Energy and Exergy Analysis of Ocean Compressed Air Energy

Research ArticleEnergy and Exergy Analysis of Ocean Compressed Air EnergyStorage Concepts

Vikram C. Patil and Paul I. Ro

North Carolina State University, Raleigh, NC, USA

Correspondence should be addressed to Paul I. Ro; [email protected]

Received 28 September 2017; Revised 22 December 2017; Accepted 1 January 2018; Published 1 February 2018

Academic Editor: Kiyan Parham

Copyright © 2018 VikramC. Patil and Paul I. Ro.This is an open access article distributed under the Creative CommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in anymedium, provided the originalwork is properly cited.

Optimal utilization of renewable energy resources needs energy storage capability in integration with the electric grid. Oceancompressed air energy storage (OCAES) can provide promising large-scale energy storage. In OCAES, energy is stored in the formof compressed air under the ocean. Underwater energy storage results in a constant-pressure storage system which has potentialto show high efficiency compared to constant-volume energy storage. Various OCAES concepts, namely, diabatic, adiabatic, andisothermal OCAES, are possible based on the handling of heat in the system.These OCAES concepts are assessed using energy andexergy analysis in this paper. Roundtrip efficiency of liquid piston based OCAES is also investigated using an experimental liquidpiston compressor. Further, the potential of improved efficiency of liquid piston based OCAES with use of various heat transferenhancement techniques is investigated. Results show that adiabatic OCAES shows improved efficiency over diabatic OCAES bystoring thermal exergy in thermal energy storage and isothermal OCAES shows significantly higher efficiency over adiabatic anddiabatic OCAES. Liquid piston based OCAES is estimated to show roundtrip efficiency of about 45% and use of heat transferenhancement in liquid piston has potential to improve roundtrip efficiency of liquid piston based OCAES up to 62%.

1. Introduction

Electricity generation from renewable energy sources playsimportant role in reducing dependence on fossil fuels andin curtailing greenhouse gas emissions. However, renewableenergy sources such as wind, solar, tidal, and wave are spo-radic in nature. The variability of power from the renewableenergy sources makes it hard to integrate with the electricgrid [1]. Utility-scale energy storage systems are needed toimprove the utilization of renewable energy resources inelectric grid [2]. Compressed air energy storage (CAES)system is a reliable large-scale energy storage method withrelatively low specific investment cost [3]. In CAES system,intermittent energy is used to compress the atmospheric airto the high-pressure and compressed air is stored in thehigh-pressure reservoir. When electricity demand is high,the stored high pressurized air is expanded through theturbine to generate electricity. Two large-scale CAES plantsare in operation, one is in Huntorf, Germany [4], and theother is in McIntosh, Alabama, USA [5]. In both the plants,compressed air is stored in an underground cavern. However,

these underground caverns are constant-volume air storagereservoirs. In constant-volume air storage systems, chargingand discharging processes result in pressure variation. Thesevarying conditions can result in low efficiencies of compres-sion and expansion due to deviation from the designed points[6]. This can be avoided by utilizing ocean depth for storageof the compressed air in which high-pressure environmentunder the water can be effectively used for creating constant-pressure storage system [7]. Such an ocean compressed airstorage (OCAES) system can effectively integrate multipleenergy sources located offshore with high system efficiency.

Various types of OCAES configurations are possiblybased on the idealized thermodynamic process of compres-sion and expansion of air. These thermodynamic processesare identified based on how heat is handled during com-pression and expansion processes. The three major types arediabatic OCAES, adiabatic OCAES, and isothermal OCAES.These types are discussed in the next section with moredetails. Roundtrip efficiency (also called end-to-end effi-ciency) is an important parameter to assess the efficacy ofan energy storage system. As processes in the OCAES system

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2 Journal of Engineering

are accompanied by heat and work transfer, it is very difficultto understand the efficiency of an OCAES system usingfirst law of thermodynamics. This is because the first law ofthermodynamics deals with heat andwork equally.Therefore,roundtrip efficiency based on exergy analysis which is basedon the second law of thermodynamics would be beneficial inbetter understanding the characteristics of the different typesof OCAES systems.

Various studies have investigated different types of CAESconfigurations based on energy and exergy analysis. Kimet al. reviewed the main drawbacks of the existing CAESsystems and presented energy and exergy analysis of variousinnovative CAES concepts [8]. They investigated conceptslike adiabatic CAES, isothermal CAES, micro-CAES com-bined with air-cycle heating and cooling, and constant-pressure CAES combined with pumped hydrostorage. Theiranalysis illustrated that drawbacks of existing CAES systemscan be addressed by employing innovative CAES concepts.Bagdanavicius and Jenkins investigated the potential forusing heat generated during compression stage of CAES witha district energy system [9]. Exergy and exergoeconomicanalysis of CAES and CAES with thermal storage wereperformed by them. Their analysis showed that utilizationof waste heat increases energy efficiency from 48% for theCAES to almost 86% for CAES with thermal storage. Theyalso observed that highest exergy destruction occurs in theheat exchangers during compression stage.

Different adiabatic CAES configurations were simulatedand analyzed by Hartmann et al. [10] using energy balance.Polytropic CAES with one, two, and three stages and anisentropic CAES were considered. They observed that highvalue of 70% efficiency is only achieved for isentropic config-uration and efficiency of the polytropic configuration is about60%. Their analysis also suggested that developing high-temperature thermal storage (>600∘C) and temperature resis-tant materials for compressors are key elements in achievinghigher efficiency. Grazzini and Milazzo presented a thermo-dynamic analysis of multistage adiabatic CAES [11]. Theyproposed a comprehensive set of criteria for the design ofadiabatic CAES based on a detailed thermodynamic analysisof the design parameters and influence on system efficiency,with attention to heat transfer devices. An exergy analysis waspresented by Tessier et al. on adiabatic CAES system utilizinga cascade of phase change materials for waste heat storageand recovery [12]. Incorporation of phase change materialspredicted to show 15% increased efficiencies of storage andrecovery over the current design. An experimental study ofCAES system with thermal energy storage by Wang et al.has shown a mere 22.6% roundtrip efficiency [13]. A recentdetailed review on CAES has been presented in [14].

