Skeletal Chemical Kinetic Mechanisms for Syngas, Methyl Butanoate

Mar 6, 2013 - Ignition delay time correlation of fuel blends based on Livengood-Wu description. Fethi Khaled , Jihad Badra , Aamir Farooq. Fuel 2017 2...
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Skeletal Chemical Kinetic Mechanisms for Syngas, Methyl Butanoate, n‑Heptane, and n‑Decane Benjamin Akih-Kumgeh*,† and Jeffrey M. Bergthorson‡ †

Department of Mechanical and Aerospace Engineering, Syracuse University, Syracuse, New York 13244, United States Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada

‡

S Supporting Information *

ABSTRACT: Skeletal chemical kinetic mechanisms are presented for combustion analysis of a series of fuels of interest in combustion systems. These models are obtained from their respective detailed chemical kinetic models using the global species sensitivity method in a formulation referred to here as alternate species elimination (ASE), reflecting the alternate elimination of chemical species from a mechanism in order to assess the resulting effect on the prediction ability of the model. Ignition delay times are used as the target global combustion property for the assessment of the chemical influence of a species. Three ignition conditions of lean, stoichiometric, and rich fuel/air mixtures at a temperature and pressure of 1050 K and 15 atm, respectively, are used to generate data for the model reduction process. The skeletal mechanisms obtained from this ignition-based reduction are tested for their ability to predict premixed flame propagation and diffusion flame structure. It is found that, by imposing an appropriate threshold on the ranked normalized changes in ignition delay times, these skeletal models capture a broad range of combustion processes beyond the homogeneous ignition process used to deduce them. The skeletal mechanisms presented in this work include syngas (31 species), methyl butanoate (MB) (88 species), n-heptane (122 species), and n-decane (89 species). These skeletal models reflect a reduction of at least 60% in the number of chemical species with respect to the detailed model. They are recommended for use in further computational combustion analysis since they result in a reduction in computational costs, and are provided as Supporting Information to this article.

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directed relations graph (DRG),10 as well as other variants of the method involving error analysis and species sensitivity.11,12 In the DRG method, using simulation results of a combustion process, the relationship of various species to a target species is assessed. Species strongly linked to the target, such as the fuel, are retained as well as their immediate dependent species. This method has been used to extract skeletal models from huge chemical kinetic models of biodiesel surrogates.13,14 In another reduction approach by Sirdeshpande et al.,15 the element flux analysis method, the activity of a chemical species is assessed based on the flux of an atom from one species to another, summed over all reactions involving the species in question. Species resulting in fluxes above a user-defined threshold are considered indispensable, and only the differential equations describing their time-dependent evolution are evaluated. The method is extensively applied to on-the-fly reduction, whereby the analyses are performed on individual computational cells with data derived from initial simulations using local conditions. Sustained efforts are still directed toward new mechanism reduction techniques, such as in refs 16−18. In Sun et al.,18 the reduction method is based on flux analysis of reaction paths, demonstrated by reducing n-heptane and n-decane models. However, the initial models are also skeletal models, with less than 125 species, and the reduced models are restricted to hightemperature applications.

INTRODUCTION AND MOTIVATION Some of the challenges encountered in computational combustion, such as the prediction of pollutant formation or flame extinction and ignition, necessitate the inclusion of models in simulations that are more descriptive of the chemical processes than empirical global reaction models. Substantial progress continues to be made in developing detailed descriptions of the elementary chemical processes during combustion.1,2 However, newly developed detailed chemical kinetic models, such as those for large alkanes3,4 and biodiesel,5,6 have thousands of species involved in over tens of thousands of reactions. Furthermore, recent modeling efforts aim at developing chemical kinetic models for multiple fuels, which further increases model complexity and size. Most experiments initially used to validate these mechanisms are homogeneous reactors, such as stirred or flow reactors and shock tube experiments. Other experiments include onedimensional (1D) laminar premixed and nonpremixed flames, whereby laminar burning velocities, extinction strain rates, and the chemical structure of flames are used to validate the mechanisms. Practical combustion often involves 2D and 3D flows in the turbulent regime, so that numerical simulations with details of the chemical processes pose a great challenge on computational resources and accuracy. There is, therefore, a need for skeletal models, which preserve essential combustion chemistry, but with fewer species. Further reduction to highly reduced mechanisms, such as in refs 7−9, is also possible; their range of application, however, may be limited. Skeletal models are obtained today using a variety of mechanism reduction techniques. A widely used method is the © 2013 American Chemical Society

Received: January 21, 2013 Revised: March 4, 2013 Published: March 6, 2013 2316

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Here, X represents a column state vector with n dependent variables, which include temperature and concentrations of all the chemical species (n − 1). The temperature and concentrations enable the thermodynamic state of the system at each time to be fully defined through an appropriate equation of state. The right-hand side of eq 1 is a nonlinear function that involves species concentrations and reaction rate parameters, usually in the Arrhenius form. An analysis of the system using methods such as computational singular perturbation24 enables the resolution of the system into fast and slow modes, with the slow modes strongly influencing the overall motion in phase space. It is observed that reacting systems, such as those encountered in combustion, have special features that could be exploited in order to understand the geometry of their dynamics in composition space. For the homogeneous reactor, the system transitions from an unburned state through a rapid ignition process to a quasi-equilibrium state. As such, the initial solution of the system is characterized by m nonzero components of the initial state vector, X0:

