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Ind. Eng. Chem. Res. 2006, 45, 6458-6467
Kinetic Modeling of Coke Oxidation of a Ferrierite Catalyst Tuomo J. Keskitalo* Helsinki UniVersity of Technology, Department of Chemical Technology, Laboratory of Industrial Chemistry, P.O. Box 6100, FI-02015 TKK, Finland
Kyo1 sti J. T. Lipia1 inen Neste Oil Corporation, Technology Centre, P.O. Box 310, FI-06101 PorVoo, Finland
A. Outi I. Krause Helsinki UniVersity of Technology, Department of Chemical Technology, Laboratory of Industrial Chemistry, P.O. Box 6100, FI-02015 TKK, Finland
Kinetic models describing coke oxidation were derived for purposes of designing a catalyst regeneration unit and to gain information on coke oxidation kinetics. The coke was formed during an alkene skeletal isomerization reaction on a ferrierite catalyst. Experiments were performed according to the temperature-programmed oxidation technique at several oxygen concentrations and heating rates. The parameters of the models were estimated by nonlinear regression. A power-law model with parametrized order of oxygen concentration described the experimental results adequately. Three other successful models, which were based on assumed reaction mechanisms, shared two main characteristics: the formation of a reactive oxygen intermediate in a fast equilibrium reaction, and the formation of CO and CO2 from one or more common precursors. All estimated parameters of the models were in a physically meaningful range. 1. Introduction Isoalkenes are used in oil refining as reactants for fuel components such as tert-amyl methyl ether (2-methoxy-2methylbutane), methyl tert-butyl ether (2-methoxy-2-methylpropane), ethyl tert-butyl ether (2-ethoxy-2-methylpropane), and isooctane (2,2,4-trimethylpentane). Isoalkenes can be produced from n-alkenes in alkene skeletal isomerization processes. The skeletal isomerization of butenes is a difficult reaction to catalyze.1,2 Present catalysts include phosphoric acid, metal halides, alumina, halogenated alumina, and aluminosilicates. Zeolites have gained interest as environmentally friendly catalysts for these processes. Catalysts that are utilized in the isomerization process deactivate relatively fast.1,2 Deactivation is mostly due to coke formation on the catalyst. Typically, the coke consists of polymers and aromatic hydrocarbons, the exact composition of which varies with the process parameters. The deactivating effect of coke formation is also significant in other industrial processes, such as fluid catalytic cracking and catalytic reforming.3 The substantial formation of coke means that catalyst regeneration is an essential part of any industrial-scale process. Catalyst activation is achieved by burning off the coke with air, with the subsequent production of carbon oxides and water. Because of the high exothermicity of the combustion reactions, a tight control is required over the regeneration process to prevent damage to the catalyst or the regeneration unit. A kinetic model, suitable for the design of an industrial process, must thus describe the rates of combustion. The composition of coke is complex and the number of possible intermediate oxidation reaction steps is many. The nature of coke, as well as the catalyst, affects the coke oxidation. Therefore, case-specific study is required to model coke oxidation kinetics.4 Temperature-programmed oxidation (TPO), * To whom correspondence should be addressed. Fax: +358-9-451 2622. E-mail address:
[email protected].
