1 box. The and subsystem only the required providing Qout the is 0 calculatedadditional coolingto achieve in HX-1a desiredis treated state 2 as′ temperature. a black box and only the required Qout is calculated to achieve 0 a desiredThe direct state 2expansiontemperature. method for the energy production subsystem consists of a cryogenic pump, heat exchangerThe direct expansion(HX-2), and method turbine for with the a energy generator production. The cryogenic subsystem pump consists pumps of liquid a cryogenic air from pump, the liquidheat exchanger reservoir (HX-2), to a desired and turbine pressure with to statea generator. 7. Heat The exchanger cryogenic 2 heats pump pressurized pumps liquid liquid air air from to ambientthe liquid temperature reservoir to by a desired the surrounding pressure to heat state or 7. available Heat exchanger waste heat 2 heats to state pressurized 8. A turbine liquid then air expandsto ambient the temperature evaporated air by to the generate surrounding electricity heat to or state available 9. The waste direct heat expansion to state method 8. A turbine is a simple then butexpands an inefficient the evaporated method air to toextract generate liquid electricity air [10]. toThe state system 9. The can direct extract expansion additional method energy is from a simple the liquidbut an air inefficient when heated method beyond to extract ambient liquid temperature air [10]. The prior system to ente canring extract the additionalturbine. The energy Qin represents from the theliquid additional air when heat heated required beyond to ambientheat the temperature liquid air above prior ambient to entering pressure. the turbine. Similar The to Q HXin represents-1′, this is 0 treatedthe additional as a black heat box required where to the heat subsystem the liquid to air achieve above the ambient required pressure. Qin to Similarreach a todesired HX-1 ,state this is8 temperaturetreated as a blackis not boxconsidered. where the subsystem to achieve the required Qin to reach a desired state 8 temperatureMultiple is combinations not considered. of state 2 pressures, state 2′ temperatures, state 7 pressures, and state 8 0 temperaturesMultiple can combinations be used in ofthis state LAES 2 pressures, system. Figure state 2 2 temperatures,shows an example state of 7 pressures,the system and dynamics state 8 oftemperatures the LAES system can be with used one in thispossible LAES combination. system. Figure The2 showsfigure anshows example the liquefaction of the system subsystem dynamics as statesof the 1 LAES through system 5′ where with oneambient possible air it combination. pressurizes air The to figure20 MPa, shows precools the liquefaction to 250 K, and subsystem expands asto 0 generatestates 1 through approximately 5 where 21.3% ambient liquid air yield. it pressurizes The remaining air to 20 gas MPa, passes precools through to 250both K, heat and exchangers, expands to coolinggenerate th approximatelye incoming 21.3% air. States liquid 6 yield. through The remaining 9 represent gas passesthe energy through production both heat exchangers, subsystem. Thecooling subsystem the incoming pumps air. States liquid 6 through air to 100 9 represent MPa, heats the energy beyond production ambient subsystem. temperature The subsystemto 350 K, pumpsand expands liquid isothermally air to 100 MPa, to heatsstate beyond9. This ambientfigure displays temperature an ideal to 350 case K, for and the expands LAES isothermallysystem where to therestate 9.is Thisisothermal figure displayscompression an ideal and case expansion, for the LAES 100% system effective where heat there exchangers, is isothermal and an compression isentropic cryogenicand expansion, pump. 100% effective heat exchangers, and an isentropic cryogenic pump.

Air Temperature Entropy Diagram 400

350 8 9

300 2 1

250 2' 5'

200

Temperature (K)Temperature 3

150

100 7 5 6 4 50 3 4 5 6 7 8 Entropy (kJ/kg)

Liquid-Vapor Dome Constant Pressure Line Constant Enthalpy Line

Figure 2. Air t temperatureemperature e entropyntropy d diagramiagram s showinghowing e eachach statestate in the LAES system.system.

Entropy 2018, 20, 770 4 of 17

3. System Energy Analysis As previously stated, this paper is investigating the upper bounds of an ideal LAES system. Therefore, all components are ideal components, the compressor isothermally compresses fluid, pumps isentropically compress fluids, heat exchangers are 100% effective, the turbine isothermally expands fluid, and there are no losses in lines. This section and the following section are organized by looking at each subsystem individually and then as a complete system.

3.1. Liquefaction Subsystem The key information needed for the liquefaction subsystem is the required work for the compressor, the liquid yield, and required heat rejection from HX-10. Using the ﬁrst and second law on the compressor, the work per unit mass required to compress air from state 1 to 2 is [9,17,21]:

. Wc . = T1(s2 − s1) + (h1 − h2) (1) m This analysis calculated the liquid yield for the simple Linde-Hampson subsystem using a control volume encompassing HX-1, the JT valve, and liquid reservoir. The control volume excludes HX-10 and therefore, state 2 equals state 20 and state 50 equals state 1. Since there is no work or heat transferred to or from this control volume, the energy balance is [9,21]:

. . . . mh2 = m f h f + m − m f h1 (2)

The ratio of liquid mass flow rate to mass flow rate provides the liquid yield for the simple Linde-Hampson subsystem: . m f h2 − h1 Y = . = (3) m h f − h1 The compressor work per unit mass liquefied is therefore the compressor work per unit mass divided by the liquid yield:

. . Wc WC h f − h1 . = . = [T1(s2 − s1) + (h1 − h2)] (4) m f mY h2 − h1

The pre-cooled Linde-Hampson system requires the use of a second heat exchanger (HX-10)[9]. . . There are two cooling streams, Qout stream and the returning air stream. The required Qout for any desired temperature at state 20 is based on the energy balance of HX-10 [9]:

