Comparison of Sulfur Dioxide Removal Reactions Kinetics by Na 2 CO 3 and Other Different Sorbents from Coal-fired Power Plants

This work deals with kinetic parameters estimation of Na 2 CO 3 +SO 2 reaction employing sophisticated random pore model. The temperature of experiments ranges from 100 to 250 °C, and various SO 2 concentrations are within 0.13–1.12 vol.%. According to the results, the reaction rate concentration dependency follows the fractional function. The values of rate constants and product layer diffusivities are expressed at various temperatures. Finally, it was attempted to describe the significance of this sorbent for SO 2 removal. Therefore, the kinetic results of Na 2 CO 3 +SO 2 reaction were compared with other similar studies on SO 2 reaction kinetics with CaO, CuO, and MgO sorbents. It was concluded that Na 2 CO 3 shows advantages of higher rate constants, lower operating temperatures, and less possibility of incomplete conversion problem. The reported kinetic constants are essential for design of flue gas desulfurization reactors, especially in coal-fired power plants.


Introduction
For preventing the acid rain problem, flue gas desulfurization (FGD) technologies include two main processes called throwaway and regeneration 1 . The throwaway process is suitable for relatively low SO 2 concentrations such as coal-fired power plants. On the other hand, regeneration methods are appropriate for high SO 2 concentrations, especially in copper smelters with further conversion of concentrated SO 2 to sulfuric acid or sulfur 1 . The sulfation reaction in coal-based power plants with SO 2 concentration of about 1000 ppm involves the throwaway method, where CaO (lime) is the most common sorbent. Because of the high ratio of molar volume of gypsum versus lime, pore mouth blockage and even incomplete conversion occur in the sulfation reaction of CaO 2 . The comparison of kinetic parameters for SO 2 removal reactions by various sorbents is of great engineering importance and is the main goal of the present work.
Furthermore, to remove high SO 2 concentration from some non-ferrous metallurgical plants, dry and wet regeneration processes are appropriate. The elemental sulfur, as a valuable by-product, can be prepared through reduction of concentrated SO 2 stream with CH 4 as a reducing agent 3 . The principal sorbent of dry regenerative FGD process is CuO.
The usual sorbents of dry FGD processes are different metal oxides and metal carbonates, including CaO, CuO, MgO, Fe 2 O 3 , Na 2 CO 3 , K 2 CO 3 , etc. [4][5][6] . The chemical reaction of Na 2 CO 3 sorbent with SO 2 can be demonstrated as follows: 2 3 2 2 2 4 2 Na CO SO 0.5O Na SO CO To survey the SO 2 adsorption efficiency by Na 2 CO 3 , many studies have been conducted. Electric Power Research Institute (EPRI) were the first to used dry sodium-based sorbent in 1977. The related experimental results revealed 70-90 % SO 2 removal for sub-bituminous coal combustion with various sodium-based sorbents containing a significant amount of Na 2 CO 3 7 . Furthermore, multiple studies were carried out to investigate the influence of NaHCO 3 thermal decomposition on the Na 2 CO 3 on SO 2 absorption yield [8][9][10][11][12] . The results demonstrated that the best performance could be achieved when the gas temperature ranges from 120 to 175 °C for the sulfation reaction of SO 2 with Na 2 CO 3 sorbent. The enhancement effect of Na 2 CO 3 addition on the promotion of limestone sulfate conversion, owing to enlarged surface area and tuned pore size distribution, was described by Han et al. 13 A packed scrubber with NaHCO 3 sorbent was employed by Ghorbani et al. to evaluate SO 2 concentration at the inlet and outlet of scrubber 14 . The results indicated the improvement of SO 2 removal efficiency through cation surfactant additives 14 . In addition, Wu et al. used non-isothermal thermogravimetry to characterize the intrinsic kinetics of the thermal decomposition of NaHCO 3 to Na 2 CO 3 via graphical and Friedman's procedures 15 . The first order reaction rate was determined by the amount of activation energy equaling 25.3 kcal mol −1 . They found that elevating the temperature of NaHCO 3 calcination from 120 to 230 °C would augment the pore diameter from 180 to 210 nm 15 .
