# One-Dimensional Heterogeneous Reaction Model of a Drop-Tube Carbonator Reactor for Thermochemical Energy Storage Applications

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{(s)}+ CO

_{2(g)}→ CaCO

_{3(s)}) focused on thermochemical energy storage conditions was developed and implemented for different material conditions. The fast gas–solid reaction kinetics conformed with the drop-tube reactor concept, as the latter is suitable for very fast reactions. Reaction kinetics were controlled by the reaction temperature. Varying state profiles were computed across the length of the reactor by using a mathematical model in which reactant conversions, the reaction rate, and the temperature and velocity of gas and solid phases provided crucial information on the carbonator’s performance, among other factors. Through process simulations, the model-based investigation approach revealed respective restrictions on a tailor-made reactor of 10 kW

_{th}, pointing out the necessity of detailed models as a provision for design and scale-up studies.

## 1. Introduction

_{e}, with an escalating trend that could even double in 2020 [1]. Increasing public attention to environmental protection and the political decisions that change the preferences of manufacturers from conventional to renewable solutions are the major factors influencing these market dynamics. Nevertheless, commercial intrusion into the global power market has so far been conservative, and definitely has not aligned with the requirements of this expanding economy.

^{3}compared with ~0.8 GJ/m

^{3}in commercially installed molten salts units) and the extremely low price of natural limestone CaCO

_{3}(~€10/ton) have been extensively discussed, among other factors, in the literature [5,6,7]. Furthermore, the commercial potential of the CSP-CaL integration for thermochemical energy storage and power production has been theoretically studied in detail by numerous authors in terms of energy analysis [5,8,9], exergy analysis [10,11] and the optimization of power cycles used for energy production [12,13], proving the potential commercialization of these systems.

_{2}capture, and reaction conditions and kinetics in these applications are different from those used in CSP-CaL processes. Typical conditions in CO

_{2}capture applications involve low CO

_{2}partial pressures that exit from the flue gases of power plants (~10% vol.) and temperatures around 650 °C during carbonation step. Under these conditions, and due to the sulphation of CaO and the multiple number of cycles, a material’s reactivity significantly drops in its residual value by 0.07–0.10 [15]. Moreover, the reactivity of the material depends on the calcination/carbonation conditions and grain size, as well as the origin of the solids [7].

_{2}capture applications in cement kilns [20]. Finally, two recent studies have presented the construction of novel experimental facilities for the carbonation of fine CaO particles in a drop-tube reactor [29] and an entrained-flow reactor [30], examining the efficiency of the decarbonization of gases when exposed to different conditions and materials. To the best of our knowledge, there has not been any published work related to an experimental or model-based investigation of CaO carbonation in a drop-tube reactor that has focused on the relevant conditions for thermochemical energy storage applications.

_{th}reactor under different conditions. Mass, energy and momentum equations were considered for the two phases (gas and solid) derived by simplified Navier–Stokes equations. Moreover, the model included radiative heat transfer mechanisms and a random pore model (RPM) for carbonation kinetics that were validated through experimental work under conditions relevant to TCES. The main scope of this work is to demonstrate the model’s capabilities, and to describe the operations of a fixed-dimension prototype drop-tube carbonator reactor. The simulation studies investigate its performance, concerning the conversion and distribution of thermal power production across the length of the reactor, under different operating conditions. Subsequently, this will lead to future optimization, design and further scale-up studies. For this reason, critical variables were parametrically studied (i.e., the reactor’s wall temperatures, flows, carbonation pressure, etc.) with respect to process performance.

## 2. Concentrated Solar Power (CSP) and Calcium Looping (CaL) Concept Description

_{3}) is decomposed towards CaO and CO

_{2}(Equation (1)) in the calciner. The products are stored in vessels through the storage section, then react in the carbonator reactor to recover a large part of thermal energy through the exothermic carbonation reaction. The concept is completed via an engine (Figure 1) in the power block where this energy is explicitly used to produce electricity.

