Modelling calcium looping at industrial scale for energy storage in concentrating solar power plants

Journal Pre-proof Modelling calcium looping at industrial scale for energy storage in concentrating solar power plants Manuel Bailera, Sara Pascual, Pilar Lisbona, Luis M. Romeo PII: S0360-5442(21)00555-7 DOI: https://doi.org/10.1016/j.energy.2021.120306 Reference: EGY 120306 To appear in: Energy Received Date: 6 October 2020 Revised Date: 28 January 2021 Accepted Date: 4 March 2021 Please cite this article as: Bailera M, Pascual S, Lisbona P, Romeo LM, Modelling calcium looping at industrial scale for energy storage in concentrating solar power plants, Energy, https://doi.org/10.1016/ j.energy.2021.120306. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2021 Elsevier Ltd. All rights reserved. Manuel Bailera: Conceptualization, Methodology, Software, Validation, Formal analysis, Writing – Original Draft, Writing – Review & Editing, Visualization. Sara Pascual: Conceptualization, Methodology, Software, Formal analysis, Writing – Original Draft, Writing – Review & Editing, Visualization. Pilar Lisbona: Conceptualization, Methodology, Writing – Original Draft, Writing – Review & Editing. Luis M Romeo: Conceptualization, Writing – Original Draft, Writing – Review & Editing, Funding acquisition. Journal Pre-proof 1 Modelling calcium looping at industrial scale for energy storage in concentrating solar power plants Manuel Bailera a , Sara Pascual a , Pilar Lisbona b and Luis M. Romeo a a Escuela de Ingeniería y Arquitectura. Universidad de Zaragoza, Campus Río Ebro, María de Luna 3, 50018, Zaragoza, Spain b Fundación Agencia Aragonesa para la Investigación y el Desarrollo (ARAID), Zaragoza, Spain Abstract: Ca-Looping represents one of the most promising technologies for thermochemical energy storage. This process based on the carbonation-calcination cycle of CaO offers a high potential to be coupled with solar power plants for its long-term storage capacity and high temperatures. Previous studies analyzed different configurations of CaL integrated into power cycles aiming to improve efficiency. However, most of these assessments based on lumped models did not account for scale effect in the most critical reactor. In this work, a detailed 1D-model of a large-scale carbonator is included in the comprehensive model of the integrated facility. The results obtained served to assess the available heat, the minimum technical part load of this equipment, the required size of the storage tanks and the overall efficiency of the plant. The main issue in the operation of large-size carbonator is the heat removal, thus a multi-tube internally cooled reactor is proposed. The designed carbonator provides 80 MWth at nominal operation and 40 MWth at minimum part load operation. The sizing of storage tanks depends on the operation management, ranging between 5,700-11,400 m 3 for 15 hours. Different efficiencies of the system were defined and presented through operating maps, as a function of the reactor loads. Keywords: Energy storage, Calcium looping, Concentrated solar power, CO2, Thermochemical energy storage 1. Introduction Deploying renewable energy sources (RES) contributes to the decarbonisation of energy systems [1]. However, curtailments are necessary when RES represent above 10% of the annual electricity generation [2], since operators only control 5–10% of wind and solar dispatch [3]. To face this situation, the European Commission proposed energy storage as solution [4] since 10–20% variable RES shares are estimated for about 50 regions in the world by 2023 [5]. In this study, we focus on concentrating solar power (CSP) plants. Dispatch of CSP has a peak around noon and significant variations over minutes or hours due to cloud coverage. To manage electricity production, half of the CSP plants worldwide use thermal energy storage (TES) [6]. TES systems retain thermal energy within specific materials and release it when needed. According to the physical phenomena occurring while absorbing/releasing the energy, thermal energy storage is classified in sensible TES, latent TES and thermochemical energy storage (TCES). Sensible TES use materials with high specific heat (131–4187 J/kg·K) to store/release the energy by heating/cooling their mass. These systems are simple, reliable and cheap, but the energy storage density is low (1001–4453 kJ/m 3 ·K) [7]. Most of sensible TES used in commercial CSP plants are based on molten salts [8], combining two tanks (packed beds) of high and low temperature for shortand long-term storage [9]. Latent TES use materials with high latent heat (112–260 kJ/kg), to store/release the energy during phase transitions at constant temperature, what reduces fluctuations in electricity production [7]. Phase change takes place between liquid and solid, in order to have small variations in volume (<10%) [10] and high energy storage densities (50 to 150 kWh/t). However, the low thermal conductivity of these materials (< 0.5 W/m·K) prolongs the time of charging and discharging energy [7]. To obtain large heat exchange surfaces in latent TES, shell and tubes configurations are commonly used [11][12]. Journal Pre-proof 