Deactivation Kinetics Model of H2S Removal over Mesoporous

Aug 6, 2014 - ... LaFeO3/MCM-41 Sorbent during Hot Coal Gas Desulfurization ... LaFeO3 active sites are 32.1 and 15.1 kJ·mol–1, respectively, based...
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Deactivation Kinetics Model of H2S Removal over Mesoporous LaFeO3/MCM-41 Sorbent during Hot Coal Gas Desulfurization Yong Son Hong,†,§ Z. F. Zhang,† Z. P. Cai,‡ X. H. Zhao,‡ and B. S. Liu*,† †

Department of Chemistry and ‡Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, P. R. China ABSTRACT: The improved deactivation kinetic model over mesoporous LaFeO3/MCM-41 sorbents for hot coal gas desulfurization was established with mass-transfer correlation based on elementary stoichiometric equation, which consisted of both the spatial and the time partial differential equations. MATLAB software was used to solve partial differential equations by means of forward finite differential method and to estimate kinetic parameters via nonlinear least-squares fitting. The rate constants ka and kd were obtained via aforementioned kinetic model over different LaFeO3/MCM-41 sorbents. The calculated results were in accordance with experimental data under various operating conditions. The kinetic model can be used successfully to predict the distributions of H2S concentration at different times and spatial positions within fixed-bed layers, compared to unreacted shrinking core model, random pore model, or grain model. It is of very great significance to obtain basical chemical engineering data for the design of new reactor. For 50%LF2/MCM-41 sorbent, the calculated apparent activation energy (Ea) and deactivation energy (Ed) for chemical reaction of LaFeO3 active sites are 32.1 and 15.1 kJ·mol−1, respectively, based on the experimental data of desulfurization process.

1. INTRODUCTION Noncatalytic gas−solid reaction occurs in many important chemical processes, such as the desulfurization of the fuel gases, coal gasification, and extractive metallurgy. A recent application is in the context of advanced electric power generation system, such as integrated gasification combined cycle (IGCC) and molten carbonate fuel cell (MCFC). However, the hot coal gases from coal gasification processes always contain H2S, which can cause acid rain and severe corrosion of downstream equipment; hence, they need to be removed prior to utilization.1,2 The conventional desulfurization process was conducted at low temperature with a loss of large latent heat. Therefore, the removal of H2S at high temperature using metal oxides has received considerable attention in the past decades.3−6 Mesoporous zeolite,7−9 for instance, MCM-41 (hereafter referred to as simply M41) with high specific surface area and regular pore structure, when used as support, can promote the diffusion of H2S molecules and attrition resistance.10 The effective utilization of active components in supported sorbents was considered to be the main reason for the improvement of desulfurization performance.11,12 Recently, the desulfurization performance of supported oxide sorbents was reported, which exhibited good regeneration stability and mechanical strength.13−15 The developments on kinetics of noncatalytic gas−solid reaction have been summarized in literature.16,17 The unreacted shrinking core model (SCM)18,19 assumes that the reaction occurs at a sharp interface between the reacted outer surface and the unreacted interior core, and the diffusion through the solid product layer obeys Fick’s law with a constant diffusion © XXXX American Chemical Society

coefficient. However, the diffusion into solid reactant (like LaFeO3) is orders of magnitude slower than reaction rate, which is not suitable for solid sorbents with mesoporous structure despite the fact that Lee et al.20 modified unreacted shrinking core model by means of chemical reaction as the rate limiting step being coupled with surface coverage effect to take into account the diffusion controlling step. In the modified grain model, the grain radius changed during the reaction as a function of Z, the ratio between the molar volumes of the solid product and the solid reactant. The diffusion path, the limit of incomplete solid conversion, can be improved by decreasing the size of sorbent pellet.21 Furthermore, Wu and co-workers22 solved this problem by the enhancement of pore volume distribution using a weak acetic acid treatment, similar to metal oxides supported mesoporous sorbents prepared by us.23 In addition, Bhatia and Perlmutter24,25 posed a random pore model (RPM) for fluid− solid reaction that was suitable for unsupported solid26,27 and utilized a pore structure parameter (ψ) to characterize solid reactivity. The authors correlated this parameter (ψ) with m used as the grain shape factor17 or the order of reaction28 in prior model. Also a large amount of work has been done on kinetic model of hot coal gas desulfurization.29−31 Yasyerli et al.32−34 applied deactivation kinetic model (DM) to predict the H2S breakthrough curves over a variety of sorbents, which agreed well with the experimental results. According to this model, the effects of the textural variation (pore structure, Received: April 21, 2014 Revised: August 6, 2014

