Ind. Eng. Chem. Res. 2003, 42, 2507-2515
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Catalytic Dry Reforming of Methane in a CREC Riser Simulator Kinetic Modeling and Model Discrimination Tarek El Solh,† Kai Jarosch,‡ and Hugo de Lasa*,§ Chemical Reactor Engineering Centre, Faculty of Engineering, University of Western Ontario, London, Ontario, Canada N6A 5B9, Imperial Oil Research Centre, Sarnia, Ontario, Canada N7T 8C8, and Velocys, Plain City, Ohio 43064
The present study deals with catalytic dry methane reforming in a fluidized Chemical Reactor Engineering Centre (CREC) riser simulator and with the modeling of the obtained results using several kinetic rate equations. Experiments were designed and developed using a statistical criterion that optimizes the effort expended for model discrimination. From the eight models originally considered, six of them were initially found to fit the data. However, only one of them was later on retained using model discrimination. Results of the study show that both the adsorption of methane and the adsorption of carbon dioxide play an important role in determining the observed rate of the methane dry reforming reaction and suggest that methane and carbon dioxide adsorb on different sites of the catalyst. The study is also valuable in providing a sound rate equation applicable in the context of a Catforming process under current development at the CREC of the University of Western Ontario. Introduction Natural gas is a large energy resource, with the former USSR and the Middle East having nearly 70% of the world’s known natural gas reserves.1 The remainder of natural gas is stranded or found in remotely located gas reserves, or associated with crude oil petroleum production, or larger gas reserves that are not currently being economically exploited because of excessive content of CO2. Because of its relative inefficient use where it is being produced, natural gas is frequently flared on a large scale. This not only represents a wasted energy resource but also contributes to global warming, with carbon dioxide being produced in very large quantities.2 In steam reforming, the highly endothermic reaction involves steam being reacted catalytically with natural gas (primarily methane) forming synthesis gas, CH4 + H2O T CO + 3H2. The H2/CO ratio is close to 3, making it very desirable for hydrogen production applications but too high to be suitable for methanol and FischerTropsch syntheses. An attractive alternative is to replace steam with carbon dioxide in the reforming reaction. This alternative is highly selective to CO and produces a lower, much more favorable H2/CO ratio suitable for the Fischer-Tropsch synthesis of long-chain hydrocarbons. Recently, this reaction, even if being more endothermic than the more conventional steam reforming, has attracted important interest as an effective means for CO2 consumption. During the past decade, there has been increasing global concern over the rise of anthropogenic CO2 emissions into the earth’s atmosphere, estimated to be around 2 × 1015 g of carbon per year.3 Reforming with CO2 has the advantage of taking two greenhouse * Corresponding author. Phone: 519-661-2144. Fax: 519661-3498. E-mail:
[email protected]. † Imperial Oil Research Centre. ‡ Velocys. § University of Western Ontario.
gases CH4 and CO2, which are relatively inexpensive because of their natural abundance, and converting them into economically viable products that do not contribute to the greenhouse gas content of the atmosphere, CH4 + CO2 T 2CO + 2H2. CO2 is a byproduct of methane steam reforming, whereas carbon dioxide reforming of methane has the potential to reduce the amounts of these gases in the atmosphere. Dry reforming of methane is particularly useful at remote natural gas fields containing large quantities of CO2, as in the case of Natuna Island, Indonesia, with an estimated 5.99 trillions of cubic meters of natural gas reserves, containing 71% CO2, 28% methane, and other light hydrocarbons.4 The Catformer concept, proposed at CREC-UWO, is expected to bring possible solutions to overcome existing constraints affecting the performance of the traditional steam reformers such as diffusional limitations and heat-transfer and mechanical constraints.5 In the Catformer the reactant gases are contacted with the hot regenerated fluidizable catalyst, and the resulting gas-solid suspension enters the downflow section of the Catformer.5 In the Catformer, the first section of the reactor contributes mainly to the NiO reduction to Ni and to the initial development of the methane reforming reaction far from equilibrium. Knowing that the NiO reduction takes place at 450 °C,6 the reduction of NiO, with the bottom of the riser at 750 °C, will occur almost instantaneously. Moreover, as the suspension flows down the tube(s), the reforming and water gas shift reactions become the dominant chemical transformations. Although the Catformer is to be operated under conditions unfavorable to carbon formation (coke), coke will be formed. This is especially true in the case of dry reforming, where the propensity for coke formation is higher than that in the case of steam reforming. Therefore, the catalyst or some fraction of the catalyst will require periodic regeneration, with this regeneration involving coke combustion. As a result, the metallic component of the catalyst will be oxidized, and alto-
10.1021/ie020749d CCC: $25.00 © 2003 American Chemical Society Published on Web 02/14/2003
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Figure 1. Schematic flow diagram of the experimental setup showing the major components and automated valves.
