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CHEMICAL ENGINEERING TRANSACTIONS
VOL. 77, 2019
A publication of
The Italian Association
of Chemical Engineering
Online at www.cetjournal.it
Guest Editors: Genserik Reniers, Bruno Fabiano
Copyright © 2019, AIDIC Servizi S.r.l.
ISBN 978-88-95608-74-7; ISSN 2283-9216
A Model Structuring Dust, Mist, Gas/Vapour and Hybrid
Explosion Behavior: the Chemical-Engineering Model
Saul M. Lemkowitza,*, Jérôme R. Taveaua,b
a
Delft University of Technology, Delft, The Netherlands
b
Fike Corporation, Blue Springs, Missouri, USA
s.m.lemkowitz@tudelft.nl
The Chemical-Engineering model describes how the synergetic combination of chemical and engineering
factors determines gas, particulate, and hybrid explosion behavior. Explosion behavior is expressed as
explosion sensitivity (e.g. probability of explosion), explosion severity (e.g. adverse effects of explosion), and
explosion types (deflagration or detonation). Chemical factors are ranked using NFPA methodology.
Engineering includes whether explosion occurs in open or enclosed spaces, equipment shape/size, and initial
T, p, and flow conditions. The model is semi-quantitative; its virtues are its unique integration of chemical and
engineering factors in determining explosion risk, its didactic qualities, provision of insight, and practical utility
to engineers who are not experts in combustion science.
1. Introduction
Explosion behaviour is here characterized in terms of Explosion Severity and Explosion Sensitivity, the latter
concerning ignition probability. Table 1 lists important explosion sensitivity terms, definitions, and units. In
general the lower the absolute values of explosion sensitivity terms (e.g. lower MIE-values), the greater the
probability of ignition and occurrence of explosion. Explosion Severity relates to possible adverse effects of
explosion; greater explosion severity (e.g. detonation rather than deflagration) causes more damaging effects.
Table 2 lists important Explosion Severity terms, meanings and units. Together, Explosion Sensitivity
(probability) and Explosion Severity (adverse effects) relate to explosion risk, risk being a term composed of
probabilities of given adverse effects. Estimating explosion risk requires knowledge of both Explosion
Sensitivity and Explosion Severity (Tables 1 and 2, next page) and how these are affected by changes in
Chemistry and Engineering parameters.
2. Explanation of terms ‘Chemistry’ and ‘Engineering’ as used in the ‘Chemical-Engineering’
model
“Chemistry” relates to the “Chemistry” half of the “Chemical-Engineering” model (Figure 1). For given
substances, the relative quantitative value of “Chemistry” in terms of explosion risk follow from fundamental
chemical properties and from instrumentally determined parameters of the substances in question.
Fundamental are the chemical thermodynamics and kinetics of relevant combustion and/or decomposition
reactions, as these determine the mass-based volumetric rate of heat production (W/kg/m3), which is a key
parameter for both Explosion Sensitivity and Severity. In spite of QSAR development, at this moment reliable
quantitative values of most of the Explosion Severity and Sensitivity parameters are still most accurately
determined via standardized test procedures.
‘Chemistry’ hazard is quantified relatively using the well-known and applied NFPA-system (Head and Wagner,
1995) that ranks substances in terms of two separate explosion-related categories, Flammability and
Instability/Reactivity, each of which has a five tier system of no hazard (zero) to highest hazard (4). For liquids
(and for certain solids of high volatility, e.g. naphthalene). Flammability is based largely on the combination of
Lower Flash Point, LFP (Table 1) and tendency to disperse in air. The lower the LFP the higher the volatility
(i.e. higher vapour pressure), and therefore the greater the Flammability. Ease of dispersion in air is a second
DOI: 10.3303/CET1977161
Paper Received: 7 January 2019; Revised: 3 May 2019; Accepted: 22 June 2019
Please cite this article as: Lemkowitz S., Taveau J., 2019, A Model Structuring Dust, Mist, Gas/Vapour and Hybrid Explosion Behavior: The
Chemical-Engineering Model, Chemical Engineering Transactions, 77, 961-966 DOI:10.3303/CET1977161
961
criterion. Obviously vapours, formed by liquids with low LFPs, and gases, disperse most easily in air. Also
considered are finely divided solids in air (dusts); idem liquids (mists). Pyrophoric substances, which
spontaneously ignite in air (i.e. MIE = zero), in any phase form (e.g. solid micro-/nano-particles of most
metals), have, along with flammable gases, the highest Flammability classification (4).
