Overview of Research at the CEFRC on

Chemical Kinetics and Reaction Mechanisms of Foundational Fuels

D. Davidson,1 F. L. Dryer,2 F. N. Egolfopoulos,3 N. Hansen,4

R. K. Hanson,1 Y. Ju,2 S. Klippenstein,5 C. K. Law,2 H. Wang,3

1Stanford University, 2Princeton University, 3University of Southern California,4Sandia National Laboratories, 5Argonne National Laboratory

Combustion Energy Frontier Research Center

2011 MACCCR Fuel Summit

Mechanism, parameters, uncertainties

Kinetics model Critical parameters

Reduced mechanism

Understanding, models

Sensitivities at relevant conditions

Thermo & kinetics parameters and methods

Kinetics parameters

Reactive flow measurements

Combustion Reaction Model Hierarchy and Foundational Chemistry

Products

H2O, CO2

H2, CO

C2H2, soot

(NOx)……H2 Oxidation

CO‐H2 Oxidation

CHxOy, C2‐4Hx OxidationCH4

Alcohols Bio‐Diesel

Critical reviewof literature kinetic data

Modelcompilation

“Tuning”

Validation

Publishmodel

Critical reviewof literature kinetic data

Modelcompilation

“Tuning”

Validation

Publishmodel

Critical reviewof literature kinetic data

Modelcompilation

“Tuning”

Validation

Publishmodel

Critical reviewof literature kinetic data

Modelcompilation

“Tuning”

Validation

Publishmodel

proliferation of models

Combustion Reaction Model Development ‐ The Problem of Model Proliferation

Combustion Reaction Model Development ‐ The Problem of Model Proliferation and Solution

While for large oxygenate and hydrocarbon fuels there 

will be continued parallel efforts leading to competing 

reaction kinetic models, kinetic knowledge for small 

hydrocarbons has converged to a point that it is 

feasible to advance a unified, collaborative reaction 

model of H2/CO/C1‐4 combustion for use as kinetic 

foundation for higher hydrocarbons and oxygenates.

CEFRC Working Hypothesis

CEFRC Foundational Fuel Chemistry

• The need to revisit and unify H2/CO/C1‐4chemistry – H2 combustion

• Other CEFRC activities on foundational fuel chemistry.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 5 10 15 20 25 30Pressure (atm)

Mas

s bu

rnin

g ra

te (g

cm

-2 s

-1)

Burke et al. (2010)Li et al. (2007)O'Connaire et al. (2004)Saxena & Williams (2006)Davis et al. (2005)Konnov (2008)Sun et al. (2007)GRI-MECH 3.0 (1999)Hong et al. (2010)

H2/O2/Ar, φ=2.5Tf ~1600K

-2 -1 0 1 2

Sensitivity Coefficient

phi=2.5

phi=1.0

phi=0.3

H+OH+M=H2O+M

O+H2=H+OH HO2+OH=H2O+O2

HO2+H=H2+O2

H2+OH=H2O+H

HO2+H=OH+OH H+O2=O+OH

H+O2(+M)=HO2(+M)

H2/O2/He, Tf~1400K10 atm

Updating of the H2/O2 model motivated by difficulties in predicting flame behaviors at high pressures and low flame temperatures.

None of the kinetic models predict P dependence across all conditions.

Motivation

Data from M.P. Burke, M. Chaos, F.L. Dryer, Y. Ju, Combust. Flame 157 (2010) 618–631.

Table 6.1. H2/O2 Reaction Model Units are cm3-mol-sec-cal-K; k = A T n exp(-E a /RT)

A n E a Reference1 H+O2 = O+OH 1.04E+14 0.00 1.53E+04 * Hong et al. (2010)2 O+H2 = H+OH Duplicate 3.82E+12 0.00 7.95E+03 * Baulch et al. (2005)

Duplicate 8.79E+14 0.00 1.92E+043 H2+OH = H2O+H 2.16E+08 1.51 3.43E+03 Michael & Sutherland (1988)4 OH+OH = O+H2O 3.34E+04 2.42 -1.93E+03 * Baulch et al. (2005)5 H2+M = H+H+M 4.58E+19 -1.40 1.04E+05 Tsang et al. (1986)

