Decay on Cyclic CO₂ Capture Performance of Calcium-Based Sorbents Derived from Wasted Precursors in Multicycles

Abstract

In order to obtain the cheap waste calcium-based sorbent, three wasted CaCO₃ precursors, namely carbide slag, chicken eggshells, and analytical reagent-grade calcium carbonate, were selected and prepared at 700 °C to form calcium-based sorbents for CO₂ capture. TGA was used to test the CO₂ uptake performance of each calcium-based sorbent in 20 cycles. To identify the decay mechanism of CO₂ uptake with an increasing number of cycles, all calcium-based sorbents were characterized by using XRF, XRD, and N₂ adsorption. The specific surface area of calcium-based sorbents was used to redefine the formula of cyclic carbonation reactivity decay. The carbonation conversion rate of three calcium-based sorbents exhibited a decreasing trend as the cycle number increased. Chicken eggshells exhibited the most significant decrease rate (over 50% compared with Cycle 1), while carbide slag and analytical reagent-grade calcium carbonate showed a flat linear decline trend. The specific surface area of the samples was used to calculate carbonation conversion for an infinite number of cycles. The carbonation conversion rates of three calcium-based sorbents were estimated to decrease to 0.2898, 0.1455, and 0.3438 mol/mol, respectively, after 100 cycles.

1. Introduction

Anthropogenic climate change, which is caused by a large number of greenhouse gas emissions, especially the emission of CO₂, is becoming a focus and severe challenge for many countries in the world [1]. According to their own national conditions, many countries have set up their own targets of carbon peak carbon neutralization by the end of 2060 or 2050 [2]. Reducing the cosumption of fossil fuels and promoting the application of CCUS (Carbon Capture, Utilization and Storage) are the most important technical measures for achieving the target of carbon neutralization on the premise of ensuring national energy security. Untill now, the fossil fuel power plants are still the primary contributor to anthropogenic CO₂ emissions, which accounted for more than 33% of global CO₂ emissions. Even the hydrogen energy, a promising alternative energy source, is still mainly produced from fossil fuels [3,4,5]. As a result, it will become more and more important to further develop high-efficiency, low-cost and large-scale CCUS technology in the near future, especially for China, which is the country with the most coal-dominant energy structure [6,7,8].

There are many CCUS technologies, such as the membrane separation method, the chemical absorption method, the solid sorption method, and the low temperature condensation method. Membrane separation technology is characterized by a small footprint, low energy consumption, easy operation and low pollution, and is considered as the most promising gas separation technology [9]. Amine absorption [10] is the most common industrial technology for capturing CO₂ from smoke flow, but it is limited to low-temperature (40–150 °C) applications, and incurs a considerable cost and requires a high degree of energy for absorber regeneration, which is vulnerable to equipment corrosion and may produce dangerous waste by-products. Solid physical sorption of microporous and mesoporous materials such as activated carbon, zeolite and carbon fiber can also capture CO₂ at low temperatures, but they are not effective above 300 °C. If the gas can exceed 500 °C, the use of activated carbon and zeolite may require cooling and additional costs [11]. Alkaline metal base chemical sorption at high temperatures can better solve the problem of CO₂ capture under high temperature conditions. CaO-based sorbents, including calcium carbonate, carbide slag and eggshell, show high CO₂ capture ability, stability and durability after a repeated cycle, good wear resistance and mechanical strength, good dynamic characteristics, strong competitive cost and good regeneration. These factors make CaO a good sorbent for capturing CO₂ [12]. The low-temperature condensation method achieves separation of CO₂ from flue gas by liquefaction, and is only applicable to mixed gas with high CO₂ concentration [13]. The main problems are its large system area and high energy consumption.