2 Thermochemical energy storage systems are based upon reversible chemical reactions (endothermic in one direction and exothermic in the other) to store/release energy through a cyclic process. As TCES works at very high temperatures (450–1300 ºC), it is the most promising candidate for thermal energy storage in new generation CSP plants working above 800 ºC [7][13]. Moreover, TCES provides seasonal storage with no heat losses (the energy is stored in the chemical bound of the compounds) with higher energy densities than sensible and latent TES (about 240-1090 kWh/t) [14]. Among many materials for TCES (hydrides, metal oxides and carbonate salts), the calcium looping reaction (CaL), CaO 3 ↔CaO+CO 2 , stands out because the material is cheap and earthabundant, products are non-toxic, and energy storage density reaches 390 kWh/t [14][15]. The utilization of CaL for TCES was proposed by Barker in 1974 [16], and the scientific community intensified its research during the last decade. Recently, several papers dealt with the integration of CaL TCES with different power cycles [17][18], efficiency optimization [19][20][21], and management of the storage system [22]. Ortiz et al. [17] and Tesio et al. [18] assessed different power plant options to find the technology that leads to better performance when integrated with calcium looping TCES. Both of them concluded that best results are achieved with CO 2 power cycles (CO 2 closed Brayton cycle according to Ortiz, and supercritical CO 2 power block according to Tesio). After identifying the most suitable technology, they optimized the efficiency of the concept by studying different plant layouts. They found overall efficiencies (net electric production to net solar thermal input) in the range 32-44% for the CO 2 closed Brayton cycle [19][20], and 40.4% for the supercritical CO 2 cycle [21]. Regarding management, Bravo et al. used a multi-objective optimization framework to determine the best operational strategy. However, authors state that further research on this issue is necessary to reach authoritative conclusions, as economic aspects were not included in the optimization [22]. So far, the reactors design has not been taken into account in the existing studies which are mainly based on lumped models of the process. However, the extension of the chemical reactions in the carbonator and calciner clearly affects the mass flows, the management of storages and the overall efficiency of the plant [14]. The main reason is that experiments on calcium looping applied to TCES are scarce making difficult the validation of detailed models of the reactors [23]. Solar calcination (CaO 3 →CaO+CO 2 , endothermic) has been tested by the Paul Scherrer Institute in a cyclone gas-particle separator with a window-less aperture. Solar thermal input of the prototype was 54 kW, reaching 85% limestone conversion with 88% energy efficiency [24]. Carbonation (CaO+CO 2 → CaO 3 , exothermic), within the framework of solar CaL, is tested in the SOCRATCES project. They use an entrained flow reactor of 10 kW thermal output, cooled by external cooling coils. The cooling fluid is air, which is later used in a Stirling engine to produce power [25]. At industrial scale, the computational fluid dynamics simulations of the Paul Scherrer Institute show that solar calcination may operate effectively at 55 MW thermal inputs by using a falling particle receiver. In this type of reactors, a curtain of falling CaCO 3 particles absorb the solar radiation that enters through the aperture of the receiver [24]. Regarding carbonation, Bailera et al. showed that energy could not be properly recovered in entrained flow reactors when scaled-up to industrial scale, if they are cooled by external coils. Since the reactor heats up, the reaction reaches the equilibrium temperature and it progresses limited by the rate at which heat is evacuated. This leads to unfeasible dimensions of reactors (7 m diameter and 52 m length for carbonators of 100 MW solar input) [26]. Therefore, other potential configurations must be evaluated to improve the heat removal in industrial carbonators for CaL TCES. In this work, we focus on the two main gaps found in literature when assessing the utilization of calcium looping as thermochemical energy storage in concentrating solar power plants: (i) the design of a suitable reactor for carbonation at industrial scale and (ii) the analysis of the concept taken into account the reactor design and its behavior at part load operation. Thus, the novelty of this work consist in quantifying a realistic efficiency for CaL TCES at industrial scale. First, the paper introduces the concept of calcium looping TCES in CSP, establishing the case under study. Then, the methodology presents the carbonator modelling and the design criteria from few kW to Journal Pre-proof 3 100 MW scale. Results show how part load operations in carbonator modify mass flows and the storage management (CaO, CaCO 3 and CO 2 ). Finally, we quantify the overall performance of the plant. 