ε H2 = 2.5, ε H2O = 12.0, ε CO = 1.9, ε CO2 = 3.8, ε Ar = 0.0, ε He = 0.0 Li et al. (2004)H2+Ar = H+H+Ar 5.84E+18 -1.10 1.04E+05 Tsang et al. (1986)H2+He = H+H+He 5.84E+18 -1.10 1.04E+05 Li et al. (2004)

6 O+O+M = O2+M 6.16E+15 -0.50 0.00E+00 Tsang et al. (1986)ε H2 = 2.5, ε H2O = 12.0, ε CO = 1.9, ε CO2 = 3.8, ε Ar = 0.0, ε He = 0.0 Li et al. (2004)O+O+Ar = O2+Ar 1.89E+13 0.00 -1.79E+03 Tsang et al. (1986)O+O+He = O2+He 1.89E+13 0.00 -1.79E+03 Li et al. (2004)

7 O+H+M = OH+M 4.71E+18 -1.00 0.00E+00 Tsang et al. (1986)ε H2 = 2.5, ε H2O = 12.0, ε CO = 1.9, ε CO2 = 3.8, ε Ar = 0.75, ε He = 0.75 Li et al. (2004)

8 H2O+M = H+OH+M 6.06E+27 -3.32 1.21E+05 * Srinivasan & Michael (2006)ε H2 = 3.0, ε H2O = 0.0, ε CO = 1.9, ε CO2 = 3.8, εO2 = 1.5, ε N2 = 2.0, ε He = 1.1 See textH2O+H2O = H+OH+H2O 1.01E+26 -2.44 1.20E+05 Srinivasan & Michael (2006)

9 H+O2 (+M) = HO2 (+M)a k ∞ 4.65E+12 0.44 0.00E+00 * Troe (2000)k 0 6.37E+20 -1.72 5.25E+02 Michael et al. (2002), M = N2

F c = 0.5, T*** = 1.0E-30, T* = 1.0E+30 * Fernandes et al. (2008)ε H2 = 2.0, ε H2O = 14.0, ε CO = 1.9, ε CO2 = 3.8, ε O2 = 0.78, εAr = 0.67, εHe = 0.8 * See textH+O2 (+M) = HO2 (+M)b k ∞ 4.65E+12 0.44 0.00E+00 * Troe (2000)

k 0 9.04E+19 -1.50 4.92E+02 Michael et al. (2002), M = Ar or HeF c = 0.5, T*** = 1.0E-30, T* = 1.0E+30 Fernandes et al. (2008)ε H2 = 3.0, ε H2O = 21.0, ε CO = 2.7, ε CO2 = 5.4, ε O2 = 1.1, ε He = 1.2, εN2 = 1.5 * See text

10 HO2+H = H2+O2 2.75E+06 2.09 -1.45E+03 * Michael et al. (2000) x 0.7511 HO2+H = OH+OH 7.08E+13 0.00 2.95E+02 Mueller et al. (1999)12 HO2+O = O2+OH 2.85E+10 1.00 -7.24E+02 * Fernandez-Ramos & Varandas (2002) x 0.613 HO2+OH = H2O+O2 2.89E+13 0.00 -4.97E+02 Keyser (1988)14 HO2+HO2 = H2O2+O2 Duplicate 4.20E+14 0.00 1.20E+04 Hippler et al. (1990)

HO2+HO2 = H2O2+O2 Duplicate 1.30E+11 0.00 -1.63E+0315 H2O2(+M) = OH+OH(+M) k ∞ 2.00E+12 0.90 4.87E+04 * Troe (2010)

k 0 2.49E+24 -2.30 4.87E+04 * Troe (2010)F c = 0.42, T*** = 1.0E-30, T* = 1.0E+30 * Troe (2010)ε H2O = 7.5, εH2O2 = 7.7, ε CO2 = 1.6, ε O2 = 1.2, εN2 = 1.5, εHe = 0.65 * Troe (2010)ε H2 = 3.7 , ε CO = 2.8 See text

16 H2O2+H = H2O+OH 2.41E+13 0.00 3.97E+03 Tsang et al. (1986)17 H2O2+H = HO2+H2 4.82E+13 0.00 7.95E+03 Tsang et al. (1986)18 H2O2+O = OH+HO2 9.55E+06 2.00 3.97E+03 Tsang et al. (1986)19 H2O2+OH = HO2+H2O Duplicate 1.74E+12 0.00 3.18E+02 * Hong et al. (2010)

Duplicate 7.59E+13 0.00 7.27E+03

Indicates that reaction parameters has been revised from that utilized in Li et al (2004)

Recommended for use in mixtures where N2 is prevalent diluent

Recommended for use in mixtures where Ar or He are the prevalent diluent(s).