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active surface area, and activity per unit area) of the solid sorbent and the formation of a dense sulfide (or sulfate) layer over sorbent on the activity of the solid sorbent were expressed in terms of deactivation rate. The deactivation rate of the solid sorbent is expressed as

da = kd0CAa dt


where k d0 is the deactivation rate constant. With the pseudosteady-state assumption, the species conservation equation for H2S in a fixed-bed reactor is


∂CA = −rA ∂z


The reaction rate rA was expressed as a function of temperature, the concentration of gas component A (H2S), and conversion (X) of solid sorbent (LaFeO3), as shown in eq 7:


rA = f (T ) ·f (CA , X ) = kaCA(1 − X )α

where k0 is the initial reaction rate constant. The following approximate expression was then derived for the H2S breakthrough curves


The change of fractional conversion in solid phase with time was expressed as a deactivation rate, as shown in eq 8:

⎡ ⎤ k 0W ⎢ 1 − exp Q [1 − exp(−kd0t )] ⎥ CA = exp⎢ ·exp( −kd0t )⎥ CA0 1 − exp( −kd0t ) ⎢ ⎥ ⎣ ⎦



However, for most noncatalytic gas−solid reactions, the concentration of component A in gas phase does not change rapidly at a given point.20,38,39 In other words, the time derivative of CA is much smaller than the spatial derivative of CA, so the second term in eq 5 can be neglected.


dC −Q A = k 0CAa dW

∂CA ∂C + ε A + rA = 0 ∂z ∂t


∂X = kdCAγ (1 − X )β ∂t


Substituting eq 7 into eq 6 and introducing dimensionless variables yields the improved deactivation kinetic model (eq 9).


The rate constants k0 and kd0 can be obtained from the given W, Q, and CA by the regression analysis of the H2S breakthrough curve using model eq 3. The results revealed that if breakthrough time of sorbents varied greatly with operating conditions, the results predicted using this model will result in large deviation for the evaluation of rate constants k0 and kd because the reaction order of H2S and sorbent is assumed to be 1, and all these factors, such as pore structure and active surface areas of sorbent, are combined in an activity term (a). Therefore, the deactivation model (eq 3) is not suitable for all complicated desulfurization reactions in hot coal gas. Dahlan et al.35 and Ficicilar et al.36 reported similarly that the deactivation rate of solid reactant (sorbent) was considered to be independent of the concentration of gaseous reactant; that is, the deactivation rate was zeroorder with respect to gaseous reactant in deactivation model. The empirical decay laws were summarized in the deactivation models of a variety of catalysis.37 The aim of this work is to establish the improved deactivation kinetic model based on chemical stoichiometric equation that can describe the hot coal gas desulfurization reaction more accurately and predict the kinetic parameters for different LaFeO3/M41 sorbents in a fixed-bed reactor at high temperature.

⎧ ∂C* k ·L = − a 0 C*(1 − X )α (9 ′) ⎪ ⎪ ∂z* u ⎨ ⎪ ∂X (9 ′′) = kd·C0γC*γ (1 − X )β ⎪ ⎩ ∂t


The initial and boundary conditions for eq 9 represent the variable rate (X) of fresh solid sorbent, the inlet concentration of gas reactant (C0), and the outlet concentration variation with position as follows: X(z*, 0) = 0