2. Calcium looping for energy storage in CSP plants The energy storage system based on calcium looping process consists of two reactors, namely calciner and carbonator. In the calciner, solids fall from the top, and solar radiation provides thermal energy for calcination (Eq. (1)). In our study, we consider 100 MW of solar power input as nominal operation. If the availability of solar energy is less than the nominal power, the calciner will operate at partial load. The calciner load is defined as the ratio between the available solar power input and the nominal solar power input (100 MW). The solids mass flow is a mixture of limestone and lime (197.7 kg/s), and its inlet temperature is set at 850 ºC through the heat exchanger HE-ER CaCO3+CaO (Fig. 1). The operating temperature inside the calciner is kept below 950 ºC, to limit degradation of the solid particles [19]. CaCO  ↔CaO+CO  ∆H  =180kJ/mol, (1) Lime and CO 2 are obtained after calcination of limestone. These products are conveyed to the second reactor, where carbonation takes place and the stored chemical energy is recovered (reverse of Eq. (1)). The heat released is transferred to the power block through a cooling fluid. The inlet temperature of the carbonator is set at 850 ºC [20], for which reason the heat exchangers HE-ER CaO and HE-ER CO2 are used. Finally, the solids leaving the carbonator are conveyed again to the calciner, thus closing the loop. Fig. 1. Thermochemical storage system based on Ca-looping process for a large scale CSP plant: nominal operation mode. Full calcination can be assumed at the outlet of the calciner. However, the mass composition after carbonation depends on the average sorption activity of the solid population, as only part of the CaO particle will react with the CO 2 [27]. An average maximum conversion of 13.54% is assumed for the selected limestone [26][28][29] and the molar ratio CaO:CO 2 at the carbonator inlet is set at 6.8:1 [28][29][30]. Additionally, a small fraction of lime is purged from the system (f p =1%) and the corresponding amount of fresh limestone is added to compensate the removal of calcium. The addition of fresh limestone to the system increases the average sorption activity of lime population given the decay of sorption capacity of individual lime particles with the number of cycles. In this layout, lime is purged after calcination, while limestone is added at the inlet of calciner. It must be noted that there is a net input of carbon and oxygen into the system, because the carbon dioxide released from fresh limestone calcination is accumulated. Therefore, a small amount of CO 2 has to be removed from the Journal Pre-proof 4 loop to close the carbon mass balance. Actually, the only CO 2 exiting the carbonator is this net mass input coming from the difference between the fresh CaCO 3 and the purged CaO, as the molar ratio in the carbonator was set to consume the rest of CO 2 during reaction. This mode of operation corresponds to the nominal point used for carbon capture applications in which neither storage nor discharge of energy take place. The energy entering the calciner is recovered in the carbonator without delaying power production. This mode of operation is not useful for energy storage applications but its proper description is significant to understand the performance of the calcium looping. In the following subsections, the layout of the system under storage and discharge operation modes is described. 2.1. Energy storage operation mode When the electricity demand from the system decays or the selling price of electricity does not cover the operating cost, part of the solar energy handled in the CSP is stored. Under energy storage operation, a fraction of the lime (f st,CaO ) and CO 2 (f st,CO2 ) obtained through calcination are stored instead of conveyed to the carbonator (Fig. 2). Thus, the thermal power released in the carbonator is reduced, and the stored products allow producing thermal energy in a later period. Additionally, to keep constant the mass flow entering the calciner, solids must be added to the loop through the discharge from a limestone and lime reservoir. The discharge flow of this tank is defined as a fraction of the nominal solid flow leaving the carbonator outlet (f dch,CaCO3 ). Fig. 2. Thermochemical storage system based on Ca-looping process for a large scale CSP plant: partial energy storage operation mode. If the fraction of CaO and CO 2 sent to storage tanks increases, the load of the carbonator may be reduced below its minimum partial load, requiring to shut-down the reactor (the part load in the carbonator is defined as the ratio between the input mas flow and the nominal input mass flow). Under this situation, the plant starts operating only in storage mode, not producing thermal power in the carbonator (Fig. 3). The discharge fraction from the limestone reservoir f dch,CaCO3 will depend on the amount of solar energy entering the receiver. Journal Pre-proof 5 Fig. 3. Thermochemical storage system based on Ca-looping process for a large scale CSP plant: energy storage operation mode. In this study, the properties of stored CO 2 are 100 ºC and 73 bar [20], through a compression stage including two cooling steps to 50 °C (HE-EE CO2 ) and 100 ºC (HE-EE CO2,C ). Solids storage temperature and pressure are 200 °C (HE-EE CaO ) and 1 bar [19]. 