. . . . . . . . mrha + mh2 + m − m f h50 = mrhb + mh20 + m − m f h1 (5)

. Assuming the mass ﬂow rate through the liquefaction subsystem, m, is equal to the mass ﬂow . rate in the black box subsystem, mr, rearranging the equation and solving for Qout per unit mass gives:

. Qout . = ha − h = (h 0 − h2) + (1 − Y)(h1 − h 0 ) (6) m b 2 5

Using the previous control volume but now including HX-10, the energy balance is [9]:

. . . . . . mrha + mh2 = mrhb + m − m f h1 + m f h6 (7) Entropy 2018, 20, 770 5 of 17

Deﬁning the black box subsystem mass ﬂow-rate ratio as [9]:

. mr r = . (8) m The yield of the pre-cooled Linde-Hampson subsystem is therefore:

. m f h2 − h1 ha − hb Y = . = + r (9) m h f − h1 h f − h1

As Equation (9) shows, pre-cooling provides additional liquid yield. This analysis uses the assumption that the ratio, r, is equal to one and 100% effective heat exchangers. Therefore, the liquid yield of the subsystem is unchanged from Equation (3).

3.2. Energy Production Subsystem The energy calculations needed for the direct expansion method is the cryogenic pump work and the turbine work. The analysis assumes that the mass flow rate of the energy production subsystem is equal to the mass flow rate of the liquefaction subsystem. Additionally, the analysis assumes the pump isentropically compresses liquid air and there are no heat losses in the pump. Using these assumptions, the pump work is defined as: . W p . = h6 − h7 (10) m Assuming isothermal expansion, the turbine work is:

. Wt . = T8(s9 − s8) + (h8 − h9) (11) m No work is associated with HX-2 for the direct expansion method. This ideal system assumes the compressed liquid air reaches ambient temperature through a heat exchanger by means of the surrounding air or by waste heat recovery. Although this is not practical in a real system, this is a step in ensuring the analysis determines the true upper bounds of the system. Providing additional heat to HX-2 allows state 8 to reach temperatures beyond ambient temperature. The analysis assumes additional heat required is only heat required beyond 300 K at a particular pressure. Therefore, assuming the mass ﬂow rate of the heating source is equivalent to the mass ﬂow rate of the energy production subsystem, the equation for additional heat is:

. Qin . = h8 − h300K (12) m where h300K is the enthalpy of air at a temperature of 300 K at a given pressure.

3.3. Complete LAES System The first law measure of performance for the complete LAES system is the overall system efficiency, or round trip efficiency. The equation to calculate the overall system efficiency is dependent on the subsystems used. The simple Linde-Hampson subsystem with direct expansion method has work inputs to the compressor and pump from Equations (4) and (10), respectively. The heat rejection . 0 required from Qout in HX-1 for the pre-cooling Linde-Hampson subsystem requires additional work to be performed. This work is calculated as the work required for a Carnot refrigerator [17]:

. . W HX10 Qout T1 . = . − 1 (13) m f m f T50 Entropy 2018, 20, 770 6 of 17

Given liquid air is the working fluid, using work per unit mass liquefied is preferred for energy efficiency calculations. When the temperature of state 8 exceeds ambient temperatures, additional work is required to add the necessary heat to achieve this temperature. This additional work is defined as the work required for a Carnot heat pump [17]:

. . WHX2 Qin T7 . = . 1 − (14) me me T8

The overall system efﬁciency is the ratio of work output to inputs:

. W = t ηsys . . . . (15) WC + W + W + W Y p HX10 HX2

4. System Exergy Analysis The below exergy analysis uses a steady-state exergy rate balance to calculate the exergy destruction within a given component, as seen in Equation (16) [17]: ! . . . T0 . . 0 = ∑ 1 − Qj − Wcv + ∑ miψi − ∑ meψe − I (16) Tj where the exergy ﬂow, ψ, is deﬁned as [17]:

V2 ψ = h − h − T (s − s ) + i + gz (17) i i 0 0 i 0 2 i This analysis assumes kinetic and potential energy terms are negligible, and therefore Equation (17) reduces to: ψi = hi − h0 − T0(si − s0) (18)

The reference state temperature, T0, is assumed to be 300 K at a pressure of 0.101325 MPa. . The analysis will present the calculations of the exergy destruction rate, I, and exergetic efﬁciency, ε, for each component and the system.

4.1. Liquefaction Subsystem From state 1 to 2, there is no temperature change, and therefore, the compressor exergy destruction rate is: . . Ic −Wc . = . + ψ1 − ψ2 (19) m m Substituting in Equation (18):

. . Ic −Wcv . = . + h1 − h2 − T0(s1 − s2) (20) m m The exergetic efﬁciency for the compressor is [17,22]:

ψ2 − ψ1 εc = . (21) −W . cv m Entropy 2018, 20, 770 7 of 17

. . Assuming the mass ﬂow rates m = mr with no work or heat loss, the exergy destruction rate for HX-10 is [23]: . I HX10 . = (ψ2 − ψ 0 ) + (ψa − ψ ) + (1 − Y)(ψ 0 − ψ1) (22) m 2 b 5 The exergetic efﬁciency for HX-10 is the ratio of the exergy increase of the hot stream to the exergy decrease in the cold streams [17,22]:

