Modeling of a Thermocline Thermal Energy Storage ... · They are working on a CSP power plant made...

Corso di Laurea Magistrale in Ingegneria EnergeticaScuola di Ingegneria Industriale e dell’Informazione

Modeling of a Thermocline ThermalEnergy Storage: application to aConcentrating Solar Power plant

Relatore: Prof. Marco BinottiCorrelatore: Ing. Massimo FalchettaCorrelatore: Ing. Andrea Giostri

Tesi di Laurea di:Avallone Fabrizio, matr. 854538

Anno Accademico 2017-2018

...

..to Maruzza and Lambrusco

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Ringraziamenti

Vorrei ringraziare chi mi ha dato la possibilita di diventare quello che sonooggi.Penso che ognuno di noi sia come un mosaico, in cui ogni tassello e unacaratteristica speciale, che ci ha particolarmente colpito, delle persone cheabbiamo intorno.Siamo cio che ci circonda. E sono contento di quello che sono. E lo devo atutti voi.Lo sfondo del mio mosaico e grandissimo, come il mare, e coloratissimo, var-iopinto: sono i miei genitori, mamma e papa.Grazie per come siete, apertissimi e veri.La tonalita ricorrente in tutto il mosaico, il nero, e Riccardo. Grazie perchemi fai crescere sempre meglio.E il protagonista del mio mosaico e un polpo, u purpetiell piu bello delmondo, Chiara, 8 tentacoli fortissimi.

Al suo fianco ci sono *inserire nome di cosa comune*, Bastia, un delfino,viscido, Simone, e un’anemone, Graziano.In un mosaico cosı marittimo non puo mancare Atlante, e io ne ho due, i mieiAtlantini, Fabio e Martina, passano gli anni ma con voi sembrano minuti.

E ci sono tasselli messi con tipica arte di Tor Vergata, senza di voi iltrienni non sarebbe stato cosı meraviglioso.

E i tasselli nordici, di maturita piacentina. Grazie anche a tutti voi.

Un grazie speciale va a Massimo Falchetta, per aver reso possibile questamia esperienza, ma soprattutto per averla resa interessante grazie ai suipreziosi spunti.Grazie anche ad Andrea Giostri, e a Marco Binotti.

Fabrizio

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Sommario

La tesi nasce da una collaborazione tra Politecnico di Milano ed ENEA perl’esigenza di creare un modello in grado di descrivere il funzionamento di unimpianto solare a concentrazione (CSP) di media taglia, formato da

- Campo solare, collettori Fresnel

- Accumulo termico di tipo termoclino

- Ciclo ORC per la produzione di elettricita

L’impianto rientra nel progetto europeo ORC-Plus, H2020, di cui ENEAe coordinatore.

In particolare l’obiettivo della tesi e quello di creare un modello dinamicoper l’accumulo termico termoclino. Nel caso specifico, un accumulo termicodiretto, caratterizzato da un letto impaccato di magnetite che va ad intera-gire con l’olio proveniente dal campo solare, assorbendone o cedendo ad essoenergia.Lo scopo principale e quello di permettere una simulazione sufficientementerapida, senza perdere eccessiva accuratezza nei risultati.Il modello e pertanto semplificato e non descrive moti radiali o circonferen-ziali del fluido all’interno del letto impaccato.

La tesi e cosı strutturata:

Dopo una descrizione del progetto europeo “ORC-Plus”, viene descrittala tecnologia di accumulo termico termoclino, le possibili classificazioni, e nevengono definite efficienze e il concetto di ”isteresi termica”.

Dopo un’analisi dei modelli esistenti in letteratura si procede con losviluppo di due modelli:

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- “1D-2P”, in cui il flusso del liquido attraverso il letto impaccato econsiderato monodimensionale, “1D”, e che valuta per ogni elementodiscretizzato temperature di fase liquida e solida, “2P”.

- “1D-1P”, in cui il flusso del liquido attraverso il letto impaccato enuovamente considerato monodimensionale,”1D”, ma liquido e solidosono considerati come mezzo equivalente, con caratteristiche intermediepesate tra i due: una sola temperatura equivalente, ”1P”, e valutata perogni elemento discretizzato, dimezzando cosı le incognite ed il tempocomputazionale.

Successivamente entrambi i modelli sono validati.

Si procede con la simulazione di un impianto completo (campo solare,accumulo e ciclo ORC) in 3 settimane tipo: Giugno, Marzo e Gennaio.L’accumulo termico termoclino e modellizzato sia con il modello 1D-2P, siacon quello 1D-1P, per analizzare le discrepanze tra i due.Esse risultano essere contenute, nell’ordine dell’ 1%.

Successivamente viene simulato il funzionamento dello stesso impianto,ma accoppiato ad un accumulo termico a due serbatoi, al fine di confrontarele due diverse tecnologie.L’impianto con accumulo termico a doppio serbatoio permette una pro-duzione elettrica annuale maggiore, di circa l’ 8%, rispetto all’impianto chesfrutta la tecnologia a termoclino.

Grazie ad una analisi economica il costo dell’impianto con serbatoio ter-moclino e quello dell’impianto con doppio serbatoio vengono successivamenteparagonati: differiscono del 15% circa, a favore dell’accumulo termoclino.Infine viene derivato il costo dell’elettricita, LCOE, per entrambi gli impianti.Esso risulta essere pari a 0.247e/kWhel per l’impianto con accumulo termo-clino e 0.262e/kWhel per l’impianto con doppio serbatoio: un risparmio del6%.

Summary

The thesis stems from a collaboration between Politecnico di Milano andENEA for the creation of a model capable of describing operations of amedium-sized Concentrating Solar Power plant, composed by

- Solar Field, Fresnel collectors

- thermocline Thermal Energy Storage (TES)

- ORC cycle for electricity production

The plant is part of the European project ORC-Plus, H2020.

In particular, the aim of the thesis is to create a dynamic model for thethermocline Thermal Energy Storage to be used within the project. In thespecific case, a direct storage, characterized by a magnetite packed-bed in-teracting with oil coming from the Solar Field, exchanging energy with it.The main purpose is to perform fast simulations, without losing too muchresults accuracy.The model is therefore a simplified model, not describing radial or circum-ferential motions of the fluid.

Here follows the structure of the thesis:

After a brief overview about the European project ”ORC-Plus”, the ther-mocline Thermal Energy Storage technology is described, togheter with itspossible classifications, efficiencies of such a storage and the concept of “ther-mal hysteresis”.

After an analysis of the existing models in literature, two models weredeveloped:

- “1D-2P”, in which the liquid flow across the packed bed is consideredone-dimensional, ”1D”, and that evaluates, for each discretized elementof the mesh, both liquid and solid phase temperatures, “2P”.

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- “1D-1P”, in which the liquid flow through the packed bed is againconsidered one-dimensional, ”1D”, but liquid and solid are consideredas an equivalent medium with intermediate characteristics, weightedbetween the two: a single equivalent temperature, “1P”, is evaluatedfor each discretized element of the mesh, halving the unknowns and thecomputational time.

Subsequently, both models are validated.

Then, three weekly-simulations of a complete power plant (Solar Field,Thermal Energy Storage, Power Block) are carried out: in June, March andJanuary. The Thermal Energy Storage is simulated both with the 1D-2Pand the 1D-1P model, in order to evaluate discrpancies between the two.These differences turned out to be limited, about 1%.

The same plant is simulated, but coupled to a two-tank Thermal EnergyStorage. Results are compared in order to highlight differences with the ther-mocline concept.The power plant exploiting the double-tank technology allows a higher an-nual electricity production with respect to the power plant exploiting thethermocline concept - about the 8% more.

Thanks to an economic analysis, the total costs of the plant coupled tothe thermocline TES and of the plant coupled to the double-tank TES arecompared: they differ by about 15%, in favor of thermocline Thermal EnergyStorage technology.

Finally LOCE’s are derived for both power plants: 0.247e/kWhel forthe thermocline-storage power plant and 0.262e/kWhel for the double-tank-storage power plant.

Extended summary

Introduction

Global energy - and electricity - demand is continuously growing and willprobably keep this trend - [1]. This is one of the main drivers of the CO2concentration increase in our atmosphere, hence of greenhouse effect and ofclimate change. In order to limit these emissions it is fundamental to gotowards improved use of energy, and increasing renewables penetrations inthe energy mix, like solar energy - [2].Among solar energy technologies, Concentrating Solar Power (CSP) exploitsthe Direct Normal Irradiation. It concentrates direct beams, by means of op-tical systems, in order to produce high temperatures through which electricpower can be produced. A CSP plant is a 3-components technology (SolarField – SF, Thermal Energy Storage – TES and Power Block-PB). The Ther-mal Energy Storage system is fundamental in order to reduce the LevelizedCost of Energy, to improve dispatchability and to increase the power plantefficiency.U.S. Department of Energy SunShot target for CSP systems is 6cent/kWhin 2020. New technical solutions has to be investigated in order to meet thisgoal.Since 2000, ENEA is developing the CSP technology pushing towards costsreduction. Among their studies, the ORC-Plus project is currently in thedevelopment stage.

This thesis has the objective of developing the numerical model of the“thermocline” Thermal Energy Storage system for the ORC-Plus projectand applying such model to a typical CSP configuration.

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ORC-Plus project

In June 2015 ORC-Plus project was initiated, funded by the H2020 EU Re-search and Development program - [3].The ORC-plus consortium is coordinated by ENEA, and it is composed bySoltigua, Fraunhofer, Enerray, Euronovia, CICenergigune and IRESEN - oneof the main Moroccan stakeholders in the field of CSP plant.They are working on a CSP power plant made of Fresnel type collectors, anOrganic Rankine Cycle Power Block and a Thermal Energy Storage exploit-ing the thermocline concept.ORC-Plus goal is to develop an optimized combination of innovative ThermalEnergy Storage and engineering solutions useful to improve the dispatcha-bility and capacity factor of a CSP plant.

Figure 1. ORC-plus project rendering. Source: Enerray website, [4].

Thermocline Thermal Energy Storage

In recent years a new technology, apparently cheaper than the well-established”double-tank”, is attracting the attention of many researchers: it is the Ther-mal Energy Storage exploiting the thermocline concept. Indeed, it requiresjust one tank to store the same amount of energy the double-tank technologystores - [5].

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Figure 2. Typical temperature profile inside a thermocline Thermal EnergyStorage, and how it would appear with infrared goggles.

In a thermocline tank, cold fluid and hot fluid are separated by an inter-mediate temperature zone (which is called ”thermocline”). Buoyancy forcesand very low speed of the fluid help to maintain this thermal stratification.There are many configuration possibilities for a thermocline Thermal EnergyStorage, and within ORC-Plus project the most investigated one is charac-terized by magnetite - as solid filler creating the so-called ”packed-bed” - andthermal oil - as Heat Transfer Fluid, directly flowing across the magnetitepacked-bed.The main reason for this choise is linked to the simplicity of the device, andto the fact that adding cheap solid filler inside the tank requires less amountof expensive oil, thus reducing costs.

Problems and main principles of functioning of such technology are anal-ysed in section 2.2 of the thesis.

Summarizing, it is fundamental to keep the thermocline zone as thin aspossible, and to let it exit from the tank just partially.

Some efficiency parameters can be introduced to evaluate thermoclinestorage performances:

Cycle efficiency:

ηcycle =Ew

Ep

(1)

Equation 1 takes into account losses to the environment: Ew is the energywithdrawn from the storage, Ep is the energy provided to the storage.

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Utilization factor:

Uf =Et,end

Cmax

(2)

In equation 2, Et,end represent the actual stored energy at the end of thecharge phase, which is generally stopped before the thermocline zone is com-pletely out of the tank, and Cmax is the energy content when the whole tankis at its maximum nominal temperature - no thermocline zone inside it.

Global efficiency - [6]:

η =Ew,end

Cmax

(3)

where Ew,end is the useful energy recovered after every cycle of charge anddischarge.If η = 1, thermocline zone tends to zero. It would be an ”ideal” thermocline.

Models

In this work two models, 1D-1P and 1D-2P, were developed and analyzed.They have been chosen because main requirements are simplicity and reduc-tion of computational time, and because they must describe plant-size tanks,while small tanks - with stronger wall effects - are not of interest.They have been both implemented in Simulink through a finite differenceapproach.Assumptions made are:

- The solid filler of the packed-bed is considered as a continuous, ho-mogenous and isotropic porous medium - it’s not modeled as a mediumcomposed of independent particles;

- No diffusers (or distributors) in the tank top and bottom are includedin the models;

- The liquid flow across the packed-bed region is laminar.

1D-2P model

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Figure 3. 1D-2P discretization along tank axis, n spatial steps.

Here are reported the equations to be solved in order to obtain the thermalbehaviour of the packed-bed of the tank - ”l” stands for liquid, ”s” for solidphase and ”ext” for environment, inspired by [7].

1st) Continuity equation:∂ρl∂t

=∂ρlu

∂x(4)

2nd) Energy equation for the liquid phase:

ε (ρc)l

(∂Tl∂t

+ u∂Tl∂x

)= kleff

∂2Tl∂x2

+ hv (Ts − Tl) +(UA)extVtotalbed

(Text − Tl)

(5)

3rd) Energy equation for the solid fillers:

(1− ε) (ρc)s∂Ts∂t

= kseff∂2Ts∂x2

+ hv (Tl − Ts) (6)

where: u is liquid velocity across the packed bed; ε (= Vl/Vtotalbed) isthe void fraction; c’s, ρ’s and T’s are respectively specific heat capacities,densities and temperatures; keff ’s are the effective thermal conductivities[W/(mK)]; hv is the interstitial heat transfer coefficient between fluid andsolid [W/(m3K)]; Vtotalbed is the volume occupied by the packed-bed; (UA)extis the global heat transfer coefficient for the evaluation of thermal losses to-wards the environment [W/K].

A typical result obtained solving these equations is reported in figure 4.

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Figure 4. Thermocline profile after 2, 4 and 6 hours from the beginning ofthe charge phase. Inlet fluid temperature is 300◦C. Initial temperature of thetank was 180◦C.

1D-1P model

Figure 5. 1D-1P discretization along tank axis, n spatial steps.

The fundamental equation describing the thermocline Thermal EnergyStorage behaviour in ”one phase”, inspired by [8] is:

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(ρc)eq∂T

∂t+ ε (ρc)l u

∂T

∂x= keq

∂2T

∂x2+

(UA)extVtotalbed

(Text − T ) (7)

where (ρc)eq = (ε (ρc)l + (1− ε) (ρc)s + η (ρc)w)and keq =

(kleff + kseff + ηkw

).

In this model, for sake of completeness, also wall thermal inertia is considered”w”.

One example of comparison between 1D-2P and 1D-1P models is reportedin fig. 6, where starting from a ”180◦C-storage” - both liquid and filler at180◦C - hot fluid at 300◦C is fed to the top of a 10m tall tank. As it can beseen differences are limited.

Figure 6. Temperature profiles inside the tank during the charging phase.1D-1P model temperature profile is in green. 1D-2P model profiles for rocksand Heat Transfer Fluid are in red and blue, respectively. Discrepancies be-tween models are about 3◦C.

For both models, the liquid phase volume variation – due to temperaturevariations – is taken into account and simulated.

Validations

Both models are validated against experimental data and against other mod-els. In figure 7, validation results are shown.

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Figure 7. TopLeft: 1D-1P and 1D-2P validation against SolarOne experi-mental data, [9]. TopRight: 1D-1P validation against CICenergigune experi-mental data and model. BottomLeft: 1D-1P validation against Xu model andPacheco experimental data, [10]. BottomRight: same validation for the 1D-2Pmodel.

Simulations results

After validations, three weekly-simulations of a complete power plant (So-lar Field, Thermal Energy Storage, Power Block) are carried out: in June,March and January. Simulations are performed modeling the Thermal En-ergy Storage both with the 1D-2P and the 1D-1P models, in order to checkdiscrpancies between the two, table 1, where

- EnergyORC is the net electric energy produced at the Power Block inone week;

- mORCTOT =∫time

m6dt;

- TORCIN,avg is the T6 averaged over time, of course just on the timeinterval characterized by m6 6= 0 - notice that when m6 6= 0, it isconstant too;

- Yearly net electricity production is computed considering 52 weeks peryear, and 13 weeks per season:

EnergyORC,Y ear = 13 ·EnORC,Sum + 26 ·EnORC,Spr/Aut + 13 ·EnORC,Win

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Table 1. Summary: Results of 1D-1P thermocline simulations.

EnergyORC

[MWhel]mORCTOT

[tons/week]TORCIN,avg

[◦]Sum week 86.17(+0.6%) 4970(+0.4%) 298(+0.0%)

Spr/Aut week 47.02(+0.7%) 2784(+0.5%) 295.5(+0.0%)Win week 37.12(+0.2%) 2177(+0.0%) 296(+0.0%)

Year 2825.29(+0.6%) - -

The percentage difference between the two models, 1D-2P and 1D-1P, isreported in brackets.The obtained differences are clearly limited, with discrepancies below 1%.

In figure 8 and 9 the simulated power plant and an example of resultscoming from simulations is reported.

Figure 8. Plant layout for Simulink simulation. Thermocline storage.

Then, the same power plant is again simulated, but coupled to a two-tankThermal Energy Storage. Results are compared with those of the 1D-2Pmodel in order to highlight differences with the thermocline concept, table2.

There are some interesting differences, expecially in Spring/Autumn whenthe implemented control logic force an higher Solar Field defocusing for thethermocline technology. Moreover the higher TORCIN,avg implies higher effi-ciency of the Power Block.

With these values of Yearly elecrticity production it is possible to assessa Levelized Cost Of Electricity, knowing the cost of the plants.

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Figure 9. 1D-2P model for TES. DNI, Ieff , Temperatures in the Solar Field,mass flow rates in the system and electricity production for a typical day inJune - the 18th.

Table 2. Summary: Results of 2-Tanks simulations.

EnergyORC

[MWhel]mORCTOT


[◦C]Sum week 90.24(+5.4%) 5168(+4.4%) 299(+0.3%)

Spr/Aut week 52.69(+12.9%) 3077(+11.0%) 297(+0.5%)Win week 37.94(+2.4%) 2203(+1.2%) 297.5(+0.5%)

Year 3036.28(+8.1%) - -

Threfore a cost analysis, producing the following results, has been carriedout - tables 3 and 4:

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Table 3. Sum up of costs for both TES technologies.

Costs in ke Thermocline Double-Tank ∆Shell 23.3 63.5 +173%

Insulation 12.0 29.4 +145%Oil 146.4 597.7 +308%

Filler 71.7 - -100%Foundations 17.8 68.9 +287%

El., Inst. ,Pip. ,Val. ,Fit. 4.1 13.2 +222%Total 304.4 772.8 +181%

Installation costs (x0.4) 110.1 309.1Total TES Cost 385.3 1081.9 +181%

For each storage the cost for shell, insulation, oil, filler, foundation, elec-trical and instrumentation, pipes, valves, fittings and installation has beenevaluated.

Table 4. Total Estimated Cost of the thermocline-TES and 2-Tanks-TESpower plants.

Total Estimated CostThermocline Double-TankCost[ke]

Share[%]

Cost[ke]

Share[%]

Solar Field 3267 70.2 3267 61.1Power Block 1000 21.5 1000 18.7

Thermal Energy Storage 385 8.3 1082 20.2Total Plant Cost 4652 5349

Indirect costs (x0.14)Owner and Conting. (x0.15)

TEC 6001 6900

And knowing the Total Estimated Cost, the LCOE can be evaluatedthanks to equation 7.4, [11]

LCOE =TEC · FCR

EY+CO&M

EY

where EY is the power plant Yearly Elecrticity production and FCR isthe ”Fixed-Charge Rate”.

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Table 5. Levelized Cost of Electricity evaluation.

Thermocline 1D-2P Double-Tank ∆TEC [ke] 6001 6900 +15%

O & M [ke] 90 103 +15%EY MWhel/yr] 2808 3036 +8%

FCR [%] 10.05 10.05 -LCOE [e/kWhel] 0.247 0.262 +6%

Where O & M is computed as the 1.5% of TEC.As it is shown in table 5, the power plant adopting the thermocline conceptfor storing energy allows more savings. In particular, the LCOE is reducedby the 6% .It is worth to notice that the results reported in this extended summary areobtained through weekly simulations, and subsequently, yearly values are ex-trapolated. Of course the accuracy of these results could be improved withfuture annual simulations: the developed models are sufficiently computa-tionally light.