2.2. Energy release operation mode Whenever solar energy is not enough to keep carbonator working at a specific load, the plant can run under energy release mode. In this case, part of the previously stored lime and CO 2 are now discharged from their reservoirs to enter in the carbonator and produce the desired thermal power (Fig. 4). The CO 2 and CaO leaving the storage tanks are defined as a fraction of the nominal flow of CO 2 (f dch,CO2 ) and CaO (f dch,CaO ) at calciner outlet. Additionally, as there is not enough available solar energy to completely calcine the mass flow exiting the carbonator, part of this is diverted to storage (f st,CaCO3 ) before closing the loop. Fig. 4. Thermochemical storage system based on Ca-looping process for a large scale CSP plant: partial energy discharge operation mode. When solar power is not available, the operation is limited to release stored energy (Fig. 5). The mass flows discharged from the reservoirs depend on the demanded thermal power to be produced. In our study, whether we store or release energy, the fractions of CaO and CO 2 entering and exiting Journal Pre-proof 6 the tanks will be the same in order to keep constant the CaO:CO 2 molar ratio in the carbonator (i.e., f st,CaO =f st,CO2 and f dch,CO2 =f dch,CaO ). Heat losses of heat exchangers are assumed as 2% of the total released energy. Fig. 5. Thermochemical storage system based on Ca-looping process for a large scale CSP plant: energy discharge operation mode. 3. Methodology Methodology covers carbonator modelling, design criteria and assessment of the storage tanks required for the correct management of the plant. 3.1. Carbonator modelling The energy removed from the carbonator represents the main source of heat sent to the power cycle. However, the operating load in the carbonator remarkably varies throughout the day due to cloud coverage, the solar radiation pattern and the demand of electricity. Therefore, its design must be assessed to quantify the effects of partial load operation in the overall efficiency of the system. In this sense, a detailed model of a large scale carbonator reactor has been developed. Besides, the minimum technical load in the carbonator have an effect on the size of storage tanks, and will determine the minimum amount of heat available for the power cycle. The carbonator is an entrained flow reactor in which reactants entrance is located at the top. This is a complex system where heterogeneous exothermic chemical reactions take place together with heat transport phenomena. The model considers carbonation kinetics, heat transfer mechanisms and the specific geometry of the reactor, in order to compute axial profiles of conversion, temperature and residence time under different operating loads. The reactor was discretized in 100 slices of constant length, for which the equations presented in the following subsections were computed. In the case of those equations that comprise an integration, some of the variables are assumed constant along the slice to perform the integration (whenever the case, it is mentioned in the text). The model is solved in steady-state through a numerical mesh with 100 discrete 1-D elements. The Fig. 6 illustrates the flowchart of the carbonator model for one slice of the discretized reactor. There are four main blocks that simulate the solid phase, the gas phase, the kinetics and the heat transfer. The ‘gas phase’ module provides information to the ‘solid phase’ module in order to compute the downward velocity of the solids falling through the reactor. Then, the ‘solid phase’ module provides the residence time of the solids to the ‘kinetics’ module to calculate the conversion. Also, both the ‘gas phase’ and the ‘solid phase’ modules transfer the mole flows data to the ‘heat transfer’ module in order to calculate the final temperature inside the reactor. At this point, the computed values of conversion and temperature must be re-introduced in the different Journal Pre-proof 7 modules (iterative process) until they converge. Once convergence is achieved, the data on residence times, conversion and temperature are provided to the next discretized slice. The former allows computing the total residence time, while conversion and temperature are used as initial values in the iterative loops of the next slice. Fig. 6. Carbonator modelling flowchart for the discretized slice of index i, and its interactions with the previous (i-1) and next (i+1) slice. It must be noted that each slice does not only depends on the previous one, but also in the following one because of the heat transfer model. Since the reactor uses a counter-current cooling configuration, the initial temperature of the cooling fluid is provided by the following slice, which is not yet solved. The boundary condition that fixed the inlet temperature of the cooling fluid, in the Journal Pre-proof 14 ¬     v . b6 0 = 3 . 66 + . 0 . 049 + 0 . 020 4 v ⁄ 0 · ·¸ v B . B 1 + 0 . 065 · ·¸ v  . Ú   (51) To compute the local Nusselt number at an axial position   , Eq. (42) is used, obtaining the following expression (Eq. (52)): ¬ v . b6 0 = 3 . 66 + ·¸ v B . B · . 1 . 8473 · ·¸ v  . Ú · 4 v + 0 . 754 · ·¸ v  . Ú − 5 . 