Unsteady Analysis of NO Reduction over Selective Catalytic

concerning prediction of NO reduction efficiency, but is suitable, in principle, for application to predictive control systems. Furthermore, the analy...
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Ind. Eng. Chem. Res. 1998, 37, 2341-2349

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Unsteady Analysis of NO Reduction over Selective Catalytic Reduction-De-NOx Monolith Catalysts Enrico Tronconi, Andrea Cavanna, and Pio Forzatti* Dipartimento di Chimica Industriale e Ingegneria Chimica del Politecnico, Piazza Leonardo Da Vinci 32, 20133 Milano, Italy

A heterogeneous 1D dynamic model of SCR-de-NOx (SCR ) selective catalytic reduction) monolith reactors is developed, based on the concept of the “active” catalyst region. Its predictions are practically equivalent to those of a previous 2D model, but its numerical solution is faster by 1 order of magnitude, making it suitable for predictive control applications. The model is successfully fitted to transient NO reduction data at different temperatures, space velocities, and NH3/NO feed ratios over two commercial SCR monolith catalysts. The data indicate characteristic times up to several minutes. The model analysis shows that: (i) SCR dynamics are determined by buildup/depletion of the catalyst NH3 coverage, which result primarily from a competition between adsorption of ammonia and its reaction with NO, the rate of NH3 desorption being markedly slower; (ii) the dynamic response of NO conversion is slow compared to changes in the NH3 feed content, which is unfavorable for a feedback control system; and (iii) positive/negative peaks of NO emissions vs progressive changes of the NH3 slip are predicted upon sudden load variations. Introduction Selective catalytic reduction (SCR) is nowadays a worldwide implemented commercial technology for NOx abatment from power plant flue gases (Bosch and Janssen, 1988; Nakajima and Hamada, 1996; Forzatti and Lietti, 1996). It is based on the reaction among nitrogen oxides (essentially nitrogen monoxide), ammonia, and oxygen according to the following primary stoichiometry,

4NO + 4NH3 + O2 f 4N2 + 6H2O If SO2 is present in the combustion gas, SO2 oxidation also occurs as a side reaction in the SCR reactor,

SO2 + 1/2O2 f SO3 Even very small SO2 conversions are undesired since they may cause precipitation of ammonium sulfates in the cold parts of the plant (Matsuda et al., 1982). Commercial SCR catalysts are made up of TiO2, WO3, and V2O5 (Forzatti and Lietti, 1996), acting as the support, the promoter, and the active component, respectively. They are shaped in the form of honeycomb monoliths or plates: such structures afford low-pressure drops and high attrition resistance while providing geometric surface areas comparable to those of packed beds of catalyst pellets (Beretta et al., 1997). There is growing interest in the dynamic behavior of SCR-de-NOx reactors, since they are often implicated in transient operations, e.g. during start-up, shut-down, or load variations: under such conditions, maintaining pollutants below the emission limits may become more critical than during steady-state operation. Furthermore, forced unsteady operation of SCR reactors, as e.g. in flow reversal processes for power stations (Agar and Ruppel, 1988; Bobrova et al., 1993; Hedden et al., 1993; * Corresponding author. E-mail: [email protected].

Noskov et al., 1996), offers interesting perspectives, too. The SCR technology has been proposed also for purification of exhaust gases from nonstationary sources (e.g. diesel engines of heavy trucks) (Andersson et al., 1994), which naturally involve fast transients primarily associated with load variations. For all of these applications, reliable engineering analysis calls for a dynamic mathematical model of the SCR reactor. If properly grounded on the physicochemical fundamentals of the de-NOx process, such a model can be helpful in rationalizing the complexities of the reacting system under transient conditions. Once successfully validated, not only can it can be used in the development and design of unsteady SCR processes, but it could as well afford improved predictive control systems of SCR plants. During recent experimental studies in our laboratories we made use of dynamic techniques based on transient response methods to address aspects of the SCR reaction mechanism over model and commercial V/TiO2-based catalysts. Both the reduction of NOx with ammonia (Tronconi et al., 1996; Lietti et al., 1997) and the parallel oxidation of SO2 (Orsenigo et al., 1996) were investigated. In particular, it was shown that ammonia is strongly adsorbed on the catalyst surface, while NO does not adsorb appreciably, in line with an Eley-Rideal mechanism. Adsorbed NH3 is stored not only on the active V-related sites but also on TiO2 and WO3, which provide a sort of buffer. It was found also that de-NOx dynamics are orders of magnitude faster than SO2 oxidation dynamics. A number of related results, including e.g. the kinetics of NH3 adsorption-desorption and of its surface reaction with gaseous NO, and the estimates of the characteristic times associated with the physicochemical phenomena prevailing in the SCR system are also strictly relevant to dynamic modeling of SCR reactors. Drawing from previous activities in steady-state modeling of SCR monolith reactors (Tronconi and

