A Shrinking Core Model for Steam Hydration of CaO-Based Sorbents Cycled for CO 2 Capture

Calcium looping is a developing CO 2 capture technology. It is based on the reversible carbonation of CaO sorbent, which becomes less reactive upon cycling. One method of increasing the reactivity of unreactive sorbent is by hydration in the calcined (CaO) form. Here, sorbent has been subjected to repeated cycles of carbonation and calcination within a small fluidised bed reactor. Cycle numbers of 0 (i.e., one calcination), 2, 6 and 13 have been studied to generate sorbents that have been deactivated to different extents. Subsequently, the sorbent generated was subjected to steam hydration tests within a thermogravimetric analyser, using hydration temperatures of 473, 573 and 673 K. Sorbents that had been cycled less prior to hydration hydrated rapidly. However, the more cycled sorbents exhibited behaviour where the hydration conversion tended towards an asymptotic value, which is likely to be associated with pore blockage. This asymptotic value tended to be lower at higher hydration temperatures; however, the maximum rate of hydration was found to increase with increasing hydration temperature. A shrinking core model has been developed and applied to the data. It fits data from experiments that did not exhibit extensive pore blockage well, but fits data from experiments that exhibited pore blockage less well.


Introduction
Calcium looping is a CO2 capture technology that has been proposed for both pre-and postcombustion capture. Its advantages include the ability to reclaim high-grade heat, the use of a 4 relatively inexpensive, abundant and benign limestone-derived sorbent, and the potential to de-carbonise both power generation and cement manufacture. Post-combustion capture using calcium looping is currently being developed on a 1-2 MWth pilot scale [1,2], with long duration trials on a smaller 200-300 kWth pilot scale [3,4]. Calcium looping makes use of the reversible carbonation of CaO (see Rn. 1) to remove CO2 from a gas stream with a relatively low mole fraction of CO2 and provides a gas stream of concentrated CO2 suitable for compression and subsequent storage, in a cyclical process [5]. One aspect of the cycle that is disadvantageous is the rapid deactivation of CaO. Deactivation occurs primarily through CaO and reactive sinteringreduction of surface area and porosity associated with the high temperatures in the calcination environment and rearrangement upon reaction to form CaCO3 and reform CaO. However, other mechanisms such as sulfation, ash fouling and mass loss from the system also contribute to reductions in sorbent performance. Several techniques have been proposed for enhancement of sorbent, such as periodic reactivation of spent (unreactive) sorbent by hydration, generation of synthetic sorbents, and simple doping or thermal pre-activation of natural sorbents [6,7]. The focus here is on periodic reactivation by hydration. A simplified typical proposed calcium looping process for post-combustion CO2 capture with a hydration step is shown in Figure 1. Hydration of calcium oxide is not thermodynamically favoured in either the carbonator or calciner and must be performed in a separate vessel. It is desirable for the hydrator to operate at as high a temperature as possible in order to reclaim heat from the hydrator at as high grade as possible. This is especially important given that the endothermic dehydration reaction (reverse of Rn. 2) will be occurring in the carbonator, reducing the available heat to recover from the carbonation reaction (of course, the stream could also go into the calciner). Assuming an atmospheric pressure hydrator, the maximum temperature of operationi.e., at 101 kPa steam pressure -would be ≈ 793 K (calculated by use of thermodynamic data from NASA Glenn [8]). In practice, the temperature would be lower than this (i) because the steam pressure is likely to be lower and (ii) in order to increase the difference between the equilibrium concentration and steam pressure to enhance the driving force of the hydration reaction. A fraction of the solids from the calciner are sent to the hydrator, rather than back to the carbonator, whereupon CaO reacts with steam exothermically to form calcium hydroxide (Rn. 2). The hydrated solids are then returned to the carbonator, whereupon they exhibit an increased reactivity towards CO2 6 [9][10][11]. The solids are taken from the calciner to ensure as high a hydration conversion as possible; CaCO3 formed in carbonation can form a shell across which limited diffusion takes place [11,12]. The solids are then returned to the carbonator in order to achieve higher conversions to CaCO3 and reduced attrition than if returned to the calciner [13,14]. Arias et al. [15] have shown that, even with hydration conversions as low as 60%, the carrying capacity of sorbents in the system could be significantly enhanced, increasing capture efficiency and reducing the necessary amount of material in the