88 · 4 v − 2 . 4 0 10  · 4 v · 3 1 + 0 . 065 · ·¸ v  . Ú 8   (52) Where the Graetz and Prandtl numbers are calculated with Eq. (37) and Eq. (40). With this methodology, the temperature along the carbonator can be calculated by knowing the initial temperature of reactants and cooling fluid. 3.2. Design criteria at different scales The scale of the system is characterized by the solar power available in the calciner,  !v (from 10 kW to 100 MW). The corresponding input flows of CaO and CO 2 entering the carbonator (at nominal load) are computed through the energy balance in the calciner (Eq. (53)).  !v = h !"# . Ü° ! 0 ·  !"# ,  ,  + h !#  . Ü° ! 0 ·  !#  ,  ,  + h !"# . Ü° ! 0 ·  !"# , m − h !"!#  . d° ! 0 ·  !"!#  ,  ,  − h !"# . d° ! 0 ·  !"# ,  ,  − h !"!#  . ° ! 0 ·  !"!#  , 7 (53) where h zY is the specific enthalpy of the component } at temperature 2,  z,, is the mole flow of component } entering the carbonator (which are outlet flows in the calciner),  z,, is the mole flow of component } exiting the carbonator (which are inlet flows in the calciner),  !"#,m is the lime purged after exiting the calciner, and  !"!#,7 is the fresh limestone introduced in the calciner to replace the purge. All these mole flows can be written as a function of  !"#,, (Eq. (54) to Eq. (57)) by fixing the conversion achieved in the carbonator (assumed as / Ý =0.1354) and the CaO:CO 2 molar ratio (R=6.8776).  !#  ,  ,  =  !"# ,  ,  R (54)  !"!#  ,  ,  =  !"# ,  ,  · / Ý (55)  !"# ,  ,  =  !"# ,  ,  · . 1 − / Ý 0 (56)  !"# , m =  !"!#  , 7 =  !"# ,  ,  · R 1 R − / Ý V (57) Operating in Eq. (53) and using enthalpy data from Aspen Plus database, it is found Eq. (58) and Eq. (59) for the calculation of the nominal input flows of CaO and CO 2 in the carbonator as a function of the solar power entering the calciner.  !"# ,  ,  =  !v 32 , 162 . 19  ß Hà H± á           §         ) !"# ,  ,  =  !v 573 . 53 ß Hà H, á  (58)  !#  ,  ,  =  !v 221 , 198 . 68  ß Hà H± á         §         ) !#  ,  ,  =  !v 5 , 027 . 24 ß Hà H, á  (59) In addition to the input flow calculation, some design criteria have been followed to keep similar conversion and temperature profiles along the reactor at different scales. First, a single tube reactor with inner cooling has been modelled, looking for proper heat removal at small scale (10 kW). This reactor is made of two concentric tubes of small diameter. The reactants flow from top to bottom through the outer tube, while cooling fluid flows in counter-current throughout the inner tube (Fig. 7). The aim is to recover few kW at this stage. The required input flows for 10 kW are 0.0174 kg/s of CaO and 0.0020 kg/s of CO 2 . Once proper dimensions are fixed for single-tube, a multi-tube configuration is stablished. This multi-tube reactor encloses 150 – 200 cooling tubes, between which the reactants flow from top to Journal Pre-proof 15 bottom. In principle, the cooling pipes are of the same diameter and length that the one used in single-tube configuration (the enclosure is also of the same length than the cooling pipes). The cooling tubes are set in triangular configuration and the distance among them is fixed in order to keep the cross-sectional area in proportion to the increment of reactants volume. In other words, the cross-sectional area through which the reactants flow is ¬ times the area of the single tube configuration, being ¬ the number of cooling tubes inside the enclosure of the multi-tube. This configuration is aimed to reach the MW scale (about  !v =2 MW), by keeping similar temperature profiles along the reactor. Fig. 7. Carbonator configurations for small and large scale. Lastly, the large-scale multi-tube configuration is designed by keeping constant the ratio between the length of the reactor and the velocity of the gas-solid mixture flowing downward (/&), and the ratio between the length of the reactor and the diameter of the enclosure (/l) [38]. Besides, the number of cooling tubes is increased, instead of increasing their diameter. The aims of this configuration is to achieve the 100 MWth scale and to quantify the behavior at partial load. Again, we look for conserving temperature profiles, and outlet temperatures of both products and cooling fluids, since power production is the main objective of this reactor. 3.3. Operation modes and efficiency definitions The two operations considered in this study are energy storage operation mode (ESOM) and energy release operation mode (EROM). Under these modes, a large number of operation points leads to different pairs of calciner-carbonator powers and different values of storage power. The operation points are related to the mass flowrates stored or released from the tanks. 3.3.1. Energy storage operation mode Two parameters are used to describe the operation points of ESOM: the fraction of the lime produced in the calciner that is sent to storage, and the fraction of limestone in the tank that is discharged. The storage fraction of lime,  ',!"# in Eq. (60), is the ratio between the mass flowrate diverted to the CaO storage tank and the maximum mass flowrate that could leave the calciner operating at full capacity (100 MW).  ',!"