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Forzatti, 1992; Tronconi et al., 1992, 1994), we developed an introductory unsteady heterogeneous model of the de-NOx reaction in monolith honeycomb catalysts (Tronconi et al., 1996). It was based on the following major hypotheses: (1) identical conditions within each monolith channel (single channel model); (2) isothermal conditions; (3) negligible axial dispersion. The model consisted of one-dimensional mass balance equations for NO and NH3 in the gas phase within the channels. It also considered gas-solid mass transport of the de-NOx reactants within the monolith channels, and their diffusional transport inside the porous catalyst matrix, resulting in continuity equations for NO and NH3 at the gas-solid interface, as well as in two-dimensional mass balance equations for gaseous NO and NH3 in the porous matrix, and for ammonia adsorbed on the catalyst. The global system of partial differential equations (PDEs) in time and two spatial dimensions was solved numerically by polynomial approximation of the unknown NH3 and NO concentration fields along both the axial and the transverse (intraporous) coordinates and integration of the resulting set of ordinary differential equations (ODEs) in time. The model was successfully fitted to a first set of transient NOx reduction data collected in our laboratories over a honeycomb SCR catalyst. Due to the 2D approach, however, its mathematical structure was too involved to allow either further extensions or on-line applications. Furthermore, numerical approximation of the steep intraporous NH3 and NO concentration gradients was found troublesome, sometimes causing convergence difficulties. On the other hand, intraporous diffusion of NO and NH3 plays a controlling role in the dynamics of SCR catalysts, which is based on the buildup and depletion of adsorbed ammonia. Thus, proper account of pore diffusion must be included in the model. In this work we first develop a simpler 1D dynamic model of the SCR-de-NOx monolith reactor, based on analytical approximations of the reactant intraporous concentration profiles. Next we show that the new model is essentially equivalent to the previous one concerning prediction of NO reduction efficiency, but is suitable, in principle, for application to predictive control systems. Furthermore, the analysis is extended by removing the hypothesis of isothermal conditions, which is relevant to simulation of practical transients resulting from temperature variations of the flue gases. Finally, the complete model is extensively validated against laboratory-scale data corresponding to various transients of NOx reduction over two commercial honeycomb SCR catalysts. In a forthcoming paper the treatment will be completed by including the dynamics of SO2 oxidation and validating the model against transient experiments both in the absence and with the simultaneous occurrence of NO reduction. Experimental Section Experimental transient data of NO reduction were obtained in a laboratory-scale flow microreactor over two commercial “high-dust” monolith honeycomb V2O5WO3/TiO2 catalysts. The vanadium loading (0.96% V2O5 (w/w) for catalyst 1, 0.45% for catalyst 2) was uniformly distributed across the wall thickness of the monoliths. Catalyst 1 and catalyst 2 had square channels, with pitch equal to 7.5 and 6.5 mm, and wall half-thickness equal to 0.6 and 0.55 mm, respectively. Catalyst samples with nine channels, 15 cm in length, were cut from commercial modules and loaded in the test reactor.

Table 1. Pore Size Distributions of the Tested Commercial SCR Honeycomb Catalysts radius micropores 1, Å porosity micropores 1, cm3/cm3 radius micropores 2, Å porosity micropores 2, cm3/cm3 radius mesopores, Å porosity mesopores, cm3/cm3

catalyst 1

catalyst 2

50 0.288 200 0.298 600 0.155

100 0.392 350 0.288

The pore size distributions of the two catalysts were determined by BET and Hg intrusion measurements: they are reported in Table 1. Synthetic gas mixtures from high-pressure bottles (300-560 ppm NO, 1000-1200 ppm SO2, 2-2.6% (v/v) O2, 10-12.6% (v/v) H2O, balance N2) were preheated to the desired reaction temperature, mixed with ammonia (300-500 ppm NH3) at the top of the reactor to prevent side reactions, and then admitted to the reactor. The gases flowing out of the reactor were passed in an aqueous solution of phosphoric acid to trap unconverted ammonia. NO/NOx were detected in a chemiluminescence analyzer (Beckman, model 955). Further details on the experimental apparatus and on the analytical methods are given elsewhere (Svachula et al., 1993). Transient experiments consisted of reactor start-up (NH3 injection into the NO-containing feed stream) and shut-down procedures corresponding to various NH3/ NO feed ratios (0.6-1.2) and operating temperatures (270-380 °C), as well as in step changes of the inlet concentration of either NO or NH3. In view of these transient runs, special care was devoted to minimizing the dead volumes existing in the rig. Diagnostic startup runs indicated that a lag time of less than 10 s was typically associated with the test reactor transients. Model Development Intrinsic De-NOx Kinetics. On the basis of our dynamic investigation of the SCR-de-NOx reaction (Lietti et al., 1997), we assume Temkin-type kinetic expressions for the local rates of ammonia adsorptiondesorption at the catalyst surface:

rNH3 ) kadsCNH3(1 - θ) - kdθ

(1)

where θ is the local NH3 surface coverage, and

(

kads ) k°ads exp -

[

kd ) k°d exp -

)

Eads RT

(2)

]