gether catalysts will be cycled continuously between oxidized and reduced states. In this respect, the specific nature of the selected Catformer design involving two circulating fluid beds, one for the dry reformer and the other for the catalyst regeneration, will help in the transport of the catalyst between units and allow for a period of catalyst regeneration. One potential catalyst candidate for such a dry reforming process is a fluidized catalyst involving nickel impregnated on zeolites.7 Development of a suitable kinetic model for such a catalyst is of primary interest in the context of the development of the Catformer process for methane dry reforming. Experimental Methods In the context of this study, catalyst preparation involved various steps including catalyst impregnation, followed by thermal decomposition, calcination at 560 °C under air atmosphere, and catalyst activation with NiO reduction. A total of 20 wt % nickel-loaded ultrastable Y zeolites (USY) was pelletized for use under fluidization conditions. Additional details about the methods for both catalyst impregnation and catalyst preparation are reported by El-Solh et al.7 Prepared catalysts were characterized using several surface science techniques:8 (a) hydrogen uptake, reduction temperature, and fraction of reducible metal (TPR), (b) metal dispersion, redispersion, and metal crystal size (chemisorption), (c) crystal structure identification and crystallinity (XRD), (d) specific surface area (BET), (e) porosimetry (mercury porosimetry), (f) particle size and shape (SEM), and (g) bulk and surface metal loading (EDX, AA, XRF, ICP). Successive TPR and TPO were also carried out. This type of sample cycling, with sequential reduction and oxidation, was valuable to establish dispersion/redispersion on the methane reforming catalysts. This test was considered particularly relevant, given the expected cycling of the reforming catalyst in the Catformer unit where reducing conditions (steam reforming) will be
followed by oxidizing conditions (carbon combustion). Consequently, it is expected that in the Catformer unit the catalyst will be oscillating between reduced and oxidized states and dispersion/redispersion could be an important factor influencing the reactor performance. The tested catalysts were also analyzed for coking using the LECO method. The LECO method is one of the few methods accepted for this type of analysis and is based on the complete combustion of carbonaceous deposits, forming CO2. The formed CO2 is measured by a thermal conductivity detector (TCD), and using the stoichiometry C + O2 f CO2, the amount of coke formed is calculated. Regarding the reactor employed, the testing apparatus was the CREC riser simulator (Figure 1), invented by de Lasa.9 The reactor consists of the reactor shell, constructed in halves for easy access to the catalyst chamber, which is placed in the reactor body beneath the turbine impeller. The riser simulator is a bench-scale reactor used to simulate the behavior and reproduce the reaction conditions of a riser/downer reactor in the fast fluidization regime. This is accomplished by trapping a sample of fluidizable catalyst in a basket between two grid plates. When the impeller is rotated at the desired rpm (5000-7000 rpm), reactant gas is drawn up through the lower grid plate, toward the center of the impeller, and pushed out toward the walls of the reactor, turbulently fluidizing the sample. Because the internal recirculation rate is high, the riser simulator can be used to follow the progress of a well-mixed plug as it flows up a riser or down a downflow reactor. The riser simulator is an internal recycle fluidized reactor where reactions are carried out in a batch fashion by injecting the reacting mixture, actively mixing the reactor, and then terminating the reaction by venting the contents of the reactor to a sample bottle. This reactor configuration offers several advantages over microcatalytic fixed-bed reactors such as providing better mixing with no mass-transfer limitations due to the fluidized state of small catalyst particles (60-70
Ind. Eng. Chem. Res., Vol. 42, No. 12, 2003 2509
µm). Gas recycling rates are very high as the catalyst is fluidized in the turbulent regime.10,11 In the CREC riser simulator, pressures in the upper and lower shells of the reactor were measured using two thin film (polysilicon) Omega transducers (PX603500G5V). The transducer accuracy was (0.4% of full scale (2 psi) with a 1 ms response time. Pressure in the blow-down bottle was measured with an Omega PX213 thin film (polysilicon) transducer. The accuracy of this transducer was (0.25% of full scale (0.075 psi) with a 1 ms response time. This pressure transducer allows one to follow closely the various methodological steps in the CREC riser simulator operation such as injection, reaction, and product evacuations. A Perkin-Elmer Sigma 115 GC was used to analyze the