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[email protected]. Chemical Engineering Science 54 (1999) 1775—1785 Selective catalytic reduction of NO x : a mathematical model for poison accumulation and conversion performance Raziyeh Khodayari*, C.U. Ingemar Odenbrand Department of Chemical Engineering II, Lund University, P.O. Box 124, S-221 00 Lund, Sweden Received 17 June 1998; accepted 7 December 1998 Abstract A common control technique for limiting nitrogen oxide emissions is selective catalytic reduction (SCR) of NO x with NH 3 . The lifetime of the catalyst, which has a critical role in overall SCR system economics, is, however, limited due to deactivation by poisoning. A two-dimensional model was developed to describe poison accumulation and activity of an SCR catalyst. The model that has no adjustable parameters accounts for simultaneous e⁄ects of internal and external di⁄usion and chemical kinetics in the SCR process. A validation of the model is accomplished by comparison with data from two di⁄erent SCR plants. A comparison of di⁄erent catalyst design variables is also made in terms of conversion after 2000 h operation in the presence of poisons. Simulations showed that it is possible to improve poison resistance of SCR catalyst monoliths by reconÞguration of their pore structure and channel diameter. ( 1999 Elsevier Science Ltd. All rights reserved. Keywords: NO x reduction; Modeling; Poison accumulation; Activity performance 1. Introduction A common control technique for limiting nitrogen oxide emissions is selective catalytic reduction (SCR) of NO x with NH 3 . Honeycomb catalysts are preferable for clean-gas or low-dust applications, while plate-type catalysts are preferable for high-dust and high sulfur applications due to low-dust deposition, high resistance to erosion, low SO 2 /SO 3 conversion and low pressure drop. The lifetime of the catalyst, which has a critical role on overall SCR system economics is, however, lim- ited due to deactivation by poisoning. The availability of catalytically active materials such as Mo and V is a more severe problem than their cost. For instance, WO 3 is used to increase catalyst resistance against chemical de- activation and to reduce SO 2 oxidation to SO 3 and NH 3 oxidation (Chen and Yang, 1992). Metal deposits deacti- vate the catalyst by simultaneous coverage of catalyst active sites and blockage of catalyst pores. Poisoning is a common type of catalyst deactivation resulting from the irreversible adsorption of compounds on the cata- lytically active sites. Hegedus and Summers (1977) dis- cuss the poison resistance of supported catalysts. The mechanism of poisoning of the V 2 O 5 /TiO 2 catalyst for the reduction of NO by NH 3 has been discussed by Chen and Yang (1990). They found that a direct correlation exists between the amount of chemisorbed ammonia and the activity of the poison-doped catalyst. Furthermore, they suggested that the chemisorbed NH 3 on the catalyst predominantly exists as NH‘ 4 , bonded to the Br/nsted acid site of V—OH. Lee and Aris (1978) and Angele and Kirchner (1980) have developed mathematical models for reaction systems including di⁄usion in the porous pellet and poisoning reaction. Poisoning in Þxed-bed reactors has been studied by Haynes (1970). Beeckman and He- gedus (1991) developed a mathematical model for de- scribing the reduction of NO with ammonia over the internal surfaces of monolith-shaped catalysts taking into account the lifetime of the catalyst after poisoning. Oh and Cavendish (1983) have developed a mathemat- ical model for automobile monolithic catalysts which predicts both the poison penetration proÞle and conver- sion performance of a monolith as a function of its 0009-2509/99/$— see front matter ( 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 0 1 7 - 2 Fig. 1. Activity as a function of poison coverage for a monolithic catalyst (pitch diameter, 7.3 mm) at 360¡C. The experimental conditions: pressure, 1.25 bar; NO, 600 ppm; NH 3 , 700 ppm; O 2 , 2%; carrier gas, He containing 3000 ppm Ar. exposure time to the poison. Pereira et al. (1988) have found an analytical solution for the performance of a monolith catalyst in the presence of di⁄usion-limited poisoning. The service life of SCR catalysts is practically assessed on the basic of subjective criteria or empirical values. To follow deactivation of SCR catalysts often demands time and many economical resources and therefore, it is of a great advantage to predict the deactivation process by means of a simulation program. The aim of this study is to develop a two-dimensional model which predicts poi- son accumulation and activity of an SCR catalyst. The model accounts for simultaneous e⁄ects of internal and external di⁄usion and chemical kinetics in the SCR process. A validation of the model is accomplished by comparison with data from di⁄erent SCR plants. A com- parison of di⁄erent catalyst design variables is also made in terms of conversion after 2000 h operation in the presence of poisons. 