system. This enhancement will involve a trade-off with the increased costs of generating steam and would be improved further by increasing the hydration conversion [16]. It should be noted that, while most researchers consider periodic hydration of sorbent, researchers at Ohio State University have developed a process whereby sorbent is hydrated between every calcination and carbonation [17]. The mechanism of enhancement is not clear, but work on the analogous reactivation process for sulfur capture from FBCs suggests that H2O molecules penetrate the product layer more readily than CO2 and result in the opening up of pores and new surface area of the sorbent [18]. Particles have also been shown to be prone to fracture upon hydration [10,19,20], which would also increase reactive porosity.
However, while there have been many general papers on the effects of using hydrated sorbent for CO2/SO2 capture, few have investigated the kinetics of the gas-solid reaction of H2O with CaO. Maciel-Camacho et al. [21] investigated the hydration kinetics of lime pellets at low temperatures (less than 373 K) and low partial pressures of water vapour (1.2 to 3.6 kPa). Shiying Lin and colleagues [22][23][24] have published several papers on hightemperature and high-pressure hydration of various calcined limestones in a pressurised thermogravimetric analyser in relation to the HyPr-RING process. HyPr-RING is a pressurised gasification process with in situ CO2 capture, which occurs under pressures that also allow in situ hydration. They investigated hydration rates at 773 to 1023 K and pressures of 0.67 to 3.8 MPa. Serris et al. [25] have investigated the hydration of calcined limestones 7 temperature range of 343 to 693 K (though mostly < 423 K) with hydration pressures of between 0.5 and 16 kPa. Serris et al. [25] report an anti-Arrhenius effect (i.e., rates decrease with increasing temperature), which is contrary to findings by Maciel-Camacho et al. [21]. All researchers reported an increase in hydration kinetics with increasing partial pressure of steam/water [21][22][23][24][25], and, where studied, low activation energies (19.9 [21], 8.4 [23] and 11-20.3 [24] kJ/mol) and reduced kinetics for more highly sintered particles/pellets [21,25]).
Criado et al. [26] and Schaube et al. [27] have recently investigated the kinetics of hydration with relation to energy storage applications. Criado et al. [26] demonstrated that a shrinking core model, with assumed equimolar counterdiffusion, could be used to effectively model the steam hydration of lime by investigating the kinetics for a variety of particle sizes.
This paper is a follow up to previous work [28], which showed that the hydration temperature and prior cycling conditions have a significant influence on the conversion to calcium hydroxide. Here, the experiments have been modified in order to further investigate the kinetics of the gas-solid reaction of H2O with calcined limestone at elevated hydration temperatures (473 to 673 K). This paper develops work previously performed by Maciel-Camacho et al. [21] and Criado et al. [26], who have shown that a shrinking core model with equimolar counterdiffussion can be used to effectively model the hydration reaction. A shrinking core model with a non-equimolar scenarioas is the case for the hydration reaction has been developed and applied to a wide range of experimental data for different hydration temperatures and CaO of different porosities. This paper does not comment on the reactivity of the hydrated sorbents towards CO2; however, the assumption is that subsequent carbonation conversion will increase with increasing hydration conversion (as shown in, e.g. Blamey et al. [28]). A shrinking core model is then applied to the experimental data. 8

Experimental
Experiments were carried out in a similar manner to experiments described elsewhere [28]; the primary difference is the mass of calcined material for kinetic experiments, which has been reduced here in order to reduce effects of mass transfer through the sample. Samples of Havelock limestone (purity 96.3% CaCO3, full elemental analysis published elsewhere [19]) were subjected to a number of cycles ( ) of carbonation and calcination in a small benchscale fluidised bed reactor (development described elsewhere [19]) before being removed following calcination. Subsequently, aliquots of these samples were taken and subjected to hydration in a thermogravimetric analyser (TGA) at various hydration temperatures for kinetics experiments. The maximum value investigated for N, the cycle number before hydration, was 13. This corresponds to a carbonation conversion of available CaO sites of 14% (or 10 g CO2/g calcined sorbent) [19]. Therefore, a system whereby reactivation of sorbent is done after a relatively small number of cycles is investigatedas discussed by Martinez et al. [16] rather than deep reactivation of highly unreactive sorbent after larger numbers of cycles (e.g., sorbent of reactivity of 6% after 50 cycles).