reaction products. The GC contained two packed columns in series, 6 in. of 1/8 in. Porapak-Q and 15 in. of 1/8 in. Carbonex 1000. Analysis of the gas samples was done using a mixture of 30% nitrogen in helium, and this was done to achieve adequate differences in thermal conductivity between analyzed gas mixtures. To achieve good species separation, the oven temperature was set at 120 °C, the detector at 100 °C, and the gas carrier flow at 50 mL/min. To feed the reactants to the CREC riser simulator, a gas injector initially developed by Pekediz12 was employed. This gas injector allows the feeding of the reactant mixture with different compositions at essentially instantaneous conditions with time lags of not more than 0.1-0.2 s. This gas injector had the following components: (a) a Plexiglas barrel (23 mm i.d.) fitted with a plunger from a 10 mL gas-tight syringe and actuated by a double-action pneumatic piston; (b) an integral slider valve, actuated by two solenoids, which control the flow through the injector; (c) a double-acting pneumatic cylinder (66 mm stroke) and an air-piloted two-way valve; (d) 33, 16.6, 12.4, and 8.3 mm spaces for limiting the stroke length and controlling the volume injected.13 In the “fill” position, feed gas was allowed to flow from the supply cylinder into the barrel and out to the vent via a needle valve. When the needle valve was adjusted, the pressure in the injector was controlled. When the slider valve was in the “inject” position, the inlet and outlet ports were closed and the third port was open such that when the plunger moved forward, the contents of the barrel was injected into the reactor through a HPV1 three-port valve. To make an injection, the spacers, in combination with the pressure in the barrel, provide the flexibility for the delivery of a wide range of gas volumes. The desired volume to be injected was set by selecting a combination of spacers to limit the stroke length, with discrete volumes, from 1.72 to 27.5 mL. During the reaction, the reactor was sealed off from the injector system and the blow-down bottle using HPV1 and HPV2 valves having the third port on each valve plugged. The valves were mounted on electrical actuators for remote operation. The outlet port on the reactor was sealed with a 1/16 in. stainless steel ball valve. To control the reaction time, a multiple-range solid-state timer was set up to control the HPV2 valve at the outlet of the reactor. When the time set for the run elapsed, the timer actuated the valve, causing the gaseous contents of the reactor to be flushed into the lower pressure blow-down bottle and terminating the run in less than 0.3 s.
Moreover, opening the HPV2 and LPV2 valves allowed the pressure to be quickly reduced with evacuation of the reactor contents to a blow-down bottle, terminating the run. The ratio of volume between the blow-down bottle and the reactor was set close to 6:1, and this provided a pressure reduction of about 18:1. Because the reactor pressures were well in excess of 100 psig, the sample bottle was maintained at atmospheric pressure. The product gases were then allowed to flow through a sample loop attached to the valve GCV. Samples of product gas could then be injected in the GC for TCD analysis. Running the reaction with differing contact times and varying impeller speeds allowed the simulation of data from different axial positions in a commercial unit. During experiments, the reactor temperature was measured using a type K thermocouple inserted into the center of the catalyst basket. Because the thermal mass of the unit is large in comparison to the mass of the catalyst and reactant gas, the riser simulator performed as an isothermal reactor with typically less than 4 °C temperature fluctuations. Design of Experiments There are different approaches to the design of experiments. A key advantage of a designed set of experiments is that the maximum amount of information can be extracted with minimum experimental effort, while ensuring the easy resolution of ambiguities arising from the data. Factors, levels, and responses have to be defined in order to set up a designed experiment. Factors can be qualitative (e.g., type of catalyst support or pretreatment) or quantitative (e.g., temperature, mass of catalyst, etc.). Other independent variables that may not appear explicitly in models can also be used as factors.14 Levels can also be qualitative or quantitative. Levels take numerical values assigned to the factors by the experimenter in the case of quantitative factors such as temperature or represent options as in the case of qualitative factors such as catalyst support. A response is the measured output that results when the experiment is run at the desired level of the various factors. For instance, the conversion of methane is an example of a response of a dependent variable measured whose value is a function of the factors. One of the challenges