E°d(1 - βθ) RT

(3)

It is worth noting that NH3 adsorption-desorption equilibrium is not assumed in this work. In fact, our dynamic kinetic study provided experimental evidence that the rate of NH3 adsorption on active V-based SCR catalysts is similar to that of its surface reaction with NO, whereas the rate of NH3 desorption is nearly negligible (Lietti et al., 1997). The same results support also the assumption that the rate expression for NO reduction is based on an Eley-Rideal mechanism between adsorbed NH3 and gaseous (or weakly adsorbed) NO (Lietti et al., 1997):

rNO ) kNOCNOθ

(4)

Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2343

with

(

kNO ) k°NO exp -

)

ENO RT

(5)

Notably, the kinetic dependence on O2 is neglected in view of previous steady-state data pointing to zeroorder kinetics with respect to oxygen for O2 feed concentrations in excess of 2% (v/v) (Svachula et al., 1993). Likewise, the inhibiting effect of water due to its competitive adsorption with NH3 is also neglected in the rate expressions: such an effect is essentially constant over the concentration range of industrial interest, namely, 12 > CH2O > 5% (v/v) (Svachula et al. 1993) and can be incorporated in the kinetic parameter estimates. Gas-Phase Equations. As in previous works (Tronconi et al., 1996), we assume negligible axial dispersion, negligible pressure drop, and identical conditions within each channel of the honeycomb monolith catalyst. We also adopt a 1D representation of the concentration and temperature fields in the gas-phase flowing inside the monolith channels. Accordingly, the following mass balance equations for NH3 and NO in the bulk gasphase apply, with symbols explained in the Notation: b ∂CNH 3

∂t

b

v ∂CNH3 4 b W )- kmat,NH3(CNH - CNH ) 3 3 L ∂z dh

(6)

b ∂CbNO v ∂CNO 4 )- kmat,NO(CbNO - CW NO) ∂t L ∂z dh

(7)

The corresponding energy balance for the gas phase

the strong intraporous diffusional limitations affecting the SCR-de-NOx reaction: they are defined by eqs 13 and 14 as follows. Solid-Phase Equations. We regard the monolith honeycomb catalyst as a porous continuum. Heat conduction in the ceramic matrix is neglected, but each channel wall is assumed isothermal along the transverse direction due to the narrow wall thickness. Accordingly, the unsteady enthalpy balance for the solid phase is given by

Fscˆ ps

Fgcˆ pg

cˆ pgv

F ∂Tg )∂t L

∂Tg 4 - h (Tg - Ts) ∂z dh

(8)

(11)

Conservation equations for gaseous NH3 and NO inside the catalyst pores are no longer required by virtue of the approximations put forward in the Appendix. Concerning the mass balance for NH3 adsorbed on the catalyst, the derivation outlined in the Appendix yields the following equation:

Ω(1 - x*)

∂θ h eff ) rNH - reff NO 3 ∂t

(12)

where θ h is the average NH3 surface coverage across the “active” portion of the catalytic wall, with dimensionless thickness (1 - x*), at any axial coordinate z. (1 - x*) is given by eq A.6 in the Appendix. Notice that, according to eq 12, only a reduced NH3 adsorption capacity, corresponding to the active fraction of the catalyst wall thickness, is involved in SCR dynamics. The effective rates per unit catalyst volume are evaluated approximately, assuming pseudo-first-order kinetics, as

is g

∂Ts h g ) (T - Ts) + (-∆Hr)reff NO ∂t s

eff ) rNH 3

kadsCW h ) - kdθ h (1 - x*) NH3(1 - θ tanh ΦNH3 (13) ΦNH3

and The following standard initial and boundary conditions are in order: b b CNH ) CNH °(t) 3 3

CbNO ) CbNO°(t) Tg ) T°g(t) b b ) CNO (z) CNH 3 3,i

CbNO ) CbNO,i(z) Tg ) Tgi (z)

at z ) 0 at z ) 0 at z ) 0 at t ) 0 at t ) 0 at t ) 0

Gas-Solid Continuity Equations. At any axial coordinate z, the bulk and wall concentrations of NO and NH3 are related by b W eff - CNH ) ) srNH kmat,NH3(CNH 3 3 3 eff kmat,NO(CbNO - CW NO) ) srNO

(9) (10)

eff and reff In eqs 4 and 5, rNH NO are effective rates of 3 NH3 adsorption and of NO reduction, respectively, per unit volume of catalyst, accounting for the influence of

h reff NO ) kNOθ

1 - [sinh(ΦNOx*)/cosh ΦNO] tanhΦNO ΦNO (14)

where ΦNH3 and ΦNO are Thiele moduli defined in the Appendix, eqs A3 and A4. Numerical Methods. The set of model PDEs, eqs 6-14, was solved numerically, using orthogonal collocation techniques (Finlayson, 1980) to approximate the unknown solutions (z,t), CNH3(z,t), CNO(z,t), Tg(z,t), Ts(z,t) along the axial coordinate. Notably, the previous 2D model (Tronconi et al., 1996) would require approximation of the concentration fields of NO and NH3 along the transverse (intraporous) coordinate, too. The resulting system of algebraic and ordinary differential equations (DAEs) was integrated in time using a library routine based on Gear’s method (Hindmarsh, 1983), with self-adjusting step size and variable method order. Convergence of the solution was checked by varying the number of collocation points along z (typically eight or nine points were sufficient) and by using the internal criteria of the DAE integrator. Concerning the model parameters, thermal properties (cpg, cps, ∆Hr) were estimated according to standard correlations (Reid et al., 1987), local gas-solid mass and heat transfer coefficients were estimated from the analogy with the Graetz-Nusselt heat transfer problem