_{2}is provided by pressurized bottles, entering from the top. A heat exchanger composed of a set of helical coils encircling the reactor is used for the removal of the heat released by the exothermic reaction. In the first reaction section, the CO

_{2}reactant passes through the coils to preheat before entering the reactor, while in the second section, fresh air is used as the heat transfer fluid to act as a cheap and effective heat sink (Figure 2) [17]. The produced hot air is later used in the power block to provide heat for electricity generation. The two reactor segments are surrounded by electric furnaces that preheat the carbonator system in order to trigger the carbonation reaction (~400–500 °C).

## 3. Experimental

#### 3.1. Materials and Methods

_{2}flow $({P}_{{\mathrm{CO}}_{2}}=1.25\mathrm{atm}$ at $T=850\xb0\mathrm{C})$ for a time period of 8 min (including the heating step to the calcination temperature). The calcination stage was carried out under a 25% vol. CO

_{2}/N

_{2 flow}at $900\xb0\mathrm{C}$ for a time period of 8 min (including the cooling step to the carbonation temperature under pure N

_{2}). Nitrogen physisorption at 77 K was applied for measuring the surface areas and pore volumes of the two materials in a Surface Area Analyzer (Autosorb-1 Quantachrome Instruments, Boynton Beach, FL, USA). Prior to these measurements, samples were degassed in a vacuum at 250 °C overnight.

#### 3.2. Laboratory Test Procedure

_{2}flow, with a gas hourly space velocity (GHSV) of 22,500 h

^{−1}to complete calcination (pre-treatment). Carbonation was initiated at the prespecified temperature by switching the flow from pure N

_{2}to 600 cc/min (GHSV = 27,000 h

^{−1}) of the desired CO

_{2}(containing 2% vol. Ar used as an internal standard)/N

_{2}mixture. The carbonation stage was carried out for 3 min isothermally. Given that Ar flow was constant, quantification of the adsorbed CO

_{2}was performed while the carbonation reaction was taking place, based on the ratio of CO

_{2}/Ar signals (represented by mass/charge (m/z) ratios 44 and 40, respectively) of the mass spectrometer. Temperature in the reactor was also recorded throughout the procedure.

## 4. Model Development

#### 4.1. The Random Pore Model (RPM)

_{2}through the CaCO

_{3}product layer. Bhatia and Perlmutter [32,33,34] developed a random pore model for the occurrence of both effects simultaneously using the general equation

_{3}accumulates in islands on CaO during carbonation, leaving free CaO surfaces that can react until the entire surface is covered by product layer and the diffusional regime starts. Moreover, Equation (2) predicts much lower reaction rates and conversions compared to the experimental results, due to the product layer’s diffusional resistance from the first moment of the reaction. Thus, for the fast regime, it can be assumed that the thickness of the product layer is zero, which implies that $\beta $ could also be considered negligible, leading to

_{2}concentration is experimentally explored, the term of CO

_{2}concentration $C$ in Equation (3) is converted to partial pressure via the gas law and introduced in the reaction’s front velocity $r$ as follows:

_{3}) after initial calcination. In the reactor simulation studies, two cases were considered using a fresh (lime after first calcination) and a sintered material after cycling (lime after 10th calcination). The properties of these materials obtained from BET and Barrett-Joyner-Halenda (BJH) measurements, along with the calculated properties (${S}_{0}$, ${L}_{0}$, ${\epsilon}_{0}$ and $\Psi $) needed for the RPM, are shown in Table 1. As reported elsewhere [37,38], the surface area and porosity of the material after cycling were substantially reduced due to sintering.

#### 4.2. Drop-Tube Carbonator Reactor Model Development

- One-dimensional (1D) reaction model. The radial dispersions of mass, energy and momentum are neglected. The reaction model is solved along the z-axis of the reactor.
- The entrained-flow system is assumed to be very dilute in the solid phase, such that the particle-wall and interparticle interactions may be neglected. Consequently, the conductive heat transfer mechanism between single particles and particles to the wall is neglected [22].
- Solids are spherical, with uniform sizes and temperatures. Change in the particle size during carbonation reaction is assumed negligible [16].
- Kinetic energy and work forces of the system are negligible in comparison with thermal energy due to the high temperature in the reactor [18].
- The gas phase is modelled after the ideal gas equation of state.
- The wall temperature of the reactor is defined explicitly by constant values.
- Due to the small particle sizes, particle–particle heat exchanges with radiation are not considered. Furthermore, gas phase (CO
_{2}) as a triatomic molecule takes part in radiative heat transfer due to its high temperature. According to the literature [40], a value of 0.7 is realistic for the reactor’s internal skin, based on stainless steel material.