commonly faced in experimental designs is a bias that generally occurs because of the presence of a lurking time-dependent variable. Randomization of experiments is thus of critical importance because it contributes to the reduction of bias in the experimental error and it breaks the correlation between the point in time at which the experiment was performed and the associated error.15 One factor at a time, Orthogonal Factorial/Partial Factorial, Sparse Orthogonal (the Taguchi method), and Sequential Design for Model Discrimination are examples of experimental design methodologies. Nonexperimental factors such as cost, feasibility, and time need to be considered when selecting a design methodology. The “one factor at a time” experimental design methodology is a method often used where one factor is set at different levels while all of the other factors are held constant and the response is measured. This completed, the first factor is set, at the level where the response is maximized, and a second factor is varied and
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so on. The “one factor at a time” method lends itself to graphical representation of data and is simple to implement. This method will not capture information about how the interaction between the factors affects the response, and results will only be reasonable if the response surface is uniform and symmetrical. The factorial tree is also a well-known method for the design of experiments, which thoroughly covers the sample space,15 by using all possible combinations of the factors/levels and thus capturing factor interaction effects on the response. The factorial/partial factorial is a common approach because it is powerful, easy to understand, and easy to implement. Unfortunately, the number of experiments required (the number of levels3 raised to the number of factors,2 resulting in nine experiments) can become large. The measurement of the effect of factor interaction (first, second, and third levels) is important because each factor may not influence the response independently. The sparse orthogonal designs of Taguchi14 are more commonly used in industrial engineering settings because the number of factors is large. This method employs partial factorial design for which all but first and second level interactions are removed from the sample space. Unfortunately, high-level interactions such as the effect of varying jointly three or more factors are lost. The sequential design of experiments for model discrimination16 is not employed as commonly. It is an iterative process for determining from a group of candidate models the model that is best able to describe the behavior of the experimental system. This technique will not only help the experimenter elucidate the effects of the factors of the response of the system but also encapsulate that behavior in a set of mathematical relationships. A mixed approach was implemented to develop an experimental design for the methane reforming studies, as proposed by Jarosch et al.17 Quantitative independent variables or factors affecting the response of an experimental system were (a) contact time, (b) reaction temperature, (c) total pressure, (d) methane to carbon dioxide ratio, and (e) catalyst to methane ratio. It can be seen that if three levels are to be used, the number of experiments required is large, 243. The number of experiments required is greater still if we were to include the qualitative factors: (a) catalyst support; (b) catalyst preparation; (c) metal loading. Thus, experiments were designed using the L9 (34; three levels and four factors) system,14 in which the catalyst to methane ratio is held constant. Three levels were selected because one of the objectives of the project is to produce a kinetic model and the use of three levels allows for the detection of curvature of the response surface. This was followed by a sequential design of experiments for model discrimination, where parameters for each model are estimated using data collected from a set of designed experiments with repeats. A discrimination criterion was then identified, and the experimental variance was determined from the repeats. Both of them were then used to find a set of experimental conditions at which the models are most likely to behave differently. After evaluation of the response at these conditions, the process was repeated until one model became more likely than the rest according to the satisfaction of the experimenter. For
additional details of the kinetic model discrimination method used, refer to El Solh.8 CREC Riser Simulator Model Because the bench-scale fluidized riser simulator can be considered an isothermal well-mixed batch reactor operating under isothermal conditions, the change of the number of moles of methane can be expressed as
dNCH4
) VR
dt
dCCH4 dt
) rCH4w
(1)