Contents

1 Overview 291.1 ORC-plus project . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.1.1 First phase: the CSP-ORC solar project at IRESEN . . 341.1.2 Second phase: the ORC-Plus project . . . . . . . . . . 38

2 Thermal Energy Storage technologies 432.1 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.1.1 Depending on the operating temperature range . . . . 452.1.2 Depending on the accumulation duration . . . . . . . . 452.1.3 Depending on the heat storage method . . . . . . . . . 45

2.2 Thermocline Thermal Energy Storage . . . . . . . . . . . . . . 472.2.1 Efficiency of thermocline Thermal Energy Storage . . . 502.2.2 Thermal hysteresis . . . . . . . . . . . . . . . . . . . . 54

3 TES Modelling 593.1 Model requirements . . . . . . . . . . . . . . . . . . . . . . . . 593.2 State of the art of TES numerical models . . . . . . . . . . . . 61

3.2.1 T.E.W. Schumann work . . . . . . . . . . . . . . . . . 633.2.2 J.E. Pacheco et al. work . . . . . . . . . . . . . . . . . 653.2.3 J.-F. Hoffmann et al. work, 1D-2P and 1D-1P . . . . . 673.2.4 Xu et al. model . . . . . . . . . . . . . . . . . . . . . . 703.2.5 Summary table . . . . . . . . . . . . . . . . . . . . . . 73

4 Numerical models implemented 744.1 1 Dimension, 2 Phases model (1D-2P) . . . . . . . . . . . . . 75

4.1.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.1.2 Numerical model . . . . . . . . . . . . . . . . . . . . . 77

4.2 1 Dimension, 1 Phase model (1D-1P) . . . . . . . . . . . . . . 784.2.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.2.2 Numerical model . . . . . . . . . . . . . . . . . . . . . 82

4.3 Buffer model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

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CONTENTS 21

5 Models validation 905.1 Validation with Solar One experimental data . . . . . . . . . . 925.2 Validation with Xu et al. model . . . . . . . . . . . . . . . . . 975.3 Validations at CIC Energigune . . . . . . . . . . . . . . . . . . 100

5.3.1 Validation with experimental data . . . . . . . . . . . . 1005.3.2 Validation with 2D-2P model . . . . . . . . . . . . . . 101

5.4 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6 Complete power plant weekly simulations 1056.0.1 Solar Field model . . . . . . . . . . . . . . . . . . . . . 1076.0.2 Power Block model . . . . . . . . . . . . . . . . . . . . 110

6.1 1D-2P Thermocline Thermal Energy Storage weekly simulations1126.1.1 Summer week . . . . . . . . . . . . . . . . . . . . . . . 1146.1.2 Spring/Autumn week . . . . . . . . . . . . . . . . . . . 1186.1.3 Winter week . . . . . . . . . . . . . . . . . . . . . . . . 1226.1.4 Considerations . . . . . . . . . . . . . . . . . . . . . . 126

6.2 1D-1P Thermocline Thermal Energy Storage weekly simulations1276.2.1 Summer, Spring/Autumn and Winter weeks . . . . . . 1286.2.2 Considerations . . . . . . . . . . . . . . . . . . . . . . 132

6.3 2-Tanks Thermal Energy Storage weekly simulations . . . . . 1336.3.1 Summer week . . . . . . . . . . . . . . . . . . . . . . . 1366.3.2 Considerations . . . . . . . . . . . . . . . . . . . . . . 139

7 Cost Analysis 141

8 Conclusions 1508.1 Future improvements . . . . . . . . . . . . . . . . . . . . . . . 151

A Derivation of model equations 153

B 1D-2P numerical model 160

C Simulations plots 166C.1 1D-1P model simulation results . . . . . . . . . . . . . . . . . 166

C.1.1 Summer . . . . . . . . . . . . . . . . . . . . . . . . . . 167C.1.2 Spring/Autumn . . . . . . . . . . . . . . . . . . . . . . 168C.1.3 Winter . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

C.2 2-Tanks model simulation results . . . . . . . . . . . . . . . . 169C.2.1 Spring/Autumn week . . . . . . . . . . . . . . . . . . . 170C.2.2 Winter week . . . . . . . . . . . . . . . . . . . . . . . . 172

D Fluids properties correlations 174

CONTENTS 22

E Solar One thermocline TES experimental data 175

List of Figures

1 ORC-plus project rendering. Source: Enerray website, [4]. . . 92 Typical temperature profile inside a thermocline Thermal En-

ergy Storage, and how it would appear with infrared goggles. . 103 1D-2P discretization along tank axis, n spatial steps. . . . . . 124 Thermocline profile after 2, 4 and 6 hours from the beginning

of the charge phase. Inlet fluid temperature is 300◦C. Initialtemperature of the tank was 180◦C. . . . . . . . . . . . . . . . 13

5 1D-1P discretization along tank axis, n spatial steps. . . . . . 136 Temperature profiles inside the tank during the charging phase.

1D-1P model temperature profile is in green. 1D-2P modelprofiles for rocks and Heat Transfer Fluid are in red and blue,respectively. Discrepancies between models are about 3◦C. . . 14

7 TopLeft: 1D-1P and 1D-2P validation against SolarOne ex-perimental data, [9]. TopRight: 1D-1P validation againstCICenergigune experimental data and model. BottomLeft:1D-1P validation against Xu model and Pacheco experimen-tal data, [10]. BottomRight: same validation for the 1D-2Pmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

8 Plant layout for Simulink simulation. Thermocline storage. . . 169 1D-2P model for TES. DNI, Ieff , Temperatures in the Solar

Field, mass flow rates in the system and electricity productionfor a typical day in June - the 18th. . . . . . . . . . . . . . . . 17

1.1 Reference case trends - source [1]. . . . . . . . . . . . . . . . . 291.2 Reference case trends - source [1]. . . . . . . . . . . . . . . . . 301.3 Typical layout of a CSP power plant with its three main com-

ponents. Source: [12]. . . . . . . . . . . . . . . . . . . . . . . . 311.4 Thermal storage uncouples electricity generation from solar

energy collection. Source: [13]. . . . . . . . . . . . . . . . . . . 321.5 Cost reductions for component as expected by DoE. Source:

[14]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321.6 IRESEN ORC-CSP plant built in Ben Guerir. . . . . . . . . . 35

23

LIST OF FIGURES 24

1.7 Linear Fresnel type technology. . . . . . . . . . . . . . . . . . 351.8 Linear Fresnel and Parabolic Trough Collectors. . . . . . . . . 361.9 ORC power block, provided by Exergy. Source: Enerray web-

site, [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371.10 IRESEN ORC-CSP, in Ben Guerir, before ORC-Plus project.

Source: Enerray website, [4], modified. . . . . . . . . . . . . . 381.11 ORC-plus project, with the additional solar field collectors in

order to feed the Thermal Energy Storage, after ORC-Plusproject. Source: Enerray website, [4]. . . . . . . . . . . . . . . 40

1.12 ORC-plus schematic layout. SF2 and Thermal Energy Storageare new components, to be added to the already existing SF1and ORC systems. . . . . . . . . . . . . . . . . . . . . . . . . 40

1.13 Overview of the thermal oil testing facility at CICenergigune. 42

2.1 Typical temperature profile inside a thermocline Thermal En-ergy Storage, and how it would appear with infrared goggles. . 47

2.2 Thermocline zone extraction issue. . . . . . . . . . . . . . . . 492.3 Scheme for the energetic evalutation of Et. . . . . . . . . . . . 522.4 Thermal profile for the solid bed (a) after the 1st and the 5th

cycle and efficiency (b) after each cycle for each fluid. Coercivetime span: θ = [0; 1]. . . . . . . . . . . . . . . . . . . . . . . . 55

2.5 Temperature profile for the solid bed after the 1st and the5th cycle for time span θ = [0.20; 0.80] (a) and efficiency forθ = [0.20; 0.80] and θ = [0.10; 0.90] (b). For air, oil and moltensalts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.6 Restrictive temperature span [181◦C; 299◦C]. First five cy-cles showing a progressive reduction of the energy provided tothe storage (end of charge states moving towards bottom-left)and a progressive reduction of the extracted energy (end ofdischarge states moving top-right). Here x = 0m is the top ofthe tank. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.7 Restrictive temperature span [181◦C; 299◦C]. Continuation offig. 2.6 - showing a progressive expansion of the thermoclineregion. Temperature profile inside the tank becomes progres-sively flat, and finally a straight line. Unusable storage. Again,here x = 10m is the top of the tank. . . . . . . . . . . . . . . . 57

2.8 Permessive temperature span [240◦C; 260◦C]. Stabilization ofthe thermocline zone thickness. Hysteresis is reduced. . . . . . 58

3.1 Reference [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

LIST OF FIGURES 25

3.2 Measured profile temperatures during a discharge cycle forthe pilot-scale thermocline Thermal Energy Storage studied inPacheco et al. work. These data are used in many validationworks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.3 Scheme of thermocline TES for Hoffmann et al. study. Source:[8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.4 Scheme of thermocline TES for Xu et al. study, [10]. . . . . . 70

4.1 Scheme of a thermocline Thermal Energy Storage. . . . . . . . 744.2 1D-2P discretization along tank axis, n spatial steps. . . . . . 774.3 Thermocline profile after 2, 4 and 6 hours from the beginning

of the charge. Inlet fluid temperature is 300◦C. . . . . . . . . 784.4 Temperature profiles inside the tank during the charging phase.

1D-1P model temperature profile is in green. 1D-2P modelprofiles for rocks and Heat Transfer Fluid are in red and blue,respectively. Discrepancies between models are about 3◦C. . . 82

4.5 1D-1P discretization along tank axis, n spatial steps. . . . . . 834.6 Buffer schematization. . . . . . . . . . . . . . . . . . . . . . . 87

5.1 The plant. Actually in this figure is not shown Solar One, butits expansion - in 1995 - named ”Solar Two”: 108 heliostatswere added to the existing Solar One. Source: [16] . . . . . . . 92

5.2 The thermocline Thermal Energy Storage, nominally 170MWhth.Source: [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.3 The 8-hours discharge cycle of Solar One TES. ”Day 179”means that this is what happened during the 179th day ofplant testing. Source: [9]. . . . . . . . . . . . . . . . . . . . . 93

5.4 Validation of 1D-2P and 1D-1P models with Solar One dis-charge cycle. Experimental data at hour 00:00 is taken asstarting point for the simulations. The green line, represent-ing solid temperature, is so close to the liquid temperature -in blue - to be visible only by zooming . . . . . . . . . . . . . 94

5.5 Method to evaluate mass flow rate for Solar One in day 179 . 955.6 Schematic layout of the 2.3 MWh thermocline flow loop. . . . 975.7 Experimental data from Pacheco’s study pilot plant. Dis-

charge cycle. Source: [7]. . . . . . . . . . . . . . . . . . . . . . 985.8 Comparison between Xu’s numerical (red) and Pacheco’s ex-

perimental (dashed blue) thermocline profiles. Discharge cycleof a packed-bed molten-salt thermocline TES. Here x = 6m isthe top of the tank. . . . . . . . . . . . . . . . . . . . . . . . . 98

LIST OF FIGURES 26

5.9 Comparison between experimantal data (dashed blue), Xumodel (red squares) and 1D-2P model results (black line). . . 99

5.10 Comparison between experimantal data (dashed blue), Xumodel (red squares) and 1D-1P model results (black line). . . 99

5.11 Comparison of Experimental data with results from CICen-regigune’s model and 1D-1P model. . . . . . . . . . . . . . . . 101

5.12 Comparison between CICenregigune’s model and 1D-1P model.Constant inlet mass flow rate. Charge phase. Time betweeneach temperature profile is 1 hour. . . . . . . . . . . . . . . . . 102

5.13 Comparison between CICenregigune’s model and 1D-1P model.Variable inlet mass flow rate. Charge phase. Time betweeneach temperature profile is 1 hour. . . . . . . . . . . . . . . . . 103

5.14 Variable inlet mass flow rate implemented for simulation infigure 5.13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.1 Plant layout for Simulink simulation. Thermocline storage.ORC-plus plant has a different layout. . . . . . . . . . . . . . 106

6.2 Simulink interface for the Solar Field model. . . . . . . . . . . 1076.3 Temperatures at the outlet of each collector of the Solar Field

and Solar Field temperature inlet. Clear sky. . . . . . . . . . . 1086.4 DNI correction to Ieff . . . . . . . . . . . . . . . . . . . . . . . 1096.5 Organic Rankine Cycle schematization used in the plant model.1106.6 Curves describing Power Block behavior, derived with [17]. . . 1116.7 Plant layout for Simulink simulation. Thermocline storage.

Same picture at the beginning of the chapter in order to facil-itate reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

6.8 Simulink interface. Simulation of 8 days in June. X-axis: timein seconds; Y-axis: [kg/s] and [MWhe] . . . . . . . . . . . . . 114

6.9 1D-2P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity productionfor a typical day in June - the 18th. . . . . . . . . . . . . . . . 115

6.10 What is happening inside the Thermal Energy Storage duringa complete charge (left) and the following complete discharge(right), June. . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

6.11 Simulink interface. Simulation of 8 days in March. X-axis:time in seconds; Y-axis: [kg/s] and [MWhe] . . . . . . . . . . 118

6.12 1D-2P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity productionfor a typical day in March - the 18th. . . . . . . . . . . . . . . 119

LIST OF FIGURES 27

6.13 What is happening inside the Thermal Energy Storage duringMarch. Thermocline profiles variation in time during a chargephase (left) and a discharge phase (right). . . . . . . . . . . . 120

6.14 Simulink interface. Simulation of 8 days in January. X-axis:time in seconds; Y-axis: [kg/s] and [MWhe] . . . . . . . . . . 122

6.15 1D-2P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity productionfor a typical day in January - the 17th. . . . . . . . . . . . . . 123

6.16 What is happening inside the Thermal Energy Storage duringJanuary. Thermocline profile variation during the charge phase.124

6.17 Comparison: thermocline profiles inside the Thermal EnergyStorage modeled with the 1D-1P approach and the 1D-2P ap-proach, June. . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6.18 Comparison: thermocline profiles inside the Thermal EnergyStorage modeled with the 1D-1P approach and the 1D-2P ap-proach, March. . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.19 Comparison: thermocline profiles inside the Thermal EnergyStorage modeled with the 1D-1P approach and the 1D-2P ap-proach, January. . . . . . . . . . . . . . . . . . . . . . . . . . . 130

6.20 Plant layout for Simulink simulation. Duble tank storage. . . . 1336.21 2-Tanks model for TES. DNI, Ieff , Temperatures in the Solar

Field, mass flow rates in the system and electricity productionfor a typical day in June - the 18th. . . . . . . . . . . . . . . . 136

6.22 Hot Tank inlet and outlet mass flow rates (top) and Temper-ature (bottom), both related with the level of Heat StorageMedium inside the Hot Tank. 18th of June. . . . . . . . . . . . 137

7.1 Schematization of foundations structure for the tank. . . . . . 145

A.1 Image of a packed bed composed by perfect spheres randomlydistributed. The liquid flow rate is very low, so turbolence isneglected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

A.2 Along the tank axis different sections show a different liquidto solid ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

A.3 Heat fluxes for liquid phase . . . . . . . . . . . . . . . . . . . 156A.4 Heat fluxes for solid phase . . . . . . . . . . . . . . . . . . . . 157A.5 Heat fluxes for the wall on the horizontal plane, here conduc-

tion with upper and lower layers is not represented . . . . . . 158

B.1 1D discretization along tank axis, n steps. . . . . . . . . . . . 160

LIST OF FIGURES 28

C.1 1D-1P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity productionfor a typical day in June - the 18th. . . . . . . . . . . . . . . . 167

C.2 1D-1P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity productionfor a typical day in March - the 18th. . . . . . . . . . . . . . . 168

C.3 1D-1P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity productionfor a typical day in January - the 17th. . . . . . . . . . . . . . 169

C.4 2-Tanks model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity productionfor a typical day in March - the 18th. . . . . . . . . . . . . . . 170

C.5 Hot Tank inlet and outlet mass flow rates (top) and Temper-ature (bottom), both related with the level of Heat StorageMedium inside the Hot Tank. 18th of March. . . . . . . . . . . 171

C.6 2-Tanks model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity productionfor a typical day in January - the 17th. . . . . . . . . . . . . . 172

C.7 Hot Tank inlet and outlet mass flow rates (top) and Temper-ature (bottom), both related with the level of Heat StorageMedium inside the Hot Tank. 17th of January. . . . . . . . . . 173

Chapter 1

Overview

Figure 1.1. Reference case trends - source [1].

29

1. Overview 30

Figure 1.2. Reference case trends - source [1].

Global energy - and electricity - demand is continuously growing and willprobably keep this trend as shown in figures 1.1 and 1.2.The ”Reference case” assumes continual improvement in known technologiesbased on current trends - [1].

This is one of the main drivers of the CO2 concentration increase in ouratmosphere, therefore of greenhouse effect and of climate changes.In order to limit these emissions it is fundamental to go towards improveduse of energy, increasing the efficiency of industrial and buildings processes(heat recovery), and increasing renewables penetrations in the energy mix,like solar energy - [2].

Among solar energy technologies, the Concentrating Solar Power (CSP)exploits the Direct Normal Irradiation. It concentrates direct beams, bymeans of optical systems, in order to produce high temperatures throughwhich electric power can be produced.

A CSP plant is a “3-components” technology, see fig. 1.3:

i Solar Field - SF

ii Thermal Energy Storage - TES

iii Power Block-PB

1. Overview 31

Figure 1.3. Typical layout of a CSP power plant with its three main com-ponents. Source: [12].

The Thermal Energy Storage system is fundamental in order to

i reduce the Levelized Cost of Energy - LCOE

ii improve dispatchability (load-production decoupling)

iii increase efficiency (solar energy provision)

See figure 1.4.

1. Overview 32

Figure 1.4. Thermal storage uncouples electricity generation from solar en-ergy collection. Source: [13].

U.S. Department of Energy SunShot target for CSP systems is 6 cent /kWh in 2020. New technical solutions has to be investigated in order to meetthis goal - figure 1.5.

Figure 1.5. Cost reductions for component as expected by DoE. Source: [14].

Since 2000 ENEA is developing the CSP technology focusing on the useof molten salts as Heat Transfer Fluid and Heat Storage Medium in LinearParabolic Trough solar fields. Such development led to the Archimede plant,in Sicily, commissioned by ENEL for improving its combined cycle powerstation of Priolo Gargallo. Such technology is briefly described in references

1. Overview 33

[18, 19, 20].

ENEA is also continuing CSP technology development, adopting differentthermal storage concepts.Among these concepts, the ORC-Plus project - described in section 1.1 - isin the development stage.This thesis has the objective of developing the numerical model of the Ther-mal Energy Storage system for the ORC-Plus project and applying suchmodel to a typical configuration.

1. Overview 34

1.1 ORC-plus project

1.1.1 First phase: the CSP-ORC solar project at IRE-SEN

At the end of 2014, Enerray won the public tender by IRESEN (Institutde Recherche en Energie Solaire et en Energie Nouvelles, Morocco) for theconstruction of the first CSP-ORC system - 1MWe capacity - in Ben Guerir,inside “Ville Vert Mohammed VI”, known as the “Green Energy Park”.The project, with a cost of 6.000.000e, is financed equally by IRESEN andthe OCP - Office Cherifien des Phosphates, the world’s largest producer ofphosphates and its derivatives - in order to study the productivity and reli-ability for possible future use in its mines - see [4].The system was completed in October 2016.

The technology proposed in this project is based on

- a Solar Field - linear Fresnel type, make Soltigua - with a net collectingsurface of 11.434m2 and a reference thermal output of 5.0MWth. It usesthermal oil as Heat Transfer Fluid.

- an Organic Rankine Cycle system - make Exergy - with a referencepower output of 1MWe

Nominal power block efficiency is about 20% - [4].

1. Overview 35

Figure 1.6. IRESEN ORC-CSP plant built in Ben Guerir.

Figure 1.7. Linear Fresnel type technology.

Linear Fresnel reflectors (LFR) use long, plate, thin segments of mirrorsto focus sunlight along a fixed linear absorber located over the reflectors -[21]. These mirrors are capable of concentrating the sun’s energy approxi-mately 70-80 times its normal intensity - [22].This concentrated energy is transferred through the absorber to a Heat Trans-fer Fluid (HTF).

1. Overview 36

Figure 1.8. Linear Fresnel and Parabolic Trough Collectors.

With respect to parabolic trough, flat Fresnel mirrors are cheaper, easierto clean and they allow more reflective surface in the same amount of space,thus capturing an higher amount of the available sunlight per unit land area- [23].On the other hand, LFR systems are generally characterized by a loweroverall optical efficiency with respect to parabolic trough collectors (PTC),therefore the trade-off should be performed case by case.

1. Overview 37

Figure 1.9. ORC power block, provided by Exergy. Source: Enerray website,[4].

The Organic Rankine Cycle Power Block - in fig. 1.9 (composed by tur-bine, condenser, HXs for vapour generation, alternator, etc.) - at the BenGuerir power plant is provided by Exergy, a company in the Maccaferri Indus-trial Group. Through a thermodynamic cycle, it transforms thermal energyinto electricity.Exergy equipped the ORC Power Block with a radial flow turbine claimingthat they are really simple to manage and maintain, using remote controlintegrated with the ORC - [4].The ORC cycle was designed to work with an air condenser, and thereforedoes not require water, in line with most recent environmental requirements.This has some negative implications: the power block efficiency is variablewith ambient temperature.

1. Overview 38

Figure 1.10. IRESEN ORC-CSP, in Ben Guerir, before ORC-Plus project.Source: Enerray website, [4], modified.

1.1.2 Second phase: the ORC-Plus project

Subsequently, in June 2015 ORC-Plus project was initiated, funded by theH2020 EU Research and Development program - [3].

ORC-Plus goal is to develop an optimized combination of innovative Ther-mal Energy Storage - optimised for the CSP scale of 1-5 MWe - and engineer-ing solutions useful to improve the dispatchability - production on demand- and capacity factor - number of hours of production - of the existing CSPplant.

Partners The ORC-plus consortium is coordinated by ENEA and com-posed by six partners from three different European countries, plus one inter-national partner from Morocco, IRESEN, that is one of the main Moroccanstakeholders in the field of CSP plants:

- ENEA - coordinator. ENEA is developing and testing a Thermal En-ergy Storage solution based on the molten salt thermocline concept. Inaddition ENEA supports the consortium for the implementation of aplant’s process control procedure and for the execution of the experi-mental campaign.

- Soltigua - developer and provider of the existing Solar Field - 11.434m2

- and of the additional LFR Solar Field - 4.900m2 - for the integrationof the new Thermal Energy Storage developed within the ORC-Plusproject;

1. Overview 39

- Fraunhofer – focuses on the comparison of different technologies forthe Thermal Energy Storage and on the simulation of the integratedsystem to optimize the overall plant performance;

- Enerray - is an Italian EPC and O & M contractor, part of MaccaferriIndustrial Group. Since 2014 Enerray is following direclty CSP-ORCprojects, in particular in Africa, with the aim of industrializing thestorage system for energy plants with an installed capacity up to 4MWe

- indicatively;

- Euronovia - provides support for access to European and internationalresearch and innovation programmes - identification of funding oppor-tunities, proposal writing, administrative and financial management;

- CICenergigune - develops a Thermal Energy Storage system based onpacked-bed thermocline.

- IRESEN - is in charge of testing the final system of the ORC-Plusproject.

As said before in order to store energy during daytime 4.900m2 - SF n.2- of Fresnel collectors have been added to the 11.434m2 - SF n.1 - already inplace - fig. 1.11 and fig. 1.12. Moreover a Thermal Energy Storage capableof ensuring electricity production for 4 hours during sunless hours has beenadded to the plant layuot – that means a thermal storage of 20MWhth,considering a Power Block nominal power of 1MWe and a nominal efficiencyof 20%.

