Experimental study on the removal of SO3 from coal-fired flue gas by alkaline sorbent

Experimental study on the removal of SO3 from coal-fired flue gas by alkaline sorbent

Fuel 259 (2020) 116306 Contents lists available at ScienceDirect Fuel journal homepage: www.elsevier.com/locate/fuel Full Length Article Experimen...

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Fuel 259 (2020) 116306

Contents lists available at ScienceDirect

Fuel journal homepage: www.elsevier.com/locate/fuel

Full Length Article

Experimental study on the removal of SO3 from coal-fired flue gas by alkaline sorbent

T

Chenghang Zheng, Cong Luo, Yong Liu, Yifan Wang, Yan Lu, Ruiyang Qu, Yongxin Zhang, ⁎ Xiang Gao State Key Lab of Clean Energy Utilization, State Environmental Protection Engineering Center for Coal-Fired Air Pollution Control, Zhejiang University, 38 Zheda Road, Hangzhou 310027, People’s Republic of China

A R T I C LE I N FO

A B S T R A C T

Keywords: SO3 Absorption Alkaline sorbent Na2CO3 Rate control model

Selective Catalytic Reduction (SCR) system can efficiently remove NOx in coal-fired power plant, while raise SO3 concentration in the flue gas. Alkaline sorbent injection is a major approach to remove SO3. Experiments were conducted to study the SO3 absorption performance of alkaline sorbent. The SO3 absorption performance of the three alkaline sorbents was Na2CO3 > Ca(OH)2 ≈ Mg(OH)2. The ratio of SO3 absorption rate to SO2 absorption rate for Na2CO3 increased with the increasing temperature. The key parameters on the SO3 absorption performance of Na2CO3 were studied. The SO3 absorption by Na2CO3 was increased by 72.7% with increasing temperature from 150 °C to 300 °C, and the temperature had little influence on SO3 absorption above 300 °C. The increasing SO3 concentration and decreasing particle size of Na2CO3 enhanced SO3 absorption. However, when the average particle diameter was less than 50 μm, the SO3 absorption was no longer significantly increased. The increasing CO2 concentration slightly reduced the SO3 absorption. After adding vapor into the flue gas, the SO3 absorption was obviously increased below 300 °C. The SO3 absorption variation above 300 °C was similar to the condition without vapor. When reaction temperature was 300 °C or above and reaction time was less than 20 min, external diffusion became the control step for SO3 absorption. On the basis of external diffusion control model, the mass transfer coefficient slightly increased from 1.68 × 10−3 m/s to 1.75 × 10−3 m/s when the reaction temperature increased from 300 °C to 400 °C.

1. Introduction The coal-fired power plant is equipped with selective catalytic reduction (SCR) system to effectively control NOx emissions. However, SCR catalyst promotes the oxidation of SO2 to SO3, which raises the concentration of SO3 in the flue gas [1–3]. After passing the wet desulfurization tower, SO3 forms submicron sulfuric acid aerosol, which makes some power plants emit visible plume [4]. Sulfuric acid will destroy buildings and vegetation, causing damage to the mucous membranes and lung structure of human respiratory tract [5]. SO3 also has an adverse effect on the operation of the power plant [6–9]. (NH4)2SO4 and NH4HSO4 generated in the SCR system are deposited on the surface of the SCR catalyst, causing catalyst deactivation and blockage [10], causing clogging of the air preheater and corrosion of the metal surface [11,12]. Below the dew point, SO3 condenses into sulfuric acid, causing low temperature corrosion [13]. For power plants that use activated carbon for mercury removal, SO3 will compete with Hg for the active site of activated carbon [14–16].



The SO3 control technologies in coal-fired power plants are mainly divided into source control technologies, synergistic removal technologies and alkaline sorbent injection technologies. The SO3 generation can be controlled by reducing the SO2 oxidation rate of SCR catalyst, decreasing the sulfur content of coal or saving energy consumption of coal-fired boiler system. Fine particles and SO3 are synergistically removed by low-low temperature electrostatic precipitator [17], wet electrostatic precipitator [18,19] and wet desulfurization tower [20]. Alkaline sorbent injection has good adaptability, and the sorbent can be injected at various positions in the flue to remove SO3 in a targeted manner [21,22]. Sorbent is injected at the economizer outlet or SCR outlet to reduce the formation of ammonium bisulfate, reduce acid dew point, and improve boiler thermal efficiency. Researchers have studied acid gas removal by alkaline sorbents [23]. Dry injection of sorbents is widely used in waste-to-energy plants to remove HCl and SO2 [24]. When SO2 or O2 existed, the reactivity of CaO with HCl decreased obviously at 750–850 °C [25]. The HCl uptake by Ca–Mg–Al mixed oxides was the highest compared to CaO, MgO and NaHCO3 in the temperature