To remove SO x and NO x simultaneously, Mortson et al. applied a regenerated NaHCO 3 / Na 2 CO 3 -based sorbent on an advanced FGD technology developed by AIRborne Technologies Inc. (ATI), producing various fertilizers with high SO 2 removal efficiency 16 . In order to absorb SO 2 and NO in a powder-particle fluidized bed reactor, Xu et al. used an Na 2 CO 3 /Al 2 O 3 sorbent 17 . Different effective parameters such as temperature, mixtures composition, and sorbent size were tested 17 . Walawska et al. studied the structural factors of NaHCO 3 and Na 2 CO 3 sorbents such as particle size, surface area, and pore volume 18 . They reported that Na 2 CO 3 sorbent had better results in SO 2 removal yield and conversion rate 18  . The model was applied to derive the equation of reaction rate constant as a function of temperature. The high dependency of reaction rate on temperature was reported by calculating the activation energy value (56.4 kJ mol -1 ) 20 . Kimura et al. studied the kinetics of Na 2 CO 3 sulfation reaction at temperatures within 80-140 °C and 0.3 % SO 2 concentration via thermogravimetry 21 . Finally, rate constants were evaluated from the expressed mechanism and the experimental data 21 . In order to develop a model based on film theory consisting of diffusion, reaction, as well as thermodynamic equilibrium, Ebrahimi et al. used NaHCO 3 /Na 2 CO 3 sorbent for SO 2 elimination in a packed column 22 . Because of its simplicity, this model cannot predict a wide range of situations 22 . Charry Prada et al. carried out the sulfation reaction of NaHCO 3 in a fixed-bed reactor for 1500 ppm SO 2 and temperatures above 122 °C 23 . A solution method was applied to predict the reaction performance in this system with respect to length of the reactor. Thus, this study introduced an economic system in comparison with activated carbon sorbent to remove SO 2 for small-scale FGD applications 23 .
As stated previously, lime-based FGD systems can be established only at high temperatures (about 800 o C). The value of molar volume of solid prod-uct to solid reactant for sulfation reaction of CaO is very high (Z=3). Hence, incomplete conversion phenomenon occurs owing to pore mouth blockage. On the other hand, the advantage of sulfation reaction by Na 2 CO 3 sorbent is low operating temperature (about 200 °C). The lower Z value for Na 2 CO 3 sulfation reaction (Z=1.28) is another superiority of this sorbent that offers the complete conversion possibility in the reaction with SO 2 . Consequently, SO 2 elimination by Na 2 CO 3 can be carried out at low temperatures with low sorbent consumption due to its complete conversions.
The sulfation reaction of solid sorbents such as Na 2 CO 3 , CaO, CuO, and MgO in FGD processes is one of the significant applications of non-catalytic gas-solid reactions. To examine the kinetics of these reactions, different mathematical models have been presented in the literature. Modified grain model and random pore model (RPM) are two comprehensive models for consideration of solid structural variations with time and specifically incomplete conversion. Because of considering the real porous sorbent pore size distribution by RPM, the higher accuracy of RPM for prediction of conversion-time profiles in comparison with the modified grain model was confirmed 24 . As mentioned, kinetic studies of sulfation reaction of Na 2 CO 3 are very rare in literature. For example, Keener et al. employed sharp interface model for this reaction 20 . Because of neglecting Na 2 CO 3 internal surfaces, the reported kinetic parameters were not real. On the other hand, Kimura et al. explored a porous model of Na 2 CO 3 by assuming no diffusion resistance between sorbent nano-grains, but this assumption is unreliable 21 . Ultimately, inherent kinetic parameters of Na 2 CO 3 +SO 2 reaction are essential for the design of FGD reactors in coal-based power plants.
Recently, our group dealt with comprehensive kinetic study of Na 2 CO 3 sulfation reaction by sophisticated RPM, evaluating concentration dependency, and applying the whole pore size distribution of the solid sorbent 25 . The resulting intrinsic kinetic parameters are required for reactor design of low temperature FGD systems. The current work presents a brief discussion of the conversion-time profiles of Na 2 CO 3 sulfation reaction at various temperatures and different concentrations from isothermal thermogravimetry. In addition, comprehensive mathematical modeling of this reaction by applying RPM is explained. The concentration and temperature dependencies of the reaction rate and product layer diffusivities are expressed. The kinetics of SO 2 removal reactions by various sorbents including Na 2 CO 3 , CaO, CuO, and MgO are compared from the results of the literature kinetic studies. Thus, the main novelty of the present work is comparison of kinetic parameters of SO 2 removal reaction by different solid sorbents.