#### 4.2.1. Continuity Equations

#### 4.2.2. Momentum Balance Equations

_{3}on CaO surface) from gas phase to solid phase (${F}_{mass}$) are considered to be the dominant terms for the momentum conservation, while pressure drop is included as the simplest expression for the surface stress in the gas phase [41].

#### 4.2.3. Energy Balance Equations

_{2}(${Q}_{C{O}_{2},flow}$) that is removed from the gas phase and transferred to the solids.

#### 4.2.4. Properties of Gas and Solid Phases

_{2}were taken from NIST data adopted from Aspen Plus software (AspenTech, Bedford, MA, USA) [44]. Specific heat capacity ${c}_{p}$, viscosity $\mu $ and thermal conductivity correlations $k$ were inferred from the quadratic or linear regressions of the estimated values referred to above. Specific heat capacity of CO

_{2}follows a non-linear correlation based on the NIST Aly–Lee equation for ideal gases [45]

_{2}was computed based on the NIST ThermoML Polynomial Equation [46], while thermal conductivity was linearly calculated by the same equation.

_{3}formed after carbonation $\left({\rho}_{{\mathrm{CaCO}}_{3}}\right)$. These values are highly dependent on a material’s origin, on the number of calcination/carbonation cycles and on the reaction conditions.

#### 4.2.5. Temperature Effect on the Conversion

_{h}is the activation energy related to the formation of CaCO

_{3}islands.

## 5. Carbonator Reactor Simulation—Solving Strategy

#### 5.1. Model Analysis and Solution

#### 5.2. Simulation Parameters—Operating Conditions

_{th}energy via the exothermic carbonation reaction.

_{th}of thermal energy via the carbonation reaction. Given this, and considering that an exothermic reaction is highly dependent on the solid’s initial conditions, a “fresh CaO” (produced after the calcination of fresh limestone) and a “sintered CaO” (produced after 10 calcination/carbonation cycles) were tested. Under these circumstances, theoretically, around 19 kg/h of fresh CaO (X

_{k}~ 0.60) should enter the reactor in order to produce 10 kW

_{th}, while on the other hand, for sintered CaO (X

_{k}~ 0.20), theoretically, around 60 kg/h of solids should enter to produce the same amount of heat. Based on this, the flow of CO

_{2}was determined to range between 10–20 kg/h, as higher flows would lead to shorter residence times in the reactor. A reference inlet temperature of 200 °C was set for the reactants, while the introduction of reactants at ambient conditions was also evaluated (Table 3). A wall temperature profile of 400–800 °C was implemented, as certain amounts of heat must be provided initially to the reactants until reaction is triggered. Finally, carbonation pressure was set at atmospheric, as is commonly applied to calcium looping applications for thermochemical energy storage, but also smaller values were applied to mitigate the instantaneous high reaction rate.

## 6. Results and Discussion

#### 6.1. Carbonation Kinetics Modeling

_{2}or mixtures of N

_{2,}with CO

_{2}partial pressures of 1.25 atm, 0.90 atm, 0.70 atm and 0.50 atm. The conversion-versus-time curves are shown in Figure 3; in all cases, carbonation reaction refers to the first cycle. The final conversion achieved during the reaction-controlled regime was approximately 0.6. As was expected, increasing the surrounding CO

_{2}gas concentration also increased the rate of carbonation reaction.

