Detailed and Simplified Chemical Kinetics of Aviation Fuels and Surrogates

Peter Lindstedt (PI), Roger Robinson1 and Sung-Woo Park 1Supported by EOARD/AFOSR via Award FA8655-09-1-3089.

MACCCR/AFOSR Fuel Research Review Argonne, September 20-22, 2011.

Background

Objectives

  Seek to improve upon current reaction class-based estimation methods.

  Seek to identify specific issues that require more detailed studies using higher accuracy methods and/or experimentation.

Approach

  The application of computational methods that can provide chemical kinetic data of sufficient accuracy to guide the development of detailed chemical kinetic mechanisms at a decent rate of progress.

  Extensive validation.

Topics

  Example of the impact of consistent use of thermodynamic data.

  Some comparisons of results obtained using different ab initio methods for the determination of rate data from the same PES. The example chosen relates to biofuels.

  Progress on the n-propyl benzene [nPB] system

  Some comments on C5-ring structures and the cyclopentadiene system.

Thermodynamic Data

  The error for the composite G4 method (Curtiss et al. 2007), as measured against a hydrocarbon test set, is estimated to be 0.48 kcal/mol with a RMS deviation of 0.70 kcal/mol.

  G4MP2 is a second order perturbation theory version of G4 with a somewhat reduced accuracy of 0.63 kcal/mol for the same test set.

  Thermodynamic data bases have been substantially updated for more than 200 species of relevance to current projects.

  Jahn-Teller effects are added in cases such as cyclopentadiene (e.g. Robinson and Linstedt 2011).

  The method appears robust, though larger molecules (say C14+) can be non-trivial and result in significant computational effort.

Impact of Thermodynamics   Fuel rich laminar (φ = 2.4)

premixed flat acetylene flame (Westmoreland and co-workers).

  Polyenes may have an impact on soot mass growth.

  No reasonable change in rate parameters resolved the issue with the C6H2 profile.

  Thermodynamic data was obtained from reputable computations.

Impact of Thermodynamics

  A re-evaluation of the

thermodynamics using c a l c u l a t i o n s a t t h e G4MP2 level produced the outcome shown.

  The agreement is notably improved and suggests that consistent use of data at this level provides reasonable agreement for the current case.

  Acetylene flames are likely to come to the fore a g a i n d u e t o n e w synchrotron data and the importance of soot.

Data for Rate Processes

  Potential Energy Surfaces at the G4/G4MP2 level in order to reduce uncertainties somewhat from G3/G3B3 used in the past.

  Reaction rates initially calculated for all reactions using Rice–Ramsperger–Kassel–Marcus/master equation theory (RRKM/ME) (Mokrushin et al. 2008; Robinson and Lindstedt 2011).

  Calculations of high pressure limit rate data using Transition State Theory (TST) and Canonical Variation Theory (CVT) with VRC-VTST computations carried out and the Canonical Unified Statistical (CUS) model was applied in some cases (Truhlar and co-workers 2010).

  Multiple well systems are also studied using a RRKM/MW technique or the Inverse Laplace Transform (ILT) method of Robertson et al. (2010).

Reaction Classes

  The studied reactions were delineated using four classes:

  bimolecular exchange reactions;   dissociation reactions with a clear transition state;   barrierless dissociation reactions;   multiwell reactions.

  Different methods were used and compared mainly on the basis of the same G4 or G4MP2 derived energy data.

  Enthalpies anchored at 298 K.

  Transition state properties for barrierless reactions were estimated using the enthalpy of formation and frequencies of both reactants and products (c.f. VRC-VTST).

  The applied rotational data was evaluated from the external rotors of the active component and Benson correction parameters including the vibrational frequency of the bond to be broken.

  Hindered internal rotors typically scanned at the B3LYP/6-31g(d) level (issues related to barrier height).

  The contribution of hindered internal rotors taken into account considering the overall energy barrier to rotation, symmetry number and the internal moment of inertia.

  Eckart quantum tunnelling corrections were applied to reactions involving hydrogen transfers with large imaginary frequencies, barrier widths obtained from IRC calculations.

