- Email: [email protected]

Modiﬁed sulfation model for simulation of pulverized coal combustion N. Punbusayakul

a,*

, J. Charoensuk a, B. Fungtammasan

b

a

b

Department of Mechanical Engineering, Faculty of Engineering, King MongkutÕs Institute of Technology, Ladkrabang, Bangkok, Thailand The Joint Graduate School of Energy and Environment, King MongkutÕs University of Technology Thonburi, Bangkok, Thailand Received 21 September 2004; received in revised form 29 September 2004; accepted 14 March 2005 Available online 27 September 2005

Abstract This work deals with the development of mathematical techniques for incorporating existing sulfation models into a CFD code for simulation of the ﬂow and heat and mass transfer in multi-phase reacting ﬂow; i.e. in the combustion of pulverized coal with the dry type sulfur absorption process. By compromising the ability to maintain some features of the sulfation, as suggested in literatures with computation time, the model was successfully embedded into FAFNIR, a CFD code by Lockwood et al. and has been used for prediction of SO2 absorption in pulverized coal combustion to compare with experimental data at various conditions. This paper focuses on mathematical representation of the sulfation process by including the eﬀects of temperature on the reaction rate at zero sulfation and during increased sulfate loading or accumulation of product layers. The model is relatively simple and is applicable over a wide range of temperatures, particle sizes and SO2 concentrations. Validation was performed and it was found that the model satisfactorily represents the amount of accumulated sulfate within the entire domain of calculation. 2005 Elsevier Ltd. All rights reserved. Keywords: Sulfation model; Pulverized coal combustion; Desulphurization; Calcium carbonate

*

Corresponding author. Tel./fax: +66 2988 3655x241. E-mail address: [email protected] (N. Punbusayakul).

0196-8904/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2005.03.006

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1. Introduction Combustion of coal generates a number of air pollutants, particularly sulfur oxide (SOx). Eiichi Yugeta [1] reports the results of a three year investigation in Thailand that coal is mainly utilized in the power industry where sulfur dioxide (SO2) emission, caused by combustion of high sulfur coal is an important environmental and social issue. Coal, however, is the cheapest and most abundant fossil fuel compared to gas and oil. It is regarded as the major energy resource of the future, at least for the ﬁrst half of the present century [2]. Thus, cleaner coal combustion technologies are being developed at a rapid rate with numerical simulation playing an increasingly important role [3–9]. Recent work by Romo-Millares [7] has incorporated global mechanisms for NOx formation and reduction into a model for simulating combustion, heat transfer and NO emission of the ICSTM furnace [10]. The present study is aimed at establishing a simpliﬁed but reasonably accurate model of the formation and reduction of sulfur oxides to be incorporated in an existing computation code. 1.1. Formation and destruction of sulfur oxides Kinetic studies of sulfur oxides formation reveal that the reaction rate is of the same order as that of light hydrocarbon reactions. In a non-premixed ﬂame typically occurring in coal combustion where the ﬂame temperature is above 1000 C, the kinetic rate is much higher than the turbulent mixing rate of the reactants, and therefore, turbulent mixing dominates the overall reaction. In contrast, the reduction mechanisms mostly take place at a much lower temperature and with longer time. A number of techniques have been established to minimize the emission of sulfur oxides, such as treatment of low grade high sulfur coal prior to combustion by blending it with higher grade coal, or separation of pyrite by washing or gravitational method etc. These techniques have proved successful in removing pyritic sulfur (FeS2) but not in removing chemically bound organic sulfur. Other alternatives are treatments during and after combustion. An intermediate treatment involves dry injection of sorbent particles into a furnace where sulfur oxides are absorbed under optimum reacting environment. Of these techniques, two types of sorbents are used: calcium carbonate, generally known as limestone, and calcium hydroxide. Post ﬂame treatments, for example, semi-dry and wet scrubbing, are achieved by spraying a sulfur oxide absorbing solution into the exhaust gas. This requires an appropriate device to collect the product of the reaction for disposal or for further use, leading to an increase in initial and operating costs. A semi-dry process also needs careful maintenance due to wearing of the spraying mechanism, and the cost of absorbing agents is relatively high [11]. Among the various techniques mentioned above, the dry injection of a sorbent is by far the cheapest but suﬀers from low absorption eﬃciency, which has been reported to be as low as 50% [11] due to the short residence time in a pulverized combustion furnace. The particle resident time depends upon the ﬂow aerodynamics resulting from the particle-gas interaction. Therefore, it is interesting to investigate the trajectories of calcine particles in the combustion chamber, so that they may provide some insights for improving the sulfur absorption eﬃciency in the reactor design. However, conducting an experiment for monitoring limestone trajectories under coal combustion conditions is diﬃcult and expensive, even at laboratory scale. An alternative approach is the use of numerical simulation.

