Application of Random-Pore Model to SO2 Capture by Lime

Ind. Eng. Chem. Res. 2010, 49, 117–122

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Application of Random-Pore Model to SO2 Capture by Lime H. Ale Ebrahim* Chemical Engineering Department, Petrochemical Center of Excellency, Amirkabir UniVersity (Tehran Polytechnic), Tehran 15875-4413, Iran

Flue gas desulfurization by lime (CaO) is widely used for coal-based power plants. The incomplete conversion of CaO poses a significant problem for such systems. An interesting method for increasing the pore radius of lime by a weak acid has been presented in the literature as a means to solve this problem. In this article, the random-pore model was applied to model the above experimental work successfully. Therefore, the effect of the CaO pore size distribution on the final conversion for SO2 removal can be predicted by this model. Introduction SO2 acid gas is one of the most important air pollutants, with destructive effects on forests, agriculture, and river ecology. There are both stationary and mobile sources for SO2. The stationary sources include metallurgical plants (copper, zinc, and lead roasting units), power plants, refineries, and petrochemical industries. The mobile sources are due to the combustion of high-sulfur-content gasoline and gas-oils in automobiles and trucks. To minimize the SO2 emissions from mobile sources, new regulations have been introduced for environmental protection. For example, low sulfur limits of 30-50 ppm for gasoline and diesel have been used in the European community and the United States since January 2005.1 Therefore, new hydrotreating methods for deep fuel desulfurization have been used by refineries.2-4 These methods propose new catalysts for hydrotreating resistant sulfur compounds such as 4,6-dimethyldibenzothiophene. Therefore, it is necessary to improve the performance of SO2 removal from stationary sources. Another option is changing the fuel of power plants or reducing agents of metallurgical units from coal to natural gas. Environmental preferences for natural gas over to coal are very interesting. Natural gas sweetening is very simple, whereas the coal desulfurization is almost impossible. Moreover, the amount of greenhouse gas (CO2) emission from natural gas-based combustion is nearly one-half that of coal-based plants. For example, the SO2 emissions from combined-cycle power plants (based on natural gas) can be completely eliminated compared to steam-turbine power plants (based on coal) with about 15 kg of SO2/MWh.5 The greenhouse gas emissions from combined-cycle power plants (with 53% efficiency) is also about 400 kg of CO2/MWh and is less than the 1000 kg of CO2/MWh of steam turbine power plants (38% efficiency).6 Another alternative is utilizing dual fuel systems to reduce the greenhouse gas emissions from power plants.7 Moreover, in some chemical and metallurgical industries, using natural gas instead of coke as the reducing agent can partially or completely eliminate the greenhouse gas emissions.8,9 However, the most significant problem in relation to natural gas is its difficult transportation from producing countries to the industrial world.10 Therefore, most power plants in industrial countries rely on coal as a fuel, and it is necessary to improve the efficiency of SO2 removal from such power plants. Flue gas desulfurization (FGD) methods are divided into two groups: regenerative and throwaway.11 The regenerative meth* To whom correspondence should be addressed. E-mail: [email protected].

ods are mainly for high SO2 values such as copper converting and zinc roasting plants. Then, the concentrated SO2 stream must be used for producing sulfuric acid11 or reduced to elemental sulfur by reducing agents such as CH4, H2, or CO.12-14 Some novel FGD methods with simultaneous sulfur generation have also been proposed.15-17 FGD processes for power plants with relatively low SO2 concentrations in the flue gas are mainly throwaway methods.18 In power plants, the heat of flue gas can evaporate the water in the adsorbent slurry, and therefore, dry FGD methods are widely used. In this method, the most common adsorbent is CaO,19-23 which is used in slurry injection24,25 or fluidized-bed26,27 FGD systems. However, in some cases, CaCO3 can be used directly for SO2 removal in high CO2 concentrations.28,29 In FGD processes with CaO as the adsorbent, the most significant problem is incomplete solid conversion.30 This phenomenon is due to the high molar volume of solid product (gypsum) compared to the solid reactant (lime) in the following FGD reaction 1 CaO + SO2 + O2 f CaSO4 2

(1)