Materials and methods
The powder of NaHCO 3 (Chem-Lab) was pelletized at pressure of 60 bar in a 10-mm diameter die with a thickness of 1 mm. The pellet was placed in a thermogravimeter (TG) (Rheometric Scientific) for 30 minutes within a temperature range of 100-250 °C under zero air flow of 150 cm 3 min -1 to decompose and generate porous Na 2 CO 3 for the reaction with SO 2 . After calcination, a mixture of zero air and predefined concentration of SO 2 (0.13-1.12 vol.%) was applied under an isothermal condition to the TG, and the weight of sample pellet was plotted versus time. The experimental plot of conversion-time was obtained from the weight-time profile as: To evaluate the pore size distribution of Na 2 CO 3 pellet, nitrogen adsorption (by Autosorb-1MP from Quantachrome) and mercury porosimetry (by Carlo Erba) tests were performed on the calcined pellet. To determine the volume of mi croand meso-pores, Horvath-Kawazoe (HK) and Barrett-Joyner-Halenda (BJH) methods were employed. Meanwhile, the macro-pores distribution was obtained by Washburn equation. The results of the PSD within the range of 3-10000 A are presented in Fig. 1 25 .

Modeling of reaction
The SO 2 removal reaction by Na 2 CO 3 sorbent is a non-catalytic gas-solid reaction. To describe the accurate kinetics of such systems, the RPM initially recommended by Bhatia and Perlmutter was applied in this work. The RPM is the most precise and sophisticated non-catalytic gas-solid reaction model due to considering pore size distribution and solid structural changes during the reaction. The main dimensionless coupled partial differential equations of RPM for a slab pellet with general concentration dependency are expressed as 24,26 : Equation (3) is pseudo-steady state diffusion-reaction conservation equation for gaseous reactant, while Equation (4) is unsteady conservation equation for the solid reactant. In the above equations, a and b denote dimensionless gaseous and solid reactants concentrations, ψ represents pore structural parameter of the RPM, φ is the Thiele modulus, and β shows product layer resistance. Z is a significant parameter in the RPM, which is defined as the ratio of the molar volume of the solid F i g . 1 -PSD of Na 2 CO 3 pellet 25 product to the solid reactant. When Z>1, the porosity diminishes during the reaction due to volume expansion. Because of the blockage of pore mouths at high Z values, incomplete conversion can occur. The Z values for sulfation reactions of MgO, CuO, CaO, and Na 2 CO 3 are 4.0, 3.52, 3.0, and 1.28, respectively. Thus, the lower Z value for Na 2 CO 3 reaction with SO 2 is a positive point for the relevant FGD reaction.
The effective axial diffusivity of SO 2 along the pores of pellet is calculated from molecular diffusion (D AM ) and the Knudsen diffusivity (D AK ) by the following equations 24,27,29 : To calculate the main RPM parameter (ψ), the following formulas are used:

Order of the reaction
To estimate the best order of the reaction, the previous equations were solved by shooting method, which replaced δ and b as unity at the zero times of reaction when the product layer thickness around the pores was negligible. The following formula was established by differentiation of simplified equations for initial slope of conversion-time profile of the sulfation reaction: Equation (15) can be reformulated by inserting the relation between actual time and θ as 24,27,30 : The highest correlation coefficient of I versus Ab plot, specifies the best order of reaction. Hence, to survey the concentration dependency, a series of experiments was conducted at 150 °C and within 0.13-1.12 vol.% SO 2 concentration, with the results of correlation coefficients reported in Table  1 25 .
Thus, the fractional form was suggested from Table 1 to qualify as the best concentration dependency of Na 2 CO 3 reaction with SO 2 due to higher regression coefficient.