1.1. Assumptions f The time scale of the poisoning reaction is much longer than that of the SCR reaction. Consequently the main reaction approaches a steady-state behavior over short time periods. f The channel walls within the squared cross-section monolith are assumed uniformly washcoated with catalyst. In the case of the two catalysts we have used for the simulations, the whole wall consisted of homogene- ously distributed active materials in the TiO 2 support. f The channel-to-channel variations or interactions are ignored. f The ßow distribution through the monolith is uniform. This assumption may be invalid in industrial SCR plants owing to unequal velocity distributions. The reactants pass through the channels in a fully de- veloped laminar ßow. — Constant ßuid properties over the cross-section of the channel. — SCR reactors are practically isothermal due to low reactant concentrations, so the assumption of iso- thermal conditions is allowable. — Axial conduction and di⁄usion of mass is negligible compared to that of radial di⁄usion. The axial di⁄u- sion of mass and heat may be neglected for Pe numbers greater than 50 (Michelsen and Villadsen, 1974), while the calculated value for our system is over 150. — The poisoning reaction is a Þrst-order reaction with respect to both the surface concentration of the poi- son and the unpoisoned fraction of adsorption sites. — An exponential relationship between the quantity of poison that is deposited and the number of active sites that are destroyed is assumed. This is based on our experimental study of deactivation e⁄ects of Na and Pb on an SCR catalyst (Fig. 1). 2. Modeling of the deactivation behavior 2.1. Poison accumulation model Catalyst deactivation has been associated with the removal of active sites via strong chemisorption of impu- rities on the surface, thus blocking access of the reactants (Chen and Yang, 1990). In an SCR environment a cata- lyst poison precursor di⁄uses from the gas phase to the external surface of the washcoat and selectively or non- selectively adsorbs on the internal surface area of the washcoat. Non-selective poisoning means that the poi- son is deposited randomly on the remaining catalytically 1776 R. Khodayari, C.U. Ingemar Odenbrand/Chemical Engineering Science 54 (1999) 1775—1785 Fig. 2. Schematic of a monolith channel with length ‚ and half-wall thickness H. active or non-active unpoisoned sites, while selective poisoning means deposition of the poison on the remain- ing catalytically active unpoisoned sites. Fig. 2 shows a schematic of a monolith channel. An irreversible pois- oning reaction occurs between the poison precursor (P) and unpoisoned adsorption sites (p) to form catalytically inactive deposit (W) according to the following reaction: P#p kpP W. (1) The choice of poisoning rate expressions depends on the particular application. However we assume an irre- versible Langmuir—Hinshelwood type of expression for the rate of formation of adsorbed poison. The poison deposition rate is both proportional to the number of unpoisoned adsorption sites and the surface concentra- tion of poison: R P "k P c s,p (t,x, z) (1!bh W ), 0)b)1, (2) where h w is the fraction of adsorption sites covered with W and c s,p (t,x, z) is the gas-phase concentration of poi- son at the surface and b is the selectivity factor. The isothermal mass conservation equation for the poison in the gas phase is e Lc g,p Lt "!t Lcg,p Lx !km,p D e,p S[c g,p (t,x)!c s,p (t, x,H)], (3) where 0(x(‚, c g,p is the gas-phase concentration of the poison along the reactor and c s,p (t,x,H) is the con- centration of the poison precursor at the outer edge of the washcoat at time t and axial position x along the monolith channel. Eq. (3) implies that at any axial loca- tion in the monolith channel the rate of change of the convective ßux of poison in the gas phase is equal to the rate of poison di⁄usion to the monolith wall. The poisoning reaction is di⁄usion inhibited, thus the di⁄usion/reaction balance equations for the washcoat are e s Lc s,p Lt "D e,p L2c s,p Lz2 !aR p , 0(z(H, (4) c W,= dh W dt "R p for all x and z, (5) where c W,= is the saturation poison concentration on the washcoat and a is the catalytic surface area per volume of the washcoat and R p is deÞned by Eq. (2). For the combined external and internal mass transfer resistances, the boundary and initial conditions are Lc s,p Lz (t,x, 0)"0, (6) Lc s,p Lz (t,x,H)"km,p D e,p [c g,p (t,x)!c s,p (t,x,H)], (7) c g,p (t, 0)"c*/ g,p , (8) h w (0, x, z)"0. (9) 2.2. Modeling of the SCR reaction The main reaction in SCR process is 4NO#4NH 3 #O 2 P4N 2 #6H 2 O. (10) Since the SCR reaction is highly selective at temperatures below 400¡C, the ammonia oxidation reaction is neglect- ed in this work. It is