RRKM/ME Calculations [CHEMRATE 1.5.8 - 2009]

RRKM/MW, Multiwell and ILT Calculations [MESMER 0.2 - 2011]

  Energies anchored at 0 K.

  Internal (not hindered) rotors currently treated through vibrational data and one-dimensional tunnelling considered through an asymmetric Eckart barrier (Miller 1979).

  Full multiwell treatment of reactions with multiple steps on more complex PESs were computed using this methodology.

  TST/SCT used for bimolecular exchange reactions and VRC-VTST for barrierless dissociation reactions.

  Data from the PES for each step of the process was required and the GAUSSRATE interface was used to provide direct dynamics calculations of energies, gradients and Hessians on the reaction path.

  VRC-VTST calculations were carried out in a similar manner. Single-faceted dividing surfaces were used with the pivot points defined at the two bonding atoms.

  The reaction coordinate (s) was varied between approximately 1.2 and 6 Å depending on the reaction studied.

TST, VTST and VRC-VTST Calculations [POLYRATE 2010-A]

  Example of a more complex PES with possible stabilisation occurring at the intermediate well.

  Work on the C3H7O potential has been performed by Zador et al. (2009) in the context of the C3H6 + OH reaction.

CH3CHCH2OH

TS17

C2H5CH2O

TS16

C2H5 + CH2O

-75.00

-50.00

-25.00

0.00

25.00

50.00

75.00

!H

f29

8K

[kJ

mol-1

]C3H6OH → C2H5CH2O → C2H5 + CH2O

  T h e a g r e e m e n t between the 10 atm r a t e a n d t h e estimation of Wilk et al. (1989) is rather good at combustion temperatures.

  Pressure fall-off is significant.

  It is not uncommon for the latter to be a source of concern.

Sample Reaction : C3H6OH → C2H5CH2O → C2H5 + CH2O

Laminar Burning Velocities for n-Propanol [MESMER Data]

  n-Propano l /Oxygen/Argon flame from Li et al. (2008) with Ф = 1.8, 40 % Ar, 4000 Pa.

  The mechanism including multiple well data results in better agreement.

  The improvement is particularly obvious for propionaldehyde.

  The experimental method can not distinguish between ketene and other mass 42 species.

  The RRKM/ME approach remains useful.

  More details can be provided.

0

0.005

0.01

0.015

0

0.01

0.02

0.03

0

0.002

0.004

0.006

Mol

e fra

ctio

n [-]

RRKM/MERRKM/ME Multiwell

0

0.005

0.01

0.015

Mol

e fra

ctio

n [-]

0 5 10 15Distance from burner [mm]

0

0.001

0.002

0 5 10 15 2001e-052e-053e-054e-05

CH3 C2H4

C3H6+C2H2O CH3CHO+C2H3OH

CH3CH2CHO C6H6

Low Pressure Flat Flame I – Fuel Rich n-Propanol Mixture

The n-Propyl-Benzene [nPB] System

  Bimolecular exchange reactions involved in the initial breakdown of n-propyl-benzene featuring a hydrogen exchange with common radical and molecular species (H, OH, O, O2 and CH3).

  Geometries for reactants, transition states, complexes and products optimised at the B3LYP/6-31G(2df,p) level. Energies calculated at the G4 and G4MP2 composite level.

  For the RRKM(/ME) calculations, energies, vibrational data and moments of inertia were taken from G4/G4MP2 calculations.

  Hindered rotors investigated at the B3LYP/6-31G(d) level and corrections included.

  TST/SCT with energies, first derivatives, gradients and Hessians computed at the B3LYP/6-31G(d) level with higher level calculations currently taking place.

The nPB System

  Standard reactant - transition state - product channels were found for reactions involving H and CH3 radicals.

  For reactions involving OH radicals, van der Waals stabilised complexes were found on both reactant and product sides of the transition state.

  Product side complexes were ignored for non-CUS based computations.

  Radical complexes on both product and reactant sides also identified for reactions involving O (work is still in progress).