(ψ − ψ 0 ) ε = 2 2 (23) HX10 (ψb − ψa) + (1 − Y)(ψ1 − ψ50 )

The exergy destruction and exergetic efﬁciency for HX-1 is:

. IHX1 . = (ψ 0 − ψ3) + (1 − Y)(ψ5 − ψ 0 ) (24) m 2 5

(ψ 0 − ψ ) = 2 3 εHX1 (25) (1 − Y)(ψ50 − ψ5) The analysis assumes there is no work or heat transfer to the surroundings for fluid flow through the JT valve. In addition, there is no change in enthalpy during a throttling process; therefore, the exergy destruction rate reduces to: . I JT . = T0(s4 − s3) (26) m The JT valve exergetic efficiency is defined as the ratio of the exergy flow out to the exergy flow in [22]: ψ4 ε JT = (27) ψ3 The analysis completes the calculation for the simple Linde-Hampson subsystem exergetic efficiency by taking the ratio of the reversible work to the actual work [21,24]. The reversible work is the difference in exergy flow of states 1 and 6 [21]:

wrev = ψ6 − ψ1 = h6 − h1 − T0(s6 − s1) (28)

The simple Linde-Hampson subsystem exergy efﬁciency is:

wrev εsLH = . (29) WC Y

The pre-cooled Linde-Hampson subsystem exergy efﬁciency must also account for the from work input to HX-10: w = rev ε pcLH . . (30) WC + W Y HX10

4.2. Energy Production Subsystem The ideal pump is assumed to be isentropic, which results in an exergy destruction rate of:

. . I p −W p . = . + h6 − h7 (31) me me Entropy 2018, 20, 770 8 of 17

The exergetic efﬁciency of the pump is:

ψ7 − ψ6 ε p = . (32) −W p . me

. . Assuming the mass ﬂow rates ma and me are equivalent, the exergy destruction and exergetic efﬁciency of HX-2 is: . It . = (ψc − ψd) + (ψ7 − ψ8) (33) me

(ψ7 − ψ8) εHX2 = (34) (ψd − ψc) The ideal turbine is assumed to be isothermal, which results in an exergy destruction rate of:

. . It −Wt . = . + ψ8 − ψ9 (35) me me

The exergetic efﬁciency of the turbine is:

ψ9 − ψ8 εt = . (36) −W . t me

4.3. Complete LAES System The total exergy destruction rate of the system is the sum of all component exergy destruction rates from Equations (19), (22), (24), (26), (31), (33) and (35). The exergetic efﬁciency for the entire LAES system is deﬁned as [22]: . . Wact − Itot εsys = . (37) Wact . where Wact is the sum of all work input:

. . . . . W = W + W + W + W (38) act C p HX10 HX2

5. Results and Discussion

5.1. First Law Results and Discussion The following results use values of enthalpy and entropy gathered from [25]. The tables available from Lemmon et al. provide only discrete iso-pressure values as shown in Table1.

Table 1. List of iso-pressures available from Lemmon et al. [25].

Pressure (MPa) 0.101325 0.2 0.5 1 2 5 10 20 50 100 200 500 1000 2000

The analysis found that the pressure range for the liquefaction subsystem to produce any liquid yield is 5 MPa to 100 MPa; at 200 MPa, the liquid yield drops to zero. Figure3 shows the liquid yield for the simple Linde-Hampson subsystem. These results match results found in [9,26]. The maximum yield point found by Joshi and Patel was 0.107 at a pressure of 32 MPa, which is represented on Figure3 with an ‘x.’ Entropy 2018, 20, x FOR PEER REVIEW 8 of 17

5. Results and Discussion

Table 1. List of iso-pressures available from Lemmon et al. [25].

Pressure (MPa) 0.101325 0.2 0.5 1 2 5 10 20 50 100 200 500 1000 2000

The analysis found that the pressure range for the liquefaction subsystem to produce any liquid yield is 5 MPa to 100 MPa; at 200 MPa, the liquid yield drops to zero. Figure 3 shows the liquid yield for the simple Linde-Hampson subsystem. These results match results found in [9,26]. The maximum yield point found by Joshi and Patel was 0.107 at a pressure of 32 MPa, which is represented on FigureEntropy 20183 with, 20, 770an ‘x.’ 9 of 17

0.12 [26] 0.1

0.08

0.06

LiquidYield 0.04

0.02

0 0 25 50 75 100 125 150 175 200 State 2 Pressure (MPa)

Figure 3. Liquid yield for simple Linde-Hampson subsystem over varying state 2 pressures. Figure 3. Liquid yield for simple Linde-Hampson subsystem over varying state 2 pressures. Figure4 shows an alternative view of the liquid yield for the simple Linde-Hampson subsystem. As FigureFigure2 4shows, shows thean alternative expansion view of air of from the liquid state 3yield to 4 for is anthe isenthalpic simple Linde process.-Hampson This subsystem. throttling Asprocess Figure must 2 shows, follow the linesexpansion of constant of air enthalpyfrom state shown 3 to on4 is a an temperature isenthalpic entropy process. diagram. This throttling Figure4 processshows the must lines follow of constant the lines enthalpy of constant followed enthalpy over the shown different on statea temperature 2 pressures. entropy This ﬁgure diagram. also Figureshows 4 the shows corresponding the lines of constant state 3 temperature enthalpy followed for each over state the 2 different pressure. state The 2 statepressures. 3 temperature This figure is alsoEntropyimportant shows 2018, when20the, x FORcorresponding considering PEER REVIEW the state required 3 temperature effectiveness for each of a state heat exchanger2 pressure. to The reach state this 3 temperature temperature.9 of 17 is important when consideringLiquid Yield the required for Varying effectiveness State 2 Pressures of a heat exchanger to reach this temperature. 180 170 162 K 160 170 K 165 K 150 144 K 140 151 K