The existing CAES plants in Huntorf and McIntosh areof a diabatic type and show roundtrip efficiency of 42% and54%, respectively. The Huntorf plant was primarily designedto provide reserve power and blackstart capability where highefficiency is of minor importance. The McIntosh plant wasdesigned to perform load shifting on a weekly basis, whichrequires the cycle efficiency to be as high as possible. TheMcIntosh plant could achieve considerably higher efficiencyover Huntorf plant using a recuperator to reduce exergy

loss. The concept of adiabatic CAES using thermal energystorage (TES) was also considered during development ofthese plants; however, diabatic CAES is preferred at that timedue to technical and economic advantages [14].

Adiabatic CAES needs a high-temperature TES with-standing the combination of thermal andmechanical stresseswhich requires special material and complex system engi-neering. Also, considerable engineering effort is needed todesign an electrically driven compressor that operates at thehigh outlet temperature essential for adiabatic operation.Recent developments in TES have shown good prospects inachieving adiabatic CAES in practice [15]. An adiabatic CAESis under development under the project name “ADELE-ING” which could show roundtrip efficiency up to 70% [16].Another approach in achieving high efficiency is throughisothermal CAES. Technically, it was very difficult to achieveisothermal operation at high power density. However, recentdevelopments in liquid piston compressor [17] and heattransfer enhancement techniques in the liquid piston [18–20]could result in near-isothermal compression and expansionat high power density.Thermodynamic and economic reviewof CAES by Rogers et al. [21] indicates that efficiencies ofadvanced adiabatic CAES and isothermal CAES have beenincreased by over 30% and energy storage densities have beenimproved by a factor of 5 using near-surface piping.

A multilevel underwater CAES system integrated withbattery pack is proposed by Wang et al. [22]. Their ther-modynamic analysis shows that roundtrip exergy efficiencyof the multilevel underwater CAES varies from 62% to81% in different working mode. Advanced exergy analysisof an underwater CAES by Wang et al. indicates exergyefficiency of 53.6% under real conditions with theoreticalmaximum exergy efficiency of 84.3% [23]. Clearly, there is agreat potential for performance improvement of underwaterCAES. A study by Cheung et al. indicates that pipe diameter,turbine, air compressor, and air storage depth have thegreatest influence on system performance of underwaterCAES [24]. Multiobjective optimization of an underwaterCAESwith objectives ofmaximizing roundtrip efficiency andoperating profit and minimizing cost rate is performed byCheung et al. using genetic algorithm [25]. Their analysisindicated roundtrip efficiency of 68.5% and operating profitof $53.5 per cycle for the preferred system designs.

Based on earlier studies on CAES, it can be observed thatthere could be a significant variation in efficiencies of variousOCAES configurations. Comparative analysis of differentOCAES systems would help in understanding these better.Preliminary studies of exergy analysis for various OCAESconfigurations and end-to-end efficiency of liquid pistonbased OCAES have been presented earlier in [26, 27]. In thispaper, detailed analysis of various OCAES concepts usingenergy and exergy analysis is presented. This would help inassessing improvement areas in achieving higher roundtripefficiency with OCAES.

Investment costs associated with different types ofOCAES would also vary as the technology used in theseconfigurations differs considerably. The compressor andexpander in the diabatic OCAES are mature technologieswhereas the same in the adiabatic and isothermal OCAES

Journal of Engineering 3

are still in the development stages. Also, the cost of thermalenergy storage (TES) used in adiabatic OCAES differs signif-icantly based on the kind of TES system used. Broadly, thereare three types of TES systems, sensible heat TES, latent heatTES, and thermochemical TES. In general, latent heat TESand thermochemical TES are more expensive than sensibleheat TES; however, former could be economically viable witha high number of operating cycles [15]. Although the costof different OCAES configurations might differ significantly,this paper only focuses on efficiency aspect without account-ing any cost difference. However, an economic assessmentof these OCAES configurations would be necessary beforeinvestment decisions. This study could provide a frameworkfor an economic assessment of different OCAES by monetiz-ing efficiencies incorporating cost difference.

2. OCAES Configurations

OCAES configurations can be broadly distinguished depend-ing on the targeted idealized process of compression andexpansion of air. It is decided based on how heat is handledduring compression and prior to expansion of the air. Threemajor OCAES configurations would be diabatic OCAES,adiabatic OCAES, and isothermal OCAES. These systemconfigurations are discussed in this section.

2.1. Diabatic OCAES. In the diabatic OCAES system, inenergy storage mode, air is compressed using conventionalcompressors and cooled to the surrounding temperaturebefore sending it to the storage system. Compression processincreases the temperature of air due to the heat of compres-sion which is dissipated before sending air to the storagedevice. This results in loss of thermal energy of compressiondue to cooling. In energy recovery mode, the air from thestorage is heated using fuel and then passed through theexpander to generate electricity.

The schematic of diabatic OCAES is shown in Figure 1.Processes 1-2 represent compression of atmospheric air usingair compressor run using electric motor operating on excesselectric energy. The motor efficiency and losses in the com-pressor would result in loss of energy/exergy during thisprocess. Compressed air from the compressor is then passedthrough the cooler (processes 2-3) before sending it to theunderwater air storage system. A significant amount of heatenergy (thermal exergy) is lost in the cooler. Processes 3-4 indicate charging and discharging from the air storagesystem. Mechanical exergy (energy in pressure form) in thehigh-pressure air is stored in the underground storage.Therecan be a small amount of loss of energy/exergy due to leakageand pressure drop in the storage system. In process 4-5,high-pressure air is heated using external heat input (thermalexergy) to increase expansion work. The processes 5-6 arethe expansion process in which mechanical exergy in theform of electrical energy is delivered. However, processes5-6 involve loss of energy/exergy due to inefficiencies inexpansion process and also loss of energy/exergy from theexhaust gas.