The nPB System

Reaction Reactant Reactant Product Product Energy Reactants Energy TS Energy

Products Activation

Energy

Number 1 2 1 2 kJ mol-1 kJ mol-1 kJ mol-1 kJ mol-1

1 C9H12 H C9H11_1 H2 225.75 244.89 194.14 19.14

2 C9H12 H C9H11_2 H2 225.75 234.34 184.40 8.59

3 C9H12 H C9H11_3 H2 225.75 228.43 150.33 2.68

C9H12

C9H11-1

C9H11-2

C9H11-3

TS1

TS2

TS3

[1,2,3] C9H12 + H = C9H11-1/-2/-3 + H2

1.0E+08

1.0E+09

1.0E+10

1.0E+11

0.4 0.6 0.8 1 1.2

Rat

e C

onst

ant [

m3 k

mol

-1 s

-1]

1000/T [K]

RRKM

TST/SCT

Dagaut et al.

  Abstraction from terminal site (top left), second site (top right) and adjacent to ring (right).

  Estimations by Dagaut et al. based on n-propyl.

1.0E+08

1.0E+09

1.0E+10

1.0E+11

1.0E+12

0.4 0.6 0.8 1 1.2

Rat

e C

onst

ant [

m3 k

mol

-1 s-1

]

1000/T [K]

RRKM Dagaut et al. TST/SCT

1.0E+08

1.0E+09

1.0E+10

1.0E+11

1.0E+12

0.4 0.6 0.8 1 1.2

Rat

e C

onst

ant [

m3 k

mol

-1 s-1

]

1000/T [K]

RRKM Dagaut et al. TST/SCT

[5] C9H12 + CH3 = C9H11-2 + CH4

1.0E+05

1.0E+06

1.0E+07

1.0E+08

1.0E+09

0.4 0.6 0.8 1 1.2

Rat

e C

onst

ant [

m3 k

mol

-1 s

-1]

1000/T [K]

RRKM

TST/SCT

Dagaut et al.

1.0E+06

1.0E+07

1.0E+08

1.0E+09

1.0E+10

0.4 0.6 0.8 1 1.2

Rat

e C

onst

ant [

m3 k

mol

-1 s-1

]

1000/T [K]

RRKM

TST/SCT

Dagaut et al.

[4] C9H12 + CH3 = C9H11-1 + CH4

[8] C9H12 + OH = C9H11-2 + H2O

Well R8 TS8 Well P8

C9H12 +

OH TS8

C9H11-2 +

H2O

WellP8

WellR8

-75.00

-50.00

-25.00

0.00

25.00

50.00 ΔH

f298K

[kJ m

ol-1

]

[8] C9H12 + OH = C9H11-2 + H2O

1.0E+08

1.0E+09

1.0E+10

1.0E+11

1.0E+12

0.4 0.6 0.8 1 1.2

Rat

e C

onst

ant [

m3 k

mol

-1 s-1

]

1000/T [K]

CUS

TST/SCT

Dagaut et al.

[9] C9H12 + OH = C9H11-3 + H2O

WellR9 TS9 WellP9

C9H12 +

OH

TS9

C9H11-3 +

H2O WellP9

WellR9

-100.00

-75.00

-50.00

-25.00

0.00

25.00

50.00 ΔH

f298K

[kJ m

ol-1

]

[9] C9H12 + OH = C9H11-3 + H2O

1.00E+08

1.00E+09

1.00E+10

1.00E+11

1.00E+12

0.4 0.6 0.8 1 1.2

Rat

e C

onst

ant [

m3 k

mol

-1 s-1

]

1000/T [K]

TST/SCT

Dagaut et al.

[15] C9H12 + O2 = C9H11-3 + HO2

1.0E-02

1.0E+00

1.0E+02

1.0E+04

1.0E+06

1.0E+08

0.4 0.6 0.8 1 1.2

Rat

e C

onst

ant [

m3 k

mol

-1 s-1

]

1000/T [K]

RRKM

TST/SCT

Dagaut et al.

  The cyclopentadienyl (CPDyl) radical forms a key part of the main reaction pathway leading from single and multiple ring aromatics to linear hydrocarbons.