1. Overview 40

Figure 1.11. ORC-plus project, with the additional solar field collectors inorder to feed the Thermal Energy Storage, after ORC-Plus project. Source:Enerray website, [4].

Figure 1.12. ORC-plus schematic layout. SF2 and Thermal Energy Stor-age are new components, to be added to the already existing SF1 and ORCsystems.

The project includes also an analysis of the techno-economic viability, ofthe environmental impact, and of the replicability of the final design of thepilot plant.

Indeed the final objective is to get to a pre-commercial solution of Ther-mal Energy Storage (TES).

Within ORC-PLUS project, two different industrial prototypes of Ther-mal Energy Storage system have been developed and tested at small scale:

- The first, proposed by ENEA, is a single tank exploiting the thermo-

1. Overview 41

cline principle, based on an innovative low-melting-point molten saltmixture. It requires also two internal innovative oil-molten salt heatexchangers since the solar field works with thermal oil.

- The second solution, proposed by CICenergigune, is a packed-bed ther-mocline storage involving thermal oil as fluid and magnetite pebbles asfiller. The filler material - pebbles - is composed by high density ceramicmaterial produced by steel industries as waste.

It is worth to notice that both of them are single tank technologies -exploiting the thermocline concept - in order to reduce as much as possibleinvestment costs.

A brief recap: To achieve the project target the following steps arebeing implemented:

i Extension and enhancement of the existing solar field - SF2 added tothe existing SF1.

ii Validation of two advanced solutions of Thermal Energy Storage sys-tem.

iii Selection of Thermal Energy Storage solution more suitable for theproject.Due to its technology maturity, simplicity and costs, the thermoclinepacked-ped thermal energy storage - developed by CICenergigune - wasfinally choosen.

iv Integration of Thermal Energy Storage in the CSP plant.

v Implementation of optimized control logic for the system in order tomaximize the benefits of using Thermal Energy Storage.

Points from i to iii have been actually achieved, while the Thermal En-ergy Storage is in construction phase.

To validate the concepts of any Thermal Energy Storage, an industrialprototype has to be designed and modelled.The prototypes were built in a scale (1/100), which is appropriate to validatethe model of the Thermal Energy Storage.The industrial prototype of molten salt mixture Thermal Energy Storage isat ENEA, while the magnetite-oil packed bed storage is at CIC energigune

1. Overview 42

(fig. 1.13).The output is used to validate the model code that simulates the final pilotplant.

Figure 1.13. Overview of the thermal oil testing facility at CICenergigune.

Chapter 2

Thermal Energy Storagetechnologies

One of the advantages of CSP technologies is the possibility of realtivelycheaply storing energy.This is true in particular comparing CSP to other technologies chatacterizedby a burdensome or even impracticable decoupling of energy demand andpower production.

In this chapter main Thermal Energy Storage classifications are described.

Furthermore some energetical considerations about thermal storages arereported.

Thermal Energy storages can be defined as systems that store energy byheating up or cooling down an Heat Storage Medium - HSM - thanks to anHeat Transfer Fluid - HTF - [2]. In such a way, the stored thermal energycan be used later on

- or for heating/cooling purposes

- or for producing electricity.

In the case of high temperature storage systems, the storage process canbe divided in:

- Charge phase: HSM is heated up by the HTF

- Inactivity phase: no heat transfer occurs, except for losses to the envi-ronment

43

2. Thermal Energy Storage technologies 44

- Discharge phase: HSM heats up the HTF

A key issue in the design of a Thermal Energy Storage system is its ther-mal capacity, C : the amount of energy that can be stored and supplied.

Let’s imagine an application, a solar power plant for example, requiringa nominal thermal power Pth - [kWth] - and let’s increase its operation by Hhours.It is required a Thermal Energy Storage with a thermal capacity

C = Pth ·H [kWhth]

Type and dimensions of the selected Thermal Energy Storage have to bechoosen through a cost benefit analysis, case by case - [2].

Mainly, its cost depends on the Heat Storage Material, on the heat ex-change mechanism between Heat Treansfer Fluid and Heat Storage Material,but also on the structure and thermal insulation of the Thermal Energy Stor-age tank.

Generally, main requirements for a Thermal Energy Storage are - [2, 24]:

i High energy density (per unit mass or, more often, per unit volume) ofthe Heat Storage Material, in order to store as much energy as possiblein a limited amount of space, hence limiting costs

ii A good HTF - HSM heat exchange mechanism

iii Chemical and mechanical stability of the Heat Storage Material

iv Compatibility between Heat Transfer Fluid, Heat Exchangers and HeatStorage Material

v Possibility of performing many cycles, hence reversibility of processesis required

vi Limited heat losses towards the environment.

2.1 Classification

There are many different principles for classifying Thermal Energy Storages:

- depending on the operating temperature range

- depending on the storage duration

- depending on the heat storage method.


2.1.1 Depending on the operating temperature range

Depending on the operating temperature range Thermal Energy Storages aretypically classified as follows:

- HTTES (High Temperature TES): above 300◦C.Thermal Energy Storages for large-size Concentrated Solar Power plants,for thermal energy produced in industrial processes or in thermal powerplants equipped with high temperature gas turbines belong to this cat-egory. Among these the most widespread technology is the one exploit-ing the double-tank technology with molten salts - [2, 18, 19, 20]

- MTTES (Medium Temperature TES): between 150◦C and 300◦C.Thermal Energy Storages for small-size Concentrated Solar Power plantsor for industrial processes are examples of application.The Thermal Energy Storage developed within the ORC-Plus projectbelongs to this category too.

- LTTES (Low Temperature TES): between 20◦C and 150◦C.Heating and cooling of buildings, greenhouses, hot water storage tanksare examples.

- CTES (Cold Temperature TES): below 20◦C.They are exploited in ambient air cooling and conditioning, or in foodindustry for keeping food fresh.

2.1.2 Depending on the accumulation duration

Depending on the time duration of the inactivity phase:

- short term storage (hours)

- long term storage (days or weeks)

- seasonal (months)

2.1.3 Depending on the heat storage method

Depending on the heat storage method:

- Sensible heat (SHTES): when the storage undergoes the charge phase,the HSM temperature increases. The higher is the temperature reached,the higher is the energy stored.This is, commercially, the most widespread technology. In fact, the


currently most popular storage technology, the ”double-tank” technol-ogy, belongs to this category.In order to increase energy density - hence reduce required volumes,then costs - other two technologies are under development:

- Latent heat (LHTES): when the storage tank undergoes the chargephase, the HSM phase change is exploited in order to store, in thesame temperature span, a greater amount of energy.Thus, this technology is chatacterized by high energy density, thereforevolumes required are smaller and costs are reduced.It’s still in Research and Development phase in order to solve someproblems such as the low thermal diffusivity of the changing phase HeatStorage Material but it clearly has good medium-short term commercialperspective.

- Termochemical (TCTES): when the storage tank undergoes the chargephase, reversible thermochemical reactions occur absorbing a greatamount of energy.This mechanism allows the highest energy density - smallest volumes.But it is still at an early stage. It will possibly reach market maturityover the long term.

For a Concentrated Solar Power plant, given its characteristics, shortterm, medium or high temperature Thermal Energy Storage systems are re-quired (short term MTTES or HTTES).

In recent years a new technology, apparently cheaper than the well-established ”double-tank”, is attracting the attention of many researchers.It is the Thermal Energy Storage exploiting the thermocline concept.Nowadays, the most popular technology utilised to store thermal energy inCSP plants, is the ”double-tank” technology, exploiting two large tanks.During the charge phase, one tank is filled with hot fluid while the other onedelivers the same amount of cold fluid to the plant in order to balance thetotal fluid mass along the pipes. During the discharge phase, the hot tankgives back the stored energy to the plant while the cold tank is filled againwith already-exploited fluid.Thermocline technology may cut cost of thermal energy storage in CSPplants, since it requires one single tank only to store the same amount ofenergy the ”double-tank” technology stores - [5].

This is the technology therefore investigated within the ”ORC-Plus”project; and it will be carefully studied in the next years.


2.2 Thermocline Thermal Energy Storage

Figure 2.1. Typical temperature profile inside a thermocline Thermal EnergyStorage, and how it would appear with infrared goggles.

In a thermocline tank, cold fluid and hot fluid are separated by an inter-mediate temperature zone (which is called ”thermocline”). Buoyancy forcesand very low speed of the fluid help to maintain this thermal stratification.

Many configurations of thermocline Thermal Energy Storage are underdevelopment:

- The storage tank can be filled with liquid only, like the one proposedby ENEA within ORC-Plus - but not selected for the project.In the specific case molten salts are stored inside the tank and, throughheat exchangers, they exchange heat with the HTF - oil.

- The storage tank can be filled with crushed material playing the samerole as liquid, but cheaper, and generally with higher energy density.The Heat Transfer Fluid can be gaseous (like air), or liquid (like ther-mal oil).An example is the one proposed by CICenergigune within ORC-Plus -and selected for the project.


- The storage tank can be filled with spheres containing Phase ChangingMaterials, in order to further enhance energy density of the storage -see section 2.1.3, [25].Again, the Heat Transfer Fluid can be gaseous or liquid.

Moreover,

- HTF can be the HSM too.

- HTF and HSM may exchange heat through direct contact.

- HTF and HSM may exchange heat indirectly through heat exchangers.

Within ORC-Plus project the mostly investigated technology is charac-terized by

- solid filler - it’s filled with crushed material that creates the so-called”packed-bed”

- direct heat exchange between solid and liquid phases

- liquid involved is an high energy density oil, thus it also works as HSM.

Therefore, from now on, the focus moves to this specific thermocline Ther-mal Energy Storage technology.

The main reason for this choise is linked to the fact that adding cheapsolid filler inside the tank allows a decrease of costs.

Oil-magnetite packed-bed Thermal Energy Storage solution As forany kind of thermocline Thermal Energy Storage, also in this case, chargingconsists in sending hot oil to the top of the tank and extracting cold oil fromits bottom.More in detail, let’s start from a discharged Thermal Energy Storage tank,at a cold temperature.At the very beginning of the charge phase, in the highest region of the tank,hot oil goes in touch with the colder oil already inside the tank: they startto exchange heat by conduction mechanism. This contact layer

- is going to reach an intermediate temperature between the cold andthe hot oil temperature

- slowly moves downwards during the charge phase, because oil is fedfrom the top of the tank while it is extracted from its bottom.


There is something more. Hot oil, moving downwards, encounters coldermagnetite stones, the colder packed-bed that until now has been in contactwith colder oil. Hot oil and colder stones start to exchange heat each otherby convection mechanism: hot oil is cooled down while cold stones are heatedup.Progressively, all these mechanisms occur at an increasingly lower height.Therefore the thermocline zone moves downwards - and it also enlarges dueto thermal diffusivity.Durnig the discharge phase the very same mechanisms occur, but opposite:cold fluid coming from the bottom of the tank is heated up by hotter stones,while hot fluid is extracted from the top of the tank. During this process thethermocline zone moves upwards, again becoming wider.

Figure 2.2. Thermocline zone extraction issue.

During the charge phase of such a tank, the outlet fluid temperature isconstant during the cold zone extraction, but increases with time during thethermocline zone extraction - black t0, red t1 and green t2 in fig. 2.2. A toohigh temperature may imply an overheating of the fluid that is coming backto the solar field, thus defocusing - Tout,cold increases.During a discharge, the outlet fluid temperature is high during the hot zoneextraction then quickly decreases with time - brown t0, blue t1 and orange t2in fig 2.2. A too low temperature would imply an efficiency decrease of thepower-block or its stop - Tout,hot decreases, see section 6.0.2.

It is therefore necessary to keep the thermocline zone as thin as possible


and to let it exit from the tank just partially - to avoid from one side defo-cusing and low cycle efficiency, and from the other side thermal hysteresis -section 2.2.2. A trade-off is required.

Moreover, thermocline zone tends to expand in the tank, during charge,discharge and stand-by periods. This expansion is mostly due to thermaldiffusion and to the non-ideal heat exchange between fluid and solid. Ther-mocline behavior has therefore been subjected to numerous numerical studies- [5].

2.2.1 Efficiency of thermocline Thermal Energy Stor-age

In order to quantitatively evaluate perfromances of a Thermal Energy Stor-age system, it is necessary to define an appropriate nomenclature and metric.

Establishing energy available from a thermocline Thermal Energy Stor-age is not trivial. For example, the energy content of the initial state couldbe not always totally exploited: starting from the very same state, if thetank looses energy to the environment, with a fast discharge cycle energyrecovered is different from energy recovered through a slow discharge cycle,since losses have a smaller impact.This simple example shows that the energetical considerations of such a stor-age system are not univocally determined but need the definition of referencecycles.

Furthermore, according to the utility - a Power Block in a CSP plant -downstream of the tank, thermal energy has a different quality based on itstemperature, so a derating function could be applied. Depending on the case,it is possible to refer to exergy, or to a specific ”derating function” calculatedon the basis of the variation with temperature of the actual yield of the utility.

A little bit of nomenclature:

- Tmin, the nominal operating temperature of the cold zone;

- Tmax, the nominal operating temperature of the hot zone;

- Tmin,op, the minimum temperature useful to the utility downstream thestorage;


- ∆Tmax is equal to Tmax − Tmin;

- Cmax, the energy content when the whole tank is at Tmax - no thermo-cline zone inside it.

Cmax = Vpacked−bed (ρscs(1− ε) + ρf cfε) ∆Tmax + Cmax,buffer (2.1)

where

- Vpacked−bed is the volume of the tank occupied by the packed-bed

- ρs and cs can be often considered constant, they are, respectively, den-sity and specific heat of the solid filler

- ρf and cf are, respectively, mean density and specific heat of the liquidaveraged whithin ∆Tmax

- ε is the void fraction of the packed-bed (= Vl/Vpacked−bed)

- Cmax,buffer: when the whole tank is at Tmin there could be some massof liquid overlying the packed-bed, the so-called ”buffer” - section 4.3.Cmax,buffer is the energy of this mass of liquid when it is brought toTmax. If the tank is precisely filled with liquid, just in order to coverthe packed-bed, Cmax,buffer = 0.

It is useful to define some quantities:

i) Rate at which energy is provided to the tank, Pp, is related to the liquidflux m. Subscript ”in” means ”into the tank”; ”out” means ”exitingthe tank”; ”hot” means ”top of the tank”; ”cold” means ”bottom ofthe tank”:

Pprovided = Pp =

∫ Thot

Tref

min,hotcldT −∫ Tcold

Tref

mout,coldcldT (2.2)

ii) Rate at which energy is withdrawn from the tank, Pw, is of courserelated to the liquid flux m too:

Pwithdrawn = Pw =

∫ Thot

Tref

mout,hotcldT −∫ Tcold

Tref

min,coldcldT (2.3)


After a charge-discharge cycle, starting from a given profile temperatureinside the tank, and ending with the very same state, discrepancies betweenPp and Pw are due to losses towards environment.

Integrating during time Pp and Pw - from t0 to t - provided energy - Ep -and withdrawn energy - Ew - can be found.And, in particular, it is true that

Et = E0 + Ep − Ew − Eloss (2.4)

Where Et is energy stored at time t, and E0 is energy stored at the be-ginning of operations - time t0.

There is also another way of evaluating Et: dividing the tank in k hori-zontal disks, figure 2.3, knowing temperature profile all along the tank, it ispossible to evaluate the energy content of each disk.

Figure 2.3. Scheme for the energetic evalutation of Et.

The smaller is the disk height, the highest is the accuracy of the calcula-tion:

Et =∑k

∫ Tk

Tref

mcdT

∣∣∣∣∣liquid

+

∫ Tk

Tref

mcdT

∣∣∣∣∣solid

(2.5)

With equation 2.5 energy of both liquid and solid present in the kth diskis evaluated. Then they are all summed togheter.

Another interesting parameter is Euseful defined as the energy stored in-side the tank at a temperature higher than Tmin,op:


Euseful =∑j

∫ Tj

Tref

mcdT

∣∣∣∣∣liquid

+

∫ Tj

Tref

mcdT

∣∣∣∣∣solid

∀j : Tj ≥ Tmin,op (2.6)

Having defined these quantities it is possible to define the following pa-rameters.

ηcycle =Ew

Ep

(2.7)

This equation, 2.7, takes into account losses to the environment.

Moreover, an interesting parameter that takes into account the thermo-cline zone thickness is the so-called ”utilization factor”:

Uf =Et,end

Cmax

(2.8)

In equation 2.8, Et,end represent the actual stored energy at the end ofthe charge phase - which is generally stopped before the thermocline zone iscompletely out of the tank.

Literature dealing with efficiencies of thermocline energy storages is wide,and metric is not univoque. Here follows a brief description taken from [6],where it is defined a global efficiency.

η =Ew,end

Cmax

(2.9)

where Ew,end is the useful energy recovered after every cycle of charge anddischarge.

If η = 1, thermocline zone tends to zero - temperature suddenly passesfrom the highest value, Tmax, to the lowest, Tmin, in an infinitesimal amountof space - and there aren’t heat losses towards the environment.This is clearly an ”ideal” situation, since it would require an infinite heattransfer rate between liquid and solid, zero conductivity of both fluid andsolid filler and zero heat losses to the environment.It is worth to notice that eq. 2.9 makes sense only if the tank is completelycharged and then discharged, if inlet temperature is constantly at Tmax dur-ing the charge phase and inlet temperature is constantly at Tmin during thedischarge phase.


Efficiency is thus influenced by the fact that during a charge and dischargecycle the stored thermal energy is less than the maximum theoretical energythat could be stored if the whole mass of materials (HTF and HSM) would beuniformly cycled beween the lower allowed temperature,Tmin, and the higherallowed temperature,Tmax: during charge, in CSP plant applications, not allthe material is heated up at the maximum temperature level.But this depends on the specific application, in fact, if there aren’t problemsin discharging high temperature heat from the bottom of the thermoclineTES, like, for example, in heat recovery applications, the Thermal EnergyStorage can be uniformly charged.

2.2.2 Thermal hysteresis

Well known phenomena in thermocline Thermal Energy Storage systems arethe efficiency, eq. 2.9, lower than unity and the eventual reduction of suchefficiency with thermal cycling, due to the so-called ”thermal hysteresis” - [6].

In fact, efficiency normally decreases if a number of equal charge anddischarge cycles are performed in sequence. Then it reaches an asymptothicvalue for infinite cycles.Such phenomenon, called ”thermal hysteresis”, is influenced by the temper-ature limits at which the charge and discharge phases are terminated.More in detail, figures 2.4 and 2.5, show the temperature profile and effi-ciency for thermocline Thermal Energy Storage systems for different HeatTransfer Fluids (air, oil and salt), cycle after cycle. Two cases are analyzed:

a) The charge phase ends when the temperature of mout,cold slightly in-creases (0% of temperature span) and the discharge phase ends whenthe temperature of mout,hot slightly decreases (100% of temperaturespan)


Figure 2.4. Thermal profile for the solid bed (a) after the 1st and the 5th

cycle and efficiency (b) after each cycle for each fluid. Coercive time span:θ = [0; 1].

b) The charge phase ends when the temperature of mout,cold increases tothe 20% of temperature span and the discharge phase ends when thetemperature of mout,hot decreases to the 80% of temperature span

Figure 2.5. Temperature profile for the solid bed after the 1st and the 5th

cycle for time span θ = [0.20; 0.80] (a) and efficiency for θ = [0.20; 0.80] andθ = [0.10; 0.90] (b). For air, oil and molten salts.

Clearly, it is shown that in case b) efficiency reduction and thermal hys-teresis are both reduced.


This has been implemented in Simulink also, producing the following re-sults.

Figure 2.6. Restrictive temperature span [181◦C; 299◦C]. First five cyclesshowing a progressive reduction of the energy provided to the storage (end ofcharge states moving towards bottom-left) and a progressive reduction of theextracted energy (end of discharge states moving top-right).Here x = 0m is the top of the tank.


Figure 2.7. Restrictive temperature span [181◦C; 299◦C]. Continuation offig. 2.6 - showing a progressive expansion of the thermocline region. Temper-ature profile inside the tank becomes progressively flat, and finally a straightline. Unusable storage.Again, here x = 10m is the top of the tank.

As also shown in [6] a possible solution to overcome the thermal hysteresisis to modify both limits of temperature, at the outlet of the charge and ofthe charge phase.The result is that the thermocline does not degrade in such dramatic waybut stabilizes after two cycles as shown in figure 2.8.


Figure 2.8. Permessive temperature span [240◦C; 260◦C]. Stabilization ofthe thermocline zone thickness. Hysteresis is reduced.

Chapter 3

TES Modelling

In this chapter a brief explanation of the aim of the model is given, withpreliminary quantitative considerations.

An excursus of thermocline thermal energy storage models developed untiltoday is also presented.

3.1 Model requirements

Assuming that the Solar Field and the ORC Power Block operate between180◦C and 300◦C, the extension of the planned Solar Field will be of 4.900m2,in order to feed to the Thermal Energy Storage 20MWhth, ensuring the stor-age of the thermal energy suffcient for an extra electricity production of 4hours.Indeed, being the nominal efficiency of the ORC cycle around 20%, 5MWth

are required to produce 1MWe: the production of 5MWth for 4 hours re-quires a Thermal Energy Storage with a capacity of 20MWhth.

From a preliminary analysis, without the use of Thermal Energy Storagethe electrical efficiency ηel of the ORC is - annual average - about 17.0% -[3].

ηel =Pel

Qin

(3.1)

where

- Pel is the electrical power output of the ORC

- Qin is the thermal power absorbed by the ORC working fluid from theHeat Transfer Fluid through heat exchangers

59

3. TES Modelling 60

The ORC-Plus target is the shifting of the thermal input to the ORCsystem in such a way that it can always work optimally. This would allowan increase of ηel up to 18.8%, as stated in [3] after preliminary simulations.Moreover shifting the production towards colder hours - it is an ORC with aircondenser - can further improve the average annual ORC system efficiencyup to 20%.

In order to verify all these preliminary estimates a comprehensive dy-namic model of the full plant is needed. Due to the peculiar characteristicof the Thermal Energy Storage the modelling of the dynamic behaviour ofthis component is not straightforward and needs a finite difference approach.On the other hand the model should be simple and computationally fast tobe included in the complete plant model comprising Solar Field, ThermalEnergy Storage system, Power Block and control procedures in real environ-ment, where DNI is variable in time.

