Reaction kinetics of dimethyl ether. II: low-temperature oxidation in flow reactors

Article abstract of DOI:10.1002/1097-4601(2000)32:12<741::AID-KIN2>3.0.CO;2-9

Dimethyl ether oxidation has been studied in a variable-pressure flow reactor over an initial reactor temperature range of 550-850 K, in the pressure range 12-18 atm, at equivalence ratios of 0.7 ≤ φ ≤ 4.2, with nitrogen diluent of approximately 98.5%. On-line extraction sampling in conjunction with FTIR, NDIR (for CO and CO₂), and electrochemical (for O₂) analyses were performed to quantify species at specific locations along the axis of the turbulent flow reactor. Product species concentrations were correlated against residence time (at constant inlet temperature) and against temperature (at fixed mean residence time) in the reactor. Formic acid was observed as a major intermediate of dimethyl ether oxidation at low temperatures. The experimental species-evolution profiles were compared to the predictions of a previously published detailed kinetic mechanism [1]. This mechanism did not predict the formation of formic acid. In the current study we have included chemistry leading to formic acid formation (and oxidation). This new chemistry is discussed and is able to reproduce the experimental observations with good accuracy. In addition, this model is able to reproduce low-temperature kinetic data obtained in a jet-stirred reactor [2] and the shock-tube results of Pfahl et al. [3].

Full text of DOI:10.1002/1097-4601(2000)32:12<741::AID-KIN2>3.0.CO;2-9

The Reaction Kinetics of
Dimethyl Ether. II: Low-
Temperature Oxidation in
Flow Reactors
1
2
2
H. J. CURRAN, S. L. FISCHER, F. L. DRYER
1
Chemistry and Materials Science Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94551
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544
2
Received 8 September 1999; accepted 16 June 2000
ABSTRACT: Dimethyl ether oxidation has been studied in a variable-pressure flow reactor over
an initial reactor temperature range of 550–850 K, in the pressure range 12–18 atm, at equiv-
alence ratios of 0.7 Յ ␾ Յ 4.2, with nitrogen diluent of approximately 98.5%. On-line extraction
sampling in conjunction with FTIR, NDIR (for CO and CO ), and electrochemical (for O ) anal-
2
2
yses were performed to quantify species at specific locations along the axis of the turbulent
flow reactor. Product species concentrations were correlated against residence time (at con-
stant inlet temperature) and against temperature (at fixed mean residence time) in the reactor.
Formic acid was observed as a major intermediate of dimethyl ether oxidation at low tem-
peratures. The experimental species-evolution profiles were compared to the predictions of a
previously published detailed kinetic mechanism [1]. This mechanism did not predict the
formation of formic acid. In the current study we have included chemistry leading to formic
acid formation (and oxidation). This new chemistry is discussed and is able to reproduce the
experimental observations with good accuracy. In addition, this model is able to reproduce
low-temperature kinetic data obtained in a jet-stirred reactor [2] and the shock-tube results
of Pfahl et al. [3] ꢀ 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 741–759, 2000
INTRODUCTION
pared calculated results based on a new, detailed ki-
netic model with the flow-reactor data and with pre-
viously published high-temperature oxidation data
from a different flow reactor, stirred reactors, and
shock tubes.
One of the important attributes of DME as a diesel
fuel is its high cetane rating [5]. An understanding of
the low- and intermediate-temperature oxidative be-
havior is therefore of practical interest. In this article,
we report the new data obtained at low and interme-
diate temperatures using a variable-pressure flow re-
actor (VPFR) [6]. These data are then considered
along with other low- and intermediate-temperature
kinetic data to further develop and validate a detailed
kinetic model for DME oxidation. A number of prior
experimental and modeling works on low and inter-
In a companion article [4], we discussed the back-
ground to the reason dimethyl ether (DME) has been
featured in the combustion literature as an alternative
for or additive to diesel fuel. In that paper, we consid-
ered only the high-temperature kinetics, presenting
new flow-reactor data on the pyrolysis and oxidation
of DME at temperatures above 1000 K. We also com-
Correspondence to: F. L. Dryer (fldryer@princeton.edu)
Contract grant sponsor: U.S. Dept of Energy, Chemical Sciences
Division
Contract grant sponsor: DE-F602-86ER-13503
Contract grant sponsor: U.S. Dept of Energy, Lawrence Liver-
more, National Laboratory
Contract grant number: W-7405-ENG-48
2000 John Wiley & Sons, Inc.
ꢀ

7
42
CURRAN ET AL.
mediate DME oxidation have appeared previously,
and these works are briefly summarized here.
In the same time period, Edgar et al. [16] reported
constant-volume bomb experiments in which DME
was injected as a liquid into a hot, gaseous, inert or
oxidizing media. Edgar et al. proposed a general de-
tailed chemical kinetic mechanism to describe the py-
rolysis, oxidation, and autoignition experiments of
DME in a constant-volume, premixed mixture. How-
ever, the experiments themselves were not sufficiently
well defined to permit testing and validation of the
proposed mechanism. The DME injection process led
to a spatial distribution of fuel/air equivalence ratio
within the volume, along with nonhomogeneous tem-
perature distributions in the bomb. The kinetic mech-
anism of Edgar et al. produced qualitative behavior
similar to their experimental observations, but the
mechanism was not compared with other experimental
data present in the literature. The authors propose for-
mic acid as a potential reactive intermediate resulting
from low and intermediate oxidative processes. How-
ever, no experimental data were generated to confirm
or deny these portions of the proposed mechanism.
The first results from the present experimental stud-
ies [6] were reported in early 1997 [17]. Oxidation of
DME at high pressures (12.5 atm) and low and inter-
mediate temperatures (490–790 K) confirmed the ex-
istence of a negative temperature coefficient regime
from 590–690 K, followed by an intermediate tem-
perature regime, ending in hot ignition above 780 K.
More important, FTIR spectral analyses of the reaction
products identified formic acid as a significant reaction
intermediate at temperatures near 500 K. Although the
formic acid was not fully quantified (calibration work
had not been completed), its presence suggested that
proposed dimethyl ether kinetic mechanisms should
include this species as a significant intermediate at low
temperatures. Calibrated, quantified data showing that
formic acid was indeed a major intermediate found at
low and intermediate reaction temperatures, substan-
tially exceeding formaldehyde concentrations, were
first presented in 1998 [18].
Atmospheric DME oxidation studies [7]–[9] have
focused on the reaction of the methoxymethyl-peroxy
radical with hydroperoxy radicals [7], the self-reaction
of methoxymethyl-peroxy radicals [8], and the reac-
tion of methoxymethyl-peroxy radicals with NO and
NO [9]. Sehested et al. [10] studied the self-reaction
2
and thermal decomposition of the methoxymethyl rad-
ical in addition to its reaction with molecular oxygen.
Masaki et al. [11] and Sehested et al. [12] also studied
the rate of methoxymethyl addition to molecular oxy-
gen and measured consistent rate-constant expres-
sions. All of these earlier studies were performed at
approximately 296 K, a temperature that is much
lower than those experienced in operating diesel en-
gines or in diesel engine fuel systems.
More recently, Hoyermann and Nacke [13] studied
some elementary reactions of the ethoxymethyl radical
in the gas phase, most notably its reactions with mo-
lecular and atomic oxygen. These experiments were
performed in the temperature range 300–700 K and
at pressures of 1–5 mbar. The low pressures of this
work leave some doubt as to whether the measured
rate expression would be valid at high pressures. Fi-
nally, Maricq et al. [14] studied the oxidation of DME
in the temperature range 230–350 K. They concluded
that the reaction between methoxymethyl radical and
molecular oxygen proceeds along two distinct path-
ways. At pressures above about 100 Torr, the peroxy
radical is predominantly formed. However, as the
pressure is reduced, a channel leading to the formation
of hydroxyl radical and two formaldehyde molecules
becomes progressively more important.
More general mechanistic studies of DME oxida-
tion have also appeared. In 1996, Dagaut et al. [15]
reported the first experimental results on the oxidation
of DME at high temperatures, including species dis-
tribution information as a function of overall residence
time. Results were obtained in a jet-stirred reactor
(
JSR) at 1 and 10 atm, 0.2 Յ ␾ Յ 2.5, and 800 Յ
Recently, Dagaut et al. [2] reported additional ex-
perimental studies of DME in their jet-stirred reactor.
Data were obtained at 10 atm in the temperature range
500–800 K, using extractive gas sampling and gas
chromatography with flame ionization detection. For-
maldehyde and hydrocarbon products were identified
and quantified, but formic acid was not observed to be
a reaction intermediate in contrast with our results. We
speculated in comments on the Dagaut et al. paper [2]
that formic acid was lost in the analytical measurement
apparatus. However, the carbon balances reported in
the work suggest that there are no significant concen-
trations of unidentified species present. Thus, we are
T Յ 1300 K. Pfahl and coworkers [3] also measured
DME ignition-delay times behind reflected shock
waves at 13 and 40 bar, ␾ ϭ 1.0, and 650 Յ T Յ
1
300 K. Although no species distributions were re-
ported in this work, the results clearly demonstrated that
DME exhibits typical “two-stage” ignition characteris-
tics common to many hydrocarbons, i.e., low temper-
ature, negative temperature coefficient, and hot ignition
phenomena. Curran et al. [1] used the combination of
the Dagaut et al. and Pfahl et al. experimental data in
developing a detailed kinetic mechanism for DME ox-
idation over wide ranges of temperature and pressure.