Compared with other capture methods, including amine absorption [14], absorption of microporous, and mesoporous materials [11], calcium looping for CO₂ capture from the fossil fuel combusiton flue gas by absorption/separation through the use of calcium-based sorbents is regarded as a cheap CO₂ capture technology with large-scale commercial application and high CO₂ capture efficiency [15,16]. Calcium-based sorbents undergo carbonation within the temperature range from 600 to 700 °C, which involves capturing CO₂ from flue gas to generate calcium carbonate (CaCO₃). Subsequently, CaCO₃ undergoes calcination within the temperature range from 850 to 950 °C, producing a highly concentrated CO₂ flue gas, which can be separated, and calcium-based sorbents can be cycled in the calcium looping process [17,18].

After a limited re-cycle number, the adsorption properties of calcium-based absorbent show a noticeable trend of decay owing to the high-temperature sintering in the calcination process [19,20,21]. The micropore characteristics as well as particle surface area could be gradually decreased due to the high-temperature sintering behavior in the multiple cyclic calcination process, and then influence the carbonate conversion rate of absorbents. Furthermore, a growth of CaO sub-grain will also decrease the surface reaction and melting of the micro-surface from the fuel or absorber impurities. Therefore, the rate and extent of the gas-solid reaction are reduced [22]. A small amount of water vapor in flue gas plays a certain role in improving sintering. Ca(OH)₂ generated by the reaction between water vapor and CaO decomposes into CaO with smaller crystal size during dehydration, which can achieve higher porosity, larger surface area and pore volume, and higher reactivity, and can promote the carbonation reaction [23,24]. CaO mixed with the polystyrene spheres by template synthesis in the desired ration to obtain innovative CaO-based sorbents, has shown a good performance of sintering resistance, too [25,26].

The decay mechanism of cyclic CO₂ capture performance by calcium-based sorbents can be evaluated by its physical and chemical characterizations [27], including XRD test (the components and crystal structure of sorbents), BET test (surface and pore size distribution) and SEM test (the surface microstructure and product characteristics), etc. Scientists have conducted numerous studies to describe the decay mechanism of calcium-based sorbents and proposed the prediction models characterizing the cyclic attenuation characteristics of calcium-based sorbents [28,29,30,31], along with the suitable methods or recommended values to determine parameters in the model. However, the precursors of CaO-based sorbents have different solid phases or polymorphs crystal structures. For example, the XRD patterns reveal that calcite belongs to a trigonal symmetry system, and it has a broad particle size distribution; aragonite belongs to an orthorhombic crystal system, and it has needle-like crystal habits; while vaterite belongs to a hexagonal crystal system, and it has no distinct morphology [27]. The critical parameters in the above model should be associated with the physicochemical characterization of sorbents for their different crystal structures.

Therefore, 20-cycle experiments with those three types of calcium-based sorbents for CO₂ capture under the non-isothermal thermogravimetric condition were performed to explore the the decay characteristics of the best sorption capacity of sorbents in the multicycle and calculate the hypothetical carbonation conversion and carbonation conversion for an infinite number of cycles by redefining them based on the physical and chemical characterization results.

2. Experiment

2.1. Preparation of Waste Calcium-Based Sorbents

In order to reduce the cost of calcium-based sorbents, carbide slag and chicken eggshells were used in this study, and analytical reagent (AR)-grade CaCO₃ was also used for comparative analysis with carbide slag and chicken eggshells. Carbide slag and chicken eggshells were obtained from a resin manufacturing plant and a cake factory in Guizhou Province, China, respectively. In order to improve the grinding quality of calcium-based sorbents (carbide slag, chicken eggshells, and AR-grade CaCO₃), the three calcium-based sorbents were dried in an electric blast drying oven (101-0ASB; Guizhou Hengtai Kelian Co., Ltd., Guiyang, China) at 120 °C for 2 h firstly, and ground and sieved to obtain 150-mesh particles (105 μm). After calcination in a muffle furnace (Smart-1, China) at 700 °C for 20 min, the sorbents were removed cooled in an airtight drying cabinet, and transferred to bottles for storage. The calcined carbide slag, chicken eggshells, and AR-grade CaCO₃ sorbent samples were named CS, RES, and APC, respectively.