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1.2. Calcination and sulfation of limestone Limestone, chemically known as CaCO3, has been used for desulphurization of ﬂue gases emitted from the combustion of sulfur containing fuel. In a dry type desulphurization technique, the limestone particle is injected into the hot combustion environment. It rapidly undergoes calcination and produces porous calcined CaO particles and carbon dioxide as shown in the following equation. CaCO3 ðsÞ ! CaOðsÞ þ CO2 ðgÞ

ðEndothermicÞ [12]

ð1Þ

The high heating rate due to immediate particle suspension in a hot, well dispersed furnace causes a rapid decomposition of the CaCO3, leading to formation of CaO whose speciﬁc area is reportedly as high as 90 m2/g [13]. The CaO further reacts with SO2 and oxygen molecules in a sulfation process, producing CaSO4 according to the following equation. 1 CaOðsÞ þ SO2 ðgÞ þ O2 ðgÞ () CaSO4 ðsÞ 2

ðExothermicÞ [12]

ð2Þ

Although the CaCO3 derived calcine is less eﬀective in capturing SO2 than Ca(OH)2 derived stones [14], the former is more widely used because of its ease of supply. In this study, the SO2 capture mechanism has been extensively investigated and the way in which SO2 is transported and reacts at the interface will be discussed, as well as the accumulation of CaSO4 layers therein. A concept of randomly distributed pore sizes was introduced [15] and validated by Ulerich et al. [16]. The accumulation of product causes pore plugging, thus reducing the surface area [17]. This is closely linked to the pore size distribution and the intra-particle mass transport resistance [18]. However, the size distribution and the interconnectedness of the pores were important factors rather than just the particle porosity [18]. The conversion versus time curve was lowered with increasing particle sizes, decreasing calcination temperature and increasing sulfation temperature. This is explained in terms of an increase in the diﬀusion limit due to external plugging. The pore structure also changes due to CO2 activated sintering [19], especially at temperatures between 900 and 1300 C, leading to a reduction in the internal speciﬁc surface area. This concept of modeling was able to represent the rate measured by Borgwardt [14], which decreases exponentially. Several semi-empirical models follow this plugging concept. Moreover, there have been extensive literatures, i.e. Refs. [17,20–29], postulating that the external or mouth plugging occurs in large pores where the reaction is controlled by diﬀusion. Uniform deposition, however, takes place in small pores due to the kinetically controlled reaction. Additionally, the SO2 gas was absorbed at the temperature window of 900–1300 C because the diﬀusion and kinetic rates limit the lower bound of the reaction, whereas the reaction stability takes control of the upper bound [19]. Maximum conversion was found to be between 1100 C and 1200 C. The concept of spherical CaCO3 particles composed of small circular grains having undergone calcination, sintering and sulfation with diﬀusing SO2 and charge transfer outward of Ca2+ and O2 is another concept of modeling [30–32]. In this model, the surface area loss due to sintering of small grains was deﬁned as a function of CO2 and H2O. A combination of existing calcination, sintering and sulfation models, based on a grain-subgrain concept with ﬁrst order calcination kinetics was proposed. The validation study conducted later [33] against the previous experimental results, i.e. calcination conversion and surface area loss, has been quite satisfactory. It was

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claimed to be the ﬁrst model that incorporated the true mechanism of diﬀusion through the solid product phase. Predictions were determined against the data at various temperatures and sorbent types, which provided further insight into the interaction mechanism with some empirical values. A number of complex mathematical expressions in the sulfation model, as suggested in the above literatures, are, however, diﬃcult to incorporate into a CFD package for the prediction of heat and mass transfer due to combustion such as the combustion of pulverized coal. To overcome this time consuming calculation, which may also lead to numerical instability, an overall empirical approach based on the pore concept is proposed. A decrease in the reaction rate with increase in sulfation loading is accurately simulated against the experimental results. The eﬀects of temperature and SO2 concentration on the particle reactivity are also taken into account. In this paper, a relatively simple empirical model has been developed by taking into account the eﬀects of particle size, diﬀusion resistance that varies with sulfation loading, ambient temperature and SO2 concentration. Validation and a parametric study is also to be conducted prior to a study on the absorption in the combustion environment as will be given in this paper [4].

2. Modeling the sulfation process The calcinations and sulfation processes described in section 1.2 are depicted schematically in Figs. 1 and 2. From Borgwardt [34], the sulfation rate, r, is deﬁned as r¼

1 dn0 g m ¼ kvc wp dt q

ð3Þ

SO2

Heat

CaCO3

Calcination

CO2

Sulfation

CaO

CaSO4

O2

Fig. 1. Overall concept for sulfur absorption.

SO2 +

1 O2 2

Pore of CaO

Fig. 2. Model of sulfation process on porous CaO particle.

