Predictive Skeletal Kinetic Model of Biodiesel Autoxidation - American

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Predictive Skeletal Kinetic Model of Biodiesel Autoxidation Navaneeth P. V,*,† G. Hemanth Kumar,† Pramod S. Mehta,†,§ and Roy T. E. Hermanns‡ †

Internal Combustion Engines Laboratory, Indian Institute of Technology−Madras, Madras, India OWI-Oel-Waerme-Institut GmbH, Affiliated Institute of RWTH−Aachen, Aachen, Germany

‡

ABSTRACT: Gradual depletion of fossil fuels, growing environmental concerns, and global warming have shifted the focus to renewable liquid fuels, such as biodiesel. Biodiesel is reported to cause less emission and can be used in engines without much modification. Even though biodiesel fuels have promising combustion and emission characteristics for use in engines, their poor oxidation stability due to aging is an inhibiting factor for wider usage. In this paper, an autoxidation model for biodiesel fuels is proposed, considering their major fatty acid constituents. The proposed kinetic parameters are optimized using a genetic algorithm with the help of experimental data available in the literature. Temperature and fuel effects on the optimized rate parameters are studied. The proposed kinetics scheme is useful to predict the oxidation of fuel constituents with a fair degree of accuracy. The model also enables prediction of a useful engineering quantity, viz., induction period, to facilitate a priori evaluation of autoxidation characteristics of biodiesel fuel.

1. INTRODUCTION

biodiesel constituents are observed to be as follows:

Because of environmental concerns and global warming due to fossil fuel, there is an emergence of alternative renewable and safe-to-handle fuels, such as biodiesel. Biodiesel is a multicomponent mixture of fatty acid methyl esters (FAMEs), produced by the trans-esterification of vegetable oil or animal fat. Biodiesel fuels have better lubricity and produce low hydrocarbon and soot emissions, compared to fossil diesel.1 However, there are issues about higher NOx emissions and their low fuel stability restricting its widespread usage. The fuel stability represents the resistance of the fuel to its degradation. Degradation of the fuel can have an effect on the fuel composition, which can change over time. Among thermal, storage, and oxidative stabilities, the oxidative stability is quite important.2 The oxidative stability, which is also termed as autoxidation, refers to the tendency of fuel to form oxygenated products on reaction with molecular oxygen. The presence of polyunsaturated fatty esters in biodiesel fuels lower their oxidative stability. The oxidative products formed during autoxidation impair fuel quality. Biodiesel autoxidation produces various types of hydroperoxides, aldehydes, acids, and ketones.3 The primary oxidative products over time polymerize to form deposits.2,4 The autoxidation chain initiators can be metals, heat, light, or trace amounts of hydroperoxides.5 Biodiesel fuels generally have FAMEs with carbon chain lengths of 6−18. The major constituents of biodiesel are methyl stearate (C18:0), methyl oleate (C18:1), methyl linoleate (C18:2), and methyl linolenate (C18:3). Each of the constituents have zero, one, two, and three double bonds in their structure, respectively. Methyl stearate is a saturated FAME. Methyl oleate have allylic hydrogen atoms in them. Methyl linoleate and methyl linolenate contain both allylic and bis-allylic hydrogen atoms in them. The bis-allylic and allylic hydrogen are very reactive, with the former being more reactive than the latter.3 Hence, the order of the oxidative stability of major © XXXX American Chemical Society

methyl stearate > methyl oleate > methyl linoleate > methyl linolenate

Therefore, it is imperative that the chemical composition of biodiesel play an important role in the oxidative stability affecting the overall oxidation rate. Based on this fact, the Rancimat oxidation test has been developed in the past, which measures the oxidative stability of biodiesel fuels, in terms of induction period: a higher induction period indicates a better oxidative stability.2,6 Many oxidative stability models that have been reported in the literature are based on an overall kinetics consideration and validated using a Rancimat induction period.7,8 Experimental and kinetic modeling studies on n-alkane autoxidation have been reported where the effect of temperature, chain length and blending ratio on induction period (IP) as well as speciation history is studied.9 Recent work of Ben Amara et al.10 stands out, from a detailed kinetics standpoint, wherein a kinetics model for autoxidation for a blend of FAME along with surrogate diesel (methyl oleate/ n-dodecane blends) at atmospheric pressure, considering 174 species and 3275 reactions, is proposed. They found that the duration of initiation and propagation phases as well as HO2 and OH propagation steps are strongly affected by methyl oleate addition. They used the rate parameters for important reactions in the kinetic scheme to obtain the temporal variation of fuel molecules and, hence, obtained the analytical induction period. The estimated induction period was validated against experimental data involving pure FAME and neat biodiesel. The comparison appeared promising. There exists a pseudochemical kinetic model11 for jet fuel autoxidation in the presence of antioxidants comprising 16 reactions developed by Zabarnick. Hydroperoxides, which are the primary products of Received: October 10, 2016 Revised: February 5, 2017 Published: March 2, 2017 A