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Figure 1. Comparison of the present dynamic SCR-de-NOx reactor model (this work) with a previous model (Tronconi et al., 1996). Calculated evolution of the NO outlet concentration during a transient caused by step changes of ammonia feed concentration from 0 to 400 ppm (at t ) 0 s) and from 400 ppm to 0 (at t ) 600 s). Other conditions: C°NO ) 500 ppm; AV ) 10 Nm/h; T ) 350 °C. Table 2. Parameter Estimates for Transient de-NOx Kinetics over Commercial SCR Honeycomb Catalyst 1 (Tronconi et al., 1996) k°ads,m3gas/(m3cat. s) Eads, cal/mol k°d, mol/(m3cat. s) E°d, cal/mol

8.5 × 106 9.0 × 103 8.0 × 108 2.6 × 104

β k°NO, m3gas/(m3cat. s) ENO, cal/mol Ω, mol of NH3/m3cat.

0.32 2.5 × 1010 18.6 × 103 210

(Tronconi and Forzatti, 1992), and effective intraporous diffusivities of NO and NH3 were evaluated from the catalyst morphological properties according to Cunningham and Geankoplis (1968), using a modified form of the Wakao-Smith random pore model recommended by Beeckman (1991) for SCR catalysts: the estimated values of Deff were close to 10-2 cm2/s. In the case of SCR catalyst 1 the kinetic constants were set to the same values previously determined by fitting the 2D model to unsteady NO reduction data (Tronconi et al., 1996); in the case of SCR catalyst 2 they were estimated by fitting the present model to unsteady NO reduction data. Model Validation Comparison with the Previous Unsteady SCR Reactor Model. The reduced 1D heterogeneous dynamic model of SCR-de-NOx monolith reactors herein developed was first systematically compared with the previous 2D treatment (Tronconi et al., 1996) in order to check the mathematical consistency of its simplifying assumptions. This provided also practical indications as to how computational efficiency and robustness had been improved. Figure 1 illustrates one of such comparisons. The previous and the present models were used to simulate start-up and shut-down of a SCR reactor, involving a step change of the ammonia feed concentration from zero to 400 ppm (at t ) 0), and then again to zero (at t ) 600 s). The assumed operating conditions are reported in the figure caption: they can be taken as representative of industrial SCR processes. The adopted estimates of the kinetic parameters listed in Table 2 are the same values determined in our previous study, where the original 2D model was fitted to a set of dynamic de-NOx data collected over SCR catalyst 1.

Figure 2. Calculated temporal evolutions of the axial profiles of (a) NH3 average surface coverage θ h and (b) fractional active wall thickness, 1 - x*. Conditions as in Figure 1.

Figure 1 shows that the NO outlet concentrations computed by the two models do not differ significantly during the whole transient. Additional comparison of the two models for different conditions and for other types of transient reactor operations provided similar results. Thus, it appears that the approximations involved in the present treatment did not alter appreciably the model predictions. On the other hand, it was found that the computation time required by the present model was shorter typically by at least 1 order of magnitude when compared to the preexisting model; it was about 100 times shorter than the simulated time when running the program on a conventional PC. Also, the numerical solution of the model equations was more robust, since the numerical approximation of the steep intraporous concentration profiles was avoided. For the conditions of Figure 1, Figure 2 illustrates the calculated evolution of the NH3 surface coverage (a) and of the active fraction of the catalyst wall 1 - x* (b) during the first 100 s of the start-up transient. The axial profiles are shifted upward in time as the catalyst is progressively saturated with NH3. They all approach zero at the reactor outlet, indicating nearly complete conversion of ammonia: the NH3 slip is about 6 ppm. According to Figure 2b, the ammonia adsorbed on the catalyst is concentrated in only about 10% of the total thickness of the monolith walls. This is also the volume fraction of the catalyst that is actually involved in the reaction dynamics. Comparison with Unsteady SCR-De-NOx Reaction Data. In this section we proceed to validate the present dynamic model of the SCR-de-NOx reaction system by comparing its predictions with experimental transient data of NO reduction over the two investigated SCR catalysts. All of the data were obtained by perturbing steady-state operation of the laboratory reactor by a step change of one of the inlet conditions and recording the system response in time. (a) Catalyst 1. Figures 3 and 4 illustrate comparisons between experimental data and model predictions during reactor start-up (NH3 injection) and shut-down procedures corresponding to different values of the NH3/ NO feed ratio R at 360 and at 270 °C, respectively. The higher temperature is typical of industrial SCR condi-

Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2345 Table 3. Characteristic Rates in SCR-de-NOx over Catalyst 1a rdes/rads rNO/rads

T ) 270 °C

T ) 330 °C

T ) 350 °C

T ) 400 °C

9.88 × 10-4 5.58 × 10-2

4.83 × 10-3 1.35 × 10-1

7.68E-03 1.75 × 10-1

2.18 × 10-2 3.11 × 10-1

a Assumed conditions: θ ) 0.1, C NO ) 200 ppm, CNH3 ) 160 ppm.