The aforementioned efforts are all motivated by the persisting need to establish simple and efficient reduction methods that can be used by more combustion researchers who have limited expertise in combustion chemistry modeling and model reduction. In this work, we use the species sensitivitybased reduction approach, formulated here and in other works by the authors19, as the alternate species elimination (ASE) method. The straightforward approach and few simulation conditions applied in this study demonstrate that the strength of the reduction method has not been fully exploited in previous works. Species sensitivity reduction methods aim to eliminate chemical species from the reactive system, each of which constitutes a dimension in species concentration, temperature, and time space. All elementary reactions involving the eliminated species are excluded from the system, and the resulting effect on a global combustion property, such as the ignition delay time, is evaluated. This approach also yields valuable kinetic information, which can be used to further improve the predictive performance of the model. Addressing the need for skeletal models in computational combustion research, we apply the ASE method to detailed models of n-heptane20 and methyl butanoate21 to obtain their respective reduced models, and also extract models for ndecane from a model for jet fuel surrogates, JetSurF 2.0,22 and for syngas/biogas from a C1−C4 mechanism.23 A wide variety of fuels are used in combustion devices, including syngas in stationary gas turbines, biodiesel and diesel in internal combustion engines, and jet fuels in jet engines. The skeletal models are recommended for combustion analysis in these application areas, where the respective fuels serve as surrogates for the real fuels, which can have complex compositions of many hydrocarbon species.

X(t0) = X 0(x10 , x 20 , ..., xm0)

with m ≪ n. After ignition, the system gradually tends to an equilibrium burned state, X∞, which is characterized by q components of the state vector, X∞, with equilibrium concentrations above a certain threshold, such as a few parts per billion: X(t∞) = X∞(x1 ∞ , x 2 ∞ , ..., xq ∞)

(3)

In addition to major combustion products, such as CO2 and H2O, some pollutants, such as CO, soot, unburned hydrocarbons (UHCs), and other volatile organic compounds (VOCs), are formed. This makes the following inequality generally valid: m < q < n. Between the initial and final states, the number of nonzero components of the system is higher and can approach the order of n, especially close to ignition. Further observations of combustion processes suggest that it is possible to replace the complete system comprising n − 1 species with another system with fewer species, r − 1, such that key combustion properties are still adequately predicted over a smaller parameter space than that for which the full detailed model was developed. Such key combustion properties could range from global combustion properties, such as ignition delay times and burning velocities, to concentrations of major species and pollutants. Reducing the number of species can be achieved by removing those involved in unimportant reaction pathways for single fuel models, or by eliminating some fuel molecules, their intermediates species, and other unimportant species from a multifuel mechanism in order to obtain a single fuel skeletal model or one with fewer fuel components. In the case of accurate species concentration prediction, for species xi in the old model, which corresponds to species xj′ in the new model, it is desired that

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MODEL REDUCTION APPROACH Extraction of skeletal mechanisms from detailed chemical kinetic models aims at retaining elementary reactions and species essential to the accurate prediction of key combustion properties. From the well-known hierarchical approach to mechanism development, a fairly linear relationship exists between the number of elementary reactions and the number of chemical species. Thus, mechanism reduction methods can focus either on the elementary reactions, such as the reaction sensitivity-based reduction methods, or on chemical species, such as the DRG method. The strong correlation between number of species and reactions guarantees a concurrent reduction in the number of elementary reactions and species with either approach. Since the number of species in a model are inherently less than the number of reactions, reduction methods that focus on species are likely to be less computationally costly. In addition to the choice of reduction method, a relevant combustion event needs to be chosen for analysis and reduction. A homogeneous gas-phase chemically reacting system constitutes a rigorous test of the gas-phase chemistry of a given fuel/oxidizer system. Such a system will evolve from an unburned state to a burned equilibrium state through a transient process of ignition. The chemical species constitute degrees of freedom of the homogeneous chemical system, whose evolution is mathematically described by a system of ordinary differential equations: dX = f (x1 , x 2 , ..., xn) dt

(2)

xi(t ) − x′j(t ) = O(ε)

(4)

where ε is a small parameter. It is interesting to consider how less important species are introduced in the detailed model. These models are constructed following the theory of chain reactions, with rate parameters of elementary reactions assigned based on reaction rate theories and experiments. Years of experimental and theoretical studies have culminated in a fairly accepted

(1) 2317

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modeling philosophy, as outlined in works by Curran et al.20 and Warnatz.25 If one considers the fate of an important initial reactant, R, participating in parallel reactions, as shown in eqs 5−7, differences in activation energy and coreactant concentrations can lead to one or more of the parallel channels playing an insignificant role: R + A ⇋ Pa + Pb

(5)

R ⇋ Pc + Pd

(6)

R + B ⇋ Pe + Pf

(7)

combustion property chosen for reduction is the ignition delay time, τ, based on maximum temperature gradient for convenience. Thus, the NC is defined as: NCi =

(8)

Pf + Pc ⇋ Pa + Ph

(9)

(11)