DOI: 10.1021/acs.energyfuels.6b02620 Energy Fuels XXXX, XXX, XXX−XXX

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reaction scheme. The concentration of initiator is kept at 1 × 10−8 M, which is very low, but rather enough to start the reactions in the model. The propagation reaction consists of the reaction of a fatty acid ester radical (Ṙ ) with oxygen to form peroxyl radicals (RO2•). The other propagation reaction is the H-abstraction reaction by peroxyl radical and is the rate-determining step in the autoxidation scheme. Reaction between the peroxyl radicals terminates the autoxidation chain. There are studies available in the literature that reported the rate constant values for propagation, bimolecular termination, and peroxy radical formation reactions.14,15 The measured propagation rate constant14 for styrene autoxidation and bimolecular termination reaction are reported to be 103 L mol−1 s−1 and 107−108 L mol−1 s−1, respectively. The rate constant for the peroxy radical formation reactions is reported to be ∼109 L mol−1 s−1.15 The model considers four major constituents of biodiesel, namely, methyl stearate (Ms), methyl oleate (Mo), methyl linoleate (Ml), and methyl linolenate (Mln). Hence, the reaction scheme has submodels of four reactions pertaining to each of these constituents, wherein peroxides (ROOH) are formed as primary products of autoxidation. The methyl stearate model assumes all saturated FAMEs as a single species, because of their similar rates of reaction and the negligible influence on autoxidation. There is an interaction model where the radicals/species in each submodels react with each other. In this model, hydroperoxide is the degenerate branching agent that undergoes unimolecular decomposition to produce two radicals. The activation energy for unimolecular peroxide decomposition is taken based on the bond dissociation energy of O−O bond in hydroperoxides and also all the peroxides are lumped into a single species. The peroxide decomposition and subsequent reactions appear in the peroxide decomposition model. The reported value of rate constant for the peroxide decomposition reaction ranges between 10−6 L mol−1 s−1 and 10−5 L mol−1 s−1.16 The biodiesel autoxidation model is shown in Figure 1.

autoxidation, are said to have an autocatalytic effect on autoxidation. The O−O bond strength in ROOH is quite low and can easily break to give two radical species. Both unimolecular and bimolecular decomposition reactions of peroxide are proposed:11

̇ ROOH → RȮ + OH

(1)

2ROOH → RȮ 2 + RȮ + H 2O

(2)

It is accepted that the bimolecular decomposition scheme is only prominent when the peroxide concentration is high. One further development of the pseudo-kinetic autoxidation model by Zabarnick and co-workers12 was the extension to 19 reactions via the addition of reverse reaction for oxygen addition to fuel radical and peroxide decomposer reaction. The inclusion of reverse reaction for oxygen addition to fuel radical was attributed to the presence of aromatic content in jet fuel, while the peroxide decomposer reaction must be due to the presence of sulfur. The reverse reaction for oxygen addition to fuel radical is only prominent at temperatures of >200 °C.13 Besides the detailed model of Ben Amara10 and the pseudokinetic model of Zabarnick for Jet-A,11,12 there is an absence of a simple kinetic scheme for first-order estimates specific to biodiesel autoxidation. In this limited domain of chemical kinetic models for biodiesel autoxidation, this work proposes a skeletal autoxidation model for biodiesel. The purpose of this model is to facilitate quantified prediction of biodiesel autoxidation characteristics a priori from its basic ester constituents and compare their trends. The effects of biodiesel composition and the temperature on the kinetic parameters of the proposed skeletal model are evaluated. Finally, the model is used to predict the available experimental data for temporal concentrations of biodiesel fuel constituents and applied to estimate a useful engineering quantity, namely, the induction period of biodiesel fuels.

