Environ. Sci. Technol. 2002, 36, 5447-5454
Development of a Kinetic Model for the NOx Reduction Process by Potassium-Containing Coal Pellets A G U S T IÄ N B U E N O - L O Ä PEZ,† A V E L I N A G A R C IÄ A - G A R C IÄ A , † A N D J O S EÄ A N T O N I O C A B A L L E R O - S U AÄ R E Z * , ‡ Departamento de Quı´mica Inorga´nica, Universidad de Alicante, Spain, Apdo, 99-E-03080 Alicante, Spain, and Departamento de Ingenierı´a Quı´mica, Universidad de Alicante, Spain
A four step kinetic model was developed to describe the NOx reduction process by potassium containing coal-pellets. The relevance and significance of the different steps considered in the model as well as the considerations assumed to introduce the equations associated to this model were properly discussed. The simulation both of the NOx reduction and carbon conversion evolution shows good agreement with the experimental data obtained throughout lifetime tests at 350 °C for samples with different potassium contents. The set of parameters predicted by the kinetic model have physical significance and are helpful in explaining the different behavior exhibited by the samples. Some of these parameters can be correlated with different features of the samples. The potassium loading influences mainly on the kinetic rate constant governing the NOx chemisorption step, thus explaining the increase in selectivity with the catalyst content exhibited by this type of samples.
1. Introduction The reactions of NO and NOx with carbonaceous materials have been studied extensively, and attention has been paid to the effects of char surface area (1-6), temperature (1, 7-11), feed gas concentration (7, 8, 10-16), and catalytic effect of metals (17-28) among other variables. The kinetics and mechanism of these reactions have also been the subject of some studies (1, 4, 7-11, 13, 14, 19, 25, 29-40). However, in terms of detailed kinetics and elementary steps, this process is not well understood. In fact, there are no satisfactory kinetic models for the reaction because of the complexity of the NOx-carbon reaction that involves several reaction steps and elementary processes (41). From the pioneer work performed by Smith et al. (30) till present, three generally acceptable issues about the mechanism of the NO-carbon reaction have been made from experimental observations: (i) although there is a very poor correlation between all available experimental kinetic data, there is a general consensus in the literature about the reaction order, being of first order with respect to NO partial pressure (1, 4, 7, 8, 13, 14, 29-32, 35-37, 41, 42); (ii) the first step is assumed to be the chemisorption of NO on carbon surface (9, 10, 19, 30, 36, 39, 41); and (iii) both surface * Corresponding author phone: +34 965909419; fax: +34 965903454; e-mail:
[email protected]. † Departamento de Quı ´mica Inorga´nica. ‡ Departamento de Ingenierı ´a Quı´mica. 10.1021/es025823y CCC: $22.00 Published on Web 11/06/2002
2002 American Chemical Society
complexes formed during reaction and carbon active sites are known to play a crucial role in the mechanism and kinetics of this reaction (4, 5, 9, 10, 19, 27, 38, 40). Regarding the type of kinetic models reported in the literature, there have been structural models applied to the uncatalyzed NOx-carbon reaction, such as the random pore model in order to describe the rate evolution data with carbon conversion (37, 38, 41). However, this model presents the drawback that does not take into account the dynamics of surface complexes during reaction. There have also been simple kinetic models with the only purpose to extract kinetic data. Therefore, an overall reaction has been described, and the effect of carbon consumption is believed to be negligible small and lumped into the overall rate constant. A recent review collects all these studies in more detail (41). Modeling the NO-carbon reaction under experimental conditions (type of samples used, operating parameters....) appropriate for a real application of the system would be of great interest both from a theoretical and practical point of view. Promising results in terms of efficiency, selectivity toward NOx against oxygen, selectivity