2.2. Experimental System and Operating Conditions for CO₂ Capture

The experiment was performed on a simultaneous thermogravimetric analyzer (STA) (STA409 PC; NETZSCH, Selb, Germany), as shown in Figure 1. Features of the STA were shown as follows: simultaneous TG and DSC signal measurements; automatic generation of TG/DSC curves; temperature ramp rate: 0.1–50 °C/min; temperature measurement range: from ambient temperature to 1500 °C; reaction atmospheres: oxidizing, reducing, inert, and certain corrosive gases (non-toxic, not highly flammable); maximum sample weight: 18 g; constant-temperature water bath.

To control the precision of sample weights, 10 mg of each calcium-based sorbent sample was measured for each experimental run using an electronic analytical balance (BT25S; Sartorius, Gottingen, Germany) with a readability of 0.01 mg.

Table 1. Experimental conditions for cyclic calcination/carbonation.

Step	Temperature Range (°C)	Reaction Gas	Gas Flow Rate (mL/min)	Rate of Temperature Increase (Decrease) (°C/min)	Stage
1	30–600	N2	50	5	Preheating
2	600–750	N2	50	5	Carbonation
		CO2	20
3	750–900	N2	50	5	Calcination
4	900–600	N2	50	5	Cooling
5	Repeat steps 2–4

shows the reaction conditions for the cyclic calcination/carbonation experiment. The various steps of the reaction process were as follows. (1) Step 1 (preheating stage): temperature was increased from 30 °C to 600 °C at a heating rate of 5 °C/min in an N₂ atmosphere; this stage is mainly to remove the moisture component of sorbents in long term storage. (2) Step 2 (carbonation stage): CO₂ at a concentration of approximately 30% was introduced for the simulation of flue gas, and the system was further heated to 750 °C at a rate of 5 °C/min for carbonation; this stage is the process of gaining weight. (3) Step 3 (calcination stage): inflow of CO₂ was stopped, the flow rate of N₂ was kept unchanged, and the temperature was increased to 900 °C at a rate of 5 °C/min for calcination; this stage is the process of losing weight. (4) Step 4 (cooling stage): The flow rate of N₂ was kept unchanged, and the system was cooled to 600 °C at a rate of 5 °C/min; this is the temperature condition for the carbonation reaction again. After the completion of one cycle, the next cycle was performed by repeating Steps 2 to 4.

2.3. Analysis Methods

To determine the reactivity of calcium-based sorbents during the carbonation stage, the initial mass of each experimental sample, the mass of the sample before and after each carbonation cycle, mass fraction of CaO in the sample, and molar masses of the reaction products were used for the calculation of carbonation conversion ($X_N$) [32,33], carbonation conversion rate ($R_N$), amount of CO₂ captured ($C_N$), and calcination decomposition ($Y_N$) using Equations (1)–(4) below:

$$X_N=\frac{m_{N,t}-m_{N,s}}{A{m}_0}\times \frac{M_{CaO}}{M_{{CO}_2}}$$

(1)

where $X_N$ is the carbonation conversion during Cycle N (mol/mol); $m_0$ is the initial mass of the sorbent (g); $A$ is the mass fraction of CaO in the sorbent; $m_{N,t}$ is the mass of the sorbent during Cycle N or at time t (g); $m_{N,s}$ is the initial mass of the sorbent for Cycle N (g); $M_{CaO}$ is the molar mass of CaO (g/mol); and $M_{CO}{}_2$ is the molar mass of CO₂ (g/mol).

$$R_N=\frac{d{X}_N}{dt}$$

(2)

where $R_N$ is the carbonation conversion rate during Cycle N (s-1); t is the reaction time (s).

$$C_N=\frac{m_{N,t}-m_{N,s}}{m_0}$$

(3)

where $C_N$ is the amount of CO₂ captured during Cycle N (g/g).