with rCH4 being a function of the partial pressure of the reactants and w being the mass of the catalyst. Moreover, the extent of the reforming reaction (XREF) can be based on the initial number of moles of methane injected (NCH40) and the number of moles consumed as follows:
dXREF -dNCH4/dt ) dt N 0
(2)
CH4
Under the conditions of the present study, the water gas shift reaction was found to be very close to chemical equilibrium and this for all of the conditions and reaction times. Therefore, the extent of the water gas shift reaction (XWGS) was estimated using the chemical equilibrium relationship
K2 )
pCO2pH2
(3)
pCOpH2O
Regarding the partial pressures of each of the chemical species, they were assessed using the combined initial number of moles (NT0) of methane and carbon dioxide injected:
P)
[
NT0
]
(5)
]
NCO20 - XREF - XWGS
pCO2 ) P
NT0
[
]
NCO0 + 2XREF + XWGS
pCO ) P
[
p H2 ) P
(4)
NCH40 - XREF
pCH4 ) P
[
NTRT VR
NT0
]
NH20 + 2XREF - XWGS
[
pH2O ) P
NT0
]
NH2O0 + XWGS NT0
(6)
(7)
(8)
(9)
When these partial pressure definitions were substituted back into the chemical equilibrium relationship, the extent of XWGS was calculated from the following quadratic relation:
Ind. Eng. Chem. Res., Vol. 42, No. 12, 2003 2511
XWGS )
-b - xb2 - 4ac 2a
(10)
Table 1. Various Kinetic Models for Dry Reforming of Methane model I, Eley-Rideal model, CH4 adsorption20
with the a, b, and c constants defined as
a ) 1 - K2
(11)
b ) -(XREF + K2XREF + NCO20)
(12)
c ) 2XREF(NCO20 - XREF)
(13)
Given these relationships, the predicted extent of the reforming reaction (XREF) was calculated for a given temperature and this once a model form for the rate of methane consumption, rCH4, was selected. Moreover, having the mass of the catalyst, the initial moles of methane, and the initial moles of carbon dioxide, eqs 1 and 2 were solved via numerical integration. It should be noticed that eqs 5-9 do not incorporate the extent due to the coke formation reaction (methane decomposition and CO disproportionation). This would be considered of negligible significance, in these calculations, given that the catalyst was changed after every dry reforming run. Integration of eqs 1 and 2 was performed using the MATLAB m-file ODE45.M available in the MATLAB Toolbox version 5.3. Numerical integration of this equation requires parameter estimation. Parameter estimates were obtained using the nonlinear leastsquares regression routine CURVEFIT.M, available in the Optimization Toolbox (version 2.0) of MATLAB release 11 version 5.3.0.10183. This nonlinear leastsquares regression minimizes the deviation of XREF obtained experimentally and the XREF resulting from the model. Statistical properties of the parameters were calculated using a modified version of REGDATA.M.18
rref ) -
rref ) -
pCH4pCO2
(
θ1 + θ2pCH4 + θ3pCO2
2
1-
pCO pH2
2
pCH4pCO2K1
)
1 kKAKB
θ2 )
1 kKB
θ3 )
1 kKA
1 + KCH4pCH4
rref ) -
(
)
pCO2pH22
krefKCO2 pCH4pCO2 -
K1
1 + KCO2pCO2
model III, noncompetitive Langmuir-Hinshelwood model20
rref ) -
(
krefKCO2KCH4 pCH4pCO2 -
(14)
(15)
It has to be mentioned that, in each of the models, the parameters θi were allowed to vary with tempera-
)
pCO2pH22 K1
(1 + KCO2pCO2)(1 + KCH4pCH4)
model IV, competitive sorption Langmuir-Hinshelwood model21
rref ) -
(
krefKCO2KCH4 pCH4pCO2 -
)
pCO2pH22 K1 2
(1 + KCO2pCO2 + KCH4pCH4)
model V, stepwise model (SW)22
(
kref pCH4 rref ) -
1+
)
pCO2pH22 K1pCO2
pCO2 KR,C-zpCO2
model VI, basic model
(
rref ) -kref pCH4pCO2 -
)
pCO2pH22 K1
model VII, simplified noncompetitive Langmuir-Hinselwood model8
rref ) -
(
kKCO2KCH4 pCH4pCO2 -
)
pH22pCO2 K1
1 + KCH4pCH4 + KCO2pCO2
model VIII, carbon monoxide adsorption
rref ) -
(
kref pCH4pCO2 -
)
pCO2pH22 K1 2
1 + KCOpCO
ture using an Arrhenius relationship centered on the average temperature:
[ (
θi ) φi exp -i/R
where
θ1 )
)
K1
model II, Eley-Rideal model, CO2 adsorption20
Kinetic Modeling and Model Discrimination Regarding the postulated rate expressions, they can lead to mathematical models that are highly nonlinear with respect to their parameters, particularly those where the adsorption constants appear both in the numerator and in the denominator of the expression. The nonlinearity in the parameters can result in a high degree of parameter correlation. As a result of this, the rate expressions used were reparametrized, as suggested by Ratkowsky,19 to provide models that are closeto-linear with respect to their parameters. For example, when model VII (Table 1) was linearized, the rate equation as postulated for model VII became
(
pCO2pH22
krefKCH4 pCH4pCO2 -
1 1 T Tc
)]
(16)
This temperature-centering method reduces the correlation between the preexponential factor φi and the activation energy i, thereby improving the statistical properties of the estimates for the preexponential factor. A first phase of the experimental program involved, as described in Table 2, 81 runs (34 experiments) planned using Taguchi’s design of experiments involving four factors (contact time, reaction temperature, total pressure, and methane to carbon dioxide ratio) and three levels for each of the factors. Following this, the