Cycling Experiments
The cycles of carbonation and calcination in the fluidised bed reactor [19] were performed Calcination was carried out at 1173 K for 900 s and carbonation was carried out at 973 K for 900 s. Both calcination and carbonation were carried out at 101 kPa under a 15% (v/v) CO2, balance N2, atmosphere with a cold (293 K) flow-rate of 47.5 cm 3 /s, which corresponded to U/Umf ≈ 7 at 973 K. Samples were cycled for 0 cycles (i.e., one calcination, with no carbonation), 2 cycles (1 calcination with 2 cycles of carbonation and calcination), 6 cycles or 13 cycles, before being removed from the fluidised bed following the final calcination and placed in a desiccator. Then, the samples were sieved to obtain sorbent particles > 500 µm -i.e., to separate the limestone from the sandand stored in a vial within a desiccated jar prior to steam hydration in the TGA.

Hydration Experiments
Hydration was carried out in a TGA (Perkin Elmer TGA 7) on 4.5 ± 0.5 mg aliquots of sorbent particles; this represents a well-dispersed monolayer of particles. Hydration was carried out at average temperatures of 473, 573 and 673 K. In each case, samples had unavoidably hydrated slightly during transfer/separation (less than 13%), and, therefore, were first heated to 673 K at 0.83 K/s under N2, cold flow-rate 10 cm 3 /s, to dehydrate before the temperature set-point was changed to the hydration temperature. The samples were < 1% carbonated; therefore, no prior decarbonation was deemed necessary. The furnace was turned off and the sample cooled prior to stabilisation at the desired temperature for 300 s. Cooling and stabilisation took 300 s at 673 K, 1080 s at 573 K, and 1620 s at 473 K. Then, reaction gas, with an equivalent total cold (293 K, 101 kPa) flow-rate of 100 cm 3 /s was injected to the system. The steam was generated using a syringe pump and a steam generation system and was preheated before injection.

Physical Properties of Cycled Sorbent
The cycled sorbent (i.e., the sorbent prior to hydration) was subjected to nitrogen adsorption (Micromeritics Tristar 3000 N2 Sorption Analyser) and mercury porosimetry (Micromeritics Autopore IV) analyses to establish the BET surface area, the BJH porosity associated with small pores, the skeletal density and total porosity (see Table 1). Data show that the BET surface area and the porosity associated with small pores (≲ 1 μm) decreased markedly upon cycling; the BJH porosity associated with small pores decreased more gradually than the surface area. The approximate total porosity (5 nm to 360 μm) also decreased and the envelope density (the density including pores) increased markedly (an increase of ≈ 40%).
The surface area and porosities of the samples shown are for the calcined sorbent prior to hydration. the overall conversion to Ca(OH)2 was low after 900 s. This is most likely from pore blockage resulting in very slow gas diffusion through pores or solid-state diffusion; though this was less clear than observed in previous work [28] with larger sample sizes (4.5 vs 18 mg). This state is reached more rapidly for the samples cycled to greater extents, because of their reduced porosity associated with small pores (see BJH porosity of Table 1), which are more prone to blocking upon formation of Ca(OH)2, which has a higher specific volume per mole of CaO present. The lower overall porosity will have an effect alsosee mercury porosimetry porosity data of Table 1.  should be noted that the model developed is for a particle of constant diameter, whereas particles have been shown to expand upon hydration [19]; this assumption is good as a first approximation, but is worthy of further study.

Model Assumptions
The assumptions of the SCM are:  The hydration of calcium oxide (Rn. 2) occurs at the interface of a pure, porous, unreacted CaO core and a pure, porous, Ca(OH)2 product layer (see Figure 3) 13  The external particle size remains constant during reaction;  Diffusion through the bulk phase to the particle surface follows Chapman-Enskog theory [29];  Particles are treated as isolated spheres;  Mass transfer through a product layer of uniform porosity and pore size is modelled considering bulk diffusivity and Knudsen diffusivity as resistances in series;  The reaction kinetics at the surface of the core are first order;  The system remains isothermal upon reaction.

Model Development
The full model derivation is outlined in Supplementary Information.