The chosen development environment is Matlab-Simulink, that is actuallyadopted in ENEA for dynamic modelling.

3. TES Modelling 61

3.2 State of the art of TES numerical models

Literature dealing with theoretical approaches describing thermocline Ther-mal Energy Storage behaviour is really wide.

A realistic Thermal Energy Storage model has to be described by partialdifferential equations - mass, momentum and energy conservation. In orderto be realistic and precise, it must solve these equations in the 3 dimensionsof space: axial, radial and circumferential.Obviously this approach is time consuming and it is useful only if the purposeof the work is a thermal and mechanical stress analysis of the tank.Additionally in dynamic modelling - even more than in stationary analysis -such a model would require an elevated computational capacity.

Several simplified models are available in literature, and some of themare reported and described in the following pages.They can be classified in the following way:

1D models - meaning ”one dimensional” models - consider that the fluidflow inside the tank is uniform and one-dimensional (in the tank axialdirection). In this way they neglect the possibility of eddies in anyplane or radial motion of the fluid

2D models consider variations of temperature and/or velocity both in axialand radial directions: an axisymmetrical problem. This implies thatmoving circumferentially from one radius to the other nothing changes.Eddies on the radial plane are evaluated, those on an horizontal planeare neglected.

3D models consider variations of temperature and velocity in each direc-tion, thus they are the most exhaustive solution.

2P models - meaning ”two phase” models - evaluate both solid and liquidtemperature for each element. Some of these models are more complexand evaluate temperature of walls also.

1P models - meaning ”one phase” models - evaluate at each spatial elementjust one ”equivalent temperature”, an average temperature betweenwalls, liquid, and solid filler.

If the model is used for energetical considerations, for Thermal EnergyStorages operation strategies assessment and not for mechanical and/or struc-tural evaluations authors are used to develop 1D-2P or 1D-1P models.The smaller the Thermal Energy Storage system is, the more unfavourable

3. TES Modelling 62

is its volume to surface ratio regarding border effects: a 3D model wouldprovide more accurate results.

This is not the case of ORC-plus project, where the tank is small/medium-scale and wall effects can be neglected without losing too much accuracy.

All the models reported in the following pages present some typical as-sumptions usually made while modeling the heat exchange of fluids travellingacross porous media:

- The solid filler of the packed-bed is considered as a continuous, ho-mogenous and isotropic porous medium - it’s not modeled as a mediumcomposed of independent particles.

- No diffusers (or distributors) in the tank top and bottom are includedin the models.

- The diameter of the spherical elements is small enough to consider a ho-

mogenous temperature inside them. The Biot number (Bi =hdpebblesksolid

)

of the solid particles does not exceed the conventional limitation ofBi < 0.1.

- Volume variations with temperature of fluid and solid may be neglected.

- The liquid flow across the packed-bed region is laminar.

- Properties of the solid fillers are constant

In the next sections a review of the selected models available in literatureis carried out. They all start from these above-mentioned assumptions.

3. TES Modelling 63

3.2.1 T.E.W. Schumann work

Figure 3.1. Reference [15].

Chronologically this is the first mathematical solution of such a problem:the formulation of laws governing the rate of heat transfer between a liquidand crushed material when the former passes through the latter - heating upor cooling down itself.

T.E.W. Schumannn work - [15] - was performed in 1929, and presents aclearly analytical approach.

Indeed, the main purpose of his paper is to present the exact analyticalsolution of the problem, that - in oder to be ”exact” - requires many simpli-fications.The experimental application of the theory is instead not addressed in thispaper - [15].

Assumptions:

(i) Continuity and momentum equations are not resolved: the numericalmodel only enables the packed-bed thermal behavior evaluation.

(ii) Conduction heat transfer within the fluid itself or within the solid itselfis considered small, thus it is neglected.

(iii) Heat losses towards the environment are neglected

(iv) Thermal properties are independent of temperature

The thermal behaviour of the system - ”liquid and crushed material” - isdescribed by the following equations - [15]

- Energy balance for the fluid phase, ”f”

∂Tf∂t

+ u∂Tf∂x

=k

ε(ρc)f(Ts − Tf )

3. TES Modelling 64

- Energy balance for the solid phase, ”s”

∂Ts∂t

=k

(1− ε)(ρc)s(Tf − Ts)

where

- u is the velocity of the fluid across the porous medium

- Tf and Ts are respectively temperature of fluid and solid

- k is a constant that describe heat transfer convection, deeper investi-gated in [15]

- ε =Vf

Vtotalbedis the porosity of the packed-bed

- ρf and ρs are respectively density of fluid and solid

- cf and cs are respectively specific heat capacity of fluid and solid

This is a 1D-2P description of the behaviour of the system, and despiteits above-mentioned simplicity it has become the starting point for all thefollowing models describing this interesting phenomenon.

Article’s aim is not to describe the Thermal Energy Storage behaviour,it is instead to describe mathematically the physics behind heat transfer be-tween crushed material and a liquid flowing through it: equations are solvedanalytically [15].

One of the first numerical models dedicated to thermocline Thermal En-ergy Storage available in literature is the study of Pacheco et al., describedin the following section - [7].

3. TES Modelling 65

3.2.2 J.E. Pacheco et al. work

Figure 3.2. Measured profile temperatures during a discharge cycle forthe pilot-scale thermocline Thermal Energy Storage studied in Pacheco etal. work. These data are used in many validation works.

Pacheco’s model [7] is a 1D-2P model, implementing exactly the equationsderived by Schumann in [15] in order to describe the heat transfer betweena fluid and a packed-bed for storage applications.

∂Tf∂t

+ u∂Tf∂x

=k

ε(ρc)f(Ts − Tf )

∂Ts∂t

=k

(1− ε)(ρc)s(Tf − Ts)

These equations are discretized with a finite difference method.The tank is divided into equal horizontal slices, 0.2 m thick.An initial vertical temperature distribution was specified as initial condition.Knowing boundary conditions the model then calculates the local tempera-tures of fluid and packed-bed using the partial differential equations reportedin the system of equations just described.

Pacheco and al., in their work, present experimental data coming from asmall pilot-scale Thermal Energy Storage Tank - with a capacity of 2.3MWhth:

3. TES Modelling 66

they tested a 5.9m tall and 3.0m diameter thermocline Tank.The packed bed was a mixture of quartzite rocks and silica sand with a di-ameter of 3 cm and a porosity, ε, of 0.22.Solar salts were used as Heat Transfer Fluid.

This is a useful work, widely cited, because there are a few experimentaldata coming from thermocline Thermal Energy Storage larger than labora-tory scale.Consequently most of authors - [10], [26], [8] - used these data (fig. 3.2), andthose coming from Solar One power plant - a 10 MW Concentrating SolarTower power plant adopting the thermocline concept for the storage system,[9] - as landmark for their validations.

In the present work the same data are used for model validations, seechapter 5.

3. TES Modelling 67

3.2.3 J.-F. Hoffmann et al. work, 1D-2P and 1D-1P

Figure 3.3. Scheme of thermocline TES for Hoffmann et al. study. Source:[8].

In order to describe the behaviour of a thermocline Thermal Energy Stor-age two numerical models were developed in J.F.Hoffmann et al. work [8].The first is 1D-1P, the second is 1D-2P.The tank is considered as a perfect vertical standing cylinder containing thepacked-bed.Fluid flows through the void fraction.

Characteristics of the models:

(i) Continuity and momentum equations are not resolved: the numericalmodel only enables a tank thermal behavior evaluation.

(ii) Conduction heat transfer within the fluid itself and within the soliditself are included in the model (k in the following equations).

(iii) Heat losses towards environment are considered too.

(iv) Physical properties changes with temperature.

3. TES Modelling 68

1D-2P model

The set of equations describing the thermal behaviour of a thermocline TEStank - by Hoffmann et al. [8] - are listed below.Here, l stands for liquid, s for solid and w for wall.

- Mass conservation equation:

u =ml

ρl

(επ

(Dtank

2

)2) (3.2)

where

- ml is the mass flow rate entering the tank

- Dtank is the diameter of the tank

- ρl is the density of the liquid

- ε

(=

VlVtotalbed

)is the porosity of the packed-bed structure.

- Energy balance for the liquid phase ”l”:

ε (ρc)l

(∂Tl∂t

+ u∂Tl∂x

)= kleff

∂2Tl∂x2

+ hv (Ts − Tl) + hwAl↔w

Vl(Tw − Tl)

(3.3)

where

- cl is the specific heat capacity of the liquid

- Tl, Ts and Tw represent the temperatures of liquid, solid fillersand wall, respectively

- kleff is the effective thermal conductivity of the liquid [W/(mK)]

- hv is the interstitial heat transfer coefficient between fluid andsolid [W/(m3K)]

- hw is the heat tranfer coefficient between wall and tank-inside[W/(m2K)]

- Al↔w is the contact area between wall and liquid

- Vl is the volume occupied by the liquid.

3. TES Modelling 69

- Energy balance for the solid phase ”s”:


= kseff∂2Ts∂x2

+hv (Tl − Ts)+hwAs↔w

Vs(Tw − Ts) (3.4)

where

- cs is the specific heat capacity of the solid pebbles

- kseff is the effective thermal conductivity of the solid phase [W/(mK)]

- Vs is the volume occupied by the solid fillers

- Energy balance for the wall ”w”:

(ρc)w∂Tw∂t

= kw∂2Tw∂x2

+ hw

[Al↔w

Vw(Tl − Tw) +

As↔w

Vw(Ts − Tw)

]+

+ hextAw↔ext

Vw(Tw − Text) (3.5)

where

- cw is the specific heat capacity of the wall

- kw is the thermal conductivity of the wall [W/(mK)]

- Vw is the volume of the wall

- hext is the coefficient of global thermal losses to the environment [W/(m2K)]

1D-1P model

Authors present also a single phase model, computationally cheaper since itevaluates just one mean temperature (instead of 3 temperatures: Tl, Ts andTw):

(ε (ρcp)l + (1− ε) (ρcp)s + (ρcp)w

) ∂T∂t

+ ε (ρcp)l u∂T

∂x=

=(kleff + kseff + kw

) ∂2T∂x2

+ hextAw↔ext

Vw(T − Text) (3.6)

3. TES Modelling 70

3.2.4 Xu et al. model

Figure 3.4. Scheme of thermocline TES for Xu et al. study, [10].

Xu’s numerical model [10] is a 2D-2P model. It is based on the followingassumptions:

(i) Continuity and momentum equations are solved. The governing equa-tions describing the storage tank are two-dimensional, in the specificcase the fluid flow and the heat transfer is considered symmetrical aboutthe axis.

(ii) Conduction heat transfer within the fluid itself and within the soliditself are included in the model (parameter k in the following energybalances).

(iii) Heat losses towards the environment are considered too.

(iv) Physical properties changes with temperature.

With these assumptions, the transient 2D-2P governing equations for theheat transfer and fluid dynamics of a tank divided axially in disks and radiallyin rings (fig. 3.4) are listed below:

- Continuity equation:

∂(ερl)

∂t+∇ · (ρl~u) = 0 (3.7)

where

3. TES Modelling 71

- ρl is the liquid density

- ε =Vf

Vtotalbedis the packed-bed porosity

- ~u = ur~er + ux~ex is the velocity vector referred to the total cross-sectional area of the tank (to get the real ~u of the fluid the divisionby ε is required)

- Momentum equation:

∂(ρl~u)

∂(εt)+∇ · (ρl~u~u)

ε2= ∇·(µ∇~u)−∇p+ρl~g−

(µ

K+CFρl√K|~u|)~u (3.8)

where

- K is the intrinsic permeability of the porous medium

- µ is the liquid viscosity

- CF is the inertial coefficient

- Energy balance for the liquid phase:

∂ (ερlclTl)

∂t+∇ · (ρlcl~uTl) = ∇ · (Γl,effective∇Tl) + hv(Ts − Tl) (3.9)

where

- Tl and Ts represent the temperatures of liquid and solid fillers,respectively

- cl is the specific heat capacity of the liquid

- Γl,effective is the effective thermal conductivity of the liquid [W/mK]

- the last term accounts for the heat transfer between the liquid andsolid fillers through a volumetric interstitial heat transfer coeffi-cient hv - in [W/m3K]

- Energy balance for the solid fillers:

∂ ((1− ε)ρscsTs)∂t

= ∇ · (Γs,effective∇Ts) + hv(Tl − Ts) (3.10)

where

- cs is the specific heat capacity of filler material

3. TES Modelling 72

- Γs,effective is the effective thermal conductivity of solid fillers [W/mK]

- Energy balance for the insulation layers and tank steel wall:

∂ (ρiciTi)

∂t= ∇ · (Γi∇Ti) (3.11)

where i means insulation layer 1, tank steel wall, and insulation layer2.

3. TES Modelling 73

3.2.5 Summary table

A sum up of last sections is here reported in tabular form, in order to easeits visualization.

Table 3.1. Summary table with main characteristics of each model.

Type ks kl Losses WallMom.

eq.Cont.

eq.Schumann 1D-2P no no no no no no

Pacheco 1D-2P no no no no no noHoffmann A 1D-2P yes yes yes yes no noHoffmann B 1D-1P yes yes yes yes no no

Xu 2D-2P yes yes yes yes yes yesAngelini 2D-2P no yes no no no yes

Schumann [15] and Pacheco [7] models are different since the former solvesequations analytically, the latter finds a solution through a discretization withfinite difference method.”Yes” in table 3.1 means that the model includes an evaluation of

Diffusivity within solid, ”ks”

Diffusivity within liquid, ”kl”

Heat losses towards the environment, ”Losses”

Thermal inertia of the wall, ”Wall”

Momentum equation, ”Mom. eq.”

Continuity equation, ”Cont. eq.”

”No”, instead, means that the model neglects the corresponding param-eter.

Chapter 4

Numerical models implemented

Figure 4.1. Scheme of a thermocline Thermal Energy Storage.

As already mentioned at the beginning of chapter 3, the ORC-Plus projecttarget is to define tools for controlling efficently the overall system - the ob-jective is to improve the efficiency of the ORC system and to realize a plantlayout that allows a correct operating strategy.

In this work two models, 1D-1P and 1D-2P, were developed and analyzed.They have been chosen because main requirements are simplicity, reductionof computational time, and they must describe plant-size tanks, while verysmall tanks - with stronger wall effects - are not of interest.They have been implemented in Simulink in order to evaluate possible dif-

74

4. Numerical models implemented 75

ferences in results.The first, presented in the next section, is a 1D-2P model, the second one is1D-1P.

It is important to notice that in the state of the art studies presentedin section 3.2 continuity equation is solved just in Xu et al. and Angelini’sworks.The other authors neglect it.Moreover, the studies analysed in section 3.2 do not describe the behaviorof a Thermal Energy Storage characterized by liquid level variations insideitself - see figure 4.1.In fact, when the mass of the liquid phase inside the tank is constant - inletand outlet mass flow rates are the same, fig. 4.1 - and a charge phase is oc-curring, the tank volume is progressively occupied by hotter, less dense fluid,therefore the volume of the liquid grows. In the specific case of ORC-Plus,density variation is about 13%.Then, during the discharge phase towards a steady-state Power Block thefluid cools down going back to its original volume.

In the presented study the description of this phenomenon is thus in-cluded.

Therefore the thermocline Thermal Energy Storage tank can be seen ascomposed by two element:

- the packed-bed, where the fluid-solid heat exchange takes place

- the buffer, where the Heat Transfer Fluid coming from the Solar Fieldis injected.

In this chapter it is carried out a description of:

- Two numerical models describing the behavior of the packed-bed -1Phase and 2Phases, both 1Dimensional.

- The buffer model, valid for any packed-bed model.

4.1 1 Dimension, 2 Phases model (1D-2P)

The 1D-2P model is inspired by Pacheco et al. work [7].


4.1.1 Theory

With respect to reference [7] some modifications have been introduced:

i Continuity equation in 1D is solved in order to evaluate lengthwisevelocities and to assess the volume of the liquid buffer overlying thepacked-bed.

ii The diameter of the spherical elements of the packed-bed is not smallenough - considering the design parameters chosen within ORC-Plusproject - to consider a homogenous temperature inside them. Biot

number (Bi =hdpebblesksolid

) of the solid particles is frequently above the

conventional limitation of Bi = 0.1.Therefore Jeffreson correlation [27, 26] is introduced: it allows to usethe lumped capacitance method with any Biot number, increasing theresults accuracy correcting the heat transfer coefficient h with a modi-fied one h′:

h′ =h

1 +Bi

5

iii Conduction is considered both in liquid and solid phase. It is evaluatedwith relations reported by Xu et al. in their work [10].

iv Heat loss towards environment are considered for sake of completeness.

Here are reported the equations to be solved in order to obtain the thermalbehaviour of the packed-bed inside the tank - ”l” stands for liquid, ”s” forsolid phase and ”ext” for environment.


=∂ρlu

∂x(4.1)

2nd) Energy equation for the liquid phase:

ε (ρc)l

(∂Tl∂t

+ u∂Tl∂x

)= kleff

∂2Tl∂x2

+ hv (Ts − Tl) +(UA)extVtotalbed

(Text − Tl)

(4.2)

3rd) Energy equation for the solid fillers:


= kseff∂2Ts∂x2

+ hv (Tl − Ts) (4.3)


where

- u is liquid velocity across the packed bed

- ε (= Vl/Vtotalbed)

- c’s, ρ’s and T’s are respectively specific heat capacities, densities andtemperatures

- keff ’s are the effective thermal conductivities [W/(mK)]

- hv is the interstitial heat transfer coefficient between fluid and solid[W/(m3K)]

- Vtotalbed is the volume occupied by the packed bed

- (UA)ext is the global heat transfer coefficient for the evaluation of ther-mal losses towards the environment [W/K].

4.1.2 Numerical model

Figure 4.2. 1D-2P discretization along tank axis, n spatial steps.

In order to solve equations 4.1, 4.2 and 4.3 it has been adopted a finitedifference method. It consists in replacing the derivates of a differential equa-tion by finite difference approximations according to a discretization scheme


- presented in fig 4.2.

A detailed description of the numerical model implemented in Simulinkis reported in appendix B.

A typical example of results provided by this 1P-2P model is reported infigure 4.3.

Figure 4.3. Thermocline profile after 2, 4 and 6 hours from the beginning ofthe charge. Inlet fluid temperature is 300◦C.

In the specific case it is shown a charging process of a 10m-tall and 5m-wide tank, with 10 kg/s of hot fluid at 300◦C; initial temperatures of fluidand packed-bed was 180◦C for both.Tl and Ts are very similar because velocity of the liquid is really low (<2mm · s−1) and interstitial heat transfer coefficient hv is high (notice thatthis is the most common case: the requirement of a thermocline TES is toenhance heat transfer between fluid and rocks).

4.2 1 Dimension, 1 Phase model (1D-1P)

Looking at fig. 4.3 it seems straight and convenient to semplify a two-phasesmodel (”2P”) of a thermocline TES into a one-phase (”1P”) description: in-


deed, difference between Ts (red line) and Tl (blue line) is small - about 1◦C.Consequently the idea is to consider just one temperature for each spatialstep of the mesh: at each step ”i” there is just one unknown - Ti - instead oftwo - Tsi and Tli - thus reducing computational time - figure 4.5.Such approach, in the specific case, has been also advised by other researchersin the field [28].

In this section the 1D-1P model implemented in Simulink - inspired bythe model developed by J.F. Hoffmann et al. [8] - is presented.

4.2.1 Theory

The chosen approach starts from Hoffmann relations (3.3, 3.4 and 3.5) thatare slightly modified - for example, continuity equation is introduced. Hereare reported the new relations chosen for the representation of the behavior ofthe packed-bed of the thermocline Thermal Energy Storage: their derivationis reported in appendix A.


=∂ρlu

∂x(4.4)

2nd) Energy balance for the liquid phase:

ε (ρc)l

(∂Tl∂t

+ u∂Tl∂x

)= kleff

∂2Tl∂x2


Vtotalbed(Tw − Tl)

(4.5)

3rd) Energy balance for the solid fillers:


= kseff∂2Ts∂x2

+ hv (Tl − Ts) + hwAs↔w

Vtotalbed(Tw − Ts)

(4.6)

4th) Energy balance for the wall:

(ρc)w∂Tw∂t

= kw∂2Tw∂x2

+ hw

[Al↔w

Vw(Tl − Tw) +

As↔w

Vw(Ts − Tw)

]+

+(UA)extVw

(Text − Tw) (4.7)

where


- ε (= Vl/Vtotalbed) is the void fraction

- cl,cs and cw are respectively the specific heat capacity of the liquid,solid phase and wall

- Tl, Ts and Tw represent the temperatures of liquid, solid fillers andwall

- kleff and kseff are the effective thermal conductivity of the liquid andsolid phase [W/(mK)]

- hv is the interstitial heat transfer coefficient between fluid and solid[W/(m3K)]

- hw is the heat tranfer coefficient between wall and tank inside [W/(m2K)]

- Al↔w and As↔w are the liquid-wall and solid-wall contact areas

- Vtotalbed is the volume occupied by the packed bed

- kw is the thermal conductivity of the wall, Vw its volume

- (UA)ext is the global heat transfer coefficient for the evaluation of ther-mal losses towards the environment

Now, considering the following relation

Tl = Ts = Tw = T (4.8)

It is possible to build the following set of equations

ε (ρc)l

∂��>T

Tl

∂t+ u

∂��>T

Tl

∂x

= kleff

∂2��>T

Tl

∂x2+ hv

Ts��0

−Tl

+ hwAl↔w

Vtotalbed

Tw��0

−Tl

(1 − ε) (ρc)s

∂��>T

Ts

∂t= kseff

∂2��>T

Ts

∂x2+ hv

Tl��0

−Ts

+ hwAs↔w

Vtotalbed

Tw��0

−Ts

(ρc)w

∂��*T

Tw

∂t= kw

∂2��*T

Tw

∂x2+ hw

Al↔w

Vw

Tl��0

−Tw

+As↔w

Vw

Ts��0

−Tw

+(UA)ext

Vw

(Text −��*

TTw

)

Hence, simplifying

ε (ρc)l(∂T∂t

+u∂T

∂x

)= kleff

∂2T

∂x2

(1− ε) (ρc)s∂T

∂t= kseff

∂2T

∂x2

(ρc)w∂T

∂t= kw

∂2T

∂x2+

(UA)extVw

(Text − T )


Multiplying the last equation by η =Vw

Vtotalbedin order to normalize it with

respect to Vtotalbed it follows:

ε (ρc)l(∂T∂t

+u∂T

∂x

)= kleff

∂2T

∂x2

(1− ε) (ρc)s∂T

∂t= kseff

∂2T

∂x2

η (ρc)w∂T

∂t= ηkw

∂2T

∂x2+

(UA)extVtotalbed

(Text − T )

Adding together this 3 equations, it follows:

(ε (ρc)l + (1− ε) (ρc)s + η (ρc)w)∂T

∂t+ ε (ρc)l u

∂T

∂x=

=(kleff + kseff + ηkw

) ∂2T∂x2

+(UA)extVtotalbed

(Text − T ) (4.9)

Let’s call for sake of simplicity (ρc)eq = (ε (ρc)l + (1− ε) (ρc)s + η (ρc)w)and keq =

(kleff + kseff + ηkw

)and the fundamental equation describing the

thermocline Thermal Energy Storage behaviour becomes:

(ρc)eq∂T

∂t+ ε (ρc)l u

∂T

∂x= keq

∂2T

∂x2+

(UA)extVtotalbed

(Text − T ) (4.10)

It is interesting to compare results coming from a 2P model with thosecoming from the simplified 1P model.


