Download Model, software for calculation of AIT and its validation

Programme “Energy, Environment and Sustainable Development”
Project SAFEKINEX: SAFe and Efficient hydrocarbon oxidation
processes by KINetics and Explosion eXpertise
Contract No. EVG1-CT-2002-00072
Model, software for calculation of AIT and its
validation
Deliverable No. 18
M.A. Silakova, V. Smetanyuk, H.J. Pasman
Delft University of Technology
April 2006
SAFEKINEX - Deliverable 33 - Report on experiments needed for kinetic model development (high pressure)
page 3 (59)
Table of Contents:
1
Introduction ....................................................................................................................................... 5
2
Approximate model of heat losses in AIT tests ............................................................................... 5
3
4
5
2.1
Basics......................................................................................................................................................... 5
2.2
Influences on natural convection ............................................................................................................. 7
2.3
Heat production in low temperature oxidation ...................................................................................... 10
Numerical modelling of cooling of heated gas............................................................................... 12
3.1
Heat loss from an inert gas to a vessel wall............................................................................................ 12
3.2
The numerical model .............................................................................................................................. 13
3.3
Calculation results with a heated inert gas ............................................................................................ 14
Time duration to gas self-ignition, IDT ......................................................................................... 18
4.1
Low temperature part (≤ 700K) with n-butane as fuel........................................................................... 18
4.2
Higher temperature part (> 700 K)......................................................................................................... 23
4.3
The effect of mixture composition .......................................................................................................... 29
4.4
The small chain hydrocarbons C1-C3 ..................................................................................................... 30
4.5
Simulations with strongly reduced mechanisms .................................................................................... 35
4.6
Alternative kinetic mechanisms and simulation software ..................................................................... 37
Characterisation of the conditions of natural convection enabling ignition .............................. 39
5.1
Basic gas-dynamic flow patterns ............................................................................................................ 39
5.2
Convection Effect on Induction Delay Time.......................................................................................... 41
5.3
Critical conditions for thermal explosion in a compressible gas........................................................... 42
6
Conclusions....................................................................................................................................... 44
7
References......................................................................................................................................... 45
Appendix I. Excel sheet to calculate heat transfer coefficient and adiabatic induction time ........... 47
Appendix II. Brief descriptions of the four current software packages for calculating ignition
processes and laminar flame. .................................................................................................................. 49
CHEMKIN 4.0.2 .................................................................................................................................................... 49
COSILAB 2.0.2 ...................................................................................................................................................... 49
CANTERA ............................................................................................................................................................. 50
Chemical Workbench (CWB) ................................................................................................................................ 50
References:............................................................................................................................................................. 51
Appendix III. Brief characterization of FLUENT CFD software....................................................... 53
Appendix IV. A Tentative Modeling Study of the Effect of Wall Reactions on Oxidation
Phenomena ................................................................................................................................................ 55
SAFEKINEX - Deliverable 33 - Report on experiments needed for kinetic model development (high pressure)
page 4 (59)
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
1
page 5 (59)
Introduction
Safety of hydrocarbon oxidation processes for cases in which no external heat source is
present, result from avoidance of run-away reactions in the process mixture leading to selfignition. So, given ambient conditions of temperature and pressure and given a mixture in a
certain section of the process equipment the first property to be established is the self-ignition
or auto-ignition temperature (AIT) for that particular system. Then the question follows of
how long does it take to reach the point of self ignition, that is how long is the ignition delay
time (IDT), and finally whether an incipient flame can propagate and what pressure can be
generated. The last of these determines the extent of product contamination and damage to
equipment, which has been the subject of other deliverables in the project.
Self-ignition temperatures play in general an important role in classifying the hazard of a
mixture with a view on the EU ATEX Directives to control gas explosion safety. As described
in Deliverable No. 5 [1] standardised test procedures exist and limited data are available, but
this extends practically not to elevated conditions. For self-ignition the pressure reached has
been proven to be important, as shown in Deliverables Nos. 5 and 33 [1, 2]. As described in
other Deliverables of the SAFEKINEX project e.g. No. 30 [3], two acceleration mechanisms
of reaction in a mixture of hydrocarbons and oxygen (or air) exist: a thermal explosion
mechanism in which an increasing reaction temperature results from the exothermic reaction
itself, and a radical chain branching mechanism in which the radical concentration increases
exponentially. Both mechanisms play a part of varying importance in the low temperature
hydrocarbon oxidation and occur, in particular, with higher alkanes and alkenes. Smaller
molecules such as methane and ethylene show slow oxidation reactions but the formation and
accumulation of peroxides, which at a certain stage acts as a source of reactive hydroxyl
radicals (·OH), does not occur as readily as in n-butane, for example. A surge of these radicals
induces cool flames. Given the right conditions the temperature (and pressure) increased by a
cool flame may induce a run-away to explosion in the mixture. This phenomenon is called
two-stage and, sometimes, multi-stage ignition.
This deliverable will develop a model for auto-ignition as far as is possible at present. To this
end (i) literature will be reviewed to obtain insight in the complexities involved, (ii) the heat
transfer of a given reacting mixture to a containing wall will be analysed, (iii) the detailed
kinetic models developed in the SAFEKINEX project will be briefly reviewed, (iv) the
software available in the market to simulate a detailed kinetic reaction scheme will be
described and (v) advice will be offered on how best to perform a simulation. The report is
concluded by some calculated examples.
2
Approximate model of heat losses in AIT tests
2.1 Basics
Following Ten Holder [9] and Pekalski [4], the Appendix of Deliverables No. 29 and the
Addendum A of Deliverable No. 33 [5, 6] give a preliminary basis to provide simple models
for the heat losses obtained in the self-ignition tests, where the main content was focussed on
experiments to measure the heat losses under a variety of conditions.
Heat loss from a gas at relatively small temperature difference with a confining wall will at
some motion of the gas mainly be by convection. When modelling, in the first place a
distinction has to be made between steady flowing mixture as is mostly the case in process
equipment and an initially quiescent gas as usually prevails in laboratory equipment. In the
case of steady flow in a pipe one can distinguish a heat exchanging surface area per unit of
length of pipe, A, a temperature of the bulk of the flow as a function of location, T(x), the wall
temperature at a certain location, Tw(x), and hence a driving force temperature difference
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 6 (59)
T(x)-Tw(x). Depending on flow conditions such as turbulence, boundary layer properties etc,
one can then estimate a heat transfer coefficient, h. Heat loss follows then from the
Newtonian relationship, h·A·(T-Tw), assuming the conditions in x-direction do not change.
For a gas in a closed vessel the situation is more difficult to describe. Heat losses from
exothermic gas-phase reactions in unstirred vessels occur by conduction and convection. At
very low gas densities and heat release rates, the gas is stagnant, heat losses are almost
exclusively conductive, so the temperature distribution in the reacting gas has a near parabolic
shape with the maximum temperature rise occurring at the centre of the reaction vessel. In the
case of an ideal conductive heat loss from a sphere filled with gas initially at uniform
temperature ∆Ti above ambient, an analytical solution of the partial differential equation
describing the temperature drop in time as a function of the temperature gradient can be
derived [7] in terms of the Fourier number, Fo = κ t/ r2, where κ is thermal diffusivity, t time
and r inner radius of sphere. At Fourier number 0.139 in the centre of the sphere the
temperature decreased to ½∆Ti and hence the cooling half-time, ∆t½ is found, or:
κ ∆t½/ r2= 0.139
(1)
For air at 1 bara and 400 K (κ = 3.5.10-5 m2/s) and a 0.5 litre flask a value for ∆t½ is thus
found of 10 seconds. For a 20 l sphere this time is roughly a factor 10 longer.
However, temperature gradients in a gas result in density differences. Lighter parts are
subjected to buoyancy force and so-called “natural convection” sets in. The onset of
convection in a gaseous reaction system can be estimated by calculation of the dimensionless
Rayleigh number (Ra). The Rayleigh number is as many other dimensionless numbers, a ratio
of forces and is defined as:
Ra = g β r 3C p ρ 2 ∆T / λη
where
g
= acceleration due to gravity
β
= coefficient of cubical expansion of the gas
(here, reciprocal of the absolute temperature)
r
= radius of the (spherical) vessel
= specific heat of the gas at constant pressure
Cp
ρ
= density of the gas
∆T
= temperature difference between the centre
and the wall of the reaction vessel
λ
= thermal conductivity of the gas
η
= viscosity of the gas
(2)
[ms-2],
[K-1],
[m],
[J kg-1 K-1],
[kg m-3],
[K],
[W m-1 K-1],
[kg m-1 s-1].
Experiments and calculations have shown that the following critical values for Ra can be
distinguished:
Ra < 600:
600 < Ra < 104 :
Ra > 104 :
conduction
conduction and convection
convection
These critical values of the Rayleigh number should be independent of the temperature of the
vessel and should apply to all gaseous systems and also to non-spherical vessels.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 7 (59)
2.2 Influences on natural convection
When the Rayleigh number is again considered it can be seen that it is a complicated function.
Its dependencies can be presented as in [9]:
Ra = f { g , β (T ), r , C p (T , Φ ), ρ ( p, T , Φ), λ (T , Φ, p ), η (T , Φ, p ), ∆T }
(3)
In the following an assessment will be given of the extent of its variation in the present
studies.
For a 9.5% n-butane in air mixture (equivalence ratio Φ = 3) an analysis is made of the
Rayleigh number as function of temperature difference. The volume of the vessel is 500 ml.
Initial pressure is 1 bara. It is assumed that mixture composition is constant. The mixture
properties were calculated as shown in Appendix I. Figure 1 shows the separate regimes of
heat transport. On the abscissa the ambient temperature is plotted, on the ordinate the
temperature difference between the centre of the vessel and the temperature of the surface (Ta)
is plotted.
80
70
Ra = 10^4
Ra = 600
60
Convection
∆ T [K]
50
40
30
Convection +
Conduction
20
10
0
500
conduction
550
600
650
700
750
800
850
900
Ambient Temperature [K]
Figure 1. Different regimes of heat transport as function of ambient temperature with
constant composition (9.5% n-butane in air). Vessel size= 500 ml, p = 1 bar.
Above the upper line (Ra = 104) convection is the dominating process of heat transfer. Under
the lowest line (Ra =600) heat transfer is purely conductive. In the region between the two
lines both convection and conduction play a role.
The lines have a parabolic shape due to the change in density (Ra ~ ρ2). The influence of
mixture properties on the Rayleigh number is evident. Since the specific heat (Cp) is in
numerator, and the product λ·η forms the denominator of the fraction in Equation 2,
Rayleigh number will decrease during consumption of n-butane, when temperature in
vessel and of the surface will remain constant.
the
the
the
the
The Rayleigh number is proportional to the cube of the radius, r3, and thus is proportional to
volume. This means that the Rayleigh number for a 20 l vessel will be 100 times that of a 200
ml vessel. Therefore, at constant ambient temperature, the temperature difference needed to
reach the critical condition of Ra = 104 value is 100 times lower. The different regimes of heat
transfer, are shown in Figure 2 as a function of vessel size. Ambient temperature (Ta) and
composition (Φ) are kept constant. The Rayleigh number is plotted as a function of vessel
radius. The curves represent various temperature differences (∆T) between the gas and the
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 8 (59)
vessel wall. It is apparent that in the range of test vessels used in the project the Rayleigh
number can vary over some orders of magnitude. In a volume of the 20-l vessel, small
temperature differences are sufficient to generate convective heat transfer. In this vessel tests
can be performed also at higher pressure. Since Ra = f(ρ2) = f(p2): the Rayleigh number will
increase strongly with pressure. This trend is confirmed by the measurements described in
Deliverable No. 33, Addendum A [4], although the relation found is linear (approximately
h = p with h in W/m2K and p in bara) rather than parabolic.
Mixture composition after 3 and last cool flame, p = 1 bar. Ta=610 K.
100 ml
1.2E+04
∆Τ = 1
∆Τ= 82
∆Τ = 5
1.0E+04
200 ml
200 ml
500 ml
∆Τ = 16
Convection
∆Τ= 41
∆Τ = 16
∆Τ = 41
Rayleigh Number [ - ]
Ra = 104
∆Τ= 5
∆Τ = 70
8.0E+03
∆Τ = 100
∆Τ= 100
6.0E+03
Convection &
Conduction
∆Τ= 1
4.0E+03
2.0E+03
Ra = 600
Conduction
0.0E+00
0
1
2
3
4
5
6
7
8
9
10
Vessel radius [cm]
Figure 2. Rayleigh number vs vessel radius. The influence of radius and temperature
differences on the mode of heat transfer. Typical post-cool flame mixture (initial 9.5% nbutane in air). p = 1 bar, Ta=610 K. The radius of a 20-l vessel is 16.8 cm.
For a gas mixture reacting exothermically in a closed vessel the above discussion, by
definition, implies the existence of a non-uniform distribution of temperature. As soon as
reaction sets in, a temperature difference between wall and gas is generated and heat transfer
to the (fixed temperature) wall will start. If the conditions are such that natural convection
occurs, warm gas in the centre will rise, flow towards the walls at the top of the vessel and
downwards along the walls, during which process cooling will occur. This way the
temperature gradients will be mitigated, but the heat transport is greatly enhanced. Due to
buoyancy the highest temperature will not remain in the centre of the vessel but be displaced
towards the top. If the rate of heat production becomes higher enough, convection flow will
become turbulent and large eddies will occur. As a result of this motion, gas pockets of
different temperature will exist which may drift through the vessel and which will exchange
heat by mixing with and by conduction to gas of different temperature.
Models of batch reactor vessels in which the full detailed kinetics of hydrocarbon oxidation
can be taken into account as in CHEMKIN’s module Aurora [10], allow at this moment at
best calculations based on zero-dimensional conditions, signifying a spatially uniform
temperature, that is with heat loss introduced on the basis of a constant heat transfer
coefficient, an surface area to volume ratio of the vessel and a temperature difference between
vessel content and wall. However, from the above it is clear that a uniform temperature of a
reacting gas can exist only in a special case where vigorous mixing is induced mechanically.
In a closed vessel it is also not possible to determine a volume or mass averaged temperature,
which would approximate to some uniform value. Since the location of a maximum
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 9 (59)
temperature is also not fixed, the alternative that remains in an attempt to keep the approach
simple, is to choose as reference temperature the temperature of the vessel centre. Therefore
in experiments to determine h, this centre temperature was measured. In the smaller glass
vessels in these experiments a small resistor in the centre was fed with a constant electric
current to heat the gas to a steady state after which current was interrupted, while in the 20 l
pressure vessel the gas (air) was heated by adiabatic compression when opening a fast acting
valve to a canister containing pressurized air.
Assuming the spatial temperature distribution to remain similar for various conditions,
Newton’s cooling law: −V ρ C ⋅ dT / dt = hA ⋅ (T − Ta ) can be integrated to yield a ‘heat transfer
V ρ C ln{(T2 − Ta ) /(T1 − Ta )}
·
(4)
A
t2 − t1
with V volume vessel, A interior surface area sphere, ρ density, C specific heat gas (here, at
constant volume), and T – Ta temperature difference with ambient at two different times t1 and
t2. Plotting the logarithmic temperature difference (T – Ta) versus time should produce a
straight line if the heat transfer coefficient is constant. From the gradient an (average) heat
transfer coefficient based on the temperature difference between centre and wall, can be
derived and determined as a function of pressure by repeating over a range of pressures. Since
as a result of natural convection, as we have discussed above, the conditions change with
temperature difference and in time, so a constant heat transfer coefficient does not exist and
the tangent produces a mean value over a certain range. As cooling just starts its value will
quickly increase to a maximum and eventually it asymptotically reduces to zero.
coefficient’ h as:
h=−
In the limiting case of pure conduction for a spherical vessel, applying Equation (4) above,
the heat transfer coefficient based on ∆t½ can be derived from:
- ln (½∆Ti /∆Ti ) = 0.69 = h A ∆t½ / (ρ C V)
(5)
Over a time interval, ∆t½, to half the initial temperature difference between centre of the
vessel and wall at any initial value of temperature, the logarithmic term yields 0.69.
