Skeletal Mechanism Generation for High-Temperature Combustion of

Jun 19, 2013 - ... method to check the chemical reality of the skeletal mechanism. ... Measurement of Laminar Flame Speed and Chemical Kinetic Model o...
2 downloads 0 Views 2MB Size
Download PDF
Article pubs.acs.org/EF

Skeletal Mechanism Generation for High-Temperature Combustion of H2/CO/C1−C4 Hydrocarbons Quan-De Wang* Low Carbon Energy Institute, China University of Mining and Technology, Xuzhou 221008, Jiangsu, People’s Republic of China S Supporting Information *

ABSTRACT: The development of the combustion mechanism for hydrogen (H2) and C1−C4 hydrocarbon fuels plays critical roles in many combustion systems. In the present work, a general framework to develop an efficient skeletal mechanism, which can maintain both accuracy of predicted combustion properties and chemical reality, has been established on the basis of the combination of the directed relation graph method for mechanism reduction and the element flux analysis method for reaction pathway analysis. Within the framework, a skeletal mechanism with 56 species and 428 reactions is developed from a detailed mechanism, including 111 species and 784 elementary reactions, for high-temperature combustion of H2, and C1−C4 hydrocarbons. Errors in the predicted combustion properties will be introduced via removing species from detailed mechanisms. Therefore, systematical error analysis is first performed for ignition over a wide range of conditions, including temperature, pressure, and equivalence ratio, to check the robustness of the skeletal mechanism. Results show that the accuracy of the skeletal mechanism in the prediction of ignition for hydrogen, methane, ethylene, ethane, and propene is within 5% and no more than 10% for propane and n-butane. Time-integrated element flux analysis is subsequently used as an efficient method to check the chemical reality of the skeletal mechanism. The results indicate that the skeletal mechanism maintains the major reaction paths for targeted fuels. Finally, the skeletal mechanism is validated via the predictions of ignition, laminar flame speed, species profiles, and diffusion counter-flow flame simulations, and the use of the skeletal mechanism in the development of simplified hightemperature combustion mechanism for large alkanes is also performed.

1. INTRODUCTION The development of detailed chemical kinetic models for combustion of hydrogen (H2), carbon monoxide (CO), and C1−C4 hydrocarbons, including methane (CH4), ethylene (C2H4), ethane (C2H6), propene (C3H6), propane (C3H8), and butane (C4H10), plays a critical role in the combustion community.1 Chemical kinetic models for these compounds are not only the base models for the investigation on combustion behaviors of large hydrocarbons but also very important in most practical engineering applications. For example, in hypersonic airbreathing propulsion systems, the liquid fuels usually undergo endothermic thermal cracking reactions before combustion to relieve the great heat load, and the design of the combustion chamber in such engines requires a good understanding of the combustion behaviors of cracked product mixtures, which are composed of H2 and C1−C4 hydrocarbons.2,3 Moreover, although natural gas is mostly methane, it also contains different amounts of larger hydrocarbons (ethane, propane, butane, etc.) depending upon its source, exploitation, transport processes, etc.4 The different compositions in natural gas affect the performance of industrial gas turbine engines through variations in the ignition delay time, flame speed, and other combustion behaviors.5−7 Generally, reliable predictions of combustion behaviors require the development of detailed reaction mechanisms. Currently, several detailed reaction mechanisms for combustion of these compounds have been developed and validated against a wide range of experimental results.8−10 However, detailed chemical kinetic models that describe the oxidation of C1−C4 hydrocarbons typically include over 100 species and 1000 elementary reactions. Such large kinetic © 2013 American Chemical Society

models cannot be directly used in complex three-dimensional reacting flow simulations in the foreseeable future because of the tremendous computational effort needed. Therefore, to make large-scale numerical simulations of combustion computationally affordable and comprehensively reliable, the development of rigorous mechanism reduction methods for detailed chemical kinetic mechanisms is essential. Mechanism reduction has been extensively studied, and a variety of methodologies have been developed, as reviewed in ref 11. Mechanism reduction methods can be classified into two classes:12 the first is skeletal reduction, which removes unimportant species and reactions from the detailed mechanism, and the other approach, which is not the focus of the present investigation, produces a number of global reaction steps, whose rates are computed on the basis of the elementary reaction rates. Because mechanism reduction attracts great attention in the combustion community, various skeletal mechanism reduction methods have been developed. In recent years, much effort has been devoted to automatic skeletal reduction of reaction mechanisms by mathematical procedures. Most commonly used methods include principal component analysis (PCA),13,14 computational singular perturbation (CSP) method,12,15 level of importance (LOI),16 connectivity method (CM),17 directed relation graph (DRG) method,18 and other DRG-based methods.19,20 Some of these methods are also incorporated Received: April 27, 2013 Revised: June 19, 2013 Published: June 19, 2013 4021