well known that NO reacts from the gas phase, or a weakly adsorbed state, with strongly adsorbed and activated ammonia molecules (Odenbrand et al., 1994; Inomata et al., 1980; Ramis et al., 1990; Svachula et al., 1993; Beeckman and Hegedus, 1991; Lefers et al., 1991). Lietti et al. (1997) have studied the unsteady-state kinetics of the SCR-reaction by means of the transient response method and conÞrmed that NH 3 strongly adsorbs onto the catalyst surface whereas NO shows no appreciate adsorption. These Þndings are in agreement with our TPD measurements of both NH 3 and NO by TAP-2. Lietti et al. (1997) have also suggested that the active sites of the catalyst represent only a frac- tion of the total adsorption sites for NH 3 . They also suggested that the rate of SCR-reaction is independent of the NH 3 surface concentration for h NH3 above a critical value that is of the same order of the magnitude of the surface coverage of vanadium. From our experiments with Pb, Na, and K, we have found a correlation between NH 3 chemisorption and poisoning (Fig. 3) and therefore we assume h NH3 "1!h w , where h NH3 is the adsorbed amount of NH 3 per total adsorption capacity for NH 3 . This condition occurs at the inlet of the reactor where the R. Khodayari, C.U. Ingemar Odenbrand/Chemical Engineering Science 54 (1999) 1775—1785 1777 Fig. 3. NH 3 chemisorption as a function of poison coverage. All measurements have been carried out at 2 Torr. The adsorption temperature was 300¡C for the sodium and potassium series and 200¡C for the lead series. ammonia concentration is relatively high. If the concen- tration of NH 3 in the gas ßow is low then there is a suƒcient number of active sites on the catalyst surface that can be covered by adsorbed ammonia. This occurs at the outlet of the reactor. A balance of active sites is given by ‚"S NH3 #S p #S a where S NH3 is the concentra- tion of active sites occupied by NH 3 and S p and S a are those of the poisoned and the available active sites. Con- sequently, the last catalyst layer near the outlet from the reactor may be poisoned without showing any e⁄ect on the NH 3 slip. We assumed that the main reaction is Þrst order with respect to both the gas-phase concentration of NO at the surface and the fraction of unpoisoned adsorp- tion sites that are free for NH 3 adsorption: R NO "!k NO c s,NO h NH3 , (11) where h NH3 " KaCNH3 1#K a C NH3 "1!h w (x, z), (12) h NH3 is the Langmuir adsorption isotherm and K a is the adsorption constant for ammonia. Combining Eqs. (11) and (12), the reaction rate would be R NO "!k NO c s,NO (1!h w (x, z)). (13) The isothermal mass balance for the gas phase is e Lc g,NO Lt "!t Lcg,NO Lx !km,NO D e,NO S[c g,NO (t,x) !c s,NO (t, x,H)] (14) and the di⁄usion/reaction balance equation for the wash- coat is e s Lc s,NO Lt "D e,NO L2c s,NO Lz2 !aR NO . (15) The initial and boundary conditions are Lc s,NO Lz (t, x, 0)"0, (16) Lc s,NO Lz (t,x,H)"km,NO D e,NO [c g,NO (t, x)!c s,NO (t,x,H)], (17) c g, NO (t, 0)"c*/ g,NO . (18) Eq. (14) describes the change in bulk gas phase concen- tration of NO along the partially poisoned reactor. The accumulation of mass in the both gas and solid phase was neglected. 2.3. Method of solution The di⁄erential equations reveal their character more easily when rearranged to make them dimensionless. Therefore, x, z, c g,p and c s,p can be replaced by x/‚, z/H, c g,p /c*/ g,p and c s,p /c*/ g,p , respectively, in Eqs. (3)—(9). The Þnal di⁄erential equations will be Lc g,p Lx #w 1 [c g,p (t,x)!c s,p (t,x, 1)]"0, (19) L2c s,p Lz2 !w 2 c s,p (1!bh w )"0, (20) dh W dt "w 3 c s,p (1!bh w ) (21) and initial and boundary conditions will be Lc s,p Lz (t,x, 0)"0, (22) Lc s,p Lz (t,x, 1)"w 4 [c g,p (t,x)!c s,p (t,x, 1)], (23) 1778 R. Khodayari, C.U. Ingemar Odenbrand/Chemical Engineering Science 54 (1999) 1775—1785 Fig. 4. Reaction rate as a function of temperature. The experimental conditions for activity measurements: temperature range, 220—320¡C; pressure, 1.25 bar; pressure drop, 0.1 bar; NO, 600 ppm; NH 3 , 700 ppm; O 2 , 2%; carrier gas, He containing 3000 ppm Ar. c g,p (t, 0)"1, (24) h w (0, x, z)"0. (25) The same kind of rearrangement was done for Eqs. (14)—(18), i.e. replacement of x, z, c g,NO and c s,NO by x/‚, z/H, c g,NO /c*/ g,NO and c s,NO /c*/ g,NO , respectively. Eqs. (19)—(25) were integrated numerically. The method employed was the Þnite di⁄erence method. The time variable (t) is left continuous while the boundary-value independent variables (x and z) are made discrete. Fur- thermore, the centered di⁄erence is generally regarded as being not very eƒcient and produces excessive numerical oscillation in the solution of Eqs. (3) and (14). Directional or upwind techniques diminish the oscillation problem but do not eliminate it. However, higher-order approxi- mations are more accurate and reduce the sti⁄ness of the resulting ODE set (Carver and Hinds, 