The ratio between the molar volumes of the solid product and the solid reactant is an important parameter and is expressed as Z. For Z > 1, the porosity of the solid pellet decreases during the reaction because of volume expansion. This problem is more drastic at the pellet surface, where the gaseous reactant concentration is high. Therefore, the porosity at the pellet surface becomes zero (pore mouth closure) after some time in systems with high Z (for example, in the CaO + SO2 reaction with Z ) 3). Consequently, incomplete conversion occurs, which decreases the efficiency of the FGD process considerably. Moreover, the quality of the solid product as gypsum is reduced. Therefore, it is essential to introduce methods for solving the incomplete conversion problem in FGD processes for power plants. The SO2 removal by solid sorbents is one of the most important series of noncatalytic gas-solid reactions. Other applications of these reactions include reduction of metal oxides, roasting of metal sulfides, coal gasification, active carbon preparation, and catalyst regeneration.31 The modeling of gas-solid reactions is very important for the prediction of their behavior. Moreover, by using a successful simulation model, it is possible to propose effective methods for improving the efficiency of FGD processes. There are several mathematical models for describing the conversion-time profiles of gas-solid reactions. These models include the sharp-

10.1021/ie901077b  2010 American Chemical Society Published on Web 11/17/2009

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Figure 2. Experimental conversion-time profiles of the CaO + SO2 reaction from ref 19.

Figure 1. Pore volume distributions of three types of lime from ref 20.

interface model, volume-reaction model, grain model, modified grain model, nucleation model, single-pore model, and randompore model.32 The structural changes (such as incomplete conversion) can be well described by some of these models, including the modified grain model and random-pore model.32 In the modified grain model, the grain radius changes during the reaction as a function of Z.33 The modified grain model has been applied to FGD processes with CaO sorbent.34 In this field, by decreasing the size of the pellets and, therefore, the diffusion path, the limits of incomplete conversion can be increased. For example, by decreasing the pellet diameter from 250 to 84 µm, the theoretical incomplete conversion limit can be raised from 0.37 up to only 0.53.34 A very interesting method for completely solving this problem has been proposed by Wu and co-workers.19,20 In this method, large pores are produced in the CaO sorbent by a weak acid (Figure 120). Therefore, the incomplete conversion problem is completely solved (Figure 219), and it is possible to use the whole capacity of the CaO for SO2 removal. However, the works of Wu and co-workers are completely experimental. Therefore, it is necessary to propose a suitable mathematical model for their technique. This article presents a model for such a process that can be used for some critical calculations about lime capacity predictions for SO2 removal. The internal structure of industrial sorbents consists of a series of cavities with a pore size distribution. Therefore, the randompore model (the most sophisticated gas-solid reaction model) must be used for accurate simulations of the system. In this work, the experimental data of Wu and co-workers are successfully predicted using this model. Mathematical Modeling The mathematical formulation for random-pore model has been studied before by Bhatia and Perlmutter.35-37 Consider the reaction A(g) + νBB(s) f C(g) + νDD(s) The following assumptions are used in the modeling:

(2)

(1) The pseudo-steady state describes the concentration of gas A in the pellet. (2) The bulk flow effect is negligible for low SO2 concentrations. (3) The system is isothermal. (4) The pellet size is constant. (5) The reaction is irreversible and first-order with respect to the gaseous reactant.30 (6) The bulk gas concentration is constant. The dimensionless governing equations of the random-pore model for a spherical pellet are as follows:36 1 ∂ ∂a φ2ab√1 - ψ ln b δy2 ) 2 ∂y ∂y βZ y [√1 - ψ ln b - 1] 1+ ψ

(

)

ab√1 - ψ ln b βZ [√1 - ψ ln b - 1] 1+ ψ The initial and boundary conditions are expressed as ∂b )∂θ

(3)

(4)

θ)0

b)1 (5) ∂a )0 (6) y)0 ∂y ∂a Sh y)1 ) (1 - a) (7) ∂y δ Dimensionless parameters are defined in the Nomenclature. In the above equations, Ψ is the random-pore model parameter. This parameter is a function of the initial pore size distribution of the pellet. The relations of Ψ for various pore size distributions were described by Bhatia and Perlmutter.37 φ is the initial Thiele modulus and is proportional to the square root of the rate constant ratio to the initial pore diffusivity. β is the resistance due to diffusion through the product layer around each pore. Sh is the Sherwood number for external mass transfer to the pellet. Z is the ratio of the molar volumes of the solid product to the solid reactant as follows Z)

νDFBMD νBFDMB

(8)

For Z < 1, the product layer volume is less than the solid reactant volume, and the porosity increases. For Z ) 1, the pore size is unaffected by the reaction. Finally, for Z > 1, the product layer volume is more than the solid reactant volume, and the porosity

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decreases with the progress of the reaction. For very large values of Z, pore mouth closure and incomplete conversion can occur. The porosity of the pellet at each time can be expressed as36 (Z - 1)(1 - ε0)(1 - b) ε )1ε0 ε0

(9)