Instability/Reactivity is based on reactivity with water (e.g. forming hydrogen) and, in particular, tendency to
explosively decompose, especially tendency to detonate. Largest values (4) are given to high explosives (e.g.
TNT, nitroglycerine) and highly unstable substances; i.e. having highly exothermic decomposition enthalpies
of decomposition (e.g. chlorine dioxide; pure liquid ozone) making detonation highly likely.
Alternatively, KG- and KSt-values can be used to estimate relative Chemistry-based explosion hazard of gases,
resp., air-particulate mixtures.
‘Engineering’ is characterized by the “environment” in which explosion occurs and ignition factors, meaning
open air or in vessels; if the latter, shape, size, and inter-connectedness; initial temperature, pressure, and
turbulence; location/energy of ignition.
Table 1: Important explosion sensitivity terms and relevant units
Lower Explosion Limit (LEL), for gases and for particulates suspended in air. For gases/vapours: mol-% or
volume-%; for particulates: typically g/m3
Upper Explosion Limit (UEL), for gases and for particulates suspended in air. For gases/vapours: mol-% or
volume-%; for particulates: typically g/m3
Explosive range (UEL) – (LEL), for gases and for particulates suspended in air: units as above
Minimum Ignition Energy (MIE), for gases and for particulates suspended in air: mJ
Minimum Ignition Temperature (MIT), for gases and for particulates suspended in air: ºC or K
Minimum Ignition Temperature (MIT), for a layer of particulates deposited on a (hot) surface: ºC (for a given
layer thickness, cm)
Lower Flash Point (LFP): ºC
Upper Flash Point (UFP): ºC
Maximum Experimental Safe Gap (MESG), in practice only for gases; theoretically also applicable for
particulates suspended in air: mm
Limiting Oxygen Concentration (LOC), for gases and for particulates suspended in air or in another gas (e.g.
nitrogen): mol-% O2
Table 2: Important explosion sensitivity terms and relevant units
Adiabatic flame temperature: the maximum theoretical temperature reached when no heat loss occurs.
Relates to constant pressure or constant volume, the latter being higher: °C or K
Maximum explosion pressure, pmax: bara
Maximum rate of pressure rise, (dp/dt)max: bar/s
For deflagrations, volume-standardized measure of explosion violence, the K-factor: K = [(dp/dt)]max • V
1/3:
bar.m/s, where V = vessel volume (m3)
Flame speed, velocity of flame relative to a fixed observer: for deflagrations: m/s
Deflagration-to-detonation transition (DDT): pmax-values: bara; DDT run-up distance: m
Pressure-piling: maximum pressures (bar), maximum rates of pressure rise, (dp/dt)max: bar/s
3. The ‘Chemical-Engineering’ model
The Chemical-Engineering model (Figure 1) schematically illustrates how Explosion Sensitivity and Explosion
Severity, which together determine explosion hazard, are based on the combination of Chemistry-based and
Engineering-based phenomena. The top part of the Chemical-Engineering model, based on heat balances,
concerns Explosion Sensitivity, which relates to probability of ignition (Table 1). The bottom part, Explosion
Severity, which is based on gas dynamics (e.g. gas expansion, turbulence), relates to the destructive potential
(“hazard”) of explosion in terms of type of explosion occurring (i.e. deflagration or detonation; for both:
maximum pressures (static and dynamic)), and, for deflagration, rate of pressure rise (Table 2). The left side
relates to Chemical aspects of the exploding substances, such as kinetics (rates of chemical reactions) and
thermodynamic properties (amounts of heat produced) these latter two determine volumetric rate of heat
production (W/m
3) A noted above, relative “Chemistry” hazards of substances are quantified using the relevant
“Flammability” and “Reactivity/Instability” ratings of the NFPA-substance hazard system, larger numbers (up to
4) indicating greater hazard.