1978; Schiesser, 1991). Thus, by combination of a second-order three- point upwind formula: A Lu LxB i "3ui!4ui~1!ui~2 2Dx and centered approximation it is possible to decrease oscillation on the both sides of step change. The simula- tion can be divided into two parts: (1) Eqs. (19)— (25) were integrated from the inlet of the monolith (x"0) to the outlet (x"1) and the poison coverage function h w (t,x, z) was calculated. (2) h w in Eq. (11), and thereby in Eq. (13), was substituted by h w after respective poisoning time and Eqs. (14)— (18) were integrated after rearrangement to di- mensionless equations. For solving each of these sep- arate ODE systems, ode15s -the ODE subroutine from the commercially available Matlab computer code- was applied. 3. Results and discussions 3.1. Model parameter values It is diƒcult to measure the true reaction kinetics in the presence of transport resistances. The intrinsic rate con- stant for the fresh BASF catalyst, calculated by a simula- tion program based on a mechanism denoted ÔElay— RidelÕ model (Brandin, 1995), was 4.6]10~5 at 360¡C. To verify the validity of this value, the intrinsic rate constant for the reaction was estimated by curve Þtting of experimental conversion data obtained between 220¡C and 320¡C for each catalyst. To avoid di⁄usion limita- tions, the monolith catalyst was ground to particles with 100/175, 177/250 and 250/350 mesh sizes. Later, 0.01 g of each sample was mixed with 0.09 g inert TiO 2 of the same mesh size as the catalyst and activity measurements were carried out in the reactor described in our previous work (Khodayari and Odenbrand, 1998). The amount of the catalyst was relatively small so that the conversion was limited (0.2—0.23) and thus may be considered to occur at a nearly constant concentration of NO. The reaction rate was then calculated according to r"F o ]Dx/…, where F 0 is the NO molar ßow into the reactor, … is the weight of the catalyst and Dx is the conversion of NO. Arrhenius plots of the reaction rate for the three di⁄erent particles sizes showed that the plots diverge in the high-temper- ature region, indicating that the kinetic data obtained by the lowest particle size could still be limited by mass transfer (Fig. 4). The pressure drop was about 0.1 bar. The apparatus and experimental conditions have been described elsewhere (Khodayari and Odenbrand, 1998). The intrinsic rate constant was estimated to be 2.17]10~5 m/s (1986/s1) at 360¡C. This value is compa- rable with the value reported by Tronconi et al. (1992) which is obtained for the same kind of catalyst (2373/s1 at 360¡C). There is thus good validity between the simulated value and the value calculated based on experimental data. The intrinsic rate constant for the Oskarshamn catalyst was also estimated by the simulation program. The rate constant for the poisoning reaction (k p ) was estimated by assuming constant gas-phase concentration (c p ) and Þrst-order adsorption of the poison. Thus, the following equation was derived from the mass balance of the poison on the surface: h w "1!e~kpcp t. (26) The higher the reaction rate, the more rapidly in- creases the concentration of the poison on the surface of the catalyst. It is diƒcult to estimate the e⁄ect of each contaminant on the NH 3 adsorption for the used indus- trial catalysts. Therefore, for each poison, the surface coverage of NH 3 was obtained by comparison of NH 3 adsorption measurements from fresh and artiÞcially poi- soned catalyst samples at 300¡C and 2 Torr. h NH3 was assumed to be equal to unity for the fresh catalyst, while the NH 3 adsorption capacity of the poisoned catalyst decreased with increasing poison coverage. Furthermore, R. Khodayari, C.U. Ingemar Odenbrand/Chemical Engineering Science 54 (1999) 1775—1785 1779 we assumed h NH3 "1!h w in the presence of an excess of NH 3 . The time for poisoning was estimated from the comparison of ICP-AES analysis of the above-men- tioned poisoned samples and di⁄erent samples of the used industrial catalyst with di⁄erent time on stream. The same kind of poisoning proÞle (exponential) inside the wall for used and poisoned catalysts was assumed. The validity of this assumption was investigated by SEM and XPS analysis which showed higher poison concen- tration on the outer surface of the monolith than inside the wall, for both the artiÞcially poisoned and the indus- trially used samples. Knowing the gas-phase concentra- tion of the poison, k p can be determined. It should be noted that according to Eq. (26), higher estimated con- centrations of an impurity in the ßue gas would result in a lower reaction rate constant for that impurity. At the same time, the deactivation of the catalyst would be inten- siÞed at higher gas-phase concentrations of the poison. White (1996) has reported alkali metal oxides (Ca, K and Na) as ßue gas constituents inßuencing catalyst design and 50 mg/Nm3 