_{2}. On the other hand, the diffusion-controlled regime was much slower, and was difficult to detect using the current experimental set up due to the very small change of CO

_{2}flow resulting from capture, compared to the total flow passing through the reactor bed. Nevertheless, by far the largest part of CO

_{2}was captured during the fast regime, which was the useable part of the conversion from a practical point of view. Two factors affected the critical conversion value at which the transition from the fast surface reaction to the slow diffusion-controlled regime took place, namely, the pore blockage and critical product layer thickness. The effect of the latter depends on the reaction temperature, as described by Equation (29), while the former is dominant if the product layer thickness is larger than the pores’ width. It is clear that under the studied conditions, the carbonation reaction was extremely fast, leading to short residence times comparable to the ones achieved in a drop-tube reactor. Figure 3a presents the conversion evolution during the carbonation along with the fitting curves of RPM (Equation (4)) during the fast initial stage. The fitted values of $r$, which represents the rate of the carbonation-reaction front movement, are presented in Table 4 for each test.

_{3}product layer, and it should be considered that the molar volume of CaCO

_{3}(0.037 m

^{3}/kmol) was almost double the molar volume of CaO (0.017 m

^{3}/kmol). This implies that the product layer thickness is also twice the reaction front movement during the reaction. For example, for carbonation under 1.25 atm of CO

_{2}, the reaction front moved with a rate of 4.5 nm/s, thus CaCO

_{3}product layer grew with a rate of approximately 9 nm/s. It has been mentioned by other researchers that the maximum product layer thickness during the reaction-controlled regime is around 49 nm [48]. Accordingly, it can be roughly estimated that this regime will be completed in 5 s, which is in agreement with the experimental results shown in Figure 3a.

_{2}partial pressure, Equation (10) is transformed to

_{2}partial pressure calculated by [49]

^{−6}m

^{4}/(kmol s) by Grasa et al. [36]; 6 × 10

^{−6}m

^{4}/(kmol s) by Bhatia and Perlmutter [34]). The first-order reaction assumption was validated through this linear dependence. This result is in agreement with Grasa et al. [36], but in contrast to Sun et al. [50], who found a first-order relation up to 0.1 atm and zero dependence for higher CO

_{2}partial pressures.

#### 6.2. Reactor Performance Under “Fresh CaO”

_{2}flow-rate effect.

#### 6.2.1. Reactor Simulation under Reference Conditions

_{2}enter the reactor at equal mass flow rates. As expected, due to the difference in molar mass of the two reactants, the molar conversion values were not identical (Figure 4a).

#### 6.2.2. Effect of Reactor Wall Temperature

#### 6.2.3. Effect of CO_{2} Flow Rate

_{2}flow rate. Literally, flow-rate selection depends mostly on capacity, but from an engineering perspective CO

_{2}should be in excess to accomplish carbonation (although constrained by inducing very short solid residence times). Thus, it was observed that flows from 10–30 kg/h resulted in a velocity range of 0.25–0.85 m/s, corresponding to mean solids residence times of ~16–5 s (Figure 6d), which is in agreement with the results of kinetic experiments (Figure 3a) where carbonation reached completion in less than 20 s. Moreover, the higher the CO

_{2}rate, the milder the temperature profile was along the reactor. This occurs because the excess CO

_{2}behaves like a sink for heat absorption (Figure 6b), and because the reaction takes place across a wider range inside the reactor (Figure 6c), which can result in a more efficient exploitation of the power produced. In all cases, the residence time in the reactor was enough to complete the reaction (Figure 6a).

#### 6.3. Reactor Performance under “Sintered CaO”

#### 6.3.1. CaO Flow Rate Analysis

_{2}phase depleted. In case of high solid flow rates, CO

_{2}was depleted quickly, as depicted in the final solid phase velocity (Figure 7d).

#### 6.3.2. Carbonation Pressure Analysis

## 7. Conclusions

_{th}thermal energy that was designed and constructed as part of the SOCRATCES project [31].

_{2}flow rate were parametrically examined by means of the reactor’s performance under the condition of “fresh CaO” (lime after first calcination). Significant effects of these variables could be seen in the final CaO conversion, reaction rate variations across the reactor and temperature profiles on the inner side of the reactor. Next, the effect of CaO flow rate and carbonation pressure were investigated for the case of “sintered CaO” (lime after 10 carbonation/calcination cycles). Carbonation pressure proved to be a critical variable, as it radically affects the reaction rate.