which is a well-known transient analysis technique,5,6 often has been used in deactivation studies as a qualitative coke characterization tool, but only rarely it has been used in kinetic analysis.3 However, TPO is suitable for studies on kinetics, as long as experimental conditions are selected so that the experiments are conducted in the kinetically controlled region. A system that is free of mass- and heat-transfer limitations is preferred; however, if concentration or temperature gradients occur, they must be taken into account in the model. Because the output flow can be determined in a short time, a temperature-programmed experiment will easily produce several hundred measurements (an analysis of output flow corresponding to a reactor temperature) over a wide temperature range. Because reaction rates are often highly dependent on temperature, TPO is a particularly suitable technique for kinetic modeling. In addition, the large number of measurements adds to the reliability of the parameter estimates. Because kinetic models have a tendency to be nonlinear, with respect to parameters, robust nonlinear regression is generally suitable for parameter estimation. TPO has occasionally been applied to extract kinetic information. Gayubo et al.7 studied coke combustion from a silicaalumina catalyst via a thermogravimetric method. However, this approach does not distinguish the carbon oxides. In an improvement to the analysis of TPO responses, Fung and Querini8 added a methanator unit to convert carbon oxides to methane, which was then detected with a flame ionization detector. Fung and Querini showed that the methanator is highly sensitive and appropriate for the quantitative analysis of carbon oxides in TPO experiments. Lipia¨inen et al.9 developed the methanator analysis further by incorporating a CO2 trap in a split stream methanator unit, thereby obtaining quantitative analysis of the two carbon oxides separately. Coke oxidation rates have been modeled with various kinetic expressions. Querini and Fung10 applied a power-law model to describe their TPO experiments, and their calculations showed
10.1021/ie060521g CCC: $33.50 © 2006 American Chemical Society Published on Web 08/12/2006
Ind. Eng. Chem. Res., Vol. 45, No. 19, 2006 6459
Figure 1. Setup of equipment for temperature-programmed experiments.
that heterogeneities in coke morphology may result in complex, multimodal thermograms. Instead of morphology, complexities such as bimodal thermograms in a TPO experiment may be due to reaction kinetics. For example, several types of active sites result in multimodal thermograms. Li and co-workers11,12 applied the TPO technique to study the coke oxidation of cracking catalysts. They have also studied oxidation of charcoal and graphite.13 The kinetic model of Li et al.11 included surface complex species (carbon-to-oxygen ratios of 1:1 and 1:2), formed by the reaction of carbon with oxygen. According to their models, the surface complexes are essential intermediates in the formation of carbon oxides. In a study of the kinetics of coke oxidation from a cracking catalyst, Kanervo et al.14 described their experimental data with a power-law model and two other models, incorporating a surface complex. The aim of this work was to study coke oxidation kinetics of a ferrierite catalyst deactivated in an alkene isomerization reaction. The focus was on carbon oxidation, where products were analyzed with a sensitive methanator setup. In a related work,15 we consider the oxidation of both coke carbon and hydrogen as a whole. However, the high quality of the experimental data of carbon oxides, which allows a detailed kinetic analysis of the carbon oxidation reactions to be performed, calls for a separate study. We derived and tested several models that described carbon combustion kinetics. The experiments were performed using the TPO technique, at several heating rates and oxygen concentrations, to obtain a sufficiently wide application range for the models. Parameters of the models were estimated by nonlinear regression. The method was applied to the data of a total of 20 TPO experiments. 2. Experimental Section Temperature-programmed desorption (TPD) and oxidation experiments were conducted in a novel modification of previously described equipment.9 The modified equipment, which is depicted in Figure 1, consisted of a glass-tube reactor furnished with a fast small-sized gold-film furnace (Neste Oil Corporation), a temperature controller (model KS40, Phillips), mass-flow controllers (Brooks), six-way valves (Valco), and a gas chromatograph (Agilent 5890).