THE REACTION KINETICS OF DIMETHYL ETHER. II
743
at a loss as to why formic acid was not observed, un-
less it was somehow converted during the sample
quenching process to other carbon/hydrogen/oxygen-
containing intermediates that were correctly quanti-
fied. As a result of their experimental evidence, Dagaut
et al. modeled their results using the low-temperature
portion of the DME mechanism from Curran et al.,
without modifications in the earlier reaction scheme.
Instead, rate expressions were adjusted to gain agree-
ment with the new JSR data. Predictions using this
mechanism continue to suggest a minor presence of
formic acid as an intermediate at low and intermediate
temperatures, consistent with their experimental ob-
servations (Figs. 22 and 24).
parison of formic acid predictions and the experi-
ments).
EXPERIMENTAL DESCRIPTION
All of the experiments reported here were performed
in the Princeton Variable-Pressure Flow Reactor
(VPFR). The VPFR can access a wide range of con-
ditions: temperature (550–1200 K), pressure (0.3–
20 atm), and equivalence ratio (pure pyrolysis to oxy-
gen-rich conditions). The VPFR facility, as well as the
sampling and analytical techniques utilized in the
present work, are fully described in the companion
article [4]. A sample flow obtained using a hot-water-
cooled, wall-convection-quenched, stainless steel
sample probe was analyzed using a Nicolet Model 730
FTIR, equipped with a heated 0.7-liter, 10-meter mul-
tireflective cell, with spectral absorbance resolution of
Finally, Liu et al. [19] have recently reported stud-
ies on the oxidation of DME (340 ppm DME in 10%
O ) in an atmospheric-pressure laminar flow reactor,
2
at temperatures from 513 Յ T Յ 973 K and residence
times in the range from 2 to 4seconds. The products
leaving the reactor were analysed using Fourier-Trans-
form Infra-Red Spectroscopy. It was found that the
products in this low-temperature region included for-
maldehyde, carbon monoxide, and formic acid. Con-
firming our measurements, formic acid was deter-
mined to be a major reaction intermediate in the
low-temperature oxidation.
Ϫ
1
0.125 cm . The cell pressure (760 mm Hg) and tem-
perature (100ꢁC) were held constant for all measure-
ments. The analytical flow exiting the cell was then
directed to a continuous-flow electrochemical analyzer
for O , to continuous nondispersive infrared (NDIR)
2
analyzers for CO and CO , and to a continuous selec-
2
tive detector for H . Each species’ concentration was
2
The current experimental and modeling collabora-
tion was undertaken to advance prior modeling efforts
to be consistent with observations of formic acid as a
major intermediate at low and intermediate reaction
temperatures. The work extends understanding of di-
methyl ether oxidation at low temperatures, i.e., tem-
peratures at which the methoxymethyl radical under-
goes addition to molecule oxygen, followed by
internal H-atom transfer, a second addition to molec-
ular oxygen, and eventual chain branching. Kinetic
measurements obtained in the VPFR were compared
to predictions from previously published detailed ki-
netic mechanisms [1,2], which did not include a direct
pathway for formic acid production from DME, a de-
ficiency immediately apparent in comparisons. A more
thorough study of the low-temperature mechanism re-
veals a new pathway for formic acid formation that is
logical and that has been overlooked previously. In the
course of the modeling studies, we also modified some
important rate-constant expressions used in prior mod-
eling in response to more current understanding
of thermochemical parameters and rate estimations.
Overall, we have obtained good agreement between
model simulation and experimental observations in the
VPFR. We also find good agreement with the earlier
shock-tube experiments of Pfahl et al. [3] and the JSR
experiments of Dagaut et al. [2,15] (neglecting com-
determined, with the exceptions of formic acid and
water, from spectral features that were isolated from
interference produced by other species. Formic acid
and water spectra interference could not be completely
separated, and a multicomponent absorbance calibra-
tion had to be performed for these two species. FTIR
species concentration uncertainties were as follows:
CH OCH (4% or Ͻ50 ppm), CH (2%), CH OH
3
3
4
3
(2%), C H6 (2%), C H4 (2%), CH O (5% or
2
2
2
Ͻ10 ppm), HOCHO (3.5% or Ͻ12 ppm), H O (10%).
2
Other analytical measurements had uncertainties as
follows: O (3%), CO (2%), CO (2%). No other
2
2
hydrocarbon species (Ͼ1 ppm) were detected in the
experiments reported here or in the companion paper.
The reaction temperature at the gas sampling location
was measured with a silica-coated Pt-13%Rh/Pt ther-
mocouple (Ϸ3 K uncertainty). Further details of the
apparatus and techniques can also be found elsewhere
[6].
Dimethyl ether was studied at equivalence ratios
(␾) in the range 0.7 Յ ␾ Յ 4.2 with nitrogen diluent
of approximately 98.5%. Experiments were performed
over an initial reactor temperature range of 550–
850 K, in the pressure range 12–18 atm. Four distinct
sets of experiments were performed to characterize the
low- and intermediate-temperature oxidation charac-
teristics. The first set of experiments were conducted

7
44
CURRAN ET AL.
at a constant fuel/oxidizer ratio of approximately 1, at
constant pressure and residence time (12.5 atm and
chemical compositional data and sample-point tem-
perature were obtained. The mixing location was
changed, and the process was repeated. Reactant, in-
termediate, and product composition and flow reaction
temperatures were then correlated for fixed initial con-
ditions as a function of reaction residence time.
The second series utilized near-stoichiometric
equivalence ratio of DME and oxygen and a number
of initial reactant temperatures corresponding to vari-
ous points in the regime of negative temperature co-
efficient (NTC) behavior; see Figures 5–10. A third
set of experiments was performed in which the equiv-
alence ratio was varied from lean, through stoichio-
metric, to rich, with product species concentrations
correlated against residence time (Figs. 11–16). These
experiments were all performed at the same pressure
(Ϸ12 atm) and at a constant initial reaction tempera-
ture of 850 K. The fourth set of experiments depicted
the oxidation effects at increasing reaction pressure,
at an initial reaction temperature of approximately
590 K, an equivalence ratio of approximately 1.0. In
these experiments, reaction pressure was held at 12.5,
17, and 18 atm (see Figs. 5–6 and Figs. 17–20).
Because reaction times between movement of the
mixing location are relative to one another, with the
same mixing and contaminant perturbations of the in-
duction chemistry, it is more useful to compare the
calculated and experimental species- and temperature-
time histories by matching them at some intermediate
extent of reaction. Further details justifying this
method of comparison appear in the companion arti-
cle [4].
1
.8 s, respectively), and with different initial reaction
temperatures. The initial reaction temperature of the
flow in the reactor was set at a particular value and the
entire reactor system, without fuel flow, was allowed
to thermally equilibrate. Fuel flow was then com-
menced, and after stabilization of the analytical meas-
urement readings at the sampling location, composi-
tional data were obtained for the sampled flow and the
reaction temperature at the sampling location. Fuel
flow was then turned off and the initial reactor tem-
perature was incrementally changed. The axial dis-
tance from the fuel vapor injection location to the sam-
pling location was varied so that, for each initial flow
temperature, the same reaction residence time was
maintained (flow density correction). The entire pro-
cedure was then repeated at the new initial reactor tem-
perature. The reaction conditions in the reactor are ad-
iabatic, so the temperature in the flow field from the
mixing point (initial reaction temperature) and the
sampling location changes, depending on the exo-
thermicity/endothermicity of the reaction. The com-
posite of many such experiments develops profiles of
reactant, intermediate, and product species concentra-
tion at fixed residence time as a function of the initial
reaction temperature (so-called “reactivity” profiles);
see Figures 3 and 4.
Comparison of such profiles with computational
modeling results typically requires that both the chem-
ical induction and postchemical induction phenomena
be modeled; i.e., reaction residence time requires the
assignment of a “zero” reaction time. This is typically
the approach taken by several other investigators util-
izing flow reactors, for example, Alzueta et al. [20].
Such comparisons include uncertainties associated
with the effects of impurities and mixing on the in-
duction chemistry. These uncertainties cannot be eas-
ily accounted for in the modeling comparisons; how-
ever, the data obtained are extremely useful in
determining the conditions under which low-temper-
ature, negative-temperature, or intermediate-tempera-
ture kinetics occur for a given fuel/oxidizer system. In
the present work, these data were very useful for set-
ting initial conditions for the remaining three sets of
experiments discussed later.
Computational Model
All of the modeling computations in this study were
carried out using the HCT modeling code [21]. The
boundary conditions used modeling flow-reactor,
stirred-reactor, and shock-tube studies are discussed in
the companion article.
Tables I and II in the companion paper summarize
the detailed kinetic mechanism and thermochemistry
used in the calculations shown in both articles. The
thermodynamic properties for the relevant radicals and
stable parents were obtained by group additivity using
THERM [22] with updated H/C/O groups and bond
dissociation groups [23]. The thermochemical data,
listed in Table II of the companion article, allow the
calculation of reverse reaction-rate constants by mi-
croscopic reversibility. A comparison of our current
THERM-generated thermochemical values with those
recommended by Dagaut et al. [2] and Yamada et al.
[24] for a number of selected species are reported in
Table I. We have updated the group values for alkyl-
Based upon the reactivity data, three other series of
experiments were performed, under fixed equivalence
ratio conditions, at a pressure of 12.5 atm, and at var-
ious constant initial reaction temperatures. In each ex-
periment, the reaction residence time was changed by
moving the position of the mixing location relative to
the sampling location. The flow reactor and sampling/
analytical systems were allowed to stabilize, and

