Chemical Engineering Science 63 (2008) 1098 – 1116
www.elsevier.com/locate/ces
Stability and performance of catalytic microreactors: Simulations of propane
catalytic combustion on Pt
Niket S. Kaisare, Soumitra R. Deshmukh, Dionisios G. Vlachos ∗
Department of Chemical Engineering, Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, DE 19716, USA
Received 27 February 2007; received in revised form 23 October 2007; accepted 3 November 2007
Available online 17 November 2007
Abstract
A pseudo-two-dimensional (2D) model is developed to analyze the operation of platinum-catalyzed microburners for lean propane–air
combustion. Comparison with computational fluid dynamics (CFD) simulations reveals that the transverse heat and mass transfer is reasonably
captured using constant values of Nusselt and Sherwood numbers in the pseudo-2D model. The model also reasonably captures the axial
variations in temperatures observed experimentally in a microburner with a 300 m gap size. It is found that the transverse heat and mass
transport strongly depend on the inlet flow rate and the thermal conductivity of the burner solid structure. The microburner is surface reaction
limited at very low velocities and mass transfer limited at high velocities. At intermediate range of velocities (preferred range of reactor
operation), mass transfer affects the microburner performance strongly at low wall conductivities, whereas transverse heat transfer affects
stability under most conditions and has a greater influence at high wall conductivities. At sufficiently low flow rates, complete fuel conversion
occurs and reactor size has a slight effect on operation (conversion and temperature). For fast flows, propane conversion strongly depends on
residence time; for a reactor with gap size of 600 m, a residence time higher than 6 ms is required to prevent propane breakthrough. The effect
of reactor size on stability depends on whether the residence time or flow rate is kept constant as the size varies. Comparisons to homogeneous
burners are also presented.
䉷 2007 Elsevier Ltd. All rights reserved.
Keywords: Catalytic combustion; Energy; Fuel; Simulation; Microburner extinction; Propane
1. Introduction
The growing interest in hydrocarbon-based sources for decentralized power generation and as replacements of existing
batteries (Fernandez-Pello, 2003; National Research Council,
2004) has spawned a significant research effort in small-scale
homogeneous (Kim et al., 2007; Miesse et al., 2004) and catalytic reactors (Kolb and Hessel, 2004, Norton et al., 2004,
2006, Ouyang et al., 2005; Pattekar and Kothare, 2004;
Rebrov et al., 2001; Srinivasan et al., 1997). These micro
chemical systems are used either for generation of hydrogen
for fuel cells (Deshmukh et al., 2004; Deshmukh and Vlachos,
2005; Ganley et al., 2004; Karim et al., 2005; Kolios et al.,
2005; Tonkovich et al., 2007) or for direct conversion of thermal energy released via combustion to electrical energy using
∗ Corresponding author. Tel.: +1 302 831 2830; fax: +1 302 831 1048.
E-mail address: vlachos@udel.edu (D.G. Vlachos).
0009-2509/$ - see front matter 䉷 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ces.2007.11.014
thermoelectrics (Federici et al., 2006) or thermo-photovoltaics
(Yang et al., 2004). Hydrocarbon combustion is typically
needed to ensure autothermal operation of these devices. Homogeneous combustion is often the preferred mode of operation at
larger scales, for example, in power plants (Kiameh, 2002) and
industrial reformers for hydrogen production (Udengaard et al.,
1995). However, the situation rapidly changes at smaller scales
due to the high surface area to volume ratio. While homogeneous combustion becomes less stable due to thermal and radical quenching (Aghalayam et al., 1998, Norton and Vlachos,
2003, 2004, Raimondeau et al., 2003), faster mass transfer can
potentially result in high effective rates of catalytic reactions
(Jensen, 2001).