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The right side relates to ‘Engineering’ aspects of the physical “environment” in which explosion occurs, such
as open or closed spaces; if the latter, dimensions, geometry; inter-connectedness of process equipment;
(turbulent) flow and initial pressure and temperature. The bottom right side relates to the (huge) influence of
turbulence. Together with Chemistry’, these parameters determine volumetric rate of heat loss (upper right
part Figure 1a) and gas dynamic behaviour, such as (acceleration of) flame speed (lower right part Figure 1a).
Figure 1a. The ‘Chemical-Engineering” model. Figure 1b. Flame speed (acceleration) in cylinder;
D = 0.15 m. X/D = ratio of [distance flame
travelled in (m)]/[diameter of cylinder (0.15 m)].
Silvestrini et al, 2008
A previous article (Lemkowitz and Schotte, 1999) describes in detail the theoretical basis of the methodology,
which is based on simplified chemical thermodynamics, kinetics and physical transport phenomena, as
applied to estimating how changes in ‘Chemistry’ and ‘Engineering’ affect explosion behaviour of gas
explosions in closed spherical vessels. This theory, not repeated here, is extended in this article to explosion
severity in two other general cases, explosions in cylinders and explosions in a type of interconnected
equipment. (Applied to Explosion Sensitivity (i.e. ignition parameters) in the two cases considered here, the
theory presented in the 1999 article leads to the same results as for explosions in spherical vessels.) While
many books (e.g. Bartknecht, 1994; Ogle, 2017) and articles (e.g. Proust, 2015) describe phenomena here
discussed, none give explanation in terms of the simple, concise, and, in particular, integrative ‘Chemical-
Engineering’ approach presented here.
3.1 Severity of explosion of gas or gases + particulates in cylinders (e.g. pipelines)
The ‘Chemistry’ of a substance or mixture is ranked using the NFPA-approach described above (or,
alternatively, the K-value system). Note that all substances entrained in air (or other gas supporting
combustion) and having an NFPA-rating (or K-value) greater than zero can potentially explode and, and many,
if not all, can under certain ‘Engineering’ circumstances (explained below), even detonate.
‘Engineering’ is, in addition to the description above (e.g. form, dimensions), for this case extended to include
parameters such as whether the cylinder is open or closed (if closed at both ends; or closed at only one end)
and the location of ignition; i.e. at open end or at closed end. What occurs after ignition of a flammable mixture
in a cylinder (pipeline) depends on the combination of ‘Chemistry’ and ‘Engineering’.
After initial ignition of a flammable mixture of given ‘Chemistry’ flame propagation can occur, or not occur. For
a given ‘Chemistry’ and ‘Engineering’ (here: cylinder) heat balances – i.e. rate of heat production relative to
rate of heat loss - determine whether or not flame propagation occurs. By approximation, heat production
occurs in the flame’s area, which increases with diameter squared. Also by approximation, heat loss occurs in
the flame’s perimeter, which increases only linearly with diameter. Increasing diameter thus increases heat
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production more than heat loss, making flame propagation possible. If diameter is too small (below a critical
diameter), then rate of heat loss is larger than rate of heat production; flame propagation is then impossible.
Rate of heat production is a chemical parameter (chemical thermodynamics and chemical kinetics). The most
reactive substances (e.g. acetylene) generally have, thermodynamically, the highest values of heat production
and also, kinetically, the highest rates of chemical reactions, particularly at or near stoichiometric
concentrations in air (and especially so in pure oxygen). Additionally, increasing temperature and pressure
usually more strongly increase rate of heat production than rate of heat loss. While rate of heat production is a
strong function of composition (i.e. maximum at or near stoichiometric) rate of heat loss is usually relatively
(much) less strongly affected by changes in composition. The values of explosion sensitivity factors specified
in (upper part of) Figure 1), all of which relate to ignition and flame propagation at extreme minima (e.g. Lower
Explosion Limits), follow from heat balances.