The Updated Model

In Press, International Journal of Chemical Kinetics, (2011)

Experiments near 1000K: suggest very different behavior.:Hippler et al. 1995 (Troe):

minimum at 1200KKappel et al. 2002 (Troe):

minimum at 1000KNo theoretical work presently

supports the above behavior.Few mechanistic studies at

conditions near the valleys of these results to test their impact.

Data at low temperatures and above ~1200 K are consistent with the rate expression of Keyser (1988). Burke et al utilizes Keyser (1988).

However:

0.5 1 1.5 2 2.5 3 3.5 4

1013

1014

1000/T (K-1)k

(cm

3 mol

-1 s

-1)

Peeters and Mahnen (1973)DeMore (1979)Lii et al. (1980)Cox et al. (1981)Kurylo et al. (1981)Braun et al. (1982)DeMore (1982)Goodings & Hayhurst (1988)Keyser (1988)Hippler & Troe (1992)

Hippler et al. (1995)Kappel et al. (2002)Srinivasan et al. (2006)Hong et al. (2010)Keyser (1988)Sivaramakarishnan et al. (2007)Chaos & Dryer (2008) - HipplerChaos & Dryer (2008) - KappelRasmussen et al. (2008)

Example: HO2+OH=H2O+O2;

Uncertainties - Model Parameters

1.E+11

1.E+12

1.E+13

1.E+14

0.00 0.50 1.00 1.50 2.00 2.50 3.00

1000/T (K-1)

k (c

m3 m

ol-1

s-1

)

Hippler et al. 1995

Kappel et al. 2002

Particularly for T-P dependence of HO2consumption/formation rxns

For example, rate constants for HO2+HO2 = H2O2 + O2 (R14) from the only two high-T studies in the literature differ by a factor of 3 yields 20% differences in predicted flame speeds

Uncertainties - Model Parameters

Rate constant expressions for k14.

11

Uncertainties – Mechanism Assumptions

H+HO2

H2OO HOOH H2O+O(3P) H2+O2

(i)(ii)

(vii)(v)

(vi)(iii)

(iv-1)

(iv-2)H2O+O(1D)

OH+OH

H2O+O(3P)HO…OH

H+HO2

H2OO HOOH H2O+O(3P) H2+O2

(i)(ii)

(vii)(v)

(vi)(iii)

(iv-1)

(iv-2)H2O+O(1D)

OH+OH

H2O+O(3P)HO…OH

For example: H + HO2 = H2O + O

Included only in some kinetic models

Experimental data available only below 400K

Previous theoretical treatments yield different answers about its role at combustion temperatures. Inclusion of the reaction using previous rate constant estimates result in up to 30% differences in predicted flame speed

Present calculations (VRC-TST) suggest this reaction may be important.

Non-statistical approaches (not considered here) necessary for accurate treatment b/c of short HOOH lifetimes

H2/O2/He flames. Mixture effects simulated by 10% higher A-factor for H+O2+M=HO2+M (R9).

Nonlinearities in bath-gas mixture rule for unimolecular reactions found to reach ~10% 15% differences in predicted flame speeds

More generally: high-pressure, dilute flames might require consideration of many “negligible”processes

Uncertainties – Kinetic Processes

Summary Hydrogen Modeling

Present model adequately reproduces previous and new targets across a wide range of conditions with substantial improvements against recent high-pressure flame speed and shock tube speciation measurements

Uncertainties in both model parameters and underlying assumptions affect predictions of relevant combustion behavior (including rate constants for HO2 rxns, potential missing rxns, and bath-gas mixture rules).