2.4. Characterization of Sorbents

The mass percentage of the main components of the sample was detected by an X-ray Fluorescence (XRF) spectrometer (Netherlands Panaco, Axiosmax wavelength dispersive).The phase composition of the calcium-based sorbent hole was tested by a small-angle X-ray Diffraction (XRD) spectrometer, (German Broker, D8 Advance), and the pore structure and specific surface area of the calcium-based sorbent were tested using the automatic specific surface microvoid analyzer (American Mick, ASAP2460 (M)).

3. Results and Discussion

3.1. Characterization Analysis of Sorbents

Figure 2 shows the XRD pattern of CS, RES, and APC. The CaO diffraction peaks with the same trend appear at 32.39°, 37.54°, 54.03°, 64.30°, and 67.52°. The peak height was the highest at 37.54°, implying that the three sample precursors were fully decomposed into CaO after calcination. The main peak of REG is higher and narrower than that of CS and APC, which means larger grain size according to Debys-Scherer’s formula. The quantitative composition analysis of CS and RES was completed by XRF, as shown in

Table 2. The chemical composition of samples (wt %).

Component Sample	CaO	SiO2	Al2O3	Fe2O3	MgO	Other	LOI
CS	73.88	4.6	2.69	0.35	0.015	0.645	17.82
RES	85.15	0.04	0.43	0.12	0.015	1.184	13.061

. Because of different precursors, the mass percentage of CaO in the sample was different. APC was the largest while CS was the smallest.

The N₂ adsorption isotherms of the samples are shown in Figure 3. They were concave in the early stage, linear in the middle stage, and convex in the late stage with the relative pressure p/p°. The isotherm had an obvious inflection point in the low-pressure region. The first layer of adsorption was before the inflection point. As the relative pressure increased, multi-layer adsorption began to occur. The isotherms showed a rapid growth trend until reaching the saturation state when the relative pressure p/p° range was within 0.85 to 1. There was a narrow H₃-type hysteresis loop when the relative pressure p/p° range was within 0.75 to 1, characterized by macroporous channels and micropore dysplasia. Hence, the isotherms were classified as type IIb according to the International Union of Pure and Applied Chemistry physical adsorption [34].

The specific surface area was calculated using the BET method (SBET) according to isotherm type using the N₂ adsorption data. The density functional theory method was applied to obtain the size distribution by solving the generalized adsorption isotherm (GAI) integral equation, which is based on the assumption that the measured isotherm is composed of a large number of single-pore isotherms, and this is how the isotherms are distributed. The total pore volumes V_total was calculated according to the adsorbed quantities of N₂ at the relative pressure p/p° of ca. 0.995. The average pore diameter was obtained using 4V_total/S_BET.

Table 3. Surface and pore structure statistics of samples measured from N₂ absorption.

Samples	SBET (m2 g−1)	Vtotal (cm3 g−1)	Average Pore Diameter (nm)
CS	18.4321	0.132978	29.0178
RES	15.2060	0.080103	21.0714
APC	23.6375	0.128815	21.7984

shows the highest adsorbed capacity and largest average pore diameter for sample CS, the largest specific surface for sample APC, and the lowest value of three parameters for sample REG. Figure 4 confirms the ordering of the above parameters. Based on pore structure, the samples were mainly composed of mesoporous (2–50 nm) and microporous (>50 nm) structures, and microporosity was scarcely developed. Sample APC had a well-developed mesoporous structure, with a pore diameter around 7–30 nm. The microporous structure was relatively developed for sample CS, and sample RES showed mesoporous characteristics within a more comprehensive pore diameter range.