Substitution of Equation (1), using κ = λ/ρ C and rearranging, in case of pure conduction an
‘equivalent value’ of h for the unsteady case can be derived via:
λ∆t½ / (0.139 ρ C r2) = h(4π r2)∆t½ /{0.69ρ C (4/3 π r3)}
yielding:
h = 1.65 λ/r
(6)
in which λ is the thermal conductivity of the gas and r is the radius of the vessel. For a vessel
filled with air at 400 K, λ is 0.032 W/(m·K); at a volume of 500 ml r is 0.0492 m, hence h =
1.1 W/(m2K), while at 20 l r is 0.168 m and h = 0.31 W/(m2K). The experimental value found
in the 500 ml vessel was lower, probably due to a systematic error in the set-up with the
resistor. In the case of the 20 l vessel with an initial temperature difference of about 10 K,
experimental results with compressed air can be fitted, see [6], with the relation: h = p.
Because thermal conductivity does not vary much with pressure heat transfer by conduction
would not be pressure dependent, so clearly natural convection plays an increasingly
important role in heat transfer at increasing density, and hence pressure.
Natural convection is very readily generated in a self-heating reacting gas. Kee et al. [11]
performed a detailed study with tritium as a heat producing fluid both experimentally and
numerically by solving the conservation equations for cylindrical and spherical geometry in
the steady state. Their results for a sphere can be correlated to a line in a diagram of the
surface averaged Nusselt number, Nu (= h’·2r/λ) and modified Grashof number, expressed as
Gr {= q·g·β·ρ2(2r)5/(λ η2)}, see Figure 3.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 10 (59)
Here h’ is based on a volumetric averaged gas temperature T and a fixed wall temperature. Gr
is modified by taking into account the volumetric heat generation q in W/(m3s) instead of the
relative density difference; all other symbols have been defined earlier (see Eqn. 2). The
correlation holds for a fluid for which Prandtl number (υ/κ) is about 0.7 where υ = η /ρ.
Figure 3. Heat transfer by natural convection in the steady state to the wall of a spherical
vessel filled with a heat producing gas. Correlation between the Nusselt number averaged
over the surface of the sphere versus a modified Grashof number, Kee et al., 1976.
Nu is minimal in the case of pure conduction and is calculated by Kee et al. for a sphere to
have the value 10 (steady state). With h based on an unsteady cooling (or heating) situation
and centre temperature Tc as a reference, according to equation (6) at time ∆t½ the equivalent
Nu would be 2×1.65 = 3.3, hence three times lower. The volume averaged temperature in
unsteady state (e.g. cooling) at that point of time can be derived from the solution in [7] of the
differential heat balance equation mentioned in relation with Equation (1). Here it yields a
ratio: (Tc-Ta)/( T -Ta) = 3.23 or Nu = 3.3×3.23 = 10.7. However in the unsteady state the ratio
of temperature differences is time-dependent and has at the start and end of a cooling or
heating process the value 1. If, by way of a mean, a parabolic temperature profile is assumed
(T = Tc-Cr2 with C = constant) the temperature ratio is 2.5 and Nu = 2.5 × 3.3 = 8.25. It is
clear that as soon as convection becomes significant, the difference Tc - T becomes
unimportant.
2.3 Heat production in low temperature oxidation
In the oxidation of hydrocarbons heat generation is not constant but increases strongly during
the process. It can increase by many orders of magnitude as shown for example by
simulations with the CHEMKIN code of a perfectly stirred batch reactor applying the detailed
kinetics model for C4-C10 hydrocarbons developed in the SAFEKINEX project (Deliverable
No. 35 [12]). For a typical case described in Deliverable No. 29 [5], of fuel rich n-butane in
pure oxygen at higher pressure the rate of heat production versus time is shown in Figure 4A.
Roughly the time weighted mean value over the first 700 seconds is 1 W/m3 and over the
remainder up to 1200 seconds 300 W/m3. These values were used to calculate h on the basis
of the graph of Figure 3, despite the graph being, strictly speaking, only applicable to a steady
state. Reading the graph can be done conveniently using the spread sheet of Appendix I. In
Table 1 also an experimental value of h is given although the reference temperature is not
exactly equal.
3
Heat production [W / m ]
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 11 (59)
1,00E+05
1,00E+03
1,00E+01
1,00E-01
1,00E-03
1,00E-05
1,00E-07
0
500
1000
1500
Time [s]
Figure 4A. Example of calculated rate of heat production, q in W/m3 in a simulation run with
CHEMKIN, Aurora for a mixture of 78% n-butane in oxygen initially at 4 bara and 500 K in
a 20 l vessel with an assumed heat transfer coefficient of 4 W/(m2K) as described in
Deliverable No. 29 [5].
For the 500 ml vessel at 575 K q has to be taken over the first 3 seconds (average 1.5 W/m3),
but increases further rapidly to a mean of 7 kW/m3 up till 5 seconds when cool flame occurs.
The value of h measured in air was similar to that by conduction alone: about 1 W/(m2K), as
described in Deliverable No. 29 [5], but when derived from the first part of cooling curves
after an AIT test in which explosion occurred, a value of about 7 W/(m2K) was obtained, see
[4] and [9]. At 685 K initial temperature two-stage ignition and explosion takes place in the
simulation. The ignition process takes 0.3 seconds and over that time the mean rate of heat
production is high: 350 kW/m3. In Table 1 the calculated values of h’ are shown in
comparison with the measured ones.
Table 1: Heat transfer coefficient values in a self-heating gas in a spherical vessel calculated
according to the method proposed by Kee et al. [11] and measured in a heated gas for two
typical volumes: 20 l steel vessel and 500 ml glass one.
Mixture
composition
[mol%]
Vessel
volume
[m3]
Initial
Pressure
[bara]
Initial
Temperature
[K]
Calculated
mean rate
of heat
3.2
9.7
4
4
4.7
6.9
generation
[W/m3]
over ([s])
Heat transfer
coefficient
[W/(m2K)]
Via Nu
Expericalculated
ment
n-C4H10-O2: 78-22
n-C4H10-O2: 78-22
0.020
0.020
4
4
500
500
n-C4H10-O2-N2:
9.5-19-71.5
n-C4H10-O2-N2:
9.5-19-71.5
n-C4H10-O2-N2:
9.5-19-71.5
5.10-4
1
575
1 (0-700)
300 (7001200)
1.5 (0-3)
5.10-4
1
575
7000 (3-5)
7.4
6.9
5.10-4
1
685
3.5.105
(0-0.3)
14.5
6.9
Heat production also varies with temperature. Griffiths et al. [13] calculated maximum rate of
heat production of n-butane oxidation in a simulated perfectly stirred batch reactor. A result is
given in Figure 4B. Thus the value of the heat transfer coefficient varies considerably.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 12 (59)
(n-C4H10 + O2 + N2 = 1.65 : 1.00 : 3.76)
φ = 10.7
R / W cm-3
0.75
φ = 6.5
(1.00 : 1.00 : 3.76)
0.50
0.25
φ =1
(0.15 : 1.00 : 3.76)
0.00
600
650
700
750
800
850
T/K
Figure 4B. Simulation of the dependence of maximum heat release rate on vessel temperature
from the isothermal reaction in a closed vessel for different mixtures of n-C4H10 + air at 1
bar according to Griffiths at al. [13]. With temperature and higher n-butane content heat
release rate increases, but at 700 K clearly a transition can be seen.
Currently the CHEMKIN suite of models is not the only one capable of simulating oxidation
processes under various conditions. There are, at least, three other software packages:
COSILAB, CANTERA and Chemical Workbench, which on the basis of detailed kinetics
calculate both ignition in a perfectly stirred batch reactor and laminar burning velocity. For
further details brief summaries are given in Appendix II of the capabilities of the packages
and some background on their producers. In Chapter 4 in comparison some further results will
be shown.
3
Numerical modelling of cooling of heated gas
3.1 Heat loss from an inert gas to a vessel wall
To obtain an improved picture of the heat loss of an exothermically reacting gas in which
natural convection develops and temperature gradients occur, the conservation equations of
mass, momentum and energy have to be solved numerically in combination with a source
term and boundary conditions. As a model vessel the 20 l one was chosen.
The equation used for determination of heat transfer coefficient is:
h=
d ln(T − Twall )
1
rCV ρ
3
dt
(7)
Where CV = 750 J / kgK , r = 0.168 m and density ρ follows from pressure and temperature
through the ideal gas law.
The heat transfer coefficient will depend on a reference temperature T. In the case of nonuniform temperature distributions inside the vessel under consideration there are three ways
for determination of the reference temperature. First of all there is the maximum temperature
but this way is not applicable in experiments. The second approach is from the average
temperature, which also is not easily estimated in experiments. And third there is the
temperature at a local point of the internal sphere, e.g. the centre. Thermocouple positions are
drawn in Figure 6. The same local points were used in simulations.
The model calculations will be compared with experimental measurements; to start with this
will be measured cooling curves from air as reported in Deliverable No. 33 Addendum A [2].
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 13 (59)
In that respect the limitation of the accuracy in the experimental measurements should be
considered. There are errors of determination of wall temperature Twall and reference
temperature T. Let us estimate the error in heat transfer coefficient related with the natural
logarithm temperature errors. Equation (7) after integration is used for this purpose:
 T − Twall 
l −n
 l −1 
 ⇒ ln 1
 = ln 1

h ~ ln 1
(8)
 l2 − n 
 l2 − 1 
 T2 − Twall 
where l1 = T1/Twall and l2 = T2/Twall at two points on the cooling curve over which the tangent
is measured and n is the quotient of real wall temperature, Ťwall and an assumed value for Twall.
Consider the example of Figure 5 taken from Deliverable No. 33 Addendum A [2] and select
for a straight line part l1 is 1.04 (312 K or 4% more then assumed wall temperature – 300 K),
and l2 is 1.003 (301 K or 0.3% more than the assumed wall temperature – 300 K). Then in this
example the value of h is:
 1.04 − 1 
2
h ~ ln
 = 13.3 W/m ·K
 1.003 − 1 
Let us suppose that wall temperature is determined with relative error n of 1%. For example:
one assumes Twall = 300 K but in reality Ťwall = 297 K. This error may occur due to nonuniform wall heating. (Temperature difference for T4 position becomes in the given example,
even if it is negative, which confirms the inaccuracy of Twall).
Figure 5. Example (Ex. 45d pini =2.1 bara, Twall = 300 K, ∆T0 = 12 K) of temperature profiles
of cooling compressed air in 20 l sphere at a wall temperature of 300 K.
Hence from the value 1 in both numerator and denominator 0.01 shall be subtracted:
 1.04 − 0.99 
2
h ~ ln
 = 3.8 W/m ·K
 1.003 − 0.99 
This means that the error in the heat transfer coefficient determination is a factor 3 and this
also explains the dispersion in the experimental results shown in [2].
3.2 The numerical model
The numerical model of a sphere1 is represented as two-dimensional circular cavity. The
initial conditions for inert gas and reactive flow are almost the same. The fluid was assumed
to remain quiescent at start. The spherical wall is constrained by no-slip and iso-thermal
condition. The internal domain is filled with air and all the fluid properties are calculated at a
reference temperature given by T. Initially the temperature of air inside the domain is
assumed constant at fixed temperature T0. In case of reactive flow a constant volumetric
source is injected.
1
The contribution of Nitesh Goyal in calculating the heat transfer coefficient is gratefully acknowledged.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 14 (59)
T6
T4
T3
T2
T1
Tcen
Figure 6. Position of thermocouples inside the 20 l sphere and used mesh.
The numerical model of the spherical shell is modelled in Gambit 2.1. The grid is meshed
with quadrilateral elements to make it structured over the entire domain.
During the simulation run the temperature in local points, average and maximum, maximum
velocity and pressure was written. The temperature-time derivative for determining the value
of h was determined as a ratio between the nearest differences and not between distant points:
∂ x x n− x n− 1
=
(9)
∂ y y n− y n− 1
The analysis is based on small temperature difference in the experimental work, so the
assumptions of constant transport and material properties are well justified. Viscous
dissipation is neglected because the velocities are small. The density variation, as it is very
small, is accounted for by using the ideal gas law.
The flow field is described by the continuity equation, and conservation of momentum and
thermal energy. The equations were solved by means of the FLUENT package, see Appendix
III for some additional information.
3.3 Calculation results with a heated inert gas
Below in Figures 7A and B results of calculation are shown. Initial parameters coincide with
the experimental values. Conditions are chosen as in Experiment 45d of Deliverable No. 33,
Addendum A [6]: Spherical volume 20 l, pini = 2.1 bara, Twall = 300 K, ∆T0 = 12 K.
The heat transfer coefficient determined by the volumetric average temperature as a reference
in the first moments is high when gas at the wall is cooled and the motion of the gas is
initiated. In this stage the change in maximum temperature is moderate and therefore the heat
transfer coefficient based on the maximum temperature as a reference is relatively low. A
similar time history is observed for heat transfer coefficients determined by a local
temperature as appears from Figure 7B.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 15 (59)
10
1
2
2
h, W/(m K)
8
6
4
2
0
1
10
100
t, s
Fig. 7A. Computed heat transfer coefficient time histories for reference temperature
determined: 1 – by average temperature, or 2 – by maximum temperature.
pini = 2.1 bara, Twall = 300 K, ∆T0 = 12 K
As a result of the evolution of gas motion after the first stage of low heat transfer coefficient
up to 10 seconds with local temperature as a reference, a second stage arrives of fast
increasing and a subsequent gradual decrease after 10 seconds. This is clearly shown in
Figure 7B.
1
2
3
4
5
12
8
2
h, W/(m K)
10
6
4
2
0
1
10
t, s
100
Fig. 7B. Heat transfer coefficient time histories in case reference temperature is determined
in different positions : 1- in P1; 2 – in P2; 3 – in P3; 4 – in P4; 5 – in P6. Points P refer to
the positions of the thermocouples in Figure 6. pini = 2.1 bara, Twall = 300 K, ∆T0 = 12 K
Therefore one cannot correlate the whole time history by a single simple dependence.
However one could pick out two different parts e.g. from 1-2 s and 10-100 s and describe
each part separately. A similar pattern was found at higher pressure, see Figures 8 and 9.
To describe the influence of initial pressure on heat exchange of a 20 l vessel over a range of
pressures calculations were made and the results shown in Figure 10. So, the pressure was
increased to 12.8 bars and other conditions kept as before: Twall = 300 K, ∆T0 = 12 K.
2
h, W/(m K)
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 16 (59)
1
2
16
14
12
10
8
6
4
2
0
1
10
100
t, s
2
h, W/(m K)
Fig. 8. Heat transfer coefficient time histories for reference temperature determined via
different ways: 1 – by average temperature; 2 – by maximum temperature. pini=4.25 bara;
Twall =300 K, ∆T0 = 12 K
1
2
3
4
5
16
14
12
10
8
6
4
2
0
1
10
100
t, s
Fig. 9. Heat transfer coefficient time histories for reference temperature determined in
different positions P of the thermocouples with the same indices shown in Figure 6: 1- in P1;
2 – in P2; 3 – in P3; 4 – in P4; 5 – in P6. pini= 4.25 bara; Twall = 300 K, ∆T0 = 12 K
30
1
25
2
h, W/(m^2K)
3
20
4
15
10
5
0
1
10
100
t, s
Fig. 10. Heat transfer coefficient time histories for volumetric average as reference
temperature at different initial pressure levels: 1– 2.1 bara; 2 – 4.25 bara; 3 – 8.4 bara;
4 – 12.6 bara; Twall = 300 K, ∆T0 = 12 K
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 17 (59)
The time curves behave very similar. Two regions of more or less constant heat transfer
coefficient can be distinguished again. The results derived from the time histories of Figure
10 are plotted in Figures 11 and 12 for the early region (1-2 s) and the late part (10-100 s) in
approximately a linear dependency of heat transfer coefficient on pressure. This was repeated
for three temperature levels: 300, 500 and 800 K.
30
30
300 K
300 K
25
500 K
800 K
20
h, W/(m^2K)
h, W/(m^2K)
25
15
500 K
800 K
20
15
10
10
5
5
0
0
0
5
10
0
15
5
Fig. 11. Calculated heat transfer coefficient
at three temperature levels as a function of
initial pressure at an early stage of cooling:
at 1 s.
15
Fig. 12. Calculated heat transfer coefficient
at three temperature levels as a function of
initial pressure in a late stage of cooling: at
100 s.
