Calcium looping as chemical energy storage in concentrated solar power plants: Carbonator modelling and configuration assessment

Corresponding author: [email protected] Calcium looping as chemical energy storage in concentrated solar power plants: Carbonator modelling and configuration assessment Manuel Baileraa*, Pilar Lisbonab, Luis M. Romeoa, Luis I. Díeza 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 This paper addresses the analysis of different configurations of carbonator for thermochemical energy storage for concentrated solar applications. The design of this equipment is different from the previous experience of calcium looping cycle for carbon capture. The use of fluidized beds and large particles are not feasible for this novel application of calcium looping. New reactors and different arrangements for the carbonation process are necessary. The design of a carbonator reactor for a specific Calcium Looping-Concentrated Solar Power application has not been addressed yet in detail in literature. In this work, a comparison of single stage reactor, two parallel reactors and two reactors in series with intercooling are simulated to calculate conversion rates, gas temperatures and flow rates, and heat transfer rates to the external cooling fluid. The modelling encompasses fluid dynamics, lime conversion kinetics and heat transfer, which are solved using a 1-D discrete mesh. The third arrangement results in the most reasonable sizes, and larger conversion rates, avoiding the occurrence of internal reactor zones in which the reaction is inhibited. Energy balance components are also quantified for each configuration. Keywords Calcium-looping; Thermochemical energy storage; Concentrated solar power; Carbonation 1. Introduction Nowadays, global warming is unequivocal and extensively endorsed by scientific community. In 2019, the global land-ocean surface temperature had increased 1.18 °C with respect to the period 1951-1980 [1][2]. Heat waves occur more often and last longer, while extreme precipitations have become more intense and frequent [3]. According to the IPCC (Intergovernmental Panel on Climate Change), this has affected many 2 species that have shifted their geographic ranges, seasonal activities or migration patterns in response to ongoing climate changes. Moreover, hydrological systems are continuously altered, what harms fresh water resources and food production [3]. Carbon dioxide is the largest single contributor to these perturbations on the energy balance of the Earth, and human beings are undoubtedly the main source [3]. Current atmospheric CO2 concentration is increasing at the fastest ever observed rate (2.0 ppm/yr), peaking the average for May 2019 at 414.8 ppm [4]. At the United Nations Climate Change Conference held in Paris at the end of 2015, about 190 countries agreed to reduce emissions of greenhouse gases (GHG). The aim is to limit global temperature increase below 2 °C by the year 2100, related to pre-industrial levels [5]. However, those scenarios that limit warming to 2 °C would require CO2 atmospheric concentrations below 450 ppm, which will be hardly accomplishable [3]. Key measures to achieve such mitigation lie in decarbonizing electricity and heat generation sector, since it produces more than two-fifths of global CO2 emissions [6]. The European Union Renewable Energy Directive sets a binding target of 20% final energy consumption from renewable sources by 2020 [7]. The role of renewable energy sources will be crucial for the reduction of European pollutant emissions while increasing the energy security through the massive penetration of local renewable energy sources (RES) and the diversification of energy vectors. The “EU Reference Scenario 2016” estimates that the share of electricity from renewable energy sources is expected to grow up to 37.2% by 2020, to 43% by 2030, and to 53% by 2050 [8]. RES present a number of barriers that limit their massive deployment. One of the most significant barriers is the control and management of fluctuations given the intermittent nature of the weather-dependent power generation systems. The security and stability of the electric grid would be strongly compromised if mismatches between supply and electrical demand could occur. This issue represents a significant limitation for the technical and economic feasibility of RES. To