Corresponding author. E-mail address: [email protected] (X. Gao).

https://doi.org/10.1016/j.fuel.2019.116306 Received 14 June 2019; Received in revised form 27 August 2019; Accepted 26 September 2019 Available online 29 September 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.

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range 300–700 °C [26]. In the temperature 120–180 °C, the product layer resistance had great influence on HCl removal [27]. Dry solid sorbents had also been used to remove SO2 or capture CO2, and the sulfation of Ca-based sorbent hampered cyclic CO2 capture [28,29]. Alkaline sorbents are suited for removing acid gas. The SO3 absorption properties of some sorbents were evaluated. Benjamin et al. [30] concluded that the stability of SO3 bound with metal oxides was MgO < CaO < Na2O < K2O. Steward et al. [31] reported that the reaction of ZnO with SO3 at 410 °C had the highest sulfation rate compared to MgO and CaO. Dean et al [32] found that MgO had a higher sulfation rate compared to CaO. Wang et al [33] found that the removal effect of CaO on SO3 was insensitive to temperature changes in the range of 250–400 °C. Wang et al [34] published an experimental and numerical study on SO3 removal in the entrained flow reactor, when the diameter of Ca(OH)2 was less than 20 μm, the SO3 absorption performance was no longer affected by the particle diameter. Moreover, SO3 is difficult to sample and measure because of its high reactivity. Previous research focused on the effect of sorbent properties on SO3 removal efficiency. However, the SO3 removal by alkaline sorbents is not only related to sorbent properties, but also flue gas characteristics. Besides chemical reaction, diffusion also has a significant impact on removal efficiency, especially in low gas concentration. The SO3 concentration in the flue gas of coal-fired power plant is only 1–2% of the SO2 concentration. The influence of operating parameters on SO3 removal has not been deeply studied. Therefore, it is urgent to develop corresponding technologies and feasible processes to ensure the normal operation of power plants burning high-sulfur coal and prevent the occurrence of visible plume. In this study, a new test bench and experimental method were designed. The SO3 absorption performance of different alkaline sorbents were compared, and the alkaline sorbent with superior SO3 absorption performance was picked out. The influence of key parameters on the SO3 absorption was researched. Finally, the SO3 absorption rate control model was established.

Table 1 The parameters of electronic balance. Parameters

Value

Measurement range Accuracy Sampling interval

200 mg 1 μg 1s

The reactor was integrated with a high-precision electronic balance. The parameters of electronic balance were listed in Table 1. The balance was vertical and a crucible was suspended at the lower part. The reactor can be manually lifted. When the reactor rose, it formed a seal with the balance, and the crucible was in the middle of the reactor. There was a thermocouple next to the crucible, and the temperature of the mixing gas was measured. When the reactor was moving down, the crucible was removed to replace the sorbent. The targeted alkaline sorbent placed on the weighing paper was poured into the crucible. The crucible was 10 mm in diameter and 2 mm in height. The temperature of exhaust gas outlet was kept at 200 °C to prevent blockage due to SO3 condensation. The heating rate, target temperature and holding time were set by computer. After starting sampling, the computer displayed the real-time temperature and mass curve. The SO3 generator was mainly composed of a heating furnace and a temperature and flowrate control cabinet. A K-type thermocouple was inserted into the middle of the quartz tube to directly measure the actual temperature of the catalyst. The mass flowmeters in the SO3 generator were used to control the flowrate of O2, N2 and SO2. The principle of generating SO3 was catalytic oxidation. SO2 and O2 were introduced into a high-temperature quartz tube filled with vanadium based catalyst, and SO2 was catalyzed into SO3. There are mainly two methods to obtain SO3 concentration: Controlled condensation is considered to be an accurate method for measuring SO3 concentration in power plants [35], but require 1–2 h to obtain the result [36]. To realize online continuous testing, optical methods including quantum cascade laser (QCL) [37] and Fourier transform infrared spectroscopy (FTIR) [38] etc. are used for SO3 measurement. However, these optical methods are easily interfered by other components like vapor or SO2 in the flue gas. In this experiment, an intelligent flue gas analyzer (F550, Germany) detected the SO2 concentration at the inlet and outlet of the SO3 generator. The oxidation rate of SO2 was calculated, and the SO3 concentration was equal to the SO2 concentration difference. The SO2 oxidation test results were shown in Table 2. When the catalyst reached 420 °C, the SO2 inlet concentration was in the range of 1–1200 ppm, SO2 was not detected at the outlet and was considered to be completely oxidized. Therefore, the initial SO3 concentration was equal to the initial SO2 concentration. After SO3 was generated, white mist could be seen in the gas washing bottle for treating the exhaust gas, as shown in