After initial ignition, effects of Engineering on a given chemical composition are as follows. If cylinder diameter
is greater than critical diameter, AND if ignition occurs at the OPEN END, then the resulting flame tends to
burn into the closed end of the cylinder at a more or less slow constant velocity. In this case the flame is
burning its way into a quiescent (i.e. non-moving: zero turbulence) mixture. The hot combustion gases are
flowing in the direction opposite to that of the flame. The flame is thus not influenced by the hot expanding
combustion gases. This more or less constant and relatively slow (order of magnitude typically 0.1. – 1.0 m/s)
flame speed is known as the laminar flame speed (laminar since the flame is propagating into the unburnt gas,
which is stationary and thus totally laminar: Reynolds number = 0). The laminar flame speed (often called the
laminar burning velocity) is thus largely a Chemical property, being, for gases, greatest for highly reactive
substances at their respective (near) stoichiometric concentrations (e.g. hydrogen) and lowest for the least
reactive flammable substances (e.g. methane).
Consider now the same cylinder (open at one end, closed at other) containing the same methane-air mixture
(same p and T). Except: ignition at closed end of cylinder instead of open end. Thus: same Chemistry
(methane-air mixture) – but different Engineering. And (possibly) totally different results. Figure 2 illustrates
this case: rather than moving in opposite directions, flame and hot expanding gases move in the same
direction. The flame is pushed forward/accelerated by hot expanding combustion gases. Shear forces
generated by gas flow along cylinder walls generate turbulence, creating turbulent eddies, increasing flame
surface area, which changes from two-dimensional to three-dimensional. Increased flame area increases rate
of combustion, which increases rate of heat production, which increases flow, which increases turbulence,
which increase flame area, enz. This positive-feedback mechanism is well-known. In the extreme case the
turbulent flame can even engulf pockets of unburned gas, which ignite/explode.
Via the above-sketched mechanism flame speed can accelerate from mild deflagration (cm/s) to more violent
deflagration (102 m/s), and even transform from deflagration to detonation, or even to a short-lived “super”
(i.e. over-driven) detonation: a Deflagration-Detonation Transition (DDT). Such behavior will again be
influenced by the combination of “Chemistry” (i.e. reactivity of mixture) and “Engineering” (i.e. cylinder L and
D, even surface roughness and obstacles in the cylinder, both of which generate extra turbulence). Such
behavior can occur with both combustible gases as well as with gases containing combustible particulates
(dusts, mists), as Table 3 summarizes.
3.2 Inter-connected equipment: two spherical/cubical vessels connected to each other via a cylinder
The combination of “Chemistry” and “Engineering” determine explosion severity in inter-connected equipment.
Chemical factors are the same as those discussed earlier; i.e. the more reactive the substance/mixture
involved (e.g. mixtures containing hydrogen; (near) stoichiometric composition; powders with high KSt-values
(> ca. 300 bar.m/s), the greater the potential for increased explosion severity.
Engineering is here more complex than in the case with cylinders. Consider the following scenario, for an
installation illustrated in Figure 2: a larger vessel V1, connected to a smaller vessel, V2, via a pipeline of length
L and diameter D. The installation is filled with a combustible gaseous mixture at room temperature and
atmospheric pressure. Figure 2 illustrates ignition to deflagration in the larger vessel. The expanding
deflagrative (thus subsonic) explosion in the larger vessel, V1, compresses the unreacted gases, increasing
their pressure and thus causing flow into the second, smaller, vessel, V2, increasing its temperature, pressure,
and turbulence intensity. If the ratio V2/V1 is sufficiently large, and the dimensions of inter-connecting pipelines
such that V2 approaches the same maximum explosion as V1 (typically 8 bara), then ignition occurs in V2 in a
heated turbulent mixture at an initial pressure of ca. 8 bara. In this particular case maximum final explosion in
V2 could theoretically approach roughly 8 x 8 bara = ca. 60 bara, with correspondingly much higher values of
(dp/dt)max than in V1. Figure 2 does not exhibit such extreme behavior, but obvious from the measured results
are the strongly increased explosion pressure and (dp/dt)max in the second vessel. This phenomenon is known
as pressure piling.