achieve the ambitious European targets for RES deployment and to develop of an energy system based on a more diversified technology mix, which allows a perfect control and match of the energy production and the instantaneous demand, the proposal and development of innovative energy storage solutions is needed. In 3 the short-term, the deployment of efficient and competitive technologies for energy storage represents one of the most challenging requirements for the energy system. Renewable energy production and energy storage capacity must grow in parallel in order to soften the intrinsic variability of RES production through storage. The different technical characteristics of the available methods for storing energy (e.g., discharge time, storage period, prices or materials) define how they are coupled with RES. Concentrated solar power plants (CSP) can operate beyond sunlight hours only when they include energy storage. Thermal energy storage systems which operate at medium (100 °C to 250 °C) to high temperature level (above 250 °C) are preferred in CSP to achieve higher round-trip efficiencies [9]. The currently most mature are the molten salt systems [10] which are used in commercial installations. Nevertheless, alternative storage materials are under studies such as natural rocks and recycled ceramics made from industrial wastes [11]. Thermochemical energy storage (TCES) was proposed as an innovative possibility to face the variability of CSP production [12][13][14]. TCES is based in the transformation and storage of thermal solar energy into chemical bounds created through endothermic chemical reactions. The density of storage of TCES is larger than other alternatives and it represents a significant advantage. The reverse exothermic reaction will be used to release the stored thermal energy when it is demanded. Prieto et al. compared different TCES under investigation such as those based in three redox reactions, sulfur-based cycles, metal oxide reduction– oxidation cycles, and perovskite-type hydrogen production, and metal oxide non-redox cycles [12]. They concluded that all these cycles are promising but the calcium carbonate is the one with most experimentation and potential economic feasibility. Thus, the use of CaCO3 in the Ca-looping process is an interesting TCES alternative given the wide experience in the carbonation/calcination equilibrium reaction, the wide availability of limestone and its low price [15]. The Ca-Looping (CaL) process has been extensively applied as a competitive option for CO2 capture [16][17][18] but also proposed as TCES in CSP plants [12][15][19]. As stated, CaL process is based upon the reversible carbonation/calcination reaction in which limestone and lime are alternatively converted. Surplus solar energy can be chemically stored through the direct endothermic calcination of limestone at high temperatures 4 producing pure streams of CaO and CO2. The stored energy will be released by means of the reverse reaction, exothermic carbonation reaction, at relatively high temperatures suitable for power cycles, both Brayton and Rankine cycles, when electricity demand raises. Chacartegui et al. and Ortiz et al. have demonstrated an outstanding performance under both situations; i.e. for a regenerative Rankine cycle an efficiency of 35.5% has been presented, but it increases to near 39.0% for a combined cycle or 42.0% for a closed Brayton cycle [15][19]. As highlighted by Bayon et al., CaL is also suitable for supercritical CO2 cycles [20]. The Ca-L process applied as TCES starts with the decomposition of CaCO3 in the solar calcination reactor producing CaO and CO2. Apart from the heat requirements in the calcination reaction, high-energy input is needed to increase the temperature of inlet streams up to the required value for the calcination reaction to occur at a sufficiently fast rate. This temperature is essentially determined by the CO2 equilibrium [21]. Once the sensible heat of outlet streams is recovered, the CaO and CO2 produced are stored at ambient temperature for their subsequent use. Storage of the products could be extended from weeks to months depending on storage conditions and energy demand pattern [22]. The reactants will be recirculated into a carbonator reactor where chemical energy is released through the exothermic carbonation reaction when energy is