dx.doi.org/10.1021/ef4007774 | Energy Fuels 2013, 27, 4021−4030

Energy & Fuels

Article

into combustion numerical simulations through adaptive or onthe-fly dynamic reductions.21−23 However, for very large detailed mechanisms, development of an efficient skeletal mechanism validated over a wide range of combustion conditions is still very useful when further used in adaptive or dynamic reductions. The validation of the skeletal mechanism is generally through comparisons of simulation results with detailed mechanism and experiments. Although great progress has been achieved in skeletal reduction using these methods, a major weakness of these mathematical treatments is that they lack a realistic reaction pathway analysis during the course of reduction. Hence, it still needs to be investigated whether the realistic chemical kinetics and the major reaction pathways are maintained in the skeletal mechanism.24 On the basis of the above considerations, the first goal of the present work is to derive a skeletal mechanism for hightemperature combustion of H2 and C1−C4 hydrocarbons, including CO, CH4, C2H4, C2H6, C3H6, C3H8, and C4H10. This is achieved using the DRG method. Previously, a lot of work has been performed to develop reduced mechanisms for combustion of H2 and C1−C4 hydrocarbons.25−28 However, most of them are usually focused on single fuels or twocomponent fuel blends. Unfortunately, less work has been conducted on analysis of major reaction pathways for the skeletal mechanisms, except the work for ethylene by Løvås.16 Therefore, the second objective is to scrutinize how well the skeletal mechanism can reproduce the chemical reality compared to the detailed mechanism using time-integrated element flux analysis. On the basis of the combination of the DRG method for skeletal mechanism generation and reaction pathway analysis by employing the time-integrated element flux analysis method, the present work provides a general framework to develop skeletal mechanisms, which can maintain both accuracy of predicted combustion properties and chemical reality compared to detailed mechanisms. Within the framework, an efficient skeletal mechanism for high-temperature combustion of H2 and C1−C4 hydrocarbons is generated. The paper is organized as following: in section 2, we present the methodologies used in the present work for mechanism reduction and analysis; results of robustness analysis and reaction pathway analysis based on the detailed and skeletal mechanisms are performed in section 3; validations and discussion of the skeletal mechanism are presented in section 4; and main conclusions are summarized in section 5.

DRG = rAB

max i|vA , iωiδBi| max i|vA , iωi|

(1)

⎧1, if the i th elementary reaction involves species B δBi = ⎨ ⎩ 0, otherwise

(2)

ωi = ωf, i − ω b, i

(3)

⎪

⎪

rDRG AB

is the relative error induced to species A by elimination of where species B, subscript i indicates the ith elementary reaction, vA,i is the net stoichiometric coefficient of species A in the ith reaction, and ωi, ωf,i, and ωb,i are the net, forward, and reverse reaction rates, respectively. In our previous work, we have shown that the interaction coefficient defined by eq 1 demonstrates significant improvements compared to other formulations.31 The computational procedure in DRG is simple: starting from some important species, a species is considered to be important if it is connected by an edge from the important species, and then this procedure is iterated until no more important species are identified. The skeletal mechanism is thus generated by including only important species and reactions involving them. The size of the reduced mechanism is controlled by a threshold value that decides the existence of the vertex. Traditionally, success of a mechanism reduction method is judged by the size (number of species and reactions) of the reduced mechanism, the decrease in simulation time, and the error tolerance of the predicted combustion properties.11 The latter is estimated on the basis of comparison of the predicted combustion behaviors using the detailed mechanism. In the present work, the error of the predicted combustion properties of the skeletal mechanism is calculated on the basis of the ignition delay time, as defined in the following equation:31

errorrel =

|τign,skel − τign,det| τign,det

× 100% (4)

where τign,skel and τign,det represent predicted ignition delay times employing the skeletal and detailed mechanisms, respectively. In the present study, the detailed USC mechanism for C1−C4 oxidation32 is employed as the starting mechanism for skeletal reduction. The detailed mechanism consists of 111 species and 784 elementary reactions. The DRG method is applied to reaction state points sampled from constant pressure autoignition simulations over a wide range of simulation conditions. Important species and related reactions are captured using DRG at each sample point, and the final skeletal mechanism is the union of the sets of selected species and reactions as described previously. To achieve a skeletal mechanism suitable for Scramjet engine and gas-turbine engine applications, the reduction is performed within the parameter range of pressure from 1 to 20 atm and equivalence ratio from 0.5 to 2.0. The initial temperature for constant pressure autoignition is set to be 1000−1700 K. The fuel mixture consisting of H2, CH4, C2H4, C2H6, C3H6, C3H8, and C4H10 with equal ratios is used for constant pressure autoignition simulations. In the DRG reduction procedure, the H radical is selected as the starting species in the graph searching, because the H radical is an important species for all of the targeted fuels in reaction mechanisms. 2.2. Time-Integrated Element Flux Analysis. Currently, the evaluation of the skeletal mechanism is usually through comparison of simulation results with detailed mechanism and experiments. However, one key issue that must be kept in mind in mechanism reduction is that the resulting skeletal mechanisms should preserve all of the important species and reactions to avoid some spurious error cancellation. Therefore, the development of the mechanism analysis method is necessary to check the robustness of the skeletal mechanism. In the present work, we have employed the timeintegrated element flux analysis to analyze the skeletal mechanism derived from DRG. The concept of element flux analysis, proposed by Revel et al.,33 provides a general methodology to identify reaction pathways with minimal computational effort. Most recently, this method has been

2. MECHANISM REDUCTION AND ANALYSIS METHODS 2.1. Skeletal Mechanism Generation with the DRG Method. The DRG method is an efficient skeletal reduction method. It can be carried out with a linear scaling algorithm, and the computational effort for mechanism reduction scales linearly with the number of species and reactions.29 Consequently, it is very suitable to be applied as the first step to reduce large kinetic mechanisms. In the DRG method, the coupling relations between species are represented by a directed graph, and each vertex in the graph denotes a species in the detailed mechanism. An edge exists from vertex A to B if and only if the removal of species B would directly induce significant error to the production rate of species A. This relation is measured by a interaction coefficient, rDRG AB , which has been proposed in various formulations by different researchers. In the present work, the interaction coefficient proposed by Luo et al.30 defined as eq 1 is adopted for skeletal mechanism reduction 4022

dx.doi.org/10.1021/ef4007774 | Energy Fuels 2013, 27, 4021−4030

Energy & Fuels

Article

Figure 1. Relative errors of predicted ignition delay times using the reduced skeletal mechanism for the targeted fuels under certain simulation conditions. element A from species k1 to k2 at instantaneous time t can be obtained via the summation of contributions from all reactions.