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Figure 2. Posterior probability of the six candidate models after each of the discrimination trials. Table 2. Description of Experimental Conditions As Advised by Taguchi’s Design of Experiments (34), Which Represents the First Set of 91 Experiments Developed for the Preliminary Model Discrimination between the Eight Models Considered (Table 1) contact time (s)
reaction temp (°C)
total pressure (kPa)
CH4/CO2 fed
5 10 15
700 750 800
513 719 925
0.33 0.5 1
suitability of eight kinetic models was analyzed. From this analysis, two models (models III and IV) were rejected and the six others were kept for further discrimination. It has to be mentioned that initial parameter estimates for the six remaining models were done on the basis of the best fitting for the initial 81 experimental observations. Settings of the new variables likely to allow discrimination were then identified using MATLAB. This was done via a linearization procedure and the MATLAB m-files.8 Using the conditions described, a trial was then carried out on the basis of the maximum possible divergence between models. With these new data and the analysis predicting the maximum divergence between models, a new set of experimental conditions was identified, following the procedures reported by Jarosch et al.17 and El Solh.8 This sequence was repeated until one of the models was considered to be more probable than the others. In summary, after the initial 81 observations, it only required 13 additional runs for achieving model discrimination. Furthermore, when the analysis developed was reviewed, it can be stated that, prior to the analysis of any of the collected data, the probability that any one of the models would best describe the data was presumed to be the same because all six models are reasonable. On this basis and as shown in Figure 2, the probability that any one of them best describes the data was 1/6 (0.167). These 81 experiments were most valuable to estimate the parameters and the posterior probability for each of the models. At this stage, the change in probability in all six models was very minor; probabilities ranged
from 15.2% for model II to 18.4% for model V. Even though the change in probability was not substantial, this step generated a new set of conditions/settings for the independent variables that will allow maximum discrimination between those models. After run 82, considered the first discrimination experiment, the posterior probability for models V, VII, and VIII increased to 31.5%, 17.9%, and 23.8%, respectively, while the posterior probability for models I, II, and VI decreased to 9.1%, 11.9%, and 5.8%, respectively. By run 84, with a posterior probability of 22.5%, model VII surpassed the posterior probability of model VIII of 21.5%. The other four models (I, II, V, and VI) maintained essentially the same posterior probability level (7.9%, 11.9%, 30.9%, and 5.3%, respectively) as the one reported in run 82 (9.1%, 11.9%, 31.5%, and 5.8%, respectively). By run 87, the posterior probability of model V fell sharply from 30.9% (in run 84) to 13.4%, while model VII accumulated a posterior probability of 44.4%. The subsequent seven discrimination trials demonstrated an increasing probability of model VII at the expense of the other models, as shown in Figure 2. By run 94, the posterior probabilities were as follows: Eley-Rideal CH4 (model I) Eley-Rideal CO2 (model II) stepwise model (model V) basic reaction (model VI) simplified noncompetitive Langmuir-Hinshelwood (model VII) CO adsorption (model VIII)
3.60% 12.5% 7.10% 0.90% 74.90% 1.00%
Thus, from the six models proposed, on the basis of the discrimination trials, the modified noncompetitive Langmuir-Hinshelwood model (model VII) appears to be the most probable rate equation. After the other models have been tested [the basic reaction (model VI), Eley-Rideal CH4 (model I), and Eley-Rideal CO2 (model II)], it can be stated that all of them maintained a level of significance throughout the discrimination process (Figure 2). A closer inspection of those three models shows that they are “subsets” of model VII and hence will always maintain a certain level of legitimacy, with however the mathematical form given by model VII being a preferred relationship. Once the mathematical form of the model was established, the parameters for model VII were estimated using the complete 94 observations collected over the Ni/USY catalyst over a wide range of temperatures, feed ratios, contact times, and total reactor pressures. Using data accumulated over the Ni/USY catalyst (94 observations), the model was fitted to the data. Parameter estimates are presented in Table 4 with their corresponding 95% confidence intervals and correlation matrix. A plot of the reconciliation between the experimentally observed conversion of methane and those predicted using the least-squares parameter estimates can be found in Figure 3. As shown in Table 4, reparametrization and temperature centering were successful in reducing the overall correlation between the parameters to very moderate levels. Upon inspection of the reconciliation, the plot shown in Figure 5, a qualitative assessment can be made. If a significant effect is not included in the parametrized model, data points may cluster in horizontal bands. This banding is a result of changes in the observed conversion