# =  ¡â¢,ZF  ¡â¢,ãâä (60) Journal Pre-proof 16 The discharge fraction of limestone,  g°,!"!# in Eq. (61), is the ratio between the mass flowrate discharged from the limestone tank and the maximum mass flowrate that could leave the carbonator operating at full capacity.  g°,!"!# =  ¡â¡¢¶¡â¢,åÖæ  ¡â¡¢¶¡â¢,ãâä (61) All the potential pairs of these two parameters cover the operation points encompassed during ESOM. The specific storage consumption (SSC) expressed in Eq. (62) provides the amount of total energy (thermal and electrical) required to store a mass unit of lime. This value is useful to understand whether the storage process is profitable or not in terms of energy under specific operation points. It must be kept in mind the qualitative interest of the parameter but its limitation as quantitative measure given the mix of energy types in its definition. The energy consumed in the process includes the fraction of heat used to produce the lime sent to the storage tank ( !v,' ), the preheating of the limestone discharged from the storage tank which is later stored in the form of lime ( Xçç½!"!#,' ) and the electric power demanded in the compression of the stored carbon dioxide (è m|6''| ). 55== é ¡p,ZFCé êNNë¡â¡¢¶,ZFCì ÖÐãhÒTZZÐÒ  ¡â¢,ZF (62) A storage efficiency, η st , is defined by Eq. (63) to compare the amount of stored energy and the net energy consumed during the storage process. The stored energy comprises the sensible heat of the stored substances (lime and carbon dioxide, =5 !#C!"#,' ) and the chemical energy potentially stored in the lime which will be latter carbonated, ∆\ ½ ∙ !"!#,!½ . This parameter provides an idea of the portion of energy that is stored and the portion that is lost during the storage process. î ' = é ZF,¡â¢ é ¡p,ZFCé êNNë¡â¡¢¶,ZFCì ÖÐãhÒTZZÐÒ = !W¡¢O¡â¢,ZFC∆XëG∙~ ¡â¡¢¶,¡ë é ¡p,ZFCé êNNë¡â¡¢¶,ZFCì ÖÐãhÒTZZÐÒ  (63) Another significant value for the operation is the efficiency of the carbonator in reference to the energy provided by this equipment, η CR , Eq. (64). It compares the amount of power released in the carbonator and the energy invested. The latter includes the heat of calcination required to produce the lime fed into the carbonator,  !v,!½ , and the preheat of this limestone prior the calciner,  Xçç½!"!#,!½ . î !½ = é ¡ë é ¡p,¡ëCé êNNë¡â¡¢¶,¡ë (64) Finally, an efficiency related to the available thermal energy is defined by Eq. (25) and Eq. (65), with the former including the sensible heat of the stored substances. This efficiency compares the available heat to the energy invested. The available heat accounts for the thermal power released in the carbonator, and the thermal power provided by the different heat exchangers (EE heat exchangers always provide thermal power, while ER heat exchangers only provide thermal power under ESOM). î "q,B = é ¡ëC∑é êNNNCé êNNë¡¢OCé êNNë¡â¢ é ¡pCé êNNë¡â¡¢¶C!W¡â¡¢¶¡â¢,åÖæ (25) î "q.çW#ï0 = é ¡ëC∑é êNNNCé êNNë¡¢OCé êNNë¡â¢ é ¡pCé êNNë¡â¡¢¶ (65) 3.3.2. Energy release operation mode Analogously, the storage fraction of the limestone produced in the carbonator, Eq. (66), and the discharge fraction of lime from the storage tanks, Eq. (67), describe the set of operation points that conform the energy release operation mode. Journal Pre-proof 17  ',!"!# =  ¡â¡¢¶¡â¢,ZF  ¡â¡¢¶¡â¢,ãâä (66)  g°,!"# =  ¡â¢,åÖæ  ¡â¢,ãâä (67) The storage fraction of limestone,  ',!"!# , represents the ratio between the mass flowrate diverted to the storage tank from the outlet stream of the carbonator and the maximum mass flowrate which could leave the carbonator operating at full capacity. The discharge fraction of lime,  g°,!"# , is the relation between the mass flowrate discharged from the CaO tank and the maximum mass flowrate of CaO leaving the calciner at full load. The energy efficiency in the carbonator, η CR , under EROM is calculated through Eq. (68). The energy invested in this process includes (i) all the heat of calcination demanded in the calciner,  !v , (since no calcined material is diverted to storage tanks under EROM) (ii) the storage consumption of the mass flowrate of lime discharged from the tanks, (iii) the preheating of this limestone before introduced into the calciner,  Xçç½!"!# and (iv) the preheating of the mass flowrates of lime and carbon dioxide,  Xçç½!# and  Xçç½!"# (if needed). î !½ = é ¡ë é ¡pCWW!∙ ¡â¢,åÖæCé êNNë¡â¡¢¶Cé êNNë¡¢OCé êNNë¡â¢ (68) Under EROM, the thermal efficiency of the system is defined both considering, Eq. (30), and not considering, by Eq. (69), the sensible heat of the stored substances. In this case, the available heat only includes the thermal power from the carbonator and EE heat exchangers. î "q,B = é ¡ëC∑é êNNN é ¡pCé êNNë¡â¡¢¶C!W¡â¢,åÖæC!W¡¢O,åÖæCWW!∙ ¡â¢,åÖæCé êNNë¡¢OCé êNNë¡â¢ (30) î "q.ç½#ï0 = é ¡ëC∑é êNNN é ¡pCé êNNë¡â¡¢¶CWW!∙ ¡â¢,åÖæCé êNNë¡¢OCé êNNë¡â¢ (69) 3.4. Sizing of storage tanks The sizing of storage tanks accounts for the operating mode and the introduced/extracted mass flowrates of CO 2 , CaO and CaCO 3 . The operating mode dictates the number of hours and the storage/discharge fractions. Storage and discharge fractions directly define the inlet and outlet flowrates, while the number of hours provides the time interval to integrate. The storage volume of the tanks is calculated through Eq. (70). w '  .