toward the desired reaction products (N2 versus N2O; CO2 versus CO), and long lifetimes have been reported by our group using conformed potassium-containing coal samples (briquettes, pellets, ...) (41-43). To achieve these so desirable features, the use of a proper catalyst is indispensable, and potassium has been revealed as the most suitable one for the process under study (28, 41-43). However, the catalytic effects introduce a remarkable difficulty in the interpretation of kinetic data and in the development of a plausible kinetic model. Furthermore, most experiments reported in the literature were conducted only up to a few percent carbon consumption (1, 7, 8, 36) to extract kinetic parameters under given conditions. To develop a real mechanistic model, the influence of carbon consumption on kinetics must be considered (41). Therefore, performing NOx-carbon reactions until complete sample consumption is highly desirable with a double purpose: to obtain realistic kinetic parameters and to simulate carbon conversion evolution and NOx reduction throughout long reaction times (lifetime tests). On the basis of Yamashita’s postulations (19) as well as the proposed analogy to other gasification reactions involving oxygen transfer (45) the following mechanism has been considered as an starting point to postulate our kinetic model for the reduction of NOx by carbon in the presence of oxygen
2Cf + 2NO f 2C(O)(or2C - O) + N2
(I)
2Cf + O2 f 2C(O)(or2C - O)
(II)
2C(O) f CO2 + nCf
(III)
C(O) f CO + nCf
(IV)
C(O) T C - O
(V)
2C(O) + 2NO f 2CO2 + N2 + nCf
(VI)
2CO + 2NO f 2CO2 + N2
(VII)
where the difference between C-O and C(O) is their relative stability (C-O species are considered to be more stable than C(O) species) (19), and Cf are viewed as highly reactive (“nascent”) carbon sites formed upon C(O) desorption and evidently attacked easily by NO and O2 (19, 38, 45). On the VOL. 36, NO. 24, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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other hand, step (VI) must be seen as an “activation” of NO on oxygen-containing sites on the carbon surface (19). The role of oxygen under these conditions consists of enhancing the concentration of oxygen complexes (39, 41). Despite the presentation and description of the mechanism, the authors did not confirm the feasibility of this model by experimental data simulation (19). Taking into account our previous experience on the field of NOx-carbon reaction in the presence of oxygen (42-44, 46), this study is mainly concerned with the development of a kinetic model that incorporates the main elemental steps governing the NOx reduction by potassium containing coalpellets. To verify the validity of the proposed model, simulations of NOx reduction curves and carbon conversion evolution, throughout lifetime tests at 350 °C, were performed for samples presenting different potassium contents, ranging from 7.9 to 21.0%. The physical significance of the elemental reaction rate constants obtained together with the profiles of active sites and carbon-oxygen complexes evolution were discussed.
and the differential equations in each iteration were solved as an implicit block. Although, the CSTR and PFR models are almost completely equivalent in our experimental conditionssresidence time lower than a second against more than 48 h of the lifetime testswe have solved equations using a PFR model. There is an important consideration to take into account related to the numerical solution of the system of equations. Due to the large difference in the magnitude order of residence time (less than a second) and the total lifetime test time (higher than 2 days), there is an important difference between the NOx reduction rate and (CO)#, Cf or C reaction rate. Conceptually, this is not a problem, but from the numerical point of view it produces a “bad conditioned system of equations”. Special care must be taken when solving the differential equations. The most common solvers fail in finding a solution or even worst they produce very inaccurate results. To overcome the problem, solvers that use implicit methods must be used with a careful control of error in each iteration.