2.2. Adiabatic OCAES. The construction of adiabatic sys-tem would require a compressor design delivering higher

C ExM/G

Underwater air storage

Co H

1

2

3 4

5

6

Clutch

C: compressorCo: coolerH: heater

Ex: expanderM/G: motor/generatorE: exergy

Q: heat transfer

EＦＩＭＭ％Ｒ

QＣＨH

EＣＨH

QＩＯＮCo

EＩＯＮCo

EＦＩＭＭC

Einc

EＩＯＮE

m m

Figure 1: Schematic of diabatic OCAES.

4

C ExM/G


1

2

3

5

6

Clutch

TES

TES: thermal energy storage C: compressor

Ex: expander

M/G: motor/generatorE: exergy

EＦＩＭＭ％Ｒ

EＦＩＭＭC

EＦＩＭＭTES

Einc

EＩＯＮE

mm

Figure 2: Schematic of adiabatic OCAES.

temperature at the outlet of compression, a reliable TESsystem to store thermal energy at high temperature andan expander design operating at high inlet air temperaturewith broad operation range. These components installed andconnected with pipelines carrying air with the layout shownin Figure 2 would result in the adiabatic OCAES system.

It can be seen that cooler and heater in the diabaticOCAES are replacedwith thermal energy storage (TES) in theadiabatic OCAES configuration. The diabatic OCAES usesfuel in the heater; therefore, it cannot be considered as a purestorage system and is actually a combination of storage and


C ExM/G


1

2 3

4

Clutch

C: compressorEx: expanderM/G: motor/generator

E: exergyQ: heat transfer

QＣＨExQ

ＩＯＮC

Einc

EＩＯＮE

m m

Figure 3: Schematic of isothermal OCAES.

power plant.This can be overcome in adiabaticOCAESwhichuses TES to store heat from the compressed air before sendingit to the air storage. The stored heat in TES is used to heatthe air before passing it to the expander. This eliminates theneed for cooler and heater in the adiabatic system as TESworks as both.Therefore, thermal energy and thermal exergylosses in the cooler and thermal heat input in the heater ofdiabatic OCAES are completely eliminated in the adiabaticOCAES. However, TES involves some energy/exergy losseswhich result in added inefficiencies in adiabatic OCAES.

2.3. Isothermal OCAES. Isothermal OCAES would eliminatethe need for fuel and high-temperature thermal energystorage. This can be done by isothermal compression andexpansion process which minimizes compression work andmaximizes expansion work. Figure 3 shows a schematic ofisothermalOCAES system.The compressor in the isothermalOCAES dissipates heat energy during compression processresulting in the conversion of electrical energy into mechani-cal exergy form in the compressed air. Ideal isothermal com-pression does not add any thermal exergy in the compressedair; therefore, loss of exergy is totally avoided. Similarly, inthe ideal isothermal expansion, mechanical exergy from thecompressed air is completely converted into electrical energy.

It is very difficult to achieve isothermal compression andexpansion using conventional compressors and expansiondevices as conventional compressors and expanders work athigh speed with the nearly adiabatic process. Special types ofcompressors and expanders are required to achieve isother-mal OCAES in reality. Liquid piston compressor can beused to achieve near-isothermal compression and expansionoperation. In the liquid piston compressor, a column of liquid(usually water) is utilized to compress a gas in the fixedvolume chamber. A hydraulic pump is used to generate the

flow of the liquid for the liquid pistons. The liquid flow inand out of compression chamber is controlled with valves.As a liquid can conform to an irregular chamber volume,the surface area to volume ratio in the gas chamber can bemaximized using a liquid piston.This results in increasing theheat transfer during the gas compression/expansion whichfacilitates near-isothermal operation [17]. Various heat trans-fer enhancement techniques like the use of porous mediainserts [19], spray cooling [18], and use of hollow spheres [20]can be effectively used in the liquid piston to achieve near-isothermal operation.

A typical liquid piston based isothermal OCAES wouldhave electric motor/generator, hydraulic pump/motor, liquidpiston compressor/expander, air cooler/heater, pipelines con-necting various components, control valves, and underwaterair storage. Figure 4 shows a schematic of a liquid piston basedOCAES system. Although liquid piston compression is effi-cient compared to the existing compressors technologies, theadded components like hydraulic pump/motor and hydrauliclines have some inefficiencies which would affect the overallefficiency of OCAES system.

3. Energy and Exergy Analysis

Inefficiencies in various components of the OCAES con-tribute to the loss of energy in the storage system. Energyefficiency of a component is the ratio of energy out from thecomponent to energy into the component. In energy analysis,energy efficiencies of various components in the OCAES aremodeled and used to evaluate the energy efficiency of overallOCAES system.

The exergy transfer to the system can happen by work,heat, and mass transfer. The exergy transfer by heat is givenby

��𝑞 = ∫ 1 − 𝑇0𝑇 𝛿��, (1)

where 𝑇 is temperature, �� is heat transfer rate, and subscript0 indicates properties at environmental conditions [28].

Exergy transfer by mass flow (��) is given by

��𝑚 = ��𝑒, (2)

where specific exergy (𝑒) of an ideal gas is given by

𝑒 = 𝐶𝑝 (𝑇 − 𝑇0) − 𝑇0 [𝐶𝑝 ln( 𝑇𝑇0) − 𝑅 ln( 𝑃

𝑃0)] , (3)

where𝐶𝑝 is specific heat at constant pressure,𝑅 is the specificgas constant, and 𝑃 is pressure.

The above specific exergy consists of two parts, mechan-ical exergy and thermal exergy. The mechanical exergy isassociated with the system pressure and is the exergy changewhen the system is brought to the state [𝑇0, 𝑃0] from thestate [𝑇0, 𝑃].The thermal exergy is associated with the systemtemperature and is the exergy change when the system is


Electric motor/generator Hydraulic pump/motor

Air cooler/heater

Atmosphericair-in Compressed

air-out

Control valve

Mechanicalcoupling

Hydraulic lines

Water

Air

Compressed air lines

Compressedair storage

Ocean

Liquid piston(left)

Liquid piston(right)

Figure 4: Schematic of a liquid piston based isothermal OCAES system.

brought to the state [𝑇0, 𝑃] from the state [𝑇, 𝑃]. Mechanicaland thermal exergies are given by (4) and (5), respectively.

