Analysis of an energy storage system using reversible calcium hydroxide in fluidised-bed reactors

Applied Thermal Engineering 217 (2022) 119180 Available online 17 August 2022 1359-4311/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Research Paper Analysis of an energy storage system using reversible calcium hydroxide in fluidised-bed reactors O. Bartoli a , b , R. Chacartegui a , d , * , A. Carro a , C. Ortiz c , U. Desideri b , J.A. Becerra a , d a Dpto. Ingeniería Energ´ etica, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain b Department of Energy, Systems, Territory and Construction Engineering, University of Pisa, Largo Lucio Lazzarino 1, Pisa 56122, Italy c Materials and Sustainability Group, Department of Engineering, Universidad Loyola Andalucía, Avda. De las Universidades s/n, 41704 Dos Hermanas, Seville, Spain d Universidad de Sevilla, Laboratory of Engineering for Energy and Envorinmental Sustainability, 41092 Seville, Spain ARTICLE INFO Keywords: Thermochemical Energy Storage Calcium Hydroxide Calcium Oxide Fluidised Bed Reactor Solar energy ABSTRACT The widespread use of renewable energy requires the support of high-capacity energy storage systems. This work proposes a thermochemical energy storage system for concentrated solar power plants based on the reversible hydration/dehydration process of the calcium hydroxide. It is a single fluidised bed reactor concept with alternating dehydration-hydration processes, charging and discharging alternating reactions, with superheated steam as fluidising agent. The system has been modelled using Aspen Plus™, including equilibrium data and hydrodynamic performance of the reactor. The model has been used to evaluate the effect of different parameters of the reactor, such as geometry, average particle size, or inlet streams conditions, on the performance of the reactor and the system. The thermal integration of the system was optimised using pinch analysis. For the proposed layouts, round-trip efficiencies values of 68 % are obtained. The economic analyses show specific investment costs between 4170 $/kWe and 3250 $/kWe for plants in the range of 31 MW to 45 MW, which are competitive with those expected for plants with storage of molten salts in this power range. LCOE values between 67 $/MWh and 83 $/MWh were obtained. The analyses show how these values highly depend on the fresh material replacement requirements related to the deactivation of the material and operational strategies. The results show the interest in further developments of this concept for concentrated solar power plants. 1. Introduction Increasing the share of renewable energy sources worldwide is crucial to reducing greenhouse gas emissions and mitigating climate change. Due to the inherent intermittency of renewables, such an increase in production requires the development of large-scale storage capacities. In this context, thermal energy storage systems (TES) are key technologies to balance supply and demand fluctuations [1]. Concentrated solar power (CSP) plants are key renewable technologies due to their capability to integrate thermal energy storage [3]. These thermal storage technologies can be classified according to the physics of the heat storage and release: sensible, latent, and thermochemical[2]. The most extended energy storage technology in CSP plants is the molten salt technology based on sensible heat storage. It is successfully operative at a commercial scale. Still, it has challenges. Storage material costs are approximately 50 % of the total energy storage system. Corrosion-related challenges affect integration and durability [4,5] and their operating temperature range is constrained to 200–600 ◦C to avoid salt solidification and degradation, respectively [6]. There is an intense research activity for alternatives to molten salts to improve some of their characteristics [7]. Latent storage systems exploit polycrystalline materials (PCMs) that absorb or release thermal energy through a phase transition [8]. Studies on PCMs show that it is possible to store around ten times more heat than sensible systems [9]. However, both physical heat storage systems (sensible and latent) are not suitable for long-term storage due to thermal losses related to their nature. Thermochemical storage systems (TCES) are emerging as an alternative to large-scale thermal energy storage [10]. TCES use reversible chemical reactions to store and release thermal energy. Energy is accumulated in chemical bonds during the endothermic reaction (charging phase) and released during the exothermic reaction (discharging phase). The main advantage of TCES is that long storage periods can be expected, as long as the components can be stored without losing their chemical potential [11]. Different reversible chemical reactions have been proposed for thermochemical energy storage, each * Corresponding author. E-mail address: [email protected] (R. Chacartegui). Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng https://doi.org/10.1016/j.applthermaleng.2022.119180 Received 6 May 2022; Received in revised form 15 July 2022; Accepted 15 August 2022 Applied Thermal Engineering 217 (2022) 119180 2 characterised by its temperature range, reaction energy and states of reactants and products [12]. Among the most promising TCES for large-scale applications are the systems based on calcium hydroxide, Ca(OH)2. The system is based on the reversibility of endothermic dehydration of Ca(OH) 2 and exothermic hydration of CaO (Eq. (1)). Its reaction enthalpy is approximately 109 kJ/mol, and the application temperature range is between 700 and 1000 K [13]. The concept is based on abundant non-toxic and low-cost materials and good reversibility of the reactions. Steam is used as the fluidising agent. It can be handled and stored efficiently. The discharge temperatures are in the range of 600 ◦C, which allows the integration of mature power technologies, such as the Rankine cycle. Ca(OH)2(s)↔CaO(s)+H2O(v)ΔHreaction =109 kJ/mol (1) Calcium hydroxide, such as TCES, has been proposed focusing on applications such as solar thermal power [26], process heat [14], heat pumps [15] or engine preheating [16]. Its use as energy storage has also been studied at the laboratory level [17,18]. These studies include different reactors: fixed bed reactors [13], small-scale fluidised bed reactors [19,20], plate exchange reactors [21] or moving bed reactors [22]. Schmidt et al. [18] developed a 10 kW proof of concept of a novel thermochemical reactor based on calcium hydroxide. Several strategies were experimentally analysed, using the exothermic step to heat air to 450 ◦C. Another experimental reactor was carried out by Cosquillo et al. [22]. They developed a moving-bed reactor filled with CaO/Ca(OH) 2 with ceramic shell and Al 2 O 3 nanostructured particles, which improved the cyclability and conversion properties of the materials. Xu et al. [23] evaluated the influence of material porosity for both direct and indirect heating strategies. Different authors have analysed the thermal cycling stability of the process. Dai et al. [24] found that after 20 cycles, there was no performance degradation, a favourable characteristic compared to deactivation in carbonate-based TCES systems [25]. However, agglomeration and poor thermal conductivity are challenging for the technology deployment [24]. The integration of CSP-TCES using calcium hydroxide technology for large-scale storage applications has only been partially studied. Bayon et al. [26] presented a techno-economic evaluation of solid–gas TCES systems for solar thermal applications, considering three plant models with a reference power of 100 MWe: a reference plant with molten salt storage, a closed loop cycle, and an open cycle. Thermal efficiency of 98.5 % was obtained by integrating a calcium hydroxide energy storage system, with a small parasitic consumption and a capital cost of 4.78 $/MJ. For molten salts presented values of 9.61–16.78 $/MJ. Criado et al. [27] studied a thermochemical energy storage process based on CaO/Ca(OH) 2 in a single circulating fluidised bed reactor coupled to large solid storage silos. In the base case, with a maximum thermal power of 100 MWth during hydration, a thermal efficiency (thermal to thermal) of the process of 63 % was obtained. Tapaches et al. [28] proposed a CSP storage system based on the Ca(OH) 2 /CaO reaction, using a single fixed bed reactor integrated with a Rankine steam cycle and estimated costs in the range of 12–60 € /MWh, depending on the location considered in the plant. Pelay et al. presented the energy and exergy analysis [29] and the LCA [30] of the integration of CSP-TCES with Rankine cycle power cycles through the conceptual study of three different configurations from a base case of a 100 MW e solar tower plant. Overall efficiency (thermal to electrical) values in the range of 34.9–39.2 % were obtained. Based on these promising results, new designs and integration schemes are needed to advance the integration of the calcium hydroxide-based TCES system in CSP plants. This work proposes and analyses a new integration layout of calcium hydroxide thermochemical storage system. It is based on a single fluidised bed reactor (FB) integration for both the charging and discharging steps that operate Nomenclature η RT Round-Trip Efficiency η PB Power Block Efficiency η tot Overall system efficiency χ HY Solids Conversion During Hydration Reaction χ DEHY Solids Conversion During the Dehydration Reaction ξ Ratio