Bulk Diffusivity and Mass Transfer Coefficients
The gas-phase diffusivity was calculated from Chapman-Enskog theory (see Table 2) [29].
The collision diameter of the gas mixture and the collision integral were calculated using a equations and data provided by Cussler [29]. The Sherwood Number for this work has been estimated using a correlation from Perry and Green [30], which is dependent on the Reynolds and Schmidt Numbers. Fluid viscosities and densities were obtained from the NIST Chemistry Webbook [31] and the fluid velocity was calculated for the temperatures of interest using a cold (293 K) inlet flow-rate of 100 cm 3 /s and an internal diameter of the TGA furnace of 17 mm. As a result, an estimate of the mass transfer coefficient ( g ) was calculated (see Table 2) for the temperatures of interest from the Sherwood Number, gas-phase diffusivity and the particle diameter.

Intra-Particle Diffusivity
The mechanism of diffusion through the particle has to be established, in order to calculate the intra-particle diffusivity. To establish whether Knudsen diffusion contributes, the mean free path of molecules has to be compared to the average pore diameter; Knudsen diffusion occurs when molecules collide with pore walls more frequently than with other molecules.
The mean free path was calculated, using as 208, 252 and 296 nm for 473, 573 and 673 K respectively. The pore size distribution of the Ca(OH)2 product layer through which the steam diffuses to react with the CaO was not directly measured. Therefore, it was calculated indirectly, using data obtained for porosity (obtained from mercury porosimetry measurements, < 360 μm) and average pore diameter (as obtained from nitrogen adsorption studies) for the cycled CaO. First, the porosity of Ca(OH)2 was calculated from a mass balance of CaO and Ca(OH)2, assuming no change in particle/layer size (see Eq. 2). Then, the average pore size was calculated, assuming a constant pore length (see Eq. 3), i.e., constant growth along the length of the pore. Experimental data for CaO and calculated data for Ca(OH)2 are presented in Table 3. The pore diameter (7-14 nm) is therefore smaller than the mean free path length ( , 210-300 nm). The Knudsen Numbers ( / pore ) are between 15 and 45depending on extent of cycling and temperature of hydration, which are within the range in where Knudsen diffusion is expected. The Knudsen diffusivity ( K ) was calculated according to Eq. 4 (see Table 4), using the molar mass of H2O [29]. Then, the effective diffusivity ( ) through the pores was derived according to Eq. 5 using the conventional expression for resistances in series [32] combined with a term to account for porosity and pore tortuosity [29] (see Table 4). The pore tortuosity ( pore ), which is a factor to account for the non-linear nature of pores, was taken as 3; this is a typical value suggested, in absence of experimental data, by Cussler [29].

Mass Balance on Ca(OH)2 Formation during Reaction
A balance on the number of moles of CaO at time has been performed. Noting that (i) the rate of production of Ca(OH)2 is the negative rate of production of CaO and (ii) the rate of production of Ca(OH)2 is also the negative rate of production of H2O, the rate of production of Ca(OH)2 can be calulated and the rate of change of the core radius can be derived. A constant external diameter of particles has been assumed; therefore, the radius at the core can be related to the conversion to Ca(OH)2 ( Ca(OH) 2 ) within the particles. This gives a relationship between experimentally derived rates of reaction and the flux of H2O at the interface of the core and the product layer. Similar derivations are given in, e.g., Fogler [33]. Eq. 8

First Order Kinetics of Reaction
First order reaction kinetics is assumed and therefore the rate of formation of Ca(OH)2 is given in Eq. 9, where A is the first order rate constant per unit surface area, V is the BET surface area per unit volume (using data presented in Table 1, expressed in m 2 /m 3 , calculated from V = BET CaO (1 − CaO )) and C and E are the mole fraction of H2O at the core and the mole fraction associated with the equilibrium partial pressure of H2O over Ca(OH)2 at the temperature of hydration respectively. ( C − E ) is chosen as the effective mole fraction of H2O driving the reaction; note that the reaction will cease if C = E .
Eq. 9 The molar rate of reaction of Ca(OH)2 is related to the flux of H2O at the interface of the core and the product layer using Eq. 10; it therefore follows that the flux of H2O at the interface can be presented by Eq. 11.