as maximum allowable partic- ulate loading into the reactor. Lin and Biswaz (1994) reported lead, lead oxide and lead chloride as the most predominant lead species in waste incineration plants. Herrlander (1990) has reported Zn and ZnCl 2 as the worst poisons for the SCR catalyst particularly in the case of waste incineration plants. Arsenic is often found in ßue gases of coal-Þred power plants. Volatile arsenic is able to reduce the accessible surface of the catalyst and therefore reduce the activity. This is, however, an impor- tant mechanism only in wet bottom furnaces with ßy ash recirculation (Gutberlet, 1988). The poisoning e⁄ect of alkali chlorides are generally much weaker than oxides of the same metal due to the promoting e⁄ect of chloride ions on the catalyst. The e⁄ect of HCl depends on the reaction temperature. The formation of NH 4 Cl at around or below 340¡C, leads to blocking of active sites. Arsenic and chloride compounds are, however, not im- portant poisons in the plants discussed in this work. The concentrations of Pb and Zn precursors were estimated to be 6—40 and 20 —100 mg/m3 in the ßue gas from waste incineration plants (Carlsson, 1986). The average emis- sion factors for Na, K, Pb and Zn were 93, 180, 50 and 71 g/ton refuse, respectively (Candreva and Dams, 1987). By combination of these data with the average ßue gas produced by 1 kg waste (6 Nm3/kg, Herrlander, 1990) the amount of Na and K species were estimated to be about 25 and 72 mg/m3. These concentrations are much higher than the maximum allowable particulate loading into the catalyst which is about 50 mg/Nm3. On the other hand, the reported particulate concentration in the SCR reac- tor is only about 3 mg/m3 for the Swedish diesel-fuel power plants, Oskarshamn. ICP-AES analysis of the catalyst from Oskarshamn after about 12 000 h on stream indicated that the total accumulated amounts of K and Na in the sample were 0.05 and 0.31 weight percent, while the values for P, Zn, Ca and S were 0.24, 0.05, 0.13 and 1.22 weight percent, respectively. ICP-AES analysis of a used catalyst similar to the BASF, from a high-dust municipal waste incinerator after 2311 h of being on stream, indicated that the accumulated amounts of Na, K, Pb, and Zn were 0.2, 0.26, 0.15, and 0.36 weight percent, respectively. Furthermore, a signiÞcant increase in concentration of the above-mentioned metals with time on stream was indicated in the both cases. The saturation concentrations (c w,= ) for di⁄erent poisons were estimated by using their crystal structures (Wycko⁄, 1963). Detailed description of the NH 3 adsorption measurements, ICP-AES and BET analysis is given else- where (Khodayari and Odenbrand, 1998). The gas ßow through each channel was calculated based on the data from a real SCR plant (Oskarshamn) with a catalyst volume of 9.2 m3 and a total gas ßow of 41 470 N m3/h. As discussed previously, we have found a correlation between activity and the amounts of NH 3 chemisorbed on the catalyst. Alkaline deterioration may occur by attack of Na or K on the -OH functional groups on the catalyst surface, while Ca may react with SO 3 to CaSO 4 and block the pores. It is very diƒcult to experimentally quantify the individual e⁄ect of each of these separate deactivation mechanisms. Depending on which deac- tivating process that dominates, the relative activity will have a di⁄erent value. On the other hand, the equivalent amount of a di⁄erent poison can have a di⁄erent impact on the activity or the amounts of NH 3 chemisorbed. This can be elucidated by the concept selectivity discussed previously. In the case of the potassium poisoned sample, the activity measurements showed that the sample was almost completely deactivated by the amount of poison required for covering all active V—OH sites. It means that potassium adsorbs preferentially on the active sites. The same result was obtained for the sodium-poisoned sample, while the amount of lead required for complete deactivation was much larger than the amount of ap- proximated active sites. Pb covers the surface of inactive TiO 2 sites, likewise active V 2 O 5 /WO 3 sites, in a thin, non-crystalline layer (Khodayari and Odenbrand, 1998). Therefore, we assumed that b was about unity for potas- sium and sodium, while the value for lead was calculated by comparison of the catalyst activity for samples poi- soned with identical amounts of lead and sodium. Phos- phorus and zinc are other examples of low selective or non-selective poisons. The poison accumulation was simulated for each poison and afterwards the cumulative e⁄ect of all the poisons was calculated using the selectiv- ity factors based on our experiments. Table 1 lists various parameters used in the simulations. All simulations were done at a constant temperature of 360¡C. It should be noted that the catalyst NH 3 adsorption capacity de- creases with increasing temperature. In addition, the oxidation of NH 3 begins around 360¡C and becomes signiÞcant above 400¡C. 1780 R. Khodayari, C.U. Ingemar Odenbrand/Chemical Engineering Science 54 (1999) 1775—1785 Table 1 Parameters applied in the simulation of the model Monolith BASF Oskarshamn SpeciÞc surface area, m2/g 70.4 187.9 Half-wall thickness, m 0.55]10~3 0.425]10~3 Washcoat thickness, m 0.55]10~3 0.425]10~3 Particle density kg/m3 1300 790 Solid density, kg/m3 3764 2880 Channel diameter, m 0.0062 0.002 Gas ßow, Nm3/s 20.02]10~6 3.05]10~6 r .!