2. THE MODEL The proposed biodiesel autoxidation model scheme is drawn from autoxidation scheme of jet fuel autoxidation by Zabarnick11 by neglecting the presence of antioxidant and secondary oxidation products. Also, it is assumed that there is enough dissolved oxygen in biodiesel. Thus, the reduced kinetics scheme has four reactions: one initiation, two propagation, and one termination reaction, as outlined in Table 1. The Table 1. Reference Autoxidation Schemea No.

a

reaction I

type

1

RH → Ṙ

initiation

2

Ṙ + O2 → RO2•

propagation

•

+ RH → ROOH + Ṙ

3

RO2

4

RO2• + RO2• → termination

termination

Figure 1. Biodiesel autoxidation model.

Data taken from refs 7 and 11.

The submodels, along with the interaction model and peroxide decomposition of the proposed chemical kinetic scheme, consist of 38 reactions and 20 species, namely, oxygen, four fuel constituents and its associated fatty ester radicals, peroxy radicals, peroxides, alkoxy radical, hydroxyl radical, water, and termination products. The proposed kinetic scheme is included in the Appendix.

initiator of the autoxidation in the model is taken to be a metal contaminant or hydroperoxides, which are generally present in biodiesel in trace amounts.5 The initiator produces the fatty acid ester radicals (Ṙ ). Since the purpose of the initiation reaction is to start the chain reactions, it is reasonable to assume a similar rate constant value and single initiator for the entire B


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Table 3. Estimates of log10 A from the Literature20 and Bounds of log10 A Used for GA

The dissolved oxygen (O2) is an important species in the autoxidation scheme. Hence, for accelerated oxidation tests, the excess air is bubbled through the sample biodiesel. For a given temperature condition of the experiment, it is reasonable to assume dissolved oxygen concentration at the saturation level. It is reported that the Hansen solubility parameter for biodiesel fuel and n-dodecane is ∼16 MPa0.5.17 The change in oxygen solubility due to temperature in the range of 100−180 °C is found to be negligible. Dissolved oxygen concentration in n-dodecane at atmospheric pressure in the given temperature range is reported to be 300 ppm mol−1 (ref 10) and the same has been assumed in the present calculation.

reaction class H-abstraction peroxide decomposition

ri = ki ∏ cj vij′

activation energy, Ea (kJ mol−1)

methyl stearate

385.346

62.362

methyl oleate

359.824

48.325

methyl linoleate

318.402

25.543

methyl linolenate

318.402

a

23.797

6 10

10 16

(5)

The reaction rate constant (ki) is written in the following form: ⎛ −Ea, i ⎞ ki = Ai exp⎜ ⎟ ⎝ RT ⎠

Table 2. Activation Energy (Ea) of H-Abstraction Reactionsa bond dissociation energy of C−H cleavage, BDE (kJ mol−1)

6.4−8.5 11−15

lower bound for log10 A

4. SOLUTION METHODOLOGY Figure 2 shows a flow diagram of the solution methodology used in optimizing the kinetic rate parameters. A simulation code is developed, using Matlab, for solving the species concentration equation, represented as dcj = ∑ (vij″ − vij′)ri (4) dt where cj is the concentration of species j and vij is the stoichiometric coefficient of the forward and backward reaction i. The rate of reaction (ri) is written as

3. MODEL INPUT The kinetic parameters required for the model are activation energy (Ea) and pre-exponential factor (A). The preexponential factor for the reactions is listed, along with the proposed skeletal scheme, in the Appendix. The reactions having nonzero activation energy are H-abstraction reactions and peroxide decomposition reaction. The activation energy of H-abstraction from the same fuel constituent is taken to be identical. The activation energies for H-abstraction reactions of the proposed skeletal kinetic scheme are arrived from correlations (refer to eq 3) and are included in Table 2. The activation energy

constituent

range of log10 A from lower bound literature for log10 A

(6)

where T is the temperature, R the universal gas constant, Ea,i the activation energy of reaction i, and Ai the pre-exponential factor of reaction i. The available accelerated biodiesel oxidation experimental data at fixed temperatures are used in the optimization of rate parameters. Initial molar concentrations of biodiesel constituents are obtained from their known composition details. While concentrations of dissolved oxygen and initiator are assumed, the initial concentrations of remaining species are set to zero. Individual chemical reactions with their rate parameters (Ai, Ea,i), reaction temperature, initial concentration, and tolerance are input to the ODE solver. The solver is provided with temporal variation of all the species involved. The least-squares error between the predicted temporal variation of species and corresponding experimental data is taken as the fitness value. GA optimizes the rate parameters to minimize the fitness value. The experimental data used for the present study are given in Table 4. The compositional details of biodiesel from different feedstock are included in Table 5. For comparison of the optimization results, the degradation history of various test fuels is considered for a duration of only 10 h. Through its iterative procedure, GA will create a large population of rate parameters over several generations, to arrive at an optimal solution. The optimized values of the preexponential factors for H-abstraction and peroxide decomposition reactions are given in Table 6.