30
30
25
25
Tcan = Tsph = 300 K, Psph = 1 bar
Tcan = Tsph = 300 K, Psph = var
Tcan = Tsph = 400 K, Psph = var
Tcan = Tsph = 500 K, Psph = var
Tcan = Tsph = 300 K, Pcan = 0 bara, reverse jet
Linear (trendline)
20
2
2
h, W/(m K)
20
h, W/(m K)
10
p, bara
p, bara
15
15
10
y = 0.9892x
R2 = 0.7994
10
Tcan = Tsph = 300 K, Psph = 1 bar
Tcan = Tsph = 300 K, Psph = var
Tcan = Tsph = 400 K, Psph = var
Tcan = Tsph = 500 K, Psph = var
Tcan = Tsph = 300 K, Pcan = 0 bara, reverse jet
5
5
0
0
0
0
5
10
15
ρ, kg/m3
20
25
30
Fig. 13. Measured heat transfer coefficient
plotted as a function of density at various
pressure and temperature levels. Data fitted
to a straight line for each temperature.
5
10
15
20
25
30
p, bara
Fig. 14. Measured heat transfer coefficient as
a function of initial pressure at different
temperature levels. All data fitted to one
straight line, Deliverable No. 33 Add. A [6]
In Figures 13 and 14 the experimental points are plotted as given in Deliverable No. 33
Addendum A [6]. The scatter in data is relatively large but can be explained by the change in
h over time. Usually late time periods were taken for the measurement of the ln (∆T – t) slope.
In Figure 13 the trend of the influence of temperature as is seen in the calculations is only
visible for the higher temperatures. In Figure 14 all data are fitted to one straight line which
corresponds fairly well with the line of calculated values at 300 K for 100 seconds after the
start of cooling in Figure 12.
In conclusion it can be stated that the heat transfer from a self-heating gas to an outside wall
can be reasonably well estimated from the experiments and calculations made.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
4
page 18 (59)
Time duration to gas self-ignition, IDT
4.1 Low temperature part (≤ 700K) with n-butane as fuel
Exothermic reactions generate heat and self-heating of the reactants occurs when only part of
the heat is transferred to the surroundings. When the process is at constant pressure the heat
generation rate is the product of enthalpy change –∆H and reaction rate, and for a constant
volume process the product of change in internal energy –∆U and reaction rate Usually
reaction rate increases exponentially with temperature as described by the Arrhenius equation,
which in a simple form is written as:
dx/dt = x k exp(-E/RT)
(10)
in which x = concentration of decomposing compound X, k is the rate constant, T is the
reactant temperature, E is the activation energy, and R is the universal gas constant. The rate
constant k can still be a weak function of temperature and may therefore, for a large
temperature range, be written as ATn. A more extensive survey of the theory of ignition and
gaseous fuel oxidation reactions is presented in Griffiths and Barnard [14]. If the overall
reaction rate and heat generation can be lumped into a Arrhenius type of equation, a wealth of
analytical models has been developed following Semenov, Frank-Kamenetzkii and
Merzhanov. A well-known example for fitting experimental results of determination of
ignition temperature T as a function of pressure p with A and B as constants, is the Semenov
relation for thermal ignition:
ln (p/T) = A/T + B
(11)
In a closed vessel where no heat losses occur and the reaction rate is not dependent on
concentration (zero-order), given an initial temperature Ti the adiabatic induction time to
ignition (at constant volume) is given by:
tad = {Cv/(–∆U)}{RTi2/(E·k)}exp(E/RTi)
(12)
where Cv is the heat capacity of the reaction mass. This represents the shortest time interval in
which ignition can develop. When heat losses occur, the induction time increases depending
on thermal conductivity and internal temperature gradients and heat transfer by convection
near a wall.
However, the importance of radical reactions in hydrocarbon oxidation processes must also be
recognized, see e.g. [25, 26]. In particular at relatively low temperature these can accelerate
and set off ignition, yet during a very substantial fraction of the overall induction time there is
very little temperature change. The acceleration of reaction rate through this period is the
result of the formation of alkyl peroxides and alkyl keto-peroxides which gradually
accumulate a reservoir of active species as they decompose at increasing rates (575 K, 1 bara:
0.1 butyl peroxide and 0.2 mol% keto-peroxide). The decomposition occurs in a dramatically
accelerating fashion (in the so called “degenerate chain branching” mode) aided by the
accompanying temperature increase in the late stages of the induction period. The reactive
hydroxyl (·OH) radicals play a crucial role in being produced in the decomposition and in
initiating further reactions. A surge of these radicals leads to the phenomenon of cool flame
which in the subsequent exothermic reactions increases temperature by tens to hundreds of
degrees – although still far from the maximum possible temperature for complete combustion
because the chemical conversion leads mainly to partially oxidised intermediate compounds
However, this stage may bring conditions of temperature and pressure to a state in which
further exothermic reactions can be induced in the complex mixture, principally through
hydrogen peroxide decomposition as the hydroxyl radical producer, and leading to the final
stage of ignition . An ignition process can therefore be two- or even multistage. Depending on
conditions of pressure, temperature and heat loss a cool flame can be extinguished but the
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 19 (59)
burst can repeat itself a number of times. Oxidation can also take place as a slow process
without a reaching this peak of activity (which is then of little concern as a combustion hazard
but may be detrimental to the quality of a product from the chemical process). In Deliverables
Nos. 5 [1], 29 [5], 30 [3] and 45-47 [15] more attention is given to details of these
phenomena.
A typical temperature-time history for the induction to a cool flame in n-butane is given in
Figure 15. This curve was calculated in the same simulation run for 78% n-butane in oxygen
as reported in Section 2.2. There the rate of heat production was shown in Figure 4. As can be
seen the temperature increase for a large part of the induction time is small. Up to 700
seconds it is 0.04 K and at 1000 seconds still 1 K. During most of the induction period
process can be called isothermal.
900
850
Temperature [K]
800
750
700
650
600
550
500
450
0
500
1000
1500
Time [s]
Figure 15. Example of calculated temperature time history in a simulation run with
CHEMKIN, Aurora with the CNRS Nancy EXGAS derived model for a mixture of 78 mol% nbutane in oxygen initially at 4.1 bara and 500 K in a 20 l vessel with an assumed heat transfer
coefficient of 4 W/(m2K) as described in Deliverable No. 29 [5]. The temperature increase up
to 700 seconds is only 0.04 K and at 1000 seconds still only 1 K. The process is almost
isothermal throughout this stage of reaction.
1570
1470
h=0,2
h=5
h=40
h=82
1370
1270
T, K
1170
1070
970
870
770
670
570
0
2
4
6
8
10
Time, s
Figure 16. Simulation of a cool flame reaction in 9.5 mol% n-butane in air at 1 bara and at
an initial temperature of 575 K based on detailed kinetics (further) developed in the Safekinex
project by CNRS Nancy, Deliverable No. 35 [12]. The simulation is in a closed batch reactor
of 20 l of uniform temperature at different levels of heat transfer at the wall, h in W/(m2K),
simulating intensity of stirring. It can be concluded that heat loss has negligible effect on
ignition delay. The effect of rate of heat loss becomes apparent from the height of the peak at
ignition (two-stage) and the tangent of the slope of the cooling curve behind the peak.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 20 (59)
In the simulation there is a transition from the cool flame into explosion (two-stage ignition)
with almost maximum heat output in the final jump in temperature and pressure (when the
vessel is a closed volume), while in the experiments at this initial temperature the phenomena
are much less violent and are limited to (repetitive) cool flame superposed on slow oxidation.
Examples are shown in Deliverables Nos. 5 and 30 [1, 3].
30
Experiments semi-open 500ml vessel
Calculation, full CNRS mechanism(Expl) (P=const)
Calculation, full CNRS mechanism(CF) (P=const)
25
IDT, s
20
15
10
5
0
550
600
650
700
750
800
850
Temperature, K
Figure 17A. Induction time to cool flame and/or explosion in 9.5 mol% (rich) n-butane-air
mixture at atmospheric pressure measured in semi-open, spherical 500 ml quartz glass vessel
[1] and for comparison, calculated with detailed kinetic model developed in the Safekinex
project by CNRS, Nancy. The best EXGAS derived model [12] shows a reactivity which at low
temperature is too high (same ignition delay time at roughly 25 K lower temperature). The
heat transfer coefficient, h, is taken as 1.5 W/(m2K). Expl = Explosion, CF = Cool Flame.
30
Experiments semi-open 200ml vessel
Experiments closed 200ml vessel
Calculation, full CNRS mechanism (Expl) (P=const)
Calculation, full CNRS mechanism (CF) (P=const)
25
IDT, s
20
15
10
5
0
550
600
650
700
750
800
850
Temperature, K
Figure 17B. The same as Figure 17A, but now for a 200 ml vessel in two versions: spherical
semi-open quartz glass [1] and cylindrical, stainless steel closed [1, 2]. The difference
between model and experiment below 700 K is as in the previous figure, but note the much
better agreement above 750 K with the closed vessel experiments. (Calculation at constant
pressure or constant volume did not show much difference). h= 1.5 W/(m2K); Expl =
Explosion, CF = Cool Flame.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 21 (59)
30
Experiments 200 ml 10 bara
25
Calculation 200 ml,10 bara closed
Experiments 200 ml 1 bara
IDT, s
20
15
10
5
0
500
550
600
650
700
750
800
850
Temperature, K
Figure 17C. Experiments with 9.7 mol% n-butane in air measuring Ignition Delay Times at
10 bara [1] in closed 200 ml cylindrical stainless steel vessels. In comparison CHEMKIN
calculation results with the CNRS n-butane mechanism with h= 1.5 W/(m2K), and as a
reference the experimental results at 1 bara closed vessel shown previously in Fig. 17B.
900
0,25
850
0,2
750
Temperature [K]
700
650
0,15
Mole fraction O2
600
0,1
Mole fraction O2
experimental
550
500
Mole fraction O2
Temperature [K]
800
0,05
450
400
0
0
5
10
15
20
25
Time [min]
Figure 18. Model calculation with detailed EXGAS kinetics of temperature-time history of
self-ignition of 78% n-butane and 22% oxygen at 4.1 bara and 500 K in a 20 l steel vessel
[5]. If performed at 38.5 K lower temperature (461.5 K) the calculation synchronised with the
measured consumption of oxygen (diamonds). Heat transfer coefficient is assumed to be 4
W/(m2K).
If low temperature oxidation is active, acceleration of reaction takes place via the radical
chain branching process and much less as a result of self heating, so heat loss has only limited
influence on ignition delay time. This is illustrated in Figure 16 showing simulation results
with 9.5% n-butane in air at 1 bara.
In Figures 17A and B and 18 comparisons are shown of simulations with experiments at quite
different conditions2. In all cases the kinetic model below 650 K behaves as if it is too
2
Although the IDT in the simulation can be determined according to the tangential method as done in the
experiment, because the highest rate of increase of temperature in the simulation is always near the maximum
temperature (steep temperature jump), for simplicity IDT is taken as calculated by the default in the program
being the time to reach the initial temperature plus 400 K.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 22 (59)
reactive. To obtain the same IDT-value the simulation has to be run at about 25 K (Figures 17
A and B respectively) and 38.5 K (Figure 18) lower than the experiments were done. The
experimental results at low temperature, such as in Figures 17A and B have been obtained by
TU Delft in semi-open glass flasks in different volumes (100, 200 and 500 ml), but have been
reproduced rather accurately at BAM in 200 ml closed steel vessels. This confirms that the
rate of heat loss does not play a significant role. It is therefore probable that the model indeed
over emphasises the reactive. Recently, Frolov et al. [16] simulated the 78% n-butane in
oxygen experiment with an alternative butane oxidation model. To reproduce the
experimental result they assumed slow decomposition of butyl hydroperoxide and hydrogen
peroxide respectively into oxygen and butane water to simulate the termination of reactive
intermediates on soot particles and walls:
C4H9O2H → C4H10 + O2
H2O2 → H2O + 0.5O2
(a)
(b)
The effective activation energies E1 and E2 of reactions (a) and (b) were assumed zero, while
the corresponding pre-exponential factors were taken equal to k1 = k2 = k = 80 s-1, hence at a
temperature independent low rate representing mass transport types of processes. When these
two reactions were included in the SAFEKINEX scheme for the test at 500 K presented in
Figure 18 the temperature difference reduced from 38.5 to 6.5 K. This appears to be the first
numerical investigation of surface destruction of this type in the low temperature oxidation
region.
In the oxidation mechanism after formation of a butyl radical followed by molecular oxygen
addition in the oxidation mechanism, butyl hydroperoxide can be formed via external Habstraction. Alternatively an intramolecular H-abstraction yields a butyl hydroperoxy radical
to which further oxygen addition occurs leading to butyl ketohydroperoxide, C3H7COOOH,
see e.g. Deliverable No. 35 [12]. On the basis of CHEMKIN calculations it turned out that
taking out the internal H-abstraction part of reaction at 500 K does not change the outcome
much, while in contrast blocking the external branch makes a marked difference and delays
the cool flame occurrence significantly. At a higher temperature the internal branch becomes
increasingly influential. At 550 K the two branches have a similar quantitative contribution,
but at 650 K the internal branch is predominant. In addition, when in analogy of reactions (a)
and (b) a decomposition of butyl keto-hydroperoxide was assumed at 575 K, even with a rate
constant as low as 6 s-1, the discrepancy for IDT between numerical simulation and
experiment disappears. A small error in the value of a rate constant in the scheme or a
termination at the wall can therefore account for the mismatch. Wall effects will be addressed
further in the next section.
At higher pressure, molecular collision frequencies go up and the lowest temperature at the
which cool flame occurs decreases considerably, as is shown in Figure 17C, while also in
small volumes much longer induction times become possible (at 10 bara in 200 ml at 543 K
IDT becomes 100 s). Figures 17A, B and C and Figure 18 also show the strong effect of
initial temperature on the IDT value. At lower temperature IDT lengthens, such that at 500 K
and 4.1 bara for 78 mol% n-butane in oxygen the IDT becomes as long as 20 minutes.
The relation between IDT and temperature can be approximated with an exponential function
in a so-called Semenov plot (log IDT vs. 1/T), although this name is used too for describing
the relation between log p and 1/Tign. If the process of ignition would be thermal rather than
chain branching and nearly isothermal the relation IDT versus T may also take the form of
Equation (12), which has the advantage of including the heat capacity, heat of reaction and
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 23 (59)
rate dependence on pressure. If the following values3 are substituted: E = 153 kJ/mol K (36.5
kcal/mol K), k = 3.3·1011·p0.5 and at atmospheric pressure -∆Q = 2·105 J/m3 or rather 2.95·105
J/kg (the overall reaction heat effect -∆Q calculated by integration over time of a CHEMKIN,
Aurora run output of the rate of heat generation is at 560 K of this order of magnitude) the
measured IDT values in the LTOM region for the 9.5% n-butane in air at atmospheric
pressure (C=Cp) are reasonably well reproduced, see Figure 19A. For the calculations use can
be made of the spreadsheet of Appendix I. For this range of conditions the relation can
therefore be used for engineering purposes. The measured IDT value for a 78% n-butane
mixture in oxygen at 500 K and 4.06 bara is about 1300 seconds [5]. With the values as above
(C=Cv, but same heat effect per unit of mass) an IDT-value is found of 1370 s.
50
45
40
35
30
25
20
15
10
5
0
550
700
Measured points
Ignition Delay Time [s]
Ignition Delay Time [s]
At higher pressure and longer ignition delay times prediction by this relation becomes worse.
This is true for the 9.7% n-butane mixtures in air at 10 bara (C=Cv), as shown in Figure 19B,
of which the experimental values have been reported in Deliverables Nos. 5 and 33 [1, 2]. To
produce Figure 19B the heat release per unit of mass has been reduced by a factor of 3. Also it
seems that the apparent activation energy at the higher pressure and lower temperature
becomes higher (roughly 50 rather than 36.5 kcal/mol). In other words at lower temperatures
the experimental IDT becomes relatively longer. An explanation can be sought in the slower
production of organic peroxides or the decomposition as mentioned before, although one
would expect the latter to be less influential at higher pressure or in a larger vessel.