THE REACTION KINETICS OF DIMETHYL ETHER. II
745
Table I Comparison of Thermodynamic Properties for Selected Species
ꢁ
f
ꢁ
H @ 298 K (kcal/mol)
S @ 298 K (cal/mol-K)
f
Species
[2]
[24]
This Study
[2]
[24]
—
This Study
63.8
CH OCH3
—
Ϫ2.0
—
—
—
Ϫ44.0
0.1
—
Ϫ33.9
Ϫ26.5
—
Ϫ43.4
1.0
Ϫ68.4—
Ϫ34.6
Ϫ24.0
Ϫ59.6
—
67.467.7
—
—
—
3
CH OCB H
67.3
83.8
3
2
CH OCH O H
3
2
2
CH OCH OB
83.1
88.0
—
82.6
85.9
101.2
3
2
2
CB H OCH O H
2
2
2
OB CH OCH O H
—
—
2
2
2
2
peroxide species based on the recent studies of Ya-
mada et al. [24] and have modified these slightly so
that the thermodynamic functions of RB ϩ O L ROB
OB CH OCH O H (peroxy-methoxymethyl-hydroper-
2
2
2
2
oxide radical), and HO CH OCHO (hydroperoxy-
2
2
methylformate).
2
2
reactions agree with the experimental and calculated
values of Knyazev and Slagle [25] for ethyl radical
At the low temperatures of the present study, the
methoxymethyl radical adds to molecular oxygen to
form the methoxymethyl-peroxy radical. This adduct
can then undergo an intramolecular H-atom isomeri-
zation, and proceed through the relatively complex re-
action scheme depicted in Figure 1. In the temperature
range 550–600 K, chain branching is primarily due to
the reaction pathway leading through the carbonyl-
hydroperoxide HO CH OCHO species with the for-
(Table II). Our chosen heat of formation for the meth-
oxymethyl radical of 1.0 kcal/mol is in good agree-
ment with 0.3 kcal/mol recommended in the NIST
structures and properties database, [26], and 0.9 kcal/
mol calculated by Good and Francisco [27].
2
2
Dimethyl Ether Oxidation Mechanism
mation of two reactive hydroxyl radicals. As the tem-
perature increases above 600 K, the ␤-scission of the
CB H OCH O H radical gradually becomes more im-
The overall reaction scheme for DME oxidation can
be depicted as follows:
2
2
2
portant. This pathway produces only one reactive hy-
droxyl radical in addition to two stable molecules of
formaldehyde, and thus the overall reactivity of the
system decreases, leading to a negative temperature
coefficient (NTC) region (600–725 K). At initial re-
actor temperatures above 730 K, H O dissociates into
2
2
two reactive hydroxy radicals, leading to a rapid in-
crease in the system’s reactivity and consumption of
the remaining fuel. DME reacts more exothermically
at these temperatures, increasing the temperature
above the initial reactor temperature. At low temper-
atures, H-atom abstraction from the fuel occurs pri-
marily by OB H radicals (reaction (274)). (Reaction
numbers refer to the number in the reaction mecha-
nism.) At higher temperatures (650–750 K), hydro-
peroxy and methylperoxy radicals also contribute to
H-atom abstraction (reactions (277) and (278)). The
rate expressions used here are based on the recom-
12
mendation of Walker [28] of 2.8 ϫ 10 exp (Ϫ17.7
3
Ϫ
1
Ϫ1
kcal/RT) cm mol
s
per H atom for the abstraction
of secondary H atoms from an alkane by HOB radicals.
Figure 1 Overall reaction scheme for dimethyl ether oxi-
dation.
2
This results in an 〈-factor of 1.68 ϫ 1013 using a
degeneracy of 6. In previous work [1], the 〈-factors
for reactions (277) and (278) were lowered to 1.0 ϫ
The species names are defined as follows: CH OCH3
3
13
(
dimethyl ether), CH OCB H (methoxymethyl radi-
10 in order to obtain better agreement of simulated
ignition delay time with the shock-tube results of Pfahl
et al. [3], particularly at about 1000 K. However,
3
2
cal), CH OCH OB (methoxymethyl-peroxy radical),
3
2
2
CB H OCH O H (hydroperoxy-methoxymethyl radical),
2
2
2

7
46
CURRAN ET AL.
Table II Comparison of Thermodynamic Functions RB ϩ O L ROB Reactions
2
2
ꢁ
ꢁ
Ϫ⌬H @ 298 K (kcal/mol)
Ϫ⌬S @ 298 K (cal/mol-K)
rxn
rxn
Citation
CH OCH2
CH OCH O H
CH OCH2
CH OCH O H
2 2 2
3
2
2
2
3
[
[
[
2]
24]
25]†
33.7
34.0
35.5
35.6
32.439.0
—
—
38.7
33.6
33.6
33.7
—
—
33.7
This study
35.6
†
Kynazev and Slagle number corresponds to ethyl radical.
model comparisons with the present flow-reactor ex-
periments indicate that faster rate expressions for re-
actions (277) and (278) are necessary. The comparison
of the revised model with the shock-tube results of
Pfahl et al. can be seen in Figure 25.
eling results showed this sequence of reactions
to be of relatively minor importance here.
3. The most important step involves isomerization
of the CH OCH OB radical via internal H-atom
3
2
2
transfer to form hydroperoxy-methoxymethyl
The methoxymethyl radical formed can undergo
two different reactions:
radical, CB H OCH O H:
2
2
2
2
93
CH OCH OB E F CB H OCH O H
R
3
2
2
2
2
2
•
•
␤-scission to yield formaldehyde and methyl rad-
icals.
The estimation of this rate constant is as de-
scribed in our previous study [1]. We estimate
addition to molecular oxygen to produce meth-
oxymethyl-peroxy radicals, CH OCH OB .
3
2
2
the activation energy, ␧ , using the expression
a
282
CH OCB H 9
9
: CH O ϩ CB H3
3
2
2
␧a ϭ ⌬Hrxn ϩ ring strain ϩ Eabst
2
87
CH OCH OB ;
9
: CH OCB H ϩ O
where ⌬Hrxn is taken to be the enthalpy of re-
action and is included only if the reaction is en-
dothermic. The activation energy for abstraction
is determined, following the analysis of Bozzelli
and Pitz [30], from an Evans-Polanyi plot,
3
2
2
3
2
2
The rate expression for CH OCH ␤-scission (reaction
82), was taken from Loucks and Laidler [29] and is
consistent with the value used in previous work [1].
The bimolecular addition of methoxy-methyl radical
3
2
2
Eabst vs. ⌬Hrxn (taken in the exothermic direc-
to O has no activation energy barrier associated with
tion), of similar H-atom abstraction reactions,
RH ϩ RB Ј ϭ RB ϩ RЈH, leading to the following
expression:
2
it. The 〈-factor for addition to O was taken to be
2
1
2
3
Ϫ
1
Ϫ1
2
.0 ϫ 10 cm mol s , i.e., twice the value used
previously. The high-pressure rate expression recom-
mended by Sehested et al. [12] seems to be closer to
Eabst ϭ 12.7 ϩ (⌬Hrxn ϫ 0.37)
1
2
3
Ϫ
1
Ϫ1
6
.0 ϫ 10 cm mol
with this upward revision.
The CH OCH OB radical formed at low tempera-
s
at 296 K, a result consistent
As this transition state involves a six-membered
ring, we assume a ring strain of 2.3 kcal/mol,
similar to our work on n-heptane [31] and neo-
3
2
2
tures can undergo three different types of reaction:
pentane oxidation [32]. In addition, ⌬H
ϭ
rxn
Ϫ1
1
. Decomposition to CH OCB H ϩ O . This rate
ϩ10.6 kcal mol and therefore, ␧ ϭ 21.6 kcal
a
3
2
2
Ϫ
1
10
constant is the reverse of reaction (287) above
and is calculated from the reverse rate constant
and from microscopic reversibility (thermo-
chemistry).
mol . The 〈-factor was chosen to be 6.0 ϫ 10
Ϫ
1
s , identical to that we now use for a (1,5) tran-
sition-state ring in our current modeling of n-
heptane oxidation. The reverse isomerization
rate constant is based on the forward rate con-
stant and on calculated thermodynamic proper-
ties using group additivity.
2
. Intermolecular abstraction of hydrogen atoms
from other hydrocarbon species to produce the
stable methoxymethyl-hydroperoxide species,
(
CH OCH O H), which then decomposes to
3 2 2
CH OCH OB ϩ OH, followed by reactions of
The hydroperoxy-methoxymethyl species formed can
react via three major pathways:
3
2
the CH OCH OB radical. Experimental and mod-
3
2