coupled with genetic algorithms for mechanism reduction and optimization,34 and it also have been implemented in numerical simulations for adaptive reductions.35 In our previous work, we have demonstrated that this method provides a simple but effective way to check the chemical reality of the skeletal mechanism generated by the DRG method,24 and the method is only briefly outlined as follows. In element flux analysis, the instantaneous element flux for each element (such as C) from species k1 to k2 through reaction i, denoted as Ȧ i,k1→k2(t), is calculated via36 Ȧ i , k1 → k 2 (t ) = qi(t )

I

Ȧk1 → k 2 (t ) =

i=1

(6)

To derive global reaction path information, a time- or space-integrated flux indicator should be used, e.g., the time-integrated flux during ignition simulations in the present work.36

NA , k1NA , k 2 NA , i

∑ Ȧi , k1 → k2 (t )

Ȧk1 → k 2 =

(5)

∫0

τ

Ȧk1 → k 2 (t )dt

(7)

On the basis of the above definitions and analysis, the time-integrated contribution of reaction i to the flux of A from k1 to k2 and the normalized weight of element flux from k1 to k2 to the total out flux of species k1 can be easily identified with eqs 8 and 9, respectively.24

where qi(t) is the instantaneous reaction rate of reaction i at time t, NA,k1, NA,k2, and NA,i are the number of atom A in species k1, species k2, and reaction i, respectively. For a mechanism consisting of I elementary reactions and K species, the total transformation for 4023

dx.doi.org/10.1021/ef4007774 | Energy Fuels 2013, 27, 4021−4030

Energy & Fuels

Article

used as the first step in mechanism reduction. In our previous studies, we found that, with the original DRG method,18 the average error of the predicted ignition delay time of the skeletal mechanism shows jump increases as the threshold value increases to larger than 0.2.31 This has also been found in other applications when the threshold value approaches 0.2. On the other hand, with the revised DRG method, neither the species number in the skeletal mechanism nor the error of predicted ignition delay time shows a sudden jump until the threshold value reaches 0.7. The error of predicted ignition delay tends to be more stable. On the basis of the new definition, a 56 species skeletal mechanism is obtained when the threshold value is defined as 0.4, at which the maximum error of the predicted ignition delay time is no more than 10% for the sampling simulation conditions in the present work. 3.2. Robustness Analysis of the Skeletal Mechanism. To validate and determine at which physical conditions and compositions the skeletal mechanism can be reliable, we have performed a robustness analysis of the skeletal mechanism over a wide range of simulation conditions. The robustness analysis have been performed over a wide range of temperatures (1000−1800 K), pressures (1−50 atm), and equivalence ratios (0.5−2.0) for H2, CH4, C2H4, C2H6, C3H6, C3H8, and C4H10. Figure 1 demonstrates error analysis of the predicted ignition delay time under certain simulation conditions. It is found that the relative error of the predicted ignition delay times for H2 and CH4 is within 1% and the error tends to increase as the molecular size increases, which is caused by the hierarchic structures of the combustion mechanisms. For example, to accurately describe the oxidation process of nbutane, the reaction pathways of ethylene oxidation should be well-maintained because ethylene is an important intermediate in the combustion of n-butane. Thus, during the course of skeletal reduction, the number of removed species for small fuel molecules is less than that for large fuel molecules. Consequently, the relative error of predicted combustion properties tends to increases as the fuel molecular size increases. However, even for the n-butane, the largest relative error is less than 10%, indicating the good performance of the skeletal mechanism. It is also noted that the error tends to increase as pressure increases. Further validation of the skeletal mechanism is also performed, as will be shown in section 4. 3.3. Reaction Path Analysis. Besides robustness analysis of the skeletal mechanism based on systematic error analysis,

τ

 i , k1 → k 2

∫ Ȧi , k1 → k2 (t )dt Ȧ i , k1 → k 2 = = 0τ Ȧk1 → k 2 ∫0 Ȧk1 → k2 (t )dt

(8)

τ

Âk1 → k 2 =

∫ Ȧk1 → k2 (t )dt Ȧk1 → k 2 = K0 τ K ̇ ∑k Ak1 → k ∑k ∫ Ȧk1 → k (t )dt 0

(9)

In the present work, both the DRG method and the time-integrated element flux analysis method have been implemented as postprocessing programs, which are coupled with the Chemkin 2.0 program package.37 Autoignition delay time simulations are performed by the Senkin program38 combined with Chemkin 2.0.

3. RESULTS AND DISCUSSION 3.1. Results of DRG Reduction. The DRG method is one of the most efficient skeletal reduction methods and is usually Scheme 1. Time-Integrated Element Flux Analysis of Methane (CH4) during Constant Pressure Autoignition Processesa

a The percentages of the conversions (Schemes 1−4) calculated from the detailed mechanism (outside the parentheses) and skeletal mechanism (inside the parentheses) represent the analysis at an initial temperature of 1250 K with an equivalence ratio of 1.0 and a pressure of 10 atm. The percentage of the conversions is defined as the percentage of the flux of element C from one species to another with respect to the total flux of C.