We previously studied homogeneous combustion of stoichiometric methane–air and propane–air mixtures in microburners
(Norton and Vlachos, 2003, 2004) (i.e., burners with characteristic dimension less than 1 mm). The burner solid structure
had a significant influence on the stability (Leach and Cadou,
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
2005), and these burners were especially prone to thermal extinction for gap sizes of ∼ 400 m or lower (Kaisare and
Vlachos, 2006). However, the range of construction materials of
the reactor walls that conduct sufficient heat for homogeneous
ignition and still provide enough insulation to reduce the heat
losses is very narrow. Even then, these stand-alone microburners are unstable at external heat loss coefficients in the regime
of free convection in air. Finally, the burner operating temperatures are locally very high—often in excess of 1500 K—due
to the large activation barriers and fast rates at these temperatures, raising concerns about stability of the wall materials
(Deshmukh and Vlachos, 2005).
In contrast to homogeneous combustion, catalytic combustion is promising at small scales. First, the transport rates as well
as the catalytic surface area per unit volume increase linearly as
the device size shrinks, leading to faster effective reaction rates,
more stable operation, and process intensification. Second,
ignition temperatures are lower. For example, hydrogen–air
mixtures self-ignite and no detectable lean-burn limit is observed in a Platinum (Pt)-catalyzed microreactor of a 250-m
gap (Norton et al., 2004). Third, catalytic microburners can
operate at lower device temperatures and with significant
heat losses, compared to their homogeneous counterparts.
For example, autothermal microburner operation with less
than 250 ◦ C outer wall temperature was feasible and the microburner was stable even when coupled with a thermoelectric
device (Federici et al., 2006).
Despite a limited number of recent studies (Karagiannidis
et al., 2007; Li and Im, 2007), the fundamentals of microcatalytic combustion are not as well understood as of their
homogeneous counterparts. Yet, these systems are inherently
more complex. The objective of this paper is to perform a
comprehensive parametric study to understand the role of operating conditions, specifically, the wall thermal conductivity,
equivalence ratio, and inlet velocity in determining microburner
stability and efficiency. The importance of heat and mass transfer effects is also analyzed. A computationally efficient pseudotwo-dimensional (2D) model employing reduced reaction kinetics is developed for this purpose. Insights into optimal reactor
length and gap size are also developed.
The organization of this paper is as follows. The next section
details the development of the reactor model and the reaction
kinetics. We then compare results of our model with computational fluid dynamics (CFD) simulations, followed with an assessment of our model against experimental data. The influence
of wall thermal conductivity and inlet velocity on microburner
operation is investigated. Finally, the effect of reactor dimensions on device performance and stability is analyzed followed
by conclusions.
2. Mathematical model
2.1. Assumptions and governing equations
The reactor, illustrated in Fig. 1, consists of two parallel
plates coated with Pt catalyst. The nominal reactor geometry
is the same as the one employed in our previous studies on
catalyst
1099
h∞(Ts - T∞)
insulated
insulated
bw
Yk0
u0, Tg0
y
d/2
x
l
Fig. 1. Schematic of the parallel plate reactor with the dash-dotted line
representing the axis of symmetry. The reactor walls are coated with Pt
catalyst.
Table 1
Operating conditions and model parameters used in simulations
Length (cm)
Plate thickness (m)
Gap size (m)
Equivalence ratio
Inlet velocity
Inlet temperature (K)
Wall conductivity
Nusselt number
Sherwood number
l
bw
d
1, 2, 4
200
150, 300, 600, 1200
0.6, 0.75, 0.95
Varies
300
Varies
4.0
3.8
u0
Tg0
ks
Nu
Sh
The boldface values represent nominal reactor dimensions.