130

120 107 K 110

Temperature (K)Temperature 100

80 5 50 MPa 6 70 20 MPa 10 & 100 MPa 5 MPa 200 MPa 60 3 4 5 6 Entropy (kJ/kg-K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa 200 MPa Figure 4. AirAir t temperatureemperature e entropyntropy d diagramiagram s showinghowing l liquidiquid y yieldield with l linesines of c constantonstant e enthalpynthalpy from sstatetate 3 to s statetate 4.

Displayed in Figure 55,, thethe resultingresulting compressorcompressor workwork perper unitunit massmass liqueﬁedliquefied showsshows thethe optimaloptimal state 2 2 pressure pressure is is around around 20 20to 50 to MPa. 50 MPa. The liquid The liquid yield yieldof this ofsystem this systemis likely is to likely be a key to bemeasure a key ofmeasure performance of performance for a building for a- building-scalescale LAES system. LAES Quickly system. replenishing Quickly replenishing liquid air liquid supply air ensures supply continuedensures continued support supportduring peak during demands. peak demands. Figure 6Figure shows6 theshows liquid the yield liquid for yield the forpre the-cooled pre-cooled Linde- HampsonLinde-Hampson subsystem. subsystem. This figure This clearly ﬁgure shows clearly the shows improvement the improvement of liquid yield of liquid over yield all pressures over all withpressures pressures with pressuresof 20 and 50 of 20MPa and producing 50 MPa producing the highest the liquid highest yield. liquid yield. Compressor Work per Unit Mass Liquefied 16000

14000

12000

10000

8000 kJ/kg 6000

4000

2000

0 0 10 20 30 40 50 60 70 80 90 100 State 2 Pressure

Figure 5. Compressor work per unit mass liquefied for simple Linde-Hampson subsystem.

Entropy 2018, 20, x FOR PEER REVIEW 9 of 17 Liquid Yield for Varying State 2 Pressures 180

170 162 K 160 170 K 165 K 150 144 K 140 151 K

130

120 107 K 110

Temperature (K)Temperature 100

80 5 50 MPa 6 70 20 MPa 10 & 100 MPa 5 MPa 200 MPa 60 3 4 5 6 Entropy (kJ/kg-K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa 200 MPa Figure 4. Air temperature entropy diagram showing liquid yield with lines of constant enthalpy from state 3 to state 4.

Displayed in Figure 5, the resulting compressor work per unit mass liquefied shows the optimal state 2 pressure is around 20 to 50 MPa. The liquid yield of this system is likely to be a key measure of performance for a building-scale LAES system. Quickly replenishing liquid air supply ensures continued support during peak demands. Figure 6 shows the liquid yield for the pre-cooled Linde- HampsonEntropy 2018 ,subsystem.20, 770 This figure clearly shows the improvement of liquid yield over all pressures10 of 17 with pressures of 20 and 50 MPa producing the highest liquid yield. Compressor Work per Unit Mass Liquefied 16000

14000

12000

10000

8000 kJ/kg 6000

4000

2000

0 0 10 20 30 40 50 60 70 80 90 100 State 2 Pressure Entropy 2018, 20, x FOR PEER REVIEW 10 of 17 Figure 5. Compressor work per unit mass liqueﬁed for simple Linde-Hampson subsystem. Figure 5. Compressor work per unit mass liquefied for simple Linde-Hampson subsystem. 0.500

0.450

0.400

0.350

0.300

0.250

0.200 Liquid Yield Liquid

0.150

0.100

0.050

0.000 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 6. Liquid yield for pre-cooled Linde-Hampson subsystem with varying state 2 pressures. Figure 6. Liquid yield for pre-cooled Linde-Hampson subsystem with varying state 2 pressures. When the liquid increases, this reduces the work required by the compressor on a per unit mass When the liquid increases, this reduces the work required by the compressor on a per unit mass liquefied basis. Figure7 shows the resulting compressor work per unit mass liquefied for the pre-cooled liquefied basis. Figure 7 shows the resulting compressor work per unit mass liquefied for the Linde-Hampson subsystem. This figure shows all pressures begin to converge, except 100 MPa, at a pre-cooled Linde-Hampson subsystem. This figure shows all pressures begin to converge, except 100 state 20 temperature around 250 K. MPa, at a state 2′ temperature around 250 K. Compressor Work per Unit Mass Liquefied 15000

13500

12000

10500

9000

7500 kJ/kg 6000

4500

3000

1500

0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature (K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 7. Compressor work for pre-cooled Linde subsystem with varying state 2 pressures.

In order to achieve a desired state 2′ temperature, the system must remove additional heat from the pressurized air stream in HX-1′. Figure 8 displays the additional heat removed from this stream by the external black box system. As the required heat removal increases, required total work of the liquefaction subsystem increases. Figure 9 presents the total work required by the pre-cooled liquefaction subsystem. This figure shows the same convergence of pressures as Figure 7, but also displays the impact HX-1′. The required work at temperatures below 220 K begins to level out and then begins to increase at approximately 150 K.