between the thermal power spent to preheat the water from the storage tank to the superheated reactor inlet conditions and the thermal power available from the reactor. All considered during hydration v The ratio of the steam flow rate reacted to the total steam flow rate entering the reactor during hydration. τ Average residence time of particles in the fluidised bed NCa Number of moles in fluidised bed FCa Molar flow rate of solid entering the fluidised bed dp Particle diameter Tsolidin Temperature of the solid input to the reactor [K] TReactor Reactor temperature [K] Tgasin Temperature of gas that enters the reactor [K] ˙ mgasin Gas mass flow incoming to the reactor [kg/s] ˙ mvap Steam mass flow incoming to the reactor [kg/s] ˙ msolidin Solid mass flow incoming to the reactor [kg/s] mHTF Heat transfer fluid (compressed air) [kg/s] pReactor Reactor pressure [bar] DReactor Reactor diameter [m] HReactor Reactor height [m] Hinlet Insertion height of solid [m] Houtlet Solid output height [m] DCyclone Cyclone diameter [m] dt Tube diameter [m] a Distance between tubes [m] Lt Tube length [m] Ns Number of layers Nt Number of tubes CC Capital investment cost [$ kW] O&Mfix Fix operation and maintenance cost [$ kW yr] O&Mvar Variable operation and maintenance cost [$ kWh] CF Capacity Factor Fcost Fuel cost [$ MM Btu] HR Heat rate [Btu kWh] Abbreviations TES Thermal energy storage CSP: Concetrated Solar Power TCES: Thermochemical energy storage PCM: Phase-change material FB: Fluidised bed HY: Hydration reaction (discharge phase of the system) DEHY: Dehydration reaction (charging phase of the system) HY-1/2: Hydration reaction for the first/second integration study DEHY-1/2: Dehydration reaction for the first / second integration study HTF: Heat Transfer Fluid (compressed air at 15 bar) PSD: Particle size distribution LCOE: Levelized cost of electricity [$ MWh] ESDeff : Effective Energy Storage Density ESDeff =QHY FCaO⋅MCaO ρ s⋅3.6[kWh m3] GCC: Grand Composite Curve BCC: Balanced Composite Curve O. Bartoli et al. Applied Thermal Engineering 217 (2022) 119180 3 sequentially. The concept simplifies plant integration and reduces costs. On the other hand, the design of the FB reactor requires special attention to ensure adequate performance in both operating stages. The present work analyses technology integration in CSP plants, and provides novel insights regarding the predesign of the reactor (FB) and the thermal integration of the systems. From a detailed assessment of the reaction and reactor conditions, equilibrium data, kinetics, and hydrodynamic performance of the FB reactor, the study delves into the potential integrations with the CSP plant, comparing operation strategies for both atmospheric and pressurised reactor configurations. Thermal integration has been optimised by the pinch analysis technique, maximising system performance with the temperature difference between reaction (450–600 ◦C) and storage temperature [31,32]. Key parameters associated with the FB reactor are discussed from the sensitivity analysis, such as reactor temperature and pressure, particle size, gas velocity, conversion, and reactor volume. The analysis is complemented with a detailed economic study and estimation of economic indicators. These analyses provide key design insights for integrating calcium hydroxidebased FB TCE systems in CSP plants. 2. Calcium hydroxide as TCES This section details the model of the calcium hydroxide system, including equilibrium data, reaction kinetics, and hydrodynamic performance in the FB reactor. The reactor model is based on the thermodynamic equilibrium of the chemical reaction. The equilibrium curves have been determined experimentally by different authors. Schaube et al. evaluated the start of dehydration and rehydration for a range of steam pressures from 4.3 kPa to 95.6 kPa [33], while Samms and Evans determined the equilibrium curve between 100 and 5000 kPa [34] This work uses the equilibrium curve data from the work of Barin [35] (Eq. (2)). Fig. 1 represents the equilibrium curves of these experimental works. Ln(Peq)= − 11607 Teq +19.254 (2) Equilibrium curves show that high temperatures and low steam pressures favour the dehydration reaction. It highlights a specific operational challenge for the charging stage. According to the suggestion of Criado et al. [36], if the fluidised bed operates at atmospheric pressure, the corresponding equilibrium temperature (following the Barin equilibrium curve and in continuity with [36]) is about 792 K. It provides one criterion for integrating dehydration reactions. Atmospheric pressure reactors must operate with temperatures above 792 K. The integration of this experimental model assures reliable numerical results regarding the development of reactions