_{2}resulted in the completion of the reaction across a wider range inside the reactor. Maximum sorbent conversions (20%) were reached in the cases of 25 and 30 kg/h of sintered CaO flow rates. The above conclusions were deduced from the reactor’s specific dimensions. Lower carbonation pressures (~0.7 atm) might be used to flatten the reaction front, making it more feasible to control the extraction of the generated heat. This could steer research towards model-based optimization strategies that will enhance future design and further scale-up studies of different carbonator reactor sizes.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

CSP | Concentrated Solar Power |

TCES | Thermochemical Energy Storage |

CaL | Calcium−Looping |

PCM | Phase Change Materials |

RPM | Random Pore Model |

## Nomenclature

Symbols | |

$A$ | Reactor cross-section area (m^{2}) |

${a}_{gs}$ | Surface area between gas and solids (m^{2} m^{−3}) |

${a}_{gw}$ | Surface area between gas and wall (m^{2} m^{−3}) |

$a,b$ | Stoichiometric coefficients of carbonation reaction (-) |

$C$ | Concentration of CO_{2} (kmol m^{−3}) |

${C}_{D}$ | Drag force coefficient between solids and gas (-) |

${c}_{p}$ | Specific heat capacity (kJ kg^{−1} k^{−1}) |

$D$ | Reactor diameter (m) and effective product-layer diffusivity (m^{2} s^{−1}) |

${D}_{0}$ | Pre-exponential factor of effective product-layer diffusivity (m^{2} s^{−1}) |

${D}_{p}$ | Apparent product-layer diffusivity (m^{2} s^{−1}) |

d_{p} | Particle diameter (m) |

${E}_{h}$ | Activation energy related to the product layer thickness (29.3) (kJ mol^{−1}) |

${E}_{aD}$ | Activation energy for product layer diffusion (kJ mol^{−1}) |

${F}_{{\mathrm{CO}}_{2},O}$ | Initial molecular flow of CO_{2} (kmol s^{−1}) |

${F}_{\mathrm{CaO},O}$ | Initial molecular flow of CaO (kmol s^{−1}) |

${F}_{D}$ | Drag force between gas and solids (kg m^{−2} s^{−2}) |

${F}_{gw}$ | Friction force between gas and wall (kg m^{−2} s^{−2}) |

${F}_{sw}$ | Friction force between solids and wall (kg m^{−2} s^{−2}) |

${f}_{gw}$ | Gas–wall friction coefficient (-) |

${f}_{sw}$ | Solids–wall friction coefficient (-) |

$g$ | Gravitational acceleration (9.81) (m s^{−2}) |

${h}_{gs}$ | Convective heat transfer coefficient between gas and solid phase (kW m^{−2} K^{−1}) |

${h}_{gw}$ | Convective heat transfer coefficient between gas phase and wall (kW m^{−2} K^{−1}) |

$k$ | Thermal conductivity (kW m^{−1} K^{−1}) and deactivation constant (-) |

${k}_{s}$ | Carbonation reaction constant (m^{4} kmol^{−1} s^{−1}) |

${L}_{0}$ | Total pore length of the material before carbonation (m m^{−3}) |

$L$ | Length of reactor (m) |

$M{W}_{g}$ | Molecular weight of gas (CO_{2}) phase (44.01) (kg kmol^{−1}) |

$M{W}_{\mathrm{CaO}}$ | Molecular weight of CaO (56.07) (kg kmol^{−1}) |

$M{W}_{{\mathrm{CaCO}}_{3}}$ | Molecular weight of CaCO_{3} (100.08) (kg kmol^{−1}) |

$N$ | Number of calcination/carbonation cycle (-) |

$Nu$ | Dimensionless Nusselt number (-) |

$P$ | Total pressure of reactor (based on partial pressure of CO_{2}) (Pa = kg m^{−1} s^{−2}) |