Data taken from refs 18 and 19.

of H-abstraction reaction is well correlated with the bond dissociation energy (BDE) for the homolytic C−H cleavage, as Ea,H‐abstraction (kJ mol−1) = 0.55(D[R − H ] − 271.96) (3) −1 18

where D[R − H] is the BDE (in kJ mol ). The activation energy for peroxide decomposition reaction is chosen to be 175 kJ mol−1, following Zabarnick.11 The initial pre-exponential factors are taken to be 3 × 109 L mol−1s−1 for H-abstraction reactions and 1 × 1015 L mol−1s−1 for peroxide decomposition reactions. The optimization of the pre-exponential factor or collision frequency is carried using the genetic algorithm (GA) in conjunction with available measured concentration histories of biodiesel constituents on autoxidation. The GA optimizes the pre-exponential factor of H-abstraction reactions and peroxide decomposition reaction, since these are the only reactions having nonzero activation energies and warrant optimization. For optimization, the GA requires the initial estimate for rate parameters, their bounds, and an inequality among the rate parameters. The bounds of pre-exponential factor are given on the basis of literature data (refer to Table 3). The H-abstraction reactions happen to be the rate-determining step in the model. The pre-exponential factors for bimolecular reactions are found to be lower than the peroxide decomposition reaction in liquid phase, and this fact is applied in the GA as an inequality.

5. RESULTS AND DISCUSSION The model predictions using the optimized pre-exponential factors are shown in terms of temporal variations of relative volume percentage of biodiesel constituents of three biodiesel fuels at 383 K in Figures 3, 4, and 5, designated as datasets F1, F2, and F3, respectively. The normalized concentrations for the constituents of these fuels as a ratio of local concentration to the initial concentration are plotted at different temperatures in Figures 6, 7, and 8 designated as datasets F4, F5, and F6, respectively. These predictions are compared with the data C


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Figure 2. Flow diagram−solution methodology for the optimization of kinetic parameters.

Table 4. Experimental Data Matrix Used for Optimization designation

feedstock

temperature (K)

air bubbling rate (L/h)

F1 F2 F3

soybean linseed rapeseed

383 383 383

10 10 10

F4 F5 F6

rapeseed rapeseed rapeseed

373 413 453

12 12 12

Table 5. Composition Data for Biodiesel from Different Feedstocks

oxidation duration (h)

fuel feedstock

methyl stearate (C18:0)

methyl oleate (C18:1)

rapeseed soybean linseed

4.207 12.791 4.746

61.696 21.073 21.784

24.544 57.008 16.844

Yamane et al.4 Yamane et al.4 Yamane et al.4

9 4.5 9

Baer et al.21 Baer et al.21 Baer et al.21

108 130 56

Table 6. Optimized Pre-exponential Factor

Composition (wt %) methyl linoleate (C18:2)

source

log10 Ai methyl linolenate (C18:3) 9.553 9.128 56.626

H-Abstraction Reactions from Fuel Constituents

available in the literature,4,21 as referenced in Table 4. The improvement in the maximum relative error of prediction using the optimized and initial pre-exponential factors for H-abstraction and peroxide decomposition reactions is shown in Table 7. D

data

C18:0 (log10 A3)

C18:1 (log10 A5)

C18:2 (log10 A7)

C18:3 (log10 A11)

peroxide decomposition reaction (log10 A15)

F1

9.9879

9.9972

8.4273

8.3115

14.4881

F2

6.4902

9.7268

7.5810

7.7474

15.9910

F3

8.6051

F4

8.7908

F5

6.0476

F6

6.0184

9.9971

8.8074

8.7553

13.5284

9.4372

9.4345

12.7821

9.9962

7.7317

7.8392

13.4056

9.9991

8.1115

8.4304

10.3174

10.000


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Figure 3. Temporal variation of the relative volume percentage of fuel constituents at 383 K simulated using the model. Markers represent data from experiment F1.