2. Experimental Section
3. Results and Discussion
2.1. Sample Description and NOx Reduction Tests. A Spanish high volatile A bituminous coal (A3 with a 7.7 wt % ash content) was used as coal precursor for this study. The commercial humic acid used in this study has a total humic extract of 16% w/w and a potassium content of 5% w/w. The method of coal-pellet preparation was described in detail in the literature (46). For the present study, four different samples were used. Different amounts of KOH (ranging from 0 to 0.31 g KOH/g coal) were dissolved in humic acid using a fixed humic acid/coal ratio (1.2 mL/g of coal). All the potassium-coal slurries were mixed for 30 min with stirring, dried at 110 °C, and conformed in pellets (2 mm in diameter, average length of 8 mm). Finally, the pellets were pyrolyzed in N2 for 2 h at 700 °C. The complete characterization of these samples (including data of atomic surface ratio, obtained by XPS) were collected elsewhere (46). The nomenclature of the samples indicate the name of the original coal and the potassium content in wt %. The samples studied are designated as follows: A3-7.9; A3-10.5; A3-16.8; and A321.0. The NOx-carbon reduction tests have been carried out at 350 °C and atmospheric pressure in a tubular quartz reactor (inner diameter of 1 cm). 0.5 g of pellets and a gas mixture (620 mL/min) which contains 0.2% NO + 5% O2/N2 were used. Under these conditions the residence time is of 0.085 s. The reactor is coupled to NDIR-UV specific gas analyzers for NO, NO2, CO, CO2, and O2 (models 1004, 100, and 1001, respectively). The samples were previously heated in nitrogen until the reaction temperature was reached, and then the reaction mixture replaced the inert gas. The lifetime tests were extended until the sample was completely consumed (leaving only the ash residue). The only reaction products emitted were N2 and CO2. Additional 2 h NOx-carbon reduction tests have been carried out to determine the experimental error in the “NOx reduction (%)” and “sample burn off (%)” estimation from NOx and CO2 concentration monitorization, respectively. Results indicate that the error in the estimation of both parameters is less than 6%. 2.2. Simulation. The simulation and parameter estimation model proposed in the next section results in a DAE (Differential and Algebraic system of Equations) form by three differential and two algebraic equations. These equations were solved under Matlab 6.0. The optimization algorithm used was a successive quadratic programming (SQP) program, where the Hessian matrix was updated by a BFGS formula (47). Derivatives were estimated by perturbations, 5448
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3.1. Development of the Kinetic Model. 3.1.1. Relevance and Significance of the Different Steps Considered in the Model. In accordance with the comments made in the introduction of this work, the following kinetic model is proposed for simulating the NOx reduction in a gas stream that goes through a carbon bed (under our experimental conditions potassium containing coal-pellets). This model is a simplified version of that proposed by Yamashita et al. (19) but complete enough to be representative of the process under study and with a not very high number of parameters to be optimized in order that the simulation has physical significance
Cf + O2 f (CO)#
(R1)
n1C + (CO)# f CO2 + n1Cf
(R2)
NOx + Cf f 1/2N2 + (CO)#
(R3)
n2C + NOx + (CO)# f CO2 + 1/2N2 + n2Cf
(R4)
where Cf makes reference to a new freshly formed site, created after the decomposition of carbon-oxygen complexes (by means of R2 or R4). This site might be viewed as an unsaturated carbon at an edge of the carbon matrix, as previously explained. (CO)# includes all the oxygenated groups of the carbon surface, whose nature, stoichiometry, and possible differences in relative stability are not fully known. Some authors designate the complexes able to evolve as CO2 with “C(O2)”. In our case, (CO)# includes all the oxygen surface complexes whose ratio C:O is not necessarily 1:1 but decomposing as CO2 (via R2 or R4). Finally, C represents the carbon atoms different from Cf and (CO)#. The significance of the different reaction steps proposed is as follows: R1 and R3: The first steps must be the chemisorption of NOx (mostly in the form of NO than NO2) and O2 on the active sites, according also to Yamashita’s mechanism (19). As the present process under study is catalyzed by potassium, it is assumed that the presence of catalyst is going to influence these relevant steps (20, 21, 25). In fact, kinetic measurements involving studies in catalyzed gasification showed that the addition of an alkali catalyst enhances the steady-state amount of carbon-oxygen complexes, rather than changing the reaction pathway (49, 50). Thus R1 and R3 must be split into two steps in order to consider the role of the catalyst. These elemental steps could be described in nonstoichio-
metric terms as follows
O2 +* f * -O
(R1a)
Cf +* -O f *+ (CO)#
(R1b)
NOx +* f * -O+ 1/2N2
(R3a)
Cf +* -O f *+ (CO)#
(R3b)
where * represents the catalytically active alkali species of which the nature and composition is not fully known under our experimental conditions, and *-O represents the oxidized catalytic species before transferring oxygen to the carbon surface. It must be assumed that the direct NO and O2 attack to active sites via R1 and R3 (as directly described) could occur after enough carbon consumption and consequently with the appearance of newly active sites. Nevertheless, the fact that the NOx-carbon reaction using the catalyst-free sample (43), hardly proceeds, supports the idea that these pathways could contribute in some extent only after a certain degree of burnoff. R2: The direct desorption of carbon-oxygen complexes to form the corresponding reaction product (CO2) is an important step for all practical oxidizing carbon gasification processes (41, 45) and must be present in the mechanistic model. R4: In addition to R3 and R2, a possible route to N2 and CO2 formation could occur. This reaction does not consist of an elemental step but in a complicated sequence, where an interaction exists between the carbon-oxygen complexes and NO to produce the reaction products and leaving free active sites, Cf.