${P}_{e}$ | CO_{2} partial pressure at equilibrium (atm) |

${P}_{{\mathrm{CO}}_{2}}$ | CO_{2} partial pressure (atm) |

$Pr$ | Dimensionless Prandtl number, $\mathit{Pr}=\frac{C{p}_{g}{\mu}_{g\xb7}}{{k}_{g}}$ (-) |

$P{V}_{0}$ | Pore volume (m^{3} g^{−1}) |

${Q}_{rxn}$ | Thermal power produced due to carbonation reaction per length of reactor (kW m^{−3}) |

${Q}_{rx{n}_{t}}$ | Total thermal power produced due to carbonation reaction (kW) |

$r$ | Reaction front velocity (m s^{−1}) |

$R$ | Ideal gas constant (R = 8.314) (m^{3} Pa mol^{−1} K^{−1}) (R = 8314.47) (Pa m^{3} kmol^{−1} K^{−1}) |

$R{e}_{s}$ | Dimensionless solids Reynolds number, $R{e}_{s}=\frac{{\epsilon}_{g}{\rho}_{g}{d}_{p}\left|{u}_{g}-{u}_{s}\right|}{{\mu}_{g}}$ (-) |

$R{e}_{g}$ | Dimensionless gas Reynolds number, $R{e}_{g}=\frac{{\epsilon}_{g}{\rho}_{g}{u}_{g}D}{{\mu}_{g}}$ (-) |

${S}_{BET}$ | BET surface area (m^{2} g^{−1}) |

${S}_{0}$ | Surface area of the material before carbonation (m^{2} m^{−3}) |

$T$ | Temperature (K or °C) |

$t$ | Time (s) |

$u$ | Cross-sectionally averaged velocity (m s^{−1}) |

${X}_{r}$ | Residual carbonation conversion (-) |

${X}_{k}$ | Carbonation conversion during the surface reaction-controlled regime (-) |

${X}_{N}$ | Carbonation conversion of the Nth cycle (-) |

${X}_{1}$ | Carbonation conversion of the 1st cycle (-) |

$X$ | Cross-sectionally averaged conversion (-) |

$Z$ | Ratio of volume of solid phase after reaction to that before reaction (2.16) (-) |

$z$ | Length of reactor (m) |

Greek Symbols | |

${\alpha}_{\kappa}$ | Dimensionless constant of Equation (29) (0.0255) (-) |

$\beta $ | Modified Biot modulus in the RPM (-) |

${\beta}_{r}$ | Dimensionless constant of Equation (29) (1.04) (-) |

${\dot{\Gamma}}_{g-s}$ | Mass transfer rate per unit volume due to the heterogeneous reaction (kg m^{−3} s^{−1}) |

$\Delta {H}_{rxn}$ | Enthalpy of reaction (kJ Kmol^{−1}) |

${\epsilon}_{g}$ | Cross-sectionally averaged voidage (-) |

${\epsilon}_{ge}$ | Emissivity of gas phase (-) |

${\epsilon}_{s}$ | Cross-sectionally averaged solid hold-up (-) |

${\epsilon}_{w}$ | Emissivity of wall surface (-) |

${\epsilon}_{0}$ | Porosity of the material before carbonation (m^{3} m^{−3}) |

$\mu $ | Viscosity (Pa s) |

$\rho $ | Cross-sectionally averaged density (kg m^{−3}) |

${\rho}_{\mathrm{CaO}}$ | Theoretical density of CaO (3340) (kg m^{−3}) |

${\rho}_{{\mathrm{CaCO}}_{3}}$ | Theoretical density of CaCO_{3} (2700) (kg m^{−3}) |

$\sigma $ | Stephan’s Boltzmann constant (5.6704·10^{−8}) (kW m^{2} K^{4}) |

$\tau $ | Dimensionless time in the RPM (-) |

$\Psi $ | Structural parameter in the RPM (-) |

Subscripts | |

${\mathrm{CO}}_{2}$ | Carbon dioxide |

$\mathrm{CaO}$ | Calcium oxide |

${\mathrm{CaCO}}_{3}$ | Calcium carbonate |

$g$ | Gas phase (CO_{2}) |

$o$ | Initial |

$s$ | solid phase |

$w$ | Wall |

## Appendix A. Algebraic Equations Related to Momentum Balances

## Appendix B. Algebraic Equations Related to Radiative Heat Transfer Rate

## Appendix C. Algebraic Equations Related to Energy Balance

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**Figure 1.**Conceptual process flow diagram of the SOCRATCES prototype plant (10 kW scale). Reprinted with permission, Elsevier, 2020 [11].