2. Experimental section 2.1. Experimental system A new corrosion-resistant experimental system was designed to study SOx absorption reaction with alkaline sorbents. The experimental system of SO3 removal by alkaline sorbents consisted of a gas distribution system, a SO3 generator, an absorption reactor and an electronic balance etc. A schematic of the experimental system was shown in Fig. 1. The mixing gas containing SO3 passed into the reaction system. The electronic balance continuously recorded the mass change of alkaline sorbent samples after absorbing acid gas. The computer was used to obtain and process thermogravimetric curve.

Fig. 1. Schematic of the experimental system. 2

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Table 2 SO2 oxidation test of the SO3 generator. SO2 inlet concentration (ppm)

SO2 outlet concentration at normal temperature (ppm)

SO2 outlet concentration at 420 °C (ppm)

150 300 600 900 1200

149 302 601 903 1207

0 0 0 0 0

Fig. 3. Comparison of SO3 absorption performance of different sorbents at 300 °C and 350 °C.

evaluated by comparing the amount of SO3 absorbed per mole sorbent in the same time. The conversion rate of the sorbent is calculated by Eq. (1).

x= Fig. 2. Change of the gas washing bottle: (a) before generating SO3; (b) after generating SO3.

m − m0 Δm 0

(1)

where m0 is the initial mass before the reaction started, m is the total mass of the unreacted sorbent and product at time t. The mass change of the sorbent in complete reaction is Δm0.

Fig. 2. The gas distribution system controlled the flowrate of N2, vapor, SO2 and CO2, and controlled heating temperature of the vapor generator simultaneously. The vapor generator, which was a metal hollow cylinder, had a gas inlet and a gas outlet at both ends, and a water inlet in the middle. The principle of generating vapor was to accurately control the water discharge by injection pump (specification: 60 mL, flow rate: 0.001 μL/min–127 mL/min). Deionized water was injected into the vapor generator to be heated and turned into vapor. The generated vapor was carried into the reactor by N2. The vapor generator was kept at 250 °C to heat and evaporate the water rapidly.

3. Results and discussion 3.1. SO3 absorption performance of different alkaline sorbents The SO3 absorption of different alkaline sorbents at 300 °C and 350 °C is illustrated in Fig. 3. The average particle size was 10.3 μm, 3.3 μm and 28.0 μm for the sorbents of Ca(OH)2, Mg(OH)2 and Na2CO3 respectively. The initial SO3 concentration was 1200 ppm. The SO3 absorption rate of Na2CO3 was 4.06 times and 4.84 times of that of Ca (OH)2 and Mg(OH)2 respectively at 300 °C. For sorbents Ca(OH)2 and Mg(OH)2, the increasing temperature led to SO3 absorption increase. However, the temperature had little effect on SO3 absorption by Na2CO3. In the range of 300–350 °C, the SO3 absorption by Na2CO3 was significantly higher than that of Ca(OH)2 and Mg(OH)2. The absorption rates of Ca(OH)2 and Mg(OH)2 were very close. From the perspective of efficient removal of SO3, Na2CO3 was a superior alkaline sorbent. The SO3 absorption by the three alkaline sorbents changed approximately linearly with time over the experimental time range. Fig. 4 exhibited an electron micrograph of the base absorbent before and after reaction with SO3. As can be seen from the figure, the surface of Ca(OH)2 and Mg(OH)2 were denser after reacting with SO3. As the reaction time increased, the product was stacked on the surface and hindered internal diffusion of sulfur trioxide. The surface of Na2CO3 was smooth before reaction, while the surface became rougher. CO2 was continuously released during the reaction. The gas diffusion channel was not easily blocked by the product, the specific surface area was increased and SO3 absorption rate was accelerated as a result of this change.