Calculated exponential
Poly. (Calculated
exponential)
Experiment 6.3 l
600
Calculated
500
Experiment 200 ml
400
Poly. (Calculated)
300
200
100
0
600
650
700
750
800
850
Temperature [K]
Figure 19A: Fit by a 6-degree polynomial of IDT
points calculated with Equation 8 at 10 K
temperature intervals with the parameter values
quoted in the text above for an atmospheric 9.5%
n-butane mixture in air, in comparison with the
measurements in a 200 ml vessel reported in
Deliverable No. 5 [1].
500
520
540
560
580
600
Temperature [K]
Figure 19B: Fit by a 6-degree polynomial of IDT points calculated with Eq.
8 with the same parameter values as for
Fig. 19 A for 9.7% n-butane mixture in
air, at a pressure of 10 bara in
comparison with the measurements in
6.3 and 0.2 l steel vessels reported in
Deliverables Nos. 33 and 5 [2, 1].
In conclusion it is clear that heat loss does not much affect the time of occurrence of a cool
flame. Prediction of ignition delay time on simulation of full kinetics in a perfectly stirred
batch reactor underestimates measured values at lower temperature and higher pressure. To a
lesser extent the same is true for a simple engineering type of equation.
4.2 Higher temperature part (> 700 K)
At higher temperature where the intermediate mechanism (ITOM) becomes important, i.e. for
n-butane above 700 K, it was thought that heat loss might have more effect on IDT.
3
Suggested in personal communication by Frolov, Basevich and Borisov (Semenov Institute, Moscow)
September 2006
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 24 (59)
Examining the experimental findings as reproduced in Figure 20A seems to strengthen that
interpretation. The IDT-values near 760 K seem to strongly increase with decreasing volume.
In Figure 20B temperature-time histories are plotted of AIT tests near 760 K. In 100 and 200
ml vessels the wall temperature has been 761 K, but in the 500 ml one it was 750 K.
Ignition delay times τT
50
500 ml
45
200 ml
40
Ignition Delay Time [s]
for a 9.5% n-butane in air mixture. P = 1 atm.
100 ml
35
CF
EXPL
SO
30
CF on SO
25
20
15
10
5
0
550
570
590
610
630
650
670
690
710
730
750
770
790
810
830
850
870
Ambient Temperature [K]
Figure 20A. Induction time versus ambient temperature showing the Negative Temperature
Coefficient (NTC)-diagrams for the AIT tests in semi-open 100, 200 and 500 ml flasks with
9.5 mol% n-butane in air at atmospheric pressure. (IDT open squares between 730 and 770 K
with 100 ml vessel was determined by hand), Deliverable No. 5 [1]. In the region CF Cool
Flame resulted, partly superposed on SO, Slow Oxidation, and finally EXPL explosion.
920
900
Temperature [K]
880
T4 500 ml
T5 500 ml
Twall 500 ml
T4 200 ml
T5 200 ml
Twall 200 ml
T4 100 ml
T5 100 ml
Twall 100 ml
860
840
820
800
780
760
740
0
20
40
60
80
100
120
140
160
180
200
Time [s]
Figure 20B. Temperature-time history of AIT test in 500ml flask at 750 K and in 200 and 100
ml at 761 K with 9.5 mol% n-butane in air at atmospheric pressure. The start of the
experiment with the injection of the mixture was at about 4.5 s on the time line. The test in the
100 ml flask did not explode but showed only slow oxidation with a maximum temperature at
160 s. Back extrapolation from the point of the maximum rate of temperature rise resulted in
the IDT value shown in Figure 10a of about 40 s. The centre temperature T4 starts higher but
remains lower in the explosion peak than the temperature near the top T5.
The peak of the 500 ml test would therefore have come out at 760 K a few seconds earlier and
with a higher temperature maximum. In general with smaller volume the peak, sometimes
accompanied by audible and visual effects, comes later and is less pronounced. In the 100 ml
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 25 (59)
volume an explosion does not develop; the reaction takes place as a long duration slow
oxidation with a maximum temperature rise of less than 5 K after about 160 seconds. It is
only that the tangent projection method for determining IDT at the intersection with the base
line [1] produces the corresponding duplicate test points of 37.5 and 42.5 seconds in Figure
20A.
However, in the simulation with CHEMKIN neither area-to-volume ratio, nor heat transfer
coefficient has much effect on induction time, although the effect is greater than that observed
below 700 K. This could already have been noted when comparing calculated IDT values
versus temperature above 700 K for 500 ml in Figure 17A with those for 200 ml in Figure
17B. Induction time is
1350
1300
500 ml
200 ml
100 ml
1250
Temperature, K
1200
1150
1100
1050
1000
950
900
850
800
750
0
1
2
3
4
5
6
7
8
9
Time, s
Figure 21. Calculated temperature-time histories at 760 K wall temperature of 9.5 mol% nbutane in air with the CNRS mechanism at atmospheric pressure with an extremely high heat
transfer coefficient of 100 W/(m2K) for three different vessel volumes: 500, 200 and 100 ml.
As can be noticed heat loss has only a minor influence on induction time, but has an effect on
the temperature reached.
920
900
Temperature [K]
880
Twall 761
T4 761
T5 761
Twall 852
T4 852
T5 852
860
840
820
800
780
760
740
0
20
40
60
80
100
120
140
160
180
200
Time [s]
Figure 23. Temperature-time histories of AIT tests at 761 K and 852 K in semi-open 100 ml
flask with 9.5 mol% n-butane in air at atmospheric pressure. The experiment at 852 K shows
that also in the 100 ml flask at higher temperature explosion is possible. Typical for sudden
reactions either cool flame or explosion, is the peak becoming highest near the top of the
vessel and not in the centre of vessel.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 26 (59)
not strongly affected. On the other hand maximum temperature decreases with volume as
shown clearly when comparing calculated T-t histories at 760 K wall temperature presented in
Figure 21 for the three volumes at relatively high heat loss: that is, in semi-open vessel
(pressure constant) and very high heat transfer coefficient of 100 W/(m2K). However, the
induction times remain much shorter than those measured and even for the 100 ml volume
there is in the calculation still a considerable heat production peak at the end of the process.
h=0.9 W/(m2K)
h=10 W/(m2K)
h=50 W/(m2K)
h=100 W/(m2K)
1950
h=0.9 W/(m2K)
h=10 W/(m2K)
h=50 W/(m2K)
h=100 W/(m2K)
1750
1550
Temperature, K
Temperature, K
1750
1950
P = constant
1350
V = constant
1550
1350
1150
1150
950
950
750
750
0
1
2
3
4
5
6
7
Time, s
Figure 22A. Results of calculated temperature-time histories with 9.5 % n-butane in air
in a semi-open 200 ml vessel at 4 different heat
loss levels at 760 K.
0
1
2
3
4
5
6
Time, s
Figure 22B.
Results
of
calculated
temperature-time histories with 9.5 % nbutane in air in a closed 200 ml vessel at 4
different heat loss levels at 760 K.
Comparison of the simulation results at constant pressure and constant volume in Figures 22A
and B reveals that closing a vessel has a noticeable effect on (calculated) explosion
phenomena. Simulations have been carried out at four extents of heat transfer coefficient. The
peaks become higher and earlier when the volume is closed (no work is exerted). It shall be
concluded that although differences are there, they are quantitatively limited. This is
consistent with the earlier noted finding that heat loss has more influence than below 700 K.
Experimentally in the semi-open 100 ml flask at higher initial temperature, explosion peaks
do develop, as illustrated by the test at 852 K presented in Figure 23, where in contrast to 760
K a reaction peak occurs instead of a slow oxidation.
Pressure has a relative strong effect on reducing the induction time. At 700 and 800 K
induction time reduces from 0.4 and 2.1 seconds respectively at atmospheric level to 0.02 and
0.03 seconds at 10 bara, whereas the H2O2 concentration just before reaching the temperature
peak of 1650 - 1730 K goes through a maximum of up to 0.7 mol%.
Instead of the progressively accelerated decomposition of accumulating organic peroxides as
butyl hydroperoxide and butyl ketohydroperoxide as ‘fuel’ for chain branching and the
occurrence of the cool flame phenomenon as in the low temperature oxidation mechanism
(LTOM), now hydrogen peroxide build-up and decomposition can lead to hot ignition. An
analysis is given by Griffiths et al. [17] about the role of H2O2 as an intermediate and the
complex pathways in which the very reactive ·OH and the slower reacting HO2· radicals act at
both sides of reaction equations. An illustration of the change in mechanism is shown by. the
open squares near the abscissa of Figure 17B above 700 K, indicating that the cool flame
mechanism in these cases is still weakly present but loses effect almost immediately after the
start of the oxidation. The accumulating hydrogen peroxide is totally consumed in the final
7
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 27 (59)
temperature jump4. At 750 K, just before the peak, the calculated H2O2 concentration is 0.63
mol% and at 800 K 0.41 mol%.
The calculated time to ignition at temperatures just above 700 K is of the order of a few
seconds and short relative to the experimentally measured IDT in AIT experiments at
atmospheric pressure: e.g. at 750 K 30 s in 100 ml, 20 s in 200 ml and 10 s in 500 ml; as
appears from Figure 20A for the experiments and the calculated ‘No wall effect’ column of
Table 2.
Table 2. Calculated induction periods, IDT in seconds, for the 9.5 mol% n-butane in air
mixture at 750 K and at pressures of 1, 2 and 10 bara, taking account of wall effects, h = 1.5
W/(m2K).
Vessel type
Experiment No wall effect Cat. I
100 ml glass
30
3.1
14.0
200 ml glass
20
3.1
10.0
500 ml glass
10
3.0
6.0
200 ml steel 1 bara
5
2.7
9.5
200 ml steel 2 bara
0.5
0.6
200 ml steel 10 bara Ca. 1
0.1
0.1
Cat. II
1890.0
198.0
14.5
178.0
0.7
0.1
T peak CatII, K
956
1346
1652
1840
1985
2051
It is known that the hydroperoxy HO2· radicals are relatively long living. In smaller vessel the
ratio of wall surface area to volume increases, radicals can travel a smaller distance to reach a
wall and surface termination reactions are more favoured, even though molecular mean free
paths are short at atmospheric pressure. Even though molecular mean free paths are short at
atmospheric pressure the species of lower reactivity are able to sustain multiple collisions in
the gas phase without reaction, and so can migrate to the wall.
As part of the SAFEKINEX project some work5 has been done to investigate this effect. In
Appendix IV a brief communication paper of this work is given. In line with the assumptions
made in this paper a number of calculations have been performed for the vessels relevant in
the experimental part of the project. All vessels were assumed spherical (The calculation
serves just to obtain an order of magnitude impression). Acidic material (Category I as
defined in Appendix IV) and salt and metal oxides (Category II, with a much stronger effect)
are known to decompose HO2· radicals and H2O2 to inert products The rates follow from the
product kwd (kw is rate constant in s-1, d = diameter vessel in m) with values of respectively
10.7 and 0.05 m/s. Category I corresponds with the first value; category II with both.
Category I is certainly relevant for glass; category II is relevant to steel. However in the
experimental tests no special care was taken to clean and pacify the glass or metal surfaces
(other than the “ageing” process that occurs with repeated experiments). So, the glass may be
contaminated to some degree with Category II substances. The activity of the stainless steel
surface of the 200 ml vessel with respect to metal oxides is unknown and may be low.
Calculation results at an initial temperature of 750 K are collected in Table 2 for semi-open
(closed by perforated stopper) quartz glass vessels, 100, 200 and 500 ml and closed stainless
steel 200 ml. For comparison experimental time values estimated from Figure 20A are given
in the second column. The column on the far right shows, as a measure of the strength of the
end-effect – the explosion- the maximum temperature reached with Category II wall activity.
The figures indicate that wall effects seem to be rather strong in the range of volumes of the
4
This jump is associated with the so called blue flame phenomenon which because of the immediate further
development to hot flame will mostly not be discernible as such.
5
This contribution is based on the Ph.D. study of F. Buda, which is gratefully acknowledged.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 28 (59)
AIT test set-up (100 – 500 ml). The stronger the wall effect, the slower the process of
oxidation and the lower the temperature reached in the peak, since heat loss is effective over a
larger time period. The deviations can easily explain the experimental results. Also striking is
the reducing effect of pressure. Doubling pressure to 2 bar almost suppresses wall effects
completely. This can be explained by the many bimolecular reactions with oxygen in which
HO2· radicals are produced. At increased pressure as a result of the higher production of HO2·
radicals the decomposition at a wall does not have a sufficiently significant effect on
concentration to compete effectively with the accelerating effect of chain branching. AIT
should therefore certainly not be determined in open vessels. Table 3 shows that the wall
effect is not influenced heavily by heat transfer, as is to be expected from the results without
wall effect taken into account.
Table 3. Calculated induction periods, IDT in seconds, for the 9.5 mol% n-butane in air
mixture at various values of the heat transfer coefficient, h, at 750 K and in a semi-open 100
ml quartz glass vessel at atmospheric pressure, taking account of wall effects
h W/m2K No wall effect/ s Category I/ s Category II/ s T peak Cat II/ K
1.5
3.1
14.0
1890
956.0
15.0
3.9
15.3
1890
751.4
45.0
4.8
17.0
1890
750.5
It is also interesting to see the effects over the temperature range of interest between 700 and
825 K. Results of these calculations are given in Table 4. It therefore appears that even the
shape of the IDT versus temperature profile as seen in Figure 20A is reproduced taking into
account wall effects.
Table 4. Calculated induction periods, IDT in seconds, for the 9.5 mol% n-butane in air
mixture at various temperatures and in a semi-open 100 ml quartz glass vessel at atmospheric
pressure, taking account of wall effects, h = 1.5 W/(m2K).
T wall/ K Experiment/ s No wall effect/ s
700
1
0.4
10
725
1.5
750
775
800
825
30
35
25
10
3.1
2.8
2.1
1.4
Cat, I/ s
0.4
2.9
14.0
12.3
6.8
3.3
Cat. II/ s
0.5
SO,
max at 55 s
1890
2420
379
11.5
T peak Cat II/ K
1632
749
956
986
1526
1688
There may however be a further explanation for the difference experiment versus simulation
not taking into account wall termination effects. The much longer ignition times in the
experiments may be still attributed also to heat losses, but in a different way than just a higher
heat transfer at the wall of the vessel. In Figure 20B it can be seen that the temperature
initially near the top of the vessel, hence the inlet of the flask, is lower than in the centre. This
temperature difference is between 5 and 10 K. The pocket with the higher temperature will
start reacting, will further increase in temperature and become buoyant, but will then
subsequently mix with cooler parts and the hydrogen peroxide produced will be diluted and/or
decomposed. This could therefore exhaust the necessary build-up of active peroxide to trigger
off the final runaway and it tends to slow the oxidation process. The open nature of the test
set-up in glass enhances the dilution. The 200 ml closed steel vessel experiments follow in the
low temperature region the glass vessel results quite precisely. On the contrary at
temperatures just beyond the NTC these tests cover the simulations and the larger 500 ml
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 29 (59)
glass test results better than the 200 ml semi-open glass ones. The simulations in Figures 22A
and B point in the same direction but are less pronounced than in actual AIT tests. At 760 K
the highest temperature reached is still near the top of the glass vessel. At even higher
temperature the induction become so short that the highest temperature in the explosion is
definitely the centre.
A more accurate approach of induction time in a semi-open set-up is not possible without
taking into account the temperature and concentration gradients. This is beyond reach of the
computational tools for the time being.
In conclusion the following can be stated:
• Determination of the ignition delay time shall be performed in a closed vessel and not
an open one, with sufficient large diameter or at sufficient high pressure to avoid wall
effects.
• Determination of the ignition temperature shall be performed at a fixed ignition delay
time.
4.3 The effect of mixture composition
Calculations of IDT have been made for three n-butane-air mixture compositions. As
compositions have been chosen the stoichiometric one (3.1 mol%), rich near the upper
explosion limit (9.5 mol%) with which all AIT tests with n-butane have been done, and very
rich, a factor three above the upper explosion limit (30 mol%). This reflects too the range of
compositions covered experimentally with a number of other fuels such as methane and
ethylene (Deliverable No. 33 Addendum B [20]) and propane (Deliverable No. 13 [27]). In
Table 5 the results have been summarised for a closed vessel of 200 ml (constant volume) at
an initial pressure of 1 bara with a heat transfer coefficient of 1.5 W/(m2K) at three initial
temperatures (Ti). For constant pressure (semi-open vessel) the IDT values are slightly larger
(2-10%), except for the stoichiometric mixture at low temperature (50% larger).