Figure 5. Temporal variation of the relative volume percentage of fuel constituents at 383 K simulated using model. Markers represent data from experiment F3.

Figure 4. Temporal variation of the relative volume percentage of fuel constituents at 383 K simulated using model. Markers represent data from experiment F2.

Figure 6. Temporal variation of normalized concentration of fuel constituents at 373 K simulated using model. Markers represent data from experiment F4.

Figures 3−5 also show that, as the autoxidation proceeds, the relative volume percentage of methyl stearate and methyl oleate increases, while that of the methyl linoleate and methyl linolenate decreases. This is due to faster degradation rates of methyl linoleate and methyl linolenate containing easily abstractable bis-allylic hydrogen atoms. The predicted temporal variations of normalized concentration of biodiesel constituents, shown in Figures 6−8, clearly indicate that, while methyl stearate does not undergo degradation, the methyl linolenate, which is a triunsaturated constituent, degrades the fastest. Note that, in Figure 6, the model prediction of methyl stearate and methyl oleate overlap each other. Furthermore, the degradation rates of unsaturated constituents increase with temperature. The role of optimized pre-exponential factor for improved predictions from the proposed model vis-à-vis nonoptimized pre-exponential factor appears to be significant and warrants discussion. It is reported that the reactions in liquid phase are influenced by the viscosity of the medium22 and it is imperative that the viscosity of the medium affects the pre-exponential

factor of reactions depending on the molecular weight and the molecular arrangements of the constituents. Biodiesel is a mixture of fatty esters, the effect of which could be significant. The viscosity values of the three biodiesels of varied composition (refer to Table 5) at 383 K are estimated using a correlation from the literature.23 Figure 9 shows the variations of pre-exponential factors for H-abstraction and peroxide decomposition reactions for the three biodiesel fuels at 383 K (refer to datasets F1−F3), with respect to their viscosities. It is observed that the preexponential factor for H-abstraction reactions from the constituents increases with viscosity. This fact corroborates with the observation of Compton et al.23 It is opined that, in the case of non-diffusion-limited reactions such as H-abstraction, an increase in molecular exchange between reactants and thereby their number of collisions are responsible for viscosity changes.24 However, a decrease in pre-exponential factor for the peroxide decomposition reaction with viscosity is due to the cage effect.25,26 The cage effect increases with viscosity, thereby E


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Figure 9. Logarithm of pre-exponential factor variation with viscosity at 383 K.

observed in Figure 9 which could not be verified due to the paucity of data. Furthermore, it is quite interesting to note that the value of the pre-exponential factor for the H-abstraction reaction has generally shown an increase at temperature of 453 K (see Figure 10). Since this temperature value is closer to the flash point temperature of the biodiesel fuel (∼453 K), the low-volatility constituents will vaporize, resulting in higher viscosity and, consequently, a change in the kinetics. The variation of pre-exponential factor for peroxide decomposition with temperature is shown in Figure 11. The observed value of pre-exponential factor for peroxide decomposition has a tendency to decrease at 413 and 453 K. Since, this behavior is at variance with that observed in the case of H-abstraction reactions and, thus, is open to further investigation. It is worthwhile to examine the values of the rate constants for the case under discussion. The values of the rate constants for the propagation, bimolecular termination and peroxy radical formation reactions at 383 K are summarized in Table 8. These rate constants are compared to the literature values and found to be comparable in case of the propagation, bimolecular termination, and peroxy radical formation reaction, as referred earlier.14,15 However, the peroxide decomposition rate constant is much lower in the present case, which is attributed to differences in the functional properties, depending on structure of the ester group present in the biodiesel, relative to those given in the literature.16 It is worth mentioning that the activation energies of H-abstraction reactions are comparable to those reported by Denisova et al.16 Incidentally, the operational temperature range in the present study are higher, and, hence, there is enough internal energy to overcome the energy barriers in the reactions of the proposed mechanism.