demanded. Detailed reviews of this TCES concept have been previously published [12][23][24][25][26] and there is a general agreement on the potential economic feasibility of carbonate systems as future TCES system if their cyclic stability and reversibility are improved. A key variable on the system is the activity of the sorbent. Cyclic limestone calcination leads to a strong deactivation of CaO under specific conditions for CaL CO2 capture which imply high calcination temperatures under high CO2 partial pressure [18] and this decay of CaO sorbent capacity is assumed to also limit the efficiency of the CaL process for TCES [27]. Recent thermogravimetric analysis studies confirm that calcination/carbonation conditions that optimize the efficiency of the CSP-CaL integration are different than those that optimize CO2 capture applications [28]. The lower calcination temperature in CSP-CaL applications, the more limited sintering in the CaO and the higher efficiency of the CaL process. A better heat distribution in the calciner keeps the temperature profile along the reactor in the proper 5 range, thus leading to less sintering of lime particles, faster reactions and minimum energy consumption in this element. Improvements in sorbent activity levels do not affect efficiency but capital costs and reductions in the required storage volume [29]. One of the most significant advantages of the CSP–CaL integration is the use of natural limestone as CaO precursor. Limestone is an abundant, non-toxic and cheap material (6-10 €/t), which presents suitable physical properties in the temperature range of interest for CSP thermal energy storage. In spite of that, different groups of researchers looks for sorbent improvements analysing the multicycle activity of the natural CaCO3 minerals [30]; doping and modifying CaCO3 [31][32], pre-processing limestone to enlarge the long-term performance of the sorbent upon iterated cycles [33], and developing synthetic Ca-based materials for energy storage [34]. Further challenges of the CaL technology are the low thermal conductivity of the sorbents, its agglomeration disposition causing the carbonation reaction to slow down and the difficulty in the design of the reactors for their efficient integration [23]. Chen et al. also mentioned the last two challenges as main factors that determine the heat storage performance, having reactors design an important role in the establishment of a reliable energy charging and releasing energy process [24]. Thus, proper design of the main reactors, carbonator and calciner, must be proposed to achieve favorable efficiency values. The designs will be circumscribed to the process and reactor limitations that will influence on the performance of the overall system. Recently, Zsembinszki et al. reviewed the reactor designs with potential use in thermochemical energy storage in concentrated solar power plants [35]. Their classification criteria of the reactors was the limiting step, which is essential for a proper design process, kinetics or diffusion controlled. Generally, thermal decomposition occurred in the calciner is controlled by chemical reaction, while solid-gas reaction in the carbonator is limited by internal and external diffusion of gas in the particle. The classification according the reactor type is divided in stack, fluidized and entrained beds. Fixed beds are recommended for solar catalytic reactions while fluidized beds and entrained beds are better suggested for reactions requiring good thermal transfer properties. 6 Fluidized and entrained beds minimize the risk of hotspots and thermal instability and present higher heat transfer coefficients. In this review, only two designs for carbonation reactor for CaL-CSP are gathered among existing experimental rigs: (i) Ortiz et al. designed a pressurized fluidized bed [19] and (ii) a carbonator/calciner fluidized bed built and run by Nikulshina et al. [36]. The carbonation reactor is a key element of the process and represents a complex system where heterogeneous exothermic chemical reactions take place together with heat transport phenomena for the production of steam for the Rankine cycle. Thus, fluidized or entrained bed are preferred for the design of this equipment. Recent investigations of Ortiz et al. of the kinetics and process integration of CaL-CSP showed that TCES applications require much