To relate the pore diffusion to the pellet porosity, two approaches exist. The first approach, from Wakao and Smith,38 is δ)

() [

De ε ) De0 ε0

2

(Z - 1)(1 - ε0)(1 - b) ε0

) 1-

]

2

(10)

The second approach assumes that the tortuosity factor of the pellet remains constant during the reaction. The result of this approach is31 δ)

[

De (Z - 1)(1 - ε0)(1 - b) ε ) ) 1De0 ε0 ε0

]

(11)

By eq 10 or 11, the variation of pore diffusion with the progress of the reaction can be considered. In this work, eq 11 was found to provide better results. Finally, the solid conversion can be computed from the solid concentration as X(θ) ) 1 - 3

∫

1 2

0

y b(y, θ) dy

(12)

In this work, the coupled partial differential equations (eqs 3 and 4) were solved by two methods. The first method (quantized technique) was well described for the modified grain model and random-pore model elsewhere.33,39 The second method is based on eight-point orthogonal collocation and has been compared with the numerical solution of the random-pore model with a good accuracy.40 However, the results of these two methods are in good agreement and will be described in the next section.

θf0

)3

a. Rate Constant Estimation. First, it is necessary to develop a relation for rate constant estimation. This evaluation is based on the initial experimental conversion-time profiles. When time approaches zero by the δ ) b ) 1 approximation, eq 3 of the random-pore model can be simplified to 1 ∂ 2 ∂a y ) φ2a 2 ∂y ∂y y Integration of the above equation yields

(

)

(13)

sinh(φy) a) y sinh(φ) Inserting eq 14 into eq 4 and integrating yields

[ dXdt ]

tf0

3ksS0CAb ) CB0(1 - ε0)

[

sinh(φy) θ (15) y sinh(φ) Now, the conversion for a spherical pellet at the initial time is

∫

1 2 y 0

[

1-

sinh(φy) θ dy y sinh(φ)

]

(16)

Integration by parts of eq 16 gives

[

]

1 coth(φ) - 2 Xθ f 0 ) 3θ φ φ Differentiation of the above equation yields

(17)

1 coth(φ) - 2 φ φ

]

(18)

( ) ksS0 νBDe0

coth R



R

ksS0 νBDe0

-

1 k sS0 R2 νBDe0

]

(19)

In eq 19, the effect of product layer diffusion (Dp) does not appear, because there is no product layer around the cylindrical pores at the initial times. Now, by comparison of eq 19 with the initial slopes of the curves in Figure 2, the average rate constant for the three cases was computed as ks ) 0.096 cm/min at 800 °C. This value is in close agreement with the 0.099 cm/min (at 850 °C) for SO2 absorption by lime reported in the literature.21 b. Other Parameters Used. Now, the other parameters used in the modeling are described. For the CaO + SO2 system, Z ) 3 is used in the literature.21 The pellets of lime are 2-mm spheres, the operating temperature is 800 °C, and there is 1500 ppm SO2 (CAb ) 1.7 × 10-8 gmol/cm3).19 External mass-transfer resistance is assumed to be negligible, and CB0 ) 3.4/56 g mol/ cm3. The effective initial diffusivity of SO2 through porous lime is determined from the equation

(

1 1 1 1 ) 2 + De0 D D ε0 AM AK

)

(20)

where DAM is the molecular diffusivity of SO2 and is estimated from the Chen and Othmer kinetic theory.41 DAK is the Knudsen diffusivity and can be determined from the following equation for the pore model31

( )

4rj 8RgT 6 πMA

1/2

(21)

c. Structural Parameters. The structural parameters of the random-pore model can be computed from the pore volume distribution by the equations35 Vp )

∫

ε0 )

Vp Vp + 1/FB

∞

0

V0(r) dr

(22) (23)

jr )

1 Vp

∫

V0(r)r dr

(24)

S0 )

2 Vp

∫

V0(r) dr r

(25)

L0 )

1 πVp

(14)

b)1-

[

Therefore, the rate constant can be estimated from the initial experimental conversion-time profile as

DAK )

Comparison of Results

Xθf 0 ) 1 - 3

[ dXdθ ]

119

Ψ)

∞

0 ∞

0

∫

∞

0

V0(r) r2

4πL0(1 - ε0) S02

dr

(26) (27)

Therefore, from the peak areas of the pore volume distributions of the three types of lime (Figure 120), the structural parameters were determined. These parameters (with the effective diffusivity from eq 20) are presented in Table 1. As this table shows, large pores can be produced in lime by the swelling