Table 7. Maximum Relative Error without and with Optimization data

F1

F2

F3

F4

F5

F6

maximum relative error without optimization (%) maximum relative error with optimization (%)

200

260

60

90

100

100

27

4

20

7

12

9

reducing the effective number of collisions, which results in the production of radicals. The recombination of alkoxy and hydroxyl radicals produced during the unimolecular peroxide decomposition takes place inside the solvent cage. In order to understand the temperature effects, the variations of pre-exponential factors of H-abstraction are plotted with temperature for different biodiesel constituents (datasets F3−F6) in Figures 10a−d. The value of pre-exponential factor for the H-abstraction reactions decreases with temperature, because of the expected decrease in viscosity at higher temperatures. Thus, it is expected that, at any other temperature, the trend of the pre-exponential factor will be identical to that

6. MODEL APPLICATION The model was applied to predict the Rancimat induction period, which is an accepted standard to quantify the oxidation stability of biodiesel fuels. In one autoxidation study,10 the induction period has been defined as time taken by fuel to degrade to 95% of its initial value. However, in the present study, the induction period is defined as the time required for unsaturated fuel constituents to decompose to 90% of its initial value. The estimate of induction periods based on both F


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Figure 10. Pre-exponential factor for H-abstraction reactions variation with temperature from (a) methyl stearate, (b) methyl oleate, (c) methyl linoleate, and (d) methyl linolenate.

Figure 11. Pre-exponential factor for peroxide decomposition reaction variation with temperature.

Figure 12. Model and experimental induction period. (Numbers represent the DUm of the fuel.)

Table 8. Rate Constants for Reactions in the Present Work reaction type

rate constant (L mol−1 s−1)

propagation bimolecular termination peroxy radical formation

2 × 103 3 × 109 3 × 109

The pre-exponential factors for the important reactions are obtained from the fuel viscosity at 383 K. The comparison of our proposed model and experimental induction periods available in the literature27−32 is shown in Figure 12. The model predicts the induction period with better accuracy for fuels with a higher degree of unsaturation, where the degree of unsaturation is defined as

these criteria showed no significant qualitative and quantitative difference in the values obtained. Hence, the definition of induction period employed in the present study is [C18:1]t + [C18:2]t + [C18:3]t = 0.90 [C18:1]t = 0 + [C18:2]t = 0 + [C18:3]t = 0

DUm = 1 × wt % C18:1 + 2 × wt % C18:2 + 3 × wt % C18:3

(8)

The model predicts the induction period well for fuels with DUm > 108 (green markers in Figure 12). The lack of predictability for fuels with DUm< 108 (red markers in Figure 12) can be attributed to the wide spectrum of saturated fuel

(7) G


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based on biodiesel compositional details, considering the major unsaturated constituents (namely, methyl oleate, methyl linoleate, and methyl linolenate) and a representative saturated constituent namely (methyl stearate). The study reveals the following: • The concentration variations of biodiesel constituents predicted from the proposed autoxidation model are quite satisfactory, within relative errors of 20%−30% for oxidation durations of 6 and 10 h, respectively. • Both composition and temperature effects on preexponential factors show the role of viscosity. While preexponential factor for H-abstraction reactions for fatty acid

constituents present in them, which have not been taken into account while developing the kinetic scheme. From the figure, it is evident that there are two distinct classes of biodiesel which show good correlation between model and experimental induction time, depending on their unsaturated constituentsone that has a higher fraction of monounsaturates and diunsaturates (U1) and another that has a high fraction of triunsaturates (U2).

7. CONCLUSIONS This paper presents a skeletal kinetic model, referenced in the Appendix, for predicting the degradation of fuel constituents

Table A1. Proposed Skeletal Kinetic Mechanism for Biodiesel Autoxidation: Steps R1−R16 step R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16

reaction I

MsH → Ms Ms + O2 → MsO2 MsO2 + MsH → ROOH + Ms MsO2 + MsO2→ termination I

MoH → Mo Mo + O2 → MoO2 MoO2 + MoH → ROOH + Mo MoO2 + MoO2 → termination I

MlH → Ml Ml + O2 → MlO2 MlO2 + MlH → ROOH + Ml MlO2 + MlO2 → termination I

MlnH → Mln Mln+ O2 → MlnO2 MlnO2 + MlnH → ROOH + Mln MlnO2 + MlnO2 → termination

A (mol L s−1) −3

Ea (kJ/mol)

submodel

1 × 10

0.0

methyl stearate model (Ms, C18:0)

3 × 109 A3 3 × 109

0.0 62.362 0.0

methyl stearate model (Ms, C18:0) methyl stearate model (Ms, C18:0) methyl stearate model (Ms, C18:0)

1 × 10−3

0.0

methyl oleate model (Mo, C18:1)