Other properties of interest could be the maximum concentration of intermediate species of interest, such as olefins, aldehydes, and key radicals. In this case, such an analysis can also indicate which species need to be properly modeled in order to achieve a desired level of accuracy in concentration prediction. All chemical species are then ranked by the absolute magnitude of their normalized changes, NC, and a skeletal model is obtained by direct truncation of chemical species whose NCs are below a user-defined threshold, NCthresh. In the case of multiple ignition conditions, the ranking is based on the average of the absolute magnitudes of NCs. The NCthresh is preferably determined from the iterative testing of the new mechanism against the detailed mechanism with respect to the prediction of a wide range of combustion properties. The simplest combustion chemistry model, the one-step global reaction, typically involves the fuel molecule, O2, H2O, and CO 2 , so that these can be retained automatically as indispensable in the mechanism. From a combustion standpoint, excluding all elementary reactions involving the fuel molecule or oxygen is not meaningful. A skeletal mechanism is generated from the detailed model by excluding all elementary reactions in which the excluded species appear as reacting partners. Inert gases, such as Ar, He, and N2, will appear as chemically insignificant, but these are needed in the mechanism for temperature and collision effects. Some small radicals, such as CH*, CH, and OH*, are useful as signatures for ignition and flame surface. However, ranking based on ignition delay obtained through temperature rise may identify them as unnecessary. Inclusion of their subchemistry is then at the discretion of the user, as they do not significantly affect the thermochemistry of the flame. Other combustion events, such as flow and stirred reactors or premixed and nonpremixed laminar flames, can also be used to generate the normalized changes, NC, for species ranking. Because of the computational time involved and potential convergence problems, flame simulations are not well suited for rapid reduction purposes. This turns out not to be a significant drawback as it will be shown that reduction based on ignition simulations successfully captures the chemistry needed for flame simulations. It is anticipated that by carefully choosing the number of combustion events and the parameter space, very rapid and reliable reduction can be achieved. In the following examples, only three ignition conditions have been considered and the resulting reduced models are tested over a much wider range of combustion conditions. An intermediate temperature, such as 1000−1100 K, is preferable as the initial temperature for ignition. The low-temperature chemistry is then captured by simply lowering the threshold of the normalized change, NCthresh.

If the elementary reaction in eq 7 consistently plays an insignificant role in the disappearance of the important species, R, then subsequent reactions of the products of this reaction, Pe and Pf, may also be insignificant in the overall evolution of the system, despite their participation in multiple other reactions, such as

Pe + A ⇋ Pg

τi − τ0 τ0

In turn, products, such as Pg and Ph, uniquely linked to Pe and Pf, will be insignificant to the overall dynamics of the system. The task of skeletal mechanism development then consists in identifying and eliminating these unimportant species, without modifying the retained species, their elementary reactions, or the associated reaction rate parameters. Further reduction of the skeletal mechanism to yield another with even fewer reactions is possible, by means of the quasi-steady-state assumption, lumping of reactions and species, or other techniques. Modification of the original reaction rates or introduction of empirical constants may then be needed in order to retain a wide-ranging predictive ability of the reduced model. However, in the present work, we only focus on the process of obtaining skeletal mechanisms for a number of fuel surrogates. The species sensitivity method, here referred to as ASE, seeks to evaluate dynamics of the chemical system in eq 1 indirectly by alternately eliminating one dimension of the system (one chemical species) at a time. Rather than focusing on the identification of slow modes or lower dimension manifolds, the method seeks to identify and eliminate any dimension that is not critical to the evolution of the system from an unburned state through transient ignition to a burnt state, as commonly encountered during combustion. The CANTERA26 software package is employed in this work because of its “setMultiplier” feature that allows the user to eliminate elementary reactions involving the species under consideration by simply setting the reaction rate multiplier to zero. It is then possible to loop over the species of interest and generate, for further analysis, a file that contains the ignition delay times and other combustion properties of interest resulting from ignition simulations with the respective species suppressed. On the basis of a characteristic combustion property, a normalized change induced by the elimination of each species can be evaluated. The normalized change, NC, is defined as p − p0 NCi = i p0 (10)

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APPLICATION OF THE ASE METHOD TO MECHANISM REDUCTION The ASE technique is employed in this work to develop skeletal models from selected detailed chemical kinetic models. Although reduction is based on ignition delay time predictions,

where p is any combustion property of interest and p0 and pi are observed before and after eliminating the subchemistry of the ith species under consideration, respectively. In this work, the 2318

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the deduced skeletal mechanisms are also tested with respect to their ability to predict flame propagation phenomena.

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SKELETAL MODEL OF METHYL BUTANOATE (MB) The detailed model for methyl butanoate (MB) by Dooley et al.21 is used to obtain an appropriate skeletal model for hightemperature combustion. As mentioned above, the combustion event used for the reduction is homogeneous gas-phase ignition of fuel/air mixtures at an initial pressure of 15 atm, a temperature of 1050 K, and for three MB/air mixtures with equivalence ratios, φ, of 0.5, 1.0, and 2.0. As it is obvious that the resulting mechanism will contain MB, O2, H2O, and CO2, these have not been subjected to the elimination process. Thus, the ASE method is applied to 271 of the 275 species in the detailed model. For consistency, during species elimination, the ignition delay time is defined as the time to maximum temperature gradient. The normalized change in ignition delay time is calculated as shown in eq 11. The absolute average value of NC for the three equivalence ratios is used to rank the species. With generic integers representing the species in their ranked order, the normalized change in ignition delay times is plotted in Figure 1. The ranking is based on the average NC of the

Figure 2. Illustration of the relative change in ignition delay times for each of the 25 most important species in the mechanism. These are in addition to the fuel, O2, CO2, and H2O that were automatically considered indispensable for the mechanism. The overall kinetic influence of each species can thus be evaluated using ASE.