lower limestone particle size than the well-known CaL processes for carbon capture (80-300 microns) [37]. Limestone particle sizes of tens of microns are required for an adequate solar calcination [37]. This technical limitation has important implications in the design of both reactors, which could require entrained flow reactors when particles are classified as Geldart C. Although several works proposed in literature show the theoretical models and simulation results of a carbonator reactor for carbon capture applications [38][39][40], up to now, the design of a carbonator reactor for a specific CaL-CSP application has not been addressed in detail. The main novelty of this study is the assessment of the conceptual design of a CaL-CSP carbonator and the influence of different parameters. In this work, the modelling of a future commercial-scale carbonator is described, in the frame of a new concentrated solar-based plant. Different lengths, diameters and configurations (one reactor, several reactors in parallel or in series) for a commercial carbonator are analysed, as well as the corresponding heat released. The diameter of the particles influences the reactor sizing through the residence times, and the heat transfer through the emissivity of the cloud of gas and particles. 2. Carbonator design and studied configurations Based on the provided information, the modelled carbonator presents an internal co-current entrained flow design and it is covered with four sections of helical coiled heat exchangers (cf1, cf2, cf3 and cf4) in which pressurized water enters at 300 bar and 350 °C. The outlet conditions of each of the cooling fluid streams (cfout) 7 are set to achieve 600 °C and a maximum pressure loss of 20 bar, to allow integration with supercritical steam cycles [41] (see Figure 1 and Figure 2). Thus, the simulations will provide as results the required cooling fluid mass flows. Heat exchanger sections 1 and 2 present a counter-current flow, while section 3 and 4 a co-current flow with respect to the internal carbonator flow direction. Entrained flow configuration with external cooling is chosen to keep technical complexity low, which in turn would help reducing costs. Other cooling options more complex are out of the scope of this paper (e.g., internal helical coils with variable surface area along the axis of the reactor). Figure 1. Conceptual design of the power production using a carbonator in a solar power plant (cf stands for cooling fluid). Figure 2. Conceptual design of the modelled carbonator (cf stands for cooling fluid). 8 Total CaO and CO2 inlet mass flow rates are 73.41 kg/s and 57.62 kg/s, respectively, and are assumed to enter to the carbonator at 800 °C. These mass flows correspond to the outlet of a calciner operating at full-load with a net thermal power input of 100 MWth, in which 100% calcination is achieved (Figure 3). Figure 3. Conceptual design of the energy storage process using a calciner in a solar power plant. The average sorbent conversion in the carbonator is assumed to be 13.3%, which corresponds to a material with a maximum residual conversion of about 9-12% that has been cycled 20-30 times in average [37]. Moreover, the solids are assumed to have a particle diameter of 60 microns. Thus, the outlet mass flows will be 17.31 kg/s of CaCO3, 63.71 kg/s of CaO, and 50.00 kg/s of CO2. The gas is separated from the solids, cooled in order to be recirculated to the carbonator using a blower, and heated again prior entering the carbonator; thus, 86.7% of the inlet CO2 circulates in a closed loop. The solid stream is cooled and stored to be later used in the calciner, where the 100 MWth solar input is invested to heat the material from room temperature and to calcine the 100% of the CaCO3 present in the solids mixture. Three different configurations (Figure 4) have been proposed and modelled to assess the behavior of the carbonation reaction, the required size of the carbonator and the potential of thermochemical energy storage.  Configuration 1 is a single reactor where the total inlet mass flows are introduced. This setup aims for simplicity of operation and reduction of costs. 9  Configuration 2 consists of two carbonation reactors operating in parallel and inlet mass flows are equally diverted among them. The objective is to reduce the released heat in each carbonator and the required sizes of carbonators.  