homogeneous microcombustion (Kaisare and Vlachos, 2006,
2007; Norton and Vlachos, 2003, 2004). Specifically, each plate
is l =1 cm long and bw =200 m thick. The plates are separated
by a gap size (height) of d = 600 m. In the last part of the paper, we vary the reactor dimensions from these nominal values
to study size effects. The parallel plate geometry implies that
the third dimension (width) of the microburner is much larger
than the gap size; wherever relevant, values (e.g., volumetric
flow rate) are reported assuming a 1 cm width into the plane
of the paper. Propane–air mixtures of varying concentrations
are fed into the reactor at room temperature (300 K). The relevant parameters used are provided in Table 1. The following
assumptions are made: the flow is laminar, the pressure drop is
negligible, gases follow the ideal gas law, and radiation effects
are neglected due to the large aspect ratio (l/d) of the reactor
(Kaisare et al., 2005). Heat losses from the walls are described
using Newton’s law of cooling (as further elaborated below,
the effect of surface radiation is lumped into an effective heat
transfer coefficient). The reactor is modeled using a pseudo-2D
model, which involves writing conservation equations in the axial direction and a lumped parameter description of transverse
heat and mass transfer (in the literature, this is often referred
to as 1D heterogeneous model). The governing model is as follows (the symbols are described in Notation section):
j j(u)
+
= 0,
jt
jx
(1)
jYk
j2 Yk
Mk u jYk
= Dk 2 +
kj rgas,j
+
jx
jt
jx
j
− âg kmt,k (Yk − Yks ),
(2)
1100
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
0 = Mk
kj rcat,j + kmt,k (Yk − Yks ),
(3)
j
The pertinent boundary conditions are written as
at inlet, x = 0:
jTg
jTg
+ uc̄p
dt
jx
2
j Tg
= kg 2 +
Hj rgas,j − âg hg (Tg − Ts ),
jx
u = u0 , Yk = Yk0 , Tg = Tg0 ,
jTs
= 0;
jx
c̄p
(9)
(4)
j
s cs
jTs
j2 Ts
= ks 2 + âs
Hj rcat,j − â∞ h∞ (Ts − T∞ )
dt
jx
j
+ âs hg (Tg − Ts ).
(5)
Our code can treat variable or constant properties. In the
gas-phase material and energy balances, the axial heat and
mass transfer (Laplacian) terms are approximated assuming the
transport coefficients to be locally constant (in order to improve numerical robustness of the model). This is unlikely
to introduce modeling errors because of the high values of
the Peclet number. In the literature, these terms are typically
neglected for our values of Peclet number. The surface area
factor , discussed below, modifies the catalytic reaction rate
in Eqs. (3) and (5). The physical properties of the reactor solid
structure (density, specific heat, and wall thermal conductivity)
are assumed constant. In the above equations,
âg =
2
d
âs = â∞ =
and
1
bw
(6)
are the surface area per unit volume computed for the gas and
solid phases, respectively. The continuity Eq. (1) is modified
using the ideal gas law to obtain:
−
jTg M̄ jYk
j(u)
−
+
= 0.
Tg jt
Mk jt
jx
(7)
k
The last terms in Eqs. (2)–(5) represent transverse transport.
A mass fraction-based formulation of transverse mass transport is used (i.e., mass flux is computed as kmt,k (Yk − Yks )).
The heat and mass transfer coefficients are computed from the
Nusselt (N u) and Sherwood (Sh) numbers according to
hg = Nu
kg
d
and
kmt,k = Sh
Dk
.
d
(8)
The Nu and Sh numbers are discussed in the next subsection.
The thermal properties (c̄p and H ) are computed using the
CHEMKIN thermodynamic database (Kee et al., 1991) and the
transport properties are computed using CHEMKIN gas-phase
transport libraries (Kee et al., 1990). In previous CFD work,
we found no gradients across the reactor wall. In this model, hg
accounts for heat transfer between the fluid and the surface. The
outside heat transfer coefficient, h∞ , accounts for all possible
heat losses from the outside reactor surface.
Dirichlet boundary conditions are imposed at the reactor entrance, and the reactor sidewalls are assumed to be insulated.
Zero-flux boundary conditions are applied at the reactor outlet.
jTg
jYk
jTs
=
= 0.
(10)
=
jx
jx
jx
The transient mass and energy conservation Eqs. (2)–(7) are
solved using the method of lines until steady state is attained.