2.2. Experimental procedure The concentration set in the experiment was higher than the actual flue gas, mainly to ensure the absorption effect, reduce the error and the experimental time. The experiment was conduct as the following procedures: (1) Turn on the balance protection gas first to prevent the reaction gas from entering the balance chamber. (2) Keep the SO3 generator and the pipeline warm to the set temperature. (3) The empty crucible was placed in the reaction atmosphere to get the baseline, and subtract the baseline from the obtained absorption curve to get the actual absorption curve. (4) The crucible was covered with a thin layer sample to sufficiently react with the gas. The mass of the alkaline sorbent was 10 mg. (5) The reaction gas was introduced when the sample reached the holding temperature in a nitrogen atmosphere and the mass remained unchangeable. (6) The mass change of the sample could be displayed and recorded in real time. The sampling stopped automatically after reaching the set holding time. (7) At the end of the experiment, stop supplying the reaction gas first, and then blow off the residual SO3. The heating equipment was turned off at last. (8) The crucible was soaked with dilute hydrochloric acid, and then ultrasonically washed and dried before replacing the experimental sample.

3.2. Comparison of SO2 and SO3 absorption performance High concentration SO2 is present in coal-fired flue gas. It was reported that competitive reaction of SO3 and SO2 with Ca(OH)2 existed, the decrease in SO2 concentration or the increase in SO3 concentration improved the SO3 absorption [39]. Thus, the absorption properties of Na2CO3 for SO2 and SO3 were compared under the same conditions.

2.3. Analysis method The SO3 absorption performance of the alkaline sorbents was 3

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Fig. 4. Electron micrograph of sorbents before and after reaction with SO3: (a) before reaction; (b) after reaction.

3.3. Effect of different factors on SO3 absorption

The initial SO2 and SO3 concentration was 1200 ppm and the balance was N2. The difference of SO2 and SO3 absorption properties under the same conditions was compared in Fig. 5. The absorption of SO2 by Ca(OH)2 and Mg(OH)2 increased with the rise of temperature. However, the increasing temperature decreased SO2 absorption by Na2CO3. The average SO3 absorption rate at 300 °C in 20 min was 0.0051, 0.0033 and 0.016 mol sorbent/(mol SO3·min) for the sorbents of Ca(OH)2, Mg (OH)2 and Na2CO3 respectively. The average absorption rates of SO3 and Ca(OH)2 were 2.28 times, 1.48 times and 1.13 times of that of SO2 respectively at the temperatures of 300 °C, 350 °C and 400 °C in 20 min. However, the reaction rates of SO3 and Na2CO3 were 1.26 times, 1.37 times and 1.56 times of that of SO2 at the temperatures of 300 °C, 350 °C and 400 °C respectively. The increasing temperature had little impact on the ratio of SO3 absorption rate to SO2 absorption rate for Mg(OH)2. The absorption performance of Mg(OH)2 and Ca(OH)2 on SO2 and SO3 were relatively close above 350 °C. The SO3 absorption by Na2CO3 was obviously larger than that of SO2. Sulfite was unstable at high temperature and was prone to decomposition if formed after the reaction of SO2 and Na2CO3 [40]. However, the sulfate produced by SO3 and Na2CO3 was relatively stable. For the preferred sorbent Na2CO3, study the influence of key parameters such as temperature, particle size, SO3 concentration, CO2 concentration and vapor on SO3 absorption performance.

3.3.1. Effect of temperature In order to fully explore the influence of temperature on the absorption performance of SO3, the temperature was expanded to the range of 150–450 °C. The average particle size of Na2CO3 was 112.6 μm. The volume fraction of O2 was 5% and SO3 concentration was 1200 ppm. The effect of temperature on the SO3 absorption was shown in Fig. 6. The SO3 absorption was increased by 72.7% when the temperature increased from 150 °C to 300 °C. In the range of 300–450 °C, the SO3 absorption did not change significantly with the increase of temperature. The absorption at 350 °C was slightly lower than that of 300 °C, which may result from sintering of sodium carbonate [40]. At temperatures below 300 °C, the reaction rate increased with the increase of temperature, the SO3 absorption reaction kinetics was controlled by chemical reaction on the gas-solid interface [41]. However, when the temperature was higher than 300 °C, the gas-solid interface reaction rate was large, and the SO3 absorption rate was mainly limited by gas diffusion.