Table 4. Parameter Estimates for Transient de-NOx Kinetics over Commercial SCR Honeycomb Catalyst 2 k°NO, m3gas/(m3cat. s) ENO, cal/mol

Figure 3. Experimental and simulated evolutions of the NO outlet concentration during reactor start-up and shut-down at T ) 360 °C over catalyst 1. C°NO ) 560 ppm, AV ) 33 Nm/h. R ) 0.6: C°NH3 ) 0 f 336 ppm (t ) 0 s), C°NH3 ) 336 f 0 ppm (t ) 500 s). R ) 0.8: C°NH3 ) 0 f 448 ppm (t ) 0 s), C°NH3 ) 448 f 0 ppm (t ) 500 s). R ) 1: C°NH3 ) 0 f 560 ppm (t ) 0 s), C°NH3 ) 560 f 0 ppm (t ) 500 s).

Figure 4. Experimental and simulated evolutions of the NO outlet concentration during reactor start-up and shut-down at T ) 270 °C over catalyst 1. C°NO ) 560 ppm, AV ) 33 Nm/h. R ) 0.6: C°NH3 ) 0 f 336 ppm (t ) 0 s), C°NH3 ) 336 f 0 ppm (t ) 500 s). R ) 0.8: C°NH3 ) 0 f 448 ppm (t ) 0 s), C°NH3 ) 448 f 0 ppm (t ) 500 s). R ) 1: C°NH3 ) 0 f 560 ppm (t ) 0 s), C°NH3 ) 560 f 0 ppm (t ) 500 s).

tions, while the lower temperature was investigated in order to slow the reaction dynamics and improve the time resolution of the data. The model results were generated using the same estimates of kinetic parameters (Table 2) and transport coefficients as those discussed for Figure 1. In all cases the agreement between experiment and model fit is satisfactory. Experimental data and computed curves suggest characteristic time constants up to several minutes, in line with indications of the SCR technical literature. This confirms that the response of the SCR system to NH3 injection is slow. At T ) 360 °C (Figure 3) both the data and the simulations show that the start-up dynamics are slower than the response associated with reactor shut-down (∼200 s versus 20-40 s). In fact the start-up transient following ammonia injection is associated with the buildup of NH3 coverage: this process results from a competition between ammonia adsorption and NO reduction, the latter occurring at the expense of adsorbed NH3. On the other hand NH3 adsorption is

7.0 × 107 12.2 × 103

absent after ammonia shut-down: in this case depletion of preadsorbed NH3 results primarily from its surface reaction with NO. On the basis of the kinetic parameter estimates in Table 2, in fact, the contribution of NH3 desorption to the overall rate is minor. In addition to smaller NO conversions, the data points and the curves at T ) 270 °C (Figure 4) show much slower responses than those observed at T ) 360 °C. In this case in fact the NH3 shut-down procedure was always begun long before the start-up transient had been completed. Also, it can be observed that in this case the shut-down time is similar to the start-up time. In fact the rate of NO reduction decreases with decreasing temperature more markedly than the rate of ammonia adsorption due to the different activation energies of the two processes. One additional set of data collected at 330 °C, not reported for brevity, showed an intermediate behavior between those of Figures 3 and 4. The agreement of the model was similar, too. Table 3 summarizes the relative rates of NH3 adsorption, desorption, and reaction at different temperatures, as estimated according to the present kinetic parameters. It is apparent that NH3 adsorption is the fastest process, with NO reduction being of comparable rate at the highest temperatures. NH3 desorption is always slower than the surface reaction by at least 1 order of magnitude. (b) Catalyst 2. Experimental data collected over this catalyst included not only start-up and shut-down transients but also step changes of either the NO or NH3 feed concentration. The selected operating conditions were close to those of the industrial practice (T ) 350 °C, AV ) 10 Nm/h, C°NO ) 500 ppm, C°NH3 ) 365 ppm). To fit the whole set of experiments over catalyst 2, the parameters of the NH3 adsorption-desorption kinetics were left to the values listed in Table 2, but it was necessary to readjust the rate parameters of the de-NOx reaction to the values presented in Table 4, which reflect a lower activity than catalyst 1. Due to the strong statistical correlation of k°NO and ENO, a direct comparison of the individual estimates of the two parameters for catalysts 1 and 2 is meaningless. According to the figures in Tables 2 and 4, however, the intrinsic de-NOx rate constant kNO at 350 °C is about two times greater for catalyst 1 than for catalyst 2, whose Vcontent is about twice as small. This is in line with previous indications that intrinsic activity of V2O5WO3/TiO2 de-NOx catalysts is proportional to their V-loading (Svachula et al., 1993), though the correlation between catalyst activity and composition is expectedly more complex. Figure 5 shows experimental and calculated evolutions of the NO outlet concentration during start-up (a) and shut-down (b) of SCR catalyst 2. The observed