Finite difference is employed to discretize the differential equations on 200 equidistant axial nodes. The resulting differential algebraic equations (DAEs) are solved using the DASPK
package (Petzold, 1983) employing a numerically computed,
banded Jacobian. For simulations with different reactor lengths,
we increased the number of axial nodes so that the distance between adjacent nodes remains the same as that in the nominal
reactor length. Natural parameter continuation is used, where
a family of solutions is obtained as a function of a parameter.
Each solution is obtained starting with an initial guess from the
solution at the previous parameter value.
at outlet, x = l:
2.2. Reaction kinetics
In spite of an extensive literature on catalytic combustion
of lower alkanes on noble metals (Aryafar and Zaera, 1997;
Ehrhardt et al., 1992; Hayes and Kolaczkowski, 1997; Hicks
et al., 1990; Lee and Trimm, 1995; Ma et al., 1996; Otto, 1989;
Yao, 1980), a kinetic model valid over a wide range of parameters was not available until recently. Literature one-step
mechanisms vary significantly in the activation energies and
reaction orders of the fuel and oxygen. Thermodynamically
consistent microkinetic mechanisms for catalytic combustion
(Mhadeshwar, 2005; Mhadeshwar and Vlachos, 2005), which
have been validated over a wide range of operating conditions,
are desirable but computationally demanding for reactor design
and optimization. We recently developed one-step kinetic rate
expressions for catalytic combustion of lean lower alkane–air
mixtures on noble metals via a posteriori model reduction of
detailed microkinetic models (Deshmukh and Vlachos, 2007).
Adsorbed oxygen is the most abundant surface species under fuel lean burn conditions and dissociative adsorption of
the alkane is the rate-determining step (RDS). Consequently,
propane total oxidation on Pt:
C3 H8 + 5O2 → 3CO2 + 4H2 O
has the following rate expression:
Cs,C3 H8
kCads
3 H8
2 .
ads
des
1 + kO2 Cs,O2 /kO2
rcat,C3 H8 = In the above expression,
ads
RT
T k −E ads /RT
s
0
ads
kk =
e k
and
2Mk Tref
des
T k −E des /RT
des
kk = A 0
e k
.
Tref
The values of rate parameters are provided in Table 2.
(11)
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
1101
Table 2
Kinetic rate constants for lean propane combustion on Pt
C3 H8 adsorption
O2 adsorption
O2 desorption
A0 (s−1 ) or s0
E (kcal/mol)
0.06
0.0542
8.41 × 1012
0.154
0.766
−0.796
0,2, or 4a
0
Surface area factor ()
Site density () (mol/cm2 )
Tref (K)
b
1.0 or 1.7a
2.5 × 10−9
300
Numbers in bold indicate values used in the majority of the paper.
a The theoretical value of activation energy for propane adsorption is 0 kcal/mol; E ads = 4 kcal/mol and = 1.7 were determined following sensitivity
C3 H8
analysis and experimental validation (see text for details).
b E des = 52.8 − 2.3(T /300) − 32.0 ∗ .
O
O2
Activation energies required in computation of the reaction
rate, according to Eq. (11), depend on the oxygen surface coverage. Since the surface coverages of all other species except
oxygen are insignificant, we use an order-one, O(1), asymptotics approximation to eliminate them and the surface site balance reduces to ∗ + O∗ = 1. Thus, the oxygen coverage is
obtained by solving the nonlinear equation:
ads C
des
kO
s,O2 /kO2
2
2 ,
0
0.1
0.2
0.3
(cm)
0.4
0.5
(12)
where the nonlinearity arises from the coverage dependent
des . Specifically, the activation energy
activation energy of kO
2
varies, in our case, in a linfor oxygen desorption EOdes
2
ear manner with the oxygen coverage, O∗ , with higher O∗
coverages decreasing the desorption energy due to lateral
repulsive adsorbate–adsorbate interactions.