Configuration 3 operates two carbonator reactors connected in series with intermediate cooling. The objective is to avoid the inhibition of the reaction along the carbonators. The sensible heat is removed through exchangers specifically designed for that purpose instead of through the helical coils around the carbonators. Heat will be evacuated from three main sources: (i) the carbonation reactors through the four superficial helical coiled heat exchangers, 𝑄󰇗𝑐 , (ii) the solid –solid heat exchanger at the outlet of the reactor, 𝑄󰇗𝑠, and (iii) the gas-gas heat exchanger at the outlet of the reactor, 𝑄󰇗𝐶𝑂2. Figure 4. Case studies for the three proposed carbonator configurations. 3. Methodology To analyze the temperature, conversion, residence times and heat exchanges of each configuration, a number of simulations has been performed. The carbonator model considers the specific geometry, heat transfer mechanisms and calcination kinetics; thus, obtaining the temperature profiles along the carbonator under 16 Since the convective coefficient inside the helical pipe is several orders of magnitude greater than inside the carbonator, the temperature of the carbonator outer wall is assumed to be equal to the temperature of the cooling fluid inside the helical pipe for each cell. Thus, the following energy balance on the cooling fluid is computed (30): 𝐶𝑝𝑐𝑓·𝑛󰇗𝑐𝑓·(𝑇𝑜𝑤,𝐿𝑖−1−𝑇𝑜𝑤,𝐿𝑖)=𝑞󰇗𝐿𝑖 ′·(𝐿𝑖−𝐿𝑖−1) (30) where 𝐶𝑝𝑐𝑓 and 𝑛󰇗𝑐𝑓 are the specific heat and the mole flow of the cooling fluid. It should be noted that (30) is valid for heat exchangers in which the cooling fluid flows from bottom to top (counter-current, HEX sections 1 and 2), and therefore it is heated from position 𝐿𝑖 to 𝐿𝑖−1, with the heat produced inside the carbonator from position 𝐿𝑖−1 to 𝐿𝑖. In case of evaluating a co-current heat exchanger (HEX sections 3 and 4), the energy balance is given by (31), where the cooling fluid flows from top to bottom. 𝐶𝑝𝑐𝑓·𝑛󰇗𝑐𝑓·(𝑇𝑜𝑤,𝐿𝑖−𝑇𝑜𝑤,𝐿𝑖−1)=𝑞󰇗𝐿𝑖 ′·(𝐿𝑖−𝐿𝑖−1) (31) Thus, the temperature along the carbonator can be computed by knowing the initial temperature of the cooling fluid. 4. Results and discussion In this section, the methodology described above is applied to three potential carbonator schemes (Figure 4). The study assesses the size requirements and technical performance of each configuration. As stated, the scale of the system is 100 MWth of useful thermal power inside the calciner. Moreover, in subsection 4.1 the model is compared with experimental results from literature, and in subsection 4.2 the influence of the particle diameter is presented. 4.1. Comparison of model results with experimental data from literature The experimental results of an entrained flow carbonator from Plou et al. [45] are used to validate the model presented in this article. 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). The reactor is kept 17 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 𝑋𝑘 (i.e., conversion at the end of the reaction controlled phase) and 𝑡0 (i.e., the time taken to reach a 𝑋𝑘/2 conversion) than the material assumed in the simulations of this study. Lime #1 has 𝑋𝑘=0.10 and 𝑡0 about 2 seconds, while the material used in our simulations has 𝑋𝑘=0.13 and 𝑡0=1.5 seconds. These are typical conversions of highly deactivated materials. Figure 5 shows the CO2 capture efficiency, which is defined as the CO2 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 2.4·10−4 kg/s). The gas is composed of 10% CO2 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. Figure 5. CO2 capture efficiency achieved in the entrained flow reactor of Plou et al. [45] 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 residence time they measured is 1.8 seconds, while the residence time calculated by the simulation is 1.78 seconds for the gas and 1.77 seconds for the solids. 18 4.2. Influence of the diameter of particles in the residence time of the solids One of the main differences that arise when using calcium looping as thermochemical energy storage instead of using it as carbon capture method is the size of particles needed. In case of CaL-CSP applications, the proper diameter of particles is of tens of microns (~60 μm). This size of particles may remarkably modify the residence time of the solids inside the carbonator with respect to other applications such as CaL for carbon capture (~300 μm) (Figure 6). With 60 microns as base case scenario, a variation in the diameter of [-42%,+32%] (i.e., particles between 35 μm and 79 μm) could be assumed keeping the variation of the residence time of the solids below ±5%, for a carbonator diameter of 7 meters. In the case of carbonator has a lower diameter, the allowable span of variation in the size of the particles increases, as can be seen in Figure 6. Figure 6. Variation of the residence time of the solids vs. the diameter of the particles. 