C*(0, t ) = 1, ∂C*/∂z*(1, t ) = 0


2.2. Calculation Process and Program. Both partial differential equations (eq 9′ and eq 9″) were solved simultaneously using forward finite differential method (eq 12)40 by employing initial (x = 0 for all position Z* at t = 0) and boundary conditions (C = C0 for all time t at z = 0). The corresponding concentration of H2S in gas phase and the variable rate of sorbent can be estimated as follows (eq 12): ⎧ kaL0 Ci*, j(1 − Xi , j)α + Ci*, j ⎪Ci*+ 1, j = −Δz*· u ⎨ ⎪ γ γ β ⎩ Xi + 1, j = Δt ·kdC0 Ci*, j (1 − Xi , j) + Xi , j

2. ESTABLISHMENT OF DEACTIVATION KINETIC MODEL 2.1. Basic Principles of Kinetic Model Establishment. The reaction order of each species was considered in the assumed deactivation model according to the equation of desulfurization reaction in hot coal gas. 2 1 1 2 4 H 2S + LaFeO3 + H 2 = La 2O2 S + FeS + H 2O 3 3 3 3 3


In the meantime, the reaction rate constants can be calculated using the nonlinear least-squares fitting of the H2S concentration obtained by solving partial differential equations to the experimental data. The object function of least-squares fitting for the rate constant calculation was described as follows (eq 13). The algorithm was programmed using MATLAB. ni


min f (ka , kd) =

Assuming that the desulfurization reaction is first-order with respect to H2S concentration, irreversible, and isothermal in the case where the internal and external diffusion are eliminated using sorbent particle size of 0.635−1.27 mm, as well as plug flow of gas in the fixed-bed reactor, the reaction component A (H2S) balance is

* )2 ∑ (Ccal* − Cexp i


3. RESULTS AND DISCUSSION The improved deactivation kinetic model for the desulfurization reaction over different LaFeO3/M41 sorbents was optimized B | Energy Fuels XXXX, XXX, XXX−XXX

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based on experimental data15 on a fixed-bed reactor operated under different reaction conditions. As shown in Figure 1, the

Figure 2. Relationship of calculated H2S breakthrough curves with experimental points over different sorbents; H2S 0.25%, H2 10.6%, CO 18%, N2 as balance gas at T = 550 °C and WHSV = 9 L·h−1·g−1.

using improved deactivation model declined slightly with the increase of active species loadings, and the rate constant over nonsupported sorbents was the lowest. According to the report of Wan et al.,15 the diffraction peaks of LaFeO3 in intensity increased and the specific surface area or active sites on the surface declined gradually with the incremental loading amount of metal oxide (Table 2); in other words, the particle size of LaFeO3 species became large. Therefore, it may be envisaged that kinetic rate constants (ka or kd) for H2S removal in hot coal gas correlate closely with the diffusion resistance of H2S molecules and active sites reacted with H2S in LaFeO3/M41 sorbents because the effects of structural factor in LaFeO3/M41 are included in the rate constants. For example, if the loaded amount of La−Fe (mole ratio of La/Fe = 1:2) increased from 40% to 100% on support M41, the kinetic rate constants ka declined from 8.89 ± 0.7 to 2.52 ± 0.25 cm/min·g and so does deactivation rate constant kd (from 6.73 ± 0.39 to 2.18 ± 0.11 min−1) except for 50% LF3/M41 and 60% LF3/M41 sorbents, which may originate from the derivation in the process of sorbent preparation. Besides, the reaction rates also depended strongly on the La/Fe ratio in sorbents, that is, the desulfurization reaction rates over LF2/M41 are remarkably faster than those over LF3/M41 sorbents, especially after breakthrough time points (Figure 2), because the dispersion of active species (like Fe and Mn) or the number of active sites increased with incremental auxiliary loadings (like La and Ce)23 despite high SBET of LF3/M41 sorbents. 3.2. Effect of WHSV and Temperature on Desulfurization Reaction over 50% LF2/M41. Assuming that the desulfurization reaction of hot coal gas over LaFeO3/M41 sorbents occurred according to elemental stoichiometric eq 4, the kinetic model rate constants ka and kd can be calculated (Table 3). As shown in Figure 3, the H2S breakthrough curves predicted by kinetic model are identical with the experimental results. The breakthrough time for H2S removal declines with incremental WHSV (L/h·g), whereas the breakthrough sulfur capacity almost maintained a constant.15 The larger the WHSV is, the shorter the desulfurization reaction time. From the viewpoint of industrialization, it is favorable for extensive output to increase WHSV. In addition, Figure 4 showed that the calculated H2S breakthrough curves related with desulfurization