3.2. Influence of Cycle Number on CO₂ Capture Characteristics of Calcium-Based Sorbents

Figure 5 shows the influence of cycle number on the CO₂ capture characteristics of the three sorbents. Figure 5a shows that the carbonation conversion (X_N) of CS and RES exhibited a decreasing trend as cycle number increased. RES exhibited the most significant decrease in X_N, with X₆ having a value of 0.331 mol/mol, which decreased by 50.68% as compared with X₁. The XN values for CS followed a linear trend of decrease. The average decay of carbonation conversion after each cycle was approximately 0.01 mol/mol. For APC, optimum carbonation conversion and stable reactivity were maintained throughout the 20 cycles. The difference in X_N with CS increased as the cycle number increased. Figure 5b shows the relationship between CO₂ captured (C_N) and cycle number. During the 20 cycles, the C_N value of APC remained higher than that of other sorbents. Except for the first six cycles, the trends of CN for CS and RES were similar. As the cycle number increased, the difference in CN between APC and CS varied within the range of 0.151–0.158 g/g. The differences between APC and RES varied within the scope of 0.313–0.325 g/g.

Furthermore, the influence of cycle number on the CO₂ capture characteristics of CS can be determined from the analysis of Figure 5 and Figure 6. As shown in Figure 5, X_N reached a maximum value of 0.726 mol/mol during Cycle 1 and subsequently decreased as the cycle increased. The value of X₂₀ was 0.514 mol/mol, which was 29.28% lower than that of X₁. To further investigate the influence of cycle number on carbonation in CS, the variations in X_N and C_N with reaction time during ten cycles, including Cycles 1 and 20, were analyzed in detail. From Figure 6, it can be seen that the curves shifted toward the right as the cycle number increased, which indicates a decrease in the duration of the rapid chemical reaction-controlled stage. This may be explained by changes in micropore structures on the sorbent surfaces caused by high-temperature sintering. In each cycle, grain growth occurred during carbonation, and grain fragmentation occurred during calcination, which may have influenced the micropore structures and porosity of the sorbent and resulted in a reduction in CO₂ capture activity. Conversion at the same reaction time point decreased as the cycle number increased. At a reaction time of 3 min, the values of X_N and C_N were 0.377 mol/mol and 0.219 g/g during Cycle 1. The corresponding values for Cycle 20 were 0.095 mol/mol and 0.055 g/g, which had decreased by 74.96% compared with Cycle 1. The degrees of carbonation during Cycles 7 to 20 were relatively similar. At a reaction time of 15 min, the values of X_N and C_N were 0.563 mol/mol and 0.327 g/g during Cycle 1. The corresponding values for Cycle 20 were 0.310 mol/mol and 0.180 g/g, which had decreased by 44.94% compared with Cycle 1. Differences in X_N and C_N were significant between adjacent cycles. During the reaction period of 3–15 min, differences in X_N and C_N between adjacent cycles gradually increased with time. They gradually decreased with an increase in the cycle number.

From Figure 5, it can be seen that X₁ and X₂₀ for RES were 0.672 mol/mol and 0.192 mol/mol, respectively, which indicates a 71.43% decrease from Cycle 1 to Cycle 20. Figure 7 shows that the reactivity of RES was significantly higher during Cycle 1. At a reaction time of 3 min, the values of X_N and C_N were 0.334 mol/mol and 0.223 g/g during Cycle 1; however, the corresponding values for Cycle 3 had decreased considerably to 0.084 mol/mol 0.056 g/g. As the cycle number increased, the degree of carbonation at the same reaction time point decreased gradually. Except for the first two cycles, there were few changes in the X_N values for RES after 3 min of reaction in each cycle.

As shown in Figure 5, the decay of X_N of APC with an increase in cycle number was less significant than CS and RES. X_N reached a maximum value of 0.747 mol/mol during Cycle 1 and subsequently decreased continuously to 0.591 mol/mol after Cycle 20; a 20.87% decrease compared with Cycle 1. From Figure 8, it can be seen that the degrees of carbonation at a reaction time of 3 min were similar among the various cycles. This may be because the rapid chemical reaction-controlled stage was mainly influenced by reaction temperature and external surface area, which limited the influence of sintering-induced micropore structure changes after multiple cycles on the degree of carbonation in APC during this stage. The X_N values after 3 min of reaction for the various cycles exhibited significant changes with an increase in reaction time. At a reaction time of 15 min, the values of X_N and C_N were 0.492 mol/mol and 0.377 g/g during Cycle 1; the corresponding values for Cycle 20 were 0.378 mol/mol and 0.292 g/g, and the difference between the maximum and minimum X_N values and difference between the maximum and minimum C_N values for APC were 0.156 mol/mol and 0.120 g/g, respectively.