n2C + NOx + (CO)# f [CO....ON]# n2C
(R4a)
[CO......ON]# n2C f CO2 + 1/2N2 + n2Cf
(R4b)
On the other hand, the formation of very stable C(N) complexes, as described by Teng et al. (9) and Suzuki et al. (39), and experimentally evidenced by N imbalance throughout the reaction (51-53) is not observed under the current reaction conditions tested. According to previous studies in our laboratories (27), the following kinetic pathway described in the literature:
2Cf + NOx f C(O) + C(N) seems to be related to the NO direct attack to very “active positions” at high temperatures (higher than 400 °C). These type of positions can be identified as the leaving sites after evolution of determined oxygen surface complexes in the reaction atmosphere. As the heat treatment temperature involved in sample preparation increases, the activity toward NO and the estimated N-imbalance decreased (27). The relationship between carbon-oxygen complex populationlong-life nitrogen species (quantifiable by N-imbalance) was also reported by other authors (39). As mentioned in previous work (42), both CO and N2O formation was negligible under similar experimental conditions, and, therefore, these species are not considered in the proposed reaction mechanism. 3.1.2. Kinetic Equations. Some previous considerations must be exposed before introducing the equations associated to the proposed kinetic model: Simulation results show that the direct evolution of the carbon oxygen complexes (CO)# to CO2, -R2-, is not affected by the remaining C atoms in the carbon matrix. However,
the formation of Cf active sites does depend strongly on C concentration. This fact is a clear indication that the second reaction is not an elementary step but a lumped representation of a more complex mechanism, as previously commented. Evolution of (CO)# to CO2 through the fourth reaction is clearly dominated by NOx concentration with no influence of the presence of C. In this last case, the Cf formation does not seem to depend on free carbon concentration, except, maybe, in the final stages of decomposition (small concentration of C species), but this degree of detail is not considered in this model. Evolution of carbon-oxygen complexes, (CO)#, seems not to be directly affected by C concentration. Formation of (CO)#, according to the proposed mechanism, proceeds through Cf and therefore is indirectly related to C concentration. Therefore, the kinetic behavior of (CO)# is fundamentally determined by the presence of (CO)# and/or NOx. Taking into account previous considerations the rate equations can be written as follows
rC ) - n1k2(CO)# C - n2k*4PNOx(CO)# C
(1)
rCf ) - k*1CfPO2 + n1k2(CO)# C - k*3PNOx Cf + n2 k*4PNOx(CO)# (2) r(CO)# ) k*1CfPO2 - k2(CO)# + k*3PNOx Cf - k*4PNOx(CO)# (3) rNOx ) - k*3PNOx Cf - k*4PNOx(CO)#
(4)
where PO2 and PNOx are, respectively, partial pressures of O2 and NOx., k/1, k2, k/3, and k/4 are the kinetic constants. Partial pressure of oxygen can be considered constant throughout the experiment, and changes in oxygen concentration due to the formation of (CO)# surface complexes and evolution to CO2 are also negligible under our experimental conditions. For the set of equations proposed, oxygen partial pressure can be included into the kinetic constant k*1. NOx concentration can also be expressed in the most usual molar concentration. Therefore, previous kinetic equations can be rewritten as follows
rC ) - n1k2(CO)# C - n2k4 NOx(CO)#
(5)
rCf ) - k1Cf + n1k2(CO)# C - k3 NOxCf + n2k4NOx(CO)# (6) r(CO)# ) k1 Cf - k2(CO)# + k3 NOxCf - k4 NOx(CO)#
(7)
+ # rNOx ) - k+ 3 NOx Cf - k4 NOx(CO)
(8)
where NOx makes reference to NOx molar concentration. Note also that in the previous set of equations, kinetic constants k1, k3, k4 and k/1, k/3, k/4 are related by the following relationships:
k1 ) k/1PO2; k3 ) k/3RT;
k4 ) k/4RT
Dimensions of kinetic constants k1 and k2 are “(h-1)”. However, dimensions of kinetic constants k3 and k4 are “litre h-1 mol-1” (eqs 5-7). It is important to remark that these dimensions are not coherent with eq 8. This is the reason we + -1 have introduced k+ 3 , k4 (dimensions: h ). However, k3, k4 + and k+ , k are not independent. Note that there is a factor 3 4 (the NOx initial concentration) that relates k+ and k. For some species we are using mass fractions and for NOx we are using molar concentrations. To make dimensions coherent we VOL. 36, NO. 24, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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express NOx as a fraction (molar or mass), consequently + k+ 3 ) k3NOxo k4 ) k4NOxo
