Applied Thermal Engineering 108 (2016) 1418–1428

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate /apthermeng

Research Paper

Thermo-Electric Energy Storage involving CO2 transcritical cycles andground heat storage

http://dx.doi.org/10.1016/j.applthermaleng.2016.07.0631359-4311/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: nicolas.tauveron@cea.fr (N. Tauveron).

Fadhel Ayachi a, Nicolas Tauveron a,⇑, Thomas Tartière b, Stéphane Colasson a, Denis Nguyen caCEA, LITEN – DTBH/SBRT/LS2T, 17 rue des Martyrs, Grenoble 38054, Franceb Enertime, 1 rue du Moulin des Bruyères, Courbevoie 92400, FrancecBRGM Languedoc-Roussillon, 1039 rue de Pinville, 34000 Montpellier, France

h i g h l i g h t s

� With ideal hypotheses roundtrip efficiencies can be up to 50%.� With ideal hypotheses roundtrip efficiencies reach 66% with the most complex cycle.� More realistic roundtrip efficiencies were evaluated between 42.5 and 55.5%.

a r t i c l e i n f o

Article history:Received 16 March 2016Revised 15 June 2016Accepted 10 July 2016Available online 11 July 2016

Keywords:StorageCO2TranscriticalGroundHeat-pumpRankine

a b s t r a c t

Multi-megawatt Thermo-Electric Energy Storage based on thermodynamic cycles is a promising alterna-tive to PSH (Pumped-Storage Hydroelectricity) and CAES (Compressed Air Energy Storage) systems. Thesize and cost of the heat storage are the main drawbacks of this technology but using the ground as a heatreservoir could be an interesting and cheap solution. In that context, the aim of this work is (i) to assessthe performance of a geothermal electricity storage concept based on CO2 transcritical cycles and groundheat exchanger, and (ii) to carry out the preliminary design of the whole system. This later includes a heatpump transcritical cycle as the charging process and a transcritical Rankine cycle of 1–10 MWel as the dis-charging process.A steady-state thermodynamic model is performed and several options, including heat regeneration,

two-phase turbine and multi-stage design, are investigated. In addition, a one-dimensional model ofthe ground exchanger is performed and coupled to the thermodynamic model to optimize the numberof wells for the ground heat storage.The results show a strong dependency between the charging and discharging processes and indicate

how the use of heat regeneration in both processes could be advantageous. The results also measurethe difference in performance between the basic and the advanced designs.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Organic Rankine Cycles (ORC) have been used in a wide range ofapplications (including geothermal, biomass, solar power plants,waste heat recovery from industrial processes and combustionengines, ocean thermal energy conversion) and a wide range ofpower outputs from a few kilowatts to tens of megawatts. The pos-sibility to use ORC to produce electricity from heat that has beenpreviously stored as a large-scale electricity storage technologyremains more confidential but has been the subject of recentstudies [1].

As it is well-known, the massive integration of intermittentrenewable energy production generates new challenges for thesupervision and regulation of electric grids. The use of flexiblebut carbon-intensive technologies such as gas turbines has beenthe main solution in order to ensure the balance between demandand supply, maintaining grid frequency and power quality. How-ever, large-scale electricity storage is a promising alternative witha much lower environmental impact. In addition, it would enable adecentralized access to electricity and lower the dependency onfossil fuels. If storage is still expensive today, it could becomeincreasingly viable as the price of carbon rises.

Several technologies exist or are under development for large-scale energy storage. Pumped-Storage Hydroelectricity (PSH) isthe most common one and covers a power range varying from a

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Nomenclature

Latin lettersA column area (m2)h specific enthalpy (J/kg)_m overall mass flow rate (g/s)_mseries mass flow rate per series (g/s)N nunmber of columns per seriesNb total column numberNu Nusselt numberP pressure (Pa) or (bar)PH cycle high pressure (Pa) or (bar)PL cycle low pressure (Pa) or (bar)Pr Prandtl numberPR Turbine pressure ratio_Q heat flux (W)Re Reynolds numbers specific entropy (J/kg K)T temperature (K) or (�C)U heat transfer coefficient (W/m2 K)_W power (W)_Wel electrical power (W)

Greek lettersd _Qcold system asymmetry (W)DP pressure drop (Pa) or (bar)

DTmin minimum temperature difference between reservoirand fluid (K)

g efficiencygth thermal efficiencygsys roundtrip efficiency of the storage systemq density (kg/m3)

Subscriptsc compressorcold cold reservoirg generatorhot hot reservoirm motorp pumpreg heat regenerators isentropict turbinetp two-phase turbinew wall