#30 , m 1]10~7 5]10~8 r .*#30 , m 1]10~8 36]10~10 Pore volume, m3/kg 0.297]10~3 0.228]10~3 k NO , m/s 2.17]10~5 0.89]10~5 c p, */,P"O , mol/m3 0.054]10~3 0.045]10~4 c p, */,K2O , mol/m3 0.318]10~3 0.11]10~4 c p, */,N!2O , mol/m3 0.25]10~3 0.16]10~4 k P"O , m/s 5.76]10~7 7.59]10~9 k K2O , m/s 1.44]10~7 6.96]10~9 k N!2O , m/s 1.97]10~7 1.10]10~8 D %&& , m2/s 8.4]10~7 2.1]10~7 e .*#30 0.4223 0.3614 e .!#30 0.1056 0.0348 Length, m 0.30 b K2O 1 b N!2O 1 b P"O 0.12 Temperature, K 633 c w,P"O , mol/m2 15.60]10~6 c w,K2O , mol/m2 16.04]10~6 c w,N!2O , mol/m2 21.56]10~6 3.2. Pore di⁄usion The e⁄ective di⁄usivities of NO and NH 3 were cal- culated according to the random pore model (Smith, 1981). This model assumes a bi-modal pore distribution of micro- and macropores. It should be noted that by micropores Smith means both micro- and mesopores. By using the random pore model it is possible to calculate e⁄ective di⁄usivities as a functions of parameters that can be measured by Hg porosimetry. Beeckman (1991) has reported a good agreement between experimental di⁄u- sion coeƒcient in commercial SCR monoliths and values calculated by the random pore model. The following approximation that can be derived from the kinetic gas theory and the Knudsen di⁄usion theory, was used for calculation of e⁄ective di⁄usivities of poisons: D %&&,P "D %&&,NOA M NO M P B 1@2 . The di⁄usion-limited nature of the poison accumula- tion process is discussed elsewhere (Hegedus, 1974). The chemical reaction over commercial SCR catalysts is strongly limited by di⁄usion in the pores (Beeckman and Hegedus, 1991). Thus, it is possible to increase the NO x removal eƒciency by introducing macropores and opti- mizing the catalyst porosity. 3.3. External mass transfer It is well known that the SCR reaction is very fast. The internal mass transfer in the washcoat of a monolith is less of a problem than the external mass transfer due to the shorter di⁄usion length in the washcoat and can become important at higher reaction rates and when the washcoat thickness is increased. For calculation of the Sherwood number, and thereby the external mass trans- fer coeƒcient, the following empirical model for the gas- solid mass transfer in monolith channels was used (Uberoi and Pereira, 1996). Sh = "2.696 (1#0.139 Sc Re(d h /‚))0.81 and k m,j "Sh = D j /(2R h ), where Sc (Sc j "k/o/D j ) and D j are the Schmidt number and the molecular di⁄usivity of NO or poison precursor, respectively, and R h is the hydraulic radius. The Reynolds number is deÞned as Re"2 R h l/k. This model predicts a higher Sh number than the theoretical values, which are valid for laminar ßow, due to a certain degree of turbu- lence in the channel ßow that will enhance the mass transfer. For a honeycomb SCR catalyst, the local Sher- wood number di⁄ers only 3% from the local Sherwood number for fully developed laminar ßow and developed concentration proÞles (Lefers et al., 1991). Figs. 5—7 show the simulated poison accumulation proÞle of sodium and potassium after di⁄erent times and for di⁄erent concentrations of sodium and potassium oxides for both catalysts. The rate constants for the poisoning reactions were calculated based on the gas- phase concentrations listed in Table 1. The active frac- tion of the surface decreases due to accumulation of the poison. At low poison coverage, the gas-phase concentra- tion of NO on the surface is very low and drops to zero towards the center of the wall. As the catalytic activity degrades, the gas-phase concentration of the reactant on the surface of the catalyst increases until it Þnally reaches the value of the bulk concentration. The amount of poison on the catalyst is seen to decrease both along the monolith reactor axis and into the wall, agreeing with our measurements made on di⁄erent catalysts used in some of the SCR plants in Sweden. Simulations showed rapid deactivation of the BASF catalyst and relatively slow accumulation of impurities on the Oskarshamn catalyst (Figs. 6 and 7). This Þnding is also in agreement with XPS and ICP-AES analysis and activity measure- ments performed on these two catalysts. As discussed previously, there is a correlation between NH 3 adsorp- tion amount and catalytic activity of the catalyst. There- fore, it is possible to compare the catalytic activity of R. Khodayari, C.U. Ingemar Odenbrand/Chemical Engineering Science 54 (1999) 