THE REACTION KINETICS OF DIMETHYL ETHER. II
747
1
2
. Reverse isomerization of CB H OCH O H radical
while addition to O leads to chain branching and
hence greater reactivity.
2
2
2
2
(
reaction 293) to CH OCH OB radical as de-
3
2
2
scribed above.
The OB CH OCH O H radical isomerizes, releasing
2
2
2
2
. The CB H OCH O H species can undergo ␤-scis-
OB H and producing a stable carbonyl-hydroperoxide
2
2
2
sion, leading to the formation of two molecules
of formaldehyde and OB H radical, as the hydro-
peroxy-methyl radical (CB H O H) is assumed to
molecule, HO CH OCHO (Fig. 1):
2
2
2
2
296
OB CH OCH O H E
RF HO CH OCHO ϩ OH
decompose into formaldehyde and OB H radical
2
2
2
2
2 2
very quickly:
The rate for this isomerization via an internal H-atom
transfer, presented in the mechanism, is based on the
analogous CH OCH OB L CB H OCH O H isomeriza-
2
94
CB H OCH O H E F CH O ϩ CH O ϩ OB H
R
2
2
2
2
2
3
2
2
2
2
2
tion. The activation energy has been calculated to be
Ϫ
1
This endothermic rate constant is unknown but
was estimated as follows. The reverse rate (i.e.,
addition of hydroperoxy-methyl radical to for-
maldehyde) was likened to a methyl radical add-
ing across the double bond in ethylene to yield
the n-propyl radical. The rate for this reaction
was taken from Baulch et al. [33] to be 2.1 ϫ
18.6 kcal mol (3.0 kcal/mol less than the isomeri-
zation of CH OCH OB ) and the 〈-factor has been re-
3
2
2
duced by two-thirds, consistent with the number of
H atoms present. The decomposition of the carbonyl-
hydroperoxide molecule leads to chain branching, as
two radicals are formed from its decomposition, OB H
and OB CH OCHO radicals:
2
1
1
3
Ϫ1 Ϫ1
1
0 exp(Ϫ7.4kcal/RT) cm mol s . The for-
ward rate-constant expression, calculated by
microscopic reversibility, was calculated to be
2
97
HO CH OCHO 9
9
: OB CH OCHO ϩ OH
2
2
2
13
3
Ϫ1 Ϫ1
1
.5 ϫ 10 exp(Ϫ20.76 kcal/RT) cm mol s .
Previously, it was found necessary to adjust the
calculated forward activation energy downward
by 3.0 kcal mol in order to predict the ignition
delay times measured by Pfahl and co-workers
Sahetchian et al. [34] published rate-constant ex-
pressions for the pyrolysis of a number of organic hy-
droperoxides. Their work indicates a rate expression
Ϫ
1
16
3
Ϫ1
of about 1.0 ϫ 10 exp(Ϫ43.0 kcal/RT) cm mol
Ϫ
1
[3]; in particular, to simulate the point at which
s
for a typical RO9OH homolysis reaction. In this
the NTC region comes into effect. However, we
find that the low-temperature ignition delays of
Pfahl et al. can be predicted with the current rate
expression (Fig. 25), which depends on the rel-
ative rates of alkyl-peroxy radical isomerization
and hydroperoxy-alkyl radical addition to mo-
lecular oxygen.
study, we have employed a rate expression of 2.0 ϫ
16
3
Ϫ
1
Ϫ1
10 exp(Ϫ40.5 kcal/RT) cm mol
s
in order to
obtain good agreement with experimental results, par-
ticularly at the lowest temperatures. It has been shown
in the previous work [1] that shock-tube ignition delay
times had the highest sensitivity to this reaction at
650 K, with very little sensitivity at higher tempera-
tures.
3
. In addition, hydroperoxy-methoxymethyl spe-
cies can react with molecular oxygen to form
the OB CH OCH O H radical:
An important change to the prior mechanism [1] is
the fate of the OB CH
OCHO radical produced from the
decomposition of the carbonyl-hydroperoxide mole-
cule. It was previously assumed that this radical de-
2
2
2
2
2
295
OB CH OCH O H ; : CB H OCH O H ϩ O
9
2
2
2
2
2
2
2
2
composed to produce formaldehyde and a HCOB rad-
2
ical. However, it is also possible for this radical to
isomerize via an intramolecular H-atom isomerization
to form another radical, a process which is exothermic:
The reverse rate constant of this reaction was
taken to be 7.0 ϫ 1011 cm mol s . This rate
expression was chosen to provide the best agree-
ment with the experimental data and is approx-
imately 20% lower than the value used previ-
ously [1].
3
Ϫ
1
Ϫ1
2
98
OB CH OCHO 9
9
: CH O ϩ HCO2
2
2
3
03
OB CH OCHO E F HOCH OCB O
R
2
2
It is important to note that the fate of the
CB H OCH O H radical determines the reactivity of the
Based on experimentally measured product yields,
2
2
2
system at low temperatures; a faster rate of ␤-scission
of CB H OCH O H radical leads to reduced reactivity,
we found that the OB CH OCHO radical does undergo
2
␤-scission to a small extent but predominantly isom-
2
2
2