Entropy 2018, 20, x FOR PEER REVIEW 10 of 17

0.500

0.450

0.400

0.350

0.300

0.250

0.200 Liquid Yield Liquid

0.150

0.100

0.050

0.000 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 6. Liquid yield for pre-cooled Linde-Hampson subsystem with varying state 2 pressures.

When the liquid increases, this reduces the work required by the compressor on a per unit mass liquefied basis. Figure 7 shows the resulting compressor work per unit mass liquefied for the

Entropypre-cooled2018, 20 Linde, 770 -Hampson subsystem. This figure shows all pressures begin to converge, except11 of 100 17 MPa, at a state 2′ temperature around 250 K. Compressor Work per Unit Mass Liquefied 15000

13500

12000

10500

9000

7500 kJ/kg 6000

4500

3000

1500

0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature (K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 7. Compressor work for pre-cooled Linde subsystem with varying state 2 pressures. Figure 7. Compressor work for pre-cooled Linde subsystem with varying state 2 pressures. In order to achieve a desired state 20 temperature, the system must remove additional heat from the pressurizedIn order to airachieve stream a desired in HX-1 state0. Figure 2′ temperature,8 displays the the additional system must heat remove removed additional from this heat stream from bythe the pressurized external blackair stream box system.in HX-1′ As. Figure the required 8 displays heat the removal additional increases, heat removed required from total this work stream of theby the liquefaction external black subsystem box system. increases. As the Figure required9 presents heat removal the total increases, work required required by total the pre-cooledwork of the liquefactionliquefaction subsystem. subsystem This increases. ﬁgure Figure shows the9 presents same convergence the total work of pressures required as by Figure the 7 pre, but-cooled also displaysliquefactio then impactsubsystem. HX-1 This0. The figure required shows work the atsame temperatures convergence below of pressures 220 K begins as Figure to level 7, outbut andalso Entropythendisplays begins 2018 the, 20 to, ximpact increaseFOR PEER HXat REVIEW-1 approximately′. The required 150 work K. at temperatures below 220 K begins to level out11 of and 17 then begins to increase Heatat approximately Removal 150 Required K. for Pre-Cooling 180

160

140

120

100

kJ/kg 80

0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2 Temperature (K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 8. Required heat removal for pre-cooled Linde-Hampson subsystem. Figure 8. Required heat removal for pre-cooled Linde-Hampson subsystem. Total Work per Unit Mass Liquefied 15000

13500

12000

10500

9000

7500 kJ/kg 6000

4500

3000

1500

0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature (K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 9. Total work per unit mass liquefied for the pre-cooled liquefaction subsystem.

The LAES system efficiency is dependent on multiple factors, including state 2 pressure, state 2′ temperature, state 7 pressure, and state 8 temperature. Figure 10 displays the resulting LAES system energy efficiency when using state 2 and 7 pressures and state 2′ temperature as chosen factors. There is a clear increase of system efficiency as the state 2′ temperature is reduced and state 7 pressure is increased. Similar to the compressor work per unit mass liquefied results in Figure 7, the LAES system efficiency peaks at state 2 pressures around 20 and 50 MPa.

Entropy 2018, 20, x FOR PEER REVIEW 11 of 17 Heat Removal Required for Pre-Cooling 180

160

140

120

100

kJ/kg 80

0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2 Temperature (K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Entropy 2018, 20, 770 12 of 17 Figure 8. Required heat removal for pre-cooled Linde-Hampson subsystem. Total Work per Unit Mass Liquefied 15000

13500

12000

10500

9000

7500 kJ/kg 6000

4500

3000

1500

0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature (K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 9. Total work per unit mass liquefied for the pre-cooled liquefaction subsystem. Figure 9. Total work per unit mass liquefied for the pre-cooled liquefaction subsystem. The LAES system efficiency is dependent on multiple factors, including state 2 pressure, state 20 temperature,The LAES state system 7 pressure, efficiency and is state dependent 8 temperature. on multiple Figure factors, 10 displays including the resultingstate 2 pressure, LAES system state 2′ energytemperature, efficiency state when 7 pressure, using and state state 2 and 8 temperature. 7 pressures Figure and state 10 displays 20 temperature the resulting as chosen LAES factors. system Thereenergy is a efficiency clear increase when of using system state efficiency 2 and as 7 the pressures state 20 andtemperature state 2′ temperature is reduced and as state chosen 7 pressure factors. isThere increased. is a clear Similar increase to theof system compressor efficiency work as per the unitstate mass2′ temperature liquefied resultsis reduced in Figure and state7, the 7 pressure LAES Entropysystemis increased. 2018 efficiency, 20, xSimilar FOR peaks PEER to atREVIEW the state compressor 2 pressures work around per 20unit and mass 50 MPa.liquefied results in Figure 7, the12 LAES of 17 system efficiency peaks at stateLAES 2 pressures System around Energy 20 and Efficiency 50 MPa.