reduced reactivity upon exclusion of the species subchemistry. This sensitivity representation, in contrast to the traditional reaction-based sensitivity, can provide further insight on reactivity and model performance. The NC signs indicate the overall effect of the subchemistry of each species on reactivity, and the magnitudes provide information on the relative importance of a species in any group of species of interest. It is observed that most of these species are from the hydrogen and methane systems. Elimination of any of the first three species, OH, H2O2, and CH2O, leads to failure of the system to ignite, even after a duration that is 3 times as long as the normal ignition delay. Closely linked to the fuel are the primary radicals, MB2J (CH3CH2CHCOOCH3), MBMJ (CH3(CH2)2COOCH2), and MB3J ((CH2)3COOCH3), in order of importance. These radicals result from the generic hydrogen abstraction reactions: MB + X ⇋ MB2J + HX (12)

Figure 1. Normalized change in ignition delay times plotted against the excluded species index, assigned to reflect decreasing averaged importance of the associated species. It is observed that less than 100 species of the 275 in the detailed MB mechanism significantly affect the ignition delay time prediction.

MB + X ⇋ MBMJ + HX

(13)

MB + X ⇋ MB3J + HX

(14)

The other important species closely linked to the fuel is MP2DMJ (CH2CHCOOCH2), which results from a betascission reaction of the most important primary radical, MB2J, to MP2D (CH2CHCOOCH3) and subsequent hydrogen abstraction therefrom by various radicals, generically denoted here as X:

three cases corresponding to equivalence ratios of 0.5, 1.0, and 2.0. Also presented in the figure are the NCs for each equivalence ratio. It is seen that, under these conditions, only the first 100 species of the 275 species in this model significantly influence reactivity of the system. Although the relative importance of the first set of species varies under different equivalence ratios, the same set of species would be retained for sufficiently low threshold values. It is, therefore, possible to achieve a substantial reduction of the detailed mechanism, comparable to reduction by DRG and similar methods. An alternative presentation of the ignition results is shown in Figure 2, where the NCs, with their respective signs, are plotted for the 25 most important species, exclusive of MB, O2, H2O, and CO2. Negative NC values indicate shorter delay times or increased reactivity when reactions involving the indicated species are eliminated, whereas the positive values indicate

MB2J ⇋ MP2D + CH3

(15)

MP2D + X ⇋ MP2DMJ + HX

(16)

MP2DMJ mainly decomposes as per the reaction MP2DMJ ⇋ C2H3CO + CH 2O

(17)

The resulting products, C2H3CO and CH2O, also feature among the first 15 species in Figure 2. This illustrates that important reaction channels can be reconstructed from the ranked species. It also demonstrates that direct application of the method preserves the connectivity of the important species to ensure a hierarchical breakdown of the fuel to simpler 2319

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molecules and radicals of the hydrogen and small hydrocarbon systems. One problem encountered during the analysis of complex mechanisms of higher hydrocarbons is the loss of insight with respect to the well-known chain-branching, chain-propagation, and chain-breaking classification found in the hydrogen/oxygen system. One may use the species sensitivity method to focus on the overall effect of the subchemistry of individual species, dividing them into overall retarding/chain-breaking or propagating/chain-branching, for the specific thermodynamic conditions and compositions investigated. From Figure 2, one may generally state that stable, molecular intermediates tend to act as chain-breaking agents, through their action as sinks for radicals, which would otherwise react with the target fuel to be consumed. Such observations on the role of fuel-radical reactions as chain-breaking have been reached previously (see Peters et al.8). This generalization has to be taken with caution since, under rich conditions, some stable intermediates can act as propagation or chain-branching agents, such as C2H4 and CH4 in the combustion of long-chain alkanes. Further, CO and all species of the H2O2/O2 system generally promote reactivity. A satisfactory skeletal model can be obtained by evaluating reduced models at various values of NCthresh. Three skeletal mechanisms are derived from the detailed mechanism21 using NCthresh values of 3.0 × 10−4, 2.0 × 10−3, and 1.0 × 10−2, correspondingly leading to mechanisms with 103, 88, and 78 species, respectively. The performance of these models with regards to ignition prediction is evaluated in Figures 3−5.

Figure 4. Comparison of ignition delay time predictions for MB/air mixtures, with an equivalence ratio, ϕ, of 2 and an initial pressure of 10 atm.

Figure 5. Comparison of ignition delay time predictions for stoichiometric MB/O2/N2 mixtures at an initial pressure of 30 atm. The N2/O2 ratio in this case is 15.

species model, not shown on the plot. Further reduction of the resulting skeletal models is possible through lumping or other techniques, which require chemical kinetic insight. In Figure 5, the mechanism is found to perform well at the higher pressure of 30 atm and higher ratio of N2/O2 (15.0). Further assessment of the performance of these skeletal models is performed based on prediction of laminar burning velocities and the structure of counterflow flames. In Figures 6−8, calculated laminar burning velocities of freely propagating flames are compared for homogeneous fuel/air mixtures at various initial temperatures and pressures. It is observed that, similar to their performance in predicting ignition delay times, the skeletal models with 103 and 88 species show good agreement. Deviations in burning velocities with the 88 species model are within 4%. Significant deviations are observed as the number of species is reduced below 80. In combustion systems where fuel and oxidizer are fed into the reaction zone separately, it is required that combustion chemistry models accurately predict the chemical structure and thermodynamic states across the flame. From the above observations, the skeletal model with 88 species is recommended for further use in computational studies which require incorporation of detailed chemistry. This reduced version is further tested for prediction of the structure of an atmospheric

Figure 3. Comparison of ignition delay time predictions for stoichiometric MB/air mixtures at an initial pressure of 14 atm. The parameter, D, denotes the molar ratio of nitrogen to oxygen, which is 3.76 for air.