7
48
CURRAN ET AL.
HOCH OB radical and CO. The HOCH OB radical then
2
2
decomposes to yield formic acid and H atom. This
product channel is necessary to obtain the agreement
between simulated and experimental formic acid yield.
DISCUSSION
In this section, the product species concentrations cal-
culated by the model and measured in the experiments
are discussed and compared. These experiments are a
stringent examination of the low-temperature portion
of the model, as they test the detailed distribution of
both primary and secondary product formation at var-
ious temperatures and pressures. Comparisons of the
product species profiles measured in the experiment
and calculated by the model simulation are shown in
Figures 3–20. It is evident that the predicted concen-
tration profiles for the fuel, oxygen, and each product
species are in good agreement with the experimental
measurements.
Figure 2 Reaction coordinate diagram for HOCH OB ϩ
2
CO ϭ HOCH OCB O ϭ CB H OH ϩ CO system.
2
2
2
erizes to the HOCH OCB O radical. The rate expression
2
for this isomerization was calculated in the same way
as for the methoxymethyl-peroxy radical discussed
11
above. A rate expression of 1.0 ϫ 10 exp (Ϫ14.0
kcal/RT) cm3 molϪ
1
s
Ϫ1
was estimated. The
HOCH OCB O radical is similar to the HOCB O radical
2
studied by Troe and co-workers [35,36] and Golden
et al. [37,38], in the reaction sequence CO ϩ OH ϭ
HOCO* ϭ CO ϩ H. The HOCH OCB O radical can
Figures 3 and 4depict experimental and simulated
species concentration profiles versus initial reactor
temperature at an experimental residence time of
2
2
decompose via two possible pathways.
1
.8 s. The experimental time is calculated from inte-
3
04
gration of the axial flow velocity distribution over the
distance from the mixing location to the sampling lo-
cation in the reactor. In Figures 5 and 6, speciation
profiles vs. time, the simulated profiles had to be time-
shifted by Ϫ0.3 s relative to the experimental results
to achieve comparison of the result of modifications
of the chemical induction chemistry due to small im-
purities in the reactants and mixing-related effectsnear
the fuel injection location. Thus, the simulation results
shown in Figures 3 and 4are calculated using a resi-
HOCH OCB O 9: HOCH OB ϩ CO
9
2
2
305
HOCH OCB O 9
9
: CB H OH ϩ CO2
2
2
Figure 2 depicts the reaction coordinate diagram for
the HOCH OB ϩ CO ϭ HOCH OCB O ϭ CB H OH ϩ
2
2
2
CO system. It is evident that the barrier heights for
2
reactions (304) and (305) are almost identical. Anal-
ysis of the HOCB O system indicates an activation en-
ergy of 29 kcal/mol for the addition of H atom to car-
bon dioxide. Our experience for addition reactions to
ethylene indicates an activation energy of 1.2 kcal/mol
for H-atom addition, with the activation energy in-
creasing to 7.4kcal/mol for the addition of a methyl
radical. Assuming that addition to CO by CB H OH rad-
2
2
ical is more similar to methyl-radical than H-atom
addition, we estimate an activation energy of (6.2 ϩ
2
9) ϭ 35.2 kcal/mol for reaction (305). The rate ex-
pression for the addition of HOCH OB radical to CO
2
11
was estimated to be 1.5 ϫ 10 exp (Ϫ4.8 kcal/RT)
3
Ϫ
1
Ϫ1
cm mol s , similar to that recommended by Tsang
and Hampson [39] for ethyl addition to carbon mon-
oxide. The reverse rate for reaction (305) was esti-
Figure 3 Measured (symbols) and calculated (curves) spe-
cies concentrations from a flow reactor. 3030 ppm DME,
mated to be 1.5 ϫ 10 exp (Ϫ35.2 kcal/RT) cm3
1
1
Ϫ
1
Ϫ1
mol s . These rate expressions result in a suffi-
ciently slow rate of reaction (305) to allow the pre-
dominance of reaction (304), the formation of the
␾
ϭ 1.19, P ϭ 12.5 atm, ␶ ϭ 1.8 s. ● O , ꢂ CH OCH ,
2 3 3
ꢃ H O, ᭛ CO, and ϫ CO . Dotted lines correspond to open
2
2
symbols.

THE REACTION KINETICS OF DIMETHYL ETHER. II
749
Figure 4 Measured (symbols) and calculated (curves) spe-
cies concentrations from a flow reactor. 3030 ppm DME,
Figure 5 Measured (symbols) and calculated (curves) spe-
␾
ϭ 1.19, P ϭ 12.5 atm, ␶ ϭ 1.8 s. ● HOCHO, ꢂ Temper-
cies concentrations from a flow reactor. 3080 ppm DME,
ature rise, ꢃ CH O, ᭛ CH , and ϫ C H . Dotted lines cor-
respond to open symbols.
␾ ϭ 1.18, P ϭ 12.5 atm, T ϭ 593 K. ● O
ꢃ CH OCH , ᭛ CO, and ϫ CO . ␶offset ϭ Ϫ0.3 s. Dotted
lines correspond to open symbols.
2 2
, ꢂ H O,
2
4
2
6
3
3
2
dence time of 2.1 s (rather than 1.8 s) to approximately
correct for these same effects on the experimentally
measured reactivity profiles. In addition, the reaction
conditions are assumed to be adiabatic, and thus the
temperature calculated at the sampling location is a
result of energetic changes due to reaction and the ini-
tial reaction temperature of the calculations them-
selves.
hydroxyl radical. This reaction is chain propagating,
competing with the chain-branching reaction, thus de-
creasing the overall oxidation rate.
At temperatures above 720 K, the overall rate of
reaction starts to increase again. When the initial re-
actor temperature reaches about 750 K, the partial re-
action of DME is great enough to raise the reactor
temperature above the threshold temperature for hy-
drogen peroxide decomposition, leading to the for-
mation of two reactive hydroxyl radicals and the ob-
served rapid increase in overall reactivity. At these
higher temperatures, ␤-scission of the alkyl radical be-
comes important, leading to the formation of methyl
radicals and accounting for the formation of methane
and ethane. The methyl radicals formed react with hy-
droperoxy radicals, leading to the formation of me-
At low temperatures the primary products formed
are carbon monoxide (CO), formic acid (HOCHO),
formaldehyde (CH O), water (H O), and carbon di-
2
2
oxide (CO ). Methane (CH ) and ethane (C H ) are
2
4
2
6
also formed at initial reactor temperatures greater than
about 730 K.
It is clear from Figures 3 and 4that dimethyl ether
exhibits NTC behavior experimentally, consistent with
that observed in the shock-tube results of Pfahl et al.
The fuel starts to react at an initial reactor temperature
of 530 K, reaching a maximum reactivity at 593 K. At
this temperature, the concentrations of formic acid,
carbon monoxide, and water peak, with values of
thoxy and hydroxy radicals CB H
ϩ HOB
ϭ CH
O ϩ HB ϩ M, a
OB ϩ
3
2
3
OB H followed by CH OB ϩ M ϭ CH
3
2
1
000, 1340, and 2450 ppm, respectively—far greater
than the 119 ppm of formaldehyde. This fast rate of
oxidation is due to the hydroperoxy-methoxymethyl
radical addition to molecular oxygen, subsequent
isomerization, and chain branching, with the produc-
tion of formic acid, carbon monoxide, two reactive
hydroxyl radicals, and one H atom (Fig. 1). Above
6
00 K, the overall rate of oxidation decreases until the
initial reactor temperature reaches 720 K. In this tem-
perature range, the concentrations of formic acid, car-
bon monoxide, and water decrease, while the concen-
tration of formaldehyde gradually increases. This can
be explained by the increasing rate of the hydrope-
roxy-methoxymethyl radical ␤-scission, reaction
Figure 6 Measured (symbols) and calculated (curves) spe-
cies concentrations from a flow reactor. 3080 ppm DME,
␾
ϭ 1.18, P ϭ 12.5 atm, T ϭ 593 K. ● HOCHO, ꢂ Tem-
perature, and ꢃ CH O. ␶
ϭ Ϫ0.3 s. Dotted lines corre-
2
offset
(294), to form two formaldehyde molecules and one
spond to open symbols.

7
50
CURRAN ET AL.
Figure 7 Measured (symbols) and calculated (curves) spe-
Figure 9 Measured (symbols) and calculated (curves) spe-
cies concentrations from a flow reactor. 3190 ppm DME,
cies concentrations from a flow reactor. 3380 ppm DME,
␾
ϭ 0.93, P ϭ 12.5 atm, T ϭ 650 K. ● O , ꢂ Temperature,
␾ ϭ 0.97, P ϭ 12.5 atm, T ϭ 710 K. ● O
, ꢂ Temperature,
2
2
and ꢃ CH OCH . Dotted lines correspond to open symbols.
and ꢃ CH OCH . Dotted lines correspond to open symbols.
3
3
3
3
process which is chain branching. The formaldehyde
produced undergoes further reaction, primarily via
CH O ϩ RB ϭ HCB O ϩ RH and HCB O ϩ O ϭ CO ϩ
to start at 730 K, but the model predicts a slower rate
of reaction, the rapid increase in reactivity starting
about 10 degrees higher, at 740 K. As observed in the
sensitivity analysis, the fuel is particularly sensitive to
H-atom abstraction by HOB and CH OB radicals in this
2
2
HOB . In the temperature range 750–775 K the mea-
2
sured concentration of formic acid increases again and
then becomes almost insignificant at 800 K, while the
concentration of formaldehyde gradually decreases
from 740–800 K.
2
3
2
temperature range. Subsequently, hydrogen peroxide
forms two reactive hydroxyl radicals, and methyl per-
oxide generates methoxy and hydroxyl radicals.
Overall, there is good agreement between the
model and experiment. However, there are some dis-
crepancies that should be addressed. At 553 K, the
experiment indicates that almost 19% of DME fuel has
reacted, although the model predicts only about 5%
conversion. The model is slow to react as the activa-
tion energy for the carbonyl-hydroperoxide species is
quite high (41–43 kcal/mol). As stated earlier, we in-
creased the rate of the carbonyl-hydroperoxide decom-
position reaction in order to improve agreement at
these low temperatures. At higher temperatures, the
rapid increase in reactivity is observed experimentally
Figures 5–10 show species evolution versus resi-
dence time at chosen inlet temperatures, correspond-
ing to various points along the NTC curve. These ex-
periments were performed under near-stoichiometric
conditions and at a pressure of 12.5 atm. Figures 5 and
6 show the results at 593 K, where the modeling data
have been offset by Ϫ0.3 s, while the data at 650 K
and 710 K did not need to be offset (Figs. 7–10). At
593 K, the model shows a little more reactivity than
that observed in the experiment. The model-predicted
temperature profile is about 10 K higher than that ob-
served in the experiment. In addition, the CH O profile
2
Figure 8 Measured (symbols) and calculated (curves) spe-
cies concentrations from a flow reactor. 3190 ppm DME,
Figure 10 Measured (symbols) and calculated (curves)
species concentrations from a flow reactor. 3380 ppm DME,
␾ ϭ 0.97, P ϭ 12.5 atm, T ϭ 710 K. ● H O, ꢂ CH O,
␾
ϭ 0.93, P ϭ 12.5 atm, T ϭ 650 K. ● H O, ꢂ CO, ꢃ CH O,
2 2
2
2
᭛
HOCHO, and ϫ CO . Dotted lines correspond to open
ꢃ CO, ᭛ HOCHO, and ϫ CO . Dotted lines correspond to
2
2
symbols.
open symbols.