The focus of this paper is on catalytic combustion, so that
rgas = 0. At some of the higher temperatures reported herein,
gas-phase chemistry could become important depending on the
gap size (Karagiannidis et al., 2007; Norton et al., 2004). However, we have left out gas-phase chemistry in this work since
we envision that temperatures of practical operation (in terms
of materials stability and safety) should be sufficiently low to
prevent the onset of gas-phase chemistry.
2.3. Nusselt and Sherwood numbers
Transverse heat and mass transport is lumped in our pseudo2D model in the form of heat and mass transfer coefficients.
Although Nu and Sh correlations have been developed before
(Di Benedetto et al., 2006; Groppi et al., 1995; Gupta and
Balakotaiah, 2001; Shah and London, 1978), these studies on
conventional size devices often lack the close coupling between
the wall and bulk-gas that gives rise to the non-monotonic Nu
number behavior observed in our previous work (Norton and
Vlachos, 2004). Hence, we use CFD simulations to obtain appropriate Nu and Sh values and subsequently verify the predictive capabilities of our pseudo-2D model.
Fig. 2 illustrates CFD simulation results for the nominal
reactor geometry and a typical set of operating conditions. An
elliptic 2D model for the reactor with planar symmetry depicted
0.2
0.0
0.4
0.8
0.6
0.05
0.1
1.0
0.15
0.2
0.25
(cm)
1500
30
Cup-mixing bulk Tg
25
1200
20
Wall Ts
15
900
10
Nu
Temperature (K)
1
300 K
Propane
conversion
1+
850 K
Nusselt or Sherwood numbers
O∗ = 1 − 1400 K
600
5
Sh
0
300
0.0
0.2
0.4
0.6
0.8
Axial coordinate, x (cm)
1.0
Fig. 2. Contours of (a) temperature and (b) propane conversion computed
using Fluent CFD simulations and (c) axial profiles of temperature and Nusselt
and Sherwood numbers for ks = 2 W/m/K, h∞ = 20 W/m2 /K, = 0.75,
and u0 = 0.5 m/s. A jump in the Nu profile is associated with a change in
the role of the reactor walls from a net heat source to a net heat sink at a
location indicated by the thin vertical line. The propane activation energy and
ads = 0 kcal/mol and = 1.0, respectively.
catalyst surface area factor are EC
H
3 8
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
3. Benchmarking of the pseudo-2D reactor model
3.1. Comparison to CFD model results
Simulations were performed for a wide range of parameters using both our simplified model and CFD simulations. We
found that our model is fairly accurate in comparison to the
computationally intensive CFD model, as evidenced in Fig. 3.
The symbols represent the CFD simulation results, with the
bulk-gas quantities being the cup-mixing averaged values, and
the lines represent our model. The conditions in Fig. 3 are
close to device extinction. While this is just one representative result where the temperature predictions from CFD and
pseudo-2D models show excellent agreement, we found that
0.04
Propane mass fraction
in Fig. 1 is solved using Fluent 6.2 (2004). The kinetics of
propane oxidation are incorporated using Fluent’s User Defined
Functions (UDF) with ECads
= 0 kcal/mol, = 1.0 and other
3 H8
kinetic constants from Table 2. Figs. 2a and b plot the contours
of temperature and propane conversion, respectively, with the
abscissas truncated to highlight the relevant portion of the reactor. The wall and cup-mixing averaged gas temperatures are
plotted in Fig. 2c. A microburner typically exhibits three zones:
the preheating, reaction, and post-reaction zones. While these
zones are clearly demarcated in homogeneous microburners,
the preheating and reaction zones often overlap in catalytic microburners, as seen in Fig. 2. The wall acts as a net heat source
in the preheating/reaction zones due to axial recirculation, via
wall conduction of the heat released by reaction, and as a net
heat sink in the post-reaction zone due to heat losses to the surroundings. This dual heat sink–source nature manifests itself as
a discontinuity in the Nu number profile in Fig. 2c. A similar
observation was also made in our earlier work on homogeneous
microburners (Norton and Vlachos, 2004). The transition in the
wall role is also demarcated at the crossover between the wall
and cup-mixing gas temperatures. The asymptotic N u∞ value
approaches the constant temperature asymptote of the Graetz
problem (i.e., Nu∞ = 3.8) in the preheating/reaction zones and
the constant flux value (N u∞ =4.15) in the post-reaction zone.