𝑒𝑀 = 𝑅𝑇0 ln( 𝑃𝑃0) , (4)

𝑒𝑇 = 𝐶𝑝 (𝑇 − 𝑇0 − 𝑇0 ln( 𝑇𝑇0)) , (5)

where superscripts𝑀 and𝑇 indicatemechanical and thermalparts, respectively.

Individual components in the OCAES system can beanalyzed based on exergy analysis. Exergy efficiency of acomponent is given by

𝜀com = ��−com��+com , (6)

where 𝜀 denotes exergy efficiency and subscripts indicatescomponent.

Energy efficiency and exergy efficiency of individualcomponents in OCAES are discussed below.

3.1. Electric Motor and Generator. Electric motor/generatorhas mechanical and electrical losses during its operation.

Energy efficiency of electric motor/generator (M/G) is theratio of power output from M/G to the power input to M/Gas calculated using

𝜂M/G = 𝑃𝑛 × Load𝑃𝑖 . (7)

As electric motor/generator deals with work transfer(electrical energy and shaft work) only, exergy efficiency ofelectric motor/generator is its energy efficiency.

3.2. Hydraulic Pump/Motor. Energy efficiency of hydraulicpump/motor depends on its displacement, speed of opera-tion, and the pressure differential between inlet and outlet.The overall efficiency of a hydraulic pump for a particularpower input is given by

𝜂HP = 𝐷 × 𝑁 × Δ𝑝𝑃in . (8)

Exergy efficiency of hydraulic pump/motor is also same asits energy efficiency because it deals only with work transfer.

3.3. Compressor. The exergy transfer to the compressor (��+𝐶)is in the form of shaft work from the motor whereas exergy


transfer from the compressor (��−𝐶) is due to air mass transferfrom the compressor at high pressure and temperature.Thereare exergy losses in the compressor due to mechanical losses.Isentropic efficiency [29] and mechanical efficiency of thecompressor can be used to evaluate exergy efficiency ofcompressor.

In case of isothermal OCAES, liquid piston compressorefficiency is defined as the ratio of stored energy to workinput. Storage energy is the amount of work extracted fromthe isothermal expansion of compressed air to the atmo-spheric pressure. Work input consists of compression work,cooling work and friction work. Atmospheric air compressedto high-pressure results in increasing temperature. Thiscompressed air is cooled to initial temperature to maintainstorage pressure [30]. This adds cooling work. In case ofliquid pistons, friction work is comparatively small (unlessdiameter is too small) and can be neglected [17]. Liquid pistoncompressor efficiency (𝜂𝐶) after neglecting viscous friction isgiven by

𝜂𝐶

=𝐸Storage⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞

ln (𝑃𝑟) + 1/𝑃𝑟 − 1(𝑃(𝑛−1)/𝑛𝑟 − 1) / (𝑛 − 1) + 𝑃−1/𝑛𝑟 − 1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

𝑊compression

+ (𝑃𝑟 − 1) (𝑃−1/𝑛𝑟 − 1/𝑃𝑟)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟𝑊Cooling

, (9)

where 𝑃𝑟 is the pressure ratio (ratio of storage pressureto the atmospheric pressure) and 𝑛 is a polytropic indexof compression. Storage pressure (hence 𝑃𝑟) depends onthe underwater air storage depth and 𝑛 depends on themagnitude of heat transfer in liquid piston compressor.

3.4. Cooler. The compressed air from the compressor con-tains both mechanical and thermal exergy. In the cooler,the compressed air is cooled to the atmospheric temperatureat a constant pressure by dissipating thermal exergy of thecompressed air to cooling media. The output compressedair from the cooler would contain only mechanical exergy.Therefore, exergy efficiency of the cooler neglecting pressurelosses in the cooler is given by

𝜀co = ��𝑒𝑀�� (𝑒𝑀 + 𝑒𝑇)

= 𝑅𝑇0 ln (𝑃co/𝑃0)𝑅𝑇0 ln (𝑃co/𝑃0) + 𝐶𝑝 (𝑇co − 𝑇0 − 𝑇0 ln (𝑇co/𝑇0)) ,

(10)

where 𝑃co and 𝑇co are pressure and temperature of com-pressed air at inlet of the cooler, respectively.

3.5. Air Pipeline Connecting Various Components. Energy/exergy loss inside the pipeline carrying air is equal to productof pressure drop and flow rate. Pressure drop for steady, fullydeveloped, incompressible flow in the pipe can be calculatedusing Darcy –Weisbach equation [31].

3.6. Thermal Energy Storage (TES). In adiabatic OCAES,high-temperature high-pressure compressed air is passed

through the TES to store thermal exergy of compressed airin the TES. This stored thermal energy is used to increasethermal exergy of compressed air before sending it throughthe expander. The thermal and pressure losses in the TESresult in the loss of energy/exergy. The exergy efficiency ofTES is given by

𝜀TES= 𝑅𝑇0 ln (𝑃out

TES/𝑃0)𝑅𝑇0 ln (𝑃in

TES/𝑃0) + 𝐶𝑝(𝑇in

TES − 𝑇0 − 𝑇0 ln (𝑇inTES/𝑇0)) ,

(11)

where 𝑃inTES and 𝑇in

TES are pressure and temperature of com-pressed air at inlet of the TES. 𝑃out

TES and 𝑇outTES are pressure

and temperature of compressed air at outlet of the TES,respectively.

3.7. Air Storage. Leakage and pressure losses in the underwa-ter air storage system result in energy/exergy losses. Leakageper unit volume per unit time can be calculated bymeasuringpressure drop in an isolated air storage system given byequation [32]

��𝑆 = 𝜌𝑠𝑡𝑒(Δ𝑃)𝑆𝑃𝑆 , (12)

where ��𝑆 is the leakage rate (kg/hr⋅m3), 𝜌𝑠 is the density ofair at storage pressure and temperature, (Δ𝑃)𝑆 is the pressuredrop in the isolated air storage system in time 𝑡𝑒, and 𝑃𝑆 is thestorage pressure.