within the reactor at this level. Regarding the chemical reaction kinetics, hydration and dehydration reactions have been experimentally shown to be first-order reactions [37]. Different reactors have been used to simulate the behaviour of the thermochemical system in the laboratory. Fuji presented an air-heated reactor [14]. Schaube et al. demonstrated the operation in a fixed-bed reactor, in which material (60 g) was in direct contact with nitrogen gas and steam mixture. Twenty-five dehydration and rehydration cycles were carried out at different partial steam pressures: 17.6, 35.5, 74.1 and 95.6 kPa [13]. Pardo et al. performed the reaction in a fluidised bed reactor using a mixture of Ca(OH)2 and an inert to facilitate the fluidisation [20]. Ogura et al. presented a reactor with indirect heating [38]. Schmidt et al. [21] used a 10 kWth plate exchange reactor prototype, where with a 20 kg of solids inventory conversions of 77 % were achieved with no material degradation. Recently, Cosquillo et al. [39] developed a 1 kWth moving-bed reactor where solid particles fall from the top to the bottom while reacting with steam, using a transfer fluid for the heat exchange. Roug´ e et al. [19] simulated the behaviour of a 4 kWth fluidised bed prototype, processing up to 20 kg/s of solid particles. Based on these experimental results, it is possible to develop models at higher scales and estimate the performance of large-scale plants with different layouts and operation modes. As reported in [40], the reaction rate depends on the difference between steam volume fraction vH2O (Eq. (4)) and equilibrium volume fraction vH2O,eq (Eq. (3)). vH2O,eq =peq preactor =2.3 ⋅108exp(−11607 T) preactor (3) vH2O=pH2O operative,inlet preactor (4) Most of the studies have considered fixed-bed reactors. The typical configuration is the shell and tube, in which the inventory of solids remains static inside the exchanger. Steam is alternately extracted or supplied to the reactor [41,42]. Although good results have been achieved, these reactor types present substantial limitations, mainly due to the low heat exchange coefficients achieved. In addition, the renewal of fresh solid material, caused by the expected reversibility loss due to the intrinsic cyclic degradation, seems complicated with a packed bed configuration. A fluidised bed configuration can solve these issues. This work analyses a FB reactor operation with Aspen Plus TM software under steady-state conditions, considering well-isolated adiabatic components and an isothermal reactor. The gas velocity in the reactor is calculated by Eq. (5). ugas =Vgas Abed (5) where Vgas is the volumetric flow of the fluidising agent, Abed is the crosssectional area of the reactor. The minimal fluidisation condition appears when the drag force of the gas is equal to the weight of the bed of particles. The drag force is equal to the product between the pressure drop through the bed and the cross-sectional area of the bed. The Ergun equation connects them (Eq. (6)). Δp hmf = ρ gu2(1− ε mf ) φdp ε mf [150(1− ε mf ) μ ρ gdpu+1.75 ](6) where hmf is the bed height under the minimum fluidisation conditions when the bed of particles are static. The overall balance of forces becomes as in Eq. (7). ΔpAbed =Abed hmf (1− ε mf )( ρ s− ρ g)g(7) Combining equations (4) and (5), the value of the minimum fluidising velocity umf solving Eq. (8). 1.75 1 ε mf 1 φ(dpumf ρ g μ )2 +150 1− ε mf ε 3 mf φ2 dpumf ρ g μ =dp3 ρ g( ρ s− ρ g)g μ 2(8) For a velocity higher than ten or more umf a greater amount of particles is dragged in the freeboard region according to the mean diameter of the particles which form the bed: some return to the bed while others Fig. 1. Equilibrium curves proposed in the literature: Shaube [33], Samms and Evans [34] and Barin [35]. O. Bartoli et al. Applied Thermal Engineering 217 (2022) 119180 4 evolve outside the reactor with the gas. For estimating the terminal velocity (ut) this work uses the relation proposed by Haider and Levenspiel [43] (eq. (9))[43]. ut=u* t( μ ( ρ s− ρ g)g ρ 2 g)1 3 (9) where u* t is a dimensionless quantity calculated as: u* t=(18 Ar2 3 +2.335 −1.744 φs Ar1 6)−1 (10) [44]. 