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257

Table 1 Summary of activation energy, reaction rates and frequency factors of dolomites [34] Dolomites

Activation energy E, cal/mol

Reaction rate constant kv, s1

Frequency factors A, s1

1337 1351 1343 1360

10,000 18,100 14,200 8100

4.8 · 103 7.2 · 103 4.0 · 103 2.3 · 103

2.4 · 105 9.0 · 106 1.1 · 106 5.5 · 104

The rate is in moles per unit gram of calcined particles per second. wp is the initial weight of solid particles. n 0 is the amount of sulfate in the solid particle in mole. c and m are the concentration of SO2 and the order of reaction, respectively. kv is a rate constant that is a function of temperature in the Arrhenius form k v ¼ A eE=RT

ð4Þ

Experimental values of kv are summarized in Table 1, along with those of the activation energy, E, and frequency factor, A. q is the density, and g is an eﬀectiveness factor, indicating a decrease in absorption rate due to sulfate loading. This parameter is related to sulfate loading, n 0 /wp, by the following equation: Acm E n0 ¼ b þ ln r0 ð5Þ ln g RT q wp b is an empirical parameter obtained by ﬁtting the experimental data. r0 is the reaction rate at zero sulfation, deﬁned as r0 ¼ g0

A0 cm E=RT e q0

From Eqs. (5) and (6), the frequency factor may be expressed as 0 g q b n A ¼ 0 A0 e w p g q0

ð6Þ

ð7Þ

Substituting A0 from Eq. (6) into Eq. (7) and combining the latter with Eqs. (3) and (4) yields the following relationship: 0

r ¼ r0 e

bwnp

ð8Þ

As will be shown below, a simple relationship between r, r0, b and n 0 /wp can be derived from Eq. (8) showing that the reaction rate is a function of only a few parameters, which is not the case observed from BorgwardtÕs experiment [34]. The data at 1 · 103 mol/g sulfate loading of the same investigator shows a linear correlation between log (r) and 1/T (K1). Thus, the reaction rate should be modiﬁed to account for this temperature eﬀect as: 0

r ¼ r0 e

bwnp

E

e RT þc0

ð9Þ

where c0 ¼

E RT ref

ð10Þ

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Tref is the reference temperature, which is 1143 K. The above relationship reduces to Eq. (8) at the reference temperature. Moreover, the rate also increases with increasing SO2. Thus, an additional term is proposed as follows: 0 cm b n ð11Þ r ¼ r0 e wp eðE=RT ÞþðE=RT ref Þ m cref where cref is the SO2 concentration of 2.9 · 108 mol/cc (wet basis). The value r0 for each type of dolomite is obtained by linear interpolation, knowing the reaction rate at 1 · 103 sulfation loading and the correlation of logðrÞ with linear n 0 /wp: Reference reactionð1143 KÞ

ln r0 ¼ ln r1 103 bð1 103 Þ

ð12Þ

b may be obtained by the following expression, knowing the reaction rates at 1 · 103 and 2 · 103 from the experiment [34], which are summarized in Tables 2 and 3. ln r2 103 ln r1 103 ð13Þ 2 103 1 103 The earlier reaction is for 1337 dolomite at the reference condition of 1143 K as illustrated in Fig. 3. The value of r0 and b of other types of dolomite may be determined similarly and are also given in Table 4. It is widely known that an Arhrenius plot (9) is used to represent the relationship of the reaction rate and the temperature, respectively, in the form of lnr and 1/T(K1). Using this technique, the SO2 limestone reaction rate at 1 · 103 mol/g of sulfation loading for diﬀerent temperatures can be determined as summarized in Table 5. Therefore, the reaction rate at other temperatures can be interpolated, which may be expressed as a modiﬁed form in Eq. (14) as follows. b¼

Table 2 Eﬀect of particle sizes on reaction rate at the sulfate loading of 2 · 103 mol/g, 1143 K [34] Dolomites 1337 1351 1343 1360

Reaction rate (mol/g s) · 105 Dp 0.0096 cm

Dp 0.025 cm

Dp 0.13 cm

4.2 3.2 2.1 2.5

3.2 2.1 1.4 1.8

1.4 1.3 0.7 1.1

Table 3 Empirical values of reaction rate at 1143 K, sulfate loading of 1 · 103 mol/g of 150/170-mesh particle size (0.0096 cm) [34] Dolomites

Reaction rate (mol/g s) · 105

1337 1351 1343 1360

6.4 5.9 3.6 3.1

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259

0

−4

ln (r0)

ln(r)

φl β

Thigh

TREF 1143K

φs 1 Tlow

φl φs

= The diameter of larger calcine particle = The diameter of small calcine particle 1 × 10 –3

2 × 10–3

n' wp (mol / g)

Fig. 3. The relationship between r0 and b.

Table 4 Reaction rate at zero sulfation and b for dolomites 1337, 1351, 1343 and 1360 [34] Dolomites

ln r0 9.24 8.97 9.69 10.16

1337 1351 1343 1360

b Dp 0.0096 cm

Dp 0.025 cm

Dp 0.13 cm

420 690 540 220

550 900 740 385

970 1140 1090 630

Table 5 The reaction rate measured at sulfation loading of 1 · 103 mol/g, 0.0096 cm of particle size Dolomites 1337 1351 1343 1360

Reaction rate (mol/g s) · 105 980 C

870 C

760 C

650 C

9.5 12.1 6.1 4.7

6.4 5.9 3.6 3.1

3.8 2.8 1.8 1.94

2.1 0.85 0.75 1.57

ln r ¼ ln rðn0 =wÞ þ ln DrT bðn0 =wÞ

ð14Þ

ln r ¼ lnðrðn0 =wÞ DrT Þ bðn0 =wÞ

ð15Þ

or where DrT is the ratio of the reaction rate at other temperatures to the reaction rate at the reference temperature (1143 K). It is used to reﬂect an eﬀect of the reaction rate at other temperatures so that Eq. (15) is robust within the range of interest.