Table 5: Calculation results of ignition delay time and final temperature for various
compositions at constant volume (200 ml) at 1 bara initial pressure.
Molar fractions of mixture
n-C4H10
O2
N2
0.031
0.204
0.765
0.095
0.190
0.715
0.300
0.147
0.553
Ti = 575 K
IDT, s
Tf, K
5.6
2638
4.7
1794
3.6
1042
Ti = 650 K
IDT, s
Tf, K
0.4
2661
0.3
1900
0.2
1073
Ti = 800 K
IDT, s
Tf, K
4.2
2688
1.95
1982
0.9
1128
The influence of composition on IDT is not very strong but increases with temperature. In
Figure 24 calculated temperature-time profiles are shown at an initial temperature of 800 K.
So, in fact one does not notice from the qualitative shape of the curves a passing of the upper
explosion limit line. The most energetic mixture (stoichiometric) produces the longest
induction time. With increase in fuel content IDT becomes shorter. The final effect depends
even more on composition. The final temperature reached, diminishes with increasing
hydrocarbon content as a result of gradually less complete combustion (and heat release). The
profiles of temperature-time at the lowest temperature of 575 K are still from low-temperature
oxidation with formation of organic peroxides, then “jump-wise” to reaching maximum
temperature followed by a slow decay due to heat loss. At 650 and 800 K for the fuel richest
composition the profile becomes a more smooth self-heating process as shown in Figure 24.
This pattern appears even more pronounced in experiments as e.g. shown in Deliverable No.
13 [27] for propane. In the experiments by natural convection temperature gradients form and
as a result the temperature increase when reaction is slow, is more gradual, while in the very
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 30 (59)
rich mixtures due to entrainment of air into the flask partial explosions of pockets of mixture
in the explosion range can occur.
3000
3.1% C4H10-air
9.5% C4H10-air
30.0% C4H10-air
Temperature, K
2500
2000
1500
1000
500
0
1
2
3
4
5
Time, s
Fig.24: Temperature-time profiles of self-heating process of various n-butane mixtures with
air calculated for a closed 200 ml vessel at an initial temperature of 800 K and 1 bara initial
pressure.
4.4 The small chain hydrocarbons C1-C3
n-Butane as a fuel is representative for the higher alkanes. In the later stages of the
SAFEKINEX project also AIT tests with methane, ethylene and finally with propane have
been carried out. Also the oxidation kinetics of these fuels has been modeled. A detailed
report on the development of the C1 – C3 kinetic model is given in Deliverable No. 26 [18].
This includes an analysis of the available knowledge on C1 – C3 kinetics as well as an
extensive description of the course that was taken in the development of the C1 – C3 kinetic
model. The most important criteria discussed in Deliverable No. 26 are the number and type
of species, the reactions and reaction rate constants, and the thermodynamic and transport
data. The validation of the model is described in Deliverable No. 34 [19].
The new C1 – C3 model, known as Konnov Safekinex, is suited for describing the pyrolysis,
slow oxidation and ignition reactions as occur in the low temperature problems investigated in
the project. It consists of 360 species and 2701 reactions and it also includes hydrogen
combustion. It is designed to be applicable at temperatures between 550 and 1600 K and
pressures up to 50 bara. A number of results with methane and ethylene in comparison with
experiments taken from Deliverable No. 33 Addendum B [20] are shown in the Figures 25A
and B, 26A and B and 27A and B.
The experimental results on the surface look similar to those of n-butane with an NTC-like
transition at a certain temperature, although the temperature level of the apparent
discontinuity in IDT as a function of temperature is 200 K higher for methane and 50 K for
ethylene. However there is no occurrence of cool flame as with n-butane. Slow oxidation is
the more common process at low temperature. At temperatures above the discontinuity, the
conversion peak becomes sharply steeper. In case of ethylene, the slow oxidation
phenomenon starts immediately after injection and does not yield a measurable IDT. Above
the discontinuity with the two compositions 14 mol% methane and 19 mol% ethylene in air,
both just within the explosion range, explosion takes place with audible and visual
consequences. For ethylene there was one point of the BAM 200 ml steel vessel self-ignition
trials, which could serve for comparison and which shows a good agreement between both
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 31 (59)
types of tests. At higher concentrations slow oxidation prevails unless initial temperature
becomes higher and explosion-like phenomena occur. This will be thermal explosion of the
reacting mixture with probably flame in part of the volume due to air entrainment as shown
also clearly in the later tests with propane (Fig.29A to H).
25
70
20
60
14% CH4-air,
experiments
Calculated
40
19% 200 ml closed
steel BAM, 1.3 bara
15
IDT (s)
IDT (s)
50
19% C2H4-air, AIT
experim ents
Calculated
10
30
20
5
10
0
0
700
800
900
1000
1100
600
1200
650
800
Fig. 25B. Auto-ignition experimental results
in the 500 ml glass and 200 ml steel vessel
with 19% ethylene-air in comparison with
simulation applying the Konnov Safekinex
C1-C3 model.
860
1000
850
980
840
960
Temperature [K]
Temperature [K]
Fig. 25A. Auto-ignition experimental results in
the 500 ml glass vessel with 14 mol% methane
in air in comparison with simulation applying
the Konnov Safekinex C1-C3 model.
M53 T4
M53 T5
820
750
Temperature (K)
Temperature (K)
830
700
810
M33 T4
M33 T5
940
920
900
880
800
860
790
0
50
100
150
0
200
50
100
150
200
Time [s]
Time [s]
Fig. 26A. Temperature-time history with 14% Fig. 26B. Temperature-time history with
methane in air at 837 K initial temperature 14% methane in air at 917 K initial tempelevel, showing slow oxidation, IDT 18.7 s
rature level, showing explosion after 12.2 s
820
950
E16 T5
780
Temperature [K]
Temperature [K]
800
E16 T4
760
740
720
900
E25 T5
850
E25 T4
800
750
700
700
0
50
100
Time [s]
150
200
0
50
100
150
200
Time [s]
Fig. 27A. Temperature-time history with 19% Fig. 27B. Temperature-time history with
ethylene in air at 744 K initial temperature 19% ethylene in air at 755 K initial tempelevel, showing slow oxidation
rature level, showing explosion after 17.4 s
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 32 (59)
The calculations with the Konnov Safekinex mechanism (360 species, 2701 reactions) take
into account many details of the oxidation mechanism, but take relatively long to perform.
The oxidation processes typically develop hydrogen peroxide first, which subsequently
decomposes. So, there is no question of low but rather of intermediate temperature oxidation.
As appears from Figure 25A in case of methane just as with n-butane calculated induction
times are systematically shorter than the ones experimentally observed. Caron et al. [28]
studied the system methane-air at elevated initial pressures up to 55 bara, initial temperatures
of 620 to 720 K and methane concentrations up to 85 mol% in a 8 l autoclave. They define a
reaction producing a significant temperature increase but lower than 200 oC accompanied by a
pressure increase lower than 2 as a ‘cool flame’. If the temperature increase is larger than 200
o
C they define the reaction as ‘auto-ignition’. At lower pressure and higher fuel concentration
rather ‘cool flames’ are found than ‘auto-ignitions’. Whether it is really justified to make this
sharp distinction and to call here the weaker temperature and pressure rises cool flame is
questionable. As has been explained before for obtaining cool flame organic peroxide
chemistry is active and the nature of the cool flame phenomenon occurring in case of e.g. nbutane is flash-like. It is more radical explosion than thermal. Below a temperature of 600 K
n-butane readily produces cool flame. At that temperature methane does not show much sign
of reaction, but at a temperature when it starts to react simulation shows hydrogen peroxide is
formed.
Also in case of ethylene as a fuel hydrogen peroxide dominates as reactant typical for
intermediate temperature oxidation. The thermal nature of acceleration mechanism becomes
stronger. Depending on conditions by self-heating temperature increases, hydrogen peroxide
concentration builds up further and self reinforcing radical oxidation reactions follow, till
finally almost jump-wise a maximum temperature is reached and all hydrogen peroxide is
consumed. So, there seems rather a gradual change in final effect than a discontinuity. It also
may be a misnomer to use in all cases the term ignition delay time, since it is often a merely
an induction time to a thermal climax event, which is surely not the initiation of a propagating
flame since it occurs with fuel concentrations far above the upper explosion limit.
The last series of AIT- experiments performed have been with propane. In Deliverable No. 13
[27] the results have been reported in more detail than of previous tested fuels, since with
increasing experience details gained significance. One series has been carried out with 12
mol% propane in air and another with 40 mol%. The first is just above the upper explosion
limit and the latter percentage was inspired by a series of recently reported experiments by
Norman et al. [21]. A summary of results and a selection of single test results are shown in
Figures 28 and 29A to H.
In Figure 30 an overview is presented of the results of the four fuels investigated in the
SAFEKINEX project in the AIT test at comparable conditions.
In general it can be concluded that the phenomena experimentally observed with propane are
in between n-butane and methane. Simulation showed that at low temperature (600 K) a
significant intermediate product consists of organic peroxides such as propylhydroperoxide
(CH3)2CHOOH, while at the moment close to the final jump the hydrogen peroxide
concentration is a thousand times smaller than of propylhydroperoxide. At an initial
temperature of 700 K the picture has changed again towards hydrogen peroxide as the
dominant intermediate as has also been put forward by Griffiths et al. [17] and others.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 33 (59)
90
12% propane in air
40% propane in air
12% propane in air*
40% propane in air*
80
70
* IDT up to other phenomenon (multiple cool
flames, for example) begins after slow oxidation
60
IDT, s
50
40
30
20
10
0
600
650
700
750
800
Initial temperature, K
850
900
Fig. 28. Ignition delay time versus initial (ambient) temperature for 12% and 40% propane-air
mixtures at constant pressure of 1 bara in semi-open vessel of 500 ml quartz-glass.
Open dots – IDT to first temperature increase (slow oxidation phenomenon or explosion);
Closed dots – IDT to second rapid temperature increase (multiple cool flame phenomenon on
underlying slow oxidation).
390
420
380
400
370
Temperature, oC
Temperature, oC
380
360
360
350
340
Series1
Series2
Series3
340
330
T1
T4
T5
320
300
320
0
12% 370C #2
50
100
150
200
0
40% 370C #3
250
Time, s
20
40
60
Time, s
100
120
b)
a)
450
435
440
430
430
Temperature, C
440
Temperature, C
425
o
o
80
420
410
420
400
415
T1
T4
T5
410
T1
T4
T5
390
380
405
370
400
0
12% 430C #2
50
100
150
Time, s
c)
200
250
0
40% 430C #3
50
100
150
Time, s
d)
200
250
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
800
page 34 (59)
650
630
750
610
700
o
Temperature, oC
Temperature, C
590
570
650
550
600
530
T1
T4
T5
550
500
T1
T4
T5
510
490
470
450
450
0
10
20
30
12% 500C #1
40
Time, s
50
60
70
0
80
10
20
40% 500C #2
30
Time, s
40
50
60
F)
E)
700
830
680
780
660
o
o
Temperature, C
Temperature, C
880
640
730
620
680
T1
T4
T5
630
580
T1
T4
T5
600
580
560
530
0
12% 610C #3
20
40
60
80
Time, s
G)
100
120
140
0
40% 610C #1
10
20
30
Time, s
40
50
60
H)
Figures 29A to H. Sample individual AIT test results with propane at various temperature
levels, A and B 642 K, C and D 696 K, E and F 768 K and G and H 882 K; at two mixture
compositions, 12.0 mol% row left (A, C, E and G), and 40.0 mol% row at right (B, D, F, and
H); 500 ml quartz glass vessel, 1 bara. A and B are classified as multiple cool flame
superposed on slow oxidation, C and D as slow oxidation, E and F as explosion with highest
temperature near the top of the flask, and G and H as explosion with highest temperature in
the centre. In case of G a second explosion takes place 50 seconds after injection due to
entrainment of fresh air.
Simulations of propane oxidation were explored also at the conditions of some of the lowtemperature oxidation tests under elevated pressure published by Norman et al. [21]. Their
measured induction times range from 200 to 1400 seconds at temperatures between 250 and
300 oC (523 – 573 K) and pressures up till 16 bara in a 8 l vessel. Their results are shown for
comparison in Figure 31. The same discrepancy occurs, as we have seen before with n-butane
and methane at low temperatures. The calculated IDT for a volume of 8 litres and a heat
transfer coefficient of 5 W/(m2.K) 3 bara pressure and 550 K (275 oC) is 13.5 seconds
whereas the measured value is close to 800 s. At 6 bara the calculated value is 9.1 s versus the
measured one of 100 s. At higher pressures the time necessary for a computation increases
rapidly and the tolerances on the iteration have to be put tighter. As has been shown by
Fairweather et al [22], some of the discrepancy for propane combustion may be attributed to
inaccurate assignments of thermochemical parameters to some of the more complex
intermediate species.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 35 (59)
90
80
methane 14%
ethene 19%
propane 12%
n-butane 9.5%
Induction time, s
70
60
50
40
30
20
10
0
550
600
650
700
750
800
850
900
950
1000
Temperature, K
Figure 30. Overview of experimental results of the determination of induction time (IDT) as a
function of initial temperature (oven) in Auto-ignition test (AIT) set-up in a semi-open
(atmospheric) 500 ml quartz glass vessel for the four hydrocarbon fuels investigated at
comparable concentration in air with respect to the upper explosion limit.
Figure 31. Ignition delay times measured by Norman et al. [21] with 40 mol% propane in air
in a 8 l vessel. Like we have seen for n-butane at higher pressure ignition can take place at
lower temperature but delays become much longer. The dot at 3 bara near the abscissa
represents the calculation result at that condition with the full Konnov Safekinex mechanism.
4.5 Simulations with strongly reduced mechanisms
In Deliverable No. 38 [29] the Leeds group has proposed reduced or skeleton mechanisms for
hydrocarbon oxidation kinetics. In two reduction steps a 1st skeleton mechanism and a 2nd one
was derived. The usefulness and reliability of the mechanisms was demonstrated by
comparing e.g. experimental values of ignition temperatures with ones calculated by the full,
the 1st and the 2nd skeleton mechanisms. In the following for n-butane and propane the 2nd
reduced skeleton mechanism was used to calculate ignition delay times. Results in
comparison with the full mechanisms are given for n-butane and propane in Figures 32 and
33A and B respectively. Konnov Safekinex was applied as the full mechanism for propane.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 36 (59)
The conclusion so far is that the skeleton mechanisms behave quite well. There is a systematic
deviation over the whole range of calculated values to a lower value produced by the 2nd
skeleton mechanism. The gain in computation time can be quite large also with the
CHEMKIN software. For example in case of propane at the lowest temperature of 525 K the
computation time with the full mechanism was 37 minutes and 23 seconds, whereas with the
2nd skeleton it was 6 seconds!
1000
C4H10 p=1, full mech
p=1, skeleton2
p=10, full mech
p=10, skeleton2
100
IDT, s
10
1
0,1
0,01
0,001
500
600
700
800
900
1000
1100
Temperature, K
Figure 32: Calculated ignition delay times (logarithmic scale) for 9.5% n-butane in air at 1
bara constant pressure in a 200 ml vessel, 1.5 W/(m2K) heat transfer coefficient, and at 10
bara in a closed 200 ml vessel, both with the full mechanism and the 2nd skeleton one.
60
50
IDT, s
40
C3H8 p=3, full
p=3, skel2
30
20
10
0
520
530
540
550
560
570
580
590
600
610
Temperature, K
Figure 33A: Calculated ignition delay times for 40.0% propane in air at 3 bara constant
pressure in a 8 l vessel, 5 W/(m2K) heat transfer coefficient with the full Konnov Safekinex
mechanism in comparison with the 2nd skeleton one.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 37 (59)
90
12% C3H8-air exp.
80
12% C3H8-air exp, 2nd peak
12% C3H8-air calc. full
70
12% C3H8-air calc. skel2
60
IDT, s
50
40
30
20
10
0
500
550
600
650
700
750
Initial temperature, K
800
850
900
Figure 33B: Calculated values of ignition delay time as a function of temperature of mixtures
of 12 mol% propane in air at atmospheric pressure in a 500 ml vessel (heat transfer
coefficient 1.5 W/(m2K)) on the basis of the full Konnov Safekinex mechanism – lower line,
and the skeleton 2 mechanism –upper line, in comparison with the experimental values.