4.3. Ideal case – Isothermal reactor The ideal case of an isothermal reactor is presented in this section to contextualize the reactor under study. The reactor is kept at 800 °C (inlet temperature of reactants). The heat removal required to operate under this condition is presented in Figure 7. An ideal heat exchanger should accomplish with this heat removal profile along the reactor (Figure 7, left). The total heat removal is presented in the right graph of Figure 7, which also corresponds with the evolution of the reaction. 19 Figure 7. Heat removal profile (left) and total removed thermal power for isothermal operation (right) vs. reactor length and internal radius dimensions. These graphs can be used to understand how far from are the solution proposed from the ideal system. 4.4. Configuration 1: One single carbonator The first configuration aims at performing the carbonation in one single reactor. However, the lengths required to achieve high conversions may be not reasonable because of the large mass flows of reactants (Figure 8). When diameters between 7 m and 4 m are considered, carbonators that are between 37 m and 56 m in length are required to reach 12% conversion. Moreover, to increase this value up to 13.2% (i.e., the 99% of the achievable conversion) it must be lengthen the reactor about 15 – 17 m. Thus, for a carbonator of 7 m in diameter, a total length of 52 m would be needed. Figure 8. Final conversion vs. reactor’s total length and internal radius dimensions (Configuration 1). 20 The main reason for the requirement of excessively long reactors is the insufficient heat removal. The unremoved thermal power rapidly heats the mass flows inside the reactor up to the equilibrium temperature (Figure 9). Hence, after the first meters the conversion growths slowly and linearly with the heat removal. Within this regime, the conversion only increases between 0.076 and 0.116 percentage points per meter of reactor depending on its diameter. Figure 9. Temperatures and conversion profiles vs. axial position (L=52m, r=3.5m, Configuration 1). The exothermal power produced during the carbonation is linearly dependent on the reactants conversion. Thus, the major release of heat takes place at the beginning of the reactor. In this study (system scale of 100 MWth of net solar input in the calciner), the total released thermal power due to carbonation is 28.4 MW when the conversion reaches 12%, while it increases to 31.1 MW at 13.2% conversions (Figure 10). However, the removed thermal power only amounts to the 35.2% – 36.6% of the cited value in reactors sized for 12% conversion (i.e., 10.0 – 10.9 MW). This percentage increases to about the 45.0% – 51.8% (i.e., 14.0 – 16.1 MW) for reactors long enough to reach 13.2% conversion. The heat removed by the cooling system continues growing linearly for greater lengths even though the carbonation reaction stops, since the reactor temperature is reduced. This effect is partially noticeable in Figure 9, at the end of the reactor. 21 Figure 10. Total exothermal power from carbonation (left) and total removed thermal power by cooling fluid (right) vs. reactor’s total length and internal radius dimensions (Configuration 1). In order to recover the rest of the heat, the mixture of gas and solids should be cooled after exiting the carbonator. This could be performed by separating both phases in a cyclone and passing them through gasgas and gas-solid heat exchangers to heat an extra amount of supercritical steam (from 350 °C to 600 °C), as depicted in Figure 4. In this study, the CO2 is cooled down to 800 °C and recirculated to the carbonator inlet. Therefore, the available thermal power from this gas ranges from 7.8 MW to 8.2 MW at reactors sized for 12% conversions (Figure 11). This represents the 27% – 29% of the exothermal heat coming from the reaction. Besides, the solids are cooled to 450 ºC, which provides an available thermal power between 36.8 MW and 38.3 MW, for reactors sized to reach 12% reactant’s conversion (Figure 11). 