Scheme 2. Time-Integrated Element Flux Analysis of Propene (C3H6) during Constant Pressure Autoignition Processes

4024

dx.doi.org/10.1021/ef4007774 | Energy Fuels 2013, 27, 4021−4030

Energy & Fuels

Article

C2H4 + H = C2H3 + H 2

reaction path analysis has been performed to confirm that the resulting skeletal mechanism preserves all of the important species and reactions to avoid some spurious error cancellation and to maintain the realistic combustion chemistry processes. This is very important, especially when the resulting skeletal mechanism is used for further optimization or mechanism development utilizations. Unfortunately, chemical analysis of the skeletal mechanism is often neglected in most mechanism reduction studies. In the present work, time-integrated element flux analysis is performed using the detailed and skeletal mechanism in simulation of the constant-pressure ignition processes. For H2, reaction path analysis results are not explicitly given, because we find that the skeletal mechanism includes all of the species for H2 combustion as the detailed mechanism. Scheme 1 shows the element flux analysis results for CH4. For CH4, it can be seen that the skeletal mechanism captures the dominant reaction pathways compared to the detailed mechanism. The H-abstraction reactions by H, O, and OH radicals together with the decomposition reactions of CH4, CH3 + H (+M) = CH4 (+M), are the dominant initial reactions for methane ignition. Following is the reactions of the CH3 radical. From Scheme 1, we can see that the CH3 radical is mostly transformed to HCO through a series of important species and reactions. However, about 9% C element in CH3 will transform to C 2H6 through the methyl recombination reaction. The reactions of singlet methylene CH2* with O and O2 to the product of CO are an important reaction pathway for the oxidation of CH3. On the basis of the timeintegrated element flux analysis shown in Scheme 1, the major reaction pathways for CH4 ignition are captured by the skeletal mechanism and the key species and reactions are maintained by the skeletal mechanism. For ethylene (C2H4) on the basis of time-integrated element flux analysis, the dominant initial reaction pathways are the Habstraction reactions by H and OH radicals to the product of ethenyl (C2H3) and the reaction of C2H4 with O to the formation of CH3 and HCO.

C2H4 + OH = C2H3 + H 2O C2H4 + O = CH3 + HCO

The percentage of conversions to C2H3, CH3, and HCO calculated from the detailed and skeletal mechanisms are 72.4 (72.8), 10.02 (9.93), and 12.68 (12.63), respectively, indicating that major initial reaction paths are captured by the skeletal mechanism. Once C2H3 is formed, it will quickly react with O2 and the hydroperoxy radical, HO2, to form formyl methyl, CH2CHO. C2H3 + O2 = CH 2CHO + O C2H3 + HO2 = CH 2CHO + OH

Another important reaction pathway for C2H3 is to the formation of C2H2 through the following reactions: C2H3 ( +M) = C2H 2 + H ( +M) C2H3 + H = C2H 2 + H 2 C2H3 + OH = C2H 2 + H 2O

From the element flux of C, it is found that C2H2 will undergo the following reaction to form another important intermediate, the ketyl radical HCCO. C2H 2 + O = HCCO + H

The intermediate CH2CHO further reacts with H, O, and OH radicals or directly decomposes to the product of CH2CO, most of which will quickly transform to CH3 and CO and a small fraction (10%) of HCCO. CH 2CO + H = CH3 + CO CH 2 + CO ( +M) = CH 2CO ( + M) CH 2CO + H = HCCO + H 2 CH 2CO + O = HCCO + OH CH 2CO + OH = HCCO + H 2O

Scheme 3. Time-Integrated Element Flux Analysis of Propane (C3H8) during Constant Pressure Autoignition Processes

The ketyl radical HCCO is very reactive and will be quickly consumed to CH2* and CO. The following reaction paths of CH3, CH2*, HCO, etc. can be found from Scheme 1. For C2H4, two skeletal mechanisms based on the USC mechanism have been developed. The skeletal mechanism by Lu et al. using the original DRG method contains 30 species.18 Another skeletal mechanism developed by Løvås based on the level of important analysis also includes 30 species.16 Løvås also analyzed the

Scheme 4. Time-Integrated Element Flux Analysis of n-Butane (C4H10) during Constant Pressure Autoignition Processes

4025

dx.doi.org/10.1021/ef4007774 | Energy Fuels 2013, 27, 4021−4030

Energy & Fuels

Article

Figure 3. Predicted mole fraction of selected important species as a function of the temperature in the oxidation of ethane (C2H6) and nbutane (C4H10) in PSR simulations using the detailed (solid lines) and skeletal (symbols) mechanisms at a pressure of 1 atm and a residence time of 0.05 s.

Figure 2. Predicted autoignition delay times for fuel mixtures as a function of initial temperatures for constant-pressure autoignition using the skeletal (symbols) and detailed (solid lines) mechanisms. The compositions of JP-7 cracked mixtures are taken from ref 3.

The initial reaction pathway for C3H6 is more complex than that of C2H4. Scheme 2 shows the major reaction paths for C3H6 at an initial temperature of 1250 K with an equivalence ratio of 1.0 and a pressure of 10 atm for ignition. It can be seen that the H-abstractions by H, O, and OH at different carbon sites of propene are the dominant initial reaction paths. Other important initial reaction paths of C3H6 include the formation of CH3, C2H3, C2H4, and CH2CO via the following reactions:

retained species in the above two skeletal mechanisms and found that four species are different, indicating that the reaction path analysis is necessary to check the robustness of the skeletal mechanism. In the present work, our purpose is not to develop a skeletal mechanism for C2H4 solely; therefore, the species retained in the skeletal mechanism cannot be directly compared to the skeletal mechanisms developed by Lu and Løvås. However, on the basis of the above reaction path analysis, it is found that the skeletal mechanism retains the key species and reactions for C2H4 compared to the detailed mechanism, indicating the reliability of the skeletal mechanism. For C2H6, time-integrated element flux analysis is performed at an initial temperature of 1250 K with an equivalence ratio of 1.0 and pressure of 10 atm for ignition. Both the detailed and skeletal mechanisms demonstrate that nearly all C2H6 is converted to C2H5 via the H-abstraction reactions by the H and OH radicals. The following reaction path analysis indicates that the percentage of conversions from the C2H5 radical to C2H4 and CH3 are 81.02 (80.73) and 11.9 (12.2) calculated from the detailed and skeletal mechanisms, respectively. The following reaction paths for C2H4 and CH3 have been discussed above. On the basis of the reaction path analysis for C2H6, the formation of the CH3 radical can explain why C2H6 exhibits a longer ignition delay time and lower laminar flame speed compared to C2H4, because the CH3 radical can remove H from the system through the recombination reaction to form CH4.39