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Figure 2: Pressure piling: p-t behaviour in Vessel 1, where ignition occurs, and smaller vessel, Vessel 2.
Increased explosion pressure and, in particular, greatly increased dp/dt in Vessel 2. Larger ratios V2/V1
increase effect pressure piling. More extreme behaviour would also seem possible. Kaufman et al, 1995
A more extreme scenario would also seem theoretically possible; namely maximum deflagrative pressure
piling into V2 (i.e. large ratio V2/V1) followed by detonation in V2. In this hypothetical case, L- and D-dimensions
of connecting cylindrical piping allow flow of unreacted gases into V2 such that in V2 these gases reach a
pressure of ca. 8 bara. Somewhat later in time, DDT occurs in connecting pipelines. Gases in V2 are thus
ignited by a detonative flame, causing them to detonate directly rather than deflagrate. Resulting pressure
explosion pressure will therefore be much higher than ca. 60 bara mentioned above, more in order of ca. (15-
20) ● 8 bara. = ca. 120-160 bar and the (near) infinite (dp/dt) of a detonation. Chemical factors influencing
probability of increased Explosion Severity are basically the same as those listed in Table 3 (e.g. mixtures of
substances with higher/highest NFPA Flammability (e.g. hydrogen, acetylene) Reactivity/Instability ratings
(e.g. ethylene oxide) and/or high K-values. Idem for flammable mixtures containing reactive particulates (e.g.
finely divided reactive metals, such as Al, Mg, Ti, in particular, micro- and nano-particulates of such metals
whose surfaces are not oxidized).
Table 3: Chemical and engineering factors increasing Explosion Severity in cylinders containing flammable
gases alone and gaseous mixtures containing flammable particulates
Chemistry: gases “Engineering” factors Gases containing particulates
1. (Mixtures of) Gases with
higher/highest NFPA
Flammability and
Reactivity/ Instability
ratings (e.g. H2)
2. (Near) stoichiometric
mixtures
3. Increasing temperature
(increases reactivity and
reaction rate)
4. Increasing pressure
(increases energy
concentration (J/m3) and,
usually, also reaction rate)
High O2-concentrations at
(near) stoichiometric
composition
1. Ignition at/near closed end of cylindrical
equipment
2. Ignition in cylindrical equipment with
L/D ≥ 5, such as silos.
3. Ignition in long pipelines (L/D >> 10)
4. High flow rates (creates turbulence)
5. Pipelines: Ideal diameter (not too small,
not too big)
6. Pipelines: Wall roughness and
obstacles (generate turbulence)
Interconnected equipment, especially
larger volume vessel connected to
smaller volume vessel via (long)
pipelines; risk of flame acceleration and
‘pressure piling’ (de-scribed further
below)
1. Originally soft deflagrations of particulate-
air mixtures can transform violent
deflagrations.
2. Even DDTs can occur in particulate
explosions in cylinders (in industrial
practice, only in exceptional cases)
3. Engineering factors applying to gas
explosions also apply to particulates
explosions (cylinders, L/D >> 10)
4. Typical chemical factors increasing
violence of explosions in cylinders
involving particulates:
a. Mixtures containing gases with
higher/highest NFPA-Reactivity/Instability
ratings (e.g. H2)
b. Drier/finer particulates
c. Reactive particulates; e.g. finely divided
reactive metals, esp. when surfaces not
(fully) oxidised);
d. Hybrid mixtures: mixtures containing
flammable gases/ vapours as well as
flammable particulates
e. Higher oxygen concentrations
f. Thermodynamically unstable substances
(i.e. substances with strongly exothermic
enthalpies of decomposition); e.g.
ethylene oxide and/or powdered high
explosives, such as TNT
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Table 4 lists how changes in Engineering affect Explosion Severity in two spherical vessels connected via a
cylinder (i.e. piping).