AcronymsCOP Coefficient Of PerformanceCFD Computational Fluid DynamicsORC Organic Rankine CycleTEES Thermo-Electric Energy Storage

F. Ayachi et al. / Applied Thermal Engineering 108 (2016) 1418–1428 1419

few hundred of megawatts to a few gigawatts. It accounts for morethan 99% of the worldwide bulk storage capacity, representingaround 140 GW over 380 locations [1]. Reported storage efficien-cies are typically between 70% and 85%. Despite having a long life-time and being the most cost-effective energy storage technology,these systems have a low energy density and require the construc-tion of large water reservoirs, leading to a high environmentalimpact. In addition, the most suitable locations have already beenused in developed countries. Other possibilities would be toinclude pre-existing dams or the ocean, as in the 30 MW Yanbaruproject in Japan [2].

At a lower power range varying from a few tens to a few hun-dreds of megawatts, Compressed-Air Energy Storage (CAES) is atan advanced stage of development and accounts only 2 powerplants until now: a 290 MW plant in Huntorf, Germany (1978)[3], and a 110 MW plant in McIntosh, USA (1991) [4]. Reportedroundtrip efficiencies are around 50% and the capital cost of CAESpower plants is competitive with PSH. A much higher efficienciesup to 70% could be achieved by Advanced Adiabatic CAES (AA-CAES) [4–6] as the second generation technology which is still atan early stage of development. Such as PSH, CAES and AA-CAESsystems require specific sites and cannot be installed everywhere.

Thermo-electric energy storage (TEES) is a promising alterna-tive to existing technologies that covers widespread and large-scale electricity storage. It couples thermodynamic cycles to inde-pendent reservoirs and is generally free from geological and geo-graphical constraints. During periods of excess electricitygeneration, a vapour compression heat pump consumes electricityand transfers heat between a low-temperature heat source and ahigher temperature heat sink. The temperature difference betweenthe heat sink and the heat source can be maintained for severalhours, until a power cycle is used to discharge the system and gen-erate electricity during peak consumption hours.

Mercangöz et al. [7] gave references of Thermo-Electric EnergyStorage studies as old as 1924 and described the general concept of

this technology, based on two-way conversion of electricity to andfrom heat. They noted that the main challenges of TEES are to clo-sely match the working fluid operation to the heat source and heatsink profiles, and to find an optimum between roundtrip efficiencyand capital cost. The authors have analysed a TEES system withCO2 transcritical cycles, hot water and ice tanks as storage reser-voirs. The ABB Corporate Research Center [8,9] described a wayto store electricity using two hot water tanks, an ice tank andCO2 transcritical cycles. For similar systems, Morandin et al.[10,11] defined a design methodology based on pinch analysisand calculated a 60% maximum roundtrip efficiency for a base casescenario with turbomachinery efficiencies given by manufacturers.

Sensible heat storage with hot water tanks is often considered,since water has high thermal capacity, cheaply available andenvironmental-friendly. Latent heat storages based on phase-change materials (PCMs) have also been widely investigated. Theheat sink of the system can be either the ambient or ice. This sec-ond option ensures a constant low-pressure for the process that isfavorable to turbomachines. A mixture of salt and water can beused to adjust the heat sink temperature between 0 �C and�21.2 �C (corresponding to the eutectic point with 23.3% NaCl inwater by mass) [10].

Different working fluids can be considered for the thermody-namic cycles. Desrues et al. [12] presented a TEES process basedon Argon in forward and backward closed Brayton cycles. Henchozet al. [13] analysed the combination of solar thermal energy withTEES based on Ammonia cycles. Kim et al. [14] reviewed currentTEES systems and showed that using CO2 transcritical cyclesinstead of Argon Brayton cycles leads to a higher roundtrip effi-ciency even if the required temperature difference between theheat storages is much smaller. They also proposed an isothermalenergy storage system based on CO2 transcritical cycles and liquidpiston compressors/expanders.

Carbon dioxide is a natural refrigerant with many advantages. Itis a low-cost fluid that is non-toxic, non-flammable, chemically

1420 F. Ayachi et al. / Applied Thermal Engineering 108 (2016) 1418–1428

stable, and cheaply available. In addition, the high fluid density ofsupercritical CO2 leads to very compact systems. Many studieshave been published to evaluate the potential of supercriticalCO2 as working fluid in power cycles and heat pumps [15,16].Cayer et al. carried out an analysis [17] and an optimization [18]of CO2 transcritical cycle with a low-temperature heat source.More recently, the use of CO2 for multi-megawatt power cycleshas reached a commercial step with the American company Echo-gen [19]. In parallel, underground thermal energy storage appearsto be an attractive solution [20].