The catalyst sample (with a mass of ∼10 mg) was loaded in the middle of the quartz glass reactor tube (2 mm diameter), over the quartz wool layer. Gas feed was introduced to the reactor, and the flow rate (30 cm3 min-1, NTP) was controlled with a mass-flow controller. If the regeneration was conducted with high oxygen concentrations (over 2 vol % on carrier gas), the sample flow was diluted in a split-splitless injector to prevent deactivation of the methanator catalyst. The product flow was split into two streams, and CO2 in one of them was trapped into ascarite. Carbon oxides were transformed to methane over a Ni/γ-Al2O3 catalyst, and the methane was detected with flame ionization detectors. The amount of CO2 was calculated from the difference in the response of the two detectors. Quantifying of the results was based on external calibration with calibration gases (0.99 vol % CO and 1.99 vol % CO2, AGA) at ambient temperature. Lag times between the reactor and detector were determined in pulse experiments, and the differences were taken into account in the calculations. The ferrierite catalyst (mean particle diameter of 120 µm) was deactivated in a 21-h skeletal isomerization run in a pilotscale reactor operating at 285 °C and 20 kPa.16 The feed to the pilot reactor consisted of alkenes ranging from C5 to C7. The experiments were conducted as follows. The coked catalyst sample was pretreated for 12 h in a helium gas stream at 200 °C in situ, to remove any humidity adsorbed during transportation. The catalyst was then treated via the TPD technique from ambient temperature to 500 °C under a helium gas flow and a heating rate of 10 °C/min. Heat treatment is known to change the nature of the coke,17 and, thus, the coke on the ferrierite was changed during this treatment. In this case, TPD was performed to obtain coke properties similar to those in the pilot reactor, which are needed to simulate the regeneration and homogenize the sample. The catalyst was maintained at 500 °C until the base output signal levels were achieved. The catalyst was then cooled to 200 °C before execution of TPO with He/O2. TPO was conducted up to 850 °C. The pressure was within the range of 1.1-1.4 bar for all experiments. Calibration of carbon oxides was performed after each experimental run. The total carbon content of the coked catalyst was also measured, using a model CHN-2000 elemental analyzer (LECO). Experiments were conducted at heating rates of 5, 10, and 15 °C/min. The minimum heating rate was selected to avoid low sensitivity and time-consuming experiments, and the maximum heating rate, to avoid heat- and mass-transfer limitations.10 Oxygen concentrations of 2, 5, 10, and 21 vol % of O2 in the feed were utilized. In total, the data from 20 TPO experiments were applied in the parameter estimation (Table 1). Three more separate experimentssat 2 vol % of oxygen in feed and at the heating rate of 10 °C/minswere conducted to calculate the cross-validation error (CVE) of the kinetic models. Several kinetic models were tested against the results of the TPO experiments. Parameters of the models were estimated by nonlinear regression method. The optimization was aimed at minimizing the sum of squared residuals over N experimental (exp) and calculated (calc) amounts of carbon oxides yCOx (mol gcat-1 s-1) in the reactor outflow, which is defined as the molar flow of the component out of the reactor normalized by catalyst mass:
SSR )
∑N (yCO ,exp - yCO ,calc)2 x
x
(1)
The residual root-mean-square error (RRMS), as well as the CVE values, used in the comparison between the models, is
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Table 1. Experimental Conditions and Results of TPO Experiments Applied in Kinetic Modeling experiment number
cO2 [vol %]
heating rate [°C min-1]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2 2 5 5 5 10 10 10 21 2 2 5 5 10 10 10 21 2 5 10
5 15 5 10 15 5 10 15 10 5 15 10 15 5 10 15 10 15 15 15
average value
carbon content [wt %]
CO/CO2 ratio
3.49 3.01 3.27 3.23 3.38 3.38 3.53 2.96 3.08 3.00 3.19 3.30 3.37 3.18 3.32 3.38 3.65 3.38 3.51 3.01
1.99 1.78 1.57 2.11 1.77 1.84 1.95 1.94 1.83 2.55 2.55 2.12 2.13 2.00 2.35 2.14 1.97 2.82 1.96 2.22
3.3 ( 0.2
2.1 ( 0.3
defined as xSSR/N. Approximately 100 measurements per thermogram for each oxide were applied in the modeling. The concentration of carbon on the catalyst prior to TPO was determined by integration of experimental CO and CO2 thermograms for each TPO experiment. GNU Scientific Library (GSL) version 1.4 functions were utilized in regression.18 The Nelder-Mead Simplex and Levenberg-Marquardt optimization methods were applied. Where needed, derivatives were evaluated numerically by central differences. The embedded fourthorder Runge-Kutta Cash-Karp method was applied for models that consisted of ordinary differential equations, and the routine RADAU5 by Hairer and Wanner19 was applied for systems of differential algebraic equations. For models that exhibit strong correlations between parameters, at least two distinct sets of initial values for parameters were tested for convergence toward a representative minimum. 3. Results and Discussion 3.1. General Remarks. Table 1 presents the experimental conditions of TPO experiments. Repetitions specified in Table 1 (experiments 10-20) were conducted to minimize the effect of experimental errors on parameters. Because the experimental errors were largest at the highest heating rate (15 °C/min), more repetitions at this heating rate (experiments 18-20) were conducted. The repetition of experiment 3 (5 vol % of oxygen in feed, heating rate of 5 °C/min) was discarded afterward, because of an apparent equipment malfunction. The shapes of the thermograms (Figure 2) are almost smooth, with a single peak. The shapes of the CO and CO2 thermograms in each experiment are very similar, which suggests that the formation mechanisms for the two oxides have a reaction step in common. It is noteworthy that CO formation dominates even at high oxygen concentrations. A possible reason for this is that the catalytic properties or the structure of the ferrierite affects the concentration of intermediate species essential to the overall oxidation reaction and, thus, hinders the formation of CO2. Minor fluctuations were detected at the thermogram peaks, especially at high heating rates. The fluctuations were correlated with variations in the temperature ramp during the experiment, which likely were due to the temperature controller adapting to the highly exothermic reactions that are occurring in the reactor.