The energy/exergy efficiency of an air storage system isgiven by [27]

𝜀𝑆 = 1 − 𝑡0 × ��𝑆𝜌𝑠 , (13)

where 𝑡𝑜 is the operation time of the OCAES.

3.8. Heater. In the diabatic OCAES, external fuel is used toheat the air. The heat (thermal exergy) added in the heaterincreases exergy of the air. Exergy efficiency of a heaterneglecting pressure losses in the heater and considering theconstant rate of heat transfer is given by

𝜀𝐻= 𝐶𝑝 (𝑇𝐻 − 𝑇0 − 𝑇0 ln (𝑇𝐻/𝑇0)) + 𝑅𝑇0 ln (𝑃𝐻,out/𝑃0)

𝑄𝑠 (1 − 𝑇0/𝑇𝑠) + 𝑅𝑇0 ln (𝑃𝐻,in/𝑃0) , (14)

where 𝑃𝐻,in and 𝑃𝐻,out are pressures at inlet and outlet ofthe heater, respectively, 𝑇𝐻 is the temperature of air at heateroutput,𝑇𝑆 is the temperature of heat source, and𝑄𝑆 is the heattransfer per unit mass of air.

3.9. Expander. The exergy transfer to the expander (��+Ex) isby compressed air inlet whereas exergy transfer from theexpander (��−Ex) is in the form of shaft work delivered tothe generator. Similar to compressor, exergy efficiency of


Table 1: Stochastic assignments in Monte Carlo simulation.

Variable Mean/max value [𝜇] (%) Standard deviationa or max/min value (%) Distribution𝜀M/G [34] 96 0.5 Normal𝜀HP/HM [8] 93 1 Normal𝜂𝐶,isen 85 2 Normal𝜂𝐶,mech 95 1 Normal

𝜂𝑃 (𝑃in − Δ𝑃) /𝑃in Max = 𝜇, TriangularMin = 𝜇 − 0.5

𝜀TES 80 2 Normal

𝜀𝑆 Using (13) Max = 𝜇 + 0.5 TriangularMin = 𝜇 − 0.5

𝜀𝐻 95 1 Normal𝜂Ex,isen 85 1 Normal𝜂Ex,mech 95 1 NormalaFor normal distribution.

expander can be calculated using isentropic efficiency [29]and mechanical efficiency of the expander.

In case of isothermal OCAES using a liquid piston, liquidpiston expansion efficiency (𝜂𝐸) for polytropic expansionindex 𝑛 is given by

𝜂𝐸

=𝑊Expansion⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞(1 − (1/𝑃𝑟)(𝑛−1)/𝑛) / (𝑛 − 1) − (1/𝑃𝑟)(𝑛−1)/𝑛 + 1/𝑃𝑟

ln (𝑃𝑟) + 1/𝑃𝑟 − 1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟𝐸Storage

.(15)

4. Numerical Simulations

Different types of OCAES systems are modeled based onenergy and exergy analysis of individual components inthe OCAES system. Storage pressure of 10 bar gauge (100mocean depth) is considered for analysis. Various compo-nents specifications designed for maximum power capacityof 0.5MW with 2MWh energy storage were used [33].Efficiencies of motor/generator and hydraulic pump/motorare considered from the industry standards [8, 34]. Pipelinesconnecting cooler to air storage and air storage to the heaterare considered with 1000m in length, 0.2m in diameter, andof 15𝜇m surface roughness [35]. For air storage, the leakagerate of 0.01 kg/hr⋅m3 [36] and operation time of 8 hours wereassumed [37].

Uncertainty analysis is performed using Monte-CarloSimulations (100000 runs) to estimate mean and confidenceinterval values of energy efficiency and exergy efficiency.Stochastic assignments considered are given in Table 1.

All the simulations were performed considering 1 atmand 20∘C environmental conditions. In all the configurations,single stage compression and single stage expansion wereconsidered. Adiabatic and isothermal OCAES systems areconsidered without the use of fuel. In the diabatic configu-ration, heat source temperature of 1500∘C is considered. Theamount of heat transfer from the heat source is evaluated

Table 2: Thermodynamic properties and mass flow rates of air atdifferent state points for diabatic OCAES system (see Figure 1 forstate points).

Statepoint

Pressure(kPa)

Temperature(K) Mass flow rate (kg/s)

1 101.3 293 1.332 1119.6 633 1.333 1114.6 293 1.334 1109.6 293 1.325 4200.0 823 1.326 101.3 364 1.32

to achieve inlet conditions to expander with 42 bar and550∘C. These values are referred from HP turbine operatingconditions of Huntorf plant [38]. In adiabatic OCAES config-uration, TES storage temperature of 327∘C is considered [39]and inlet air conditions to the expander of 10 bar and 327∘Care considered. In isothermal OCAES configuration, liquidpiston based compression and expansion are considered.

To simplify the thermodynamic model, all the analysisis performed for steady state operation of the system. Also,the kinetic and potential energy of the fluids are assumedto be negligible and the air is considered as an ideal gas[23]. For these system considerations, the thermodynamicproperties and mass flow rate of air at different state points ofthe system are evaluated.Those are listed in Tables 2, 3, and 4for diabatic, adiabatic, and isothermal OCAES, respectively.Finally, different types ofOCAES systems are compared usingenergy/exergy flow, energy efficiency, and exergy efficiencyevaluations.

5. Results and Discussion

Figures 5, 6, and 7 show exergy flow in various OCAESconfigurations. In figures, each box represents a componentin the OCAES system. The height of the box representsqualitative exergy flow to the component.The arrows indicatethe exergy flow direction and the amount of exergy flow is


Losses in motorCompressor losses Thermal exergy

removal in cooler Pressure loss inpipelines

Pressure lossin storage

Pressure loss inpipelines

Loss in heaterExpander lossesLosses in

generator

2.6kW

1.4 kW

1.4 kW

266 kW

268.6 kW

152kW

270 kW

264.6 kW

370 kW

58kW

422 kW

603 kW

32kW

20kW

480 kW

495 kW

108 kW

500 kW

475 kW

20kW

StorageS = 0.99

PipelineP = 0.995

PipelineP = 0.995

Coolerco = 0.64

HeaterH = 0.95

Heat sourceQ = 443 kW

CompressorC = 0.88

ExpanderEx = 0.82

Electricmotor

M = 0.96

GeneratorG = 0.96

Figure 5: Exergy flow in diabatic OCAES.