2346 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998

Figure 5. Experimental and simulated evolutions of the NO outlet concentration during reactor start-up (a) and shut-down (b) at T ) 360 °C over catalyst 2. C°NO ) 500 ppm, AV ) 10 Nm/h. C°NH3 ) 0 f 365 ppm (a), C°NH3 ) 365 f 0 ppm (b).

Figure 7. Calculated evolution of the NO outlet concentration (a) and the NH3 slip (b) following step variation of the inlet gas temperature: T ) 380 °C f 350 °C (t ) 0 s). Other conditions: catalyst 1, C°NO ) 500 ppm, C°NH3 ) 400 ppm, AV ) 10 Nm/h. Kinetic parameters as in Table 2.

different conditions of NH3 coverage as corresponding to R < 1 and R > 1. The results of Figure 6 were confirmed by additional runs with either less marked step changes of NO feed content or with step changes of the NH3 feed concentration. Simulation of Thermal Transients Figure 6. Experimental and simulated evolutions of the NO outlet concentration following step variation of NO inlet concentration C°NO at T ) 350 °C, C°NH3 ) 400 ppm, AV ) 10 Nm/h. Run 1: C°NO ) 500 f 600 ppm (t ) 0 s). Run 2: C°NO ) 500 f 400 ppm (t ) 0 s). Run 3: C°NO ) 500 f 300 ppm (t ) 0 s).

dynamic behavior is similar to that presented in Figure 3 for SCR catalyst 1, though with slower responses: characteristic times of 200 s are required to achieve steady state after start-up and of about 100 s to restore the initial conditions after NH3 closure. Similarly to catalyst 1, the model fit represents successfully the experimental data. Figure 6 illustrates the evolution of the SCR system upon three different step changes of the NO feed concentration over catalyst 2. Again, the model was able to reproduce the characteristic times of the experimental transients. Both the data and the calculations indicated that such characteristic times were longer for runs 2 and 3 corresponding to final C°NO < 500 ppm, which implies an overstoichiometric NH3 feed content (i.e. R > 1). In fact, under such conditions the buildup of adsorbed ammonia, that is the controlling step in SCR dynamics, is not limited to the narrow active catalyst layer but entails the whole catalyst volume. It is noteworthy that the present dynamic model can predict the time response of SCR catalysts under such vastly

Experimental validation of the model predictions concerning the unsteady thermal behavior of SCR reactors was not possible due to intrinsic limitations of our laboratory test rig: even at the highest heating rates, only a sequence of steady states of the reactor could be achieved due to its large thermal inertia. We report however a few related simulation results which are informative of the expected reactor response to step changes in the temperature of the feed gas stream, as resulting e.g. from load variations in the burners of a power station. Figure 7 shows calculated temporal evolutions of outlet CNO (a) and CNH3 (b) following sudden cooling of the incoming gas from 380 to 350 °C. The initial and final steady-state concentration levels are similar, because the NO conversion is limited by the substoichiometric NH3 feed. While the NH3 slip exhibits a monotonic increase, however, the outlet NO concentration goes through a maximum. In fact, the temperature decrement results in a sudden decrease of NO conversion (with a corresponding buildup of adsorbed NH3) because of the reduced rate of reaction. Then, the initial conversion level is almost entirely recovered as the new steady state is approached, corresponding to a greater equilibrium value of the NH3 surface coverage. Sharp maxima and minima in NO emissions had been reported already upon simulation of load variations in

Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2347

SCR reactors (Tronconi et al., 1996). The maximum in Figure 7a is less marked, however. In fact, the temperature of the SCR catalyst varies slowly due to its considerable thermal inertia: over 10 min are required to accommodate the T-change of Figure 7. Conclusions The present simplified 1D model based on the concept of the “active” catalyst region can effectively represent the dynamic behavior of SCR-de-NOx monolith reactors. While it retains the same physicochemical features incorporated in the previous 2D treatment, it is computationally faster by at least 1 order of magnitude. This affords potential applications to predictive control systems: the ratio of CPU time to real time in simulations is about 1/100 using conventional PCs. Inclusion of enthalpy balances allows simulation of thermal transients, too. We have successfully fitted the model to a variety of transient NO reduction data collected over two commercial SCR honeycomb catalysts at different temperatures, space velocities and NH3/NO feed ratios. The data point out characteristic times in the order of several minutes, in line with typical records from SCR industrial installations. In the case of temperature variations of the combustion gases, the considerable thermal inertia of the SCR catalytic material results in even more prolonged transients, spanning over tens of minutes. Rephrased in terms of process control, this means that the response of the controlled variable (i.e. the NO emission level) to changes of the controlling variable (i.e. the NH3 feed content) is markedly delayed. In this respect, the value of a predictive control system for SCR-de-NOx reactors is clearly apparent. The model analysis clarifies further how such time constants are related to the process of NH3 buildup/ depletion at the catalyst surface. It appears that the rate of ammonia adsorption is comparable to the rate of its surface reaction with NO, whereas NH3 desorption is much slower. A similar conclusion had been obtained in our study of SCR-de-NOx dynamics over model V2O5/ WO3/TiO2 catalysts (Lietti et al., 1997) and is herein confirmed for commercial SCR monolith catalysts under industrial-type operating conditions. This result implies that the dynamics of the SCR-de-NOx reaction, as well as the NH3 surface coverage at steady state, are determined by the competition between adsorption and reaction of ammonia. Particularly, the assumption of NH3 adsorption-desorption equilibrium, commonly made for steady-state de-NOx kinetics, is incorrect. Since NH3 is strongly adsorbed on the catalyst, while NO is not, the dynamics of NO conversion is intrinsically faster than that exhibited by the NH3 slip. In fact, the model simulations indicate the possibility of peaks of NO emissions upon sudden changes in either the temperature or the flow rate of the gas feed stream; on the other hand, only regular, monotonic variations of the NH3 slip are predicted. Acknowledgment This work was performed under contract with ENEL DSR-CRT, Pisa. The authors wish to thank Dr. Natale Ferlazzo for his valuable contributions to the present work.

Notation AV ) area velocity [Nm3/(m2 h)] Ci ) gas-phase concentration of species i (mol/m3gas) cp ) specific heat [cal/(kg K)] D ) molecular diffusivity (m2/s) De ) effective intraporous diffusivity (m2/s) dh ) hydraulic diameter of the monolith channels (m) Eads ) activation energy for NH3 adsorption (cal/mol) E°d ) activation energy for NH3 desorption at zero coverage (cal/mol) ENO ) activation energy for NO reduction (cal/mol) k°ads ) preexponential factor for NH3 adsorption [m3gas/ (m3cat. s)] k°d ) preexponential factor for NH3 desorption [m3gas/(m3cat. s)] k°NO ) preexponential factor for NO reduction [m3gas/(m3cat. s)] kads ) rate constant for NH3 adsorption [m3gas/(m3cat. s)]] kd ) rate constant for NH3 desorption [mol/(m3cat. s)]] kmat ) gas-solid mass transfer coefficient [m3gas/(m2cat. s)]] kNO ) rate constant for NO reduction [m3gas/(m3cat. s)] h ) gas-solid heat transfer coefficient [cal/(m2cat. h K] L ) monolith length (m) rNH3 ) net rate of NH3 adsorption [mol/(m3cat. s)] rNO ) rate of NO reduction [mol/(m3cat. s)] s ) half-thickness of monolith wall (m) t ) time (s) T ) temperature (K) v ) gas linear velocity (m/s) x ) dimensionless monolith transverse (intraporous) coordinate x* ) coordinate of inner boundary of active region, eq A6 z ) dimensionless monolith axial coordinate Greek Letters R ) NH3/NO molar feed ratio β ) parameter for surface coverage dependence, eq 3 -∆HR ) heat of reaction (cal/mol) θ ) NH3 surface coverage F ) density [kg/m3] Φi ) Thiele modulus of species i Ω ) catalyst NH3 adsorption capacity [mol/m3cat.] Superscripts b ) bulk gas conditions eff ) effective rate g ) gas phase s ) solid phase W ) conditions at the monolith wall ° ) conditions at reactor inlet

Appendix: Derivation of the Approximate Mass Balance of Adsorbed NH3, (Equation 12) Gas-Phase Intraporous Concentration Profiles. In our previous dynamic analysis of the SCR monolith reactor (Tronconi et al., 1996), intraporous NO and NH3 concentration profiles in the catalyst matrix (CNH3(x), CNO(x), θ(x)) were obtained by numerical solution of diffusion-reaction equations across the monolith wall thickness at any axial coordinate z. In this work the intraporous gaseous concentration distributions of NO and NH3 are approximated by the following well-known analytical expressions, typical of steady-state diffusion and reaction within an isothermal slab of catalyst, with reaction obeying irreversible first-order kinetics (Froment and Bischoff, 1990):

2348 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 W CNH3(x) ) CNH 3

cosh(ΦΝΗ3x)

(A1)

cosh(ΦΝΗ3)

cosh(ΦΝΟx) CNO(x) ) CW NO cosh(ΦΝΟ)

(A2)

where x is the dimensionless intraporous coordinate orthogonal to the catalytic wall (x ) 0 at the centerline, W and CW x ) 1 at the gas-solid interface), and CNH NO are 3 NO and NO concentrations at the gas-solid interface, respectively, and ΦNH3 and ΦNO are Thiele moduli, herein defined as