0.6 200 K

250 K 0.5 300 K 0.4

0.3

0.2 Efficiency System

0.1 LAES

0.0 50 100 10 20

1000 5 500 50 100 200 20

100 10 50 5 100

20 20 50 10 5 5 10

0.0-0.1 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6

Figure 10. Resulting LAES LAES s systemystem e energynergy e efficiencyfficiency with with v varyingarying s statetate 2 2 and and 7 7 p pressuresressures and t threehree 0 sstatetate 2 ′ ttemperatures.emperatures. Figure 11 presents a narrower view of Figure 10 by reducing to only three state 2 pressures Figure 11 presents a narrower view of Figure 10 by reducing to only three state 2 pressures of of 10, 20, and 100 MPa. This figure depicts a clear gain in energy efficiency choosing 20 MPa and 10, 20, and 100 MPa. This figure depicts a clear gain in energy efficiency choosing 20 MPa and lower lower state 20 temperatures. Although the ranges presented on the figure may not be achievable in a state 2′ temperatures. Although the ranges presented on the figure may not be achievable in a building-scale LAES system. Maximum state 7 pressure is likely to be approximately 100 MPa given building-scale LAES system. Maximum state 7 pressure is likely to be approximately 100 MPa given size restrictions for a building-scale system. A state 20 temperature of 250 K is likely to be attainable. size restrictions for a buildingLAES-scale system.System A stateEnergy 2′ temperature Effeciency of 250 K is likely to be attainable.

0.6

0.5

0.4

0.3 Efficiency

0.2

0.1

0 0 100 200 300 400 500 600 700 800 900 1000 State 7 Pressure (MPa) State 2' Temp = 300 K State 2' Temp = 250 K State 2' Temp = 200 K State 2 Pressure = 10 MPa State 2 Pressure = 20 MPa State 2 Pressure = 100 MPa

Figure 11. Resulting LAES system energy efficiency over full range state 7 pressures and three selected State 2′ temperatures and state 2 pressures.

At these factors, the approximate LAES system efficiency at 20 MPa is 18.4%. Increasing the temperature into the turbine inlet increases the energy efficiency of the LAES system. Figure 12 depicts this increase in energy efficiency using a state 2′ temperature of 250 K and state 7 pressure of 100 MPa. Although not depicted in Figure 12, there is a maximum temperature where gains in efficiency would reach an asymptotic limit.

Entropy 2018, 20, x FOR PEER REVIEWLAES System Energy Efficiency 12 of 17

0.6 200 K

250 K 0.5 300 K 0.4

0.3

0.2 Efficiency System

0.1 LAES

0.0 50 100 10 20

1000 5 500 50 100 200 20

100 10 50 5 100

20 20 50 10 5 5 10

0.0-0.1 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6

Figure 10. Resulting LAES system energy efficiency with varying state 2 and 7 pressures and three state 2′ temperatures.

Figure 11 presents a narrower view of Figure 10 by reducing to only three state 2 pressures of 10, 20, and 100 MPa. This figure depicts a clear gain in energy efficiency choosing 20 MPa and lower state 2′ temperatures. Although the ranges presented on the figure may not be achievable in a building-scale LAES system. Maximum state 7 pressure is likely to be approximately 100 MPa given Entropy 2018, 20, 770 13 of 17 size restrictions for a buildingLAES-scale system.System A stateEnergy 2′ temperature Effeciency of 250 K is likely to be attainable.

0.6

0.5

0.4

0.3 Efficiency

0.2

0.1

Figure 11. ResultingResulting LAES LAES s systemystem e energynergy e efficiencyfficiency over f fullull r rangeange s statetate 7 7 p pressuresressures and three three s selectedelected 0 State 2 ′ ttemperaturesemperatures and s statetate 2 p pressures.ressures. At these factors, the approximate LAES system efficiency at 20 MPa is 18.4%. Increasing the At these factors, the approximate LAES system efficiency at 20 MPa is 18.4%. Increasing the temperature into the turbine inlet increases the energy efficiency of the LAES system. Figure 12 depicts temperature into the turbine inlet increases the energy efficiency of the LAES system. Figure 12 this increase in energy efficiency using a state 20 temperature of 250 K and state 7 pressure of 100 MPa. depicts this increase in energy efficiency using a state 2′ temperature of 250 K and state 7 pressure of Although not depicted in Figure 12, there is a maximum temperature where gains in efficiency would 100 MPa. Although not depicted in Figure 12, there is a maximum temperature where gains in Entropyreach an2018 asymptotic, 20, x FOR PEER limit. REVIEW 13 of 17 efficiency would reach an asymptoticLAES System limit. Energy Efficiency

0.350

0.300

0.250

0.200

0.150 Efficiency 0.100

0.050

0.000 300 325 350 375 400 425 450 475 500 State 8 Temperature (K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 12. Effects of increasing state 8 temperature on LAES energy efficiency at a state 20 temperature Figure 12. Effects of increasing state 8 temperature on LAES energy efficiency at a state 2′ temperature of 250 K and state 7 pressure of 100 MPa. of 250 K and state 7 pressure of 100 MPa. 5.2. Second Law Results and Discussion 5.2. Second Law Results and Discussion The exergy destruction and exergetic efficiency of the compressor, HX-10, the pump, HX-2, and the turbineThe are exergy trivial destruction due to using and ideal exergetic cases. efficiency The exergy of destructionthe compressor, for each HX- of1′, thesethe pump, components HX-2, and are thezero turbine and the are exergetic trivial due efficiency to using is equal ideal tocases. one. The Although exergy this destruction is not the for case each for of the these turbine components when the are zero and the exergetic efficiency is equal to one. Although this is not the case for the turbine when the temperature at state 8 exceeds 300 K. The largest attributer to exergy destruction in this system is the JT valve. Figure 13 shows the JT valve exergetic efficiency over different state 2 pressures when decreasing the state 2′ temperature. The optimal state 2 pressure in terms of exergetic efficiency for the JT valve is 20 MPa when state 2′ temperatures are below 270 K. JT Valve Exergetic Efficiency 0.8

0.7

0.6

0.5

0.4

0.3

Exergetic Efficiecny Exergetic 0.2

0.1

0 150 170 190 210 230 250 270 290 State 2' Temperature

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 13. JT valve exergetic efficiency with varying state 2 pressures and state 2′ temperatures.