**Figure 2.**Drop-tube carbonator reactor assembly according to the SOCRATCES prototype plant [17].

**Figure 3.**(

**a**) Conversion vs. time (experimental data and RPM) for carbonation reaction of limestone-derived CaO under ${P}_{{\mathrm{CO}}_{2}}=1.25,0.9,0.70\mathrm{and}0.50\mathrm{atm}$ at $T=820\xb0\mathrm{C}$. (

**b**) Reaction rate r vs. $\left(\frac{{P}_{e}}{RT}\right)\left(\frac{{P}_{{\mathrm{CO}}_{2}}}{{P}_{e}}-1\right)$ for the carbonation reaction of limestone-derived CaO under ${P}_{{\mathrm{CO}}_{2}}=1.25\mathrm{atm},0.9\mathrm{atm},0.70\mathrm{atm}\mathrm{and}0.50\mathrm{atm}$ at $T=820\xb0\mathrm{C}$.

**Figure 4.**Process variable profiles of reference conditions under a “fresh CaO” regime with respect to the (

**a**) CaO and CO

_{2}conversion, ${X}_{\mathrm{CaO}}$ & ${X}_{{\mathrm{CO}}_{2}}$; (

**b**) solid and gas phase temperatures, ${T}_{s}$ & ${T}_{g}$; (

**c**) pressure and gas voidage, $P{\epsilon}_{g}$; (

**d**) solid and gas phase velocities, ${u}_{s}$ & ${u}_{g}$.

**Figure 5.**Process variable profiles with wall temperatures under the “fresh CaO” regime with respect to the (

**a**) CaO conversion, ${X}_{\mathrm{CaO}}$; (

**b**) solid phase temperature, ${T}_{s}$; (

**c**) thermal power produced, ${Q}_{rxn}$; (

**d**) solid phase velocity, ${u}_{s}$.

**Figure 6.**Process variable profiles with CO

_{2}flow rate under a “fresh CaO” regime with respect to (

**a**) CaO conversion, ${X}_{\mathrm{CaO}}$; (

**b**) solid phase temperature, ${T}_{s}$; (

**c**) thermal power produced, ${Q}_{rxn}$; (

**d**) solid phase.

**Figure 7.**Process variable profiles with CaO flow rate under a “sintered CaO” regime with respect to the (

**a**) CaO conversion, ${X}_{\mathrm{CaO}}$; (

**b**) solid phase temperature, ${T}_{s}$; (

**c**) thermal power produced, ${Q}_{rxn}$; (

**d**) solid phase velocity, ${u}_{s}$.

**Figure 8.**Process variable profiles with carbonation pressure under a “sintered CaO” regime with respect to the (

**a**) CaO conversion,${x}_{\mathrm{CaO}}$; (

**b**) solid phase temperature, ${T}_{s}$; (

**c**) thermal power produced, ${Q}_{rxn}$; (

**d**) solid phase velocity, ${u}_{s}$.

Property | Fresh CaO | Sintered CaO |
---|---|---|

BET surface area (m^{2}/g) | 16.97 | 4.36 |

Mean particle diameter, d_{p} (×10^{−6} m) | 60 | 60 |

Pore volume, PV_{0} (×10^{−6} m^{3}/g) | 0.173 | 0.075 |

Pore surface area, S_{0} (×10^{7} m^{2}/m^{3}) | 3.58 | 1.16 |

Total pore length, L_{0} (×10^{14} m/m^{3}) | 2.79 | 0.54 |

Porosity, ε_{0} | 0.37 | 0.20 |

Ψ | 1.72 | 3.99 |

Process Parameters | Value |
---|---|

${d}_{p}$ (m) | 60 × 10^{−6} |

${\rho}_{\mathrm{CaO}}$ (kg m^{−3}) | 3340 |

${\rho}_{{\mathrm{CaCO}}_{3}}$ (kg m^{−3}) | 2700 |