Despite the significant reduction from 275 species based on ignition at 1050 K, the skeletal model with 103 species (over 60% reduction) accurately predicts ignition delay times even for temperatures as low as 800 K. The use of such a reduced model for tabulated chemistry would result in a tremendous saving in memory and data retrieval times while retaining the prediction capabilities of the detailed model. Further reduction to 88 species is possible, especially for combustion at temperatures above 900 K. The skeletal model with 88 species has 843 reactions (ratio of reactions to species of about 9.6) compared to the detailed model with 275 species and 2891 reactions (ratio of reactions to species of about 10.5). At high temperatures, good performance is still observed with a 59 2320

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Figure 9. Comparison of detailed and skeletal model performance with respect to predictions of the structure of an MB opposed flow flame. Here, a stream of MB/N2 (50% MB and 50% N2) with an inlet velocity of 5 cm/s flows against a stream of air, with an inlet velocity of 10 cm/s. The initial temperature for both streams is 450 K. Shown are profiles of temperature and fuel and oxygen concentrations.

Figure 6. Comparison of laminar burning velocity predictions for atmospheric MB/air flames at unburned temperature of 300 K.

can also be compared, and it is seen in Figure 10 that the profiles of OH and CO are reasonably predicted, with the maximum CO mole fraction underpredicted by less than 2.0%.

Figure 7. Comparison of laminar burning velocity predictions for MB/ air flames at unburned temperature of 300 K and pressure of 10 atm.

Figure 10. Comparison of detailed and skeletal model performance with respect to predictions of the structure of an MB opposed flow flame. Concentration profiles of OH and CO for the diffusion flame described in Figure 9.

It is thus observed that the ASE method is successful, using only a very limited selection of combustion conditions, in deriving a skeletal model with a capability to predict a wide range of combustion properties: ranging from global properties, such as laminar burning velocities, to the chemical structure of diffusion flames. The model was derived using only ignition delay calculations for three MB/air mixtures at an initial temperature of 1050 K and pressure of 15 atm. It has further been observed that using ASE with a single ignition condition, such as stoichiometric, can also yield a satisfactory species ranking for a skeletal mechanism.

Figure 8. Comparison of laminar burning velocity predictions for MB/ air flames at unburned temperature of 450 K and pressure of 20 atm.

opposed-flow diffusion flame, stabilized between a fuel stream (50% MB and 50% N2) and a stream of air with inlet temperatures of 450 K. As shown in Figure 9, the temperature, fuel, and oxygen concentration profiles are compared, revealing the excellent capability of the skeletal model to predict these profiles in agreement with the detailed model calculations. Other major species and reaction zone markers, such as OH,

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SKELETAL MECHANISM OF N-HEPTANE The size of the MB mechanism considered above is moderate compared to those for most components of practical hydrocarbon fuels. As a further example, skeletal mechanisms 2321

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for n-heptane combustion are developed from the detailed model by Curran et al.,20 which has 561 species and 4564 elementary reactions. Reduction by the ASE method is based on simulations of ignition in a constant volume reactor at a pressure of 15 atm and temperature of 1050 K for n-heptane/ air mixtures with equivalence ratios, ϕ = 0.5, 1.0, and 2.0, as was used for MB model reduction. Similar to the discussion for MB presented above, a plot of the normalized changes against the species index, in order of decreasing importance, is shown in Figure 11. It is also seen

normalized change of ignition delay from Figure 11. This ranking shows that most species important to ignition are also significant in the prediction of C2H4 formation. Exclusion of the subchemistry of the 106th species, C5H11-1 (or C5H11, for simplicity), does not significantly affect ignition but does affect the prediction of C2H4 by up to 17%. This influence is found to arise mainly through the following reactions nC7H16 ⇋ C5H11 + C2H5

(18)

nC7H15 ⇋ C5H11 + C2H4

(19)

whereby C2H5 leads to C2H4 formation through unimolecular decomposition and H abstraction. Elimination of these reactions leads to an underprediction of C2H4 concentrations, noting that the ordinate axis in Figure 12 is the absolute magnitude of the change in XC2H4. At the semidetailed modeling level, this could be remedied by replacing C5H11 in eqs 18 and 19 with the products of its decomposition, C2H4 and nC3H7, making the reactions semiglobal. Three skeletal mechanisms are also derived from the detailed mechanism using the NC thresholds, 2.0 × 10−3, 5.5 × 10−3, and 1.0 × 10−2, correspondingly leading to mechanisms with 122, 81, and 59 species, respectively. The performance of these mechanisms with respect to ignition prediction is shown in Figures 13 and 14. It is observed that the skeletal model with Figure 11. Normalized change in ignition delay times plotted against the excluded species index, assigned to reflect decreasing averaged importance of the associated species. It is observed that only about 100 species of the 561 in the detailed n-heptane mechanism affect the ignition delay time prediction.

that only approximately 100 of the 561 species in the detailed model have a significant influence on model predictions of ignition delays, thus suggesting the possibility of eliminating over 400 species contained in the detailed model. Using ASE to investigate the influence of the subchemistry of each species on the concentration of an intermediate or pollutant species is demonstrated for n-heptane by focusing on the prediction of maximum ethylene (C2H4) concentration during ignition. The species indices used in Figure 12 are based on the ranking realized on the basis of the absolute magnitude of the average

Figure 13. Comparison of ignition delay time predictions for stoichiometric n-heptane/air mixtures at an initial pressure of 14 atm.