However does exception confirm also here the rule? The odd one appeared to be propane at
atmospheric pressure as shown in Figure 33B together with the experimental data already
shown in Figure 28. No good explanation can be given. The detailed calculation results do not
show a systematic deviation. The hydrogen peroxide concentration slowly builds up toward
the end of the induction period and is then completely exhausted in the final temperature
jump. At lower temperatures than shown in the graph (550 K with full; 625 K with skeleton 2)
calculation did not produce a peak.
4.6 Alternative kinetic mechanisms and simulation software
An alternative mechanism for n-butane suited for low temperature oxidation simulation has
been developed by Strelkova [23]. The mechanism was developed on the software
infrastructure of Chemical Workbench (see Appendix II). It consists of 34 species and 48
reactions and is on the same chemical basis as the EXGAS derived model. An example
calculation result is shown in Fig. 34. Also here at relatively low temperature the calculated
IDT falls short of the measured value. Although in theory the kinetics as stored in the
Chemical Work Bench data base CARAT can be converted to the CHEMKIN format and the
other way around. In practice when importing other mechanisms, even in the CHEMKIN
format, there appear problems of trivial nature resulting in solutions which not converge
which are rather time consuming to resolve. Manual interaction and correction is needed. The
robustness of the software is not ideal yet. The Help offered is not always clear and contains
cryptic expressions.
With COSILAB little experience was obtained but also there importation of mechanisms
generated problems such as not checking for duplicates. CANTERA could not be
implemented and run in the time available.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 38 (59)
50
Experiments closed 200ml vessel
45
Skeletal mechanism (CWB) (V=const) (Expl)
40
Skeletal mechanism (CWB) (V=const) (CF)
35
IDT, s
30
25
20
15
10
5
0
550
600
650
700
750
800
850
900
Temperature, K
Figure 34. 200 ml closed steel vessel experiments in comparison with the outcomes of the
calculation of the 9.5 mol% n-butane in air mixture oxidation with the Strelkova skeletal
mechanism [23] without heat loss on the Chemical Workbench software package (see
Appendix II).
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
5
page 39 (59)
Characterisation of the conditions of natural convection
enabling ignition6
There exist numerous in-direct experimental observations (prior and during the SAFEKINEX
project) indicating that an evolution of gaseous auto-ignition with its specific features inside a
vessel (sphere, cylinder or else) is governed by not only a balance between the chemical heat
release and thermal conductivity (as it was documented in the classical theory of FrankKamenetskii [30] for thermal explosion), but also by gravity and convection effects. To this
can be added that compressibility and viscosity of the gas mixtures can have an impact too.
Due to the complexities in performing direct experimental studies of the mentioned factors,
especially with a high spatial and temporal resolution, a role of theoretical analysis and
numerical simulation shall not be underestimated.
Systematic reactive Computational Fluid Dynamics studies of gaseous thermal auto-ignition
inside of a closed sphere were initiated and described in references [24, 31, 32] with taking
explicitly into account gravity, convection, compressibility and viscosity effects.
5.1 Basic gas-dynamic flow patterns
In [31] it was revealed that two basic gas-dynamic flow patterns and associated thermal heat
transfer mechanisms can be delineated. Numerical simulations were performed for 2dimensional geometry of the evolution of the gas-dynamic fields during auto-ignition of the
initially quiescent (velocity vector Vi = 0 ), premixed exothermic reactive gas (initial
~
temperature T , initial density ρ~ , initial volume fraction of limiting reagent (chemical
0
0
reaction extent - 0) inside of a closed spherical vessel (radius Rɶ 0 ) with a given temperature of
~ ~
wall ( Ta = T0 ). Overall reaction rate and heat generation can be represented by a zero-order
Arrhenius type of equation (one-step kinetics). The following dimensionless parameters have
been introduced: effective Froude (inverse Richardson or Rayleigh7) number ~2
~
~3
2
Fr = V0 ( g~ ⋅ R0 ) = ν~0 ( g~ ⋅ R0 ) with gɶ gravitational acceleration vector, Prandtl number ~ ~ ~
Pr = ν~0 χ~ 0 , Arrhenius number - Ar = ( R ⋅ T0 ) E a with Rɶ gas constant and Eɶ a activation
~ ~
energy. Further, use was made of the Frank-Kamenetskii number - FK = tT tch , with
~ ~
~2 ~
~
~
~
t = ( ρ~ ⋅ c~ ⋅ R λ ) characteristic thermal time, and ~
t = ( ρ~ ⋅ c~ ⋅ T ⋅ Ar ) (k (T ) ⋅ ϕ (η ) ⋅ ∆H )
T
0
V
0
0
ch
V
0
0
0
r
- characteristic chemical time, in which cɶV is specific heat capacity at constant volume, λɶ is
*
m
heat conductivity, kɶ0 (Tɶ0 ) is rate constant at initial temperature, ϕ (c ) = (1 − ci ) with ci is
~
concentration and m chemical reaction order and ∆H r chemical reaction enthalpy. Next is
~ ~
~
~
Todes number - Td = ( ρ~0 ⋅ c~V ⋅ T0 ⋅ Ar ) ( k (T0 ) ⋅ ϕ (c*) ⋅ ∆H r ) , dimensionless temperature
~ ~
~
T * = (T − T0 ) (T0 ⋅ Ar ) and finally the effective Strouhal (Damköhler) number
~
~ ~
~2
~
Sh = R0 ((ν~ R0 ) ⋅ tch ) = R0 (ν~ ⋅ tch ) = FK (γ ⋅ Pr) , with νɶ is kinematic viscosity, γ ratio of
specific heats at constant pressure and volume and Pr is Prandtl number.
6
The following section has been part of a study in the framework of the Russian-Netherlands scientific
cooperation, project NWO No. 046.016.012 2004-2006 cosponsored by Russian Foundation for Basic Research,
projects 05-08-50115a and 05-08-33411a. It is work mainly carried out by Prof. A.V. Panasenko of
TSNIIMASH under guidance of Professors I.A. Krillov and A.I. Lobanov.
7
Strictly speaking, a definition of the Rayleigh number, used at page 6 of this report (see formula (2)), is valid
for stationary problems only, where temperature difference between two given specific spatial points is constant
during natural convection. Use of the effective Froude number and Frank-Kamentskii number is more relevant
for natural convection effect studies of a substantially non-stationary process of thermal auto-ignition.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
a)
page 40 (59)
b)
Figure 35. Snap-shots ( t = 1 ) of the convective stream-lines for thermal auto-ignition with
conductive-dominated heat removal ( Fr = 0.6 , Sh −1 = 0.065 , Td = 0.06 , Ar = 0.05).
a) – FK=5, b) – FK=30
a)
b)
Figure 36. Snap-shot ( t = 1 ) of the convective stream-lines for thermal auto-ignition with
convective-dominated heat removal ( Fr = 0.0006 , Sh −1 = 0.065 , Td = 0.06 , Ar = 0.05).
a) – FK=5, b) – FK=11.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 41 (59)
Along with a validation against the well known limit thermal explosion limit (reaction heat
release- thermal conductivity balance as described in the framework of the Frank-Kamenetskii
theory [30]; no gravitation field), two basic natural convection flow patterns, which are
evolving during auto-ignition, were documented: a radial streamline pattern and a toroidal
convection one. For large values of the effective Froude numbers, Fr (viscosity effects
dominate over the gravitational ones) the chemical reaction heat release induces a radial
convective flow from centre to the wall of the spherical vessel. The stream-lines (see Figure
35) are practically radial within the inner part of the vessel. Temperature iso-surfaces preserve
a spherical symmetry. The location of the centres of the temperature iso-surfaces practically
coincides with the vessel centre and does not depend on the value of the Frank-Kamenetskii
number. Convective contribution to overall heat removal is small.
Under super-critical conditions with the effective Froude number value below a certain
threshold depending on the Frank-Kamenetskii number, buoyancy disturbs essentially both
the stream-line and temperature fields. Here, the main feature of the stream-line structure is
the onset of a large toroidal vortex (see Figure 36). During the auto-ignition process, this
vortex is forming in the bottom part of the vessel and floating to the top. Intensity of the
toroidal convective flow and its evolution depends on the Frank-Kamenetskii number. The
higher the initial Frank-Kamenetskii number, the quicker the center of the temperature isosphere is moving away from the vessel center. Appearance of the well-defined toroidal
convection within the vessel core results in the following changes: 1) shift of the dominating
overall heat removal mechanism – from conduction-driven to convection-driven; 2) changes
of the critical conditions for thermal explosion – in comparison with the classical thermal
explosion theory.
5.2 Convection Effect on Induction Delay Time
From Figure 37 it can be seen that a well developed convective flow reduces the ignition
delay time, computed for the time history of the maximum temperature. The maximum
temperature (over the vessel volume) was taken as a characteristic temperature suitable for
comparison of thermal behaviour for the different initial conditions. However, in the real
experiments, it is hardly possible to track accurately (in time and space) a location of the point
with maximum temperature. In order to obtain spatially-averaged information, which can be
obtained in experiments, a dependence upon time was computed of the Nusselt number
averaged over the vessel surface Nu a . The following definition was used:
1 dT
Nu = ∫∫
ds
a S dn
S
heгe n is external normal to the spherical vessel surface, and S – the surface area.
In Figure 38, the time profiles of the averaged Nusselt numbers are shown. In both cases
( FK = 7 and 11), time period to attain the maximum value of thermal flux from gas to vessel
walls is shorter for situations, where well-defined convection takes place ( Fr =0.0006).
Interpretation of the observed interplay of the convection and auto-ignition is the following.
For small values of the Froude number, even a small chemical heat release during the
induction period results in substantial convective flow, ascending at symmetry axis. This
enhances heat transfer from the ‘hot’ central region to the top inner part of the vessel in
comparison with pure conduction, resulting in an overall larger reaction heat release and a
faster local thermal runaway. Convection from the hottest central part plays the role of an
“igniter” for the upper points, located near the top of the spherical vessel.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 42 (59)
Figure 37. Characteristic time history of the maximum temperature Tmax inside of a spherical
vessel for situations with thermal explosion taking place and a well-developed toroidal
convection present (FK = 6)
Figure 38. Convective effect on induction delay time: Nusselt number averaged (over sphere
volume) versus time.
5.3 Critical conditions for thermal explosion in a compressible gas
The summary of the parametric computations is shown in Figure 39 where the boundaries for
the critical phenomena (natural toroidal convection, thermal explosion), and their interplay is
visualized in a two-dimensional phase plane ( FK / FK 0 , lg(1 Fr ) , where FK 0 is the critical
value8 of the Frank-Kamenetskii number as derived in the standard theory of thermal
explosion [30]). Here a solid, red line represents a thermal bifurcation. Any phase point,
located below the solid red line represents the conditions, which do not result in a thermal
explosion. Any phase point, located above the solid, red line, represents the conditions which
induce the thermal explosion. Accordingly, a dashed, black line represents a gas-dynamic
bifurcation boundary (above – convection is absent, below – convection exists). The
mentioned borders break the phase plane into three regions: region I – no explosion, no welldeveloped toroidal convection, only a weak radial convection is present; region II – thermal
8
This value is defined as the FK -number at which the rate of the (dimensionless) temperature increase is
highest.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 43 (59)
explosion, well-developed toroidal convection; region III – thermal explosion, no welldeveloped toroidal convection, only a weak
3,5
FK/FKo
3
II
2,5
III
explosion
boundary
(above Yes/below
- No)
toroidal
convection
boundary
(above No/below Yes)
2
I
1,5
1
0
1
2
3
Lg(1/Fr)
Figure 39. Critical phenomena during thermal auto-ignition in compressible, viscous,
thermally conductive gas. Region I – no explosion, toroidal convection. Region II – explosion,
toroidal convection. Region III – explosion, no toroidal convection. FK 0 - Critical value of
the Frank-Kamenetskii number according to classical theory of thermal explosion
radial convection is present. For hazard analysis in case of engineering application, the
boundary between the explosion and non-explosion regimes at the phase surface (FK, Fr) is
approximated by the following formula:
FK
2.8 ⋅ 10 −4
=1+
FK 0
Fr (1 − 129 ⋅ Fr )
the boundary between the well-defined (toroidal) convective and non-convective regimes can
be approximated by the following formula:
FK
1.3 ⋅ 10 −3
= 1+
FK 0
Fr (1 − 95 ⋅ Fr )
The main goals of the reported study have been the following: 1) to extend the FrankKamenetskii’s thermal explosion framework in order to take into account explicitly the effects
of gravity, convection, and viscosity for compressible reactive gaseous systems; 2) to define
quantitatively the boundaries between the basic patterns of the thermal and gas-dynamic
behaviour of the system under consideration in the phase space of key dimensionless
parameters. This was realised by solving the full Navier-Stokes flow equations by rigidly nondimensionalising the problem and solving the resulting equations by two-dimensional
numerical simulations in a very fine mesh with a powerful computer by means of
parallelization techniques; 3) to obtain engineering correlations for experiment planning and
engineering applications, via fitting of the mentioned computed boundaries by simple
analytical formulae.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
6
page 44 (59)
Conclusions
Summarising, if an estimate has to be given of the possibility of auto-ignition and the ignition
delay time in a process flow at a given temperature and pressure on the basis of a kinetics
model and a model of heat (and mass) transfer several problems have to be solved:
a. Within a certain residence time temperature, pressure and mixture composition have to
be known. If conditions are such that low temperature oxidation takes place (n-butane,
T < 700 K) heat loss seems not to be critical. Ignition delay is determined by the
occurrence of cool flame caused through the progressively accelerated decomposition
of accumulating organic peroxides. The maximum time to consider depends on
pressure and temperature level. At low pressure it is no more than half a minute; at
higher pressure fuels such as n-butane and propane can still self-ignite at even lower
temperatures after 20 or more minutes. Also at a given temperature the induction time
shortens considerably with an increase of pressure.
b. Present detailed kinetic models appear to behave too reactive at low temperature. They
strongly underrate the measured induction times. Also they produce hot
flame/explosion where tests show only cool flame or slow oxidation. The closest one
coming in simulation of tests, is by adding to the model organic peroxide destruction
reactions at low temperature. A simple overall approach, not taking into account this
mechanism, is fitting the formula for the adiabatic induction period. Such a formula
calculates the induction time for temperatures below those for the NTC region.
c. At higher temperature (n-butane > 700 K) and low pressure (atmospheric or lower)
HO2· radicals and hydrogen peroxide decomposing at the wall of the vessel seem to
influence the result rather strongly at atmospheric pressure and below and explain the
increase of duration of induction for small vessels (5-10 cm diameter) as used in
atmospheric AIT tests.
d. For the experimental set-ups (0.5 l and 20 l vessels) heat losses have been measured
and calculated. When expressed in a heat transfer coefficient and a temperature
difference between vessel centre and wall, natural convection changes the heat transfer
coefficient in time and temperature difference. In simulation no temperature gradient
can be handled yet by the batch reactor models (other than the simplest onedimensional, pure conduction case, as discussed in Deliverable No. 38). In such case
heat loss has a much less drastic effect on the ignition delay time than expected.
However it is not certain how heat losses interfere when a faster reacting, warmer
pocket of gas loses heat and active species to a surrounding gas of lower temperature.
e. The aim of auto-ignition tests is to determine ignition temperatures and ignition delay
times. It is common understanding that ignition is followed by flame propagation. In
many experiments however slow oxidation phenomena culminating in a final rapid
rise in temperature occur with various fuels e.g. methane, ethylene and propane far
outside the explosion range. This is confirmed by simulation. Kinetics simulation does
not justify sharp distinction between cool flame and explosion in case of fuels other
than n-butane and higher alkanes. A gradual shift of mechanism with temperature
takes place. Explosion limit concentration does not show up as a discontinuity or even
a steep change. Pressure increase varies with final temperature achieved. So, again an
upper explosion limit should be determined on the basis of ability of the mixture to
propagate flame.
f. Reduced kinetic models behave very well in predicting IDT in comparison with full
ones.
g. Several software packages are available now for simulating stirred batch reactor
processes. The most expensive one is at present still the best in performance.
Portability of kinetic models developed on a certain software infrastructure to other
packages is however still limited. Problems arise with stability and accuracy.