Figure 4.4. Temperature profiles inside the tank during the charging phase.1D-1P model temperature profile is in green. 1D-2P model profiles for rocksand Heat Transfer Fluid are in red and blue, respectively. Discrepancies be-tween models are about 3◦C.

One example of comparison is reported in fig. 4.4, where starting from a”180◦C-storage” - both liquid and filler at 180◦C - hot fluid at 300◦C is fedto the top of a 10m tall tank.As it can be seen the difference is limited as far as it is related to practicalapplication in power plants - it is the same order of magnitude of practicalexperimantal error measurements of real Thermal Energy Storage systems.

4.2.2 Numerical model

In order to solve equation 4.10 a finite difference method has been adopted.The discretization scheme is represented in fig 4.5.


Figure 4.5. 1D-1P discretization along tank axis, n spatial steps.

So, for each i-th disk generated by this discretization we can write

(ρc)eqTi + ε (ρc)l uTi − Ti−1

∆x= keq

Ti−1 − 2Ti + Ti+1

(∆x)2+

(UA)extVtotalbed

(Text − Ti)

(4.11)that is

Ti =

(ε(ρc)lu

(ρc)eq∆x+

keq(ρc)eq(∆x)2

)Ti−1+

+

(− ε(ρc)lu

(ρc)eq∆x− 2keq

(ρc)eq(∆x)2− (UA)ext

(ρc)eqVtotalbed

)Ti+

+keq

(ρc)eq(∆x)2Ti+1 +

(UA)ext(ρc)eqVtotalbed

Text (4.12)

There’s a second order derivative: two boundary conditions are required.Indeed for the initial disk it does not exist a Ti−1 while for the last disk itdoes not exist a Ti+1.


Packed-bed Boundary Conditions

• if ml > 0 the tank is undergoing the ”charge phase” (conventionally):hot fluid is entering the packed-bed from the overlying buffer - whichis in turn fed by the Solar Field at temperature Thot - at temperatureTBuffer, heating up cold pebbles - it flows downwards.:

Tx=top = TBuffer

∂T

∂x

∣∣∣∣x=bottom

= 0

• if ml = 0 the tank is still, ”inactive”. Thermal diffusion will promotethermocline degradation:

∂T

∂x

∣∣∣∣x=top

= 0

∂T

∂x


= 0

• if ml < 0 the tank is ”discharging”: cold fluid is fed from the bottomof the tank (coming from ORC outlet, at temperature Tcold) and afterbeing heated up by hot pebbles, it is extracted from top of the tank:

∂T

∂x

∣∣∣∣x=top

= 0

Tx=bottom = Tcold

Equation 4.12 can be simplified as follow in order to ease its visualization:

ε(ρc)l(ρc)eq∆x

= p1

keq(ρc)eq(∆x)2

= q1

(UA)ext(ρc)eqVtotalbed

= q2

where ρ, cl and k are all functions of temperature, thus they have to becomputed at each temporal and spatial step - this is precisely described in


the following paragraph.

These equations allow to rewrite the equation 4.12 as follow.

Ti = (p1u+ q1)Ti−1 + (−p1u− 2q1 − q2)Ti + q1Ti+1 + q2Text (4.13)

In order to ease its visualization, again

Ti = (A)Ti−1 + (B)Ti + q1Ti+1 + q2Text (4.14)

T1T2...

Ti...

Tn

=

B q1 0 0 · · · 0 0A B q1 0 0

0 A B q1. . .

...

0 0. . . . . . . . . 0 0

.... . . A B q1 0

0 0 A B q10 0 · · · 0 0 A D

T1T2...Ti...

Tn

+

q2Text + ThotAq2Textq2Text

...

q2Textq2Text

where D = −p1u − q1 − q2 is different from B because the imposed top

boundary condition is different from the bottom boundary condition (adia-baticity has been imposed, ∂T/∂x|x=bottom = 0).

The system thus becomes:

~T = M · ~T + ~V (4.15)

This is valid for the charge phase, of course for the discharge phase littlevariations have to be made: the advection term has to describe a fluid movingupwards, and the implemented boundary conditons have to be changed.

Algorithm explained Starting from an initial condition ~Tinitial the modelcomputes at each disk i - of the n disks in which the tank is subdivided -physical and thermal properties thanks to a specific function implemented inmatlab. This is possible knowing boundary conditions - TBuffer during thecharge phase and TfromORC

during the discharge pahse.Velocity and mass flow rate are different at each disk too:


i Knowing inlet or outlet conditions u0 =mliquid

ρl

(επ

(Dtank

2

)2) can be

evaluated: this is the boundary condition for the continuity equation -eq. 4.4

ii Knowing temperature at each spatial step i, ρli at the ith step can beevaluated and - starting from an initial vector of densities composedby ρt=0

i - it is possible to solve the continuity equation 4.4 as followsρti − ρt−1i

∆t=ρti−1u

ti−1 − ρtiutidx

iii In such a way velocity at each step i is thus evaluated.

where

- ρti and uti the density and the velocity of the liquid at step i and time t

- ∆t is the time step imposed

- dx is the thickness of the ith step.

Now, if the packed-bed is subdivided in n steps, n p1, q1 and q2 are eval-uated - one for each spatial step - and the description of the thermoclinebehavior can be performed.

Precisely, the model solves the following

T1T2...

Ti...

Tn

=

B1 q11 0 0 · · · 0 0A2 B2 q12 0 0

0 A3 B3 q13

. . ....

0 0. . . . . . . . . 0 0

.... . . An−2 Bn−2 q1n−2 0

0 0 An−1 Bn−1 q1n−1

0 0 · · · 0 0 An Dn

T1T2...Ti...

Tn

+

q21Text + ThotA1

q22Textq23Text

...

q2n−1Textq2nText

where the last subscript indicates the mesh step i.

Solving this system of equations the variation of tempeature in time foreach disk is found (Ti). Integrating (Ti) during time, the thermal behaviourof the tank can be described: this is what the Simulink implemented modelperforms.


4.3 Buffer model

At the beginning of chapter 4 it has been mentioned the importance of thebuffer: the variable volume of liquid overlying the packed-bed inside a ther-mocline Thermal Energy Storage .

When a given mass of a substance with density inversely proportionalto temperature is heated up, its volume increases. This is something thatcontinuity equation accounts for.In this section it is described how this buffer has been modeled.

Looking at figure 4.6 will help in the description.

Figure 4.6. Buffer schematization.

During a charge phase, the mass flow rate coming from the Solar Field,mHOTSF , enters the buffer from the distributor. At the very same timethe same mass flow rate, mCOLDSF , - at a lower temperature, due to thethermocline - is exiting the tank from the bottom.This is true if the Solar Field is working in steady-state regime

mHOTSF = mCOLDSF

In order to evaluate, at each timestep, the mass of liquid constituting thebuffer Mbuffer, mHOTSF and mpb are required - where mpb is the mass flow


rate actually flowing across the packed-bed - fig. 4.6.

- mHOTSF is provided by the Solar Field model according to solar irra-diation - see section 6.0.1.

- mpb is computed as follows:

i Velocity un of the liquid phase at the nth step is evaluated throughmCOLDSF = ρnunApbε - since Tn is known, ρn is also known.

ii Continuity equation is solved from the nth to the 1st spatial step throughρti − ρt−1i

∆t=ρti−1u


in order to evaluate u1, at the 1st step.

iii Knowing u1, it is possible to evaluate mpb = ρ1u1Apbε

Thus, it is possible to track the mass of liquid composing the buffer atany time:

Mbuffer = M time=0buffer +

∫time

(mHOTSF − mpb) dt

In order to evaluate the temperature of the buffer Tbuffer a simple energybalance is performed:

Mbuffer · c ·∂T

∂t= Pin −��*

0Pout − Ploss (4.16)

where

- Mbuffer and c are evaluated for simplicity at the beginning of thetimestep

- Pin is the power injected into the buffer through mHOTSF :

Pin = mHOTSF

∫ TSF

Tbuffer

c(T ) · dT

- Pout is the energy per unit time exiting the buffer through mCOLDSF .It is always at Tbuffer, therefore it can be simplified since Treference =Tbuffer.

- Ploss is the power lost to the environment.


Thus, it is possible to evaluate∂T

∂t- eq. 4.16. Hence, integrating it during

time, it is possible to track the buffer temperature, , at any time.

Tbuffer is an important parameter because it is the top boundary conditionof the packed-bed during the charge phase - see subsection 4.2.2, paragraph”boundary conditions”.

Similar calculations are perfomed during the discharge phase of a ThermalEnergy Storage.

Chapter 5

Models validation

Validation of computer simulation models is conducted during the develop-ment of a simulation model with the ultimate goal of making it the mostaccurate and credible.Simulation models are increasingly being used to solve problems and to aidin decision-making. They are approximate imitations of real-world systemsand they never exactly describe the real-world system. Therefore, a modelshould be verified and validated to the degree needed for the models purposeor application.The most straightforward way of validating a computer model is against ex-perimental data. Unfortunately, in the specific case of this study, these arenot available. Indeed the ORC-plus Thermal Energy Storage is not yet built,and other experimental results found in literature are not fully exhaustive.

In addition small tanks normally adopted in laboratory tests can be moredifficult to simulate due to stronger 3D effects - e.g. wall effects.

Other limitations related to the modeling of a thermocline Thermal En-ergy Storage are that

- possible thermal bridges and vortexes are not modeled in a simplified1D model;

- in thermocline storages there could be an uncertainty related to whichtemperature is actually measured by the thermocouples: the HTF tem-perature or the filler one.

In this section, the previously described 1D-2P and 1D-1P models - chap-ter 4 - are validated. Two validations per each were perfromed, since - again- exhaustive experimental data of thermocline TES are not available:

90

5. Models validation 91

- one validation is performed with respect to experimental data of alarge-size Thermal Energy Storage -Solar One power plant, [9].

- the other one is performed with respect to another validated model,XU’s model, a 2D-2P model developed in [10]. G.Angelini in his masterthesis at Politecnico di Milano - [26] - uses the same article for validatinghis model.

Regarding the 1D-1P model even other two validations were performedduring a visit, in May 2018, at CIC Energigune, an energy cooperative re-search centre in Vitoria-Gasteiz, Alava, Spain, involved in the ORC-Plusproject.Among the various fields of interest, they are dealing with thermocline Ther-mal Energy Storages simulations.These validations are reported in the last part of this chapter, in section 5.3.


5.1 Validation with Solar One experimental

data

Figure 5.1. The plant. Actually in this figure is not shown Solar One, butits expansion - in 1995 - named ”Solar Two”: 108 heliostats were added to theexisting Solar One. Source: [16]

Solar One was a pilot solar-thermal project built in 1986 in the MojaveDesert, CA, USA. It was the first test of a large-scale thermal solar powertower plant.

Solar One was designed by Sandia National Laboratories in Livermore,California for the U.S. Department of Energy (DOE).

Despite its age, due to lack of reliable and published experimental data,many validations of thermocline models refer to the Solar One report - fig.5.3, [9].

Solar One was a Concentrating Solar Power (CSP) plant with a 170MWhththermocline energy storage - fig. 5.2 - almost 10 times ORC-plus’. It workedwith a mixture of granite rocks and sand as solid fillers, and Caloria HT 43as heat transfer fluid - [9].


Figure 5.2. The thermocline Thermal Energy Storage, nominally170MWhth. Source: [9].

Figure 5.3. The 8-hours discharge cycle of Solar One TES. ”Day 179” meansthat this is what happened during the 179th day of plant testing. Source: [9].

From curves in fig. 5.3, describing a discharge phase, several points wereextracted and interpolated in Matlab - appendix E. Thus, they have beenreproduced in figure 5.4 in order to validate boththe 1D-2P model and the1D-1P model - chapter 4.Main model parameters required for this validation are taken from [8, 29, 9,30]; fluid properties correlations are reported in appendix D.


Table 5.1. Parameters for model implementation. Source: [8, 29, 9, 30]

Parameters ValueTank height, m 12.0Tank radius, m 18.2Diameter of quartzite rock, m 0.0046Porosity, ε 0.22Thickness of insulation layer, m 0.35Thickness of stainless steel wall, m 0.02Temperature of hot HTF, ◦C 296Temperature of cold HTF, ◦C 180Density of filler mixture, kg/m3 2643Specific heat capacities, J/kg/KFor filler mixture 1020for stainless steel 475Thermal conductivities, W/m/◦CFor filler mixture 2.2For insulation layer 0.038For stainless steel 47.0Inlet mass flow rate, kg/s 25.75*

Figure 5.4. Validation of 1D-2P and 1D-1P models with Solar One dischargecycle. Experimental data at hour 00:00 is taken as starting point for thesimulations. The green line, representing solid temperature, is so close to theliquid temperature - in blue - to be visible only by zooming


As it is possible to see from figure 5.4, deviations between models andexperimental data are of the order of 7 − 10◦C: considered an acceptablevalue.Moreover differences between the 1D-1P and the 1D-2P models are almostinvisible.

Inlet mass flow rate in table D.1 has been derived from an energy balance,because mass flow rate values reported in [9] apparently lead to a wrong de-scription of the thermocline behaviour.Indeed, it was noticed that flow rate measurements were affected by leaksand subjected to inaccuracies: an estimated 15–20% positive bias was alsopreviously reported in the oil flow measurements [29].In order to compute the actual mass flow rate it has been performed thefollowing energy balance:

Figure 5.5. Method to evaluate mass flow rate for Solar One in day 179

At each dx both solid and fluid phases pass from an higher temperatureto a lower one 5.5, loosing

Ereleased =

∫ T8h

T0h

mc(T ) dT

∣∣∣∣liquid

+

∫ T8h

T0h

mc(T ) dT

∣∣∣∣solid

(5.1)

Ereleased = εdxπD2

4

∫ T8h

T0h

ρl(T )cl(T ) dT + (1− ε)dxπD2

4ρscs

∫ T8h

T0h

dT (5.2)


Being cl(T ) and ρl(T ) linear functions of temperature these Ereleased iseasy to be computed (= 2.17 · 1011Joule).Thus, assuming a constant fluid mass flow, this can be computed as:

Ereleased = ml

(∫ Tout

Tin

cl(T ) dT

)·∆t (5.3)

Where ∆t = 8 hours, Tin is 180.4 ◦C and Tout is an average between Tout0hand Tout8h - Tavg = 290.6◦C).


5.2 Validation with Xu et al. model

Figure 5.6. Schematic layout of the 2.3 MWh thermocline flow loop.

The experimental results of Pacheco et al. - [7] - based on a pilot moltensalt thermocline storage system of 2.3 MWhth - 1/10th of the ORC-plus size -are generally used to validate thermocline Thermal Energy Storage numericalmodels. It’s a pilot storage system using a low-cost mixture of quartzite rockand sand as solid filler material and solar salt (a mixture of 60%wtNaNO3and 40%wtKNO3) as heat transfer fluid.

In figure 5.7 - same data of figure 3.2 - experimental data coming fromthe pilot thermocline storage cycle are reported - a 2-hours discharge pro-cess. The observed irregular trend may be related to measurement errors orto possible vortices of molten salt flowing through the packed-bed - in thelatter case, it would be required a more sophisticated modeling to describethem.


Figure 5.7. Experimental data from Pacheco’s study pilot plant. Dischargecycle. Source: [7].

In this section a comparison with both the experimental data of Pacheco’spilot-plant - [7] - and the Xu et al. model results - [10] - is shown. In figure5.8 results of Xu’s model are reported, togheter with experimental data.

Figure 5.8. Comparison between Xu’s numerical (red) and Pacheco’s exper-imental (dashed blue) thermocline profiles. Discharge cycle of a packed-bedmolten-salt thermocline TES. Here x = 6m is the top of the tank.

In figures 5.9 and 5.10 the validation of the new developed models - ”1D-2P” and ”1D-1P” - is shown.1D-2P model and 1D-2P models, in fact, do not show significant differences


with respect to Xu’s model (discrepancies are < 4◦C).

Figure 5.9. Comparison between experimantal data (dashed blue), Xu model(red squares) and 1D-2P model results (black line).

Figure 5.10. Comparison between experimantal data (dashed blue), Xumodel (red squares) and 1D-1P model results (black line).


5.3 Validations at CIC Energigune

During May 2018 it was possible to visit CIC Energigune facility, where itis located the laboratory-scale of the thermocline Thermal Energy Storagethat is going to be built in Ben Guerir, within ORC-plus project.

Since the aim of this thesis is to investigate the possibility of developinga simple and computationally fast model in order to include it in a completeplant model - comprising Solar Field, Storage system, Power Block and con-trol procedures - at CIC Energigune a work focused only on the 1D-1P modelwas done.

Two validations were performed:

- with respect to experimental data coming from the laboratory-scaleStorage system

- with respect to the CICenergigune’s 2D-2P model. In the specific casea comparison with both constant and variable inlet mass flow rate wasperformed.

5.3.1 Validation with experimental data

CICenergigune operates a laboratory-scale thermocline Thermal Energy Stor-age.An electric resistance heats up an oil flow coming from a ”cold tank” in orderto fill a ”hot tank”.After being heated up, oil from the ”hot tank” is sent to the thermoclinestorage system in order to simulate a charge phase.When the charge phase is finished, in order to simulate a discharge phase,oil from the TES is sent back to the ”hot tank”.Nine thermocouples placed longitudinally - a few centimeters apart from eachother - monitor liquid temperature during time. Each thermocouple is placedinside a steel bar radially positioned inside the tank. Along the bar, actuallyfive thermocouples are placed in order to also evaluate temperature radialdistribution.In the following graph, that refers to a charge phase, the experimental resultsare shown togheter with the results coming from the 1D-1P model and CIC-energigune model simulations. The temperatures are referred to the axialposition.


Figure 5.11. Comparison of Experimental data with results from CICenregi-gune’s model and 1D-1P model.

Results look really satisfactory, except for the third thermocouple. Com-mon thought is that it is bended and it is actually showing the temperatureat a different height of the packed-bed.

5.3.2 Validation with 2D-2P model

Another test was performed simulating a larger-scale tank. In this case thevalidation is just a model-to-model validation: between the CICenergigune’s2D-2P model and the 1P-1D model - chapter 4.

Two simulations - charge phases - were performed:

- setting a constant mass flow rate fed to the top of the thermoclineThermal Energy Storage as input;

- setting a variable mass flow rate as input.

Results are here reported.Constant inlet mass flow rate simulation, in figure 5.12.


Figure 5.12. Comparison between CICenregigune’s model and 1D-1P model.Constant inlet mass flow rate. Charge phase. Time between each temperatureprofile is 1 hour.

Variable inlet mass flow rate simulation, in figure 5.13.


Figure 5.13. Comparison between CICenregigune’s model and 1D-1P model.Variable inlet mass flow rate. Charge phase. Time between each temperatureprofile is 1 hour.

The variable inlet mass flow rate given as input to the models, in orderto obtain the results reported in figure 5.13, is shown in figure 5.14.


Figure 5.14. Variable inlet mass flow rate implemented for simulation infigure 5.13.

5.4 Remarks

Concluding, in any analyzed case it looks clear that both 1D-2P and 1D-1Pmodels are good in representing reality. Of course the latter looses some in-formation with respect to the former, therefore it cannot be always adoptedin describing thermal behavior of a fluid crossing crushed material.

Chapter 6

Complete power plant weeklysimulations

Having regard to the considerations made in the previous sections, simula-tions of the operations of a complete Concentrating Solar Power plant areperformed in this chapter.In particular, three specific weeks were simulated:

- from 14th to 20th of January

- from 14th to 20th of March

- from 14th to 20th of June

Each simulation is performed implementing the storage system in threedifferent ways:

i Thermocline TES modeled with the 1D-2P model - chapter 4

ii Thermocline TES modeled with the 1D-1P model - chapter 4

iii Double-tank TES - section 6.3

The simulated CSP plant is slightly different from the ORC-plus projectpower plant: it has one Solar Field only, with a total extension equal to thesum of SF1 and SF2 extensions - see ORC-plus power plant, fig. 1.12.Indeed, simulating one Solar Field only - instead of SF1 and SF2 separately- allows faster simulations.

The reason of this simplification lies in the aim of this chapter.

The goal is to evaluate the annual electric energy produced by the powerplant if:

105

6. Complete power plant weekly simulations 106

- different storage technologies are applied - thermocline TES or double-tank TES - in order to assess the Levelized Cost of Electricity for bothtechnologies;

- the thermocline Thermal Energy Storage is modeled with a 1D-1P or a1D-2P approach - in order to assess the discrepancies between the two.

Hence, the purpose of this chapter is to perform long term simulationsof a generic CSP plant - scheme in figure 6.1 - and not of the specific plantdesigned for the ORC-Plus project.

Figure 6.1. Plant layout for Simulink simulation. Thermocline storage.ORC-plus plant has a different layout.