3.3.2. Effect of SO3 concentration The initial SO3 concentration significantly influenced the mass transfer process, and led to diverse SO3 absorption performance. The SO3 concentration was in the range 150–1200 ppm. The average particle size of Na2CO3 was 112.6 μm, volume fraction of O2 was 5% and the experimental temperature was 300 °C. The relationship between the 4

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SO3 absorption (mol SO 3/mol Na 2CO3)

Fig. 5. SO2 and SO3 absorption performance of different sorbents.

0.24

5 min 10 min 15 min 20 min

0.20 0.16 0.12 0.08 0.04 0.00

0

200

400

600

800

1000

1200

SO3 concentration (ppm) Fig. 6. Effect of temperature on SO3 absorption.

Fig. 7. Effect of SO3 concentration on the SO3 absorption.

SO3 absorption at different time and different SO3 concentrations was illustrated in Fig. 7. The concentration of SO3 had a great effect on the SO3 absorption performance of Na2CO3. The SO3 absorption increased significantly with the increasing SO3 concentration. The conversion rate of Na2CO3 was less than 0.1 when the SO3 concentration was less than 300 ppm. When the SO3 concentration was 1200 ppm, the conversion rate was close to 0.2. At 300 °C or above, the SO3 absorption was little

impacted by temperature, the SO3 absorption rate was mainly limited by gas diffusion.

3.3.3. Effect of particle size The relationship between the SO3 absorption at different times and particle size was shown in Fig. 8. The SO3 concentration was 1200 ppm, the O2 volume fraction was 5%, and the balance was N2. The reaction 5

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0.35 0.30

5 min 15 min

SO3 absorption (mol SO3/mol Na2CO3)

SO3 absorption (mol SO3/mol Na2CO3)

C. Zheng, et al.

10 min 20 min

0.25 0.20 0.15 0.10 0.05 0.00

50-100

100-200

200-300

300-400

0.25

5 min 10 min 15 min 20 min

0.20 0.15 0.10 0.05 0.00

0

2

4

6

8

10

12

14

Volume fraction of CO2 (%)

Particle size of Na 2CO3 (mesh)

Fig. 9. Effect of CO2 on the SO3 absorption.

Fig. 8. Effect of particle size on the SO3 absorption. Table 3 Characteristics of sodium carbonate particles. Mesh range (mesh)

Particle size (μm)

Measured average particle size (μm)

BET specific surface area (m2/g)

50–100 100–200 200–300 300–400

150–270 75–150 48–75 38–48

231.9 112.6 49.9 41.1

0.31 0.85 0.96 1.02

temperature was 300 °C. The grinding sodium carbonate was screened through a standard sieve. The mean particle size was measured by laser particle sizer (LS-230, USA). The specific surface area of the sieved particles was measured by a specific surface area analyzer (ASAP 2460, USA). The results were shown in Table 3. When the average particle size of Na2CO3 reduced from 231.9 μm to 112.6 μm, the specific surface area increased, the internal diffusion resistance decreased, and the SO3 absorption increased by approximately 110% in 20 min. However, the SO3 absorption increased by 4.8% as the particle size continued to decrease from 49.9 μm to 41.1 μm, the internal diffusion had a small restriction on the absorption rate, and the growth rate of SO3 absorption gradually became slower. The experimental results showed that the SO3 absorption didn’t increase significantly with the decreasing particle size when the average particle diameter was less than 50 μm.

Fig. 10. Effect of vapor on the SO3 absorption of Na2CO3 at different temperatures.