The calculations took these variations into account by following the measured temperature with linear interpolation between the measurements. Figure 2 shows that there are variation in results, especially at 15 °C/min, which are due to experimental errors. For example, small deviations in pulse experiments applied in calibration result in slightly different scale of a TPO thermogram. A shift in the position of the thermogram may occur because of variations in the exact location of the thermoelement inside the reactor. The mean value of the initial carbon content of the catalyst before the TPO step, calculated by integration of the thermograms, was 3.3 ( 0.2 wt % (gC/gcat). Adding the mean total carbon content from the TPD step (0.8 ( 0.1 wt %) gives an initial carbon content of 4.1 ( 0.3 wt %. The carbon content of 4.3 wt %, determined with the LECO elemental analyzer, agrees with the calculated value. The CO to CO2 ratio of all experiments together was 2.1 ( 0.3. The ratios exhibited no clear trend as a function of either oxygen concentration or temperature ramp. 3.2. Reactor Model. The microreactor system was examined for mass- and heat-transfer effects to choose a proper reactor model for the calculations. A relatively high volumetric flow rate (V ) 30 cm3/min, NTP) and small volume of the packed microreactor gas phase (estimated value of Vg ) 0.08 cm3 for 10 mg of catalyst) give a space time of ∼0.2 s. The short space time, in relation to the observed reaction rates, suggests that the reactor gas phase can be considered homogeneous, in regard to temperature and concentrations. Kinetic modeling requires that the experimental conditions are in the kinetically controlled regime. Because the catalyst is highly porous, mass transfer could limit the evolution of oxides. Thus, the Weisz-Prater criterion20 was calculated to test for the effect of internal diffusion, according to
CWP )
-rO2,obsFcRp2 DecO2
(2)
where rO2,obs is the observed oxygen reaction rate, Fc the bulk density of the catalyst, Rp the particle radius, De the effective diffusion coefficient, and cO2 the gas-phase oxygen concentration. To make a worst-case estimate, we applied values that maximize CWP. The values were rO2,obs ) 3.0 × 10-6 mol gcat-1 s-1, Fc ) 500 gcat dm-3, Rp ) 6 × 10-5 m, De ) 10-6 m2/s (estimated order of magnitude), and cO2 ) 2.3 × 10-4 mol dm-3, and the value of CWP was 0.03, ,1. Evidently, internal diffusion does not affect the observed reaction rate. The gas-phase oxygen concentration for the experimental conditions of 15 °C/min and 2 vol % was calculated to estimate the amount of oxygen consumed during the TPO experiment. The maximum amount consumed in the reactions was 6 vol % of the gas-phase oxygen. Because the reactions do not change the gas-phase oxygen concentration substantially, the molar balance of O2 was not taken into account in parameter estimation, and oxygen gradients in the reactor were assumed insignificant. The concentration of oxygen in the gas phase was calculated with the ideal gas law. The maximum intraparticle temperature gradient between the bulk gas phase and particle center,20 because of exothermic reactions, was studied with the equation
∆Tmax )
-∆HrDecO2 λ
(3)
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Figure 2. Results of selected temperature-programmed oxidation (TPO) experiments. Bold lines denote the CO responses (upper curves) and narrow lines the CO2 response (lower curves). Solid, dot-dashed, and dashed lines denote different experiments.