3.3. Influence of Reaction Time on CO₂ Capture Characteristics of Calcium-Based Sorbents

Figure 9 shows the variation in X_N and R_N during Cycles 1 and 20 (X₁, R₁, X₂₀, and R₂₀) of the three calcium-based sorbents with reaction time.

From Figure 9, it can be seen that the variations in X₁ for CS and RES with carbonation time were consistent, exhibiting a rapid increase during the initial stage and a gradual increase during the later stage. P₁ and P₂ on the R₁ curves for the three sorbents represent the peak carbonation conversion rate and inflection point, respectively. Parameters corresponding to P₁ can be calculated from the first and second derivatives of the carbonation curves. For CS, P₁ and P₂ occurred at approximately 30 s and 52 s, respectively; the corresponding timings for RES were 84 s and 108 s, with the significant lag possibly caused by the presence of the eggshell membrane in RES. The period between t = 0 and the time point at which P₂ occurred represents the rapid chemical reaction-controlled stage. The CO₂ captured by CS and RES during this stage accounts for 46.45% and 54.06% of the total CO₂ captured. It was observed that CS exhibited better CO₂ capture ability and achieved a shorter reaction time. This may be because carbide slag mainly consists of Ca (OH)₂, which underwent dehydration during the calcination process to form CaO.

Consequently, hydraulic fracturing occurred, leading to increased surface area and porosity in the sorbent and an enhanced ability to react with CO₂ [35]. For APC, the time at which R₁ peaked was close to that of CS, but the peak value of 5.34 × 10⁻³ s⁻¹ was much lower than the peak value of 14.37 × 10⁻³ s⁻¹. The amount of CO₂ captured during the rapid chemical reaction-controlled stage accounted for 19.38% of the total CO₂ captured, which is lower than the corresponding proportions for CS and RES. One possible reason for this is that during the rapid chemical reaction-controlled stage of the carbonation reaction, it was mainly controlled by the total specific surface area of sorbent, which consisted of the external and micropore surface area of the sorbent particles. After the maximum carbonation conversion rate had been reached at P₁, R₁ started to decrease with an increase in the thickness of the CaCO₃ product layer formed on the external surfaces and pores of the sorbent through reaction with CO₂. Subsequently, the reaction entered the slow diffusion-controlled stage at P₂, during which R₁ was mainly determined by the diffusion resistance encountered by CO₂ when passing through the CaCO₃ product layer before further reaction with CaO within the internal pores of the sorbent.

During Cycle 20, carbonation conversion and carbonation conversion rates were significantly lower compared with those for Cycle 1. For CS, P₁ and P₂ occurred at approximately 54 s and 80 s, respectively, considerably later than that of Cycle 1. In addition, the proportion of total CO₂ captured contributed by CO₂ captured during the rapid chemical reaction-controlled stage also decreased significantly to 16.70%. For RES, the peak R₂₀ value at 84 s was relatively indistinct, which indicates the occurrence of severe sintering-induced pore collapse and blockage in the sorbent. Reductions in the rate and degree of carbonation may be explained by the decrease in specific surface area of the sorbent after multiple cycles, as high-temperature sintering led to decreased grain growth in the micropores [36]. For APC, R₂₀ peaked at approximately 60 s with a value of 4.02 × 10⁻³ s⁻¹, slightly higher than the value of 3.86 × 10⁻³ s⁻¹ for CS. It merely decreased by 1.32 × 10⁻³ s⁻¹ compared with the peak R₁ value. This shows that APC was influenced by high-temperature sintering to a smaller extent.