3. Ca(OH) 2 /CaO thermochemical energy storage integration A sequential modelling approach has been implemented to evaluate the overall performance of the system from the reactor performance, the thermal integrations, and the economic analysis (Fig. 2). The conceptual layout of the system is presented in Fig. 3. It is considered the base case for the study of the performance of the fluidised bed reactor in dehydration and hydration processes to define adequate performance conditions for integrating a single fluidised bed for hydration and dehydration reactions. The fluidised bed reactor temperature will be maintained using a heat transfer fluid (HTF). A design criterion is to lower the charging temperature of the system as much as possible. This can be achieved by changing the partial pressure of the steam. The fluidisation gas can be diluted with inert gas, where air is used to keep the reactor at atmospheric pressure and decrease steam pressure. In the present study, nitrogen gas as a diluent was also considered to avoid possible undesirable carbonation reactions between CO 2 in air and CaO. This choice also allows for a reduction in pressure and consequent operation with lower reactor temperatures. Still, it requires the insertion of a separator between incondensable N 2 and steam downstream of the reactor to operate in a closed loop. This solution is disregarded as it introduces a greater complexity to the plant layout and higher installation and operating costs, although in future integrations under different layouts could be of interest. The discharge phase of the system (hydration reaction) occurs to the left of the equilibrium curves, Fig. 1, and is promoted at low temperatures and high steam pressures. The temperature during the heat release phase is lower than the required for the charging phase under the same pressure for both reactions. Based on the equilibrium curve [35], operating temperatures around 743 K are needed in an atmospheric pressure reactor for a sufficient degree of hydration reaction. Two thermal integrations of the thermochemical storage system within an integrated solar power plant and a steam power cycle are considered. They differ in the discharge and reactor strategies: the first integration operates with a fluidised bed at a pressure close to atmospheric pressure, and the second with a fluidised bed pressurised at 6 bar, Fig. 4. An indirect thermal integration for the reactor was adopted, using compressed air at 15 bar as the heat transfer fluid of the receiver. Air was chosen as the working fluid to avoid the possibility of residues being formed on the walls of the heat exchanger tubes, where the heat transfer fluid and steam will alternately evolve. The residues could be dragged by the steam during the discharge phase of the system, with consequent damage to the turbine blades. The solar receiver chosen is a volumetric metal foam type [41]. Hydration and dehydration reactions operate for 12 h each, and system dynamics during stage inversion are neglected, although a transition period will appear in practice. The analyses and results of this work are valid under steady-state conditions. The layout of the charging stage system is the same for both integrations (Fig. 5). Hot air from the solar receiver maintains the fluidised bed at a temperature of 800 K and heats, evaporates, superheats, and then reheats for the power cycle. The heat exchangers network provides thermal coupling between the hot and cold currents of the system, recovers heat, and avoids the need for external heating units. The hot solids leaving the reactor are stored at the reactor outlet temperature. It allows using these hot solids during the next step, thus reducing the heating loads [36]. The condenser operating at a temperature of 322.1 K and a pressure of 0.1 bar is cooled using air coolers. The layouts of the two integrations related to the hydration phase differ in a turbine downstream of the reactor. In the case of the pressurised reactor, Fig. 6b, energy is recovered by expanding excess steam that has not been involved in the hydration reaction [41]. The stored water must be heated, evaporated, and superheated to reach the necessary hydration reaction conditions before entering the fluidised bed. It requires a tank with these capacities. Heat recovery is possible from solids that leave the reactor to increase efficiency. Fig. 2. Modelling methodology followed in this work. O. Bartoli et al. Applied Thermal Engineering 217 (2022) 119180 5 4. Process simulation and analysis Process simulation is carried out using Aspen Plus TM . The analysis is oriented to assess the estimated performance of the system in terms of solid conversion and heat available during the charging and discharging phases. Table 1 presents the ranges of the parameters used in the analysis. The simulation conditions were presented in previous sections. The reactor model is based on the thermodynamic equilibrium of the chemical reaction, using thermochemical data for the equilibrium curve from the work of Barin [35]. The reactor operation is simulated with Aspen Plus TM software under steady-state conditions, considering wellisolated adiabatic components and an isothermal reactor. Fluid dynamics and reactor operation conditions for both charging and discharging stages were discussed in Sections 2 and 