ΦNH3 ) s

[

]

W kads(1 - θ) - (kdθ/CNH ) 3 eff DNH 3

[ ]

ΦNO ) s

kNOθ

(A4)

(A5)

Considering also eq A1, eq A5 can be solved for x*:

x* )

1 ln[f cosh(ΦNH3) + [f 2 cosh2(ΦNH3) - 1]1/2] ΦNH3 (A6)

In our calculations we have used f ) 0.01; accordingly, the active region includes the layer of catalyst where the ammonia concentration is greater than 1% of the interface value. Sensitivity tests indicated that smaller

∫x*1θR(x) dx 1 - x*

θ(x) ) 0

(A3)

Equations A1 and A2 had been already adopted successfully for approximating intraporous NH3 and NO concentration profiles in steady-state modeling of SCR monolith reactors (Tronconi et al., 1994). Equations A3 and A4 imply pseudo-first-order and irreversible kinetics for NH3 adsorption and for NO surface reaction with adsorbed ammonia, respectively. Active Catalyst Region. Next we notice that NO reduction is severely limited by pore diffusion under typical SCR operating conditions (Tronconi et al., 1992). This implies ΦNH3 .1 and ΦNO .1, so that the intraporous concentration of the limiting reactant (typically NH3 under SCR industrial conditions) drops rapidly along x from its gas-solid interface value to zero, while the concentration of the other reactant falls to a nonzero constant value. In fact, in the case of NH3/NO feed ratio R less than one, as in industrial SCR practice, the concentration of gaseous ammonia within the porous monolith catalyst is significantly greater than zero only in a thin layer of the catalytic wall near the gas-solid interface, while it is negligible in the inner part of the catalyst walls. However, only the portion of catalytic wall associated with significant concentrations of gaseous ammonia is involved in reactive phenomena (ammonia adsorption-desorption and NO reduction). This leads to identification of an “active” fraction of the catalytic monolith wall: we define quantitatively this “active” region as the one where the gaseous NH3 concentration is greater than a set (small) fraction f of the NH3 concentration at the gas-solid interface, W . Thus, if x* is the value of the intraporous CNH 3 coordinate at the inner boundary of the active region, W )f CNH3(x*)/CNH 3

θ(x) ) θ h)

1/2

1/2

Deff NO

values of f do not appreciably modify the results. In the case of ammonia being the excess reactant, the value of x* is set to 0, since NH3 is present throughout the catalytic wall. Once the active region is defined, we replace the actual intraporous distribution of the NH3 surface coverage with its average value relative only to the active portion of the catalyst wall. This implies that at any axial coordinate the θ profile across the monolith catalyst wall adopted in our model is the following:

x* e x < 1

(A7)

0 < x < x*

where θ(x) is the assumed simplified ammonia coverage distribution, θR(x) is the actual (unknown) distribution, and θ h is the average ammonia coverage within the active region. Integral Mass Balance for Adsorbed NH3. We now make use of the above results in order to obtain an integral approximate form of the local unsteady mass balance for NH3 adsorbed on the catalyst (Tronconi et al., 1996),

Ω

∂θ ) kadsCNH3(1 - θ) - kdθ - kNOCNOθ (A8) ∂t

On integrating eq A8 across the active region of the catalyst wall and introducing the approximate intraporous distributions for adsorbed NH3, eq A7, as well as for gaseous NH3 and NO, eqs A1 and A2, the following equation for θ j is easily derived: W

h) ∂θ h kadsCNH3(1 - θ tanh ΦNH3 - kdθ h (1 ) Ω(1 - x*) ∂t ΦNH3 x*) -

(

)

sinh(ΦNOx*) kNOCW h NOθ 1tanh ΦNO (A9) ΦNO coshΦNO

which eventually results in eq 12. The Thiele moduli ΦNH3 and ΦNO are evaluated according to eqs A3 and A4, replacing θ with θ h . Likewise, x* is computed according to eq A6 as a function of ΦNH3. Notably, both the Thiele moduli and x* vary along the monolith axial coordinate z. On the other hand, the dependence of the model equations on the intraporous coordinate x has disappeared. Notwithstanding the strong simplification associated with the introduction of an average NH3 surface coverage across the monolith wall thickness, the main physical characteristics of the SCR system are essentially preserved. In fact, θ j is defined with respect to the active portion of the catalytic wall, which generally extends over a minor fraction of the wall thickness due to the strong intraporous concentration gradients of the SCR reactants. Averaging of θ over the whole catalyst volume would be equally respectful of the global mass balance of adsorbed NH3. However, it would imply the existence of significant ammonia coverages across the whole thickness of the monolith walls: this is inconsistent with the true spatial distribution of the reactive phenomena in SCR monolith catalysts. Indeed, test calculations

Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2349

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Received for review October 20, 1997 Revised manuscript received February 17, 1998 Accepted February 24, 1998 IE970729P