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Eq. (11) suggests that the reaction rate does not relate to an eﬀectiveness factor (g). This factor reﬂects a decrease in reaction rate with an increase in sulfation loading. However, experimental evidence suggests that smaller particles absorb SO2 at a higher rate than larger ones, whereas the rate varied proportionally with temperature [34]. This diﬀerence is clearly observable at zero sulfation, and this is due to the diﬀusion resistance at zero sulfation. Eq. (5) may be re-written as ln g0 gA

cm E n0 ¼ b þ ln r0 q RT wp

ð16Þ

where g0 denotes the diﬀusion resistance at zero sulfation. Therefore, ln g0 g0T gA

cm E n0 ¼ b þ ln r0 q RT wp

ð17Þ

where g0T is the ratio of pore diﬀusion resistance to that due to the inﬂuence of temperature at zero sulfation. Rearrange the terms to yield ln g0 þ ln g0T þ ln gA

cm E n0 ¼ b þ ln r0 q RT wp

which may be written as cm E n0 r0 ln gA ¼ b þ ln q RT wp g0 g0T

ð18Þ

! ð19Þ ln(η0 )

( ) ∆y = { ln (η ) ln η 0* T

{

{

* 0

0

ln (r)

-4

β

1

1 × 10

–3

–3

2 × 10

n' (mol/g) wp

Fig. 4. The relationship between r0 and b with g0 and g0T modiﬁcation.

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261

It is important to note here that Eq. (19) is similar to Eq. (6). This parameter is, however, different from g, which is the eﬀectiveness factor for the entire reaction, indicating the reduction in absorption rate due to sulfate loading, which is unique for each particle size. The decrease of reaction rate per unit change of sulfation loading may be deﬁned as ! r0 ln r2 103 ln ¼ 0:0 g0 g0T 0 n =wp ð20Þ b¼ 2 103 This parameter reﬂects the overall kinetic rate of reaction (3) without the inﬂuence of the inparticle mechanism. This is characteristic of each type of particle. Experimental values are given in Table 4, whereas the conceptual representation of the method for determining b is given in Fig. 4.

3. Validation 3.1. Eﬀect of particle size Fig. 5 shows the eﬀect of diﬀusion resistance on the sorption of sulfur oxides calculated using Eq. (11) with g0 varying from 1 (no resistance at zero sulfation) to 0.4 for the diﬀerent types of dolomites. The results are compared with experimental data [34]. It is important to note here that the values of b given in Table 4 are determined from Eq. (13) assuming that the reaction rate at zero sulfation is unique for a certain type of dolomite regardless of the eﬀect of particle size variation. Thus, those values only represent the relationship of ln(r) and the sulfate loading n 0 /wp in the absence of initial diﬀusion resistance, g0 . Generally, the simulation under predicts the 10

mg sulfate / 30 mg calcined CaO

9 8 7 6 5 4

η0* = 0.4

3

η0* = 0.7

2

η0* =1.0

1 0

Expt. Borgwardt, 1970 0

20

40

60 80 Time (s)

100

120

Fig. 5. Eﬀect of zero sulfation diﬀusion resistance on sorption of sulfur oxides against experimental data, dolomite 1351, Dp = 0.0096 cm.

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experimental data. A change in diﬀusion resistance generally aﬀects the shape of sulfate accumulation with time. A decrease in reaction rate at zero sulfation leads to a decrease in the amount of sulfate absorbed, which is most notable at the early stage of the reaction. At a sulfate loading of 2 · 103, the reaction rate equals the value given in Table 2. This is a break even point of the reaction rate where the values are the same for all g0 . As the reaction rate decreases linearly with increasing sulfate loading, the decrease in reaction rate for the case of g0 < 1 is less than that of g0 ¼ 1. This leads to a higher reaction rate at a sulfate loading greater than 2 · 103. The sulfate accumulation for the case of g0 < 1 is, therefore, greater than that for the case of g0 ¼ 1 after a certain period of time. Fig. 6 suggests a similar trend of evolution with a change in g0 . The reaction rate is generally lower than that for Dp = 0.0096 cm due to the lower b. At t = 0 s, for g0 ¼ 1, both cases have the same reaction rate. As for t greater than 0 s, the reaction rate of the 0.025 cm particles becomes less than that of the 0.0096 cm ones, and the gap becomes greater as time increases. Its eﬀect on the accumulative amount of sulfate with time, thus, follows this trend. It appears, however, that the simulated result for g0 ¼ 0:35 yields the best ﬁt to the measurements (see Fig. 7). The measured data clearly shows that there is a signiﬁcant diﬀusion resistance at zero sulfation. As for the absorption of the 0.13 cm particle size, the value of g0 ¼ 0:09 yields the best ﬁt to the measured data (see Fig. 8). At g0 ¼ 0:05, the accumulation level increases almost linearly with time, suggesting that the reaction rate is very much less inﬂuenced by the sulfate loading (see Fig. 9). The eﬀect of b on SO2 absorption may be illustrated in Fig. 10. At a constant value, g0 ¼ 1, a decrease in magnitude of b leads to an increase in the reaction rate. The parameter b indicates that the rate of ln(r) decreases with sulfate loading. Thus, the greater is the magnitude of b, the lesser is the rate of reaction.