At this point it is important to remark the different mathematical treatment between species such as C, Cf or (CO)# and NOx. NOx is included in a flow stream that is continuously going through a bed of K/carbon pellets. The change of NOx concentration depends on the species present at a given moment and on the residence time of NOx in the reaction bed. However, the residence time is much smaller than the total time of the experiment (residence time less than a second against more than 48 h for the whole lifetime experiment). On the other hand, C, (CO)#, and Cf are forming or disappearing in the bed of the reactor, being their formation and disappearing rate much smaller than that corresponding to NOx. According to the whole considerations, the kinetic behavior for C, Cf, and (CO)# is that observed for a batch reactor, consequently
dC ) rC ) - n1k2(CO)# C - n2 k4 NOx(CO)# C dt
(9)
dCf ) rCf ) - k1Cf + n1 k2(CO)# C - k3 NOxCf + dt n2 k4 NOx(CO)# (10) d(CO)# ) r(CO)# ) k1Cf - k2(CO)# + dt k3 NOxCf - k4 NOx(CO)# (11) The kinetic of solid decomposition is usually expressed in terms of mass fraction, in this case, it is also a convenient representation. Throughout a lifetime test, we are continuously measuring CO2 in the output stream (besides NOx concentration), and we calculate the total weight loss by integrating the measured CO2 evolution with reaction time. Due to we do not know the exact nature of some active sites, it is more convenient to express the kinetic equations referred to these chemical species in term of mass instead of moles. It is important to note, as well, that previous considerations do not reduce the validity or generality of the kinetic study. If we are able to determine the exact chemical nature of each one of the active sites, there is a direct relationship between kinetic constants presented here and those expressed if the molecularity was exactly known. NOx reduction depends on the concentration of Cf and (CO)# active sites, on the residence time of NOx inside the reaction zone, and on the flow characteristics inside the reactor. Two ideal extreme situations are usually adopted: to suppose that the reactor behaves like a continuous stirred tank reactor (CSTR) or to suppose that the reactor behaves like a plug flow reactor (PFR). The actual flow is between these two extreme situations. However, when the residence time is small enough, the model flow tends not to be important. In fact the results obtained using CSTR or PFR models are almost identical. The mass balances for NOx are going to be presented assuming these two extreme situations: (a) Assuming CSTR behavior
Q[NOx - (NOx)0] ) VrNOx ) + # (- k+ 3 NOx Cf - k4 NOx(CO) )V (12)
where Q is the volumetric flow rate, and V is the reactor volume. Note that in previous equation there is not an accumulation term. Despite the fact that there is a variation of NOx concentration with time inside the reactor, it is due 5450
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to the change in Cf and (CO)# concentrations. However, taking into account that the residence time of NOx in the reaction zone is much lower than a second, Cf and (CO)# concentrations can be considered constant. Remember that the change of concentration of Cf and (CO)# takes place in a period of more than 48 h, while the change of concentration of NOx between the inlet and outlet concentrations takes place in less than a second. From previous equation, NOx concentration can be calculated as
NOx )
(NOx)0 1+
τ(k+ 3
# Cf + k + 4 (CO) )
(13)
where τ is the residence time calculated as the volume divided by volumetric flow rate. (b) Assuming PFR behavior + # d(QNOx) ) rNOx dV ) (- k+ 3 NOxCf - k4 NOx(CO) )dV (14)
where comments made for CSTR are still valid here. Under isothermal conditions, the volumetric flow can be considered constant The change in moles produced by CO2 formation or NOx reduction are negligible against the total flow, 620 cm3/min. Thus, the previous equation can be rearranged to
d(NOx) + # ) rNOx ) - k+ 3 NOxCf - k4 NOx(CO) dτ
(15)
Integrating eq 15 +C
NOx ) (NOx)0e[-τ(k3
+(CO)#)]
f+k4
(16)
The total mass at a given moment can be estimated from a mass balance
w ) mass fraction ) C + Cf + (CO)# + ash w0
(17)