1775—1785 1781 Fig. 5. Calculated poison accumulation proÞle of Na and K on the zeolite containing SCR catalyst from Oskarshamn after 12 000 h; the gas phase concentration of both Na and K are 1 mg/m3. The other parameter values are the same as those in Table 1. Fig. 6. Calculated poison proÞle of K on the zeolite containing SCR catalyst from Oskarshamn after 1000 h; the parameter values are the same as those in Table 1; conversion"0.995. Fig. 7. Calculated poison proÞle of K on the BASF catalyst after 1000 h; C g,K "1 mg/m3. The other parameter values are the same as those in Table 1; conversion"0.927. Fig. 8. Isosteric heat of adsorption as a function of ammonia coverage. di⁄erent SCR catalysts by comparing their isosteric heat of adsorption (q 45 ) which indicates how strongly the gas is adsorbed on the active sites of the catalyst. q 45 for these two catalysts was obtained by NH 3 chemisorption at di⁄erent temperatures between 150¡C and 350¡C and using Clausius—Clapeyron equation, A L ln p L„ B" q 45 R„2 As shown in Fig. 8, the isosteric heat of adsorption for the zeolite containing Oskarshamn is higher than that of the BASF catalyst over the whole range, indicating stronger NH 3 adsorption for the former catalyst. At the same time, the Oskarshamn catalyst shows larger NH 3 adsorp- tion capacity than the BASF catalyst. This equates to lower relative poison coverage for the same amount of alkali poison for the Oskarshamn catalyst compared to the BASF catalyst. On the other hand, alkali metals are basic and therefore tend to adsorb better on the Oskar- shamn due to stronger acid sites. These Þndings should be taken into account when comparing deactivation of these two catalysts. The other important parameters in- ßuencing the deactivation of these two catalysts are the gas-phase concentrations of the impurities into the SCR reactor and the rate constant for the poisoning reaction and as discussed previously, there is a large di⁄erence between the particulate loading into these di⁄erent plants. 1782 R. Khodayari, C.U. Ingemar Odenbrand/Chemical Engineering Science 54 (1999) 1775—1785 Fig. 9. Conversion as a function of pore radius for the BASF catalyst; the parameter values are the same as those in Table 1. Fig. 10. Conversion as a function of mesoporosity for the BASF cata- lyst; the parameter values are the same as those in Table 1. Fig. 11. Conversion as a function of channel diameter for the BASF catalyst; the gas ßow used for each case was recalculated based on data from a real SCR plant (9.2 m3 catalyst and F"41 470 Nm3/h), while all other parameter values were held constant according to Table 1. From NH 3 adsorption measurements at 150¡C and 2 Torr, the number of Br+nsted acid sites for the fresh Oskarshamn catalyst can be estimated as 661 lmol/g. On the other hand, ICP-AES analysis indicated that the total amounts of sodium and potassium atoms on the surface of the industrially used catalyst, after 12,000 h on stream, can be estimated to 110 lmol/g. It means that these two poisons cover about 16.6% of the surface active sites. This is comparable with the poison coverage obtained by the simulation which was 17.3% (Fig. 5). It should be noted that the approximated e⁄ective di⁄usivity of the poison is one of the critical parameters applied in the simulations. In the case of potassium, the calculated conversion for D %&&,p "4.7]10~7 was 0.33, while the values for 1.0]10~7 and 0.5]10~7 were 0.54 and 0.60, respectively. As discussed previously, we assumed that ammonia coverage is equal to unity for the fresh catalyst and decreases with increasing poison coverage. Conse- quently, the calculated values for the conversion will be higher than the observed values from industrial plants. 3.4. E⁄ect of catalyst design parameters on SCR conver- sion A more open catalyst pore structure will ease the di⁄usion of the poison into the catalyst, and as a result shortening its life time, and at the same time favoring the di⁄usion of the main reaction into the catalyst, thus increasing the catalyst activity at any given depth of poison penetration. The micropore diameter has a sub- stantial e⁄ect on catalyst performance since both catalyst surface area and pore di⁄usion are strongly dependent on it. Consequently, it is interesting to investigate the e⁄ect of variation of the micropore diameter and microporos- ity on poison accumulation and conversion whilst keep- ing all other parameters constant. The total porosity a⁄ects the physical strength of the catalyst and therefore it was held constant in the simulations. Fig. 9 illustrates the inßuence of variation of the micropore radius on SCR performance at a poisoning time of 2000 h for the BASF catalyst, when all other parameter values were kept con- stant. As the Þgure shows, variation of the micropore radius has almost no e⁄ect on SCR performance for a catalyst poisoned with lead. However, it