$D$ (m) | 0.1541 |

$L$ (m) | 4.0 |

${c}_{p,s}$ (kJ kg^{−1} K^{−1}) | 1.00 |

$\mathsf{\Delta}{H}_{rxn}$ (kJ mol^{−1}) | 178.7 |

${\epsilon}_{w}$ | 0.7 |

$\sigma $ | 5.6704 × 10^{−8} |

Operating Conditions | Reference Value | Range in Sensitivity Analysis |
---|---|---|

Inlet reactants temperature (°C) | 200 | 25–200 |

Carbonator pressure (atm) | 1.0 | 0.5–1.0 |

Inlet solids flow rate (kg/h) | 20 | 10–30 |

Initial gas flow rate (kg/h) | 20 | 10–20 |

Reactor’s inner wall temperature | 700 | 400–800 |

**Table 4.**Reaction rate $r$ values for carbonation of limestone derived CaO under different ${P}_{{\mathrm{CO}}_{2}}$ conditions at $T=820\xb0\mathrm{C}$ obtained from RPM.

${\mathit{P}}_{{\mathbf{CO}}_{2}}\left(\mathbf{atm}\right)$ | 1.25 | 0.9 | 0.7 | 0.5 |
---|---|---|---|---|

$r$ (nm/s) | 4.5 | 2.5 | 1.6 | 0.7 |

Operating Conditions | Reference Conditions | Wall Temperature Effect | CO_{2} Flow Rate Effect |
---|---|---|---|

Inlet reactants temperature (°C) | 200 | 200 | 200 |

Carbonator pressure (atm) | 1.0 | 1.0 | 1.0 |

Inlet solids flow rate (kg/h) | 20 | 10 | 10 |

Initial CO_{2} flow rate (kg/h) | 20 | 10 | 10–30 |

Reactor’s inner wall temperature | 700 | 400–800 | 700 |

Maximum sorbent conversion | 70% | 70% | 70% |

Operating Conditions | CaO Flow Rate Study | Carbonation Pressure Study |
---|---|---|

Inlet reactants temperature (°C) | 25 | 100 |

Carbonator pressure (atm) | 1.0 | 0.5–0.9 |

Initial solids flow rate (kg/h) | 10–30 | 20 |

Initial CO_{2} flow rate (kg/h) | 10 | 10 |

Reactor’s inner wall temperature | 800 | 800 |

Maximum sorbent conversion | 20% | 20% |

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**MDPI and ACS Style**

Karasavvas, E.; Scaltsoyiannes, A.; Antzaras, A.; Fotiadis, K.; Panopoulos, K.; Lemonidou, A.; Voutetakis, S.; Papadopoulou, S. One-Dimensional Heterogeneous Reaction Model of a Drop-Tube Carbonator Reactor for Thermochemical Energy Storage Applications. *Energies* **2020**, *13*, 5905.
https://doi.org/10.3390/en13225905

**AMA Style**

Karasavvas E, Scaltsoyiannes A, Antzaras A, Fotiadis K, Panopoulos K, Lemonidou A, Voutetakis S, Papadopoulou S. One-Dimensional Heterogeneous Reaction Model of a Drop-Tube Carbonator Reactor for Thermochemical Energy Storage Applications. *Energies*. 2020; 13(22):5905.
https://doi.org/10.3390/en13225905

**Chicago/Turabian Style**

Karasavvas, Evgenios, Athanasios Scaltsoyiannes, Andy Antzaras, Kyriakos Fotiadis, Kyriakos Panopoulos, Angeliki Lemonidou, Spyros Voutetakis, and Simira Papadopoulou. 2020. "One-Dimensional Heterogeneous Reaction Model of a Drop-Tube Carbonator Reactor for Thermochemical Energy Storage Applications" *Energies* 13, no. 22: 5905.
https://doi.org/10.3390/en13225905