where w is the mass at a given time, w0 is the initial mass of coal, and ash is the mass fraction of ash in the carbon sample. The resulting system is formed by three differential equations (9, 10, 11) and two algebraic equations (13 or 16) and (17). The system can be integrated in order to predict Cf, (CO)#, C, and NOx concentration evolution throughout the lifetime test for every sample. In the kinetic model six parameters (k1, k2, k3, k4, n1, n2) are unknown, besides the initial Cf and (CO)# active sites concentration. As the initial concentrations of Cf and (CO)# are very influenced by the sample characteristics and its preparation procedure, Cfo and (CO)#o can also be considered unknown parameters; however, they are constrained to a narrow range of feasible values. As it has been previously commented on the Experimental Section, during the lifetime tests, outlet concentrations of CO2 and NOx (NO+NO2) are continuously monitored. Therefore, it is possible to estimate the kinetic parameters by fitting experimental data to calculate results minimizing the sum of square errors
∑[(mass
min
exp(ti)
- masscal(ti))2 +
i
red red λ(NOxexp (ti) - NOxcal (ti))2] (18)
where the index set i makes reference to the experimental data; ti is the time at which the experimental value i was
FIGURE 1. (a-d) NOx reduction evolution and total weight fraction evolution from lifetime tests (symbols ) experimental data; solid lines ) model fitting): (a) A3-7.9; (b) A3-10.5; (c) A3-16.8; and (d) A3-21.0. measured; and mass makes reference to the total mass fraction calculated through eq 17. The subscript exp refers to experimental values, and the subscript cal refers to calculated values. NOxred is the reduced NOx. λ is a weight parameter introduced in order to force both terms in eq 18 to be of the same magnitude. Finally, it is worth mentioning that the total mass (experimental values as well as calculated ones) does not correspond exactly with the actual sample mass. Note that the weight loss is measured by integrating the CO2 in the output stream with time, and then transformed to an equivalent mass of C loss by the sample. However we are not taking into account the oxygen that the sample can retain on its surface as (CO)#, that will increase the total weight of the sample. As a measure of the mathematical quality of the adjust, a variation coefficient is introduced (54), defined as
V.C.(%) )
‚100 xNO.F. -P
(19)
where O.F is the objective function calculated according eq 18, N is the total number of experimental values, and P is the number of adjustable parameters. 3.2. Discussion about the Simulation Profiles and Kinetic Parameters Obtained. 3.2.1. Simulation Results. Figure 1(ad) represents the corresponding fittings (according to the kinetic model above developed) to the experimental data obtained from the lifetime tests, namely, NOx reduction capacity and total weight fraction evolution versus time for the set of potassium-containing coal pellets studied. Both parameters are expressed in a 0-1 scale. On the other hand, Figure 2(a-d) illustrates the corresponding predictions
(estimated by the model) of the evolution of the different carbon species under our experimental conditions: Cf, (CO)#, and C. For clarification purposes, Figure 3(a,b) collects the complete profile of NOx reduction and CO2 evolution, monitored along the lifetime test. The simulation results presented in the set of Figure 1 as solid lines show good agreement with the experimental data (symbols), indicating that an adequate description of the reaction data is obtained with the proposed model. Only important deviations arise at the beginning and the end of the lifetime tests. The origin of the deviations appreciated at the beginning of the lifetime can be ascribed to (sub)gasification conditions. In fact, the evolution of CO2 is very low in the first hours of the reaction, causing an increase population of carbon-oxygen complexes on the samples. This step presents intrinsic difficulty to be simulated by the model, due to O2 and NOx conversion which is occurring to some extent (depending on every sample) although very poor oxygenated-product evolution occurs. In this zone, the deviations are higher as the potassium content decreases on samples, attributed to higher activities for the low potassium content samples. On the other hand, deviations are also appreciated at the end of the lifetime, the reasons for which can be ascribed to the fact that the model fails in simulating reaction data at very low carbon contents