Figure 14 displays the exergetic efficiency of HX-1 over varying state 2′ temperatures and state 2 pressures. This component shows 20 MPa as the worst pressure in terms of exergetic efficiency. Although, at this pressure, the exergy destruction rate of HX-1 is substantially less than the JT valve, and therefore, has less impact on the overall system exergetic efficiency. Figure 15 depicts these two components exergy destructions at a state 2 pressure of 20 MPa.

Entropy 2018, 20, x FOR PEER REVIEW 13 of 17 LAES System Energy Efficiency 0.350

0.300

0.250

0.200

0.150 Efficiency 0.100

0.050

0.000 300 325 350 375 400 425 450 475 500 State 8 Temperature (K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 12. Effects of increasing state 8 temperature on LAES energy efficiency at a state 2′ temperature of 250 K and state 7 pressure of 100 MPa.

5.2. Second Law Results and Discussion The exergy destruction and exergetic efficiency of the compressor, HX-1′, the pump, HX-2, and Entropy 2018, 20, 770 14 of 17 the turbine are trivial due to using ideal cases. The exergy destruction for each of these components are zero and the exergetic efficiency is equal to one. Although this is not the case for the turbine when temperaturethe temperature at state at state 8 exceeds 8 exceeds 300 K.300 The K. The largest largest attributer attributer to exergy to exergy destruction destruction in this in this system system is the is JTthe valve. JT valve. FigureFigure 13 13 showsshows thethe JTJT valve exergetic efﬁciencyefficiency overover differentdifferent statestate 22 pressures whenwhen decreasingdecreasing thethe statestate 220′ temperature.temperature. The The optimal optimal state state 2 2 pressure pressure in in terms terms of of exergetic exergetic efﬁciency efficiency for for the the JT JT valve valve is 20is 20 MPa MPa when when state state 20 temperatures2′ temperatures are are below below 270 270 K. K. JT Valve Exergetic Efficiency 0.8

0.7

0.6

0.5

0.4

0.3

Exergetic Efficiecny Exergetic 0.2

0.1

0 150 170 190 210 230 250 270 290 State 2' Temperature

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 13. JT valve exergetic efficiency with varying state 2 pressures and state 20 temperatures. Figure 13. JT valve exergetic efficiency with varying state 2 pressures and state 2′ temperatures. Figure 14 displays the exergetic efficiency of HX-1 over varying state 20 temperatures and state 2 Figure 14 displays the exergetic efficiency of HX-1 over varying state 2′ temperatures and pressures. This component shows 20 MPa as the worst pressure in terms of exergetic efficiency. state 2 pressures. This component shows 20 MPa as the worst pressure in terms of exergetic efficiency. Although, at this pressure, the exergy destruction rate of HX-1 is substantially less than the JT valve, Although, at this pressure, the exergy destruction rate of HX-1 is substantially less than the JT valve, and therefore, has less impact on the overall system exergetic efficiency. Figure 15 depicts these two and therefore, has less impact on the overall system exergetic efficiency. Figure 15 depicts these two Entropycomponents 2018, 20, exergyx FOR PEER destructions REVIEW at a state 2 pressure of 20 MPa. 14 of 17 components exergy destructionsHX at a- 1state Exergetic 2 pressure Efficiencyof 20 MPa. 0.8

0.7

0.6

0.5

0.4

0.3 1 Exergetic Efficiency Exergetic1

- 0.2 HX

0.1

0.0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature 5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 14. HX-1 exergetic efﬁciency with varying state 2 pressures and state 20 temperatures. Figure 14. HX-1 exergeticExergy efficiency Destruction with varying Comparison state 2 pressures for and state 2′ temperatures. JT Valve and HX-1 350

300

250

200

150

100 Exergy Destruction Destruction Exergy (kJ/kg) 50

0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature

JT Valve at 20 MPa HX-1 at 20 MPa

Figure 15. Exergy destruction comparison of the JT valve and HX-1 at a state 2 pressure of 20 MPa over varying state 2′ temperatures.

Figure 16 shows the exergetic efficiency of the liquefaction subsystem. This figure again shows that 20 MPa to 50 MPa are an optimum pressure range. Figure 17 displays the changes in the LAES system exergetic efficiency when changing the state 2′ temperature and pressure. The optimum pressure displayed on the figure is 20 MPa.

Entropy 2018, 20, x FOR PEER REVIEW 14 of 17 HX-1 Exergetic Efficiency 0.8

0.7

0.6

0.5

0.4

0.3 1 Exergetic Efficiency Exergetic1

- 0.2 HX

0.1

0.0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature 5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Entropy 2018Figure, 20, 770 14. HX-1 exergeticExergy efficiency Destruction with varying Comparison state 2 pressures for and state 2′ temperatures. 15 of 17 JT Valve and HX-1 350