  Potential Energy Surfaces (PES) were calculated at the G4 level using Gaussian09 and compared to previous work (e.g. Emdee et al. 1992; Zhong and Bozzelli 1998; Tokmakov et al. 2004; Harding et al. 2007).

  A substantial update of the CPD chemistry has been made (Robinson and Lindstedt 2011) and the impact evaluated against experimental data from Butler (2001) and Butler and Glassman (2009).

  Some of the PES are rather complex with multiple wells and selected cases were subsequently investigated using multiwell techniques (MESMER).

The Cyclopentadienyl System

Thermal Decomposition of CPDyl

Potential energy diagram with energies determined at the G4 level for the thermal decomposition of the cyclopentadienyl radical (CPDyl).

TS17

TS18

C H -15 5

TS19650.00

550.00

450.00

350.00

250.00

C H

+

C H

3 3

2 2

C H5 5

CHCCH CHCH2

Thermal Decomposition of CPDyl

1.0E-03

1.0E-01

1.0E+01

1.0E+03

1.0E+05

1.0E+07

0.4 0.6 0.8 1 1.2

Rat

e Con

stan

t [s-1

]

1000/T [K]

RRKM/ME HPRRKM/MW 1 atmRRKM/MW 10 atmKern et al. HPRoy et al.Moskaleva et al. 1 atmKeifer 4% ~0.26atmKeifer 2% ~0.26 atm

CPD Oxidation [Data Butler and Glassman 2009/Computations Robinson and Lindstedt 2011]

  Concentration profiles during CPD oxidation in a flow reactor. Φ = 1.03 (2243 ppm fuel, T = 1198 K) and Φ = 1.03 (1051 ppm fuel, T = 1148 K).

0

500

1000

1500

2000

2500

3000

0

5000

10000

15000

20000

0 50 100 1500

2000

4000

6000

8000

50 100 150 0

500

1000

1500

2000

2500

C5H6

O2

CO CO2

Time [ms]

Mol

e Fr

actio

n [p

pm]

0

10

20

30

40

0

20

40

60

80

0 50 100 1500

5

10

15

20

50 100 150 0

50

100

C3H4(A) C3H4(P)

C3H6 1,3-C4H6

Time [ms]

Mol

e Fr

actio

n [p

pm]

CPD Oxidation

0

50

100

150

200

0

5

10

15

20

0 50 100 1500

50

100

150

50 100 150 0

50

100

150

C10H8 C7H8

C6H6 C4H4

Time [ms]

Mol

e Fr

actio

n [p

pm]

0

100

200

300

400

500

600

0100200300400500600700

0 50 100 1500

50

100

150

200

250

50 100 1500102030405060

CH4 C2H2

C2H4 C2H6

Time [ms]

Mol

e Fr

actio

n [p

pm]

  Concentration profiles during CPD oxidation in a flow reactor. Φ = 1.03 (2243 ppm fuel, T = 1198 K) and Φ = 1.03 (1051 ppm fuel, T = 1148 K).

Further CPD Related Data

  Burning velocities for CPD (private communication Egolfopoulos 2011) – preliminary modelling result.

  CPD and CPDyl concentrations in the acetylene flame of Westmoreland and co-workers.

Summary/Current Work

  Critical reaction paths in the oxidation of aromatic surrogate fuel components have been analyzed and rates of reaction determined via ab initio methods.

  Particular attention has been given to the critical cyclopentadiene system and a key oxidation reactions studied.

  Work has commenced on the initiation reactions in the n-propyl benzene system and this is expected to conclude over the next few months.

  Decomposition reactions in the nPB system will also be studied in order to determine rates and fall-off.

  Selected complex PES in the CPDyl system will be explored further using multiwell methods.

  Uncertainties in barrier heights and the corresponding impact on rate parameters are being evaluated using a wider subset of available methods (e.g. G4MP2, G4, B3LYP/6-31G(d), M062X/6-311G(2df,p) and CCSD(T)/aug-cc-pVQZ; c.f. Zheng and Truhlar 2010).