The purpose of this article is to introduce a new concept ofThermo Electric Energy Storage process for large scale electricapplications, based on CO2 transcritical cycles and ground heatstorage. The association of such cycles and ground storage consti-tutes the originality of the project. The conceptual design of suchTEES system is addressed here only from a thermodynamic pointof view and economic analysis are left for future work.

2. Problem definition

The investigated Thermo-Electric Energy Storage system is ageothermal storage concept that includes:

i. a hot reservoir made of ground heat exchangers organized ina serial-parallel layout and set up in a superficial bedrock(unfractured crystalline dry rock)

ii. a cold reservoir using a phase-change material that could beice (Tcold 6 0 �C) or other material (Tcold > 0 �C)

iii. two thermodynamic cycles as a charging process and a dis-charging process both using carbon dioxide as a workingfluid.

Fig. 1. Charging process: (a) proce

The basic overviews of these two processes are given respec-tively by Figs. 1 and 2. All the components of each process are con-sidered as open systems in steady state condition.

During off-hours, the charging process consists of a transcriticalheat pump cycle characterized by 6 main steps: the working fluidleaves the cold reservoir heat exchanger as a saturated vapour atT1 = Tcold � DTmin and is internally superheated (1? 2) through aregenerator, before being adiabatically compressed (2? 3) into amechanical compressor with an isentropic efficiency gs,c. At thecompressor outlet, the fluid at T3 = (Thot)max +DTmin and supercrit-ical high pressure P3 = PH is first cooled through the hot reservoirexchanger (3? 4) releasing heat to the ground, then cooled furtherthrough the regenerator (4? 5) releasing heat to the low pressurevapour. The fluid at a liquid state passes into an expansion valve(5? 6) to reach the subcritical low pressure PL and is finally evap-orated through the cold reservoir exchanger (6? 1).

For given storage temperatures Tcold and (Thot)max and a givenhot pressure PH, the thermodynamic states can be obtained fromthe energy balances of the system components:

ðh1 � h2Þ þ ðh4 � h5Þ ¼ 0 ð1Þ_Wc þ _mðh2 � h3Þ ¼ 0 ð2Þ_Qhot þ _mðh3 � h4Þ ¼ 0 ð3Þh5 � h6 ¼ 0 ð4Þ_Qcold þ _mðh6 � h1Þ ¼ 0 ð5Þ

hi (J/kg K) and _m (kg/s) being respectively the specific enthalpy atstate i and the mass flow rate relating to the charging cycle._WcðWÞ ¼ _mðh3s � h2Þ=gs;c > 0, _QhotðWÞ < 0 and _QcoldðWÞ > 0 arerespectively the compressor power, the heat flux transferred tothe hot reservoir and the heat flux transferred from the coldreservoir.

ss layout, (b) (T, _ms) diagram.

3

5

4

TurbineHot reservoir

Regenerator

Pump 6

Cold reservoir

1

2

(a) (b)

Fig. 2. Discharging process: (a) process layout, (b) (T, _ms) diagram.

F. Ayachi et al. / Applied Thermal Engineering 108 (2016) 1418–1428 1421

By adding Eqs. (1)–(5), it appears the energy balance of thecharging cycle:

_Wc þ _Qhot þ _Qcold ¼ 0 ð6ÞDuring peak-hours, the discharging process consists of a trans-

critical Rankine cycle characterized by 6 main steps: the workingfluid leaves the cold reservoir heat exchanger as a saturated liquidat T1

0= Tcold + DTmin and is adiabatically compressed (1? 2) into a

feed pump with an isentropic efficiency gs,p. At the outlet of thepump, the fluid at a supercritical high pressure P2

0= PH

0is first

preheated through the regenerator (2? 3), then heated furtherthrough the hot reservoir exchanger (3? 4) destocking heatfrom the ground. At the entrance of the turbine, the fluid atT4

0= (Thot)max � DTmin is adiabatically expanded (4? 5) to the

subcritical low pressure PL0delivering a mechanical work with an

isentropic efficiency gs,t. Finally, the fluid is internally cooledthrough the regenerator (5? 6) before being condensed throughthe cold reservoir exchanger (6? 1).