is possible to optimise the SCR performance of sodium- and potassi- um-poisoned monoliths by modiÞcation of the micro- pore radius. The surface coverage of the poison increases with increasing micropore radius with an optimum point for SCR performance, especially in the case of potassium poisoned catalyst. Fig. 10 shows the inßuence of me- soporosity on SCR performance of a catalyst poisoned during 2000 h by sodium and potassium, while total porosity was kept constant. It is possible to improve both the catalystÕs poison resistance against potassium and SCR performance by modifying mesoporosity of the catalyst. On the other hand, variation of mesoporosity has very little e⁄ect on sodium accumulation and there- by, on SCR performance. Consequently, inclusion of some degree of di⁄usional limitation is beneÞcial for catalyst eƒciency and resistance against deactivation. Fig. 11 illustrates conversion as a function of channel diameter. The total gas ßow was recalculated for each case. The ßow through each channel will decrease with R. Khodayari, C.U. Ingemar Odenbrand/Chemical Engineering Science 54 (1999) 1775—1785 1783 a decrease in the channel diameter, while the geometrical surface area of the channel will increase. The wall thick- ness and all other parameter values were kept constant. The results show that there is an optimum channel dia- meter, where the NO x conversion reaches the highest value. Consequently, it is possible to improve the catalyst resistance against poisoning by modifying the channel diameter. 4. Conclusions The model can describe the poison accumulation and performance of an SCR reactor. The quality of the model is, however, highly dependent on the quality of the physical and chemical parameters applied to it. There- fore, a wholly quantitative prediction of catalyst behavior in a real plant is diƒcult at present. The model requires many parameters, such as gas-phase concentration of each poison, NH 3 adsorption amounts on fresh and poisoned catalysts, rate constants of poisoning and main reactions, and e⁄ective di⁄usion coeƒcients of reactants and poisons. Some of these parameters can be measured experimentally for every catalyst, while others cannot be determined. The concentration of poisons in the ßue gas has been estimated by means of reported data from some waste incineration plants. For calculation of the rate constants for poisoning reactions it is necessary to have poison accumulation data from the same catalyst as used in the real plant. The values determined for one catalyst may be transferred to the others if they have properties that are common to both. The uncertainties in the e⁄ec- tive di⁄usion coeƒcients of the poisons are large due to the estimation, while the uncertainties are estimated to be $10% of the calculated values for di⁄usion of NO and NH 3 . It is important to note that both the rate constant for the poisoning reaction and the catalyst morphologi- cal conÞguration are central to the deactivation behavior. In conclusion the present model predicts semi- quantitatively the performance of an SCR reactor in the presence of di⁄erent poisons. Acknowledgements Financial support from NUTEK, the Swedish Nation- al Board for Industrial and Technical Development, is gratefully acknowledged. We also wish to thank Mrs. Birgitta Svensson for help with NH 3 adsorption and BET analysis and Dr. Bernt Nilsson for all fruitful discussions. Notation c species molar concentration, mol/m3 c s,NO gas-phase concentration of NO at the surface, mol/m3 c s,p gas-phase concentration of poison at the sur- face, mol/m3 c w,= saturation poison concentration, mole of poi- son/m2 BET D molar di⁄usivity in the reactive mixtures, m2/s D e e⁄ective di⁄usivity in the washcoat ("D %&& ), m2/s H washcoat thickness, m k intrinsic rate constant, m/s K a ammonia adsorption equilibrium constant ("K !$4 /K $%4 ) k m mass transfer coeƒcient, m/s k p intrinsic rate constant for the poisoning reac- tion, m/s M molecular weight, kg/mol P poison r macro- or micropore radius, m R reaction rate, mol/m2/s Re Reynolds number Sc Schmidt number Sh Sherwood number S geometric surface area per unit reactor vol- ume, m2/m3 t time on stream, s u dimensionless concentration … catalytically inactive deposit w 1 k m,p S‚/l w 2 aH2k p /D e,p w 3 c*/ g,p k p /c w,= w 4 Hk m,p /D e,p x axial coordinate, m Dx incremental conversion z coordinate for depth within the washcoat, m Greek letters a catalytic surface area per unit washcoat vol- ume, m2/m3 b selectivity parameter e void fraction of the monolith e s void fraction of the washcoat k gas viscosity, kg/m/s l gas velocity, m/s h NH3 adsorbed amount of NH 3 /total adsorption capacity for NH 3 h w poison coverage o gas density, kg/m3 p unpoisoned adsorption site Subscripts g gas phase p poison precursor s solid phase i grid index 1784 R. 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