C2H3 + CH3 ( +M) = C3H6 ( +M) C3H6 + H = C2H4 + CH3 C3H6 + O = CH 2CO + CH3 + H

C 2 H 2 , C 2 H 3 , aC 3 H 4 , and pC 3 H 4 are very important intermediates during the oxidation of C3H6. It should be noted that, during the isomerization reaction from aC3H4 to pC3H4, the percentage of conversion from the skeletal mechanism is larger than that from the detailed mechanism because aC3H4 also converts to C3H3 (31.16), while C3H3 is removed in the skeletal mechanism. This would not affect the carbon flux of aC3H4 because C3H3 will further convert to pC3H4 through the recombination reaction with hydrogen. However, it should be noted that C3H3 is one of the most important intermediates for benzene and polycyclic aromatic hydrocarbon (PAH) formation, and it should be added in the skeletal mechanism when the skeletal mechanism is used for the investigation on benzene and PAH formation processes. Nearly 4026

dx.doi.org/10.1021/ef4007774 | Energy Fuels 2013, 27, 4021−4030

Energy & Fuels

Article

Figure 5. Predicted heat release and temperature profiles together with major species mole fractions in an atmospheric opposed flame configuration by employing the detailed and skeletal mechanisms.

Figure 4. Predicted laminar flame speed versus equivalence ratio using the detailed (lines) and skeletal (symbols) mechanisms.

all pC3H4 will react with H to the products of CH3 and C2H2, the reaction paths of which have been discussed above. Once the reaction pathway for C3H6 is obtained, the reaction path for propane can be easily described. Scheme 3 demonstrates the time-integrated element flux analysis results during the constant pressure autoignition process of propane. It is shown that the H-abstraction reactions are the major initial reactions and the formed nC3H7 and iC3H7 radicals quickly decompose to CH3, C2H4, and C3H6. The results from the skeletal mechanism agree well with those from the detailed mechanism. For n-butane, the initial reaction pathways are very simple. The H, O, and OH radicals react with n-butane via the Habstraction reactions to the formation of 1-butyl (pC4H9) and 2-butyl (sC4H9) radicals. The 1-butyl radical will quickly undergo β-scission reaction to the products of C2H4 and C2H5. The subsequent reactions of 2-butyl are complex compared to those of 1-butyl radical. The percentages of conversions to C3H6 plus CH3 and butene (1-butene and 2-butene) are nearly equal via the β-scission reaction and dehydrogenation reaction. The butene will further decompose to C3H6, C2H4, and other small molecules. Although a large amount of C4H6 forms via the dehydrogenation reaction from C4H7, the total carbon flux from n-butane to C4H6 is still very small. It can be seen from Scheme 4 that the skeletal mechanism captures the major reaction pathways of n-butane compared to the detailed mechanism. On the basis of the reaction path analysis from time-integrated element flux analysis, the skeletal mechanism derived from the DRG method maintains the dominant

reaction pathways for targeted fuels, namely, CH4, C2H4, C2H6, C3H6, C3H8, and C4H10. It should be noted that the current skeletal mechanism is not directly reduced for applications in practical computational fluid dynamics simulations, and it should be further reduced via the method of quasi-steady-state approximation and so on for certain fuel mixtures to be used for engine designs.

4. EXTENDED VALIDATIONS Because the present reduced skeletal mechanism captures major reaction pathways for targeted fuel components, it can be expected that the current skeletal mechanism can be used for different amounts of surrogate components adjusted for mimicking real fuels, and the performance of the skeletal mechanism for different mixture compositions is validated. The constant pressure autoignition delay time for different fuel compositions is shown in Figure 2. It can be seen from Figure 2 that the reduced mechanism reproduces closely the behavior of the detailed mechanism. Moreover, to further validate the performance of the skeletal mechanism, major species profiles during the oxidation of ethane and n-butane in a perfectly stirred reactor (PSR)40 are also predicted using the detailed and skeletal mechanisms, respectively. Figure 3 shows the calculated mole fraction of some important species as a function of the temperature in PSR with an equivalence ratio of 1.0 at a pressure of 1 atm and a residence time of 0.05 s for ethane and n-butane. It can be seen that the mole fractions of the 4027

dx.doi.org/10.1021/ef4007774 | Energy Fuels 2013, 27, 4021−4030

Energy & Fuels

Article

Figure 7. Predicted laminar flame speed versus equivalence ratio for nheptane and n-dodecane using the reduced mechanism (the simplified model proposed by You et al.36 combined with the resulting skeletal mechanism in the present work). Lines represent numerical simulation results, and symbols represent experimental results from Ji et al.45