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
7
page 45 (59)
References9
1. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 5, Report on
experimentally determined self-ignition temperature and the ignition delay time, January
2005.
2. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 33, Report
on experiments needed for kinetic model development (high pressure), April 2006.
3. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 30, Report
on experiments needed for kinetic model development (CVB approach), April 2005.
4. Pekalski, A.A., 2004, Theoretical and experimental study on explosion safety of
hydrocarbons oxidation at elevated conditions, Dissertation, Delft University of
Technology, 18 November, Delft, The Netherlands.
5. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 29, Report
on intermediate species concentration during the ignition process, October 2005
6. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 33, Report
on experiments needed for kinetic model development (high pressure), April 2006,
Addendum A, Heat loss measurements explosion sphere, March 2006.
7. Carslaw H.S. and Jaeger J.C., Conduction of Heat in Solids, 2nd ed. Oxford Science
Publications, 2003, p. 233 ISBN 0 19853368 3 (PbK)
8. Barnard J.A., Harwood, B.A.; Physical Factors in the Study of the Spontaneous Ignition
of Hydrocarbons in Static Systems; Department of Chemical Engineering, University
College, London, England; Combustion and Fame 22, 35-42 (1974)
9. Ten Holder, G. P., “The influence of the overall heat transfer coefficient on combustion
phenomena of n-butane-air mixtures”, M.Sc Thesis, Delft University of Technology, May
2003.
10. Reaction design, San Diego CA., 2006, http://www.reactiondesign.com/
11. Kee R.J., Landram C.S. and Miles J.C., “Natural Convection of a Heat-Generating Fluid
Within Closed Vertical Cylinders and Spheres”, Journal of Heat Transfer February 1976,
p. 55- 61.
12. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 35,
Validated detailed kinetic model for C4 - C10 hydrocarbons, May 2005.
13. Griffiths J.F. et al., private communication about work performed in the SAFEKINEX
project framework, November 2006
14. Griffiths J.F. and Barnard J.A., Flame and Combustion, Chapman & Hall, 1995, ISBN 0
7514 0199 4.
15. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable Nos. 45-47,
Workshop Teaching Material, November 2006.
16. Frolov, S. M., Basevich, V. Ya., Smetanyuk, V. A., Belyaev, A. A., & Pasman, H. J,
2006, Oxidation and combustion of fuel-rich n-butane–oxygen mixture in a standard 20liter explosion vessel. European Conference on Computational Fluid Dynamics,
ECCOMAS CDF, P. Wesseling, E. Oñate, J. Périaux (Eds), Egmond, 5–8 September
2006, The Netherlands.
17. Griffiths, J.F., Hughes, K.J. and Porter, R., 2005, The role and rate of hydrogen peroxide
decomposition during hydrocarbon two-stage auto-ignition, Proc. Combust. Inst, 30 (1):
1083-1091.
18. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 26, Report
on ongoing progress of C1 - C3 detailed kinetic model development, April 2004.
9
All Project SAFEKINEX Deliverables can be found on www.safekinex.org
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 46 (59)
19. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 34,
Validated C1 - C3 kinetic oxidation model, October 2005.
20. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 33, Report
on experiments needed for kinetic model development (high pressure), April 2006,
Addendum B, Additional experiments on the self-ignition temperature and the ignition
delay time: ETHENE and METHANE, February 2006
21. Norman F., Van den Schoor, F., Verplaetsen H., “Auto-ignition and upper explosion limit
of rich propane-air mixtures at elevated pressures”, Journal of Hazardous Materials A137
(2006) 666-671.
22. Kevin J. Hughes, John F. Griffiths, Michael Fairweather and Alison S. Tomlin, Evaluation
of models for the low temperature combustion of alkanes, Phys. Chem. Chem. Phys.,
2006, 8, 3197 – 3210
23. Strelkova M.I., Kirillov I. A., Pasman H. J., Skeletal mechanism of n-butane oxidation,
submitted to Physico-chemical Kinetics in Gas-Dynamics (in Russian); Strelkova M.I.,
Safonov A., Sukhanov L.P., Kirillov I.A., Potapkin B.V., Pasman H.J., First principles
based estimation of the low temperature mechanism of n-butane oxidation, submitted to
the 3rd Imternational Symp. on Non-Equilibrium Processes, Combustion and
Atmospheric Phenomena, NEPCAP-2007, Dagomis, Russia 25-29 June, 2007
24. Kirillov I. A., Panasenko A V., Zaev I.A., Pasman H. J., Modeling of the Buoyancy Effects
on Thermal Auto-Ignition of the Compressible Gas, submitted to J. Haz. Mat., Feb 2007
25. Rogers, R.L., 1979, Studies of the Combustion of Decane, Dissertation The City
University, London; see also Cullis C.F., Hirschler M.M., and Rogers, R.L., 1982, The
Cool Flame Combustion of Decane, Proc. Roy. Soc. London A382, 429-440.
26. Griffiths J.F., and Barnard J.A., 1996, Flame and Combustion, 3rd edition, Blockie
Academic & Professional.
27. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 13, Report
on Additional Experiments, May 2007.
28. Caron M., Goethals M., De Smedt G., Berghmans J., Vliegen S., Van ’t Oost E., van den
Aarssen A., 1999, Pressure dependence of the auto-ignition temperature of methane/air
mixtures, Journal of Hazardous materials A65, 233-244.
29. Project SAFEKINEX, Contract No. EVG1-CT-2002-00072, Deliverable No. 38, Reduced
Kinetic Models for Different Classes of Problems, February 2007.
30. Frank-Kamenetskii D.A., Diffusion and Heat Transfer in Chemical Kinetics, (1967),
Nauka, pp. 352
31. Kirillov I.A. Panasenko A.V., Pasman H.J. On convective flow dynamics during selfignition of gas mixture in spherical vessel, Cosmonautics and Rocket Engineering, 2006,
v.3(44), pp.150-156 (in Russian)
32. Kirillov I.A. Panasenko A.V., Pasman H.J. Effects of thermal conductivity, thermal
convection and gravity on gas phase autoignition in a closed explosion sphere, poster at
the 31st Int. Symp. on Combustion, Heidelberg, Germany, August 6-11, 2006
SAFEKINEX - Deliverable 18 - Model, software for calculation of AIT and its validation
page 47 (59)
APPENDIX I
Appendix I. Excel sheet to calculate heat transfer coefficient and adiabatic induction time
Picture of the Excel-sheet used to calculate values of Rayleigh and Grashof number, to derive the heat transfer coefficient from the Grashof number
via a curve fitted to the graph produced by Kee et al. [11], and to calculate the induction time as if a thermal explosion under adiabatic conditions is
taking place, given values of reaction rate constant and activation energy.
For Excel sheet picture see next page
APPENDIX I
SAFEKINEX – Deliverable No. 18 - Model, software for calculation of AIT and its validation
page 48 (59)
Calculation of Rayleigh Number
Ra
= g β C p ρ 2 / λη
r 3 ∆T
Ra = g β r 3C p ρ 2 ∆T / λη
q = heat production, W/m3
1. Temperature to calculate the specific heat, viscosity and thermal conductivity of the pure species
Nu = h*(2r) / λ
2. Mixture composition to calculate the mixture properties
Input variables are in red, other parameter values in black and calculated output data in blue
yi
yi
Mix properties T [K] and p [bara]:
N2 (Nitrogen)
0,7900
0,7149
Molar mass
O2 (Oxygen)
0,2100
0,1900
density
M =Σ yiMi
T
ρ = (pM /RT)
C4H10 (n-Butane)
0,1050
0,0950
heat cap.
CpT=Σ yiCpi; Cv
H20 (Water)
0,0000
0,0000
Cp
T
T
mass;
Cv
570
3,16E-02
[J/mol·K]
4,39E+01
3,33E+01
[J/kg·K]
1389
1054
0,0000
0,0000
viscosity
η =Σ yiηi
[Pa·s]=[kg/ms]
2,76E-05
normalise!
1,1050
1,0000
conductivity
λ =Σ yiλi
[W·mk]
0,044
check
Specific Heat
T
1,3
q
Nu
300
11,28
[m-3·K-1]
8,66E+06
Pr
Gr,mod
h'
Vol. litre
0,50
0,86
6,27E+05
5,1
∆T [K]
Ra
0,1
log Ra
1,03E+02
2,01
0,67
CO (Carbon monoxide)
T
Ra/r3·∆
∆T
1
[kg/mol]
3
[kg/m ]
Nu–10
---->read from Fig. 2:
8,66E+06
p [Pa]
g [m/s2]
1,00E+05
9,81
Cp= A + B·T +C·T^2 + D·T^3 + E·T^4 [J/mol*K]
Tmin Tmax
A
B
C
D
E
γ
[J/mol·K]
[J/kg·K]
N2
300 1000
2,93E+00
1,49E-03
-5,68E-07
1,01E-10
-6,75E-15
1,40
30,00
1071,22
O2
300 1000
3,19E+00
1,57E-03
-6,91E-07
1,32E-10
-9,24E-15
1,40
32,31
1009,74
C4H10
300 1000
7,71E+00
2,78E-02
-9,62E-06
1,55E-09
-9,53E-14
1,20
172,08
2960,81
H20
300 1000
2,68E+00
3,10E-03
-9,31E-07
1,35E-10
-7,70E-15
1,20
34,65
1922,92
CO
300 1000
3,03E+00
1,44E-03
-5,63E-07
1,02E-10
-6,91E-15
1,40
30,62
1093,34
η (25C)
η (Tmin)
η (Tmax)
η = A + B·T + C·T^2 [micropoise]
Viscosity
Tmin Tmax
A
B
C
N2
150 1500
42,606
4,75E-01
-9,88E-05
175,52
111,67
O2
150 1500
44,224
5,62E-01
-1,13E-04
201,85
C4H10
150 1200
-4,946
2,90E-01
-6,97E-05
75,33
H20
280 1073
-36,826
4,29E-01
-1,62E-05
89,68
CO
68 1250
23,811
5,39E-01
-1,54E-04
170,95
[micropoise]
[Pa·s]
533,12
281,26
2,81E-05
126,04
633,08
327,85
3,28E-05
36,99
242,75
137,73
1,38E-05
82,07
404,97
202,44
2,02E-05
59,78
457,31
281,22
2,81E-05
λ = A + B·T + C·T^2 [W/m·K]
Thermal Conductivity
Tmin Tmax
λ (25C)
λ (Tmin)
λ (Tmax)
A
B
C
N2
78 1500
0,00309
7,59E-05
-1,10E-08
0,02475
0,00895
0,0922
0,04279165
O2
80 1500
0,00121
8,62E-05
-1,33E-08
0,02571
0,00802
0,10042
[W/m·K]
0,04598337
C4H10
225 675
-0,00182
1,94E-05
1,38E-07
0,01625
0,00954
0,07423
0,0541304
H20
275 1073
0,00053
4,71E-05
4,96E-08
0,01898
0,01723
0,10811
0,04347213
CO
70 1250
0,00158
8,25E-05
-1,91E-08
0,02448
0,00726
0,0749
0,04241185
Molar mass
Calculation of radius of sphere
M [kg/mol]
r^3
Volume
Radius
Area
[m]
[m^2]
π=
3,14159265
100
0,02801
[ml]
[cm^3]
[m^3]
O2
0,03200
100
23,87
2,39E-05
0,0288
1,042E-02
Fit of Nusselt vs. Grashof
C4H10
0,05812
200
47,75
4,77E-05
0,0363
1,654E-02
Gr
H20
0,01802
500
119,37
1,19E-04
0,0492
3,046E-02
CO
0,02801
20000
4774,65
4,77E-03
0,1684
3,563E-01
Adiabatic induction time :
t ad = {C /(–∆Q )}{RT i2/(Ek )}exp(E /RT i)
Log Gr
3,00E+04
C J/mol.K
E kcal/mol
4,39E+01
k 1/s
0 –∆Q J/kg
1,97E+05
2,95E+05
n in p n
36,5
3,30E+11
0,5
t ad s
25,2
Nu
4,47712125
0,03
1,00E+05
5
0,17
4,00E+05
5,60205999
0,9
1,00E+06
6
1,8
4,00E+06
6,60205999
3,5
1,00E+07
7
5
4,00E+07
p const = 0
otherwise 1
Nu-10 vs. mod. Gr
APPENDIX I
N2
7,60205999
9
1,00E+08
8
12
4,00E+08
8,60205999
19
1,00E+09
9
24
4,00E+09
9,60205999
34
1,00E+10
10
44
4,00E+10
10,60206
60
10
Nusselt -10
Fill in:
Gr,mod = q g β( 2 r) 5 ρ 2 /( λ η 2 )
1
0,1
y = 5E-05x6 - 0,0005x5 + 0,0024x4 + 0,077x3 - 0,7239x2 + 1,5994x
R2 = 0,9998
0,01
4
5
6
7
8
modified Grashof
9
10
11
SAFEKINEX - Deliverable 18 - Model, software for calculation of AIT and its validation
page 49 (59)
APPENDIX II
Appendix II. Brief descriptions of the four current software
packages for calculating ignition processes and laminar
flame.
CHEMKIN 4.0.2
Reaction Design® is the exclusive developer and distributor of CHEMKIN® [AA1], the de facto
standard for modeling of gas and surface-phase chemistry. As both a software developer and a
services provider, Reaction Design focuses on reactor and combustor design and improvement.
Engineers, chemists, and programmers have expertise that spans multi-scale engineering from
the molecule to the plant.
The collection of data is accumulated by Sandia National Laboratories over the period from 1980
to 1995. The data fits in this collection are based on a variety of sources, including JANAF
Tables, NASA, and computational chemistry calculations performed at Sandia and elsewhere.
This data set has been fixed and not updated in order to assure backwards compatibility and
consistency with published CHEMKIN results. The CHEMKIN data format is a minor
modification of that used by Gordon and McBride [AA2] for the Thermodynamic Database in
the NASA Chemical Equilibrium code. However, CHEMKIN allows a different midpoint
temperature for the fits to the properties of each chemical species. Additional extensions allowed
by CHEMKIN for multiple temperature ranges and for very large molecular clusters. The format
has become the de facto international standard for the description of reactions, thermodynamics,
and transport properties.
The CHEMKIN software enables the simulation of complex chemical reactions in order to
predict how chemistry will affect overall process or device. CHEMKIN software consists of a
suite of idealized reacting flow models that predict detailed chemical kinetics and reaction
behavior. These models are designed to provide a compact description of transport phenomena
and an unlimited description of chemistry details in a computationally efficient package.
CHEMKIN can address gas-phase and gas-surface chemical kinetics in a variety of reactor
models that can be used to represent the specific set of systems of interest.
CHEMKIN is a commercial package.
COSILAB 2.0.2
SoftPredict® in Ruhr-Universität Bochum [AA3] is a subdivision of ROTEXO GmbH & Co.
KG [AA4]. COSILAB is a general combustion simulation tool that can be used to simulate a
variety of laminar flames including, in some cases, radiating flames, droplets and sprays. Under
the COSILAB hood resides the RUN1DL laminar-flame and flamelet code. This code has been
developed since the early eighties, and it has been used by numerous research groups worldwide.
RUN1DL is a computer program for the numerical simulation of one-dimensional and "quasi
one-dimensional" laminar flames. Moreover it provides reactor tools for a variety of geometries,
including stirred reactors, plug flow reactors, calculation of ignition-delay times and many more.
COSILAB supports all popular data formats for chemical reaction mechanisms, thermodynamic
data and molecular transport data as well as CHEMKIN.
A variety of different popular models for chemistry are implemented, including detailed
mechanisms of elementary reactions, systematically reduced kinetic mechanisms, global onestep reaction models and the flame-sheet model for diffusion flames. Similarly, various popular
models of thermodynamics and molecular transport are implemented, ranging from detailed
SAFEKINEX - Deliverable 33 - Report on experiments needed for kinetic model development (high pressure)
page 50 (59)
molecular models for thermal conductivities, dynamic viscosities and diffusion coefficients to
simple constant-property models. The models implemented for chemistry, molecular transport
and thermodynamics can be overwritten by a user’s own models. The programming languages
Fortran, C or C++ can be used.
Parts of the source code can be purchased, e.g., code that defines the discretized governing
equations. Currently this is Fortran code. The user can modify, augment or eventually
completely rewrite these portions of the code and hence adapt it to his particular physical
problem at hand.