CEFRC Foundational Fuel Chemistry

• The need to revisit and unify H2/CO/C1‐4chemistry.

• Other CEFRC activities on foundational fuel chemistry.

Ab initio & reaction rate theory predictions of elementary reaction rate constants

Klippenstein/ANL

Davidson & Hanson/Stanford

Ethylene Oxidation

Ethylene PyrolysisRate Determination: C2H4 → C2H2 + H2

1.0% C2H4/Ar1895 K, 2.6 atm 

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0

0.1

0.2

0.3

0.4

0.5

Wei et al. (2011) Marinov et al. Healy et al. Wang et al. Ranzi et al.

Time [ms]

C2H

4 M

ole

Frac

tion

[%]

0.5% C2H4/3% O2/Ar1221 K, 3.4 atm 

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0

1.2

Wei et al. (2011) Best Fit (C2H4=C2H2+H2) JetSurF 2.0

Time [s]

C2H

4 M

ole

Frac

tion

[%]

Shock tube/laser absorption measurements:Ethylene time‐Histories

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

0.5 0.7 0.9 1.1 1.3 1.5 1.7

Equivalence Ratio

Lam

inar

Fla

me

Spee

ds, c

m/s

1 atm

1 atm

2 atm

2 atm

4 atm

4 atm

10

15

20

25

30

35

40

45

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Laminar Flame Speeds, cm/s

Equivalence Ratio

n-Butane/Air, p=1 atm

Egolfopoulos/USC

Measurement and model validation: laminar flame speeds

Methane/Air

Symbols: experimental dataLines: USC‐Mech II predictions

Measurement and model validation: burner stabilized flames

Hansen/Sandia

10.5%i-C4H8/39.5%O2/Ar Flame

Measurement and model validation: burner stabilized flames

Hansen/SandiaYang/Sandia/USC

Relative Energy (kcal/mol)

CCSD(T)/6‐311G(d) // B3LYP/6‐311G(d)

+ CH3

Data structure that describes a chemical model + associated uncertainty

,0 , ,1 1

N N N

r r r i i r ij i ji i j i

a x b x x

x

Predictions of a chemical model (e.g. mass burning rate)+ associated uncertainty

0, ,

1 1

ˆˆ,m m m

r r r i i r ij i ji i j i

x ξ x

Represents some physics model,e.g. a laminar flame

Sheen, et al. (2009 & 2011)

0 x x αξ ,0lnln

i ii

i

k kx

f

Knowledge (Uncertainty) Quantification by Polynomial Chaos Expansions

Data structure that describes a chemical model + associated uncertainty

,0 , ,1 1

N N N

r r r i i r ij i ji i j i

a x b x x

x

Predictions of a chemical model (e.g. mass burning rate)+ associated uncertainty

0, ,

1 1

ˆˆ,m m m

r r r i i r ij i ji i j i

x ξ x

Sheen, et al. (2009 & 2011)

0 x x αξ

Knowledge (Uncertainty) Quantification by Polynomial Chaos Expansions

Chemical model + associated uncertainty

,0 , ,1 1

N N N

r r r i i r ij i ji i j i

a x b x x

x

Predictions + associated uncertainty

0, ,

1 1

ˆˆ,m m m

r r r i i r ij i ji i j i

x ξ x

Physics model

0 x x αξ

k1

k2

h1

0

2 2obs,0 0 0,*

0 2 2obs1 1min

M Nr r n

r n nr

x

x

xx

1

0 0 0 02obs1

1 4n

T T T T T

rr

* * * *bx x b ax b b x a aa I

1/2 *α

Uncertainty Minimization by Polynomial Chaos Expansions

Considering no combustion experiments

Model constrained by knowledge prior to 2010

Model constrained by the latest knowledge

Uncertainty Minimization by Polynomial Chaos Expansions – Measured Progress!

The Future

•Detailed H2/CO/C1‐4 reaction model with well defined uncertainties

•Active design of experiments

•Two‐way knowledge propagation.

Kinetic expt./electronicstructure

calc.

Reaction rate theory

Review of literature kinetic data

ModelcompilationValidation

Sensitivityanalysis

Newexperiments

Response surfacedevelopment

Uncertainty minimization

A New Approach