+0=oL  rµM ÐÑF f Ql+  G +w ',  (70) The maximum storage flowrate of CO 2 and CaO takes place when solar calciner operates at nominal load and carbonator operates at minimum load. 4. Results In this section, the model validation and the results for the smalland large-scale carbonators are presented. Besides, it is assessed the partial load operation for the large-scale carbonator. Lastly, a model of the coupled CaL TCES and CSP systems is run at threshold operation conditions to provide the sizing of storage tanks. 4.1. Model validation The first important issue to be validated is the independency of results with respect to the number of discretized elements (i.e., with the length of each discretized slice). As case of study, it has been Journal Pre-proof 18 chosen the single-tube configuration operating at 50% partial load (the part load in the carbonator is defined as the ratio between the input mass flow and the nominal input mass flow). The Fig. 8 presents the relative error that exists in the most important computed variables versus the number of discretization elements, with respect to 300 discretization elements (in a 4-meter reactor, the latter means slices of 1.3 cm). It can be seen that the relative error remains below 1% in all cases whenever the number of discretization elements is above 15. Therefore, we select 100 discretization elements for the simulations presented in Section 4.2. Fig. 8. Relative error in the most relevant computed variables vs. the number of discretization elements (with respect to 300 discretization elements). These small variations in the computed variables come from assuming constant volume flow in Eq. (8) when integrating over the length of each discretized element. This can be clearly seen in Fig. 9 when comparing the temperature and conversion profiles of a simulation with 100 discretization elements (depicted with symbols) with a simulation with 300 discretization elements (depicted with lines). In those regions in which the variation of volume flow occurs faster (i.e., with higher reaction rates), the error becomes noticeable. It must be noted that, since the case chosen as example is operating at 50% partial load, the reaction occurs in a shorter length, what accentuates the relative error. If the reactor operates at full load, the variation in volume is less steep, and the error less significant. Furthermore, the selected operating conditions in our simulations make CO 2 to react almost completely, so any variation in volume flow is remarkable compared to the total volume flow in the reactor. This makes the relative error to be more significant. Still, our simulation keeps relative errors below 1% in the variables of interest. In the case of analysing a reactor setup with higher ratio of CO 2 :CaO, the error would be even lower. Journal Pre-proof 19 Fig. 9. Comparison between 100 (symbols) and 300 (lines) discretization elements, for the results on CaO conversion and temperature profiles (reactor and cooling sides) vs. length (from top to bottom), in a single-tube carbonator operating at 50% partial load. The second important issue to be validated is the reproducibility of experimental results. In this aspect, the model is validated using experimental results of an entrained flow carbonator from Plou et al. [39]. The reactor of Plou et al. is a 24-meter spiral-shaped stainless steel tube, with an external diameter of 3/8” (inner diameter of 7.54 mm). The gas velocity used during the experiments avoids saltation conditions within the entrained flow regime (i.e., avoids falling of particles towards the wall). The reactor is kept isothermal at 650 °C along the whole path. Three different materials were analysed: two types of high-purity calcined lime and one cement raw meal. The results of the material tagged as “Lime #1” are used in this study for comparison as it has a similar value of / H (i.e., conversion at the end of the reaction controlled phase) and +  (i.e., the time taken to reach a / H /2 conversion) than the material assumed in the simulations of this study. Lime #1 has / H = 0.10 and +  about 2 seconds, while the material used in our simulations has / H =0.1354 and +  =1.515 seconds. These are typical conversions of highly deactivated materials. The Fig. 10 shows the CO 2 capture efficiency, which is defined as the CO 2 captured versus the maximum possible according to the equilibrium. The experiments were carried out with a gas velocity of 13.5 m/s at 650 °C and 1 bar (about 2.4·10 M kg/s). The gas is composed of 10% CO 2 and 90% air. The mass ratio between the solid and the gas was varied between 0.125 and 0.400 by modifying the mass of CaO entered in the reactor. Fig. 10. CO 2 capture efficiency achieved in the entrained flow reactor of Plou et al. [39] and in the simulations of this study under the same setup, as a function of the solid/gas mass ratio. The results show a good agreement with the experiments of Plou et al. for Lime #1. The measured residence time is 1.8 seconds, while the simulated residence time 1.78 seconds for the gas and 1.77 seconds for the solids. 