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Table 1. Structural Parameters for the Three Types of Lime jr × 105 (cm) Vp (cm3/g) ε0 S0 × 10-5 (1/cm) L0 × 10-10 (1/cm2) Ψ De0 (cm2/min)

raw

water-swelled

acetic-acid-swelled

1.11 0.373 0.56 5.08 2.88 0.62 2.12

5.05 0.746 0.72 3.38 1.68 0.52 6.1

37.7 1.84 0.86 2.14 5.92 2.27 64

Table 2. Random-Pore Model Parameters for the Three Types of Lime

φ β τ (min)

raw

water-swelled

acetic-acid-swelled

15.17 0.83 32.4

7.29 0.795 30.9

1.79 0.63 24.5

method especially with acetic acid. The effective diffusivity of SO2 in these large pores is considerably increased, and thus, the incomplete conversion problem can be solved successfully (see Figure 219). d. Simulation Parameters. Now, the final random-pore model parameters for the simulation are described. These parameters are presented in Table 2 for the three types of lime considered. As this table shows, the system goes from the diffusion-controlled regime (high Thiele modulus) to the reaction-controlled regime (low Thiele modulus) by swelling.

e. Final Comparison. The simulation results of this work were successfully compared to the experimental data of Wu and co-workers.19 This comparison is presented in Figure 3. As this figure shows, there is a good agreement between the random-pore model simulations and the experimental data for three types of lime. Moreover, solving the incomplete conversion problem for the swelled limes is predicted by random-pore model clearly. In Figure 3, Dp ) 2 × 10-7 cm2/min was used as the best value of product layer diffusivity for all three curves. Higher Dp values shift the model predictions upward (overestimation), and lower Dp values shift them downward. This value is on the order of 4.8 × 10-7 cm2/min of the literature value for the CaO + SO2 reaction.34 Conclusions In this work, random-pore model was applied to flue gas desulfurization (FGD) by lime. The behavior of swelled lime (which has solved the incomplete conversion problem of conventional FGD methods) was well simulated in this article. Therefore, by determining the pore size distribution of the swelled lime, it is possible to predict the conversion-time profile and lime capacity for SO2 removal from this work. FGD with complete conversion produces gypsum as a constructional material. This byproduct will decrease the cost of FGD methods for SO2 removal from the flue gas. Finally, this model can be

Figure 3. Comparison of the random-pore model predictions with experimental data from ref 19 for the CaO + SO2 reaction.

Ind. Eng. Chem. Res., Vol. 49, No. 1, 2010

extended to other concentration processes such as CO2 separation from the flue gas by lime.42,43 Nomenclature a ) CA/CAb ) dimensionless gas concentration b ) CB/CB0 ) dimensionless solid concentration CA ) gas concentration in the pellet (kmol/m3) CAb ) bulk gas concentration (kmol/m3) CB ) solid reactant concentration (kmol/m3) CB0 ) FB/MB ) initial solid reactant concentration (kmol/m3) De ) effective diffusivity of gas A in the pellet (m2/s) De0 ) initial effective diffusivity of gas A in the pellet (m2/s) Dp ) effective diffusivity of gas A in the product layer (m2/s) km ) external mass-transfer coefficient (m/s) ks ) surface rate constant (m/s) L0 ) pore length per unit volume (1/m2) MB ) molecular weight of solid reactant (kg/kmol) MD ) molecular weight of solid product (kg/kmol) r ) pore radius (m) rp ) distance from the center of the pellet (m) jr ) average pore radius of the pellet (m) R ) radius of the pellet (m) S0 ) reaction surface area per unit volume (1/m) Sh ) kmR/De0 ) Sherwood number for external mass transfer t ) time (s) V0(r) ) pore volume distribution function (m2/kg) Vp ) total pore volume (m3/kg) X(θ) ) solid conversion at each time y ) rp/R ) dimensionless position in the pellet Z ) ratio of molar volume of solid product to solid reactant β ) 2ks(1 - ε0)/(νBDpS0) ) product layer resistance ε ) pellet porosity ε0 ) initial pellet porosity δ ) De/De0 ) variation ratio of the pore diffusion θ ) ksS0CAbt/[CB0(1 - ε0)] ) t/τ ) dimensionless time νB ) stoichiometric coefficient of the solid reactant νD ) stoichiometric coefficient of the solid product FB ) true density of the solid reactant (kg/m3) FD ) true density of the solid product (kg/m3) φ ) R(ksS0/νBDe0)1/2 ) Thiele modulus for the pellet ψ ) random-pore model parameter

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ReceiVed for reView July 5, 2009 ReVised manuscript receiVed October 24, 2009 Accepted November 4, 2009 IE901077B