The storage system as shown in fig. 6.1 is connected to the solar field,SF, and to the ORC Power Block, PB.


6.0.1 Solar Field model

Figure 6.2. Simulink interface for the Solar Field model.

The Solar Field model - already available at ENEA, fig. 6.2 - producesas output

- Heat Transfer Fluid mass flow rate m4 - point 4 of fig. 6.1

- HTF temperature T4 - point 4 of fig. 6.1 - and also T1, T2 and T3

assuming as input data

- the real DNI daily pattern - sampled at 1 minute

- HTF temperature T0 - point 0 of fig. 6.1.

It must be pointed out that in order to have a sufficiently hot T4, duringstart up and/or during cloudy periods a simple logic is added to the SF ar-rangement: a by-pass valve - ”x” in the figure - is activated as long as thetemperature T4 is lower than 260◦C (the limit temperature for ORC opera-tions).Therefore, if the temperature from the SF is too low, Heat Transfer Fluid isrecirculated back to the SF input through the dashed line.If the temperature is sufficiently high, the fluid goes directly from point 4 topoints 5 and/or 9 - fig. 6.1 - without ”x-valve” deviation.This procedure implies a transient in the Solar Field temperatures when theby-pass valve is operated producing temperature oscillations along the SolarField receiver line (243m long) since the residence time is of the order of 5-10minutes - see figure 6.3.


Figure 6.3. Temperatures at the outlet of each collector of the Solar Fieldand Solar Field temperature inlet. Clear sky.

Looking at fig. 6.3, until sunrise - around 6 a.m. - the temperature of theHeat Transfer Fluid inside the Solar Field descreases due to heat losses to theenvironment. Inside each collector of each loop HTF does not circulate andit is everywhere at the same temperature: T1, T2, T3 and T4 are the same.The Solar Field is composed by ten loops, each of them composed by fourcollectors in series: the model assumes that all the loops behave in the sameway since the DNI is the same and the mass flow is equally shared.

In figure 6.3 are reported temperatures at the

- Solar Field inlet - point 4 during ricirculation, else point 0 - figure 6.1

- Outlet of Solar Field collector 1 - point 1



- Solar Field outlet - point 4.

It is possible to check in fig. 6.3 that as soon as T4 reaches 260◦C, x-valveis switched, stopping recirculation and sending the Heat Transfer Fluid tothe Thermal Energy Storage or to the Power Block. This is depicted in fig.6.3 as a discontinuity of TINSF - inlet of the Solar Field.Indeed, when recirculation is stopped, Heat Transfer Fluid is no longer takenfrom the outlet of the Solar Field - at T4, but from point 0 - where m12 andm8 mix togheter - at a lower temperature (of the order of 180◦C).


The oscillating temperature following the switching of the valves is linkedto the transient behaviour of the receiver line: inlet fluid temperature de-creases spikely and, as said before, the residence time of the Heat TransferFluid is in the order of 5-10 minutes. In addition the temperature controlalgorithm is based on DNI and on the difference between T4 and a set pointtemperature - 300◦C in the specific case. Moreover the mass flow rate pro-duced by the pump has a minimum and maximum value.The result is a very non linear phenomenon.

It must be pointed out that the radiation concentrated to the receiver(the so-called ”efficient radiation”, Ieff ) is lower than the DNI since somereduction factors due to incident angles must be applied - see fig. 6.4. Suchfactors are called ”Incident Angle Modifiers”, IAM1 and IAM2: for fixed-receiver Concentrated Solar Power systems two IAMs are required: one forthe transversal plane and one for the longitudinal plane of the fresnel col-lector. For parabolic trough instead - as they always allow to cancel theincidence angle in the transversal plane - just one IAM is required.In order to produce the nominal outlet temperature in steady state condi-tions the mass flow must be controlled on the base of Ieff .

Ieff is obtained as follows

Ieff = DNI · IAM1 · IAM2 (6.1)

Figure 6.4. DNI correction to Ieff .

The pattern of the mass flow in the Solar Field in steady state conditionsis therefore similar to that of Ieff . Further variations are linked to transienteffects - e.g. during heating up or cooling down.

It must be also considered that for technical reasons the mass flow islimited between a minimum and a maximum value.


6.0.2 Power Block model

Figure 6.5. Organic Rankine Cycle schematization used in the plant model.

A simplified Power Block was modeled to perform simulations. This isnot exactly the same ORC cycle of the ORC-Plus project in Ben Guerir, butsimilar.It has been implemented with ”Thermoflex” - scheme in fig. 6.5, [17].

It produces as output

- the electric power generated by the turbine, Pel

- HTF temperature T7 at the outlet of the ORC heat exchangers train -fig. 6.1 (or T9 in fig. 6.5)

requiring as input data

- ambient temperature

- HTF temperature T6 - fig. 6.1

- mass flow rate m6 - fig. 6.1.


The simulated Power Block is a regenerative Organic Rankine Cycle us-ing an air cooled condenser.The nominal net electric power output is 1 MW.Heat exchangers work nominally between the operating temperatures of180◦C and 300◦C.

Here are reported some curves produced by ”thermoflex”:

Figure 6.6. Curves describing Power Block behavior, derived with [17].


6.1 1D-2P Thermocline Thermal Energy Stor-

age weekly simulations

Figure 6.7. Plant layout for Simulink simulation. Thermocline storage.Same picture at the beginning of the chapter in order to facilitate reading.

Fig. 6.7 - here reported again to facilitate reading - represents the schemeof the power plant simulated.A simple control logic was implemented to run the simulations:

i If the Solar Field produces a mass flow rate m4 higher than the nominalone required by the Power Block, m6,nom,

a if the Thermal Energy Storage is at least half charged, m6,nom isdirectly sent to Power Block heat exchangers, through the line”4-5-6” - fig. 6.7.The remaining mass flow rate coming from Solar Field - if presentand if not too high for a thermocline technology - is sent to theThermal Energy Storage through the line ”4-9” - if it is not com-pletely charged.This is implemented in order to avoid an excessive intermittenceof the power block.Moreover it is worth to notice that thermocline Thermal EnergyStorages require optimal velocities along the packed-bed, so m9

has been limited to about 16 kg/s.


b If the Thermal Energy storage is not half charged the mass flowrate coming from Solar Field - if not too high for a thermoclinetechnology - is sent to the Thermal Energy Storage through theline ”4-9”.

ii If the Solar Field produces a mass flow rate m4 lower than m6,nom,there are two possibilities:

a if the state of charge of the Thermal Energy Storage is sufficient,the mass flow produced in the Solar Field is sent to point 5 andit is mixed with m10 coming from the storage in order to generatethe required m6,nom in point 6;

b if Thermal Energy Storage is not sufficiently charged, the massflow produced in the Solar Field is sent to point 9 and it is storedin order to be later exploited.

iii If the Solar Field is not producing any mass flow rate m4 - it’s nighttimeor it is ricirculating oil through the dashed line in fig. 6.7 because of lackof solar irradiation - the ORC can be operated extracting m10 = m6,nom

from the Thermal Energy Storage.

This logic is clearly visible in the charts reported in the following sections.

It is worth to notice that actually each simulation is made of 8 days: thefirst day is a standard day included in simulations to preliminary charge thethermocline Thermal Energy Storage - in order to start the charge phasefrom a common starting temperature profile.


6.1.1 Summer week

Figure 6.8. Simulink interface. Simulation of 8 days in June.X-axis: time in seconds;Y-axis: [kg/s] and [MWhe]

During typical ”clear sky” days, characterized by very favourable summercondition, the plant does not present major problems from the point of viewof process control.

Let’s focus on one day of the simulated summer week, the 18th of June.Here follows an explanation of figure 6.9.

- In the upper chart the DNI and Ieff patterns are shown - section 6.0.1.

- In the second chart temperature at the Solar Field inlet and tempera-tures at the outlet of each collector are shown.

- In the third chart the trend of some mass flow rates of figure 6.7 isreported.As soon as solar irradiation is sufficient to produce a useful m4 a redpeak of mass flow rate coming from the Solar Field is produced - thecontrol logic works in order to keep T4 constant, section 6.0.1.During this initial phase m4 is totally sent to the storage - within thelimit of 16kg/s due to the adopted thermocline technology.Nothing is sent to the ORC Power Block until the Thermal EnergyStorage is half charged - as defined in the control logic, case i.b andcase ii.b, in section 6.1. Thus, it is possible to see a thin dark blue line- m9 - perfectly superimposed to m4 as long as it is below 16kg/s.Around 9:00 a.m. the storage is sufficiently charged, but still not neces-sary: a black line appears in the third graph of fig. 6.9, case i.a. Fromnow on, a constant mass flow rate m6,nom is sent to the Power Blockwhile the the additional mass flow rate coming from the Solar Field issent to the Thermal Energy Storage - m9 - that continues its chargephase.


Figure 6.9. 1D-2P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity production for a typicalday in June - the 18th.

It’s interesting to notice that at the end of the TES charging process,around 11:00 a.m., there’s an increase of m4 and of T4 - second graphin figure 6.9: at that moment T12 starts to increase to values higherthan the nominal one - at the end of the charge phase of a thermo-cline Thermal Energy Storage the temperature of the outlet mass flowrate increases. Therefore, Solar Field’s pumps react increasing m4 untiltheir limit. After pumps limit is reached, also T4 starts to increase, andmirrors defocusing is required - dotted red line in figure 6.9.From now on Thermal Energy Storage is completely charged and en-ergy contained in (m4 − m6) is lost.As soon as m4 falls down to values below m6,nom - around 5:00 p.m. -a light blue line appears - case ii.a. Indeed, in this phase the nominal


mass flow rate required by the Power Block - m6,nom - is provided by m5

- equal to m4 - togheter with m10 extracted from the Thermal EnergyStorage: the LCOE of the plant is thus improved.

- In the bottom chart, in fig. 6.9, ORC energy production is shown,togheter with m6 - the same of the third chart.

An analysis of the thermocline Thermal Energy Storage behavior is nowcarried out.The thermocline Thermal Energy Storage is completely charged from 6:45 to10:55 a.m. and completely discharged from 5:15 to 9.50 p.m. as it is shownin figure 6.10 more in detail.

Figure 6.10. What is happening inside the Thermal Energy Storage duringa complete charge (left) and the following complete discharge (right), June.

Something worth to be noticed:

- The complete charge phase can be seen from figure 6.9 also. The darkblue line - m9 - starts at 6.45 and ends at 10.55 a.m.This mass flow rate, m9, increases in time - following the trend of m4

- and at 7.45 a.m. becomes constant at its allowed maximum value.From 9:00 a.m. m4 is sent both to the Thermal Energy Storage and tothe Power Block - case i.a of the control logic. Thus, a discontinuityin m9 is visible.From 9:00 to 10:00 a.m. m9 increases again following m4, until itreaches again its maximum allowed value.


This velocity variation is clearly visible in the left plot of fig. 6.10:first-second curves distance and third-fourth curves distance are smallerthan second-third curve and fourth-fifth curve distances.

- The discharge phase begins with a low mass flow rate - light blue linein the third chart in figure 6.9. Then proceeds at nominal mass flowrate.This is clear in the right plot of fig. 6.10, where the first two tempera-ture profiles are closer than the other.

- Focusing on the right figure in 6.10, the bottom layers of the packed-bed present a temperature slightly lower than the nominal one (180◦C)at 9.15 and 9.50 p.m.The reason lies in T6 of figure 6.7: at the end of the discharge phase ofthe Thermal Energy Storage, T10 tends to decrease, therefore T6 alsodecreases making the ORC Power Block operating in off-design - section6.0.2. It follows that T7 is lower than its nominal value, therefore T11decreases too.


6.1.2 Spring/Autumn week

Figure 6.11. Simulink interface. Simulation of 8 days in March.X-axis: time in seconds;Y-axis: [kg/s] and [MWhe]

March, like spring and autumn, is characterized by medium-high valuesof DNI, but generally strongly intermittent.For example, the 18th of March is representative of a ”worst case” of variableconditions of DNI, due to frequent clouds passage.Operating a Concentrating Solar Power plant in such a day is very criticaldue to its strongly variable conditions - figg. 6.11 and 6.12.The operation of a system composed by a Solar Field directly connected to aPower Block is supposedly not possible. The addition of the storage systempermits to exploit some energy even if the total solar energy of the day is inthe order of 1/3 of the 18th of June.

Let’s focus on one day of the simulated spring week, the 18th of March.


Figure 6.12. 1D-2P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity production for a typicalday in March - the 18th.

Here follows an explanation of figure 6.12.

- DNI - then Ieff - is really intermittent. Such frequent clouds produce afrequent switching of the by-pass line in the Solar Field. This is clearlyvisible in the second graph of figure 6.12.Ieff results enough to produce m4 - fig. 6.7 - at a sufficient temperaturejust in few occasions:

i from 8:00 to 8:30 a.m.

ii from 10:00 to 10:15 a.m.

iii from 11:25 a.m. to 1:55 p.m.

iv from 2:05 to 3:15 p.m.


v from 3:25 to 4:00 p.m.

vi from 5:00 to 5:45 p.m.

- Despite DNI intermittency, m6 provided to the Power Block is constant,meaning that the Thermal Energy Storage worked properly - light blueline in the third chart is really active.

- The bottom chart shows energy production at the Power Block, relatedto m6.

The Thermal Energy Storage is not fully charged during the day due tolack of irradiance - fig. 6.13.

Figure 6.13. What is happening inside the Thermal Energy Storage duringMarch. Thermocline profiles variation in time during a charge phase (left) anda discharge phase (right).

Highlights of figure 6.13:

- At 3:00 p.m. only two thirds of the tank are charged, whereupondischarge phase begins - until 6:30 p.m.

- Strongly variable irradiance entails an inlet temperature to the ThermalEnergy Storage - T4 - highly oscillating, therefore profile temperature


inside the tank is mainly at a temperature lower than the nominal one(300◦C).This phenomenon has a negative effect on the Power Block efficiency -strongly dependent on T6 - see curves in Power Block section 6.0.2.


6.1.3 Winter week

Figure 6.14. Simulink interface. Simulation of 8 days in January.X-axis: time in seconds;Y-axis: [kg/s] and [MWhe]

Same considerations made for the Spring/Autumn week can be made:such strongly variable conditions of DNI, due to frequent clouds passage,makes operating a Concentrating Solar Power plant in such a period highlycritical. - figg. 6.14 and 6.15.A Thermal Energy Storage is required in order to exploit some irradiation.

Something peculiar happens during the 17th of January: due to the lackof solar radiation, the Power Block is never activated.Energy stored will be exploited the day after.

This is shown in figure 6.15, where some feature of the power plant arereported, and most of all in figure 6.16, where the daily thermal behavior ofthe Thermal Energy Storage is shown.


Figure 6.15. 1D-2P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity production for a typicalday in January - the 17th.


Figure 6.16. What is happening inside the Thermal Energy Storage duringJanuary. Thermocline profile variation during the charge phase.


Thermal Energy Storage is just charged during the 17th of January, sinceit is never sufficiently charged in order to start the ORC - see control logicin section 6.1.


6.1.4 Considerations

A summary of the main results obtained from simulations is reported in table6.1, where

- EnergyORC is the net electric energy produced at the Power Block inone week

- mORCTOT =∫time

m6dt

- TORCIN,avg is the T6 averaged over time, of course just on the timeinterval characterized by m6 6= 0 - notice that when m6 6= 0, it isconstant too

- Yearly net electricity production is computed considering 52 weeks peryear, and 13 weeks per season:

EnergyORC,Y ear = 13 ·EnORC,Sum + 26 ·EnORC,Spr/Aut + 13 ·EnORC,Win

Table 6.1. Summary: Results of 1D-2P thermocline simulations.

EnergyORC

[MWhel]mORCTOT


[◦C]Summer week 85.62 4947 298

Spring/Autumn week 46.66 2769 295.5Winter week 37.04 2176 296

Year 2807.74 - -


6.2 1D-1P Thermocline Thermal Energy Stor-

age weekly simulations

Results coming from the simulations of weekly operations of the CSP plantwith a 20MWhth thermocline Thermal Energy Storage simplified with a 1D-1P model are presented in this section.

Actually results are extremely similar to the results derived in section 6.1- where the Thermal Energy Storage was modeled with a 1D-2P approach.

Therefore here only a superposition of thermocline profiles in both cases -1P and 2P - is reported. In this way it is possible to have a visual comparisonof the two models.

For typical-day plots, like the graphs reported in the previous section 6.1,please check appendix C.


6.2.1 Summer, Spring/Autumn and Winter weeks

Figure 6.17. Comparison: thermocline profiles inside the Thermal EnergyStorage modeled with the 1D-1P approach and the 1D-2P approach, June.


Figure 6.18. Comparison: thermocline profiles inside the Thermal EnergyStorage modeled with the 1D-1P approach and the 1D-2P approach, March.


Figure 6.19. Comparison: thermocline profiles inside the Thermal EnergyStorage modeled with the 1D-1P approach and the 1D-2P approach, January.


Concluding, in any case, thermocline profiles developed with the simplermodel - 1D-1P - look steeper: the thermocline zone is thinner.With the simplified approach the Thermal Energy Storage is capable of stor-ing a little more energy in each cycle with respect to the storage modeledthrough the 1D-2P approach. This difference is actually really limited asreported in the next section, 6.2.2.



Comparison between

- figures 6.9 and C.1



show how 1D-1P and 1D-2P models work similarly.

Hence a numerical comparison between these two models is performed:in tab. 6.2 the same summary presented in subsection 6.1.4 is reported .

Table 6.2. Summary: Results of 1D-1P thermocline simulations.

EnergyORC

[MWhel]mORCTOT


[◦]Sum week 86.17(+0.6%) 4970(+0.4%) 298(+0.0%)

Spr/Aut week 47.02(+0.7%) 2784(+0.5%) 295.5(+0.0%)Win week 37.12(+0.2%) 2177(+0.0%) 296(+0.0%)

Year 2825.29(+0.6%) - -

The percentage difference between the two models, 1D-2P and 1D-1P, isreported in brackets.The obtained differences are clearly limited, with discrepancies below 1%.


6.3 2-Tanks Thermal Energy Storage weekly

simulations

Figure 6.20. Plant layout for Simulink simulation. Duble tank storage.

Fig. 6.20 represents the scheme of the simulated power plant, now witha double-tank storage.

The thermal behaviour of these tanks is simulated exactly the same waythe buffer of a thermocline Thermal Energy Storage is simulated - see section4.3.Knowing energy fluxes entering and exiting the tanks it is possible to eval-uate - through energy balances - the temperature of the liquid filling bothtanks at any time.

In this section results coming from the simulation of this new power plantlayout are presented.The aim is to assess differences between thermocline and double tank con-figurations, in particular from the ORC energy production standpoint.

Comparison

The comparison is performed between two technologies with same energeticalcapacity: both thermocline and double-tank Thermal Energy Storages canstore 20MWhth.


It is worth to notice that regarding the thermocline this value correspondsto its maximum capacity, Cmax, but the actual storable energy is of coursesomething less - look at the ”utilization factor” definition, eq. 2.8.

In particular, for the doubl-tank technology, knowing the energy capacityrequired, Cmax, the temperature operating range, ∆Trange, and mean specificheat capacity, c, and density, ρ, in the specific ∆Trange of the liquid exploited,it is possible to evaluate the required volume of the tanks:

V olume =Cmax

ρ · c ·∆Trange

=[J ][

kg

m3

]·[

J

kgK

]· [K]

Considering cyclindrical tanks, made of walls with constant thickness,

once this thickness δ is given, it is possible to minimize bothSurface

V olumeratio

and required material:

Vshell = 2πδ(rtank + δ)2 + π((rtank + δ)2 − r2tank

)H

and being

H =V olume

πr2tank

it is possible to minimize Vshell

Vshell = 2π(rtank + δ)2 + π((rtank + δ)2 − r2tank

)· V olumeπr2tank

In particular performing

∂Vshell∂rtank

= 0

The best rtank is found.

In the specific case of the ORC-Plus project in order to match the ther-mocline Thermal Energy Storage energy content - D=5 m and H=11 m - therequired dimensions for the two tanks are:

- Diameter: 7.7 m (+54%)

- Height: 7.1 m (-35%)


In order to have a consistent comparison, the implemented control logicis the same of sections 6.1 and 6.2.The only difference is that inlet velocity to the hot tank - m9 - is not sub-jected to limitations since there is no thermocline to preserve.

In this section only the description of the Summer week simulation isreported. It is possible to check results of the Spring/Autumn and Winterweeks in appendix C.At the end of the section yearly considerations are made.


6.3.1 Summer week

Figure 6.21. 2-Tanks model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity production for a typicalday in June - the 18th.

It is interesting to highlight some features of the resulting charts, in fig.6.21:

- DNI and Ieff are obviously the same as the two previously analyzedcases, where the Thermal Energy Storage was a 1D-2P and a 1D-1Pthermocline technology.

- Despite the solar irradiation is the same, there’s a clear difference inT4 and m4 produced by the Solar Field - second and third chart in fig.6.21 : they don’t present the discontinuity around midday.As already explained, when a thermocline Thermal Energy Storage is


giong to be completely charged its outlet temperature increases, causingan increase of mass flow rate along the Solar Field. This is not the casefor a double tank Thermal Energy Storage, which allows a smootheroperation for the Solar Field.

- Electricity production is slightly higher - fourth chart in fig. 6.21 -with respect to the simulations performed with thermocline TES sys-tems because, when both completely charged, the double-Tank is ac-tually storing more energy - the thermocline zone is never completelyextracted.

Figure 6.22. Hot Tank inlet and outlet mass flow rates (top) and Tempera-ture (bottom), both related with the level of Heat Storage Medium inside theHot Tank. 18th of June.

In figure 6.22 is shown the behavior of the Hot storage Tank:

- In the first chart are shown m9 and m10 - the same of figure 6.21 -togheter with the level of liquid stored inside the tank, which increasesfrom few centimeters to more than 7 meters in 4 hours.