122 of the original 561 species is able to accurately predict ignition delay times and capture the negative temperature coefficient (NTC) behavior at low temperatures. While the skeletal model with 81 species is able to accurately predict ignition delay times at temperatures above 1000 K, it fails to capture the NTC behavior. Key species included in the 122 species, and not in the 81 species, model are related to the alkyl peroxy chemistry that becomes competitive at lower temperatures. This reduction demonstrates the strength of the technique for large mechanisms. A similar reduction of this nheptane detailed mechanism using the DRG method was reported by Yoo et al.27 A skeletal model with 188 species, including low-temperature chemistry, was developed and subsequently used to derive a smaller skeletal model with 88 species. Smaller skeletal models could be obtained by using additional methods, including quasi-steady state approximation (QSSA) and lumping. It is thus remarkable to observe that ASE captures the low-temperature combustion chemistry with 122

Figure 12. Normalized change in maximum concentration of the intermediate species, C2H4, plotted against the index of the excluded species. Species order is the same as that in Figure 11. 2322

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reactions and is applicable to a range of fuels from C1−C12, as well as methylcyclohexane, toluene, and others. The recommended reduced mechanism using ASE contains 89 species and 680 reactions, obtained with NCthresh = 1.0 × 10−3. The performance of the recommended model with respect to ignition prediction is shown in Figure 15. Under these

Figure 14. Comparison of ignition delay time predictions for stoichiometric n-heptane/O2/N2, with a N2/O2 ratio of 15 and initial pressures of 30 atm.

species (78.3% reduction), compared to the 188 species (66.4% reduction) obtained using DRG. Further reduction to 81 species using ASE is accomplished by simply applying a higher NC threshold to the ranked species to obtain a hightemperature skeletal mechanism. In a related manner, He et al.28 applied the element flux analysis (on-the-fly) to the simulation of n-heptane combustion in a homogeneous charge compression ignition engine. The detailed mechanism with 635 species29 is an updated version of the n-heptane mechanism,20 incorporating submodels for 1hexene and toluene. The authors report an average species count of 93.8 out of the original 635 (561 species, when restricted to n-heptane submodel). This average is comparable with the skeletal models with 59, 81, and 122 species obtained through ASE. At higher temperatures, about 60 species are sufficient to capture the combustion chemistry, whereas a complete coverage of the low-temperature region requires the reduced model with 122 species. A one time ranking of the species in a mechanism using ASE can thus be used to generate an ordered mechanism for on-the-fly simulations, without recurrent analysis of fluxes.

Figure 15. Comparison of ignition delay time predictions for stoichiometric n-decane/air mixtures at initial pressures of 14 and 40 atm.

conditions, and many others, it is observed that the skeletal model accurately predicts ignition delay times. It is observed that the JetSurF mechanism does not predict a strong NTC behavior for n-decane, under these and other conditions. With respect to laminar burning velocity predictions, Figures 16 and 17 show that the skeletal model with 89 species

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EXTRACTION OF SKELETAL MECHANISMS FROM MULTICOMPONENT MODELS A new development in chemical kinetic modeling aims at establishing comprehensive mechanisms for a wide range of fuels. While this is useful for comparative studies and for the extension to new systems, it presents a tremendous challenge when investigations are focused on one or a few of the components included. The ASE method can serve as a useful mechanism extraction tool in such scenarios. Here, we use two “master” mechanisms to obtain skeletal models: a syngas skeletal mechanism is obtained from the C1−C4 chemical kinetic model by Wang et al.,23 while a skeletal mechanism for n-decane is obtained from the jet fuel surrogate model, JetSurF 2.0.22 As in the case of MB and n-heptane, ignition delay times of a constant volume reactor are chosen as the combustion parameter for analysis. Average NC values from lean, stoichiometric, and rich conditions are used to rank the species. n-Decane from JetSurF 2.0. Similar to the reduction approach applied to MB and n-heptane above, a skeletal mechanism for n-decane is extracted from the JetSurF 2.0 Mechanism.22 This model contains 348 species and 2163

Figure 16. Comparison of laminar burning velocity predictions for atmospheric n-decane/air flames at unburned temperature of 300 K.

provides accurate predictions (maximum deviation of 4%). Also shown on these plots is the performance of a further reduced model with 65 species, obtained by applying an NCthresh = 3.4 × 10−3. While the latter model also shows good performance in terms of ignition prediction, it leads to lower laminar burning velocities for premixed flames. Thus, the 89 species model is recommended for further use. Although no similar reduction of the detailed mechanism has been reported in the literature, it is observed that the size of the n-decane skeletal mechanism is comparable with those of MB 2323

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Figure 19. Comparison of detailed and skeletal model performance with respect to predictions of the structure of an n-decane opposed flow flame. Concentration profiles of OH and CO for the diffusion flame described in Figure 18.

Figure 17. Comparison of laminar burning velocity predictions for ndecane/air flames at unburned temperature of 450 K and pressure of 20 atm.

and n-heptane, suggesting similar effectiveness in this case compared to other methods. It would appear that about 100 species are sufficient to capture combustion chemical kinetic effects in the form of skeletal models for many fuels. It is observed that imposing a low NCthresh, such as 1.0 × 10−4, can guarantee good predictions of flame propagation by the ignition-based skeletal model. Figures 18 and 19 show the performance of the recommended model with respect to the calculation of a

single fuel component is conveniently extracted using ASE from a detailed model developed for multiple fuel components.