The reservoir temperatures Tcold and (Thot)max and the high pres-sure PH

0 � PH being known, the thermodynamic states can beobtained from the energy balances of the system components:

_W 0p þ _m0ðh01 � h02Þ ¼ 0 ð7Þðh02 � h03Þ þ ðh05 � h06Þ ¼ 0 ð8Þ_Q 0hot þ _m0ðh03 � h04Þ ¼ 0 ð9Þ_W 0t þ _m0ðh04 � h05Þ ¼ 0 ð10Þ_Q 0cold þ _m0ðh06 � h01Þ ¼ 0 ð11Þ

hi0(J/kg K) and _m0 (kg/s) being respectively the specific enthalpy at

state i and the mass flow rate relating to the discharging cycle._W 0pðWÞ ¼ _m0ðh02s � h01Þ=gs;p > 0, _W 0tðWÞ ¼ _m0ðh05s � h04Þgs;t < 0,_Q 0hotðWÞ > 0 and _Q 0coldðWÞ < 0 are respectively the pump power,the turbine power, the heat flux transferred from the hot reservoirand the heat flux transferred to the cold reservoir.

By adding Eqs. (7)–(11), it appears the energy balance of the dis-charging cycle:

_W 0p þ _Q 0hot þ _W 0t þ _Q 0cold ¼ 0 ð12ÞBy specifying the net power output of the discharging cycle

_W 0el ¼ ggð _W 0t þ _W 0pÞ and by assuming similar charging and dis-charging times, _Q 0hot ffi � _Qhot . This gives the mass flow rates _mand _m0 and then the net power input of the charging cycle_Wel ¼ _Wc=gm.

Furthermore, by adding Eqs. (6) and (12) and since _Q 0hot ¼ � _Qhot ,it follows that:

_Wc þ _Qcold þ _W 0p þ _W 0t þ _Q 0cold ¼ 0 ð13ÞEq. (13) shows that there is an asymmetry between the two pro-cesses which can be expressed as an additional need of cooling:

d _Qcold ¼ _Qcold þ _Q 0cold ¼ �ð _Wc þ _W 0p þ _W 0tÞ < 0 ð14ÞThis additional need of cooling can be provided by an auxiliary

CO2 chiller that processes independently and simultaneously withthe charging cycle (Fig. 1a). The electrical consumption of the chil-ler _W 00elðWÞ as expressed by Eq. (15) is calculated using a singlestage chiller model with a condensing temperature at 20 �C.

_W 00el ¼�d _QcoldCOP

ð15Þ

On the other hand, the low diffusivity of the ground ensures theheterogeneity of the temperature therein (Figs. 1b and 2b), whichseems to be favorable to maintain the cycles uniforms at theirnominal conditions over a long period of time. Assuming similarcharging and discharging times, the roundtrip efficiency of thewhole system can be defined as:

gsys ¼_W 0el

_Wel þ _W 00elð16Þ

Table 1Input parameters.

StorageHot storage max temperature (Thot)max 130 �CCold storage temperature Tcold VariableMin temperature difference between reservoir and

fluid DTminVariable

Charging cycleCompressor isentropic efficiency gs,c 0.85Motor efficiency gm 0.98(T4)min 30 �CRegenerator pinch 5 KRegenerator pressure drop [0–5 bar]

Discharging cycle

Net power output _W0el [1–10 MWel]

Pump isentropic efficiency gs,p 0.80Turbine isentropic efficiency gs,t 0.90Generator efficiency gg 0.98Regenerator pinch 5 KRegenerator pressure drop [0–5 bar]

ChillerCompressor isentropic efficiency 0.85Motor efficiency 0.98Condensing temperature 20 �CEvaporating temperature Same as for discharge

cycle

1422 F. Ayachi et al. / Applied Thermal Engineering 108 (2016) 1418–1428

It is worth noting that the system performance as expressedabove also relies on the stabilization of the ground temperatureat the start of each process i.e. Thot = (Thot)min at the start of thecharging process and Thot = (Thot)max at the start of the dischargingprocess. This implies the achievement of a certain control duringthe shutdown sequence of each process in order to set and stabilizethe ground temperature at the convenient value for the start ofeach following process.

Thereby, this steady-state analysis can be useful as a firstapproach for the assessment of the system performance especiallyat nominal conditions. This could be sufficient as a comparativetool for the selection of the system design (non-regenerative,regenerative, single-stage, multi-stage) before coupling

70

90

110

130

150

170

190

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0

40%

42%

43%

44%

46%44%42%

46%44%42%

Hig

h pr

essu

re (

bar)

Cold storage t

non-regenera�ve regenera�ve discha

regenera�ve charge & discharge r

Fig. 3. Performance map of the basi

dynamically the charging and discharging processes to the groundproperties.