- In the second chart the temperature inside the Tank is shown. It isworth to notice that it changes only during the charge phase - whilethe liquid level, the black line, is increasing. During inactivity anddischarge phases, the temperature Thot−tank slightly decreases due tolosses to the environment.It is worth to notice that at the beginning of the charging phase liquid is


fed to the Hot Tank at a temperature lower than 300◦C, about 260◦C.Therefore, even if at 7.30 a.m. T4 is already equal to 300◦C - as shownin the second chart of fig. 6.21 - Thot−tank reaches 300◦C only around10.00 a.m. - because of the thermal inertia of the liquid filling the tank.



In this section a summary of results obtained from simulations are reportedin tabular form.

As already done in subsection 6.2.2, in table 6.3 are shown both resultsand percentage difference with respect to 1D-2P results.

Table 6.3. Summary: Results of 2-Tanks simulations.

EnergyORC

[MWhel]mORCTOT


[◦C]Sum week 90.24(+5.4%) 5168(+4.4%) 299(+0.3%)

Spr/Aut week 52.69(+12.9%) 3077(+11.0%) 297(+0.5%)Win week 37.94(+2.4%) 2203(+1.2%) 297.5(+0.5%)

Year 3036.28(+8.1%) - -

There are some interesting differences, expecially in Spring/Autumn.They are due to the difference in energy defocused: thermocline technol-ogy requires more defocusing because it has a maximum allowed inlet valuefor m9.Moreover it is worth to notice that the percentage increase of total energyproduced - ∆EnergyORC - is always higher than the percentage increase ofmass flow to the ORC - ∆mORCTOT .The reason lies in the ORC block operations. Since TORCIN,avg - last columnof table 6.3 - is favoured using the double-Tank technology, also the efficiencyof the ORC is higher - section 6.0.2: both m6 and TORCIN,avg contribute tothe increase of EnergyORC - observing that Tamb is kept constant during sim-ulations - section 6.0.2.

With these values of Yearly elecrticity production it is possible to assessa Levelized Cost Of Electricity.

Moreover it is interesting to check the amount of energy defocused be-cause the storage could not accept energy from the Solar Field and the cycleefficiency in the days analysed - 18th of June, 18th of March and 17th of Jan-uary.

In winter there is no defocusing at all, practically for any technology, be-cause storages are completely charged with difficulty. The little defocusingfor the thermocline storage is related to the control logic - which limits themaximum mass flow rate.


Table 6.4. Energy defocused and efficiency of the storage technologies on the18th of June, on the 18th of March and on the 17th of January

Endefocused

[MWhth]ηcycle

2P 1P 2T 2P 1P 2TSum week 195.6 192.4 171.6 99% 99% 99%

Spr/Aut week 47.3 45.1 20 95% 96% 99%Win week 3.8 3.5 0 0% 0% 0%

The efficiency is zero since Ewithdrawn = 0 - section 2.2.1.

In summer defocusing is related to the premature filling of the storages;efficiencies are high because Eprovided and Ewithdrawn are similar:

- For thermocline TES in June ηcycle =16.96

17.18= 99percent

- For double-tank TES in June ηcycle =19.68

19.82= 99percent

The difference in the energy involved in the two cases are related to the pres-ence of the thermocline zone, as already explained.

In Spring and Autumn there is a big difference in the Endefocused betweenthermocline TES and double-tank TES. This is related to the fact that forthe former technology since the inlet mass flow rate is limited, the energydefocused won’t be recpurated with successive sunlight as it occurs in Sum-mer, because the tank won’t be completely charged: that is energy lost andcannot be recovered.Efficiencies are lower probably because of the variable inlet temperature tothe storage, which enhances the thermocline zone enlargement.

Chapter 7

Cost Analysis

Fixed-Charge Rate method

An economic assessment to establish the convenience of the thermocline tech-nology with respect to the 2-Tanks technology is performed in this chapter.The so-called ”Fixed-Charge Rate” method is used below - [31].

Through the Fixed-Charge Rate (FCR) method the investment cost isdistributed over the total plant life: the FCR is defined as the fraction ofthe total investment cost that the investor has to cover every year to facethe yearly depreciation or return of the capital, tax expense, and insuranceexpense associated with the installation of a particular generating unit forthe particular utility or company involved - [11] .

The FCR can be calculated as follows:

FCR = UCRF + p1 + p2 (7.1)

UCRF =d (1 + d)n

(1 + d)n − 1(7.2)

d = iEE% + iDD% (7.3)

where

- p1 and p2 are annual costs for property and insurance of the powerplant;

- UCRF is the Uniform Capital Recovery Factor

- n is the analysis year

- d is the nominal discount rate weighted on cost of debt and of equity.

141

7. Cost Analysis 142

Table 7.1. Economic assumptions for the evaluation of the FCR

AssumptionsPower plant life [y] 30

O & M costs [%] 1.5Debit share [%] 60

Equity share [%] 40Cost of debt [%] 5

Cost of equity [%] 13p1 + p2 [%] 1

With the assumptions reported in table 7.1 it is possible to find

FCR = 10.05%

Then, Levelized Cost of Electricity (LCOE) can be evaluated knowingthe yearly electric productivity of the plant (EnergyORC,Y ear in chapter 6,abbrev. EY ) and its Total Estimated Cost (TEC) through

LCOE =TEC · FCR

EY+CO&M

EY(7.4)

Total Estimated Cost

The TEC of the power plant can be obtained summing up Solar Field, PowerBlock and Thermal Energy Storage costs and increasing them by indirect,contingencies and owner’s costs.While for Solar Field and Power Block typical specfic costs are found inliterature, [11, 32], for the Thermal Energy Storage a specific cost evaluationis here carried out.

Thermocline TES The cost of components here evaluated are:

- Solid Filler

- Heat Transfer Fluid

- Tank shell

- Tank insulation

- Foundations


- Electrical, Instrumentation, Pipes, Valves, Fittings, as a percentage ofTank cost (shell and foundations).

For the first four components volumes are evaluated; thereafter, the costfor each of them is evaluated knowing density and specific cost, sc:

Cost = V ol · ρ · sc(

=[m3] [ kgm3

] [e

kg

])(7.5)

Regarding solid filler and Heat Transfer Fluid, once the void fraction co-efficient, ε is known, knowing the diameter, the height of the packed-bed andthe height of the buffer overlying the packed-bed at a given temperature,volumes can be easily evaluated.

Vfiller = Apb ·Hpb · (1− ε) (7.6)

Vl = Apb ·Hpb · ε+ Apb ·Hbuffer,@T (7.7)

where Apb and Hpb represent area and height of the packed-bed andHbuffer,@T is the height of the buffer at a given temperature.

Therefore the material specific cost [e/kg] and fluid and filler densitiesare the only parameter missing, looking at eq. 7.5 - see table 7.2.Notice that density of the fluid and height of the buffer have to be referredto the same temperature.

Regarding the Tank shell, since temperatures are not exceeding 300◦C itis possible to use carbon steel as construction material.Considering, for simplicity, a cylindrical shape for the Tank, knowing thediameter of the tank, height of the tank and thickness of the walls δ:

Vshell = 2πδ

(Dtank

2+ δ

)2

+ π

((Dtank

2+ δ

)2

−(Dtank

2

)2)Htank (7.8)

Then, carbon steel specific cost and density are required for shell costevaluation - table 7.2.

Regarding insulation, knowing its thickness λ, its volume can be evaluatedconsidering that it is placed all around the tank, except for the bottom side:


Vins = πλ

(Dtank

2+ δ + λ

)2

+π

((Dtank

2+ δ + λ

)2

−(Dtank

2+ δ

)2)Htank

(7.9)Also in this case, density and specific cost are required - table 7.2.

Table 7.2. Cost evaluation for filler, liquid, shell and insulation. Thermoclineconcept.

V [m3] ρ [kg/m3] Specific Cost [e/kg] Price [ke]Filler 107.0 4962 [24] 0.135 [24] 71.7

Liquid @ 180◦C 75.5 717.8 [30] 2.7 [24] 146.4Shell 4.7 7800 [33] 0.64 [24] 23.3

Insulation 60.1 100 [34] 2.0 [35] 12.0

Regarding foundations cost, this has been evaluated following reference[36]: mainly five layers are considered - see fig. 7.1

i 0.61 meters slab made of concrete, reinforced with steel

ii 1 centimeter of thermal foundation - insulating concrete

iii 0.40 meters of foamglass

iv 1 layer of firebricks

v steel slip plate of 6 mm.


Figure 7.1. Schematization of foundations structure for the tank.

Considering a square foundation area, as in figure 7.1, the volume of eachlayer can be easily calculated, therefore its cost - as reported in table 7.3.

Table 7.3. Foundations cost evaluation. Thermocline concept.

Quantity Specific Cost Price [ke]Layer 1, concrete 33.6 m3 85 e/m3

4.8Layer 1, steel 2456 kg 0.8 e/kgLayer 2, insulat. con. 0.5 m3 100 e/m3 0.04Layer 3, foamglass 22 m3 356 e/m3 7.8Layer 4, firebricks 1800 bricks 1 e/brick 1.8Layer 5, steel slip pl. 2581 kg 1.3 e/kg 3.4Total 17.8

For the first layer both concrete and steel costs are evaluated separately.For firebricks the number of bricks is evaluated knowing brick dimension -229x114x76 mm - [37].

Finally, Electrical, Instrumentation, Pipes, Valves and Fittings costs areevaluated as the 10 % of the cost of Tank shell and foundations.

Double-Tank TES For the double tank technology the very same evalu-ation is carried out. Liquid required by this technology has to be evaluated


through an energy balance, as already shown in paragraph ”Comparison” ofsection 6.3: indeed, knowing the energy capacity required, Cmax, the tem-perature operating range, ∆Trange, and mean specific heat capacity, c, anddensity, ρ, in the specific ∆Trange of the liquid exploited, it is possible toevaluate the liquid - oil in this case - volume required

Vliq =Cmax

ρ · c ·∆Trange

=[J ][

kg

m3

]·[

J

kgK

]· [K]

In the same paragraph it is also explained how tanks volumes are evalu-

ated, minimizing the external surface.

Table 7.4. Cost evaluation for filler, liquid, shell and insulation. Double-Tankconcept.

V [m3] ρ [kg/m3] Specific Cost [e/kg] Price [ke]Filler - - - -

Liquid @ 180◦C 308.4 717.8 [30] 2.7 [24] 597.7Shell 12.7 7800 [33] 0.64 [24] 63.5

Insulation 147.2 100 [34] 2.0 [24] 29.4

Table 7.5. Foundations cost evaluation. Double-Tank concept.

Quantity Specific Cost Price [ke]Layer 1, concrete 129.4 m3 85 e/m3

18.6Layer 1, steel 9448 kg 0.8 e/kgLayer 2, insulat. con. 1.8 m3 100 e/m3 0.2Layer 3, foamglass 84.1 m3 356 e/m3 29.9Layer 4, firebricks 7310 bricks 1 e/brick 7.3Layer 5, steel slip pl. 9930 kg 1.3 e/kg 12.9Total 68.9

It is useful to sum up results obtained until now in a table, 7.6:


Table 7.6. Sum up of costs for both TES technologies.

Costs in ke Thermocline Double-Tank ∆Shell 23.3 63.5 +173%

Insulation 12.0 29.4 +145%Oil 146.4 597.7 +308%

Filler 71.7 - -100%Foundations 17.8 68.9 +287%

El., Inst. ,Pip. ,Val. ,Fit. 4.1 13.2 +222%Total 304.4 772.8 +181%

Installation costs (x0.4) 110.1 309.1Total TES Cost 385.3 1081.9 +181%

Results in line with those reported in reference [36].

Installation costs are taken from [38], considering two tanks with workingtemperature lower than 300◦C.

∆ is the percentage difference between the two technologies investigated.It is clear that a Double-Tank Thermal Energy Storage implies higher costs,both because everything is doubled and because, in this case, it adopts tankswith larger diameter.Each component cost is at least doubled, except for the filler, that is notrequired. In any case, the final total TES cost results almost triplicated: 1.8times higher than thermocline Thermal Energy Storage cost.

Thus, the Total Estimated Cost can be evaluated assuming

- Solar Field specific cost : 200 e/m2 - [32, 11].The power plant simulated in chapter 6 is made of a Solar Field withan extension of 16334 m2 - it’s the sum of SF1 and SF2 of section 1.1.

- Power Block specific cost : 1000 e/kW - [32].The Power Block included in the power plant of chapter 6 has a netpower of 1 MW .


Table 7.7. Total Estimated Cost of the thermocline-TES and 2-Tanks-TESpower plant analyzed in chapter 6.

Total Estimated CostThermocline Double-TankCost[ke]

Share[%]

Cost[ke]

Share[%]

Solar Field 3267 70.2 3267 61.1Power Block 1000 21.5 1000 18.7

Thermal Energy Storage 385 8.3 1082 20.2Total Plant Cost 4652 5349

Indirect costs (x0.14)Owner and Conting. (x0.15)

TEC 6001 6900

Then LCOE can be evaluated thanks to equation 7.4:

LCOE =TEC · FCR

EY+CO&M

EY

Table 7.8. Levelized Cost of Electricity evaluation.

Thermocline Double-Tank ∆TEC [ke] 6001 6900 +15%

O & M [ke] 90 103 +15%EY MWhel/yr] 2808 3036 +8%

FCR [%] 10.05 10.05 -LCOE [e/kWhel] 0.247 0.262 +6%

- Operation & Maintenance costs are assumed to be 1.5% of the TotalEstimated Cost - table 7.1.

- Fixed-Charge Rate is evaluated at the beginning of this chapter.

- Energy produced annually by power plants is derived in chapter 6.

Conclusions Concluding, adopting a thermocline Thermal Energy Storageproduces a lower LCOE.It is possible to save 15 e/MWhel, despite it is a technology that inherentlydegrades the quality of a part of the heat introduced. Indeed, while thesavings on the TEC is about 15%, at the end of the year savings on the


LCOE are lower, meaning that the productivity of the plant has worsened.The Levelized Cost of Electricity of the power plant using the Double-Tanktechnology is 6% higher than the LCOE of the same power plant exploitingthe thermocline Thermal Energy Storage, with same storage capacity.

Chapter 8

Conclusions

Thermocline Thermal Energy Storage system is a technology cheaper thanthe state of the art double tank TES because it requires only one vessel.The storage is responsible of about 15-20% of the total investment cost inConcentrating Solar Power plants: research is pushing to reduce TES cost,leading to cheaper large storages, therefore to higher working hours of thepower plant and to lower Levelised Cost of Electricity.Packed-bed thermocline TES looks a good solution also because the storageis filled with low cost, high energy density, magnetite filler which displacesthe more expensive oil.Comparing costs of a double-tank storage with those of a thermocline stor-age having the same thermal capacity, main differences are related to theamount of oil required - 4 times higher - and to the foundations - their cost isalmost tripled. This costs are more than doubled, because magnetite energydensity is higher than oil energy density, and because tanks diameter, for thedouble-tank technology are found to be higher than the thermocline TESdiameter - foundation cost increases.

Unfortunately, thermocline TES is less performing than the double-tankTES configuration: in thermocline TES, a significant amount of thermal en-ergy is stored in the ”thermocline zone” at temperatures between Tmax andTmin: hence, a share of injected thermal energy at Tmax is degraded.

To predict thermocline behavior, so temperature distribution in the tank,two finite difference models have been developed and validated, both withexperimental data or with other validated models. Results are satisfactory.

The two simplified models, utilised for the simulation of thermocline ther-mal energy storages operations, have been implemented in Matlab-Simulink

150

8. Conclusions 151

environment.Differences between models are acceptable as long as the simulated heat ex-change between solid and fluid is efficient. If velocity of the fluid and/or heattransfer coefficient overcome a threshold - that depends on the tank design -the heat exchange between media becomes inefficient and the 1D-1P modelis no longer able to describe the phenomenon. But, in the field of ThermalEnergy Storages, since the heat transfer is maximized, the 1D-2P model andthe 1D-1P model give almost the same results: for a 20MWhth storage sys-tem discrepancies between the two models after one year are lower than 1%.This result is obtained simulating the operations of a complete power plant(SF, TES and PB) during typical weeks. TES operations has been simulatedwith both models, for the first set of simulation with the 1D-2P model andfor the second block of simulations with the 1D-1P model.

Coming back to the comparison with the double-tank technology, thesame plant was simulated having a double-tank TES instead of a thermoclineone. This analysis was performed in order to quantify the above-mentionedlower performances of the latter: exploiting the double-tank technology it ispossible to produce yearly the 8.1% more than what it is produced adoptingthe thermocline concept - 3036 MWhel against 2808 MWhel.This performance reduction is due to the fact that a big share of the with-drawn thermal energy is withdrawn at a temperature below its nominal value,hence it is converted at the power block in off-design conditions. Moreoverthe existence of the thermocline reduces the maximum storable energy in thethermocline TES.

Despite this, the 20MWh thermocline TES costs 385 ke while the 20MWhdouble-tank TES has a price of 1082 ke, allowing the 15% savings on theTotal Estimated Cost of the whole plant.Therefore the thermocline TES permits an LCOE reduction of the 6%.

8.1 Future improvements

In order to simulate the complete power plant the ORC model implementedwithin this thesis is simplified.Within the ORC-Plus project the power plant model is going to be improved,making also the Power Block realistic as much as possible.

Moreover the results coming from the simulations performed in this workare weekly results. Subsequently, yearly values were extrapolated. Of course

8. Conclusions 152

the accuracy of the simulation results could be improved with annual, longersimulations: the developed models are sufficiently computationally light.

Finally, the control logic implemented for the power plant operations issimple and not optimized. Future studies, exploiting the developed model,are expected to optimize the operations of the power plant.

Appendix A

Derivation of model equations

Here is reported how to obtain the system of equations used to describe thetwo models. The result to be reached is here recalled:

(i) Velocity equation:

u =ml

ρl

(επ

(D

2

)2) (A.1)

and continuity equation:∂ρl∂t

=∂ρlu

∂x(A.2)

(ii) Energy equation for the liquid phase:

ε (ρcp)l

(∂Tl∂t

+ u∂Tl∂x

)= kleff

∂2Tl∂x2


Vtotal(Tw − Tl)

(A.3)

(iii) Energy equation for the solid fillers:

(1− ε) (ρcp)s∂Ts∂t

= kseff∂2Ts∂x2

+ hv (Tl − Ts) + hwAs↔w

Vtotal(Tw − Ts)

(A.4)

153

A. Derivation of model equations 154

(iv) Energy equation for the wall:

(ρcp)w∂Tw∂t

= kw∂2Tw∂x2

+ hw

[Al↔w

Vw(Tl − Tw) +

As↔w

Vw(Ts − Tw)

]+

+(UA)extVw

(Text − Tw) (A.5)

Let’s analyze them one by one.

(i) Velocity equation A.1 comes from:

ml = ρluAavailable tothe liquid

(A.6)

But the Aavailable tothe liquid

is a parameter continuously varying through the

tank length. In the following pictures this concept is shown.

Figure A.1. Image of a packed bed composed by perfect spheres randomlydistributed. The liquid flow rate is very low, so turbolence is neglected.

Aavailable tothe liquid

(x) is function of height: the cross section of the packed bed

taken at the yellow level shows a high value of the liquid to solid su-perficial ratio (yellow area over grey area in A.2, b) ); while the crosssection of the packed bed highlighted in blue shows a low value of theliquid to solid superficial ratio (blue area over grey area in A.2, c)).


Figure A.2. Along the tank axis different sections show a different liquid tosolid ratio.

Velocity oscillates continuously along the x axis (actually in each di-rection!). In order to simplify calculations velocity u is kept constantevaluating a mean value of Aavailable to

the liquid, as follows

A =

∫ H

0Aavailable to

the liquid(x) dx

H(A.7)

This can be evaluated if ε is known:∫ H

0Aavailable to

the liquid(x) dx

AtankH=VliquidVtotal

= ε (A.8)

Where H is the total length of the packed bed and Atank = π

(Dtank

2

)2

Indeed combining A.7 and A.8

A = εAtank = επ

(Dtank

2

)2

(A.9)

Hence, finally, equation A.6 can be written as

u =ml

ρl

(επ

(D

2

)2) (A.10)

that is eq. A.1.

Continuity equation A.2 derives from a logical reasoning:If in a given volume V is entering a mass flow rate min and exiting


mout, the mass inside V - minside - will change in the unit of time asminside = min − mout.That is

ρinsideV = ρinuinAin − ρoutuoutAout

Considering Ain = Aout and dividing everything by the volume V

ρinside =ρinuin − ρoutuout

dx

Infintesimally∂ρl∂t

=∂ρlu

∂x

that is eq. A.2.

(ii) Energy equation for the liquid phase A.3 comes from the fol-lowing energy balance (fig. A.3):

Figure A.3. Heat fluxes for liquid phase

(mcp)l

(∂Tl

∂t+ u

∂Tl

∂x

)= klA

∂2Tl

∂x2dx + hconvAl↔s (Ts − Tl) + hconvAl↔w (Tw − Tl) (A.11)

Dividing by Vtotal

ρlVlcpl

Vtotal

(∂Tl

∂t+ u

∂Tl

∂x

)=

klA∂2Tl

∂x2dx

Atankdx+hconvAl↔s

Vtotal

(Ts − Tl) +hconvAl↔w

Vtotal

(Tw − Tl) (A.12)

That is

ε(ρcp)l

(∂Tl

∂t+ u

∂Tl

∂x

)= εkl

∂2Tl

∂x2+hconvAl↔s

Vtotal

(Ts − Tl) +hconvAl↔w

Vtotal

(Tw − Tl) (A.13)

Setting εkl = kleff ,hconvAl↔s

Vtotal= hv and hconv = hw we get


ε(ρcp

)l

(∂Tl

∂t+ u

∂Tl

∂x

)= kleff

∂2Tl

∂x2+ hv (Ts − Tl) + hw

Al↔w

Vtotal

(Tw − Tl) (A.14)

That is A.3 (and 4.5).