Rate constants
To attain the k s values at different temperatures, iteration method was established using Equation (16). An Arrhenius plot was employed to estimate the frequency factor and activation energy. For this purpose, various experiments were carried out at 0.66 vol.% SO 2 concentration and temperatures within 100-250 °C plus conversion-time curves, as presented in Fig. 2 25 . The values of k s at different temperatures are summarized in Table 2 25 . Fig. 3 illustrates the Arrhenius plot of these data, where the rate constant's temperature dependency is expressed as follows 25

Product layer diffusion
According to the RPM principle, SO 2 radial product layer diffusivity around each pore (D p ) can be evaluated as a fitting parameter through compar-ison between the conversion-time profiles obtained from solving the governing coupled partial differential RPM equations numerically (by Matlab software) and experimental data. Thus, a D p value was guessed and the coupled partial differential equations were solved by finite element method. The best fit with all experimental conversion-time points generated appropriate values for SO 2 diffusivity in the product layer (Na 2 SO 4 ). The obtained D p values at different temperatures are presented in Table 3 25 . The RPM conversion-time predictions and experimental profiles at various temperatures are plotted  Table 4 presents the main structural parameters of Na 2 CO 3 pellet 25 .
Finally, D p as a function of temperature can be stated with the following formula 25 :

Discussion
The main application of sulfation reactions of Na 2 CO 3 , CaO, CuO and MgO is SO 2 elimination. In this part, based on the obtained results of this study and other similar investigations in the literature, rate constants, Z values, and diffusivities of the aforementioned sorbents are compared. Table 5 reports the rate constant equations and diffusion coefficients of SO 2 through the product layers for different sorbents extracted from previous works and this study.
The values of these mentioned parameters and Z values were calculated within the range of reported operating temperatures, with the results summarized in Table 6. It is obvious from Table 6 that the rate constant of Na 2 CO 3 is higher than that of other similar sorbents.
To compare the rate constant of this study with other works, the approximate solution of RPM governing equations was rearranged as 31 :

Ta b l e 4 -Structural parameters of RPM for Na 2 CO 3 pellet after calcination 25
Pellet (1 ) 1 ( Hence, k s S 0 is the efficient kinetic term in conversion-time improvement, which is listed in the right column of Table 6. It is clear from Table 6 that values of k s S 0 for CuO sorbent are low, while those for the CaO sorbent are within the medium range. Meanwhile, k s S 0 values for Na 2 CO 3 and MgO sorbents are relatively high. Finally, it was concluded that high values of k s S 0 for Na 2 CO 3 and MgO sorbents could reduce the required residence time in an industrial FGD reactor for these sorbents. The size of these reactors can be reduced for more efficient sorbents (Na 2 CO 3 and MgO), and thus the capital cost lowered.
The values of SO 2 diffusivities through the product layer generated from sulfation reactions of CuO and CaO sorbents are low. The diffusion coefficients in the product layer for MgO and Na 2 CO 3 sorbents are in the medium range.
As stated previously, the value of Z is an important parameter for progression of the reaction due to possibility of the pore mouths blockage. For the reaction of sodium carbonate sorbent with SO 2 , the value of Z is 1.28, which is minimum in Table  6. Conversion-time profiles of SO 2 removal reactions by CaO, CuO, and MgO sorbents are illustrated in Fig. 5. It is obvious from comparison of Fig.  4 and Fig. 5 that the lower value of Z for Na 2 CO 3 sulfation reaction is a superior condition to achieve higher conversions in comparison with the other aforementioned sorbents.
The last major advantage of Na 2 CO 3 sorbent for SO 2 removal reaction is its ability to operate at lower temperatures (second column of Table 6).

Conclusion
In this study, the inherent kinetic parameters of Na 2 CO 3 reaction with SO 2 were presented using sophisticated RPM. The fractional concentration dependency was specified for the reaction rate and its activation energy was obtained as 22.5 kJ mol -1 .
The diffusion coefficient of SO 2 through the product layer was established as a function of temperature with values ranging from 12.5·10 -19 m 2 s -1 to 15·10 -18 m 2 s -1 when temperature changed from 100 to 250 o C. The results of Na 2 CO 3 sulfation reaction in comparison with CaO, CuO, and MgO sorbents revealed a higher rate constant. Thus, Na 2 CO 3 sulfation reaction progresses significantly at initial times. The incomplete conversion possibility for Na 2 CO 3 was lower than for other sorbents due to its lower Z value. Finally, Na 2 CO 3 potential to react with SO 2 within a low temperature range is the main superiority of this sorbent versus similar CaO, CuO, and MgO sorbents.

CONfLICT Of INTEREST
Authors state that there is no conflict of interest.