Figure 1. Plots of the conversion of H2S (a) as well as the fractional conversion of sorbent (b) simulated by eq 12 as a function of time (t) and position (Z) on a fixed-bed reactor.

variation of H2S concentration in gas phase and fractional conversion of the sorbent with reaction time (t) and fixed-bed position (z) can be described clearly. It can be seen that at a given reaction time (t), the concentration of H2S in gas phase decreased gradually from the inlet to the outlet of fixed-bed layers (Figure 1a), whereas the conversion of the sorbent occurred first at the inlet position of reactor (Figure 1b). If the length of reactor is given (designed), the H2S breakthrough time (when the H2S concentration is lower than 50 mg/m3) can be predicted precisely, which is of great significance to obtain basical chemical engineering data for the design of new reactor in the case of no experimental data on a large scale. 3.1. Relationship of Kinetic Model Parameters with Composition of LaFeO3/M41. Figure 2 shows the relationship of calculated desulfurization curves with experimental points over different LaFeO3/M41 sorbents. It can be seen that the breakthrough time curves calculated using kinetic model equation is almost identical with experimental results, and the obtained correlative coefficient (R2) (Table 1) approaches unity. This suggests that the desulfurization reaction of hot coal gas over LaFeO3/M41 is attributed to the noncatalytic gas−solid reaction as expressed in eq 4. As for 40−100 wt % LF2/M41 sorbents, the kinetic rate constants ka and kd (Table 1) estimated C | Energy Fuels XXXX, XXX, XXX−XXX

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Table 1. Calculated Rate Constants ka and kd for Different LaFeO3/M41 Sorbents sorbents ka × 103 (min−1·g−1) kd × 10−2 ((mol·cm−3)−3/2·min−1) R2

40% LF2M41a 8.89 ± 0.7 (3.70 ± 0.6) 6.73 ± 0.39 (3.47 ± 0.26) 0.994 (0.984)

50% LF2M41a 8.52 ± 0.85 (2.91 ± 0.38) 5.42 ± 0.39 (2.75 ± 0.16) 0.989 (0.990)

60% LF2M41a 7.61 ± 0.57 (5.32 ± 0.54) 3.41 ± 0.17 (2.89 ± 0.16) 0.997 (0.995)

100% LF2a 2.52 ± 0.25 (2.16 ± 0.14) 2.18 ± 0.11 (1.99 ± 0.07) 0.995 (0.998)


The data in parentheses are the rate constants over 40−100 wt % LF3/M41 (LF2 and LF3 represent the molar ratio of La/Fe = 1:2 and 1:3 in sorbents, respectively).

Table 2. Surface Area (SBET), Pore Volume (VT), Micro- (Vmic) and Meso- (Vmeso) Volume of Fresh and Used Sorbents15 samples

SBETa (m2/g)

VTb (mm3/g)

Vmicc (mm3/g)

Vmeso (mm3/g)

fresh 40% LF2M41 fresh 40% LF3M41 fresh 50% LF2M41 fresh 50% LF3M41 fresh 60% LF2M41 fresh 60% LF3M41 fresh 100% LF2 fresh 100% LF3

319 337 181 262 128 190 19 35

210 210 130 230 110 150 40 70

110 110 60 80 40 60 10 10

100 100 70 150 70 90 30 60


SBET was estimated from relative pressure range from 0.05 to 0.3 in N2 adsorption isotherm. bVmic was calculated according to the volume of N2 adsorbed at p/p0 = 0.10. cVT was calculated according to the volume of N2 adsorbed at p/p0 = 0.95.