(iii) Energy equation for the solid phase A.4 comes from the fol-lowing energy balance (fig. A.4):

Figure A.4. Heat fluxes for solid phase

(mcp)s∂Ts

∂t= ks(Atank − A)

∂2Ts

∂x2dx + hconvAl↔s (Tl − Ts) + hconvAs↔w (Tw − Ts) (A.15)

Dividing by Vtotal

ρsVscps

Vtotal

∂Ts

∂t=

ks(Atank − A)∂2Ts

∂x2dx

Atankdx+hconvAl↔s

Vtotal

(Tl − Ts) +hconvAs↔w

Vtotal

(Tw − Ts) (A.16)

That is

(1 − ε)(ρcp)s∂Ts

∂t= (1 − ε)ks

∂2Ts

∂x2+hconvAl↔s

Vtotal

(Tl − Ts) +hconvAs↔w

Vtotal

(Tw − Ts) (A.17)

Setting (1− ε)ks = kseff ,hconvAl↔s

Vtotal= hv and hconv = hw we get

(1 − ε)(ρcp

)s

∂Ts

∂t= kseff

∂2Ts

∂x2+ hv (Tl − Ts) + hw

As↔w

Vtotal

(Tw − Ts) (A.18)


(iv) Energy equation for the wall A.5 comes from the followingenergy balance (fig. A.5):


Figure A.5. Heat fluxes for the wall on the horizontal plane, here conductionwith upper and lower layers is not represented

(mcp)w∂Tw

∂t= kwAwall

∂2Tw

∂x2dx + hconv [Al↔w (Tl − Tw) + As↔w (Ts − Tw)] + (UA)ext (Text − Tw)

(A.19)

Dividing in this case by Vwall, the result is here reported

ρwVwallcpw

Vwall

∂Tw

∂t=

kwAwall

∂2Tw

∂x2dx

Awalldx+ hconv

[Al↔w

Vwall

(Tl − Tw) +As↔w

Vwall

(Ts − Tw)

]+

+(UA)ext

Vwall

(Text − Tw) (A.20)

That is

(ρcp)w∂Tw

∂t= kw

∂2Tw

∂x2+ hconv

[Al↔w

Vwall

(Tl − Tw) +As↔w

Vwall

(Ts − Tw)

]+

(UA)ext

Vwall

(Text − Tw) (A.21)

Setting hconv = hw we get

(ρcp)w∂Tw

∂t= kw

∂2Tw

∂x2+ hw

[Al↔w

Vwall

(Tl − Tw) +As↔w

Vwall

(Ts − Tw)

]+

(UA)ext

Vwall

(Text − Tw) (A.22)


Global heat transfer coefficient U Heat losses - across insulationlayers - towards the environment can be described with a global heattransfer coefficient U. In order to evaluate qlost the electrical circuitanalogy is adopted (fig A.5).

R1 =lnrinsrwall

2πkinsdx(A.23)


where kins is the conduction coefficient of the insultaing material anddx the height of the cylinder.

R2 =1

hext 2πrinsdx︸︷︷︸Aext

(A.24)

where hext is the external heat tranfer coefficient.

Rtot = R1 +R2 (A.25)

∆Twall↔ext

Rtot

= qlost (A.26)

R−1tot =1

lnrinsrwall

2πkinsdx+

1

hext2πrinsdx

(A.27)

so,

R−1tot =1

lnrinsrwall

rins

kins+

1

hext︸︷︷︸Uext

Aext (A.28)

And it is possible to write

qlost = (UA)ext∆Twall↔ext (A.29)

Appendix B

1D-2P numerical model

Here is described how to implement a code for the solution of thermoclineTES equations through finite difference method.

Figure B.1. 1D discretization along tank axis, n steps.

So, being ”l” for liquid phase and ”s” for solid phase, it is possible towrite for each disk i

160

B. 1D-2P numerical model 161

(mcp)l

∂Tl∂t

+ (mcp)l∂Tl∂x

dx = klAdx∂2Tl∂x2

+ hconvAl↔s (Ts − Tl) + (UA)ext (Text − Tl)

(mcp)s∂Ts∂t

= ks(Aserb − A

)dx∂2Ts∂x2

+ hconvAl↔s (Tl − Ts)

Now, let’s divide the first equation by ε(mcp)l and the second one by(1− ε)(mcp)s

Tl = −

ml︷︸︸︷ρluA cpldx

ρl Adx︸︷︷︸Vl

cpl

∂Tl∂x

+klAdx

ρlAdxcpl

∂2Tl∂x2

+hconvAl↔s

ρlVlcpl(Ts − Tl) +

(UA)extρlVlcpl

(Text − Tl)

Ts =ks(Atank − A

)dx

ρs(Atank − A)dxcps

∂2Ts∂x2

+hconvAl↔s

ρsVscps(Tl − Ts)

Simplifying and recalling Vl = εVtotal

Tl = −u∂Tl

∂x+

εklερlcpl

∂2Tl∂x2

+hconvAl↔s

ερlcplVtotal(Ts − Tl) +

(UA)extερlcplVtotal

(Text − Tl)

Ts =(1− ε)ks

(1− ε)ρscps∂2Ts∂x2

+hconvAl↔s

(1− ε)ρscpsVtotal(Tl − Ts)

Through finite difference method

Tl,i = −uTl,i − Tl,i−1∆x

+kleffερlcpl

Tl,i−1 − 2Tl,i + Tl,i+1

∆x2+

hvερlcpl

(Ts,i − Tl,i) +

+(UA)extερlcplVtotal

(Text − Tl,i)

Ts,i =kseff

(1− ε)ρscpsTs,i−1 − 2Ts,i + Ts,i+1

∆x2+

hv(1− ε)ρscps

(Tl,i − Ts,i)

where

- kleff and kseff are evaluated with packe-bed correlations reported inreference [10]


- hv =hconvAl↔s

Vtotal

More schematically the system can be written as follows

Tl,i = Tl,i−1

B︷︸︸︷(u

∆x+

kleffερlcpl∆x

2

)+

+Tl,i

A︷︸︸︷(− u

∆x− 2kleffερlcpl∆x

2− hvερlcpl

− (UA)extερlcplVtotal

)+

+Tl,i+1

B1︷︸︸︷kleff

ερlcpl∆x2

+Ts,i

C︷︸︸︷hvερlcpl

+Text

E︷︸︸︷(UA)extερlcplVtotal

Ts,i = Ts,i−1kseff

(1− ε)ρscps∆x2︸︷︷︸F

+Ts,i

(−2kseff

(1− ε)ρscps∆x2− hv

(1− ε)ρscps

)︸︷︷︸

G

+

+Ts,i+1kseff

(1− ε)ρscps∆x2︸︷︷︸F

+Tl,ihv

(1− ε)ρscps︸︷︷︸D

There are second order derivatives, hence four boundary conditions arerequired. In fact, for the initial disk (i = 1) there is no Ti−1 while for thelast one there’s no Ti+1, both for solid and liquid phase.

Boundary conditions

• in any case, for solid filler it is chosen∂Ts∂x

∣∣∣∣x=top

= 0

∂Ts∂x


= 0


• if ml > 0 the tank is charging (conventionally):Tl,x=top = Tbuffer

∂Tl∂x


= 0

• if ml = 0 the tank is still:∂Tl∂x

∣∣∣∣x=top

= 0

∂Tl∂x


= 0

• if ml < 0 the tank is discharging:∂Tl∂x

∣∣∣∣x=top

= 0

Tl,x=bottom = Tcold

Then, introducing

A0 = A+B1

andG0 = G+ F

it is possible to rewrite the set of equations in a clearer form.

Tl,1...

Tl,nTs,1

...

Ts,n

=

A B1 0 0 C 0 0 0

B A. . . 0 0 C 0 0

0. . . . . . B1 0 0

. . . 00 0 B A0 0 0 0 CD 0 0 0 G0 F 0 0

0 D 0 0 F G. . . 0

0 0. . . 0 0

. . . G F0 0 0 D 0 0 F G0

Tl,1Tl,2

...Tl,nTs,1Ts,2

...Ts,n

+

EText + ThotBEText

...EText

00...0

It is possible to write the system simpler:

~T = M · ~T + ~V (B.1)


Algorithm explained Starting from an initial condition ~Tinitial the modelcomputes at each disk i - of the n disks subdividing the tank - physical andthermal properties thanks to a specific function implemented in matlab. Thisis possible knowing boundary conditions - TBuffer during the charge phaseand TfromORC during the discharge pahse.Velocity and mass flow rate are different at each disk too:

i Knowing inlet or outlet conditions u0 =mliquid

ρl

(επ

(Dtank

2

)2) can be

evaluated: this is a spatial boundary condition fot the differential con-tinuity equation - 4.4

ii Knowing temperature at each spatial step i, ρli at the ith step canbe evaluated, and - starting from an initial vector of densities madeof ρt=0

i - it is possible to solve the continuity equation 4.4 as followsρti − ρt−1i

∆t=ρti−1u


iii In such a way velocity at each step i is thus evaluated.

being

- ρti and uti the density and the velocity of the liquid at step i and time t

- ∆t is the time step imposed

- dx is the thickness of the ith step.

Now, if the packed-bed is subdivided in n steps, n Ai, Bi, B1i, Ci, Di,Ei, Fi and Gi are evaluated - one for each spatial step - and the descriptionof the thermocline behavior can be performed.

More precisely, the model solves the following

Tl,1...

Tl,nTs,1

...

Ts,n

=

A1 B11 0 0 C1 0 0 0

B2 A2. . . 0 0 C2 0 0

0. . . . . . B1n−1 0 0

. . . 00 0 Bn A0n 0 0 0 Cn

D1 0 0 0 G01 F1 0 0

0 D2 0 0 F2 G2. . . 0

0 0. . . 0 0

. . . Gn−1 Fn−10 0 0 Dn 0 0 Fn G0n

Tl,1Tl,2

...Tl,nTs,1Ts,2

...Ts,n

+

E1Text + ThotB1

E2Text...

EnText00...0


where the last subscript indicates the mesh step i.

Solving this system of equations, the variation of tempeature in time foreach disk is found (Tl,i and Ts,i). Integrating the vector of (Ti) during time,the thermal behaviour of the tank can be described: this is performed bySimulink solvers.

Appendix C

Simulations plots

C.1 1D-1P model simulation results

166

C. Simulations plots 167

C.1.1 Summer

Figure C.1. 1D-1P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity production for a typicalday in June - the 18th.


C.1.2 Spring/Autumn

Figure C.2. 1D-1P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity production for a typicalday in March - the 18th.


C.1.3 Winter

Figure C.3. 1D-1P model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity production for a typicalday in January - the 17th.

C.2 2-Tanks model simulation results


C.2.1 Spring/Autumn week

Figure C.4. 2-Tanks model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity production for a typicalday in March - the 18th.

Since during the 18th of March the thermocline is never completely chargedthere is no effect on m4 related to T12 - fig. 6.7.This is the reason why the second charts of figures C.4, 6.12 and C.2 areexactly the same.


Figure C.5. Hot Tank inlet and outlet mass flow rates (top) and Temperature(bottom), both related with the level of Heat Storage Medium inside the HotTank. 18th of March.

Liquid height variations are much more frequent in such a day, because ofthe intense compensation action performed by the Thermal Energy Storage- figure C.5.Values of Thot−tank in the second chart of figure C.5 are strictly related tovalues of T4 in figure C.4.


C.2.2 Winter week

Figure C.6. 2-Tanks model for TES. DNI, Ieff , Temperatures in the SolarField, mass flow rates in the system and electricity production for a typicalday in January - the 17th.

Again, since during the 17th of January the thermocline is never com-pletely charged also in this case the second charts of figures C.6, 6.15 andC.3 are exactly the same.


Figure C.7. Hot Tank inlet and outlet mass flow rates (top) and Temperature(bottom), both related with the level of Heat Storage Medium inside the HotTank. 17th of January.

It is interesting to notice that at the end of the day the Tank has storedsome energy, but not enough for starting a discharge phase.Unused energy will be exploited the following day.

Appendix D

Fluids properties correlations

Table D.1. Parameters for model implementation - [8]

Caloria HT 43 ρ kg ·m−3 871.1− 0.713 · Tcp J · kg−1 ·K−1 1836.8 + 3.456 · Tk W ·m−1 ·K−1 0.125 + 0.00014 · Tµ Pa · s 72.159 · T−2.096

Solar salt ρ kg ·m−3 2090− 0.636 · Tcp J · kg−1 ·K−1 1443 + 0.172 · Tk W ·m−1 ·K−1 0.443 + 0.00019 · Tµ Pa · s (22.174− 0.12 · T+

+2.281 · 10−4T 2+−1.474 · 10−7T 3)/1000

174

Appendix E

Solar One thermocline TESexperimental data

175

E. Solar One thermocline TES experimental data 176

Solar One experimental data. Discharge cycle. Day 179

00:00 04:00 08:00

ft ◦F m ◦C ft ◦F m ◦C ft ◦F m ◦C40 562,2 12,19 294,6 40 556,2 12,19 291,2 40 550,1 12,19 287,837,5 559,9 11,43 293,3 37,5 551,6 11,43 288,7 37,5 543,3 11,43 284,135 556,9 10,67 291,6 35 548,6 10,67 287,0 35 530,5 10,67 276,932,5 554,7 9,91 290,4 32,5 541,1 9,91 282,8 32,5 500,3 9,91 260,130 550,9 9,14 288,3 30 527,5 9,14 275,3 30 442,8 9,14 228,227,5 544,8 8,38 284,9 27,5 500,3 8,38 260,1 27,5 383,1 8,38 195,125 529,7 7,62 276,5 25 454,9 7,62 235,0 25 359,7 7,62 182,122,5 496,5 6,86 258,0 23,3 395,2 7,10 201,8 22,5 356,7 6,86 180,420 430,7 6,10 221,5 22,5 378,6 6,86 192,5 20 356,7 6,10 180,417,5 382,4 5,33 194,6 21 367,3 6,40 186,3 17,5 356,7 5,33 180,415 360,5 4,57 182,5 20 362,0 6,10 183,3 15 356,7 4,57 180,412,5 356,7 3,81 180,4 17,5 356,7 5,33 180,4 10 356,7 3,05 180,410 356,7 3,05 180,4 16,5 356,7 5,03 180,4 5 356,7 1,52 180,47,5 356,7 2,29 180,4 15 356,7 4,57 180,4 0 356,7 0,00 180,45 356,7 1,52 180,4 10 356,7 3,05 180,42,5 356,7 0,76 180,4 5 356,7 1,52 180,40 356,7 0,00 180,4 0 356,7 0,00 180,4

Table E.1. Points for experimental data interpolation.

Bibliography

[1] Energy Information Administration. Eia international energy outlook2017 (ieo2017). 2017.

[2] Tommaso Crescenzi; Massimo Falchetta; Alfredo Fontanella; EnzoMetelli; Adio Miliozzi; Francesco Spinelli; Luigi Sipione. Opportunita’di applicazione delle tecnologie solari termodinamiche in italia. 2016,ISBN 978-88-8286-355-7.

[3] ORC-Plus project. www.orc-plus.eu.

[4] Enerray web site. https:/www.enerray.com/solar-services/epc/case/studies/csp/iresen/morocco/.

[5] T. Fasquelle; Q. Falcoz; P. Neveu; F. Lecat; N. Boullet; G. Flamant.Operating results of a thermocline thermal energy storage included in aparabolic trough mini power plant. SolarPACES 2016.

[6] Mario Cascetta; Giorgio Cau; Pierpaolo Puddu; Fabio Serra. Numeri-cal investigation of a packed bed thermal energy storage systems withdifferent heat transfer fluids. 2013.

[7] James E. Pacheco; Steven K. Showalter; William J. Kolb. Developmentof a molten-salt thermocline thermal storage system for parabolic troughplants. 2002.

[8] J.-F. Hoffmann; T. Fasquelle; V. Goetz; X. Py. A thermocline thermalenergy storage system with filler materials for concentrated solar powerplants: Experimental data and numerical model sensitivity to differentexperimental tank scales. 2016.

[9] McDonnell Douglas Astronautics Company. 10 mwe solar thermal cen-tral receiver pilot plant mode 5 (test 11 50) and mode 6 (test 11 60) testreport. 1986.

177

BIBLIOGRAPHY 178

[10] Chao Xu; Zhifeng Wang; Yaling He; Xin Li; Fengwu Bai. Sensitivityanalysis of the numerical study on the thermal performance of a packed-bed molten salt thermocline thermal storage system. 2012.

[11] Marco Binotti. Linear fresnel reflectors: Study of the technology andsteps toward optimization. 2013.

[12] Massachusetts Web site of Mount Holyoke College.https://www.mtholyoke.edu/.

[13] International Energy Agency IEA. Technology roadmap: Thermal solarelectricity. 2014.

[14] director of SunShot Program R. Ramesh. The sunshot program review,u.s. department of energy, doe.energy.gov.

[15] T.E.W. Schumann. Heat transfer: a liquid flowing through a porousprism. 1929.

[16] Wikipedia web site. https://en.wikipedia.org/wiki/the-solar-project.

[17] Web site https://www.thermoflow.com/.

[18] M. Falchetta; T. Crescenzi; D. Mazzei; L. Merlo. Design of the archimede5 mw molten salt parabolic trough solar plant - proc. of solarpaces 2009conference, 15-18 september 2009, berlin, isbn 978-3-00-028755-8.

[19] M. Falchetta. Control and automation of the archimede molten salt op-erated solar field - proc. of solarpaces 2009 conference, 15-18 september2009, berlin, isbn 978-3-00-028755-8.

[20] M. Falchetta. Molten salts concentrating solar plants: their potentialcontribute to a better grid integration of solar power - proc. 1st int.workshop on integration of solar power into power systems - 24 october2011, aarhus (dk), energynautics, isbn 978-3-98 13870-4-9.

[21] Wikipedia web site. https://en.wikipedia.org/wiki/compact-linear-fresnel-reflector.

[22] IEA-ETSAP and IRENA. Csp technology brief e10. January 2013.

[23] Wikipedia web site. https://en.wikipedia.org/wiki/concentrated-solar-power. January 2013.

BIBLIOGRAPHY 179

[24] Y. Grosu; I. Ortega-Fernandez; L. Gonzalez-Fernandez; U. Nithiyanan-tham; Y. Filali Baba; A. Al Mers; A. Faik. Natural and by-productmaterials for thermocline-based thermal energy storage system at cspplant: Structural and thermophysical properties. 2018.

[25] Davide Ferruzza. Thermocline storage for concentrated solar power:Techno-economic performance evaluation of a multi-layered single tankstorage for solar tower plant. 2015.

[26] G.Angelini. Numerical modelling of molten-salt thermocline storage sys-tems: feasibility and criteria for performance improvement. 2012.

[27] C.P. Jeffreson. Prediction of breakthrough curves in packed beds: I.applicability of single parameter models.

[28] Personal communication with Pedro Azevedo. Visiting researchers atENEA.

[29] S. Flueckiger; Z. Yang; S. V. Garimella. Thermomechanical simulationof the solar one thermocline storage tank. 2012.

[30] A. Miliozzi; G.M. Giannuzzi; P. Taruini; A. La Barbera. Fluido ter-movettore: Dati di base della miscela di nitrati di sodio e potassio -enea/sol/rd/2001/07. 2001.

[31] W. Short; D. J. Packey; T. Holt. A manual for the economic evaluationof energy efficiency and renewable energy technologies. March 1995.

[32] NREL. System advisor model (sam) database.

[33] Sito web per densita’ acciaio. http://www.matweb.com/search/datasheetprint.aspx? matguid=9ccee2d0841a404ca504620085056e14.

[34] Sito web per densita’ lana di roccia.http://www.rockwool.it/prodotti/226.

[35] A. A. Robbiati. Sviluppo di un codice di calcolo per l’ottimizzazionedi un impianto solare termodinamico con fluido termovettore gassoso.2012.

[36] B.Kelly; D.Kearney. Thermal storage commercial plant design study fora 2-tank indirect molten salt system. 2004.

[37] Wikipedia web site. https://en.wikipedia.org/wiki/fire-brick.

BIBLIOGRAPHY 180

[38] G. Glatzmaier. Developing a cost model and methodology to estimatecapital costs for thermal energy storage. 2011.

[39] Gregory J. Kolb; C. K. Ho; T. R. Mancini; J. A. Gary. Power towertechnology roadmap andcost reduction plan.

[40] Inigo Ortega-Fernandez; I. Lorono; A. Faik; I. Uniz; J. Rodriguez-Aseguinolaza. Parametric analysis of a packed-bed thermal energy stor-age system.

[41] IEA International Energy Agency. Technology roadmap: Energy stor-age. 2014.

[42] R. Pfeffer. Heat and mass transport in multiparticle systems.

[43] N. Wakao; S. Kaguei. Heat and mass transfer in packed-beds.

[44] Maggioni P. Modellizzazione e ottimizzazione di accumuli termici gas-solido in impianti solari termodinamici. 2013.

[45] Cascetta M. Modellizzazione di un impianto solare termodinamico op-erante con fluidi termovettori gassosi ad alta temperatura. 2010.

[46] Manfredi C. Simulazione termofluidodinamica di collettore a concen-trazione parabolico lineare per centrali ad alta temperatura. 2003.

[47] Y. Grosu; I. Ortega-Fernandez; J. M. Lopez del Amo; A. Faik. Naturaland by-product materials for thermocline-based thermal energy storagesystem at csp plant: Compatibility with mineral oil and molten nitratesalt. 2018.

[48] Aleksi Simol. Insulation and application of thermal energy storage.

[49] Colombo M. et al. Le potenzialita’ dei motori a fluido organico nel solaretermodinamico.

[50] Lenert Andrej; Youngsuk Nam; Evelyn N. Wang. Heat transfer fluids.

[51] Modi Anish; Perez-Segarra; Carlos David. Thermocline thermal storagesystems for csp plants:one-dimensional numerical model and compara-tive analysis. 2014.

[52] Z. Yang ; S. V. Garimella. Cyclic operation of molten salts thermalenergy storage in thermoclines for solar power plants.

BIBLIOGRAPHY 181

[53] Elio E. Gonzo. Estimating correlations for the effective thermal conduc-tivity of granular materials.

[54] R. Bayon; E. Rojas. Analysis of packed-bed thermocline storage tankperformace by means of a new analytical function.

[55] J. H. Lienhard IV; J. H. Lienhard V. A heat transfer textbook, fourthedition.

[56] Y. A. Cengel; M. A. Boles. Thermodynamics, an engineering approach.

[57] A. Amiri; K. Vafai. Analysis of dispersion effects and non-thermalequilibrium, non-darcian, variable porosity incompressible flow throughporous media.

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