consisted of 21% O2 and 79% N2, while the fuel side is a mixture of methane and n-butane, which is diluted with N2. The mole fraction of the fuel side mixture is 20% methane, 30% n-butane, and 50% N2. Again, the results from the skeletal mechanism are very close to that from the detailed mechanism and reveal that the skeletal mechanism also exhibits good performance in diffusion flame simulations. On the basis of previous studies, it is shown that large normal alkanes undergo quick β-scission reactions to form small molecules, including H2, CH4, and C2−C4 alkenes at high temperatures, and the oxidation processes of these small molecules control the high-temperature combustion properties of these large alkanes.24,43 Thus, the fuel cracking models can be decoupled from the oxidation processes of their corresponding cracked small molecules.43 Therefore, in the present work, the reduced skeletal mechanism is also combined with the simplified fuel cracking models for n-alkanes to further check the robustness of the present skeletal mechanism. For n-heptane, only two species, n-heptane and 1-pentene, together with the related lumped reactions that describes the hightemperature pyrolysis of n-heptane are needed in the reduced mechanism. For larger n-decane and n-dodecane, only 1-pentene and 1-hexene together with the fuel molecules are needed to describe combustion properties of the fuels. Figure 6 demonstrates the ignition delay time for n-heptane, n-decane, and n-dodecane under different simulation conditions using the detailed mechanisms (JetSurf, version 1.0)44 and the reduced mechanism. It can be seen that the results for n-heptane and ndecane agree well, while the error shows large discrepancy at low temperatures and high pressures because the detailed mechanism contains a 4 species, 12 step lumped, lowtemperature n-dodecane oxidation model43 to capture some of the low to intermediate temperature chemistry, which is not considered in the current work. Figure 7 shows the laminar flame speed for n-heptane and n-dodecane using the present skeletal mechanism combined with simplified fuel cracking models for n-alkanes. To reduce the computational cost, Figure 5 gives the simulation results using the reduced mechanism together with experimental results,45 because the results from the detailed mechanism have been validated and documented elsewhere. 45 Overall, the reduced skeletal mechanism demonstrates high feasibility. Finally, the reduction

Figure 6. Predicted ignition delay times for n-heptane, n-decane, and n-dodecane as a function of initial temperatures for constant-pressure ignition using the skeletal (symbols) and detailed (solid lines) mechanisms. The detailed mechanism is JetSurf, version 1.0, which employs the C1−C4 detailed mechanisms as the base model.

important species resulting from the skeletal mechanism are rather close to those from the detailed mechanism. To validate the skeletal mechanism in flame simulation involving transport properties, the laminar flame speeds during one-dimensional (1D) flame simulations41 are evaluated using the detailed and skeletal mechanisms. It can be seen from Figure 4 that the skeletal mechanism also demonstrates good performance for laminar flame simulations for targeted fuels. Figure 5 demonstrates the heat release and temperature profiles together with major species mole fractions in an atmospheric opposed flow diffusion flame, which is modeled using the OPPDIF program.42 The oxidizer mixture is air, which 4028

dx.doi.org/10.1021/ef4007774 | Energy Fuels 2013, 27, 4021−4030

Energy & Fuels

Article

of the computational cost of the H2/CO/C1−C4 skeletal mechanism developed in the present study is also measured with various applications for both homogeneous ignition and diffusive flame systems. It is found that the central processing unit (CPU) time cost of the skeletal mechanism is about 1/3 of the detailed mechanism for ignition, laminar flame speed, and diffusion counter-flow flame simulations. Further, the computational cost of the developed reduced mechanisms for n-heptane, n-octane, and n-dodecane is much less compared to that of the detailed mechanisms, which consists of hundreds of species.

only provides a skeletal mechanism for targeted fuels but also emphasizes that the chemical reality of the resulting skeletal mechanism should also be checked besides comparisons of simulation results to that from the detailed mechanism.

■

ASSOCIATED CONTENT

S Supporting Information *

Resulting skeletal mechanism for H2 and C1−C4 targeted fuels and reduced mechanisms for n-heptane, n-decane, and ndodecane. This material is available free of charge via the Internet at http://pubs.acs.org.

■

5. CONCLUSION Currently, the development of systematic and efficient mechanism reduction methods and algorithms has made great progress during the past few decades and has been applied to develop various reduced mechanisms for computational fluid dynamics simulations. To achieve fast reduction of the size and stiffness of large detailed reaction mechanisms, mathematical and computational methods are widely adopted in mechanism reduction. The various mathematical procedures for the same detailed mechanism will lead to different skeletal mechanisms, which will affect the performance of the resulting skeletal mechanism.46 However, one key issue that should be kept in mind is that the reduced mechanisms should maintain the realistic combustion chemistry processes and preserve all of the important species and reactions. Otherwise, the developed reduced mechanism not only represents a wasted effort but may also lead to erroneous practical design decisions. However, unfortunately, chemical analysis of the reduced mechanism is often neglected in most mechanism reduction studies. In the present work, a skeletal mechanism for hightemperature combustion of H2 and C1−C4 hydrocarbons, including CO, CH4, C2H4, C2H6, C3H6, C3H8, and C4H10, is achieved using the DRG method. Besides robustness analysis of the skeletal mechanism based on systematic error analysis of the predicted ignition delay time, reaction path analysis employing the time-integrated element flux analysis are performed to check whether the realistic combustion chemistry of the detailed mechanism is maintained in the resulting skeletal mechanism. Robustness analysis based on error analysis for ignition reveals that the error for ignition increases as the molecular size of the fuel increases. However, the largest error is no more than 10% for the targeted fuels in the present work. Reaction path analysis using the time-integrated element flux analysis demonstrates that the major reaction pathways are captured by the resulting skeletal mechanism compared to the detailed mechanism, indicating that the skeletal mechanism is chemically realistic. Further, both the detailed and skeletal mechanisms show high hierarchical structures. The skeletal mechanism is validated against ignition delay time, species profiles, laminar flame speeds, and diffusion counter-flow flame structures for targeted fuels over typical simulation conditions. Because the skeletal mechanism maintains major reaction pathways for each fuel component, the skeletal mechanism is also validated for different fuel mixtures, and good agreement is obtained in comparison to the detailed mechanism. Finally, the use of the derived skeletal mechanism for the development of the combustion mechanism for larger hydrocarbon fuels has also been tested and validated. However, it should be noted that, because the original detailed mechanism is developed for high-temperature combustion applications, the skeletal mechanisms provided in the present work are only suitable for hightemperature combustion applications. The present work not