THE REACTION KINETICS OF DIMETHYL ETHER. II
751
Figure 11 Measured (symbols) and calculated (curves)
Figure 13 Measured (symbols) and calculated (curves)
species concentrations from a flow reactor. 2130 ppm DME,
species concentrations from a flow reactor. 2730 ppm DME,
␾
ϭ 0.81, P ϭ 12 atm, T ϭ 849 K. ● O , ꢂ H O, ꢃ CO, and
␾ ϭ 1.17, P ϭ 12 atm, T ϭ 849 K. ● O
, ꢂ H O, ꢃ CO, and
2 2
2
2
᭛
CH OCH . ␶ ϭ Ϫ0.2 s. Dotted lines correspond to
offset
᭛ CH OCH . ␶offset ϭ Ϫ0.15 s. Dotted lines correspond to
3
3
3
3
open symbols.
open symbols.
is overpredicted by about a factor of 3. However, the
formic acid, water, carbon monoxide, and carbon di-
oxide are all in good agreement with the experimental
results. At 650 K the overall agreement between ex-
periment and model is better than at 593 K. At 710 K
yields increase. The formaldehyde yield peaks at an
equivalence ratio of 1.17. As the equivalence ratio is
increased from 1.17 to 2.41, the fuel oxidation rate
slows, and the overall reaction becomes less exother-
mic. Overall, we believe that there is good agreement
between simulation and experiment. The peak heights
and the shape of each species profile match one an-
other quite well. However, in simulating these three
experiments, the data had to be offset in order to over-
lap with the experimentally measured product profiles.
Under lean conditions, for example, in order to match
the measured peaks in the formaldehyde and methane
profiles it was necessary to offset the prediction pro-
files by Ϫ0.4s (Figs. 11 and 12). In so doing, the
simulation profiles match fairly well the measured
fuel, oxygen, carbon monoxide, and water profiles.
Finally, Figures 5 and 6 and 17–20 show the effect
upon oxidation of increasing the pressure, at a tem-
perature of approximately 590 K, an equivalence ratio
(Fig. 9), the model predicts very well the DME con-
sumption. The predicted water profile (which is a good
indication of the quantity of hydroxyl radical in the
system) is underpredicted, as are the concentrations of
the other primary products (Fig. 10).
The influence of equivalence ratio on DME oxi-
dation has also been investigated, at a pressure of 12
atm and at an average temperature of 850 K. The
equivalence ratio varied from lean (␾ ϭ 0.81) (Figs.
1
(
1
1 and 12), through near-stoichiometric (␾ ϭ 1.17)
Figs. 13 and 14), to rich (␾ ϭ 2.48) (Figs. 15 and
6). Product species concentrations are correlated
against residence time. As the equivalence ratio is in-
creased from 0.81 to 2.41, the methane and ethane
Figure 12 Measured (symbols) and calculated (curves)
species concentrations from a flow reactor. 2130 ppm DME,
Figure 14 Measured (symbols) and calculated (curves)
species concentrations from a flow reactor. 2730 ppm DME,
␾ ϭ 1.17, P ϭ 12 atm, T ϭ 849 K. ● CH O, ꢂ CH ,
␾
ϭ 0.81, P ϭ 12 atm, T ϭ 849 K. ● CH O, ꢂ CH ,
2 4
2
4
ꢃ Temperature, ᭛ C H , and ϫ C H . ␶
ϭ Ϫ0.2 s. Dot-
ꢃ Temperature, ᭛ C H , and ϫ C H . ␶
ϭ Ϫ0.15 s.
2
6
2
4
offset
2
6
2
4
offset
ted lines correspond to open symbols.
Dotted lines correspond to open symbols.

7
52
CURRAN ET AL.
Figure 15 Measured (symbols) and calculated (curves)
species concentrations from a flow reactor. 2430 ppm DME,
Figure 17 Measured (symbols) and calculated (curves)
species concentrations from a flow reactor. 3580 ppm DME,
␾ ϭ 0.85, P ϭ 17 atm, T ϭ 600 K. ● O , ꢂ H O, ꢃ CO, and
␾
ϭ 2.48, P ϭ 12 atm, T ϭ 852 K. ● O , ꢂ CH OCH ,
2 3 3
2
2
ꢃ CO, and ᭛ H O. ␶
ϭ Ϫ0.5 s. Dotted lines correspond
᭛ CH OCH . ␶
ϭ Ϫ0.2 s. Dotted lines correspond to
2
offset
3
3
offset
to open symbols.
open symbols.
of approximately 1.0 and at pressures of 12.5, 17, and
8 atm. Product species concentrations are correlated
addition, the model predicts a faster-than-observed ig-
nition at about 1000 K, due primarily to the ignition
delay sensitivity to reactions of the fuel with hydro-
peroxy, reaction (277), and methylperoxy radicals, re-
action (278), at this temperature. As discussed earlier,
we increased the rate expressions of these reactions to
achieve good agreement with the current flow-reactor
data.
1
against residence time. No significant change in the
profiles over this pressure range was observed. The
overall agreement between predictions and experiment
is similar to that achieved at the lower pressure con-
ditions.
Shock-Tube Comparison
Stirred-Reactor Comparison
The chemical kinetic mechanism developed here was
used to simulate the experimental results of Pfahl
et al. [3] in a high-pressure shock tube. A comparison
of the current model prediction with the experimental
results can be seen in Figure 25. There is good agree-
ment between simulation and experiment. However,
the model underpredicts the overall rate of fuel oxi-
dation at lower temperatures, resulting in longer-than-
measured total and cool-flame ignition delay times. In
Finally, we have simulated again the recently pub-
lished experimental results of Dagaut et al. [2] but with
the revised mechanism presented here. These data
were taken in a jet-stirred reactor in the temperature
range 550–800 K, with 0.2% DME at equivalence ra-
tios of 0.2 and 1.0, at a pressure of 10 atm, and a
constant residence time of 1.0 s. Overall, there is good
agreement between model and experiment. However,
Figure 16 Measured (symbols) and calculated (curves)
species concentrations from a flow reactor. 2430 ppm DME,
Figure 18 Measured (symbols) and calculated (curves)
species concentrations from a flow reactor. 3580 ppm DME,
␾ ϭ 0.85, P ϭ 17 atm, T ϭ 600 K. ● HOCHO, ꢂ Temper-
␾
ϭ 2.48, P ϭ 12 atm, T ϭ 852 K. ● CH O, ꢂ CH ,
2 4
ꢃ Temperature, ᭛ C H , and ϫ C H . ␶
ϭ Ϫ0.5 s. Dot-
ature, ꢃ CO , and ᭛ CH O. ␶
ϭ Ϫ0.2 s. Dotted lines
2
6
2
4
offset
2
2
offset
ted lines correspond to open symbols.
correspond to open symbols.