The thermodynamic model is implemented through the Engi-neering Equation Solver (EES) software [21]. The model inputparameters are reported in Table 1. The component efficienciesincluding the generator and the rotary machines are fixed at com-monly used values at nominal conditions [22–30].

3. System design analysis

From the thermodynamic model described above, it is possibleto carry out a parametric study of the whole system. As the aim ofthis section is to perform a comparative design analysis basing onthe maximum reachable efficiencies, the quasi-limit case(DTmin = 1 K) is then first considered and the pressure losses withinthe hot reservoir exchanger are preliminarily neglected. The com-ponent efficiencies including the rotary devices are fixed at nomi-nal values (Table 1). Once these settings are given, two cycleindependent variables, namely the cold storage temperature Tcoldand the high pressure PH are sufficient for describing the wholesystem.

The performance map given by Fig. 3 illustrates the iso-efficiencies according to the couple (Tcold, PH) and with respect tothe system design. The map indicates that the roundtrip efficiencyof a non-regenerative system reaches an optimal value of 45% atpotentially high pressures. This could lead to more expensivedevices. The implementation of heat regeneration in the discharg-ing cycle leads to comparable performances with the advantage oflower operating pressures. Moreover, the implementation of heatregeneration in both charging and discharging cycles leads to anoptimal roundtrip efficiency slightly higher than 50%. It is worthnoting that the lower the cold temperature Tcold is, the lower thehigh pressure PH is.

Figs. 4a and b represent the entropy diagrams of respectively anoptimal non-regenerative system and an optimal regenerative sys-tem. By comparing the two diagrams, it can be seen that the doubleregeneration reduces the system high pressures PH and PH

0and

2 4 6 8 10 12 14 16 18 20 22 24

50%

48%

46%

50%

48%

46%

44%44%

42%42%

45%

emperature (°C)

rge regenera�ve dicharge (ΔPreg = 5 bar)

egenera�ve charge & discharge (ΔPreg = 5 bar)

c storage system (DTmin = 1 K).

0,10 0,35 0,60 0,85 1,10 1,35 1,60-30-20-10

0102030405060708090

100110120130140150160

Entropy (kJ/kgK)

Tem

pera

ture

(°C

)

Charge

1,7 [C]

3,7 [C]

129 [C]131 [C]

38,39 [bar]

36,45 [bar]

137 [bar]

136,7 [bar]

14,72 [C]

30 [C]27,44 [C]

Discharge

0,10 0,35 0,60 0,85 1,10 1,35 1,60-30-20-10

0102030405060708090

100110120130140150160

Entropy (kJ/kgK)

Tem

pera

ture

(°C

)

Charge

-0,5 [C]

1,5 [C]

129 [C]131 [C]

15,64 [C]

36,25 [bar]

34,39 [bar]

112,3 [bar]

107 [bar]

25 [C]

30 [C]42,64 [C]

Discharge

(a)

(b)

Fig. 4. Entropy diagram (DTmin = 1 K, _W0el = 1 MWel). (a) non-regenerative basic system (gsys = 45%), (b) regenerative basic system (gsys = 51%).

F. Ayachi et al. / Applied Thermal Engineering 108 (2016) 1418–1428 1423

reduces in more the turbine pressure ratio PR, the heat flux trans-ferred to the hot reservoir _Qhot and the additional supply of cooling

because of the asymmetry existence d _Qcold. Thereby, the doubleregeneration appears very attractive to meet high efficiency andlow investment cost.

The improvement of the roundtrip efficiency could be made bycomplicating the system design. Therefore, it would be interestingto thermodynamically assess the performance of:

– a storage system including a two-phase turbine in the chargingcycle. In this case, the two-phase turbine substitutes the expan-sion valve in the evolution (5? 6) and the net power input isthen reduced by the two-phase turbine generation

– a storage system including a two-stage discharging cycle. In thiscase, Fig. 5 shows that the heat transfer is made via two pres-sure levels and the thermoelectric conversion is done via twoexpansion stages

– a storage system including a two-phase turbine in the chargingcycle and a two-stage discharging cycle.

Figs. 6a, b and c respectively illustrate the improvement in effi-ciency given by the aforementioned designs. The two first oneslead to comparable improvements e.g. the addition of a two-phase turbine in the charging cycle or a second stage in thedischarging cycle lead to a gain in the range of [9–14%] by consid-ering the regenerative system. Notice that the higher (Tcold, PH) are,the bigger is the gain in efficiency. Furthermore, the addition ofboth two-phase turbine in the charging cycle and second stage inthe discharging cycle lead to a promising gain range of [17–29%]depending on the couple (Tcold, PH) i.e. an efficiency range of[60–66%]. Fig. 7 gives the entropy diagram of this advanceddesign and highlights the specific effect of the heat regenerationin the discharging cycle as a consequence of the second stageaddition.