Application of the Shrinking Core Model
To recap, the key equations are: (i) Eq. 1 for mass transfer of H2O to the particle surface; (ii) Eq. 7 for mass transfer of H2O through the product layer; (iii) Eq. 11 for mass transfer of H2O 19 to form Ca(OH)2 by reaction; and (iv) Eq. 8 relating mass transfer of H2O at the interface of the core and the product layer to experimental data.
A solution for A was found for each set of experimental conditions separately (i.e., for each hydration temperature and number of cycles before hydration). Initially, 41 data points were taken from each experiment at equal conversion increments for conversions to Ca(OH)2 of between 0.05 and either 0.95, if full conversion was achieved, or the final conversion at = 1080 s. Subsequently, S and C were calculated for all data points, using values of Ca(OH) 2 / and Ca(OH) 2 determined experimentally. S and C could not be calculated analytically and, therefore, were established numerically using a script written in Matlab.
Then, A was calculated for each experiment from Eq. 11 by a least squares method across all data points using a script written in Matlab. In this way, a value of A was established for each set of experimental conditions. The values of A obtained were then used to obtain projected idealised model results for S , C and Ca(OH) 2 as a function of time.

Shrinking Core Model Results and Discussion
Data obtained for A are given in Table 5 The reason for the over-prediction at higher conversions for the samples at (i) higher cycling extents and (ii) higher temperatures is likely to result from pore closure as well as the method of solution of the model. Pore closure owing to surface sintering is more likely in these cases, because (i) the samples are less porous at higher cycling extents and, even if the larger pores do not close, smaller reactive pores will be prone to closure upon formation of the less dense Ca(OH)2 from CaO, and (ii) sintering of Ca(OH)2 is accelerated at higher temperatures. Pore closure would result in a necessary change of mechanism from gaseous diffusion of H2O molecules to an -OH solid-state diffusion mechanism. It should be noted that, if porosity is to be closed in the model, lower values of initial porosity should be used (i.e., less than 180 μm rather than 360 μmor only those associated with small pores, e.g., < 1 μm). Another reason for the significant overshoot of conversion at higher times is that the model was developed with data chosen at incremental steps of conversion. As a result, there are fewer data points from higher time periods (because the rate of change in conversion is much lower). This results in an increased weighting to the kinetic data obtained at lower times. If 22 time had been used as the increment the conversion after ≈ 600 s would be much more accurate; however, the initial rate would then be considerably underestimated. There may also be further errors in the geometrical assumptions of the model introduced by (i) the nonspherical nature of particles and (ii) the fact that large cracks and large pores will be present in the limestone.  Table 5 shows that no significant trends for A are observed, except that it decreases with increasing number of cycles and there is a general tendency to decrease with increasing temperature. The value of A should be constant for all cycle numbers at the same hydration temperature, because this is the intrinsic rate of reaction of CaO per available surface area.
The fact that it is not consistent suggests a breakdown of the model at higher cycle numbers.
One potential explanation for the deviation at higher cycle numbers is the shift to a reaction based on solid state diffusion, which is more important in systems where pore closure is observed. Accurate modelling of this process would require additional terms in the shrinking core model. A decreasing value of A with increasing temperature would be consistent with anti-Arrhenius behavior observed by Serris et al. [25] 23

Concluding Remarks
A study has been undertaken in a TGA that investigates the kinetics and maximum conversion to Ca(OH)2 of cycled CaO upon reaction with steam at three temperatures between 473 and 673 K. It has been shown that:  Samples cycled minimally (1 calcination or 2 cycles) readily hydrate to completion across all temperatures;  Rate of hydration decreases with increasing cycle number, because of the lower reactive surface areas;  Maximum hydration extent over the 900 s of hydration decreased with increasing cycle number and increasing hydration temperature;  A shrinking core model incorporating non-equimolar counterdiffusion has been developed and fitted to data, which fits the data well  However, inconsistencies of the value of A at higher cycle numbers suggest a breakdown of the shrinking core model, likely due to pore closure and mechanism change from gaseous diffusion to solid-state diffusion.
These findings have important ramifications for the use of hydration as a reactivation strategy.
Ideally, higher hydration temperatures would be used to reclaim higher grade heat from the exothermic hydration reaction; this might have to be done at the expense of hydration conversion, which decreases at higher temperatures. In addition, there is likely to be more benefit from reactivating extensively cycled/sintered sorbent; however, the most highly cycled sample tested here showed the lowest hydration conversion and is therefore likely to show the lowest reactivity upon further carbonation (hydration extent and subsequent carbonation extent have been linked elsewhere [28]). It should be noted that this can correspond to a greater increase in comparative carbonation conversion than samples achieving full conversion after fewer cycles, which already showed high carbonation conversions.