3.3.5. Effect of vapor The effect of vapor on SO3 absorption performance was shown in Fig. 10. The average sorbent diameter was 112.6 μm. The O2 volume fraction was 5%, the initial SO3 concentration was 1200 ppm. Volume fraction of vapor was chosen as 1% to avoid appearing obvious SO3 condensation and blockage phenomenon in the experiment. Compared with the condition without vapor, the SO3 absorption significantly increased below 300 °C after adding vapor. The presence of vapor may promote the conversion of SO3 to H2SO4. From 150 °C to 300 °C, the proportion of H2SO4 decreased, the proportion of SO3 increased, and the absorption of SO3 decreased. From 300 °C to 450 °C, SO3 mainly existed in the form of SO3, and the proportion of H2SO4 was low. The change of SO3 absorption was similar to the condition without the presence of vapor.

3.3.4. Effect of CO2 concentration CO2 was produced through the reaction between Na2CO3 and SO3. The high concentration of CO2 in the flue gas may affect the diffusion of gaseous products. Hence, it was necessary to study the influence of CO2 concentration, the CO2 volume fraction was in the range 0–12.5%. The particle size of Na2CO3 was 112.6 μm. The O2 volume fraction was 5%, the SO3 concentration was 1200 ppm and experimental temperature was 300 °C. The relationship between the SO3 absorption and CO2 concentration was shown in Fig. 9. It can be seen that the SO3 absorption of sodium carbonate dropped slightly with the increase in initial CO2 concentration. The reason was probably that CO2 was formed after the reaction of SO3 with Na2CO3, the CO2 concentration in flue gas rose, and the diffusion of product was limited. However, the effect of CO2 on SO3 absorption was little. The SO3 absorption by 1 mol Na2CO3 was 0.212 mol, 0.196 mol, 0.189 mol and 0.178 mol for the initial CO2 volume fraction of 0, 2.5%, 5% and 12.5% respectively. When the CO2 concentration was higher than 5%, the SO3 absorption was not significantly affected by the CO2 concentration. Therefore, the injection of Na2CO3 can effectively remove SO3 even under the condition of oxygenenriched combustion.

4. SO3 absorption rate control model The shrinking core model can be applied for the non-catalytic gassolid reaction [42]. A schematic of the model is shown in Fig. 11. RP and RC represent the radius of particle and unreacted core (m), respectively. CG, CP, and CC represent the concentration of SO3 at the gas phase, the particle surface, and the interface of the product and unreacted core (mol/m3), respectively. The reaction process can be simplified to the following steps: 1) SO3 diffuse from the gas phase to the outer surface of the particles; 2) SO3 diffuse through the pores of the product layer to the surface of the unreacted core; 3) SO3 reacts with Na2CO3 on the surface of the 6

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SO 3 absorption (mol SO 3/mol Na 2CO 3)

C. Zheng, et al.

Fig. 11. Schematic diagram of the shrinking core model.

0.35 0.30

50 ȝm Exp.

50 ȝm Sim.

41ȝm Exp.

41 ȝm Sim.

0.25

y = 1.5435 x + 0.8357

0.20 0.15 0.10 y = 1.5004 x + 0.2389

0.05 0.00

0

5

10

15

20

Time (min) Fig. 14. Comparison of simulated curve and experimental data of SO3 absorption at different particle sizes.

unreacted core (m2); hD is mass transfer coefficient; ks is reaction rate constant (m/s). According to the formula (1) and (2), the differential equation of the reaction is obtained as

dRC =− dt

CG 2

1 R ρP ⎡ h RC2 + ⎣ D P

1 ⎛RC D





RC2 RP

⎞+ ⎠

1⎤ ks

(4)



where t is time (s); ρP is absorbent molar density (mol/m3). Boundary condition: t = 0; RC = RP. The conversion rate is defined as

Fig. 12. Comparison of simulated curve and experimental data of SO3 absorption at different temperatures.

3

R x Na2 CO3 = 1 − ⎛ C ⎞ ⎝ RP ⎠ ⎜



(5)

The relationship between the conversion rate and time is [44–46]

t=

ρP RP ρ RP2 ρ RP 2 x Na2 CO3 + P + P ⎡3 − 3(1 − x Na2 CO3 ) 3 − 2x Na2 CO3⎤ ⎦ 3hD CG 6DCG ⎣ ks CG 1

1 − (1 − x Na2 CO3 ) 3 ⎤ ⎡ ⎣ ⎦

Fig. 13. Comparison of simulated curve and experimental data of SO3 absorption at different SO3 concentrations.

t=

unreacted core. The pseudo-steady state method was used to establish the differential equation [43].

d ⎛ dC ⎞ 2 dC D + D =0 dR ⎝ dR ⎠ R dR

(2)

t=

where D is diffusion coefficient of gas in product layer (m /s); C is the SO3 concentration (mol/m3); R is the reaction radius (m). Gas diffuses from the gas phase to the reaction interface. According to the quasisteady state assumption, the three diffusion rates are equal.