3

Regenerator

Turbine HPHot reservoir

Pump

Cold reservoir

1

2

……

……

………

……

…

Turbine LP

4 4 LP

5 LP

5 HP

4 HP

6

Fig. 5. Two-stage discharging process: process layout.

1424 F. Ayachi et al. / Applied Thermal Engineering 108 (2016) 1418–1428

It is obvious that these high performances would be lowered bythe impact of the pressure losses mainly through the high-pressureheat exchanger. In the following section, the heat transfer simula-tion will enable to estimate the head losses in that component andadjust the system parameters, in particular the minimum temper-ature difference DTmin.

4. Heat transfer modelling and exchanger preliminary design

The hot reservoir heat exchanger is made of multiple verticalcolumns having the same geometry. Series of columns are set inparallel lines as shown in Figs. 1 and 2.

It is worth noting that the quasi-limit case (DTmin = 1 K), anal-ysed in the previous section, could be constrained on one handby the exchange area and then the number of drillings and col-umns to implement and on the other hand by the pressure dropthat it generates. Thus, it is particularly important to considerthese constraints in the thermodynamic study of the system, whichwould need to process to a preliminary design of the hot reservoirheat exchanger according to the minimum temperature differenceDTmin setting.

In this regard, the one-dimensional modelling is a simple andfast tool requiring few computing resources. This makes easy thecoupling of the hot reservoir heat exchanger model to the thermo-dynamic model of the storage system. While it provides limitedaccuracy, the one-dimensional model of the heat exchanger couldbe useful to determine the suitable DTmin setting and particularlyhelpful to indicate how optimizing the geometric configurationof the unitary column. The heat exchanger design would be conve-niently refined thereafter by using advanced tools such as the CFDsimulation.

4.1. Model description

Fig. 8 gives the conceptual scheme of the 1D discretizationapplied to a series of columns. The fluid at supercritical pressureis injected at the bottom of each column through a central tubeand then flows up to an annular exit, exchanging heat with the sur-

rounding rock. We consider each column as a homogeneous rodthermally insulated from the other columns. We assume that thereis no radial or vertical temperature gradient within each column,and therefore the temperature within one column is homogeneous.The central injection tube is assumed adiabatic by considering athin insulation coating. The column specifications are reported inTable 2.

The preliminary design of the heat exchanger is performedthrough EES on the basis of the nominal conditions of the discharg-ing process. This preliminary design could also be valid for thecharging process when adapting the initial ground temperature(Thot)min (Fig. 1b).

For a given DTmin, the boundary conditions of the hot reservoirheat exchanger are:

{T[1,1] = T30, T[N,K + 1] = T4

0, Thot[N] = (Thot)max,Thot[1] J

(T30+ DTmin)}. For a given power output, the overall mass flow rate

_m0 (kg/s) and then the overall heat flux _Q 0hot ¼ � _Qhot are distributedaccording to the number of series:

_Q 0hot ¼ _Q 0series �Nbcolumns

N; _m0 ¼ _m0series �

NbcolumnsN

ð17Þ

On the other hand, the heat flux transferred through one seriesverifies the discretization concept:

_Q 0series ¼XNi¼1

XKj¼1

_Q ½i; j� ð18Þ

where

_Q ½i; j� ¼ AKU½i; j�LMTD½i; j�

¼ _m0seriesðh½i; jþ 1� � h½i; j�Þð19Þ

For each elementary segment, the log mean temperature differ-ence is given by:

LMTD½i; j� ¼ DT½i; j� � DT½i; jþ 1�ln DT½i;j�DT½i;jþ1�

� � ð20Þ

with

90

100

110

120

130

140

150

160

170

180

-6 -4 -2 0 2 4 6 8 10 12

50%51%

45%

52,1%

52,8%

53,2%

53,6%

53,9%

55,1%

55,3%

55,7%

56,2%

56,8%

56,6%56,8%

57,0%

regenera�ve basic system (ΔPreg = 5 bar)

non-regenera�ve basic system+ two-phase turbine (charge)

Hig

h pr

essu

re (b

ar)

Cold storage temperature (°C)