THE REACTION KINETICS OF DIMETHYL ETHER. II
753
Figure 21 Experimental JSR results (points) [2] vs. model
predictions (lines) at 0.2% DME, ␾ ϭ 1.0, P ϭ 10 atm,
Figure 19 Measured (symbols) and calculated (curves)
species concentrations from a flow reactor. 3700 ppm DME,
␶
ϭ 1 s. ● O and ꢂ CH OCH . Dotted lines correspond to
2 3 3
␾
ϭ 1.16, P ϭ 18 atm, T ϭ 580 K. ● O , ꢂ H O, ꢃ CO, and
2
2
open symbols.
᭛
CH OCH . ␶
ϭ Ϫ0.5 s. Dotted lines correspond to
3
3
offset
open symbols.
an analysis of possible theoretical formation pathways.
Earlier work [1] proposed that the OB CH OCHO radi-
at an equivalence ratio of 1.0 the model predicts more
reactivity than observed in the experiment (Figs.
2
cal decomposed to form formaldehyde and HCOB rad-
2
ical, which decomposed to form carbon dioxide and
2
1–24). The revised mechanism overpredicts the con-
hydrogen atom. If it is assumed that the HCOB radical
centration of carbon monoxide formed but is in good
agreement with experimentally observed formalde-
hyde and carbon dioxide profiles. In addition, we show
predicted formic acid profiles (Figs. 22 and 24), even
though this species was not reported by Dagaut and
co-workers. Formic acid is predicted to be a major
species present in the experiment, containing consid-
erable amounts of the total carbon present in inter-
mediates and reaction products.
2
does not decompose, but reacts with hydrogen per-
oxide or hydroperoxyl radical to yield formic acid,
concentrations of formic acid and formaldehyde of
nearly the same order would be expected. This as-
sumption cannot be correct because at 593 K, the point
of highest reactivity at low temperatures, the observed
concentration of formic acid is almost an order of mag-
nitude greater than that of formaldehyde (Fig. 4).
We suggest, however, that there are two main path-
ways contributing to formic acid formation. The first
Formic Acid Formation
is through the OB CH OCHO radical, created from the
2
decomposition of the dimethyl ether carbonyl-hydro-
peroxide molecule, which is produced directly from
As stated earlier, our previous mechanism did not con-
tain any formic acid chemistry. However, the high
yield of formic acid observed in these flow-reactor ex-
periments at low temperatures prompted us to perform
one fuel molecule. The OB CH OCHO radical under-
2
goes an internal H-atom shift and generates the
HOCH OCB O radical, which decomposes to form the
2
HOCH OB radical and CO. The HOCH OB radical pro-
2
2
Figure 20 Measured (symbols) and calculated (curves)
species concentrations from a flow reactor. 3700 ppm DME,
Figure 22 Experimental JSR results (points) [2] vs. model
predictions (lines) at 0.2% DME, ␾ ϭ 1.0, P ϭ 10 atm,
␶ ϭ 1 s. ● CO, ꢂ CH O, ꢃ CO , and · · · HOCHO (prediction
␾
ϭ 1.16, P ϭ 18 atm, T ϭ 580 K. ● HOCHO, ꢂ Temper-
ature, ꢃ CO , and ᭛ CH O. ␶ ϭ Ϫ0.5 s. Dotted lines
2
2
offset
2
2
correspond to open symbols.
only). Dotted lines correspond to open symbols.

7
54
CURRAN ET AL.
Figure 23 Experimental JSR results (points) [2] vs. model
predictions (lines) at 0.2% DME, ␾ ϭ 0.2, P ϭ 10 atm,
Figure 25 Experimental shock-tube ignition delays
points) [3] vs. model predictions (lines) for stoichiometric
dimethyl ether oxidation in air. ● total ignition and ꢂ first-
stage ignition delay at 13 bar. ꢃ total ignition and ᭛ first-
stage ignition delay at 40 bar. Dotted lines correspond to
open symbols.
(
␶
ϭ 1 s. ● O and ꢂ CH OCH . Dotted lines correspond to
2 3 3
open symbols.
duces HOCHO (formic acid) and a H atom. The fact
that the experimental concentrations of formic acid
and carbon monoxide are very similar in the temper-
ature range 500–600 K lends additional support to this
proposed pathway.
hydroxyl radical to acetaldehyde, who recommend
a high-pressure limit rate coefficient of 3.0 ϫ
15
Ϫ1.1
3
Ϫ1 Ϫ1
1
0
T
cm mol s . Analysis of HCT output edits
The second route to formic acid formation that we
indicates that at 560 K, the HOCH OB radical is pre-
2
propose also involves the HOCH OB radical but results
2
dominantly produced from the decomposition of the
from the addition of hydroxyl radical to formaldehyde,
reaction (307). This pathway is somewhat controver-
sial, as Niki et al. [40] studied the reaction of hydroxyl
radicals with formaldehyde at a temperature of 299 K
and at a pressure of 700 Torr and found that formal-
dehyde exclusively undergoes abstraction rather than
addition. However, as pointed out by Stief et al. [41],
HOCH OCB O radical rather than the OB H addition to
2
CH O in the ratio of 6.5 : 1. The importance of the
2
route through formaldehyde increases steadily, and at
a temperature of 660 K its contribution to the forma-
tion of formic acid is equal to the direct route from
dimethyl ether. Our analysis is supported by experi-
ment because from 600–750 K there is a profound
decrease in the concentration of formic acid. However,
from 750–775 K the concentration of formic acid
measured increases again, as predicted by the HCT
simulation. This increase is due to the increased con-
centration of hydroxyl radicals, formed from the de-
composition of hydrogen peroxide, which add to for-
maldehyde and produce formic acid and hydrogen
atom.
pressure dependence in k(OB H ϩ CH O) may be ex-
2
pected, since the addition reaction is likely to proceed
via a chemically activated adduct. We have employed
a rate expression of 4.5 ϫ 1015
Ϫ1.1
3
Ϫ1 Ϫ1
T
cm mol
s
for
reaction (307). This rate is based on the recommen-
dation of Taylor et al. [42], for the addition of
This type of reaction has implications, too, in the
oxidation of acetaldehyde, or any other aldehydic spe-
cies. It may be possible in the case of acetaldehyde,
for example, for the hydroxyl radical to add to the
aldehydic carbon atom, according to Figure 26, pro-
Figure 24 Experimental JSR results (points) [2] vs. model
predictions (lines) at 0.2% DME, ␾ ϭ 0.2, P ϭ 10 atm,
␶
ϭ 1 s. ● CO, ꢂ CH O, ꢃ CO , and · · · HOCHO (prediction
Figure 26 Possible routes of acetaldehyde oxidation by
2
2
only). Dotted lines correspond to open symbols.
hydroxyl radicals.

THE REACTION KINETICS OF DIMETHYL ETHER. II
755
ducing formic acid and a methyl radical, or acetic acid
and a hydrogen atom.
We also investigated the importance of the addition
of hydroperoxyl radical to formaldehyde, reaction
conversion compared with the baseline simulation and
express this as a percentage. A positive sensitivity co-
efficient indicates an increase in the amount of fuel
consumed, while a negative sensitivity coefficient in-
dicates a decreased level of fuel conversion. The re-
action rate constants that exhibited the highest sensi-
tivity are shown in Figure 28. Reactions in which we
multiplied both forward and reverse rate constants by
a factor of 2 are denoted with an equal to, ϭ, sign
between reactants and products, and reactions in which
we multiplied only the forward rate constant (i.e.,
effected a change in the equilibrium constant) are
denoted with an arrow, Q, between reactants and
products.
(325), and the reaction of hydroperoxyl radical with
hydroxymethyl (CB H OH) radical, reaction (306):
2
325
HO CH OB 9: HOB ϩ CH O
9
2
2
2
2
306
CB H OH ϩ HOB 9: HOCH OB ϩ OB H
9
2
2
2
Analysis of HCT edits indicate that reaction (325) does
not contribute to the oxidation of formaldehyde, and
reaction (306) does not contribute to the formation of
formic acid.
We also considered an alternative route to the de-
composition of the carbonyl-hydroperoxide species,
At all temperatures the reaction with one of the
largest positive sensitivities (most effective in pro-
moting the overall rate of oxidation) is the addition
of hydroperoxy-methoxymethyl radical to molecular
oxygen:
HO CH OCHO, depicted in Figure 27. This route has
2
2
also been suggested by Marinov [43] and is presently
being further investigated by him. We estimate that
the transition state through this system has an energy
barrier of about 40–45 kcal/mol. However, the 〈-fac-
tor is about two orders of magnitude lower than that
for the decomposition to carbonyl-alkoxy radical and
a hydroxyl radical. Thus, we believe that this reaction
channel cannot successfully compete with that of the
O9O homolysis, reaction (297).
2
95
OB
CH
OCH
O
2
H ;9
: CB H
OCH O H ϩ O
2 2 2 2
2
2
2
At low temperatures isomerization of the
OB CH OCH O H radical (reaction 296) leads to the
2
2
2
2
formation of the carbonyl-hydroperoxide molecule,
HO CH OCHO, and a hydroxyl radical. Subsequent
2
2
decomposition of the carbonyl-hydroperoxide mole-
cule leads to the formation of another hydroxyl radical
and an oxygenated-alkoxy radical, a sequence which
produces a total of three radicals (two of which are
reactive hydroxyl radicals) and is, therefore, chain
branching. It is interesting to note that this reaction
appears to be sensitive only to the radical addition to
molecular oxygen (forward rate constant) and not the
reverse rate constant. The sensitivity coefficients as-
sociated with changing both the forward and reverse
rate constants by a factor of 2 are almost identical to
those in which we effected a change only in the for-
ward rate constant at all temperatures.
Sensitivity Analysis
A sensitivity analysis was performed by multiplying
the rate constant of a reaction by a factor of 2 (both
forward and reverse rate constants) and then calculat-
ing the percentage change in fuel conversion. Three
different temperatures were chosen (593, 650, and 750
K) in order to indicate sensitivity of each reaction to
the onset, middle, and end of the NTC region, at an
average pressure of 12.5 atm. Fuel conversion is a
good measure of overall reactivity, and hence we de-
fine the sensitivity coefficient as the change in fuel
The reactions that are next greatest in promot-
Figure 27 Alternative pathway for formic acid formation from HO CH OCHO.
2
2