Ind. Eng. Chem. Res., Vol. 42, No. 12, 2003 2513 Table 3. Operating Conditions Used during the 13 Additional Experiments Used for the Second Phase of Model Discrimination run temperature (°C) total pressure (kPa) catalyst weight (×101 g) contact time (s) CH4/CO2 fed CH4 conversion (%) carbon balance (%) H2/CO
82 700 341 0.86 30 0.5 44.4 22.7 0.35
83 664 925 2.28 30 0.33 52.5 -7.3 0.23
84 799 973 2.37 21.6 0.39 55.9 4.1 0.36
85 800 1135 3.21 30 0.47 69.0 -8.1 0.45
86 800 1186 3.69 30 0.54 75.0 -7.6 0.47
87 703 994 2.69 30 0.4 62.0 -2.5 0.25
88 700 736 3.39 15 1.0 34.1 -8.7 0.49
89 699 417 1.67 30 0.98 39.5 13.2 0.56
90 700 1056 4.42 15 0.5 51.7 -5.7 0.27
91 700 755 3.49 15 1.0 34.7 -9.3 0.52
92 700 366 0.94 30 0.5 52.2 22.6 0.12
93 708 957 2.67 35 0.33 90.8 -5.2 0.15
94 700 620 3.59 15 1.0 35.7 -13.5 0.56
k0, K°A, and K°B and the activation energies E1, EA, and EB were evaluated as follows:
φ1 , E1 ) 1 - 2 - 3 φ2φ3
(17)
KAo )
φ2 , EA ) 1 - 2 φ1
(18)
KBo )
φ3 , EB ) 1 - 3 φ1
(19)
k0 )
Figure 3. Reconciliation plot showing the results when parameters are estimated using model VII for a 20 wt % Ni/USY catalyst. Table 4. Parameters Estimated Using Data Collected over a 20 wt % Ni/USY Catalyst with a Linearized 95% Confidence Interval for the Model VII φ1 × 10-10 1 × 10-6 φ2 × 10-8 2 × 10-4 φ3 × 10-8 3 × 10-4 estimate interval
4.24 1.133
1.09 -1.91 8.29 0.015 0.789 7.573 residual variance ) 0.009 41
-1.53 0.394
-2.80 4.245
Parameter Correlation Matrix
φ1 1 φ2 2 φ3 3
φ1
1
φ2
2
φ3
3
1 0.4109 0.1472 0.4624 -0.4601 0.2625
1 0.1605 -0.0420 -0.3987 0.4419
1 0.7703 -0.7767 -0.3218
1 -0.5486 -0.5588
1 0.032 77
1
caused by an independent variable not included in the model. Vertical banding can be the result of overparametrization. Neither of these effects can be seen in the reconciliation plot, and parameters were determined with maximum cross-correlation between φ2 and 2 at 0.77 and φ3 and 2 at -0.77. It has to be stated that if one or more parameters were not significant and/or highly correlated, the correlation would have been closer to 1.0. From this, it can be concluded that the model is not overparametrized. Once the various parameter estimates, the cases of φi and i, were obtained, the preexponential coefficients
Table 5 reports the preexponential coefficients k0, K°A, and K°B and the activation energies E1, EA, and EB for the 20 wt % Ni/USY catalyst; all values were significant at the 95% confidence level. For instance, when the activation energy was calculated as 1.04 × 106 J mol-1, an associated 95% confidence interval was (0.088 × 106 kJ mol-1 was obtained. Moreover, when the value of the rate constant was 1.45 × 10-6 mol gcat-1 s-1, the 95% confidence interval was (0.81 × 10-6 mol gcat-1 s-1. Similarly, the values of the exponential coefficients and the activation energies for the methane and carbon dioxide adsorption constants were also obtained with adequate 95% confidence intervals, and all of this supported the results of the discrimination experiments. On the basis of the parameters obtained, it is demonstrated using model discrimination that eq 14 or model VII provides a most probable rate equation to describe the kinetic data of dry methane reforming in the CREC riser simulator. This strongly suggests that the adsorption of both carbon dioxide and methane plays an important role in determining the observed rate dry reforming of methane and that adsorption takes place in two different sites, with one being presumably in the support and the other in the nickel. This may be justified considering that the zeolite, a well-known support to which hydrocarbons have high affinities, could adsorb the CH4 while the CO2 may be adsorbed on the metal sites. Moreover, the mathematical form of the model obtained is consistent, in general, with findings from a kinetic study performed on steam reforming on methane.17 Jarosch et al.17 did not account, however, for the
Table 5. Preexponential and Activation Energy Values Evaluated Using a 20 wt % Ni/USY Catalyst with Linearized 95% Confidence Interval for Model VIIa units estimate interval a
k0 × 106
E1 × 10-6
mol gcat-1 s-1 1.45 0.81
J mol-1 1.04 0.088
K °A × 103 Pa-1 -4.50 2.22
EA × 10-6
K °B × 103
EB × 10-6
J mol-1 1.01 0.087
Pa-1 -3.61 1.34
J mol-1 1.12 0.098
k ) k0 exp{-(E1/R)[(1/T) - (1/Tc)]}, KA ) K °A exp{(EA/R)[(1/T) - (1/Tc)]}, and KB ) K °B exp{(EB/R)[(1/T) - (1/Tc)]}.