90

100

110

120

130

140

150

160

170

180

-6 -4 -2 0 2 4 6 8 10 12

50%51%

45%

46,9%

47,4%

47,7%

47,9%

48,1%

55,6%

55,9%

56,3%

57,1%

58,4%

57,6%57,9%

58,2%

regenera�ve basic system (ΔPreg = 5 bar)

non-regenera�ve basic system+ two-stage discharge

Hig

h pr

essu

re (b

ar)

Cold storage temperature (°C)

90

100

110

120

130

140

150

160

170

180

-6 -4 -2 0 2 4 6 8 10 12

50%51%

60,2%

61,3%

62,7%

64,1%

65,7%

63,8%64,5%

65,1%

regenera�ve basic system (ΔPreg = 5 bar)+ two-phase turbine (charge)

+ two-stage discharge

Hig

h pr

essu

re (b

ar)

Cold storage temperature (°C)

(a) (b)

(c)

Fig. 6. Efficiency improvement (DTmin = 1 K) given by: (a) two-phase turbine (gtp = 0.75), (b) two-stage discharging process, (c) advanced design.

F. Ayachi et al. / Applied Thermal Engineering 108 (2016) 1418–1428 1425

DT½i; j� ¼ T½i; j� � Thot½i� ð21ÞThe model includes the calculation of both the regular pressure

losses occurred within the central tube and the annular and thesingular pressure losses due to the elbows, the sudden narrowingat the top of the column and the sudden enlargement at the bot-tom of the column:

P½iþ 1;1� ¼ P½i;Kþ 1� � ðPtube½iþ 1� þP

DPsing½iþ 1�ÞP½i; jþ 1� ¼ P½i; j� � DPannular½i; j�

�ð22Þ

By assuming a column wall temperature equal to thesurrounding rock temperature (Tw[i,j] = Thot[i]), the elementaryheat transfer coefficients U[i,j] are computed using the localNusselt number correlation recommended by Jackson [31] for theforced convection case along a vertical turbulent flow of supercrit-ical CO2:

Nu½i; j� ¼ 0:0183 Re0:82½i; j�Pr0:5½i; j� q½i; j�qw½i; j�

� ��0:3ð23Þ

4.2. Results and discussion: DTmin impact

Coupling the thermodynamic model of the storage systemdescribed in Section 2 and the hot reservoir heat exchanger modeldescribed in Section 4.1 gives the results illustrated inFigs. 9a and b, with reference to the regenerative basic systemand 1 MWel power output; the cold storage temperature Tcold andthe operating pressures being optimal. The figures show that thenumber of columns, the overall pressure drop (P3

0–P4

0) and the

roundtrip efficiency gsys are all sensitive to the minimum temper-ature difference DTmin setting. By analysing the (2 series/MWel)case, a DTmin located between 5 and 8 K could be a good compro-mise between these three variants. Nevertheless, the overall pres-sure drop remains significant and contributes to the degradation ofthe roundtrip efficiency. On the other hand, the addition of seriesof columns to (4 series/MWel) allows to further reduce the pressuredrop and then to improve the roundtrip efficiency. However, it isobvious that this is at the expense of the number of drillings andcolumns. Here, the choice could be submitted to technical and eco-

0,15 0,40 0,65 0,90 1,15 1,40 1,65-30-20-10

0102030405060708090

100110120130140150160

Entropy (kJ/kgK)

Tem

pera

ture

(°C

)

Charge

2,5 [C]

4,5 [C]

129 [C]131 [C]

15,95 [C]

39,19 [bar]

37,21 [bar]

121,7 [bar]

116,4 [bar]

25 [C]

30 [C]

82,51 [C]

Discharge

70 [bar]

Fig. 7. Entropy diagram of a regenerative advanced system including a two-phase turbine in the charging cycle and a two-stage discharging cycle (DTmin = 1 K, _W0el = 1 MWel,gsys = 65%).

0

2

4

6

8

10

0

20

40

60

80

100

120

140

160

180

200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

P3 ' -P

4 ' (bar)

Num

ber o

f col

umns

/ M

Wel

ΔTmin (K)

2 series / MWel 4 series / MWel

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Roun

dtri

p effi

cien

cy η

sys(%

)

ΔTmin (K)

× × × ×× × × ×

× 2 series / MWel × 4 series / MWel

(a)

(b)

Fig. 9. DTmin impact on: (a) number of columns and pressure drop, (b) roundtripefficiency.

i = 1i = N i. . . . .

. . . . .

. . . . .

Fig. 8. Conceptual scheme of a one series discretization.

Table 2Column geometry.