3 × 10 A7 3 × 109

0.0 48.325 0.0

methyl oleate model (Mo, C18:1) methyl oleate model (Mo, C18:1) methyl oleate model (Mo, C18:1)

1 × 10−3

0.0

methyl linoleate model (Ml, C18:2)

3 × 109 A11 3 × 109

0.0 25.543 0.0

methyl linoleate model (Ml, C18:2) methyl linoleate model (Ml, C18:2) methyl linoleate model (Ml, C18:2)

1 × 10−3

0.0

methyl linolenate model (Mln, C18:3)

3 × 10 A15 3 × 109

0.0 23.797 0.0

methyl linolenate model (Mln, C18:3) methyl linolenate model (Mln, C18:3) methyl linolenate model (Mln, C18:3)

9

9

Table A2. Proposed Skeletal Kinetic Mechanism for Biodiesel Autoxidation: Steps R17−R38 step

reaction

A (mol L s−1)

Ea (kJ/mol)

R17 R18 R19 R20 R21 R22 R23 R24 R25 R26 R27 R28

MlnO2 + MsH → ROOH + Ms MoO2 + MsH → ROOH + Ms MlO2 + MsH → ROOH + Ms MlO2 + MoH → ROOH + Mo MlnO2 + MoH → ROOH + Mo MsO2 + MoH → ROOH + Mo MoO2 + MlH → ROOH + Ml MsO2 + MlH → ROOH + Ml MlnO2 + MlH → ROOH + Ml MoO2 + MlnH → ROOH + Mln MlO2 + MlnH → ROOH + Mln MsO2 + MlnH → ROOH + Mln

A3 A3 A3 A7 A7 A7 A11 A11 A11 A15 A15 A15

62.362 62.362 62.362 48.325 48.325 48.325 25.543 25.543 25.543 23.797 23.797 23.797

interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction interaction

R29 R30 R31 R32 R33 R34 R35 R36 R37 R38

ROOH → RO + OH RO + MsH → ROH + Ms OH + MsH → H2O + Ms RO + MoH → ROH + Mo OH + MoH → H2O + Mo RO + MlH → ROH + Ml OH + MlH → H2O + Ml RO + MlnH → ROH + Mln OH + MlnH → H2O + Mln RO + RO → termination

A29 A3 A3 A7 A7 A11 A11 A15 A15 3 × 109

175.000 62.362 62.362 48.325 48.325 25.543 25.543 23.797 23.797 0.0

peroxide peroxide peroxide peroxide peroxide peroxide peroxide peroxide peroxide peroxide

H

submodel model model model model model model model model model model model model

decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition decomposition

model model model model model model model model model model


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methyl esters increases with viscosity and decrease in case of peroxide decomposition reaction. • The skeletal kinetic scheme is able to predict the experimental induction period of fuels with a high degree of unsaturation (DUm > 108). The effect of monounsaturated and diunsaturated constituents on oxidation rate is different than that of the triunsaturated constituents. The presence of triunsaturates has greater influence on low oxidation stability of biodiesel fuels.

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APPENDIX The proposed skeletal kinetic mechanism for the biodiesel autoxidation is presented in Tables A1 and A2. AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Navaneeth P. V: 0000-0003-4201-9079 Present Address §

Currently at Indian Institute of Technology, Palakkad, India.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors wish to acknowledge the Department of Science and Technology (DST), Government of India, and the IndoGerman Centre for Sustainability (IGCS) for providing the necessary funding to perform this work. The authors are also grateful to the DAAD for the financial support for the mobility. The thanks are also due to Prof. Heinz Pitsch (RWTH Aachen), Dr. Krithika N (IIT Madras), and Dr. Debarati Chatterjee (IIT Palakkad) for discussions and useful suggestions.

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SYMBOLS I = initiator O2 = oxygen MsH = methyl stearate MoH = methyl oleate MlH = methyl linoleate MlnH = methyl linolenate Ms = methyl stearate radical Mo = methyl oleate radical Ml = methyl linoleate radical Mln = methyl linolenate radical MsO2 = methyl stearate peroxy radical MoO2 = methyl oleate peroxy radical MlO2 = methyl linoleate peroxy radical MlnO2 = methyl linolenate peroxy radical ROOH = hydroperoxide RO = alkoxy radical OH = hydroxyl radical H2O = water ROH = alcohol

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Predictive Skeletal Kinetic Model of Biodiesel Autoxidation - American

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