3, respectively. The NRTL-RK model (Non-Random-Two-Liquid) was used to simulate the Fig. 3. Conceptual scheme for: a) Dehydration looping process layout; b) Hydration looping process layout. Fig. 4. T-s diagram for a) Dehydration 1st thermal Integration; b) T-s diagram for Hydration 1st thermal Integration; c) Dehydration 2nd thermal Integration; d) T-s diagram for Dehydration 2nd thermal integration. O. Bartoli et al. Applied Thermal Engineering 217 (2022) 119180 6 solid–gas reaction in the reactor, using the Redlich-Kwong equation of state for the steam phase. The downstream cyclone of the reactor, which provides solid–gas separation, is a Stairmand-HT type with the calculation method based on the model suggested by Muschelknautz et al. [44]. 4.1. Dehydration stage The effect of the particle size in the dehydration process was evaluated for different height/diameter ratios of the reactor, Fig. 7. It shows that almost complete dehydration is expected in all cases. Small particles (50 µm) have high conversion rates due to improved kinetics but are easily transported with the gas out of the reactor, being fluidisation operation more challenging. Particles with large diameters reduce the efficiency of the reactor with lower conversion values. For the presentation of the subsequent analyses, an intermediate particle size of 200 µm was selected, with a stable and efficient reactor behaviour. The charging phase of the system achieves almost complete conversion at temperatures above 750 K. Fig. 8 shows the conversion degree as a function of the temperature for different aspect ratios of the reactor. For the ranges of particle sizes and temperatures analysed, the impact of the geometry of the fluidised bed reactor is almost irrelevant as far as the chemistry of the reaction is concerned. Still, it has Fig. 5. Process flow diagram for the dehydration stage. Fig. 6. Process flow diagram for the hydration stage: a) Atmospheric FB reactor (HY-1); b) Pressurised FB reactor -6 bar- (HY-2). O. Bartoli et al. Applied Thermal Engineering 217 (2022) 119180 7 noticeable effects on the fluidised bed fluid dynamics. For larger reactors, the flow of solid particles out of the fluidised bed decreases, Fig. 8. Besides the impact on the reactor through successive cycles, having relevant values of solids in the outflow stream would penalise the performance of the cyclone and the separation of solids and gases. During the dehydration phase, high inlet steam flow rates reduce the conversion of solids. For the selected geometry, a steam flow rate of 2.5 kg/s was imposed based on the model in Section 2, assuring fluidification conditions in the analysed range. Steam must be produced from water stored at ambient temperature, and a reduction in the flow rate reduces heat requirements, improving performance during the charging phase. Fig. 9 shows the solids in the outflow stream as a function of the diameter of the reactor for the fixed steam flow. Fig. 9 shows that operating at the same Ca(OH)2 flow rate, reactors with larger diameters decrease the transport effect of solid particles outside the fluidised bed. Fig. 10 shows the gas velocities at the reactor inlet and outlet. Low and wide reactors require lower inlet fluid velocities than those used in high and narrow reactors. The dehydration reaction of Ca(OH)2 leads to an increase in the value of the gas velocity at the reactor outlet compared to that at the inlet. This effect increases the possibility of transporting solid particles out of the reactor. 4.2. Hydration stage Unlike dehydration, the hydration reaction is less effective, making it challenging to achieve conversion values up to 80 % for reactors at ambient pressure. The reaction is favoured at high temperatures. Fig. 11 shows the conversion rates obtained for different reactor temperatures and different steam flow rates. For the reference geometry, steam flows of 30 kg/s led to high CaO conversion values. The hydration reaction is affected by the size of the reactor. As the volume of the reactor increases, both the conversion value and the heat released by the reactor increase. A larger reactor volume leads to greater contact between the solid and gaseous particles; increasing the contact surface between the gas bubbles and the emulsion phase increases the exchange of matter, so the reaction is favoured. Fig. 12 shows the conversion fraction with a reactor temperature of 750 K, and the steam temperature and the CaO inlet temperature at 550 K. Fig. 12 shows that each reactor configuration has a maximum solid conversion fraction, varying from 0.33 to 0.65 in a volume range between 441.8 m3 and 1406.6 m3. These results are taken as references for the integrated layouts. According to the equilibrium curve, Fig. 1, the