The average reaction enthalpy ∆Hr was assessed to be -200 kJ/mol, and the oxygen concentration was cO2 ) 3.6 mol/m3. The heat conductivity of fused silica21 (λ ) 1.8 J s-1 m-1 °C-1) was applied in the absence of a measured value. These values give a maximum temperature difference of ∼0.4 °C, which suggests that intraparticle temperature gradients can be ignored. The heat balance of the entire packed bed was studied with the equation
dTbed ) rCW∆Hr + Fcp(Tin - Tbed) dt
Cp,bedW
(4)
which takes into account the catalyst heat capacity and assumes that the reactor outlet temperature equals the catalyst bed temperature (Tbed). The inlet temperature (Tin) was assumed to be equal to the measured temperature. The specific heat capacity of the catalyst, Cp,bed ) 1.05 J g-1 °C-1, was utilized. F denotes the total molar flow rate of gas, and rC is the reaction rate for carbon oxidation. The specific heat capacity of helium,21 Cp ) 20.8 J mol-1 °C-1, was applied. Calculation of eq 4 for an experiment conducted at 15 °C/min and 10 vol %, and with a catalyst mass of W ) 9.7 mg gave a maximum difference between the inlet temperature and bed temperature of 5 °C. The value is consistent with the slight fluctuations in temperature at the thermogram peak maxima at high heating rates. However, the thermocouple was located immediately after the reactor, so that the measurements should approximate actual temperatures well. Because the experiment utilized in the calculation represents the worst case, in regard to heat gradients, we conclude that the reactor can be treated as thermally uniform. Because the oxygen concentration in the reactor is effectively uniform and the coke oxidation is dependent on the concentrations of coke and oxygen, there should be no significant concentration gradients of coke along the reactor length. Because the previously described calculations showed that the space time is small, in relation to the observed reaction rates, internal diffusion is not a limiting factor and no significant heat or concentration gradients are present in the reactor, the microreactor was modeled as gradientless. The mass balances for the
molar amounts of oxides (nCOx) in the reactor gas phase are, accordingly,
dnCOx dt
) rCOxW -
VnCOx
(for x ) 1 or 2)
Vg
(5)
where Vg is the reactor gas-phase volume and rCOx is the formation rate of oxide COx (mol gcat-1 s-1). The second term on the right-hand side of eq 5 represents the outflow and is related to the amounts applied in minimizing eq 1:
yCOx,calc )
VnCOx
(6)
V gW
3.3. Kinetic Models. For the overall oxidation reactions
1 C + O2 f CO(g) 2
(7)
C + O2 f CO2(g)
(8)
we tested several kinetic models to describe the reaction rates in TPO experiments. All the reaction rate constants ki for the reaction i, unless otherwise stated, were calculated with the reparametrized Arrhenius equation
ki ) kref,i exp
[ (
-Ei 1 1 R T Tref
)]
(9)
to decrease the correlation between the Arrhenius parameters. The parameters in eq 9 are the pre-exponential factor (the rate constant at the reference temperature kref,i) and the activation energy (Ei). The reference temperature was Tref ) 850 K. All reaction equations of the given models are stoichiometric, and mass balances not explicitly given were calculated by summing all reaction rates of steps that involve the particular species. In reporting the results, we state correlations for all parameter pairs exhibiting correlation coefficients over the absolute value of 0.95, calculated from the covariances estimated at the given
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Table 2. Estimated Parameter Values and Corresponding 95% Confidence Intervals, Residual Root-Mean-Square Values, and Cross-Validation Errors for Models 1 and 2 parameter
model 1
model 2
(6.6 ( 0.5) × 10-2 dm3 mol-1 s-1 127 ( 2 kJ/mol 0.59 ( 0.02 (1.7 ( 0.3) × 10-2 dm3 mol-1 s-1 99 ( 3 kJ/mol 0.50 ( 0.03