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CO2 in the reaction rate equation denominator. This appears to be the result of the much lower CO2 concentrations experienced in methane steam reforming versus the much higher CO2 levels attained in methane dry reforming, making in a practical sense the CO2 term in the denominator of the steam reforming rate equation negligible. Moreover, the resulting negative K°A and K°B adsorption constants suggest that the adsorption processes for both methane and CO2, under the condition of methane dry reforming, involve physisorption-type isotherms. This observation is also consistent with other studies developed by Jarosch et al.17 showing negative values for K°A. Finally, the signs assigned to the activation energies for both the reaction and the adsorption are consistent with the expected dependence of both constants with temperature (refer to the Nomenclature section and the caption of Table 5). A positive E1 shows a dry reforming intrinsic constant favored by higher temperatures while positive EA and EB show an adsorption process negatively affected by temperature increases. Conclusions Based on the results obtained in this chapter, the following conclusions can be drawn: 1. The use of a statistical criterion such as the BoxHill function is a powerful tool for the design of experiments that optimize the effort expended for model discrimination. For instance, it was shown here that there is an effective discrimination between 6 different plausible models with as few as 13 additional sequential experiments with respect to the original 81 to select a best model. 2. All six models were found to fit the data but were rejected by the discrimination function either because of inadequate form or because of parameters that were not significant at the 95% confidence level. 3. Results of the model discrimination indicate that both the adsorption of methane and the adsorption of carbon dioxide play an important role in determining the observed rate of the “dry” reforming of the methane reaction. The results of model discrimination show that a model based on the adsorption of methane and adsorption of carbon dioxide on different sites of the catalyst proved the most probable. Nomenclature Ci ) molar concentration of component i, kgmol m-3 E ) activation energy, J mol-1 k ) rate constant for dry reforming, k0 exp{-(E1/R)[(1/T) - (1/Tc)]}, mol gcat-1 s-1 k0 ) preexponential factor, mol gcat-1 s-1 KA ) adsorption constant for methane, K °A exp{(EA/R)[(1/ T) - (1/Tc)]}, Pa-1 KB ) adsorption constant for CO2, K °B exp{(EB/R)[(1/T) (1/Tc)]}, Pa-1 Ki ) adsorption constant for the “i” species, Pa-1 K1 ) equilibrium constant for dry reforming, kPa2 K2 ) equilibrium constant for water gas shift K °A ) preexponential factor, adsorption constant for methane, Pa-1 K °B ) preexponential factor, adsorption constant for CO2, Pa-1 Ni ) number of moles of the “i” species, mol pi ) partial pressure of species i, Pa
P ) total pressure, Pa r ) rate of consumption, mol gcat-1 s-1 R ) universal gas constant, J mol-1 or Pa cm3 mol-1 K-1 T ) temperature, °C Tc ) center value temperature, °C VR ) reactor volume, mL v ) total number of models proposed w ) mass of the catalyst, g XREF ) extent of the methane reforming reaction, mol XWGS ) extent of the water gas shift reaction, mol Greek Symbols φi ) preexponential factor for generalized parameter θi i ) activation energy for generalized parameter θ /i , J mol-1 θi ) generalized parameter following an Arrhenius temperature relationship ν ) stoichiometric number Subscripts/Superscripts CO2 ) carbon dioxide CO ) carbon monoxide C ) centre value H2 ) hydrogen i ) generic “i” chemical species 0 ) initial CH4 ) methane r ) model number T ) total ν ) total number of models H2O ) water/steam Abbreviations AA ) atomic absorption BET ) Brunauer-Emmett-Teller CREC ) Chemical Reactor Engineering Centre EDX ) energy-dispersive X-ray GC ) gas chromatograph ICP ) induced coupled plasma SEM ) scanning electronic microscopy TPO ) temperature-programmed oxidation TPR ) temperature-programmed reduction XRD ) X-ray diffraction XRF ) X-ray fluorescence
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Received for review September 24, 2002 Revised manuscript received December 11, 2002 Accepted December 13, 2002 IE020749D