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SKELETAL MODEL FOR SYNGAS COMBUSTION FROM A C1−C4 MECHANISM Recent efforts on improving mechanisms for short-chain hydrocarbons have led to multifuel mechanisms capable of modeling up to C423 and C530 hydrocarbons. However, there are increased research activities focused on natural gas, syngas, and biogas. Detailed mechanisms for these fuels usually involve a smaller number of species that can be identified using species sensitivity methods, such as ASE. The C1−C4 mechanism by Wang et al.23 is used in this case to derive a skeletal mechanism for syngas combustion. The average NCs are generated using ignition delays of fuel/air mixtures, with 50% H2/50% CO and CH4 as fuels (equivalence ratios of 0.5, 1.0, and 2.0) at an initial temperature of 1050 K and pressure of 15 atm. A skeletal mechanism is obtained by setting NCthresh = 2.0 × 10−4, resulting in a mechanism with 31 species and 188 reactions, as compared to 111 species and 784 reactions in the detailed C1− C4 mechanism. This 31 species skeletal mechanism for syngas is comparable with the 32 species reduced version for ethylene, derived from the same detailed mechanism using the DRG method by Lou et al.31 This skeletal mechanism is verified to predict ignition delay times in agreement with the detailed model, as exemplified in Figure 20. In this case, representative compositions of biogas and syngas have been used to demonstrate the possibility of using these mechanisms to investigate methane, biogas, and syngas combustion. In Figure 21, it is shown that the recommended skeletal model can reproduce the performance of the detailed model with respect to laminar burning velocity prediction. Figures 22 and 23 show temperature and selected species concentration profiles for an opposed flow flame. The concentration profile of H2O2, whose maximum value is only a few parts per million, is also well predicted. This syngas skeletal model further shows that ASE can be used to derive skeletal models for multicomponent fuels from a master mechanism. Through these examples, the application of ASE to analyze, understand, and reduce chemical kinetic models for computational combustion is demonstrated. This

Figure 18. Comparison of detailed and skeletal model performance with respect to predictions of the structure of an n-decane opposed flow flame. Here, a stream of n-decane/N2 (50% n-decane and 50% N2), with an inlet velocity of 5 cm/s, flows against a stream of air, with an inlet velocity of 10 cm/s. The initial temperature for both streams is 450 K. Shown are profiles of temperature, fuel, and oxygen concentrations.

diffusion flame structure. As in the case of MB, a fuel stream of 50% n-decane and 50% N2 with an inlet velocity of 5 cm/s flows against a 10 cm/s stream of air. Inlet temperatures of both streams are maintained at 450 K. Temperature and concentration profiles of n-decane, O2, and OH are well predicted. The maximum CO concentration is underpredicted by the reduced model by 7.5%. However, improved prediction of CO can be realized through evaluation of the NCs related to peak CO formation during ignition. Thus, a skeletal model of a 2324

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Figure 22. Comparison of detailed and skeletal model performance with respect to predictions of the structure of a syngas opposed flow flame. Here, a stream of syngas (35% H2, 5% CH4, 25% CO, and 35% CO2) flows against a stream of air, both with an inlet velocity of 10 cm/s and an initial temperature of 450 K. Shown are profiles of temperature, fuel, and oxygen concentrations.

Figure 20. Comparison of ignition delay time predictions for stoichiometric fuel/air mixtures at an initial pressure of 20 atm. The fuel compositions are: syngas, 25% CO, 35% H2, 5% CH4, and 35% CO2; biogas, 65% CH4 and 35% CO2. The detailed mechanism has 111 species and 784 elementary reactions, whereas the recommended skeletal model has 31 species and 188 elementary reactions.

Figure 21. Comparison of laminar burning velocity predictions for fuel/air flames at pressures of 10 atm. The initial temperature for the syngas (25% CO, 35% H2, 5% CH4, and 35% CO2) flame is 400 K. For the biogas (65% CH4 and 35% CO2), the initial temperature is 450 K.

Figure 23. Comparison of detailed and skeletal model performance with respect to predictions of the structure of a syngas opposed flow flame. Profiles of OH and H2O2 for the diffusion flame described in Figure 22.

suggests that species sensitivity methods of mechanism reduction, such as the ASE formulation, have a potential to contribute toward the development of effective moderate size chemical kinetic models. Because of the much smaller number of conditions required to capture the essential combustion chemistry, species ranking for mechanisms of interest can be established once and a reduced mechanism, or on-the-fly mechanism reduction, is obtained by imposing various NCthresh values. In all the reduction cases presented, it is observed that some species, such as OH, HO2, H2O2, and CO, are indispensable to the prediction of ignition delay times. In most cases excluding OH, HO2 and H2O2, leads to a nonigniting system, irrespective of the simulation time. The importance of these species has been highlighted in previous works on highly reduced chemical kinetic mechanisms.8,9 Thus, they can generally be retained during ASE, in addition to the fuel, O2, H2O, and CO2. It is interesting to note that the comparable sizes of the resulting skeletal mechanisms for MB, n-heptane, and n-decane are in line with similarities observed in experiments on ignition delay times32,33 and laminar burning

velocities.34 This suggest that, for typical long-chain fuel components, skeletal mechanisms with about 100 species are capable of predicting important combustion properties, such as ignition delay, laminar burning velocities, and flame structures.