Table 3: Thermodynamic properties and mass flow rates of air atdifferent state points for adiabatic OCAES system (see Figure 2 forstate points).

State point Pressure(kPa)


1 101.3 293 1.332 1119.6 633 1.333 1114.6 293 1.334 1109.6 293 1.325 1104.6 600 1.326 101.3 354 1.32

Table 4: Thermodynamic properties and mass flow rates of air atdifferent state points for isothermal OCAES system (see Figure 3 forstate points).

State point Pressure(kPa)


1 101.3 293 2.102 1119.6 300 2.103 1114.6 293 2.084 101.3 286 2.08

mentioned on each arrow. The arrows pointing away fromthe boxes indicate exergy loss to the environment.The exergyefficiencies of the individual components are mentioned inthe boxes. The input power of 500 kW is considered for theanalysis.

5.1. Diabatic OCAES. Exergy flow in the diabatic OCAES ispresented in Figure 5. Inefficiencies in electric motor result inexergy loss of 20 kW. It is observed that a significant amountof exergy is lost from the cooler to the surrounding. Losses inthe pipelines and storage are very small compared to otherlosses. The addition of heat energy to the heater from theheat source adds exergy to the system. Although energy inputfrom the heat source to the heater is 443 kW, the exergy valueof this heat is only about 370 kW. This addition of exergy inheater compensates the loss of exergy in the cooler to achievethe same level of power output. The expander is the nextexergy inefficient component after the cooler in the diabaticsystem. Inlet air to the expander contains exergy in boththermal and mechanical forms. Irreversibility in expansionprocess results in exhaust air with a significant amount ofthermal exergy, which results in higher exergy loss in theexpander. The recuperator is not considered in the currentconfiguration. In recuperative process waste heat from theexhaust of the expander can be used to heat expander inlet air.This would reduce exergy burden from the heat source andhence improve overall exergy efficiency of OCAES system.

The overall exergy efficiency of diabatic OCAES is 55%whereas energy efficiency is 50%. As diabatic OCAES hasfuel input in the heater system, it is not a pure energystorage system but the combination of energy storage andpower plant. Therefore, exergy efficiency is a good measureof diabatic OCAES for comparison with other systems.

5.2. Adiabatic OCAES. The thermal exergy lost from thecooler in the diabatic OCAES is stored in the adiabaticOCAES using TES which can improve exergy efficiency of


Losses in motorCompressor losses

TES lossesPressure loss in pipelines

Pressure loss in storage

Pressure loss in pipelinesExpander lossesLosses in

generator

2.6kW

268.6 kW

266 kW

1.4kW

270 kW

264.6 kW30

kW

20kW

58kW

73kW

13kW

1.4 kW

422 kW

386

kW

480 kW

313 kW

500 kW

300 kW

StorageS = 0.99

PipelineP = 0.995

PipelineP = 0.995

TES４％３ = 0.80

CompressorC = 0.88

ExpanderEx = 0.81

Electricmotor

M = 0.96

GeneratorG = 0.96

Figure 6: Exergy flow in adiabatic OCAES.

Losses in motorPump losses

Compressor lossesPressure loss in pipelines

Pressure loss in storage

Pressure loss in pipelinesExpander losses

Hydraulic motor losses

Losses ingenerator

4 kW

2 kW

2 kW

422 kW

418 kW

416 kW

424 kW

22kW34

kW20kW

21kW

15kW

446 kW

395 kW

480 kW

367 kW

28kW

500 kW

352 kW

StorageS = 0.99

PipelineP = 0.995

ExpanderP = 0.95

PipelineP = 0.995

CompressorC = 0.95

Hydraulicpump

HP = 0.93

Hydraulicmotor

HM = 0.93

Electricmotor

M = 0.96

GeneratorG = 0.96

Figure 7: Exergy flow in isothermal OCAES.

adiabaticOCAES significantly over diabaticOCAES. Figure 6shows exergy flow in adiabatic OCAES. Exergy loss in thecooler of diabaticOCAES can be avoided by use of TESwhichstores a significant amount of thermal energy. TES suppliesheat to the air before the expander thus increasing the exergypotential of air. With the use of TES, the external heat sourceis removed in the adiabatic OCAES configuration. However,inefficiencies in TES account for exergy loss which contributeto reduction energy output. Comparison of diabatic andadiabatic exergy flow reveals that adiabatic CAES gives less

exergy output (electric energy) from the generator. This isbecause the fuel source used in the diabatic OCAES allowsthe expander to be operated with higher power capacity.

Overall exergy efficiency of adiabatic OCAES is 60%which is 5% higher than that of diabatic OCAES. Thisimprovement is due to reuse of thermal exergy of the airusing TES. Improvement in TES efficiency from currentconsideration of 80% would further improve the efficiencyof adiabatic OCAES. As external fuel is not used in adiabaticOCAES, overall energy efficiency of adiabaticOCAES is same


Diabatic OCAES Adiabatic OCAES Isothermal OCAES

Exer

gy effi

cien

cy (%

)

0

10

20

30

40

50

60

70

80

Figure 8: Overall exergy efficiency of different types of OCAES.

as overall exergy efficiency. Careful observation of exergylosses in adiabatic OCAES shows that losses in compressorand expander are major contributors of inefficiencies inadiabatic OCAES.

5.3. Isothermal OCAES. The need of TES and fuel sourceis eliminated in the isothermal OCAES. Exergy flow in theisothermal OCAES is shown in Figure 7. Liquid piston basedcompressor and expander requires a hydraulic pump anda hydraulic motor as added components in the isothermalOCAES. Inefficiencies of these components would contributeto the exergy loss in the system. It can be observed inFigure 7 that hydraulic pump/motor show high exergy lossesin comparison with losses in other components in isothermalOCAES. However, the use of liquid piston in conjunctionwith hydraulic pump and motor has the potential to improveefficiencies of the compressor and expander significantly.Thisresults in a reduction of exergy losses in compressor andexpander. Also, the absence of TES and heater eliminateslosses associated with those which helps in improving theoverall efficiency of the system. Overall exergy efficiency ofthe isothermal OCAES is about 70% which is significantlyhigher than diabatic and adiabatic OCAES.