4πD 1 RC



1 RP

ρP RP x Na2 CO3 3hD CG

(7)

When the control step of the reaction is internal diffusion, the model can be simplified to

2

hD SP (CG − CP ) =

(6)

The first term of the expression indicates the external diffusion resistance, the second term is the product layer diffusion resistance, and the third term is the gas-solid interface reaction resistance. The shrinking core reaction is controlled by external diffusion, product layer diffusion and gas-solid interface reaction. If the three resistances are on the same order, the reaction is considered to be in the mixing control step. When the resistance of one item is much greater than other resistances, the entire reaction process is controlled by this step under the test conditions, and the resistance of other steps can be ignored, and this step is called the control step of the reaction. When the control step of the reaction is external diffusion, the model can be simplified to

ρP RP2 2 ⎡1 − 3(1 − x Na2 CO3 ) 3 + 2 1 − x Na2 CO3 ⎤ ⎦ 6DCG ⎣

(

)

(8)

When the control step of the reaction is interfacial reaction, the model can be simplified to

t=

(CP − CC ) = ks SC CC (3)

ρP RP 1 ⎡1 − (1 − x Na2 CO3 ) 3 ⎤ ⎦ ks CG ⎣

(9)

According to the experimental results, when the temperature was 300 °C or above, the SO3 absorption was no longer significantly

where SP is the particle surface area (m2); SC is the surface area of the 7

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was less than 20 min, external diffusion was the limiting step of the SO3 absorption rate. The external diffusion control model for SO3 absorption rate was established, which was highly fitted to experimental data.

changed with the increasing temperature, and interfacial reaction had little effect on SO3 absorption rate. The reaction time was 20 min in the experiment; the reaction proceeded mainly on the particle surface and had not yet penetrated into the interior of the particles. Besides, continuous release of CO2 promotes product layer diffusion. Internal diffusion was not rate control step. Therefore, the experimental data was simulated using the external diffusion control model. The comparison of simulated curve and experimental data of SO3 absorption at different temperatures was illustrated in Fig. 12. The average particle size of Na2CO3 was 41.1 μm, the SO3 concentration was 1200 ppm, the volume fraction of O2 was 5%, and the balance was N2. The conversion rate changed linearly with the reaction time, the mass transfer coefficient can be calculated through the slopes of the straight lines. On the basis of external diffusion control model, the mass transfer coefficient was 1.68 × 10−3 m/s, 1.72 × 10−3 m/s and 1.75 × 10−3 m/s for the reaction temperatures of 300 °C, 350 °C and 400 °C respectively. The mass transfer coefficient of SO3 slightly increased with the increase in temperature. The comparison of the simulated curve and experimental data of SO3 absorption at different SO3 concentrations was illustrated in Fig. 13. The sorbent particle size was 112.6 μm. The reaction temperature was 300 °C. The volume fraction of O2 was 5%. Based on external diffusion control model, the mass transfer coefficient was 1.21 × 10−3 m/s, 1.52 × 10−3 m/s and 1.70 × 10−3 m/s for the SO3 concentrations of 600 ppm, 900 ppm and 1200 ppm respectively. The mass transfer increased significantly when the SO3 concentration increased. The comparison of the simulated curve and experimental data of SO3 absorption with different particle sizes was illustrated in Fig. 14. The SO3 concentration was 1200 ppm. The reaction temperature was 300 °C. The O2 volume fraction was 5%. The mass transfer coefficient was 1.72 × 10−3 m/s and 1.74 × 10−3 m/s for the average particle sizes of 50 μm and 41 μm respectively. When the particle size was reduced, the SO3 mass transfer coefficient hardly changed. The change of particle size had little influence on external diffusion. As seen from the simulation results, the calculated result of external diffusion control model was highly fitted to the experimental data. When reaction temperature was 300 °C or above and reaction time was less than 20 min, the control step for SO3 absorption rate was external diffusion.

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