Column length 15.3 mCentral tube length 15 mColumn internal diameter 0.4 mCentral tube internal diameter 0.2 m

1426 F. Ayachi et al. / Applied Thermal Engineering 108 (2016) 1418–1428

nomic criteria which are typically depending on the targetedpower output. Furthermore, the review and the optimization ofthe geometric configuration of the unitary column might also bedecisive.

By considering the hot reservoir heat exchanger constraints,Table 3 gathers the nominal operations and performances of thevarious system designs, with reference to DTmin = 5 K and 1 MWelpower output. By comparing the assessed performances with the

highest ones given in Section 3 for DTmin = 1 K and zero pressurelosses, the decrease in roundtrip efficiency is nearly the same forthe various system design and is around [13–19%] depending onthe column number.

The regenerative basic system would finally lead to moderateefficiencies at nominal conditions:

Table 3TEES systems: operations and performances (DTmin = 5 K, 1 MWel power output).

a

a

a

a Values related to the discharging process.

F. Ayachi et al. / Applied Thermal Engineering 108 (2016) 1418–1428 1427

1428 F. Ayachi et al. / Applied Thermal Engineering 108 (2016) 1418–1428

– gsys � 44% with a ground exchanger of around 1800 columnsfor a 10 MWel power output

– gsys � 42.5% with a ground exchanger of around 1000 columnsfor a 10 MWel power output.

A regenerative system including a two-stage discharging cyclewould lead at nominal conditions to:

– gsys � 49% with a ground exchanger of around 1800 columnsfor a 10 MWel power output

– gsys � 47% with a ground exchanger of around 1200 columnsfor a 10 MWel power output.

A regenerative advanced system including a two-phase turbinein the charging cycle and a two-stage discharging cycle would leadat nominal conditions to:

– gsys � 55.5% with a ground exchanger of around 1800 columnsfor a 10 MWel power output

– gsys � 53.5% with a ground exchanger of around 1200 columnsfor a 10 MWel power output.

5. Conclusion

The work presented in this paper deals with a new concept ofthermo-electric energy storage system combining CO2 transcriticalcycles and ground heat storage. The conceptual design of such TEESsystem is addressed only from a thermodynamic point of view andthe assessment is limited, as a first approach, to the nominal-operation charging/discharging time.

In the first part of the work, various system designs are assessedand compared basing on the maximum reachable roundtrip effi-ciencies where the ground exchanger constraints are first side-stepped (DTmin = 1 K, zero pressure losses). The main results haveshown roundtrip efficiencies up to 50%, able to reach 66% withthe most complex system. This part has also emphasized theimportance to provide heat regeneration in both charging and dis-charging processes. This double regeneration appears very attrac-tive to meet high efficiency and low investment cost. It isparticularly significant when considering a multi-stage dischargingprocess.

In the second part of the work, a one-dimensional model of themulticolumn ground exchanger is performed and coupled to thethermodynamic model of the storage system. This model couplinghas indicated that the number of drillings and columns, the overallpressure drop and the roundtrip efficiency are all sensitive to theminimum temperature difference DTmin setting. The results havealso shown that a DTmin located between 5 and 8 K could be a goodcompromise between these three variants. Also, the addition ofseries of columns in a serial-parallel arrangement allows to furtherreduce the exchanger pressure losses and then to improve theroundtrip efficiency. This part has revealed roundtrip efficienciesfrom 42.5 to 55.5% with a DTmin of 5 K.

This steady-state simulation is in fine important to introducethe new concept, to give a comparative analysis for the selectionof the system design and to provide a preliminarily design of theground exchanger according to the system design and the netpower output. Further work through the SELECO2 project wouldinclude turbomachinery modelling and transient simulation sothat it will be possible to (i) study the heat transfer evolution dur-ing the off-design condition times (ii) better understand the depen-dency between the charging and the discharging processes and (iii)gather for each process the nominal-condition time and the off-design condition times in the calculation of the roundtrip efficiencyof the storage system. This would lead to a complete overview ofthe new concept and a better evaluation of the general interest.

Acknowledgement

The authors acknowledge the support of the French ResearchNational Agency (ANR) under grant ANR-13-SEED-0004 (SELECO2project) and the contribution of all partners of the project (ENGIE,Toulouse University, BRGM, CEA, ENERTIME).

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Thermo-Electric Energy Storage involving CO2 transcritical cycles and ground heat storage1 Introduction2 Problem definition3 System design analysis4 Heat transfer modelling and exchanger preliminary design4.1 Model description4.2 Results and discussion: ΔTmin impact

5 ConclusionAcknowledgementReferences