COSILAB is a commercial program.
CANTERA
CANTERA [AA5] by D. Goodwin (Stanford University) is a suite of object-oriented software
tools for problems involving chemical kinetics, thermodynamics, and/or transport processes. The
suite is designed to efficiently simulate problems with large elementary reaction mechanisms,
and includes tools to model stirred reactor and stagnation flows with surface chemistry, to
compute chemical equilibrium, and to generate reaction path diagrams automatically, among
many others. It can be used on all common programs, and interfaces are provided for MATLAB,
Python, C++, or Fortran.
CANTERA is designed with the dual objectives of ease of use and high performance. It consists
of a kernel written in C++ that provides the core numerical capabilities and is optimized for
efficiency, and user interface package that provide an intuitive, high level way of interacting
with the kernel. CANTERA is particularly useful for simulations with large, elementary reaction
mechanism. It places no limit on the number of species and reactions, uses efficient algorithms to
evaluate reaction rates of progress, and includes fully-implicit integrators and solves designed for
use with stiff system of equations.
The developer and project manager of CANTERA is David Goodwin. The first public release of
the package as CANTERA 1.1, was in 2001. This package is still under development, new
capabilities are still added. The input file is converted from CHEMKIN format input files to CTI
files. A CANTERA input file may contain more than one phase specification, or may contain
specifications of interfaces (surfaces). Several reaction mechanism files in this format are
included in the CANTERA distribution, including ones that model high-temperature air, a
hydrogen/oxygen reaction mechanism, and a few surface reaction mechanisms.
CANTERA is freely-available software.
Chemical Workbench (CWB)
Chemical Workbench is developed by “Kinetic Technology” (KINTECH) [AA6] which is a
company taking a leading place among Russian software developers in the field of modelling
physical and chemical processes.
Chemical Workbench is a tool with easy-to-use graphical user interface (GUI) which helps the
users to simulate, optimize, and design a wide range of thermodynamic and kinetic aspects of
chemical processes and reactors for important industrial, research, or educational applications.
Combustion and detonation waves, safety analysis, CVD, heterogeneous, and catalytic reactions
and processes are the main areas of interest. The GUI permits the user to build his simulation
model of the processes from universal reactor models by creating reactor chains containing
SAFEKINEX - Deliverable 33 - Report on experiments needed for kinetic model development (high pressure)
page 51 (59)
linked reactors objects. This option dramatically increases the program's capability to study
physical and chemical processes.
Chemical Workbench contains built-in, tightly integrated thermodynamic and kinetic databases.
The databases can be used in two modes: first, as a source of data during input and formation of
initial data and conditions for calculation, second, as an independent instrument for calculating
various thermodynamic functions of matter and analyzing the data contained in the database. The
following databases are available: The Molecular Properties Database, The Thermodynamic
Properties Database, The Processes Database, The Mechanism’s Database.
There are three ways for entering substance properties data to database: the user enters all
information by himself (manual entering); information is extracted automatically from the
Substances Database and converting CHEMKIN format input file to Database.
A structure of input of initial data to database allows to add supplementary new data, as well as
to adjust and delete information, what makes the application easily extendable with using Wizard
program which allows users themselves easily to add new models.
This package is a commercial product.
References:
A1. http://www.reactiondesign.com
A2. S. Gordon and B. J. McBride, Computer Program for Calculation of Complex Chemical
Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks and
Chapman-Jouguet Detonations, NASA Report SP-273, 1971.
A3. http://www.ruhr-uni-bochum.de
A4. http://www.softpredict.com
A5. http://www.cantera.org
A6. http://www.kintech.ru
SAFEKINEX - Deliverable 18 - Model, software for calculation of AIT and its validation
page 52 (59)
SAFEKINEX - Deliverable 18 - Model, software for calculation of AIT and its validation
page 53 (59)
APPENDIX IV
Appendix III. Brief characterization of FLUENT CFD software
CFD stands for Computational Fluid Dynamics. It is technology that enables to study the
dynamics of fluids in flow. Using CFD, one can build a computational model that represents a
system or device under investigation. Then one applies the fluid flow physics and chemistry to
this virtual prototype, and the software will output a prediction of the fluid dynamics and related
physical phenomena. Therefore, CFD is a sophisticated computationally-based design and
analysis technique. CFD software gives the power to simulate flows of gases and liquids, heat
and mass transfer, moving bodies, multiphase physics, chemical reaction, fluid-structure
interaction and acoustics through computer modeling. Using CFD software, one can build a
'virtual prototype' of the system or device that wished to analyze and then apply real-world
physics and chemistry to the model, and the software will provide images and data, which
predict the performance of that design.
At the core of any CFD calculation is a computational grid, used to divide the solution domain
into number of elements where the problem variables are computed and stored. In FLUENT,
unstructured grid technology is used, which means that the grid can consist of elements in a
variety of shapes: quadrilaterals and triangles for 2D simulations, and hexahedra, tetrahedra,
prisms, and pyramids for 3D simulations. These elements, created using automated controls in
GAMBIT, FLUENT’s companion preprocessor, form an interlocking network throughout the
volume where the fluid flow analysis takes place.
Fig. 1 Cell types.
FLUENT will solve the governing integral equations for the conservation of mass and
momentum, and (when appropriate) for energy and other scalars such as turbulence and chemical
species. In both cases a control-volume-based technique is used that consists of:
• Division of the domain into discrete control volumes using a computational grid.
• Integration of the governing equations on the individual control volumes to construct
algebraic equations for the discrete dependent variables (“unknowns”) such as velocities,
pressure, temperature, and conserved scalars.
• Linearization of the discretized equations and solution of the resultant linear equation
system to yield updated values of the dependent variables.
Discretization of the governing equations can be illustrated most easily by considering the
steady-state conservation equation for transport of a scalar quantity φ . This is demonstrated by
the following equation written in integral form for an arbitrary control volume V as follows:
∫ ρφυ ⋅ dA= ∫ Γφ ∇φ ⋅ dA + ∫V Sφ dV
where ρ - density, υ - velocity vector, A - surface vector, Γφ - diffusion coefficient for φ , ∇φ gradient of φ , Sφ - source of φ .
FLUENT's post processing tools can be used to generate meaningful graphics, animations and
reports that make it easy to convey CFD results. Shaded and transparent surfaces, pathlines,
vector plots, contour plots, custom field variable definition and scene construction are just some
SAFEKINEX - Deliverable 33 - Report on experiments needed for kinetic model development (high pressure)
page 54 (59)
of the post processing features that are available. Solution data can be exported to third party
graphics packages, or to CAE packages for additional analysis.
Reference
http://www.fluent.com/
SAFEKINEX - Deliverable 18 - Model, software for calculation of AIT and its validation
page 55 (59)
APPENDIX IV
Appendix IV. A Tentative Modeling Study of the Effect of
Wall Reactions on Oxidation Phenomena
P.A. GLAUDE*, F. BUDA, F. BATTIN-LECLERC
Département de Chimie-Physique des Réactions,
Nancy Université, CNRS, ENSIC,
1 rue Grandville, BP 20451, 54001 NANCY Cedex, France
Brief communication
Shortened running title :
EFFECT OF WALL REACTIONS ON OXIDATION PHENOMEMA
*
E-mail : [email protected] ; Tel.: 33 3 83 17 51 01 , Fax : 33 3 83 37 81 20
SAFEKINEX - Deliverable 33 - Report on experiments needed for kinetic model development (high pressure)
page 56 (59)
Summary
Simulations have been run to assess, when diffusion is neglected, the effect of tentative wall
reactions on autoignition delay times and on a pressure-temperature diagram of oxidation
phenomena in the case of n-butane. Two types of reactions depending of the type of wall coating
have been considered for HO2 radicals with estimated rate constants. Simulations show a clear
influence of these wall reactions on autoignition delay times, as well as on some ignition limits,
for pressures below 1 atm.
Keywords : wall effects, oxidation phenomena, HO2 radicals, autoignition, modeling.
Introduction
Previous studies [B1, 2] have shown that the coating of the wall of the reactor can significantly
influenced the position of the autoignition limit of hydrogen/oxygen and the limits between the
different oxidation phenomena (slow reaction, cool flame, single or multiple stages autoignition)
of organic compounds in a pressure-temperature diagram. For instance, Cherneskey and
Bardwell [B3] have observed an increase of about 200 Torr (26 kPa) for the ignition limit at 623
K of an equimolar n-butane/oxygen mixture by just coating their silica reactor by a PbO layer.
The purpose of this work is to define heterogeneous reactions, which could be of importance,
and to qualitatively assess their effect on a detailed gas phase kinetic model of the oxidation of
n-butane. Details about the writing of this detailed mechanism and its validation can be found in
a recent paper [B4].
Definition of the wall reactions and their rate parameters
According to previous work [B5-8], amongst the radicals present in oxidation conditions, only
HO2 radicals would be sufficiently unreactive to diffuse to the surface and promote
heterogeneous reactions. According to Cheaney et al. [B6], two categories of surfaces can be
defined, each related to a specific heterogeneous reaction:
♦ Category I includes surfaces treated with acid and is related to reaction (W1):
(W1),
HO2 + H+ → ½ H2O2 + ½ O2 + H+
♦ Category II includes surfaces coated with salt or metal oxides and is related to reaction
(W2):
HO2 + e- → ½ H2O + ¾ O2 + e(W2).
As predicted by these reactions, H2O2 was experimentally observed when the surfaces were of
category I, but not for those of category II. Nevertheless, as the formation of H2O2 from the
reaction between HO2 radicals and hydrocarbon molecules cannot be neglected, an additional
reaction has been proposed for surfaces of category II [B6]:
H2O2 + e- → H2O + ½ O2 + e(W3).
These three reactions are taken into account in our modeling study, with rate parameters
estimated as explained thereafter, with the assumption of control by surface reactions, i.e.
diffusion can be neglected. According to Blackmore [B9], when neglecting diffusion, the rate
constant of the termination of radicals to the wall of a reactor is :
3 γc
γc
kw =
for a spherical reactor
kw =
for a cylindrical reactor
2 d
d
with : γ :
Probability of reaction on each collision,
c:
Radicals average molecular velocity, which can be obtained from the kinetic
theory of gases (at an average temperature of 800 K, for c ≈ 71700 cm.s-1for HO2 radicals
and H2O2 molecules),
d:
Diameter of the reactor.
SAFEKINEX - Deliverable 33 - Report on experiments needed for kinetic model development (high pressure)
page 57 (59)
Results and discussion
Figure 1 presents the influence of wall effects on simulated autoignition delay times for
stoichiometric n-butane/air mixtures in an spherical reactor (10 cm diameter). Simulations were
performed using SENKIN of CHEMKIN II [B10] and the gas-phase mechanism [B4] including
no wall effect, reaction on surface of category I and reactions on surface of category II,
respectively.
For the reactions of HO2 radicals, we have assumed a low probability of reaction, γHO2, of 0.01.
Zils et al. [B8] propose values of γHO2 between 0.017 and 0.062 according to the efficiency of
treatment of the reactor with PbO. We have then obtained kw1 = kw2 equal to 107 s-1 and, kw3 =
0.5 s-1, assuming the same relationship for H2O2 molecules with a much lower probability of
reaction, as they are not radicals, γH2O2 = 5x10-5. The figure shows that the effect of
heterogeneous reactions depends strongly on pressure. At 5 bar, this effect is weak whatever the
category of surface, whereas at 0.5 bar, the delay times are multiplied by a factor up to 10 when
considering reaction on surface of category I and by a factor more than 1000 when considering
reaction on surface of category II. As this simulation neglects diffusion, it certainly strongly
overestimates the influence of heterogeneous reactions at high pressure. That involves that
termination of free radicals at wall in high pressure applications, such as in engines, are certainly
of very minor importance.
Figure 2 displays simulated pressure/temperature diagrams of oxidation phenomena for
equimolar n-butane/oxygen mixtures obtained under the conditions of Cherneskey and Bardwell
[B3] with and without the two kinds of wall reactions. In this case, the reactor is cylindrical (6
cm diameter) and has been strongly treated involving a high probability of reaction: γHO2 = 0.06
and γH2O2 = 3x10-4, corresponding to kw1 = kw2 = 717 s-1 and kw3 = 3.6 s-1. The heat transfer
coefficient at the pyrex wall has been taken equal to 30 W m-2 K-1.
These diagrams were constructed automatically using a software developed at University of
Leeds by Griffiths et al. [B11] and based on UNIX shell scripts to control the execution of a
modified version of SPRINT in which the various non-isothermal behaviour i.e., ignition, cool
flames, and slow reaction are characterised. This characterisation of the reaction modes is based
on monitoring the temperature increase and temperature gradient within the simulated time.
The diagram obtained without considering heterogeneous reactions is qualitatively similar to that
experimentally observed [B3], even if quantitative differences are encountered for the position of
some limits, e.g. the simulated minimum ignition temperature is about 515 K and the simulated
pressure ignition limit above 550 K ranges between 100 and 250 Torr, whereas the experimental
minimum ignition temperature is about 530 K and the experimental pressure ignition limit above
550 K varies between 250 and 300 Torr.
Simulations considering heterogeneous reactions do not show changes in the minimum ignition
temperature as encountered by Cherneskey and Bardwell [B3], but display well an increase of
the pressure ignition limit above 550 K. Below 550K, the influence of HO2 radicals is less
important than that of alkylperoxy radicals (RO2) and wall reactions of these last radicals should
probably be taken into account to reproduce a change in the minimum ignition temperature. The
increase of the pressure ignition limit above 550 K ranges between 50 and 100 Torr below 670 K
and is even larger at higher temperature. While the inhibiting effect of walls of category II is
only slightly more pronounced than that of wall of category I below 670K, the difference is
much more important at higher temperature, which was not experimentally observed [B3].
Ignition times (s)
SAFEKINEX - Deliverable 33 - Report on experiments needed for kinetic model development (high pressure)
0.5
0.4
no wall effect
Category I
page 58 (59)
Category II
0.3
0.2
0.1
(a)
0.0
700 750 800 850 900 950
Ignition times (s)
300
200
no wall effect
Category I
Category II/1000
100
(b)
0
700 750 800 850 900 950
Temperature (K)
Figure 1. Influence of wall effects on simulated autoignition delay times for stoichiometric nbutane/air mixtures for an initial pressure of (a) 5 bar and (b) 0.5 bar .
No Wall Effect
Category I
Category II
Ignition
Cool
Flames
Slow Reaction
Figure 2. Influence of wall effects on the pressure/temperature diagram of oxidation phenomena
for equimolar n-butane/oxygen mixtures (1 Torr = 0.13 kPa).
Acknowledgements
Financial support of this work by the European Union within the “SAFEKINEX” Project EVG1CT-2002-00072.
SAFEKINEX - Deliverable 33 - Report on experiments needed for kinetic model development (high pressure)
page 59 (59)
References
B1.
C. H. Bamford, C.F.H. Tipper, Gas phase combustion, Comprehensive Chemical Kinetic,
vol. 17., Elsevier (1977).
B2. J.F. Griffiths, S.K. Scott, Prog. Energ. Combust. Sci., 13 (1987) 161-197
B3. M. Chernesky, J. Bardwell, Canad. J. Chem., 38 (1960) 482-492.
B4. F. Buda, R. Bounaceur, V. Warth, P.A. Glaude, R. Fournet, F. Battin-Leclerc, Combust.
Flame 142 (2005) 170-186.
B5. G.H.N. Chamberlain, D.E. Hoare, A.D. Walsh, Discus. Faraday Soc., 14 (1953) 89-97.
B6. D.E. Cheaney, D.A. Davies, A. Davis, D.E. Hoare, J. Protheroe, A.D. Walsh, Proc.
Combust. Inst., 7 (1959) 183-187
B7. K.A. Sahetchian, A. Heiss, R .Rigny, J. Chim. Phys., 84 (1987) 27-32.
B8. R. Zils, R. Martin, D. Perrin, Int. J. Chem. Kin., 30 (1998) 657-671.
B9. D.R. Blackmore, J. Chem. Soc., Faraday Trans. 1, 74 (4) (1978) 765-775.
B10. R.J. Kee, F.M. Rupley, J.A Miller, Sandia Laboratories Report, SAND 89 - 8009B (1993).
B11. J.F. Griffiths, K.J. Hughes, R. Porter, private communication (2005).