Table 4: Possible effects of ‘Engineering’ factors on explosion severity in two spherical vessels inter-
connected via a cylinder: pressure piling, and/or flame acceleration, and/or DDT
Changes ‘Engineering’ Effect on Explosion Severity
Ignition in larger vessel
rather than smaller vessel
Larger V1/V2 ratios allows pressure in V2 to approach maximum explosion
pressure in V1 (i.e. ca. 8 time initial pressure) before ignition in V2 occurs. Result:
significant pressure piling effects. Small V1/V2 ratios hardly raise pressure in V2
Diameter connecting
piping > Dcritical allowing
flame propagation
If pipe diameter less than critical value, then pipe extinguishes flame: no
explosion in V2. If pipe diameter greater than critical diameter flame acceleration
possible, probability and intensity increasing with greater chemical reactivity.
Idem, but additionally:
Piping long enough to
assure appreciable flame
acceleration
No appreciable flame acceleration in short pipe. Longer lengths allow greater
flame acceleration, increasing turbulence and T of unreacted gases in V2. Flame
acceleration increases causes flame to more powerful ignite unreacted gases in
V2. In extreme cases, acceleration to DDT potentially possible.
3.3 The contrasting effects of turbulence
Increased turbulence generally decreases explosion sensitivity. Reason is that explosion sensitivity terms
relate to the extreme possibilities of ignition (i.e. lowest LEL; highest UEL; lowest MIE). Increased turbulence
causes increased mixing with unreacted gases, hampering ignition by removing heat. While turbulence
generally reduces explosion sensitivity, turbulence can both increase and decrease explosion severity. Near to
explosion limits, increased turbulence tends to extinguish combustion by mixing a weakly combustible mixture
with cold air. However, as reactivity of a given mixture increases (e.g. more reactive substances;
stoichiometric concentrations), increased turbulence increases explosion severity. The main mechanism is
increased flame surface area. Since risk is a function of probability of occurrence (i.e. ignition) and severity of
effects, it is probable that a certain level of turbulence creates maximum risk.
4. Conclusions
Explosion behavior of gases and mixtures of gases and particulates can be understood, explained and semi-
quantitatively estimated using a unique ‘Chemistry-Engineering’ approach. Chemical hazards of substances
are ranked using NFPA-methodology (or K-factors). Engineering aspects are considered in terms factors like
shape, form, inter-connectedness of equipment, pressure, temperature, and location of ignition. Applied to
explosions in cylinders, the model explains and estimates increasing likelihood of flame acceleration, even
deflagration to detonation transition (DDT), as mixture reactivity increases, ignition occurs at the closed end of
a cylinder open at one end, mixture reactivity increases, cylinder length increases and cylinder diameter
increases to a value ensuring maximum turbulence. Applied to explosions occurring in equipment consisting of
two spherical vessels connected via a cylinder (i.e. piping), explosion severity (e.g. flame acceleration)
increases with increasing mixture reactivity, ignition occurring in the larger of the two vessels, greater cylinder
length, and an ideal diameter favoring maximum turbulence. The model’s greatest utility is providing insight
into explosion risks to engineers who are not explosion specialists.
References
Bartknecht, W. Explosions-schutz Grundlagen und Anwendung, Springer-Verlag; especially p. 251-289.,
Head, G. L. and Wagner, B.C., 1995, The NFPA 704 diamond, Professional Safety, 40(12), 20
Kaufman, C.W., Sichel, M., Wolanski, P., 1995, Paradoxes in Combustion, Archivum Combustionis, 15(3-4),
275-287.
Lemkowitz, S.M., Schotte, R.M., 1999, Using simple theory to predict how process changes affect gas
explosion risk, NPT Procestechnologie, 2, 19-24.
Ogle, R.A., 2017, Dust Explosion Dynamics, Elsevier, pages 548-549.
Proust, C., 2015, Gas flame acceleration in long ducts, Journal of Loss Prevention in the Process Industries,
36, 387-393.
Silvestrini, M, Genova, B., Parisi, G., Trujillo, F.J.L., 2008, Flame acceleration and DDT run-up distance for
smooth and obstacles filled tubes, Journal of Loss Prevention in the Process Industries, 21, 555-562.
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