The overall exergy efficiencies of all the three config-urations with 95% confidence interval bounds are shownin Figure 8 for comparison. The uncertainties in variousassumptions show about 3-4%variation in exergy efficiencies.Clearly, isothermal OCAES is the most efficient and diabaticOCAES is the least efficient among three configurationsconsidered based on exergy analysis. Energy efficiency ofdiabatic OCAES is about 50% whereas that of adiabaticand isothermal OCAES is same as their exergy efficiencies.Energy efficiency might not be a reliable comparative param-eter as it would undervalue the efficiency of the diabaticsystem.

5.4. Liquid Piston Based OCAES. Although isothermalOCAES shows high exergy efficiency, such a high level of effi-ciency is contingent upon near-isothermal compression andexpansion. Liquid piston compressor is experimentally testedto investigate its effectiveness in achieving near-isothermal

Hydraulic pump

Solenoid values

Compression chambers

Air storage

Temperature and pressure sensors

Figure 9: Experimental setup of liquid piston compressor.

(Adiabatic) (Experiment) (Isothermal)

Roun

dtrip

effici

ency

(%)

0

10

20

30

40

50

60

70

80

1.2 1.14 1.1 1.05 11.4

Polytropic index (n)

Figure 10: Roundtrip efficiency of liquid piston based OCAES fordifferent polytropic indices.

compression. Figure 9 shows the experimental setup of aliquid piston compressor. The compression chamber wasdivided into four parallel copper pipes, each having an innerdiameter of 76mm and length of 760mm. Two compressionchambers were used in the experimental setup to ensurecontinuous production of compressed air. The compressionchambers were enclosed in a plastic cylinder filled withwater to maintain the temperature of the outer copper walla constant. A hydraulic pump was used to alternatively drivewater from one compression chamber to the other. Thepump delivers a constant flow rate of 10 gpm at a maximumpressure of 13.1 bar gauge (190 psi). A K-type thermocoupleof diameter 0.0508mm (0.002 in) and a pressure sensor wereinstalled at the top of each compression chamber as indicatedin Figure 9. Experiments were performed with a pressureratio of 6 and the stroke time of 10 s.

The liquid piston compressor and expansion efficiencycan be calculated using the polytropic index of compressionand expansion in (9) and (15), respectively. The polytropicindex is calculated from the𝑃-𝑇 curve (pressure-temperaturecurve) considering 𝑃(1−𝑛)𝑇𝑛 = constant relation.

Roundtrip efficiencies of liquid piston based OCAESsystem with various polytropic indexes of compression/expansion are shown in Figure 10. Uncertainty bars represent


95% confidence interval valves. It can be observed thatestimatedmean value of end-to-end efficiency increases from24% to 72% with a decrease in the polytropic index ofcompression from 1.4 (adiabatic process) to 1 (isothermalprocess).This clearly indicates liquid piston compression andexpansion efficiency has a major influence on the end-to-end efficiency. For a polytropic index of 1.14 observed withan experimental liquid piston, a roundtrip efficiency of 45%was shown. Noticeably, this efficiency value is way belowefficiency level of isothermal OCAES. However, the liquidpiston setup used in the experimental investigation did notinvolve any heat transfer enhancement mechanism to abatetemperature rise. Various designs of liquid pistons leadingto a lower polytropic index of compression/expansion wouldincrease roundtrip efficiency for the OCAES system.

5.5. OCAESwith Heat Transfer Enhancement in Liquid Piston.Various heat transfer enhancement techniques in liquidpiston have been observed to be effective in improving effi-ciency and power density. Various heat transfer enhancementtechniques considered are use of optimal trajectories, use ofhollow spheres, spray cooling, and use of porous media. Theeffectiveness of these heat transfer enhancement techniquesin achieving an efficiency level of isothermal OCAES isfurther investigated. Heat transfer enhancement techniquesconsidered in this analysis are discussed below.

5.5.1. Optimal Trajectories. The Pareto optimal trajectoriesfor the liquid piston compressor/expander that maximizesefficiency for a given power have been found by Saadat etal. [40]. They considered general heat transfer models, theviscous friction, and system constraints in the optimiza-tion process. These optimal trajectories were experimentallytested by Shirazi et al. [41]. It was observed that optimalprofiles show up to 4% higher efficiency for the same powerdensity or 30% higher power density for the same theefficiency compared to ad hoc constant flow rate profiles.

5.5.2. Use of Hollow Spheres. Hollow spheres floating at theliquid-air interface in the liquid piston have been observedto be effective in reducing the temperature of the compressedair in the liquid piston compressor. Hollow spheres made ofSilicon Carbide (SiC), High-Density Polyethylene (HDPE),and Polypropylene (PP) were tested by Ramakrishnan et al.in a liquid piston compressor [20]. It was observed that thosehollow spheres are effective in bringing down the temperatureof the compressed gas and hence enhance heat transfer inthe system. The polytropic index of compression with use ofhollow spheres reduces to 1.08 from 1.15 which correspondsto increase in compression efficiency from 79% to 87% for acompression ratio of 10.

5.5.3. Spray Cooling. In the spray cooling concept, smallwater droplets and highmass loading create a large interfacialsurface area for heat transfer. The droplet spray heat transferin the liquid piston compressor has been investigated byQin and Loth [42]. They developed a detailed multiphasethermodynamicmodel and validatedwith experimental data.

Base

liqu

idpi

ston

With

opt

imal

traj

ecto

ries

With

hol

low

sphe

res

With

spra

yco

olin

g

With

por

ous

med

ia

Isot

herm

al

Roun

dtrip

effici

ency

(%)

0

10

20

30

40

50

60

70

80

Figure 11: Roundtrip efficiency of liquid piston based OCAES withvarious heat transfer enhancement techniques.