hydration reaction is preferred at high pressures for a given temperature. High inlet steam pressures considerably increase the conversion values, approaching complete conversion around 6 bars. An increase in conversion allows for greater thermal power during system discharge. However, operating at higher steam pressures requires high gas flow rates to fluidise the bed. Fig. 13 shows the effect of pressure on the conversion to hydration for a reactor with a diameter of 8 m and a height of 14 m. 4.3. Process integration The previous subsections presented the definition of the optimum parameters for reactor operation. This section evaluates the Table 1 Values of the parameter used for the analysis of hydration and dehydration. Units Hydration Dehydration Parameter Range dp µm 50–700 50–700 Tsolid in K 300–700 300–800 TReactor K 550–870 600–900 ˙ mgas in kg/s 27–60 1–30 pReactor bar 1–6 1 DReactor m 6–12 5–11 HReactor m 5–20 5–12 Threshold Value ˙ msolid in kg/s 100 100 Tgas in K >400 >400 Hinlet m 10%HReactor 10%HReactor Houtlet m 90%HReactor 90%HReactor DCyclone m 3 3 Fig. 7. Effect of particle size on dehydration conversion for different Height/ Diameter ratios (V =441.8 m 3). Fig. 8. Solid conversion versus temperature of the reactor for a FB volume of 441.8 m 3. Fig. 9. Solids transported outside the reactor as a function of reactor diameter. Fig. 10. Gas velocities at reactor inlet and outlet. O. Bartoli et al. Applied Thermal Engineering 217 (2022) 119180 8 performance of the integrated layouts, Fig. 5, which vary with hydration pressure. Two cases are considered from the previous discussion: ambient pressure (HY-1) and 6 bar (HY-2). The second case aims to maximise the power produced by the plant. However, the water consumption for fluidisation of the bed increases significantly. Each case will have an optimal thermal integration of the process. For the thermal integration, a reactor of Dr =10 m, Hr =17 m was selected to maximise the heat released from the reactor to the transfer fluid. The operation at atmospheric pressure (HY-1) produces during the discharge phase 87.15 MWth to heat the process steam through an internal heat exchanger. Hydration at 6 bars (HY2) increases substantially the heat released, 126.5 MWth. The conversions obtained as the hydration reaction are favoured at high pressures but also increase the required cold water from the storage that must be overheated up to 550 K before entering the fluidised bed. To minimise it, a fraction of the steam coming out of the turbine downstream of the fluidised bed can be recirculated. For the thermal integration of this second case, a reactor of size Dr =8 m, Hr =15 m was selected. Table 2 shows the geometric characteristics of the reactor for both cases. Table 3 and Table 4 show the mass and energy balances in the reactor. Recirculating steam during the discharge phase reduces the energy used in preheating the cold water flow from the storage tank. Internal fluidised bed heat exchanger sizing aims to optimise performance during the charging and discharging phases of the system. During dehydration, the objective is to select HTF velocities and tube diameters to ensure a reactor temperature of at least 800 K for a high conversion level. Fig. 14 shows the reactor temperature as a function of the HTF velocity and pipe diameters for different reactor aspect ratios. It shows that achieving the temperature objective with high velocities of the fluid inside the tubes is possible. High velocities imply high-pressure drops inside the tubes, increasing heat transfer fluid pumping costs. For the hydration phase, Fig. 11. CaO conversion as a function of reactor temperature. Fig. 12. Hydration conversion curves for different reactor volumes. Fig. 13. FB solid conversion versus pressure (D =8 m; H =14 m). Table 2 FB geometrical characteristics. Description Symbol Units INT-1 INT-2 HY DEHY HY DEHY Reactor Temperature TFB K 750 800 750 800 Diameter FB DFB m 10 10 8 8 Height FB HFB m 17 17 15 15 Diameter pipe dt mm 20 20 40 40 Distance pipe a mm 20 20 20 20 Pipe length Lt m 6.97 6.97 5.56 5.56 N◦layer Ns – 25 298 41 175 N◦pipes Nt – 4369 52083 3811 16297 Table 3 Mass flows in the reactor for the analysed integrations. Symbol Units Atmospheric pressure (hydration) Pressurised - 6 bar (hydration) Mass flow HY-1 DEHY-1 HY-2 DEHY-2 Inlet mgas,total kg/s 37 2.5 60 2.5 mgas,recirculated kg/s 10.71 0 25.03 0 mgas,feed kg/s 26.29 2.5 34.97 2.5 mCaO kg/s 100 0 100 0 mCa(OH)2 kg/s 0 100 0 100 Outlet mgas kg/s 14.7 26.1 29.0 26.2 mCaO kg/s 30.6 73.3 3.6 73.6 mCa(OH)2 kg/s 91.7 3.1 127.4 2.7 Table 4 Energy balance for each integration scheme. Units Atmospheric pressure (hydration) Pressurised -6 bar-(hydration) Welect,hy MW e 23.16 36.7 Welect,dehy MW e 38.96 53.5 