300

250

200

150

100 Exergy Destruction Destruction Exergy (kJ/kg) 50

0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature

JT Valve at 20 MPa HX-1 at 20 MPa

Figure 15. Exergy destruction comparison of the JT valve and HX-1 at a state 2 pressure of 20 MPa over Figure 15. Exergy destruction comparison of the JT valve and HX-1 at a state 2 pressure of 20 MPa varying state 20 temperatures. over varying state 2′ temperatures. Figure 16 shows the exergetic efficiency of the liquefaction subsystem. This figure again shows that 20Figure MPa 16 to shows 50 MPa the are exergetic an optimum efficiency pressure of the range. liquefaction Figure 17subsystem. displays theThis changes figure again in the shows LAES thatsystem 20 MPa exergetic to 50 efficiencyMPa are an when optimum changing pressure the staterange. 2 0Figuretemperature 17 displays and pressure.the changes The in the optimum LAES Entropysystempressure 2018 exergetic displayed, 20, x FOR efficiency PEER on the REVIEW figureLiquefaction when is 20changing MPa. Subsystem the state 2′ temperature Exergetic and pressure. The optimum15 of 17 pressure displayed on the figure is 20 MPa. Efficiency 0.7

0.6

0.5

0.4

0.3

0.2

EfficiencyExergetic 0.1

0.0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 16. Exergetic efﬁciency of the liquefaction subsystem. Figure 16. Exergetic efficiency of the liquefaction subsystem. LAES System Exergetic Efficiency 1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3 Exergetic Efficiency Exergetic 0.2

0.1

0.0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature (K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 17. LAES system exergetic efficiency at a state 7 pressure of 100 MPa and state 8 temperature of 300 K.

6. Conclusions This paper conducted an energy and exergy analysis of an ideal, combined liquid air energy storage and expansion system. The results showed that the pre-cooled Linde-Hampson subsystem was superior to the simple Linde-Hampson subsystem and heating liquid air beyond ambient temperature was superior to heating to only ambient. The optimal state 2 pressure range was 20 to 50 MPa where there was maximum liquid yield. Pre-cooling resulted in an increase in liquid yield, energy efficiency, and exergy efficiency. Although, pre-cooling below 150 K will result in increased total work per unit mass liquefied. Heating the liquid air beyond ambient temperature results in increased electrical generation and increases the overall efficiency of the system. Additional improvement of the energy and exergy efficiency may be found with alternative liquefaction subsystems, which utilize an expander, such as the Claude and Heylandt systems. The

Entropy 2018, 20, x FOR PEER REVIEWLiquefaction Subsystem Exergetic 15 of 17 Efficiency 0.7

0.6

0.5

0.4

0.3

0.2 Exergetic EfficiencyExergetic

0.1

0.0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Entropy 2018, 20, 770 16 of 17 Figure 16. Exergetic efficiency of the liquefaction subsystem. LAES System Exergetic Efficiency 1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3 Exergetic Efficiency Exergetic 0.2

0.1

0.0 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 State 2' Temperature (K)

5 MPa 10 MPa 20 MPa 50 MPa 100 MPa

Figure 17. LAES system exergetic efficiency at a state 7 pressure of 100 MPa and state 8 temperature of 300 K. Figure 17. LAES system exergetic efficiency at a state 7 pressure of 100 MPa and state 8 temperature 6. Conclusionsof 300 K. This paper conducted an energy and exergy analysis of an ideal, combined liquid air energy 6. Conclusions storage and expansion system. The results showed that the pre-cooled Linde-Hampson subsystem was superiorThis topaper the simple conducted Linde-Hampson an energy and subsystem exergy and analysis heating of liquidan ideal air, beyondcombined ambient liquid temperature air energy storagewas superior and expansion to heating system. to only ambient.The results The showed optimal that state the 2 pressurepre-cooled range Linde was-Hampson 20 to 50 MPasubsystem where wasthere superior was maximum to the liquid simple yield. Linde Pre-cooling-Hampson resulted subsystem in an and increase heating in liquid liquid yield, air beyond energy efficiency, ambient temperatureand exergy efficiency. was superior Although, to heating pre-cooling to only belowambient. 150 The K will optimal result state in increased 2 pressure total range work was per 20 unit to 50mass MPa liquefied. where there Heating was maximum the liquid airliquid beyond yield. ambient Pre-cooling temperature resulted in results an increase in increased in liquid electrical yield, energygeneration efficiency, and increases and exerg they overall efficiency. efficiency Although, of the pre system.-cooling below 150 K will result in increased total Additionalwork per unit improvement mass liquefied. of the Heating energy the and liquid exergy air efficiency beyond ambient may be foundtemperature with alternative results in increasedliquefaction electrical subsystems, generation which and utilize increases an expander,the overall suchefficiency as the of Claudethe system. and Heylandt systems. The systemAdditional would improvement be improved of further the energy by incorporating and exergy coldefficiency and heat may recovery be found systems, with alternative as used by liquefactionprevious work subsystems, which achieved which roundutilize tripan expander, efficiencies such of 45–57%. as the Claude and Heylandt systems. The

Author Contributions: Conceptualization, T.H., A.G.P. and A.J.G.; Formal analysis, T.H., A.G.P. and A.J.G.; Funding acquisition, A.G.P.; Investigation, T.H.; Methodology, T.H., A.G.P. and A.J.G.; Project administration, A.G.P.; Supervision, A.G.P.; Validation, A.G.P. and A.J.G.; Visualization, A.J.G.; Writing, original draft, T.H.; Writing, review & editing, T.H., A.G.P. and A.J.G. Funding: This work was sponsored by ESTEP (Energy Systems Technology Evaluation Program) funded by the Office of Naval Research under the technical monitors of Richard Carlin and Marissa Brand. Conflicts of Interest: The authors declare no conflict of interest.

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