kref,CO ECO RO2,CO kref,CO2 ECO2 RO2,CO2 kCO2 kref,X* EX* RO2,X* RRMS cross-validation error, CVE a
115 nmol gcat-1 s-1 111 nmol gcat-1 s-1
0.44 s-1a 124 ( 3 kJ/mol
0.21 s-1a (8.1 ( 0.5) × 10-2 dm3 mol-1 s-1 118 ( 1 kJ/mol 0.56 ( 0.01 118 nmol gcat-1 s-1 102 nmol gcat-1 s-1
if the carbon molecules are located as a monolayer. This value is not contradictory to the hypothesis of a thin coke layer. Model 1 describes the results of the TPO experiments. However, because of the empirical nature of the model, its parameters cannot be directly assigned to any specific reaction step. To study the oxidation kinetics on a level deeper than model 1 allows, we derived models that are based on assumptions of the reaction mechanism of coke oxidation. Such models were hoped to reveal information of the overall mechanism of coke oxidation. As an intermediate stage toward these moredetailed models, model 2 incorporates an unspecified intermediate surface complex X*. The reactions and corresponding rate expressions of model 2 are +O2
(rX* ) kX*[C]cO2RO2,X*)
C 98 X* +O2
X* 98 CO(g)
Large confidence interval.
+O2
optimum values of parameters. If the absolute value is over 0.99, the correlation is described as high, strong, or severe. Model 1 for reactions 7 and 8 is a power-law model that is described by the equations
d[C] ) -(rCO + rCO2)W dt rCOx ) kCOx[C]cO2RO2,COx
(for x ) 1 or 2)
(10) (11)
The order of the oxygen concentration RO2,COx is a parameter in the model. The model exhibited high correlations between the order parameters and the pre-exponential factors of the two oxides. Despite these high correlations, convergence to a unique optimum was not prevented, as was shown by the application of different initial values for parameters. Model 1 fits the experimental data well (RRMS ) 115 nmol gcat-1 s-1). Model 1 is used as a reference later when the model fits are discussed or compared. Optimized parameters are presented in Table 2. A modification of model 1 that included the order of the coke carbon concentration as an additional parameter in eq 11 gave the same model fit (RRMS ) 115 nmol gcat-1 s-1). However, both parameters approached unity and, therefore, were unnecessary. In another modification, the order of oxygen was forced to unity, and the coke order was the only order parameter. This model resulted in an order of carbon of ∼1.5 for both rate expressions, but the model fit was poor (RRMS ) 168 nmol gcat-1 s-1). As a conclusion, model 1 is the simplest power-law model that describes the experimental data. The coke order in the power-law model may reflect the coke morphology.10 The order of unity seems to fit the experimental data best, which suggests that, on average, all coke is accessible to the oxidation reactions at all times and the combustion occurs evenly throughout the catalyst particle. The kinetic modeling thus suggests that the coke was located on the catalyst as thin layers. We made a crude estimation of the maximum coke coverage to assess the possibility of having a near monolayer of coke on a catalyst with 3.3 wt % carbon. The catalyst surface area given by the manufacturer is 320 m2/gcat. Assuming a carbon-carbon bond length22 of 1.5 × 10-10 m, and that one carbon molecule occupies an area equal to the squared bond length, we obtain an area of 2.25 × 10-20 m2 for the area covered by one C atom. Calculating the number of C atoms on one gram of catalyst as 1.65 × 1021 gcat-1, we obtain a coverage of 12% on the catalyst
X* 98 CO2(g)
(12)
(rCO ) kCO[X*])
(13)
(rCO2 ) kCO2[X*])
(14)
This model also gave a good fit (RRMS ) 115 nmol gcat-1 s-1). Initially, the order of the oxygen concentration was included as a parameter in all three reaction steps; however, for reactions 13 and 14, the order approached zero without deterioration in the model fit. The activation energy of reaction 14 approached values of