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This work is supported by the Fundamental Research Funds for the Central Universities of China (2013QNA08). REFERENCES

(1) Simmie, J. M. Detailed chemical kinetic models for the combustion of hydrocarbon fuels. Prog. Energy Combust. Sci. 2003, 29, 599−634. (2) Colket, M. B.; Spadaccini, L. J. Scramjet fuels autoignition study. J. Propul. Power 2001, 17, 315−323. (3) Puri, P.; Ma, F.; Choi, J.-Y.; Yang, V. Ignition characteristics of cracked JP-7 fuel. Combust. Flame 2005, 142, 454−457. (4) Spadaccini, L. J.; Colket, M. B. Ignition delay characteristics of methane fuels. Prog. Energy Combust. Sci. 1994, 20, 431−460. (5) Petersen, E. L.; Kalitan, D. M.; Simmons, S.; Bourque, G.; Curran, H. J.; Simmie, J. M. Methane/propane oxidation at high pressures: Experimental and detailed chemical kinetic modeling. Proc. Combust. Inst. 2007, 31, 447−454. (6) Healy, D.; Kalitan, D. M.; Aul, C. J.; Petersen, E. L.; Bourque, G.; Curran, H. J. Oxidation of C1−C5 alkane quinternary natural gas mixtures at high pressures. Energy Fuels 2010, 24, 1521−1528. (7) Brower, M.; Petersen, E. L.; Metcalfe, W.; Curran, H. J.; Füri, M.; Bourque, G.; Güthe, F. Ignition delay time and laminar flame speed calculations for natural gas/hydrogen blends at elevated pressures. J. Eng. Gas Turbines Power 2013, 135, 021504. (8) Healy, D.; Kopp, M. M.; Polley, N. L.; Petersen, E. L.; Bourque, G.; Curran, H. J. Methane/n-butane ignition delay measurements at high pressure and detailed chemical kinetic simulations. Energy Fuels 2010, 24, 1617−1627. (9) Petrova, M. V.; Williams, F. A. A small detailed chemical kinetic mechanism for hydrocarbon combustion. Combust. Flame 2006, 144, 526−544. (10) CRECK Modeling Group. C1−C3 Mechanism, Version 1201; CRECK Modeling Group: Milano, Italy, Dec 2012; http:// creckmodeling.chem.polimi.it/index.php/current-version-december2012/c1c3-high-temperature-mechanism. (11) Lu, T. F.; Law, C. K. Toward accommodating realistic fuel chemistry in large-scale computations. Prog. Energy Combust. Sci. 2009, 35, 192−215. (12) Valorani, M.; Creta, F.; Goussis, D. A.; Lee, J. C.; Najm, H. N. An automatic procedure for the simplification of chemical kinetic mechanisms based on CSP. Combust. Flame 2006, 146, 29−51. (13) Vajda, S.; Valko, P.; Turanyi, T. Principal component analysis of kinetic models. Int. J. Chem. Kinet. 1985, 17, 55−81. (14) Esposito, G.; Chelliah, H. K. Skeletal reaction models based on principal component analysis: Application to ethylene−air ignition, propagation, and extinction phenomena. Combust. Flame 2011, 158, 477−489. 4029