reaction temperature. As shown in Figure 4, the breakthrough time curve after breakthrough points is very steep it means that the deactivation rate at high temperature (873 K) is quick. However, too high reaction temperature may result in the evaporation of active species and the sintering of metal oxides. According to the Arrhenius formula k = k0 exp(−Ea/RT) the plots of reaction rate constants ka or kd estimated by kinetic model to reaction temperatures are shown in Figure 5. The apparent activation energy can be calculated by linear regression of Arrhenius equation. As shown in Figure 5, the plots of ln ka or ln kd against 1/T are almost linear, and the obtained apparent activation energies are 32.1 and 15.1 kJ/mol, respectively, which are very close to those (Ea = 25.1 kJ/mol, Ed = 22.2 kJ/mol) of Ce1−Mn3 mixed oxide reported by Yasyerli.34 Subsequently, the obtained kinetic parameters were substituted into eq 9, and an improved deactivation kinetic model for the 50% LF2/M41 sorbent is established as follows. ⎧ ∂C* (849 800)·L0 ⎛ 3860 ⎞ 2/3 ⎟C *(1 − X ) =− exp⎜− ⎪ ⎝ T ⎠ ⎪ ∂z* u ⎨ ⎛ 1818.4 ⎞ 3/2 ⎪ ∂X ⎟C * = 0.5056·C03/2· exp⎜− (1 − X ) ⎪ ⎝ ⎩ ∂t T ⎠

Figure 3. Calculated H2S breakthrough curves of 50% LF2M41 at different WHSV (L/h·g); T = 550 °C; H2S 0.25%, H2 10.6%, CO 18%, N2 as balance gas.

(14) Figure 4. Calculated H2S breakthrough curves of 50% LF2M41 at different reaction temperatures (WHSV = 9 L·h−1·g−1, H2S 0.25%, H2 10.6%, CO 18%, N2 as balance gas).

3.3. Sulfidation-Regeneration Process over 50% LF2/ M41. Figure 6 shows the relationship of the calculated H2S breakthrough time curves with experimental data during successive sulfidation-regeneration cycles, and the obtained kinetic parameters are listed in Table 4. It can be seen that the calculated breakthrough curves are in accordance with experimental value and that the correlated coefficients R2 are

very nearly 1. It is interesting to note that the obtained rate constants ka and kd (Table 4) declined slightly due to the sintering of active species and the deterioration of mesoporous

Table 3. Reaction Rate Constants ka and kd Obtained over 50 wt % LF2/M41 Based on Reaction Order: α = 2/3, β = 1, γ = 3/2 WHSV (L·h−1·g−1) ka × 103 (min−1·g−1) kd × 10−2 ((mol·cm−3)−3/2·min−1) R2

9 7.52 ± 0.85 5.42 ± 0.39 0.989

12 7.08 ± 0.47 5.39 ± 0.16 0.998 D

15 6.15 ± 0.4 6.14 ± 0.15 0.998

18 5.81 ± 0.24 6.16 ± 0.09 0.999 | Energy Fuels XXXX, XXX, XXX−XXX

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As shown in Figure 7, the average deviation between calculated value and experimental data is lower than 1%. Therefore, this

Figure 5. Plots of ln ka and ln kd against 1/T for 50% LF2M41; (WHSV = 9 L·h−1·g−1, H2S 0.25%, H2 10.6%, CO 18%, N2 as balance gas). Figure 7. Calculated vs experimental dimensionless concentration of H2S for different initial concentration of H2S; T = 550 °C, WHSV = 9 L· h−1·g−1, H2 10.6%, CO 18%, N2 as balance gas.

kinetic model establishes very good prediction ability for hot coal gas desulfurization and can be used extensively in other system besides LaFeO3/M41 according to chemical stoichiometric equations. The relative studies will be reported in the near future.