4.2. Carbonator assessment The technical data regarding the three carbonators under study are presented in Table 2 (single-tube at lab scale, 7.6 kW, multi-tube at pilot scale, 1.4 MW, and the large-scale multi-tube, 79.9 MW). The reactants enter at 850 ºC and 2 bar, and the cooling fluid is CO 2 entering at 100 ºC and 50 bar. The mass of the cooling fluid is calculated to set its exit temperature at 650 ºC. Table 2. Technical data of the studied carbonators. Single-tube Multi-tube Large-scale multi-tube Carbonator Length (m) 4.0 5.0 15.0 Design criteria (Section 3.2) Enclosure inner diameter (m) 0.074 0.970 3.3 Design criteria (Section 3.2) CaO mass inlet (kg/s) 0.01740 3.2533 178.6 Eq. (58) Journal Pre-proof 20 CO 2 mass inlet (kg/s) 0.00198 0.3712 20.8 Eq. (59) Final CaO conversion (%) 13.53 13.54 13.54 Output of the model Gas residence time (s) 7.1 10.0 7.55 Output of the model Solid residence time (s) 4.8 6.6 6.51 Output of the model Inlet T (ºC) 850.0 850.0 850.0 Boundary condition Outlet T (ºC) 850.7 844.8 841.1 Output of the model Average T (ºC) 850.8 871.5 850.6 Output of the model Pressure (bar) 2.0 2.0 2.0 Fixed Reynolds (-) 34 – 493 0.4 – 5.5 1.5 – 21.3 Output of the model Cooling tubes Length (m) 4.0 5.0 15.0 Design criteria (Section 3.2) Inner diameter (m) 0.02 0.02 0.02 Design criteria (Section 3.2) Number of tubes (-) 1 187 2,705 Design criteria (Section 3.2) CO 2 mass inlet (total) (kg/s) 0.0121 2.32 127.4 Output of the model (fixed 2 7 ,  ) Recovered heat (MW) 0.0076 1.45 79.9 Output of the model Inlet T (ºC) 100.0 100.0 100.0 Boundary condition Outlet T (ºC) 650.0 650.0 650.0 Fixed Pressure (bar) 50.0 50.0 42.8 – 50.0 Output of the model Reynolds (-) 9,862 – 19,995 10,098 – 20,476 38,411 – 77,804 Output of the model The CaO conversion and temperature profiles along the reactor are preserved at the different scales (Fig. 11). At pilot scale (multi-tube reactor), the convective coefficient diminishes one order of magnitude in the reactants side; i.e. shell side. Therefore, the reactor has to be extended 1 meter in length (from 4 m in single tube to 5 meter in multi-tube) in order to bring the products again to 850 ºC and thus recover their sensible heat. Otherwise, part of the exothermal heat from carbonation would not be recovered in the reactor. Besides, when following the criteria of constant /& and /l ratios to pass from mid to large scale, the mass of cooling fluid per tube has to be increased to maintain its exit temperature at 650 ºC. Doing so, the length of the reactor can be shortened to 15 m (instead of the 19 m that would result from the /l restriction). The final configuration is suitable for a large-scale carbonation, in terms of operating temperature (average 850.6 ºC, computed as ∑2 v B ÇB 100 ⁄), residence time (6.5 – 7.5 s) and dimensions (15 m length and 3.3 m diameter). Journal Pre-proof 21 Journal Pre-proof 22 Fig. 11. CaO conversion and temperature profiles (reactor and cooling sides) vs. length (from top to bottom) for the single-tube, multi-tube and large-scale multi-tube configurations. Profiles are kept similar at the different scales (arrows depict the direction of the flow). Once the reactor at large-scale is defined, partial load operation is assessed (the part load in the carbonator is defined as the ratio between the input mass flow and the nominal input mass flow). Reducing the load in the carbonator means that the inlet mass flowrates of reactants are proportionally reduced, so the available exothermal heat from carbonation will diminish. Therefore, the amount of cooling fluid that can be heated diminishes (always keeping its exit temperature at 650 ºC). The definition of minimum partial load of the reactor corresponds with the point in which the cooling mass flowrate is reduced to the half of its nominal value; i.e. the minimum flowrate of cooling fluid will be 63.7 kg/s of CO 2 at 650 ºC (below this mass flow we assumed that the coupling with the power block cannot longer take place) [40]. This point corresponds to a partial load of 23.9% in the carbonator (Fig. 12) (only the 23.9% of the nominal input flow of CO 2 and CaO is entering the carbonator). Journal Pre-proof 23 Fig. 12. Cooling mass flow and recovered heat vs. operating load (ratio between the input mass flow in the carbonator and its nominal input mass flow) for the large-scale multi-tube. Outlet temperature of cooling fluid is kept at 650 ºC. When load is reduced, the volume of reactants is lowered and so does their velocity throughout the reactor. The reaction ends earlier, and the cooling fluid starts recovering sensible heat from the products. 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[41] Song C, Wang P, Makse HA. A phase diagram for jammed matter. Nature 2008;453:629–32. doi:10.1038/nature06981. Journal Pre-proof • Calcium looping thermochemical energy storage has been modelled at large scale. • The minimum operating load of carbonator is 23.9% due to technical limitations. • The available energy efficiency of the overall system is in the range 55 – 97%. • The require size to store CaO and CaCO 3 solids during 15 h is 5,700 – 11,400 m 3 . Journal Pre-proof Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Journal Pre-proof