mg sulfate / 30 mg calcined CaO

8 7 6 5 4 3

η 0* = 0.2

2

η 0* = 0.5 η 0* =1.0

1

Expt. Borgwardt, 1970

0

0

20

40

60 80 Time (s)

100

120

Fig. 6. Eﬀect of zero sulfation diﬀusion resistance on sorption of sulfur against experimental data, dolomite 1351, Dp = 0.025 cm.

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263

mg sulfate / 30 mg calcined CaO

8 7 6 5 4 3 2 η0* = 0.35

1

Expt. Borgwardt, 1970

0

0

20

40

60 80 Time (s)

100

120

Fig. 7. Comparison between mathematical modeling at g0 ¼ 0:35 and measurement for dolomite 1351, Dp = 0.025 cm.

mg sulfate / 30 mg calcined CaO

6

5

4

3

2 η0* = 0.09

1

Expt. Borgwardt, 1970 0

0

20

40

60 80 Time (s)

100

120

Fig. 8. Comparison between mathematical modeling at g0 ¼ 0:09 and measurement for dolomite 1351, Dp = 0.13 cm.

Fig. 10 shows an increase in the accumulative sulfate loading against the same corresponding time when decreasing the magnitude of b to 90% and 85% of its original (b), respectively. The proﬁle of sulfate loading, which is compared between mathematical simulation and the measurement for dolomite 1351, has been given in Fig. 11. For diﬀerent types of dolomites, the mathematical model for SO2 absorption may be obtained in a similar manner. However, the chemical and physical structures of dolomite are diﬀerent from one dolomite to another. Thus, speciﬁc g0 and b values should be identiﬁed for the diﬀerent types of particles.

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mg sulfate / 30 mg calcined CaO

6

5

4

3 η 0* = 0.05

2

η 0* = 0.1

η 0* = 0.2

1

Expt. Borgwardt, 1970 0

0

20

40

60 80 Time (s)

100

120

Fig. 9. Eﬀect of zero sulfation diﬀusion resistance on sorption of sulfur oxides against experimental data, dolomite 1351, Dp = 0.13 cm.

10

mg sulfate / 30 mg calcined CaO

9 8 7 6 5 4 3

β 2 = 0.90β 1

2

β 2 = 0.85β 1

1 0

Expt. Borgwardt, 1970 0

20

40

60 80 Time (s)

100

120

Fig. 10. Eﬀect of b on sorption of sulfur oxides against experimental data, dolomite 1351, Dp = 0.0096 cm.

3.2. Eﬀect of temperature The experimental data of Borgwardt (9) are compared with the simulation obtained from Eq. (11) with b from Eq. (20). The results show the inﬂuence of diﬀusion resistance on the sorption of sulfur oxides by varying g0T (resistance at zero sulfation) and DrT (inﬂuence of temperature change

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265

10

mg sulfate / 30 mg calcined CaO

9 8 7 6 5 4 3

Avg. dia. = 0.0096 cm

2

Avg. dia. = 0.025 cm

1 0

Avg. dia. = 0.13 cm 0

20

40

60 80 Time (s)

100

120

Fig. 11. Comparison between mathematical simulation and the measurement for dolomite 1351.

on reaction rate) while increasing the sulfate loading. This reaction rate was diﬀerent from the reaction at the reference condition. Fig. 12 shows the inﬂuence of diﬀusion resistance that aﬀects the sulfate accumulation. The simulation result was taken for comparison with the experimental data of Borgwardt at 980 C when DrT was ﬁxed at the value of 1.0. The parameter, g0T , was varied between 0.45 (Case A), 1.0 (Case B, the base case) and 1.2 (Case C). Analysis of the simulation results found that the case

18

mg sulfate / 30 mg calcined CaO

16 14 12 10 8 6

A η 0*T = 0.45 ∆rT =1

4

B η 0*T =1

∆ rT =1

C η 0*T =1.2

∆ rT =1

2

Expt. Borgwardt, 1970 0

0

20

40

60

80

100

120

Time (s)

Fig. 12. Inﬂuence of g0T on sulfate accumulation compared to the experiment at 980 C, dolomite 1351, Dp = 0.0096 cm.