and, consequently, very high ash contents. Different effects such as O2 chemisorption on determined ashes can occur in these conditions and have been described in the literature (55). For this reason, simulations were represented up to a certain reaction time, close to the end of the lifetime test, as deduced from comparisons with Figure 3(a,b). VOL. 36, NO. 24, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. (a-d) Predictions of the corresponding carbon species together with the experimental total mass fraction from lifetime tests: (a) A3-7.9; (b) A3-10.5; (c) A3-16.8; and (d) A3-21.0. The interpretation of Figure 2 must be as follows: the sum of every carbon species in addition to the ash content provides the total mass fraction (thus fulfilling the mass balance). Regarding the profiles collected in Figure 2, the symbolfree lines correspond to the evolution of the total mass fraction (representative of carbon conversion) for the samples. The Cf appearance along the reaction is predicted to be very low if compared with the evolution of carbon-oxygen complexes formation. This prediction is consistent with the idea that Cf species are highly reactive and can be defined as short-life positions (19, 39, 41, 45). Actually, under our experimental conditions, these active sites will be fastly transformed to (CO)#, of much longer life. The Cf/(CO)# ratio is low for all the samples, proving that the gasification behavior is dominated by the slow desorption of relatively stable surface complexes. The highest value of Cf population is reached by the sample A3-7.9 (a maximum value of 0.04 is achieved at 10 hours, expressed as weight fraction). This point coincides with a high CO2 peak, without the presence of important NOx reduction, that as previously pointed out, could correspond with an important contribution of O2 direct attack to these Cf positions (46). Regarding the (CO)# profiles, the maximum in (CO)# population is achieved after 16 h of reaction for sample A3-7.9. Conversely, the rest of the samples (presenting more similar features regarding NOx conversion and CO2 evolution) exhibit the maximum in (CO)# formation around 34-36 h coincident with the zone of maximum NOx activity. As a summary, the predictions made by the kinetic model concerning evolution of the different species involved in the reaction have physical significance and show good agreement with the overall reaction schemes and with the general acceptable conclusions about the NOx reduction process by 5452
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carbon that other authors have made from experimental observations (19, 25, 39). 3.2.2. Kinetic Parameters Obtained. At this point, it is important to remark that no data of kinetic parameters involved in the elemental steps are available in the literature concerning the catalyzed NOx reduction by carbon in the presence of oxygen; therefore, comparisons are not possible in this sense. In Table 1 the estimated reaction rate constants of the elementary steps (k1, k2, k3, k4) for the set of samples studied, together with predictions of the initial concentration of active sites (Cfo), carbon-oxygen complexes (CO)#, and the stoichiometric coefficients (n1 and n2 that appear in R2 and R4, respectively), are listed together with the objective and the variation coefficient. Due to the corresponding units, only k1 versus k2 and k3 versus k4 are comparable in absolute values. k1 is one magnitude order higher than k2, showing that the step of oxygen chemisorption (via the catalyst or via direct attack to Cf positions) presents a higher value of rate constant than that corresponding to the evolution of CO2 by direct decomposition of the carbon-oxygen complexes (R2). The value a little higher of k2 for A3-7.9 with regard to A3-10.5 and A3-16.8 is tempting to assign to the fastest CO2 evolution presented by these samples. On the other hand, k3 and k4 are similar in magnitude, presenting differences only the sample A3-7.9 (being k4 one magnitude order higher than k3). To plot the kinetic rate constants as a function of the potassium content on samples, those ones have been normalized and corresponding results have been collected in Figure 4. As clearly appreciated, potassium loadings mainly
FIGURE 4. Representation of the normalized kinetic rate constants (corresponding to the different elemental steps proposed) and the values of rmax as a function of the potassium content.