dx.doi.org/10.1021/ef4007774 | Energy Fuels 2013, 27, 4021−4030

Energy & Fuels

Article

(15) Massias, A.; Diamantis, D.; Mastorakos, E.; Goussis, D. A. An algorithm for the construction of global reduced mechanisms with CSP data. Combust. Flame 1999, 117, 685−708. (16) Løvås, T. Automatic generation of skeletal mechanisms for ignition combustion based on level of importance analysis. Combust. Flame 2009, 156, 1348−1358. (17) Nagy, T.; Turányi, T. Reduction of very large reaction mechanisms using methods based on simulation error minimization. Combust. Flame 2009, 156, 417−428. (18) Lu, T. F.; Law, C. K. A directed relation graph method for mechanism reduction. Proc. Combust. Inst. 2005, 30, 1333−1341. (19) Pepiot-Desjardins, P.; Pitsch, H. An efficient error-propagationbased reduction method for large chemical kinetic mechanisms. Combust. Flame 2008, 154, 67−81. (20) Sun, W.; Chen, Z.; Gou, X.; Ju, Y. A path flux analysis method for the reduction of detailed chemical kinetic mechanisms. Combust. Flame 2010, 157, 1298−1307. (21) Yang, H.; Ren, Z.; Lu, T. F..; Goldin, G. M. Dynamic adaptive chemistry for turbulent flame simulations. Combust. Theory Modell. 2013, 17, 167−183. (22) Gou, X.; Chen, Z.; Sun, W.; Ju, Y. A dynamic adaptive chemistry scheme with error control for combustion modeling with a large detailed mechanism. Combust. Flame 2013, 160, 225−231. (23) He, K.; Androulakis, I. P.; Ierapetritou, M. G. On-the-fly reduction of kinetic mechanisms using element flux analysis. Chem. Eng. Sci. 2010, 65, 1173−1184. (24) Wang, Q.-D.; Fang, Y.-M.; Wang, F.; Li, X.-Y. Systematic analysis and reduction of combustion mechanisms for ignition of multi-component kerosene surrogate. Proc. Combust. Inst. 2013, 34, 187−195. (25) Stefanidis, G. D.; Heynderickx, G. J.; Marin, G. B. Development of reduced combustion mechanisms for premixed flame modeling in steam cracking furnaces with emphasis on NO emission. Energy Fuels 2006, 20, 103−113. (26) Liu, W.; Kelley, A. P.; Law, C. K. Flame propagation and counterflow nonpremixed ignition of mixtures of methane and ethylene. Combust. Flame 2010, 157, 1027−1036. (27) Luo, Z. Y.; Lu, T. F.; Liu, J. W. A reduced mechanism for ethylene/methane mixtures with excessive NO enrichment. Combust. Flame 2011, 158, 1245−1254. (28) Zsély, I. G.; Nagy, T.; Simmie, J. M.; Curran, H. J. Reduction of a detailed kinetic model for the ignition of methane/propane mixtures at gas turbine conditions using simulation error minimization methods. Combust. Flame 2011, 158, 1469−1479. (29) Lu, T. F.; Law, C. K. Linear time reduction of large kinetic mechanisms with directed relation graph: n-Heptane and iso-octane. Combust. Flame 2006, 144, 24−36. (30) Luo, Z. Y.; Lu, T. F.; Maciaszek, M. J.; Som, S.; Longman, D. E. A reduced mechanism for high-temperature oxidation of biodiesel surrogates. Energy Fuels 2010, 24, 6283−6293. (31) Wang, Q.-D.; Fang, Y.-M.; Wang, F.; Li, X.-Y. Skeletal mechanism generation for high-temperature oxidation of kerosene surrogates. Combust. Flame 2012, 159, 91−102. (32) Wang, H.; You, X.; Joshi, A. V.; Davis, S. G.; Laskin, A.; Egolfopoulos, F.; Law, C. K. USC Mech Version II. High-Temperature Combustion Reaction Model of H2/CO/C1−C4 Compounds; University of Southern California (USC): Los Angeles, CA, May 2007; http:// ignis.usc.edu/USC_Mech_II.htm. (33) Revel, J.; Boettner, J. C.; Cathonnet, M.; Bachman, J. S. Derivation of a global chemical kinetic mechanism for methane ignition and combustion. J. Chim. Phys.-Chim. Biol. 1994, 91, 365−382. (34) Perini, F.; Brakora, J. L.; Reitz, R. D.; Cantore, G. Development of reduced and optimized reaction mechanisms based on genetic algorithms and element flux analysis. Combust. Flame 2012, 159, 103− 119. (35) Zhang, S. L.; Broadbelt, L. J.; Androulakis, I. P.; Ierapetritou, M. G. Comparison of biodiesel performance based on HCCI engine simulation using detailed mechanism with on-the-fly reduction. Energy Fuels 2012, 26, 976−983.

(36) He, K.; Ierapetritou, M. G.; Androulakis, I. P. Exploring flux representations of complex kinetics networks. AIChE J. 2012, 58, 553−567. (37) Kee, R. J.; Rupley, F. M.; Miller, J. A. Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics; Sandia National Laboratories: Albequerque, NM, 1989; Sandia Technical Report SAND-89-8009. (38) Lutz, A. E.; Kee, R. J.; Miller, J. A. Senkin: A Fortran Program for Predicting Homogeneous Gas Phase Chemical Kinetics with Sensitivity Analysis; Sandia National Laboratories: Livermore, CA, 1990; Sandia National Laboratories Report SAND-87-8248. (39) Ranzi, E.; Frassoldati, A.; Grana, R.; Cuoci, A.; Faravelli, T.; Kelley, A. P.; Law, C. K. Hierarchical and comparative kinetic mode ling of laminar flame speeds of hydrocarbon and oxygenated fuels. Prog. Energy Combust. Sci. 2012, 38, 468−501. (40) Glarborg, P.; Kee, R. J.; Grcar, J. F.; Miller, J. A. PSR: A FORTRAN Program for Modeling Well-Stirred Reactors; Sandia National Laboratories: Livermore, CA, 1986; Sandia National Laboratories Report SAND-86-8209. (41) Kee, R. J.; Grcar, J. F.; Smooke, M. D.; Miller, J. A. A FORTRAN Program for Modeling Steady Laminar One-Dimensional Premixed Flames; Sandia National Laboratories: Livermore, CA, 1985; Sandia National Laboratories Report SAND-85-8240. (42) Lutz, A. E.; Kee, R. J.; Grcar, J. F. OPPDIF: A Fortran Program for Computing Opposed-Flow Diffusion Flames; Sandia National Laboratories: Livermore, CA, 1997; Sandia National Laboratories Report SAND-96-8243. (43) You, X. Q.; Egolfopoulos, F. N.; Wang, H. Detailed and simplified kinetic models of n-dodecane oxidation: The role of fuel cracking in aliphatic hydrocarbon combustion. Proc. Combust. Inst. 2009, 32, 403−410. (44) Sirjean, B.; Dames, E.; Sheen, D. A.; You, X.; Sung, C. J.; Holley, A. T.; Egolfopoulos, F. N.; Wang, H.; Vasu, S. S.; Davidson, D. F.; Hanson, R. K.; Pitsch, H.; Bowman, C. T.; Kelley, A.; Law, C. K.; Tsang, W.; Cernansky, N. P.; Miller, D.; Violi, A.; Lindstedt, R. P. A high-temperature chemical kinetic model of n-alkane oxidation. JetSurF, Version 1.0; Sept 15, 2009; http://melchior.usc.edu/JetSurF/ JetSurF1.0/Index.html. (45) Ji, C.; Dames, E.; Wang, Y. L.; Wang, H.; Egolfopoulos, F. N. Propagation and extinction of premixed C5−C12 n-alkane flames. Combust. Flame 2010, 157, 277−287. (46) Tosatto, L.; Bennett, B. A. V.; Smooke, M. D. Comparison of different DRG-based methods for the skeletal reduction of JP-8 surrogate mechanisms. Combust. Flame 2013, 160, 1572−1582.

4030

dx.doi.org/10.1021/ef4007774 | Energy Fuels 2013, 27, 4021−4030