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mg sulfate / 30 mg calcined CaO

16 14 12 10 8 A η0*T =1 ∆ rT = 0.8

6

B η0* =1 ∆ r =1 T T

4

C η0* =1 ∆ r =1.8 T

2

T

Expt. Borgwardt, 1970 0

0

20

40

60

80

100

120

Time (s)

Fig. 13. Inﬂuence of DrT on sulfate accumulation compared to the experiment at 980 C, dolomite 1351, Dp = 0.0096 cm.

where g0T < 1 provides a higher diﬀusion resistance at the ﬁrst step of the reaction than the case where g0T > 1. Thus, lower values of g0T lead to higher resistance. However, the level of sulfate accumulation at 120 s. for g0T < 1 is higher than that for g0T > 1. Similar studies were also conducted for the eﬀect of DrT . From Fig. 13, the value of g0T was ﬁxed at 1.0 and DrT was varied between 0.8 (Case A), 1.0 (Case B, the base case) and 1.8 (Case C), and the simulation results were

18

mg sulfate / 30 mg calcined CaO

16 14 12 10 8 6 4

η0* = 0.65, r =1.15 T T

2 0

Expt. Borgwardt, 1970 0

20

40

60

80

100

120

Time (s)

Fig. 14. Comparison of mathematical simulation results at g0T ¼ 0:65 and DrT ¼ 1:15 with experiment at 980 C, dolomite 1351, Dp = 0.0096 cm.

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267

taken for comparison with the experimental data of Borgwardt at 980 C. For DrT < 1, the reaction rate was lower than that for DrT > 1, leading to lower sulfate accumulation. The best ﬁt for the simulation result for 980 C was obtained when g0T ¼ 0:65 and DrT ¼ 1:15 (Fig. 14). Fig. 15 shows a change in diﬀusion resistance g0T on sulfate accumulation when DrT ¼ 1 and g0T was varied between 0.8 (Case A), 1.0 (Case B, the base case) and 6.0 (Case C). The simulation results were taken for comparison with the experimental data at 760 C. It appeared that when t = 0 s and t > 0 s, the reaction rate ln(r0) at 760 C was lower than the value at 980 C (Fig. 14). Furthermore, the reaction rates for g0T < 1 were generally lower than those for g0T > 1. In contrast, for g0T > 1, the level of sulfate accumulation at 120 s was higher than that for g0T < 1. Fig. 16 shows that when g0T ¼ 1 and DrT was varied between 0.6 (Case A), 1.0 (case B, the base case) and 1.1 (Case C) at 760 C, it appears that for DrT < 1, the reaction rate and sulfate accumulation were lower than those for the case where DrT > 1. However, the best ﬁt of the simulation result for 760 C was obtained at the values of g0T ¼ 4:75 and DrT ¼ 0:6175 (Fig. 17). In Fig. 18, DrT was ﬁxed at the value of 0.3 and g0T was varied for 3.0 (Case A) 5.0 (Case B) and 10 (Case C) at 650 C. The simulation of the base case where DrT ¼ 1 and g0T ¼ 1 (Case D) was also given for reference. It was found that the reaction rates were, in general, lower than the reaction rates at 980 C and 760 C. Moreover, it appears that the reaction rate of SO2 absorption remains almost constant up to the period of interest (120 s). The higher value of g0T implies greater sensitivity, in an adverse manner, of diﬀusion resistance (at zero sulfation) with temperature. As seen at the early stage of the reaction, the reaction rates for g0T ¼ 3 and g0T ¼ 5 are lower than that for g0T ¼ 10, leading to the sulfate accumulation at g0T ¼ 10 being at the highest level among all the other cases. The idea of how DrT aﬀects the reaction rate is presented in Fig. 19, where g0T was ﬁxed at the value of 10.0 and DrT was varied for 0.1 (Case A), 0.15 (Case B) and 0.3 (Case C). Also, the calculation at the same temperature (650 C), g0T ¼ 1 and DrT ¼ 1 (Case D) was given

mg sulfate / 30 mg calcined CaO

6

5

4

3 A η 0*T = 0.8 ∆ rT =1

2

B η 0* =1

∆ r =1

C η 0*T = 6

∆ rT =1

T

1

T

Expt. Borgwardt, 1970 0

0

20

40

60

80

100

120

Time (s)

Fig. 15. Inﬂuence of g0T on sulfate accumulation compared to the experiment at 760 C, dolomite 1351, Dp = 0.0096 cm.