On the other hand, the Sh number displays a monotonic profile
with an asymptotic value of Sh∞ = 3.8, which is equal to the
constant temperature asymptote for the equivalent heat transfer
problem.
Based on these observations, two possibilities for Nu and Sh
correlations were considered for the pseudo-2D model: (i) using a constant Nu value of 4.0 (intermediate to the two asymptotic values of 3.8 and 4.15) and a constant Sh value of 3.8, or
(ii) fitting the Nu and Sh CFD profiles. As demonstrated in the
next section, constant Nu and Sh values are sufficient to nearly
quantitatively predict the CFD results. Using axially varying
Nu and Sh fits did not provide much improvement. Hence, for
the sake of simplicity, the second option was deemed unnecessary for the purpose of this paper. Our choice should not be
interpreted as a claim that exact mass and heat transfer correlations are unimportant in microreactors; we merely claim that
carefully chosen Nu and Sh values are sufficient for the conditions of our problem.
Bulk YC3H8
0.03
0.02
Surface YC3H8
0.01
0
700
Wall Ts
600
Temperature (K)
1102
500
Gas Tg
400
Symbols: CFD simulations
Lines: pseudo-2D model
300
0.0
0.2
0.4
0.6
0.8
1.0
Axial distance, x (cm)
Fig. 3. Comparison of axial profiles of (a) propane mass fraction and (b)
wall and bulk-gas temperatures obtained from CFD simulations (symbols)
and pseudo-2D model (lines) near an extinction point, i.e., ks = 20 W/m/K,
u0 =0.5 m/s, =0.75, and h∞ =135 W/m2 /K. The kinetic model parameters
ads = 0 kcal/mol = 1.0.
are EC
H
3 8
the two models deviate somewhat at higher velocities and lower
heat losses. However, the maximum deviation between the temperatures predicted by our model and CFD simulations was
less than 10% in all cases investigated. Larger differences are
seen in the surface mass fraction, but these are limited to the
near entrance region and do not seem to substantially affect
reactor stability. More importantly, the simplified model was
able to accurately match the extinction trends predicted using
CFD (e.g., CFD and pseudo-2D simulations predicted extinction at 145 and 147 W/m2 /K, respectively, for the conditions of
Fig. 3). This finding indicated that we could reliably use the
pseudo-2D model for assessing operating conditions for improved microburner stability and performance.
3.2. Model uncertainty to surface reaction model parameters
The activation energy for dissociative adsorption of propane
was obtained using the Unity Bond Index-Quadratic Exponential Potential (UBI-QEP) theory as ECads
= 0 kcal/mol.
3 H8
The UBI-QEP theory has an uncertainty of ±5 kcal/mol
(Shustorovich and Sellers, 1998). We previously reported
(Deshmukh and Vlachos, 2007) that a value of ECads
=
3 H8
4 kcal/mol yields a better prediction of the experimental data
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
Heat loss coefficient, h∞ (W/m2/K)
200
Efuel=0; η=1
150
100
Efuel=0; η=0.25
Efuel=2; η=1
50
Efuel=4; η=1
u0=0.5 m/s; =0.75
0
100
101
Wall conductivity, ks (W/m/K)
102
Fig. 4. Critical values of external heat loss coefficient vs. wall thermal conductivity for various activation energies of propane adsorption (in kcal/mol)
and catalyst surface area factor, . The model is very sensitive to both of
these parameters.