22 Figure 11. Available thermal power from CO2 (left) and solids (right) vs. reactor total length and internal radius dimensions (Configuration 1). In summary, the total recovered thermal power amounts to 55.5 – 56.5 MW (i.e., 56% of the net solar input in the calciner) for reactors that achieve 12% conversion. This values increases to 58.3 – 59.6 MW when reactors are sized for 13.2% conversion, which is not a significant increase considering the additional length required. 4.5. Configuration 2: Two carbonators in parallel The second proposed configuration presents two carbonator reactors operating in parallel where inlet mass flowrates of reactants are equally diverted among them. The aim is to assess heat transfer mechanisms when flowrates are reduced and the subsequent influence on the required lengths and diameters to achieve acceptable sorbent conversion. Conversions above 12% are achieved for carbonator lengths between 20 m and 39 m for diameters between 7 m and 3 m. The lengths required to achieve these conversions are still high, but become more reasonable for reactors of 6 and 7 meters in diameter (Figure 12). If the maximum sorbent capacity for a cycled material is to be reached, 13.3%, the carbonator length must be increased in about 10 meters; i.e. a 7 m diameter carbonator would require a total carbonator length of 30 m. Figure 12. Final conversion vs. reactor total length and internal radius dimensions (Configuration 2). 23 As already mentioned, the heat released during the carbonation reaction follows a linear relation with the sorbent conversion. During the first meters of the carbonator, the larger amount of heat is released since the reaction rate is enhanced by high reactants concentrations and moderate temperatures. The total heat from carbonation amounts to 14.1 MW when the sorbent conversion is 12%. This value is increased up to 15.6 MW if 13.2% conversion is achieved (Figure 13). Figure 13. Total exothermal power from carbonation (left) and total removed thermal power by cooling fluid (right) vs reactor total length and internal radius dimensions (Configuration 2). The recovered heat considering the design of the cooling system and the profile of heat released by carbonation amounts to the 36.0% – 38.0% of the carbonation heat in reactors sized for 12% conversion (i.e., 5.1 – 5.4 MW). The recovered heat is increased up to 7.1 – 7.8 MW which corresponds to a 45.8 – 50.4% of the carbonation heat released when sorbent conversion in the reactor achieves 13.2%. As mentioned in section 4.3, the heat recovered with the cooling fluid is increased for larger lengths of the carbonator even when maximum carbonation conversion has been reached. This is due to the gradual cooling of the carbonator in the last meters. Figure 13 illustrates this phenomenon and the value of recovered heat as a function of reactor dimensions. The amount of heat which cannot be removed from the carbonator rapidly heats the mass flows inside the reactor up to the equilibrium temperature and the carbonation reaction is favoured in the three initial meters 24 of the carbonator (Figure 14). After this first stage, the conversion rate dramatically diminishes and the conversion growth becomes slow and linear with heat removal. The specific conversion increment during this lineal stage ranges between 0.122 and 0.220 percentage points per meter of reactor. Again, specific heat removal per unit length is insufficient to increase reaction rate and long reactors are required to control the residence time and the conversion of the sorbent. Figure 14. Temperatures and conversion profiles vs. axial position (L=30m, r=3.5m, Configuration 2) The heat not recovered in the carbonator itself through the cooling system leaves the reactor with the mixture of gas and solids as sensible heat. This energy can be recovered by means of cooling these streams after exiting the carbonator. Solid and gas are separated in two cyclones and, then, each stream is directed to a gas-gas and a gas-solid heat exchanger to increase the temperature of an extra amount of supercritical steam. CO2 stream is cooled down to 800 °C and the available heat in the gas-gas heat exchanger ranges from 4.0 MW to 4.1 MW for reactors with 12% final sorbent conversion (Figure 15) which represents the 28.1% - 29.0% of the carbonation reaction. Solids are cooled down to 450 °C and the available heat in the gas-solid heat exchanger varies from 17.9 MW to 18.1MW, for reactors with a 12% of solid sorbent conversion (Figure 15). 