268

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mg sulfate / 30 mg calcined CaO

6

5

4

3 A η0* =1

∆ r = 0.6

B η 0*T =1

∆ rT =1

C η 0* =1

∆ r = 1 .1

T

2

1

T

T

T

Expt. Borgwardt, 1970 0 0

20

40

60

80

100

120

Time (s)

Fig. 16. Inﬂuence of DrT on sulfate accumulation compared to the experiment at 760 C, dolomite 1351, Dp = 0.0096 cm.

mg sulfate / 30 mg calcined CaO

7 6 5 4 3 2

η0*T = 4.75, rT = 0.6175

1

Expt. Borgwardt, 1970 0

0

20

40

60

80

100

120

Time (s)

Fig. 17. Comparison of mathematical simulation at g0T ¼ 4:75 and DrT ¼ 0:6175 with experiment at 760 C, dolomite 1351, Dp = 0.0096 cm.

for reference. It appears that when DrT ¼ 0:3, the reaction rate was higher than the reaction rate at DrT ¼ 0:15 and DrT ¼ 0:1. The best ﬁt of the simulation results for 650 C was observed at the value of g0T ¼ 8:5 and DrT ¼ 0:235 (Fig. 20) Based on the data obtained, it is indicated that the temperature can aﬀect the reaction rate at zero sulfation and during product accumulation. This comparison between the experimental data and the result obtained from the mathematical model is limited to CaCO3 type 1351 as shown in

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269

3.5

mg sulfate / 30 mg calcined CaO

3 2.5 2 A η0* = 3 ∆ r = 0.3

1.5

T

T

B η0* = 5 ∆ r = 0.3 T T

1

C η0* =10 ∆ r = 0.3 T

0

T

D η0* =1 ∆ r =1 T T

0.5

Expt. Borgwardt, 1970 0

20

40

60

80

100

120

Time (s)

Fig. 18. Inﬂuence of g0T on sulfate accumulation compared to the experiment at 650 C, dolomite 1351, Dp = 0.0096 cm.

mg sulfate / 30 mg calcined CaO

3.5 3 2.5 2 A η0*T =10 ∆ rT = 0.1

1.5

B η0*T =10 ∆ rT = 0.15

1

C η0*T =10 ∆ rT = 0.3

D η0* =1 ∆ r =1 T T

0.5

Expt. Borgwardt, 1970 0

0

20

40

60

80

100

120

Time (s)

Fig. 19. Inﬂuence of DrT on sulfate accumulation compared to the experiment at 650 C, dolomite 1351, Dp = 0.0096 cm.

Fig. 21. Table 6 shows the reaction rate ratio at zero sulfation, ðg0T Þ, and the reaction rate ratio during the increase of sulfation loading, ðDrT Þ, or product accumulation for the accurately predictable absorption rate range of the mathematical model.

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mg sulfate / 30 mg calcined CaO

4 3.5 3 2.5 2 1.5 1

η 0* = 8.5, ∆ r = 0.235 T T

0.5 0

Expt. Borgwardt, 1970 0

20

40

60

80

100

120

Time (s)

mg sulfate / 30 mg calcined CaO

Fig. 20. Comparison of mathematical simulation results at g0T ¼ 8:5 and DrT ¼ 0:235 with experiment at 650 C, dolomite 1351, Dp = 0.0096 cm.

16

Temp = 980 oC

14

Temp = 870 oC

12

Temp = 760 oC Temp = 650 oC

10 8 6 4 2 0

0

20

40

60 80 Time (s)

100

120

Fig. 21. Comparison of mathematical simulation results with experimental data using various temperature levels, dolomite 1351, Dp = 0.0096 cm.

Table 6 The ratio of g0T and DrT for the accurately predictable absorption rate range of mathematical model Parameter g0T DrT

Temperature (C) 980 C

870 C

760 C

650 C

0.65 1.15

1 1

4.75 0.6175

8.5 0.235

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271

4. Conclusion Based on the results obtained after a signiﬁcant improvement of this overall mathematical model, the prediction of the absorption of sulfur dioxide is more precise and accurate. The validation process was performed by adjustments of DrT and g0T according to the changes in temperature and particle sizes, which caused no eﬀect to the original model. With this model, apart from other known and already concerned inﬂuences, the diﬀusion resistance at zero sulfation have, for the ﬁrst time, accounted for the temperature of the particle itself. This model can be easily incorporated into the CFD code for prediction of dry particle adsorption suspension inside the reacting chamber.

Acknowledgement The authors would like to acknowledge the Thailand Research Fund for ﬁnancial support of this research.