4. CONCLUSIONS The kinetic behavior for H2S removal over LaFeO3/M41 sorbents in a fixed-bed reactor at high temperature can be evaluated effectively by using the improved deactivation kinetic model. The results indicated that the average deviation between calculated H2S concentration in gas phase and experimental data was lower than 1%, and the reaction rate constants depended strongly on the channel structure of MCM-41 support, La/Fe molar ratios, and the loadings of active species under the same reaction conditions. For 50% LF2/M41 sorbent, the calculated apparent activation energy (Ea) of H2S removal and deactivation energy (Ed) of sorbent were 32.1 and 15.1 kJ/mol, respectively. Therefore, the kinetic model established can be extensively applied to the kinetic analysis of noncatalytic heterogeneous reaction or adsorption processes in fixed-bed reactor without the requirement of structural property for sorbents and has very good prediction ability for hot coal gas desulfurization.

Figure 6. 50% LF2M4 sulfidation over multiple cycles; WHSV = 9 L· h−1·g−1, T = 550 °C, H2S 0.25%, H2 10.6%, CO 18%, and N2 as balance gas; regeneration: T = 700 °C; 5% O2/N2 mixture.

structure in LaFeO3/M41 during successive sulfidation-regeneration cycles. It indicated that 50% LF2/M41 sorbents was almost stable in structure and remained intact during desulfurization of hot coal gas at high temperature. 3.4. Prediction Ability of Improved Deactivation Kinetic Model. To investigate the prediction ability of improved deactivation kinetic model and verify the reliability of estimated kinetic parameters, we calculated sulfur contents in gas phase using reaction conditions beyond fitting kinetic model parameters, and the obtained results were compared to experimental data under the aforementioned reaction conditions.


Corresponding Author

*E-mail: [email protected] Phone:+86-22-27892471. Fax: +86 22 27403475. Notes

The authors declare no competing financial interest.

Table 4. Calculated Rate Constants ka and kd for Sulfidation of 50% LF2/M41 over Multiple Cycles regeneration cycles ka × 103 (min−1·g−1) kd × 10−2 ((mol·cm−3)−3/2·min−1) R2 a

fresha 8.52 ± 0.85 5.42 ± 0.39 0.989

3 7.40 ± 0.46 6.55 ± 0.27 0.997

5 7.07 ± 0.43 7.02 ± 0.4 0.995

7 6.96 ± 0.4 7.17 ± 0.48 0.993

9 6.81 ± 0.37 7.17 ± 0.48 0.993

Fresh data is from Figure 7 in reference 15. E | Energy Fuels XXXX, XXX, XXX−XXX

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Senior visiting scholar from Chemistry Department, Kim Hyong Jik Normal University, Pyongyang, D. P. R. Korea.

ACKNOWLEDGMENTS The work was supported by the National Natural Science Foundation of China and BAOSTEEL Group Corporation (50876122) and also by the National Training Programs of Innovation and Entrepreneurship for Undergraduates (201210056146).

NOMENCLATURE a = activity of the solid reactant C = H2S% concentration in gaseous reactant CA = outlet H2S concentration, mol·cm−3 CA0 = inlet H2S concentration, mol·cm−3 C = H2S concentration, mol·cm−3 C0 = inlet H2S concentration, mol·cm−3 C* = dimensionless H2S concentration (= CA/CA0) C*exp = experimental dimensionless H2S concentration C*cal = calculated dimensionless H2S concentration ka = the rate constant of apparent chemical reaction, g−1·min−1 kd0 = deactivation rate constant, min−1 kd = deactivation rate constant, (mol·cm−3)−3/2·min−1 ko = initial rate constant, cm3·g−1·min−1 L0 = length of the fixed-bed reactor, cm ni = number of experiment data points Q = volumetric flow rate, cm3·min−1 rA = chemical reaction rate t = reaction time, min T = reaction temperature, K u = inlet flow rate of gas, cm·min−1·g−1 W = sorbent weight, g WHSV = weight hourly space velocity of gaseous reactant, L· h−1·g−1 X = fractional conversion of the sorbent z = distance from the reactor entrance, cm z* = dimensionless distance from the reactor entrance (= z/ L0) α, β, γ = reaction orders ε = reaction bed porosity


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