25 Figure 15. Available thermal power from CO2 (left) and solids (right) vs. reactor’s total length and internal radius dimensions (Configuration 2). The overall results obtained for this second configuration (Table 1), e.g. available heats from carbonator and heat exchangers and sorbent conversion, are near to those obtained for Configuration 1. Also, the dimensions of the two reactors in parallel are of the same order of magnitude when added and compared to the single reactor configuration. Table 1. Length required, and removed thermal power by cooling fluid and available thermal power in the products in Configuration 1 and 2 (carbonators sized for 12% conversion). Configuration 1 Configuration 2 (only 1 reactor) r [m] 𝑋𝑓 [%] 𝐿 [m] 𝑄󰇗𝑜𝑢𝑡[MW] 𝑄󰇗𝐶𝑂2[MW] 𝑄󰇗𝑠 [MW] 𝐿 [m] 𝑄󰇗𝑜𝑢𝑡[MW] 𝑄󰇗𝐶𝑂2[MW] 𝑄󰇗𝑠 [MW] 2.0 0.12 56 10.6 8.0 38.1 32 5.3 4.0 18.0 2.5 0.12 48 10.4 8.1 38.2 27 5.3 4.1 18.1 3.0 0.12 42 10.3 8.2 38.3 23 5.2 4.1 18.1 3.5 0.12 37 10.1 8.2 38.3 20 5.1 4.1 18.1 4.6. Configuration 3: Two carbonators in series with intermediate cooling The third configuration presents two reactors operating in series with a cooling stage between them (Figure 2). The aim is to carbonate the material only during the rapid regime in which reaction is not yet inhibited. To 32 https://data.giss.nasa.gov/gistemp/ (accessed December 15, 2019). [2] Lenssen NJL, Schmidt GA, Hansen JE, Menne MJ, Persin A, Ruedy R, et al. Improvements in the GISTEMP Uncertainty Model. J Geophys Res Atmos 2019;124:6307–26. doi:10.1029/2018JD029522. [3] Intergovernmental Panel on Climate Change. Climate change 2014 - Synthesis report. 2014. doi:10.1017/CBO9781107415324. 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React Chem Eng 2019:899–908. doi:10.1039/c9re00015a. 35 List of figures Figure 1: Conceptual design of the power production using a carbonator in a solar power plant (cf stands for cooling fluid). Figure 2: Conceptual design of the modelled carbonator (cf stands for cooling fluid). Figure 3: Conceptual design of the energy storage process using a calciner in a solar power plant. Figure 4: Case studies for the three proposed carbonator configurations. Figure 5: CO2 capture efficiency achieved in the entrained flow reactor of Plou et al. [45] and in the simulations of this study under the same setup, as a function of the solid/gas mass ratio. Figure 6: Variation of the residence time of the solids vs. the diameter of the particles. Figure 7: Heat removal profile (left) and total removed thermal power for isothermal operation (right) vs. reactor’s length and internal radius dimensions. Figure 8: Final conversion vs. reactor’s total length and internal radius dimensions (Configuration 1). Figure 9: Temperatures and conversion profiles vs. axial position (L=52m, r=3.5m, Configuration 1). Figure 10: Total exothermal power from carbonation (left) and total removed thermal power by cooling fluid (right) vs. reactor’s total length and internal radius dimensions (Configuration 1). Figure 11: Available thermal power from CO2 (left) and solids (right) vs. reactor’s total length and internal radius dimensions (Configuration 1). Figure 12: Final conversion vs. reactor’s total length and internal radius dimensions (Configuration 2). 36 Figure 13: Total exothermal power from carbonation (left) and total removed thermal power by cooling fluid (right) vs reactor’s total length and internal radius dimensions (Configuration 2). Figure 14: Temperatures and conversion profiles vs. axial position (L=30m, r=3.5m, Configuration 2) Figure 15: Available thermal power from CO2 (left) and solids (right) vs. reactor’s total length and internal radius dimensions (Configuration 2). Figure 16: Temperatures and conversion profiles (first stage: up, second stage: down) vs. axial position (r=1.5 m, Configuration 3) List of tables Table 1: Length required, removed thermal power by cooling fluid and available thermal power in the products in Configuration 1 and 2 (carbonators sized for 12% conversion). Table 2: Sizes of carbonators, final conversion and thermal heats for Configuration 3.