References [1] Eiichi Y. Research survey on eﬃcient and environmentally friendly coal utilization systems in Thailand. Clean Coal Technology Seminar in Thailand 1999(Feb):1–12. [2] International Energy Agency: IEA. [3] Magnussen BF, Hjertager BH. On Mathematical Modeling of Turbulent Combustion with Special Emphasis on Soot Formation and Combustion. Sixteenth Symposium (Int.) on Combustion. The Combustion Institute, 1976, pp. 719. [4] Salooja AP. Mathematical Modeling of and Experimental Studies in Axi-Symmetrical Combustors. PhD Thesis of University of London and the Diploma of Membership of the Imperial College, 1979. [5] Lockwood FC, Rizvi SMA, Lee FK, Whalet K. Coal Combustion Model Validation Using Cylindrical Furnace Data. Twentieth Symposium (Int.) on Combustion. The Combustion Institute, 1994, p. 513. [6] Sloam DF, Smith PF, Smoot LD. Modeling of swirl in turbulent ﬂow system. Progress in Energy Combustion Science 1986;12:163. [7] Romo-Millares CA. Mathematical Modeling of Fuel NO Emissions from PF Burners. PhD Thesis of University of London and the Diploma of Membership of the Imperial College, 1992. [8] Lockwood FC, Jones WP. The Mathematical Modeling of Combustion Chambers. Furnaces and Fires: Prediction of NO Emissions from a Staged Burner. Outline of Lecture Notes. Post Experience Course Lectures. London: Department of Mechanical Engineering, ICSTM; 1993. [9] Shen B. The Application of Second—Moment Turbulence Closures to 2D Pulverised—Coal Flames. PhD Thesis of University of London and the Diploma of Membership of the Imperial College, 1994. [10] De Soete FF. Fundamentals of NO formation and destruction (gas phase). Course on combustion of solid fuels. Noordwijkerhout, The Netherlands: IFRF; 1988. [11] Tetsuo K. Flue gas desulfurization technology. Clean Coal Technology Seminar in Thailand 1999(Feb):26–36. [12] Alvfors P, Svedberg G. Modeling of the sulphation of calcined limestone and dolomite-a gas–solid reaction with structural changes in the presence of inert solids. Chemical Engineering Science 1988;43(5):1183–93. [13] Borgwardt RH. Calcination kinetics and surface area of dispersed limestone particles. AIChE J 1985;31(1):103–11. [14] Borgwardt RH, Bruce KR. Eﬀect of speciﬁc surface area on the reactivity of CaO with SO2. AIChE J 1986;32(2):239–46. [15] Christman PG, Edgar TF. Distributed pore-size model for sulfation of limestone. AIChE J 1983;29(3):388–95.

272

N. Punbusayakul et al. / Energy Conversion and Management 47 (2006) 253–272

[16] Ulerich NH, OÕ Neill EP, Keairns DL. The Inﬂuence of Limestone Calcination on the Utilization of the Sulfur Solvent in Atmospheric Pressure Fluid-Bed Combustors, EPRInFP-426, Final Report, 1971. [17] Simons GA, Garman AR. Small pore closure and the deactivation of the limestone sulfation reaction. AIChE J 1986;32(9):1491–9. [18] Zarkanitis S, Sotirchos SV. Pore structure and particle size eﬀect on limestone capacity for SO2 removal. AIChE J 1989;35(5):821–31. [19] Newton GH, Chen SL, Kramlich JC. Role of porosity loss in limiting SO2 capture by Calcium based sorbents. AIChE J 1989;35(6):988–94. [20] Georgakis C, Chang CW, Szekely J. A changing grain size model for gas–solid reaction. Chemical Engineering Science 1979;34:1072. [21] Lee DC, Geotgakis C. A single-particle size model for sulfur retention in ﬂuidized bed coal combustors. AIChE J 1981;27:472. [22] Hartman M, Coughlin RW. Reaction of sulfur dioxide with limestone and the inﬂuence of pore structure. Ind Eng Chem Proc Des Dev 1974;13:248. [23] Hartman M, Coughlin RW. Reaction of sulfur dioxide with limestone and the grain model. AIChE J 1976;22:490. [24] Hartman M, Coughlin RW. Inﬂuence of porosity of calcium carbonate on their reactivity with sulfur dioxide. Ind Eng Chem Proc Des Dev 1978;17:411. [25] Bhatia SK, Perlmutter DD. The eﬀect of pore structure on ﬂuid–solid reactions. I: Application to the SO2–lime reaction. AIChE J 1981;27:226. [26] Bardakci T. Diﬀusional study of the reaction of Sulfur dioxide with reactive porous matrices. Thermochim Acta 1985;76:287. [27] Marsh DW, Ulrichson DL. Rate and diﬀusional study of the reaction of calcium oxide with sulfur dioxide. AIChE Ann Meet, Los Angeles 1982. [28] Ramachandran PA, Smith JM. A single-pore model for gas–solid moncatalytic reactions. AIChE J 1977;23:353. [29] Simons GA. The Pore Tree Structure of Pore Char. 19th International Symposium on Combustion, The Combustion Institute, 1982. [30] Mahuli SK, Rajeev R, Raja J, Shriniwas Chauk L-SF. Combined calcination, sintering and sulfation model for CaCO3-SO2 reaction. AIChE J 1999;45(2):367–82. [31] Milne CR, Pershing DW. An experiment and theoretical study of the fundamentals of the SO2 control. Symposium, EPA/EPRI. St. Louis, MO, October 1988. p. 25–8. [32] Milne CR, Silcox GR, Pershing DW, Kirchgessner DA. Calcination and sintering models for application to hightemperature, short-time sulfation of Calcium-based sorbent. Ind Eng Chem 1990. [33] Mahuli SK, Agnihotri R, Chauk S, Ghosh-Dastidar A, Wei SH, Fan LS. Pore structure optimization of calcium carbonate for enhanced sulfation. AIChE J 1997. [34] Borgwardt RH. Kinetics of the reaction of SO2 with calcined limestone. AIChE J 1970;4(1):59–64.

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