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CONCLUSIONS Skeletal chemical kinetic mechanisms of a series of fuels of interest in combustion systems have been developed using a species sensitivity technique, ASE. The method is based on the alternate elimination of the subchemistry of each of the constituent chemical species. Subsequent assessment of the resulting changes induced in a defined combustion property permits the ranking of chemical species in the order of greatest influence. A user-defined threshold is then used to determine which species should be retained in the skeletal model, and the reduced model is generated from the detailed mechanism by eliminating the excluded species and all associated elementary reactions. 2325

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(13) Seshadri, K.; Lu, T.; Herbinet, O.; Humer, S.; Niemann, U.; Pitz, W.; Seiser, R.; Law, C. Proc. Combust. Inst. 2009, 32, 1067−1074. (14) Luo, Z.; Lu, T.; Maciaszek, M. J.; Som, S.; Longman, D. E. Energy Fuels 2010, 24, 6283−6293. (15) Sirdeshpande, A.; Ierapetritou, M.; Androulakis, I. AIChE J. 2001, 47, 2461−2473. (16) Esposito, G.; Chelliah, H. Combust. Flame 2011, 158, 477−489. (17) Karadeniz, H.; Soyhan, H.; Sorusbay, C. Combust. Flame 2012, 159, 1467−1480. (18) Sun, W.; Chen, Z.; Gou, X.; Ju, Y. Combust. Flame 2010, 157, 1298−1307. (19) Akih-Kumgeh, B.; Bergthorson, J. ASME Turbo Expo 2013, Paper Number GT2013-94813, 2013. (20) Curran, H.; Gaffuri, P.; Pitz, W.; Westbrook, C. Combust. Flame 1998, 114, 149−177. (21) Dooley, S.; Curran, H.; Simmie, J. Combust. Flame 2008, 153, 2−32. (22) Wang, H.; et al. A high-temperature chemical kinetic model of n-alkane (up to n-dodecane), cyclohexane, and methyl-, ethyl-, npropyl and n-butyl-cyclohexane oxidation at high temperatures, JetSurF version 2.0, September 19, 2010 (accessed January 4, 2011). http:// melchior.usc.edu/JetSurF/JetSurF2.0. (23) Wang, H.; You, X.; Joshi, A.; Davis, S.; Laskin, A.; Egolfopoulos, F.; Law, C. USC Mech Version II: High-Temperature Combustion Reaction Model of H2/CO/C1−C4 Compounds; 2007 (accessed January 4, 2011). http://ignis.usc.edu/USC_Mech_II.htm (24) Lam, S.; Goussis, D. Proc. Combust. Inst. 1989, 22, 931−941. (25) Warnatz, J. Proc. Combust. Inst. 1985, 20, 845−856. (26) Goodwin, D. In Proceedings of the International Symposium CVD XVI and EuroCVD 14; The Electrochemical Society, Inc.: Pennington, NJ, 2003; Vol. 14, pp 155−162. (27) Yoo, C. S.; Lu, T.; Chen, J. H.; Law, C. K. Combust. Flame 2011, 158, 1727−1741. (28) He, K.; Androulakis, I. P.; Ierapetritou, M. G. Energy Fuels 2011, 25, 3369−3376. (29) Mehl, M.; Pitz, W.; Westbrook, C.; Curran, H. Proc. Combust. Inst. 2011, 33, 193−200. (30) Bourque, G.; Healy, D.; Curran, H.; Zinner, C.; Kalitan, D.; de Vries, J.; Aul, C.; Petersen, E. J. Eng. Gas Turbines Power 2010, 132, 021504. (31) Luo, Z.; Plomer, M.; Lu, T.; Som, S.; Longman, D. E. Combust. Sci. Technol. 2012, 16, 369−385. (32) Shen, H.-P.; Steinberg, J.; Vanderover, J.; Oehlschlaeger, M. Energy Fuels 2009, 23, 2482−2489. (33) Akih-Kumgeh, B.; Bergthorson, J. M. Energy Fuels 2010, 24, 2439−2448. (34) Davis, S.; Law, C. Combust. Sci. Technol. 1998, 140, 427−449.

The skeletal models developed in this work include MB from a detailed model by Dooley et al.,21 n-heptane from a detailed model by Curran et al.,20 a syngas/biogas model from a C1−C4 detailed model,23 and an n-decane model from the jet fuel surrogate model, JetSurF 2.0.22 In these reduction cases, it is observed that at least 60% of the species in the original model can be identified as less important and, therefore, can be eliminated without significantly compromising the prediction of key combustion properties. It is shown that model reduction based on three conditions for ignition delay time calculations can enable good prediction of ignition delays over a wide range of temperature and pressures, as well as accurate prediction of laminar burning velocity and diffusion flame structures with respect to predictions of the detailed models. These skeletal models are provided in the Supporting Information for computational combustion studies of the various fuels addressed, and their sizes are smaller or comparable with those of skeletal models obtained using other, more complex, methods.

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ASSOCIATED CONTENT

S Supporting Information *

Skeletal models of syngas, MB, n-heptane, and n-decane. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding is gratefully acknowledged from the L. C. Smith College of Engineering and Computer Science at Syracuse University and from the Natural Sciences and Engineering Research Council of Canada.

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REFERENCES

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