FIGURE 3. NOx reduction percentage (a) and CO2 evolution (b) during lifetime tests.
FIGURE 5. Representation of Cfo+(CO)#o as a function of the carbon surface percentage for the different samples.
TABLE 1. Kinetic Parameters for the NOx-Carbon Reduction Process Obtained by the Simulation
5 shows that a correlation exists for the set of samples studied. Obviously, the higher the surface potassium, the lower the carbon concentration for the samples investigated.
sample (h-1)
k1 k2 (h-1) k3 (l h-1 mol-1) k4 (l h-1 mol-1) n1 n2 (CO)#0 Cf0 objective (λ)5) V.C. (%)
A3-7.9
A3-10.5
A3-16.8
A3-21.0
1.241 0.0821 3.26‚107 3.50‚108 4.36 1.00 0.0824 0.0054 0.0706 4.33
1.178 0.0385 2.57‚108 4.53‚108 4.28 2.00 0.0487 0.0141 0.0655 3.36
1.715 0.0611 5.88‚108 9.05‚108 3.88 2.93 0.0212 0.0020 0.0221 1.79
2.439 0.121 9.72‚108 2.12‚109 3.46 2.63 0.0019 0.0014 0.0549 2.86
affect the variation of k3, being the rest of constants less influenced. This issue could be the key when trying to explain the high selectivity of this type of samples toward NOx reduction against oxygen combustion as potassium content increases (46). Trying to deepen into this idea, it has been included in Figure 4 (2Y-axis) the values of the maximum reaction rate for NOx reduction, rmax, which is defined as the maximum ratio of NOx reduced extracted from the lifetime test for every sample, and expressed as µmol NOx reduced/gsamples. The lines that join the corresponding points describe parallel trends and confirm the existing relationship between the parameters represented. Other species predicted by the model such as the initial concentrations of active sites and carbon-oxygen complexes, Cfo and (CO)#o, respectively, have been treated to correlate with some features of the samples. It can be stated that the concentration of these species mainly depend on the surface carbon concentration on samples, determined by XPS. Figure
CO2 has been confirmed to be a primary product in NO gasification (41). This reaction product is postulated to evolve mainly from direct desorption of unstable complexes (as proposed in R2) and the interaction between the surface complexes and the gaseous reactant (as proposed in R4). Therefore, these general assumptions accepted in the literature (41) are integrated as the routes to CO2 release and are considered as plausible by means of the present simulation. Finally, it should be mentioned other more complicated parameters to interpret (also predicted by the model): the stoichiometric coefficients n1 and n2, accompanying Cf in the elemental steps R2 and R4, respectively. Although the mechanisms involved in (CO)# desorption (via both elemental steps) to yield CO2 (of great importance for the understanding of the coefficients obtained from this modeling) are not completely understood, some observations can be made about this issue. Intuitively, if CO2 release by direct desorption of oxygenated complexes (via R2) proceeds by decomposition of lactone type-complexes, the area of surrounding atoms affected by this decomposition will be greater than that derived from CO2 desorption by interaction of NO (via R4) with carbonyl-type complexes, for example. These expected trends correspond with the higher values of parameter n1 with regard to n2. Nevertheless, more reliable asseverations related to this point need further study.
Acknowledgments This study was made possible by financial support from CICYT (PB98-0983). VOL. 36, NO. 24, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Received for review May 23, 2002. Revised manuscript received September 18, 2002. Accepted October 2, 2002. ES025823Y