3.4. Characteristics of Decay of Carbonation Reactivity

During the rapid chemical reaction-controlled stage, a CaCO₃ product layer with a thickness of approximately 0.2 μm was formed on the grain surfaces of CaO [37], constituting the main resistance to CO₂ diffusion during the slow diffusion-controlled stage. Pores within CaO can be classified as micropores if they have a diameter of ≤0.2 μm and macropores if they have a diameter of >0.2 μm. Micropores allow the carbonation reaction to remain in the rapid chemical reaction-controlled stage. By contrast, macropores promote an increase in the thickness of the CaCO₃ product layer, which drives the carbonation reaction toward the slow diffusion-controlled stage. During multiple cycles, carbonation reactivity in the sorbent is regained through calcination. However, prolonged high-temperature sintering effects also result in the fusion of grains on CaO surfaces. This causes a gradual decrease in micropores and a gradual increase in the number of macropores in CaO as the cycle increases, reducing sorbent activity and carbonation conversion. To describe the relationship between carbonation conversion in calcium-based sorbents and cycle number, researchers have proposed several prediction models for the characterization of cyclic carbonation reactivity decay in calcium-based sorbents, as shown in Equations (4) [28], (5) [29], (6) [30] and (7) [31].

$$X_N=f_m^N\left(1-f_w\right)+f_w$$

(4)

$$X_N=\frac{1}{1+kN}$$

(5)

$$X_N=\frac{1}{\frac{1}{1-X_r}+kN}+X_r$$

(6)

$$X_N=\frac{X_1}{\frac{X_1}{X_1-X_r}+k\left(N-1\right)}+X_r$$

(7)

where X_N is the carbonation conversion rate during Cycle N (mol/mol); N is the cycle number; f_m and k are the deactivation constants; f_w and X_r are the carbonation conversion values for an infinite number of cycles (mol/mol); and X₁ is the carbonation conversion value during Cycle 1.

Abanades and Alvarez [28] regarded f_m and f_w as fitting parameters associated with micropores and macropores, respectively, with values of 0.77 and 0.17. Wang and Anthony contended that Equation (4) was only applicable to cycle numbers < 20 and proposed a simplified single-parameter equation (see Equation (5)) with a k value of 0.06, on the basis that the reaction conditions do not primarily determine the decay of the reactivity of calcium-based sorbents; however, Equation (5) implies that carbonation conversion will approach 0 when cycle number approaches infinity, which is not consistent with reality. Bouquet et al. [38] contended that carbonation during the cyclic reaction occurs on the surfaces of CaO micrograins and that carbonation conversion is proportional to the number of micrograins. During the calcination process, a particular portion of micrograins loses their reactivity because of sintering, which leads to a reduction in the effective specific surface area of the sorbent grains and a consequent decay of reactivity. In successive cyclic reactions, the carbonation conversion of a sorbent is proportional to the effective specific surface area of the sorbent grains during the cycle. When cycle number becomes large, the effective specific surface area of the sorbent is essentially the external surface area of the sorbent grains, as all micrograins would have fused because of sintering. Ultimately, the carbonation conversion will gradually converge to a constant, expressed as f_w in Equation (5) and X_r in Equations (6) and (8).

Equation (6) is a semi-empirical equation proposed by Grasa and Abanades [30] following the investigation of a long series of carbonation/calcination cycles performed using limestone. For most limestone sorbents, values of 0.075 and 0.52 are used for k and X_r, respectively. As sintering begins during the calcination stage of Cycle 1, a hypothetical carbonation conversion rate X₀ can be defined. By setting N as 0 and assuming that all CaO micrograins participate in the reaction, the value of X₀ = 1, as given by Equations (5) and (6). Subsequently, Valverde [31] proposed Equation (7) by incorporating the carbonation conversion of Cycle 1 (X₁).