It was observed that the total surface area of aloft dropletsis critical to achieving high performance in a liquid pistonand the best can be achieved with small droplets and highmass loading combined with direct injection. It is shownthat compression efficiency could be increased from 71% foradiabatic compression to as high as 98% with spray injectionfor a compression ratio of 10. The mass loading, dropletdiameters, and direct versus premixed injection influenceeffectiveness of spray cooling and hence compression effi-ciency. For a compression ratio of 10 andmass loading of 1, thecompression efficiency of 93% is shown with spray cooling inthe liquid piston.

5.5.4. Porous Media. The porous media inserts increase heattransfer surface area significantly; hence their addition tothe liquid piston compression/expander increases the com-pression efficiency at a fixed power density. Experimentalinvestigations on heat transfer with porous media in a liquidpiston during compression and expansion have been carriedout by Yan et al. [19]. A baseline case without inserts and fivecases with different porous inserts were tested in a compres-sion experiment. It was found that, in compression, porousinserts increase power density by 39-fold at 95% efficiencyand increase efficiency by 18% at 100 kW/m3. Similarly, inthe expansion, porous media inserts increase power densitythreefold at 89% efficiency and increase efficiency by 7% at150 kW/m3.

The end-to-end efficiency of liquid piston based OCAESsystem with various heat transfer enhancement techniquesin liquid piston is shown in Figure 11. The base liquid pistonwithout any heat transfer enhancement technique considersexperimental observed liquid piston compressor/expanderefficiency. The isothermal OCAES is one in which com-pression and expansion happen isothermally which indicates100% compression and expansion efficiency. Uncertainty barsrepresent 95% confidence interval valves.


It can be observed that estimated mean value of end-to-end efficiency is consistently higher with the use of heattransfer enhancement technique over the base liquid piston.The optimal trajectories can improve OCAES efficiency byabout 5%. Although this improvement is comparatively asmall value, this improvement happens without introducingany other media in the liquid piston. Therefore, optimaltrajectory technique can be considered as an efficiencyimprovement technique without affecting other performanceof the liquid piston like volumetric efficiency, power density,and long-term reliability. The use of hollow spheres haspotential to improve the efficiency ofOCAES systemby about9%. The addition of a layer of floating spheres in liquidpiston increases heat transfer area and helps in temperatureabatement in the liquid piston during compression. Thisresults in improved efficiency of compression and similarlyfor expansion.

Further, spray cooling and porousmedia inserts can showabout 17% improvement in the OCAES efficiency achievingend-to-end efficiency of about 62%. Both of these methodsincrease heat transfer medium inside the liquid piston andhence help to curtail the temperature rise in the liquid pistonduring compression and temperature fall during expansion.The high surface area and high specific heat of the waterspray help in heat transfer enhancement andhence improvingcompression/expansion efficiency of liquid piston. In porousmedia inserts, higher heat transfer surface area in porousmedia helps in absorbing the thermal energy from the airduring compression and dissipates it to the liquid. In expan-sion mode, the same porous media transfers thermal energyfrom the liquid to the air. Although spray cooling and porousmedia improves the efficiency of OCAES significantly, theseheat transfer enhancement techniques require other media tobe introduced in the liquid piston. This results in a reducedvolumetric efficiency of compression/expansion. Also, spraycooling and porous media inserts might require special carefor continuous reliable heat transfer performance. This isbecause of the change in spray characteristics and porousmedia characteristics over time due to their degradation.

An isothermal liquid piston compressor would define anupper limit for roundtrip efficiency ofOCAES, which is about72% for the given system considerations. This indicates thatinefficiencies in themotor/generator, hydraulic pump/motor,pipelines, control valves, and storage result in about 28% ofenergy loss. End-to-end efficiencies of existing compressedair energy storage (CAES) plants in Huntorf (Germany) andMcIntosh AL (USA) are 42% and 54%, respectively [14].Clearly, liquid piston based OCAES with the use of heattransfer enhancement technique such as spray cooling orporous media inserts in liquid piston can show significantlyhigher end-to-end efficiency over existing CAES plants.

6. Conclusions

In pursuit of developing efficient economical large-scaleenergy storage, ocean compressed air energy storage can

play an important role. Various OCAES concepts are pos-sible, namely, diabatic, adiabatic, and isothermal OCAES.Energy and exergy analysis of these concepts is performedfor OCAES system of the maximum power capacity of0.5MW and 2MWh energy storage with storage pressure of10 bar (100m of ocean depth). Analytical models for energyand exergy analysis of various components in OCAES arepresented. The exergy flow, energy efficiency, and exergyefficiency of various OCAES concepts are analyzed for com-parative assessment.

The analysis shows that energy efficiency of diabaticOCAES is about 50% whereas its exergy efficiency is about55%. Clearly, energy efficiency undervalues efficiency ofdiabatic OCAES; therefore, exergy efficiency would be agoodmeasure of efficiency for comparison with other storageconcepts. Adiabatic OCAES shows about 5% improvement inexergy efficiency over diabatic OCAES. Isothermal OCAESshows significantly higher efficiency over diabatic and adia-batic OCAES. Analysis of liquid piston based OCAES withthe use of experimental liquid piston compressor indicatedroundtrip efficiency of 45%.With heat transfer enhancementin the liquid piston, roundtrip efficiency of about 62% ispossible with the use of either spray cooling or porous mediainserts. Overall, liquid piston based OCAES with use ofheat transfer enhancement has potential to show significantlyhigher efficiency than existing compressed air energy storageplants.

Disclosure

Portions of this study have been presented in a poster form at2017 MAE Graduate Research Symposium of North CarolinaState University, Raleigh, USA. Also, part of the work in thispaper was presented in ASME 2017 Power Conference andTechConnect World Innovation Conference 2017. Dr. Paul I.Ro served in the capacity of technical advisor for this work.

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper.

Acknowledgments

The authors gratefully acknowledge support from the UNCCoastal Studies Institute of North Carolina, USA.

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Energy and Exergy Analysis of Ocean Compressed Air Energy