7
56
CURRAN ET AL.
Figure 28 Sensitivity coefficients for dimethyl ether oxidation. 3030 ppm DME, ␾ ϭ 1.19, P ϭ 12.5 atm,
ϭ 2.1 s.
␶
5
1
ing the rate of fuel oxidation are those involving
abstraction of hydrogen atoms from the fuel by
OB H, HB , HOB , and CH OB :
H O ϩ M 9
9
: OB H ϩ OB H ϩ M
2
2
191
2
3
2
CH O H 99
: CH OB ϩ OB H
3
2
3
2
93
CH OCH OB E F CB H OCH O H
R
2
74
3
2
2
2
2
2
CH OCH ϩ OB H 9
9
: CH OCB H ϩ H O
3
3
3
2
2
Indeed, reaction (51) shows a very high positive sen-
sitivity at 750 K (Fig. 28).
2
75
CH OCH ϩ HB 9: CH OCB H ϩ H
9
3
3
3
2
2
Adjusting the equilibrium of the methoxymethyl-
peroxyl radical isomerization to hydroperoxy-meth-
oxymethyl radical also promotes fuel oxidation, re-
action (293). At all temperatures, this leads to the
formation of hydroxyl radicals, which abstract hydro-
gen atoms from the fuel, thus leading to increased re-
activity.
The reaction that shows the largest negative sensi-
tivity (most effective in decreasing the overall reactiv-
ity at all temperatures) is the ␤-scission of the hydro-
peroxy-methoxymethyl radical, reaction (294):
2
77
CH OCH ϩ HOB 9: CH OCB H ϩ H O
9
3
3
2
3
3
2
2
278
CH OCH ϩ CH OB 9: CH OCB H ϩ CH O H
9
3
3
3
2
3
2
3
2
The sensitivity coefficients pertaining to these reac-
tions increase with increasing reaction temperature,
but the effect is more pronounced for abstractions by
HOB and CH OB radicals (Fig. 28). The concentration
2
3
2
of both of these radicals steadily increases with in-
creasing reaction temperature, and, at an initial reactor
temperature of about 750 K, the H O and CH O H
294
2
2
3
2
CB H OCH O H E F CH O ϩ CH O ϩ OB H
R
2
2
2
2
2
molecules produced decompose more readily to pro-
duce reactive hydroxyl and methoxy radicals, reac-
tions (51) and (191):
As indicated earlier, this reaction generates just one

THE REACTION KINETICS OF DIMETHYL ETHER. II
757
2
2
hydroxyl radical and inhibits the addition of hydro-
peroxy-methoxymethyl radical to molecular oxygen, a
reaction that leads to the formation of two reactive
hydroxyl radicals and chain branching.
CB H ϩ HOB 9: CH OB ϩ OB H
9
3
2
3
45
CB H ϩ HOB 99 : CH ϩ O
3
2
4 2
Another reaction that shows a negative sensitivity
is the abstraction of H atoms from formaldehyde by
hydroxyl radicals, reaction (32):
CONCLUSIONS
The oxidation of DME has been studied in a variable-
pressure flow reactor, in the temperature range 550 Յ
T Յ 855 K, in the pressure range 12 Յ P Յ 18 atm
with the equivalence ratio (␾) varying from 0.7 Յ ␾
Յ 4.2. It was found that dimethyl ether does exhibit
negative temperature coefficient (NTC) behavior, in
agreement with the shock-tube results of Pfahl et al.
These experiments found that formic acid is a major
product of the low-temperature oxidation of dimethyl
ether, consistent with the results presented by Liu et
al. [19]. A detailed chemical kinetic mechanism has
been used to simulate these experimental results and,
overall, there is good agreement between the model
and experiment. Two pathways leading to the forma-
tion of formic acid have been proposed and are sup-
ported by experimental observation.
Previously, we estimated activation energy of hy-
droperoxy-methoxymethyl radical ␤-scission based on
that measured by Loucks and Laidler [29] for meth-
oxymethyl radical ␤-scission, but we had to reduce the
activation energy for the hydroperoxy-methoxymethyl
radical ␤-scission in order to reproduce the experi-
mental results of Pfahl et al. [1]. Here, we are able to
employ an activation energy for hydroperoxy-meth-
oxymethyl radical ␤-scission consistent with that for
the methoxymethyl radical and still achieve satisfac-
tory agreement with the previous experiment.
3
2
CH O ϩ OB H 9: HCB O ϩ H O
9
2
2
26
HOB ϩ M 9: HB ϩ O ϩ M
9
2
2
This reaction competes with abstraction by hydroxyl
radicals from the fuel and thus inhibits the overall re-
activity of the system. Another reaction that produces
similar behavior is the addition of H atoms to molec-
ular oxygen, reaction (26). This reaction competes
with abstraction of H atoms from the fuel by H
atoms.
The self-reactions of hydroperoxyl radicals show
negative sensitivity coefficients at all temperatures,
with the largest values occurring at 750 K. The self-
reaction results in the formation of only one molecule
of hydrogen peroxide. However, reaction of hydro-
peroxyl radical with the fuel or formaldehyde would
result in two molecules of hydrogen peroxide and ul-
timately four hydroxyl radicals:
5
0,187
HOB ϩ HOB 99 : H O ϩ O
2 2 2
2
2
54
CH O ϩ HOB 9: HCB O ϩ H O2
9
2
2
2
Concentration profiles of reactants, intermediates,
and products of the oxidation of DME measured in a
JSR [2] at 10 atm, an equivalence ratio of 1.0, in the
temperature range 550–800 K, have shown that the
model can reasonably predict both primary and sec-
ondary product formation. The detailed model was
also used to simulate the shock-tube experiments of
Pfahl et al. [3] for stoichiometric mixtures of DME in
air, at temperatures of 650–1300 K and reflected
shock pressures of 13–40 bar. It was found that the
model was able to predict accurately total ignition-
delay times and the trends in the first-stage of “cool-
flame” ignition times. The good agreement found be-
tween experimental and modeling predictions under
JSR and shock-tube conditions gives us added confi-
dence in the reliability of the reaction mechanism and
further evidence of an experimental aberration in the
failure to observe formic acid in earlier JSR experi-
ments.
Sensitivity to ␤-scission of the methoxymethyl rad-
ical (reaction (282)),
282
CH OCB H 9: CH O ϩ CB H3
9
3
2
2
shows a negative sensitivity coefficient at 750 K. This
reaction competes with the addition of CH OCB H rad-
3
2
ical to O , which results in the generation from the
2
CB H OCH O H radical of a hydroxyl radical, which is
2
2
2
more reactive than a methyl radical.
Finally, at 750 K the system shows sensitivity to
the reaction of methyl and hydroperoxyl radical, re-
actions (22) and (45). Reaction (22) shows a positive
sensitivity, as it produces two reactive (methoxy and
hdyroxyl) radicals; while reaction (45) is inhibiting, as
it generates two unreactive molecules, namely, meth-
ane and oxygen:

7
58
CURRAN ET AL.
The experimental work discussed in this article and com-
putational work appearing in the thesis of S. Fischer were
conducted at Princeton University. The U.S. Department of
Energy, Chemical Sciences Division, Office of Basic Energy
Sciences, supported these contributions and those of Prof.
Dryer under Contract No. DE-FG02-86ER-13503. S. Fis-
cher also wishes to acknowledge the support of her thesis
research under the National Defense Fellowship Program.
Mr. Paul Michniewicz, Mrs. Yolanda Stein, and Dr. Steve
Klotz are acknowledged for their assistance in completing
the experimental portions of the work. The authors wish to
thank Dr. W. J. Pitz and Dr. C. K. Westbrook for their com-
ments and discussions in the preparation of this manuscript.
The computations appearing in this paper and the contribu-
tions of Dr. Curran were performed under the auspices of
the U.S. Department of Energy by the Lawrence Livermore
National Laboratory under contract No. W-7405-ENG–48.
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