To use the models described above in predicting the decay characteristics of the calcium-based sorbents, the carbonation conversion rates for an infinite number of cycles based on the actual conditions of the various calcium-based sorbents were calculated as follows:

$$X_r=X_0\frac{A_r}{A_0}$$

(8)

where X_r is the carbonation conversion for an infinite number of cycles (mol/mol); X₀ is the hypothetical carbonation conversion (mol/mol); A₀ is the hypothetical specific surface area of the sorbent (m²/kg), and A_r is the specific surface area of the sorbent for an infinite number of cycles (m²/kg).

Based on the variation patterns of carbonation conversion for 20 cycles of the various sorbents, the Cycle 0 hypothetical carbonation conversion values of CS, RES, and APC were calculated as 0.7535 mol/mol (correlation coefficient R = 0.9989), 0.7208 mol/mol (R = 0.9871), and 0.7652 mol/mol (R = 0.9986) by polynomial extrapolation, respectively. Using the diameters of the initial CaO and CaO generated from calcination, the values of 9.1 m²/kg and 1.6 m²/kg were calculated for A₀ and A_r, respectively [38]. By substituting these values into Equation (8), the carbonation conversion values of CS, RES, and APC for an infinite number of cycles were calculated as 0.1325 mol/mol, 0.1267 mol/mol, and 0.1345 mol/mol, respectively.

Table 4. Parameter fitting for models of carbonation reactivity decay.

Model	Coefficient	CS	RES	APC
$X_N=f_m^N\left(1-f_w\right)+f_w$	fm	0.9462	0.7953	0.9563
	fw	0.1325	0.1267	0.1345
	R	0.9976	0.9872	0.9983
$X_N=\frac{1}{1+kN}$	k	0.0633	0.3117	0.0491
	R	0.9917	0.9928	0.9963
$X_N=\frac{1}{\frac{1}{1-X_r}+kN}+X_r$	Xr	0.1325	0.1267	0.1345
	k	0.0977	0.5661	0.0742
	R	0.9857	0.9765	0.9934
$X_N=\frac{X_1}{\frac{X_1}{X_1-X_r}+k\left(N-1\right)}+X_r$	Xr	0.1325	0.1267	0.1345
	X1	0.7264	0.6719	0.7471
	k	0.0343	0.3492	0.0237
	R	0.9983	0.9966	0.9976

shows the fitted parameter values for the various prediction models and the corresponding correlation coefficients when the models were fitted to the curves in Figure 5.

Table 4 shows that the highest correlation coefficients were obtained with Equation (8). Figure 10 shows the calculated carbonation conversion values for CS, RES, and APC using Equation (8) and the corresponding experimental values. With an increase in cycle number, the goodness of fit between the calculated and experimental values increased, demonstrating the feasibility of using the model to predict the decay characteristics of calcium-based sorbents. The predicted carbonation conversion values after 100 cycles for CS, RES, and APC were 0.2898 mol/mol, 0.1455 mol/mol, and 0.3438 mol/mol, respectively. These prediction values are similar to those found by Li [39] (the carbonation conversion of CaCO₃ remain as high as 0.35 mol/mol after 100 cycles).

4. Conclusions

The decay of CO₂ uptake performance in 20 cycles of three calcined sorbents (carbide slag, chicken eggshells, and pure CaCO₃ sorbent) were studied by using TGA analysis, and the samples at each stage were tested by XRF, XRD and and N₂ adsorption. The experimental and calculation results have shown that the carbonation conversion of all samples exhibited a decreasing trend as the cycle number increased. RES exhibited the most significant rate of decrease (over 50% compared with Cycle 1) due to high temperature sintering after 6 cycles. CS exhibited a flat linear decline trend, the average decay of carbonation conversion after each cycle was approximately 0.01 mol/mol because CS mainly consists of Ca(OH)₂, which underwent dehydration during the calcination process to form CaO. Carbonation conversion of APC remained higher than that of other sorbents. The specific surface area of the samples was used to calculate carbonation conversion for an infinite number of cycles, and the carbonation conversion rates of CS, RES, and APC were estimated to decrease to 0.2898, 0.1455, and 0.3438 mol/mol, respectively, after 100 cycles.