Wfeed,H2O hy MW th 76.8 101.9 Wfeed,H2O dehy MW th 7.3 7.3 WFB,hy MW th 87.15 126.5 WFB,dehy MW th 187 187 Fig. 14. Reactor temperature as a function of tube diameter and HTF velocity. O. Bartoli et al. Applied Thermal Engineering 217 (2022) 119180 9 the aim is to size the exchanger according to the operating conditions of the steam cycle. The study of the heat exchanger network aims to thermally integrate the different streams of the system, to minimise the heating and cooling consumption. The optimisation was carried out by the pinch analysis [45] by using the Aspen Energy Analyser tool to optimise the energy plant for both thermal integrations. The inlet and outlet temperatures of the hot and cold streams are considered for the analysis of their thermal integration by heat exchangers. During hydration, the cold current of the water from storage that must be brought to the superheated steam limits the thermal integration, as it is the most energy-intensive current in the entire system. Figs. 15 and 16 show the balanced composite curves and the grand composite curves obtained for the second thermal integration during both the charging and discharging phases of the system, respectively. Table 5 shows the results obtained from the application of the pinch analysis. More heat exchangers must be installed during the dehydration reaction, although it is not necessary to cool the solids leaving the reactor, unlike during the charging phase of the system. The heat exchange surfaces used during dehydration are high due to the high steam flow rates produced during the reaction. 4.4. Performance parameters In this section, the two integrations are compared using the following relevant parameters to evaluate the efficiency of the cycle. These parameters are: –Power block efficiency. Wel,PB represents the electrical power produced in the power cycle, while Wth,heaters is the heat output required by the steam cycle heat exchangers. It integrates both hydration and dehydration periods, Eq. (11): η PB =Wel,PB Wth,heaters (11) – Overall efficiency, defined as the ratio of the total electrical power produced by the power cycle to the thermal power input to the system, Eq. (12): η tot =Wel,tot Qsolar =Wel,HY +Wel,DEHY Qsolar (12) – Round trip efficiency is the ratio between the heat released by the storage system during discharge (heat provided by the fluid-bed reactor) and the heat required by the system during the charging phase, Eq. (13). η RT =Qhy Qdehy (13) It excludes any type of thermal integration, such as the preheating line at the entrance to the reactor. Round-trip efficiencies reach values of 47 % in the first case while rising to 68 % with the second integration. – Solid conversion. It is defined as Eq.14: χ =FCa,in −FCa,out FCa,in (14) FCa,in represents the molar flow rate (of hydroxide or calcium oxide, depending on whether it is hydration or dehydration) entering the reactor, meanwhile FCa,out is the molar flow rate at the exit of the reactor. The cyclability and hence the reversibility of the reaction are functions of this parameter. When this parameter is closer to one, less solid replenishment is required. – Water Consumption. The choice of using superheated steam instead of nitrogen gas, on the one hand, simplifies the plant scheme by eliminating steam/nitrogen separation; on the other hand, it increases the heat demand for preheating the water from the storage tank. Therefore, the following parameters are defined: ξ=Wth,feed H2O WHY (15) V=mvap,converted mvap,used (16) The first number indicates the energy consumption of the water used to heat the steam compared to the heat released during the hydration reaction. In both cases, the value of ξ is around 0.81/0.88, which shows that the process is very energy intensive. The second number represents the ratio of the mass flow rate of steam converted during the hydration reaction to the total flow rate required to fluidise the fluidised bed. Fig. 17 compares and summarises the performance of the two configurations based on these parameters. The indicators in Fig. 17 show that the second integration is overall successful compared to the first one. The performance indexes according to Equations (3)–(8). Clear improvements can be seen in the round-trip yield, the total yield, and the conversion value achieved during calcium oxide hydration. These values are considered for the economic evaluation in the next section. The system charging phase, which presents higher costs than the discharging phase, was taken as the reference for LCOE calculation. 5. Economic analysis The economic analysis is developed considering the integration Fig. 15. a. BCC for Dehydration 2nd Thermal Integration Figgure 15b: GCC for Dehydration 2nd thermal integration. O. Bartoli et al.