of Garetto and Apesteguia (2000). In addition, there is an
uncertainty regarding the amount of catalyst available for reaction, which is accounted in our model using the catalyst surface area factor, . This uncertainty arises because (i) the total
catalyst surface area available for reaction may be greater than
the geometric surface area since the precious metal is often
dispersed in a porous catalytic insert or a monolith washcoat
(either the insert or the washcoat is adhered to the wall); (ii) active sites may sinter; (iii) the catalyst may get deactivated; and
(iv) there may be internal mass transfer limitations. The parameter lumps all these uncertainties.Therefore, we analyze the
sensitivity of model predictions to the parameters ECads
and .
3 H8
Fig. 4 shows the effects of these two parameters on the critical values of the external heat loss coefficient above which the
burner loses stability. The behavior seen in this graph will be
analyzed extensively below. As the activation energy increases
or the catalyst surface area factor () decreases, the reactor stability drops drastically. The dashed lines, representing activation energies of 2.0 and 4.0 kcal/mol, indicate that even relatively small changes in the activation energy have a significant
impact on reactor stability. Likewise, the region of stable combustion shrinks significantly when the surface area factor is decreased to = 0.25. From a practical standpoint, increasing the
amount of catalyst, decreasing the particle size, and minimizing internal mass transfer in case of washcoats are important
factors for improving microreactor stability.
3.3. Comparison to experimental data
The next task is to estimate ECads
and by comparing
3 H8
the model predictions with experimental data for propane–air
1103
combustion in a Pt-catalyzed microburner (Norton et al., 2006).
The reactor consisted of two 790-m-thick stainless steel
plates with catalytic inserts made of anodized alumina with Pt
dispersed in them. The reactor length was 6 cm and the catalyst
occupied the central 5 cm. Metal thermal spreaders made of
stainless steel or copper were optionally mounted on a reactor plate to vary its thermal conductivity and improve the
axial thermal uniformity. Three different reactor configurations are considered for model validation: (i) “no spreader”
case, simulated assuming 790 m walls with ks = 35 W/m/K;
(ii) “steel spreader” case, simulated assuming 2.5 mm walls
with ks = 35 W/m/K; and (iii) “Cu spreader” case, simulated
assuming 2.5 mm walls with ks = 216 W/m/K. The wall thermal conductivity for the first two cases is higher than that for
stainless steel to account for the nut-bolts and the reactor housing. The conductivity values are just estimates that provide
reasonable description of the experimental system.
In all these cases, we set the value of the external heat loss
coefficient to h∞ =20 W/m2 /K and the emissivity of the external surface for radiative heat losses to 0.7. The same convective
and radiative heat losses were applied to the reactor end walls
as well. In a typical simulation of the “no spreader” case at
an equivalence ratio (dimensionless composition) of = 0.75,
the heat losses via radiation were ∼ 70% of the total heat
losses. Thus, the equivalent heat loss coefficient that accounts
for both convective and radiative heat losses would be as high
as h∞,net = 64.5 W/m2 /K (this is in agreement with values
used in our previous work). In the remaining of the paper, the
heat loss coefficient reported should be interpreted as an effective one since surface radiation is not explicitly accounted for
to reduce the number of model parameters.
For the two different values of activation energy (ECads
=0
3 H8
or 4 kcal/mol), we varied the catalytic surface area factor, ,
so that for a feed rate of 12.2 m/s (approximately 2.0 SLPM),
we obtain extinction for the “no spreader” case at = 0.65
in close agreement with experiment. Temperature profiles for
ECads
= 4.0 kcal/mol and = 1.7 are shown in Fig. 5. The
3 H8
value of = 1.7 is on a lower side, considering that the catalytic inserts, made of anodized alumina, were highly porous.
This may be attributed to catalyst sintering or to the fact that
heat losses through the mechanical fittings and sidewalls (third
dimension, into the plane of the paper) were neglected in the
model. One could potentially use an even higher value of ECads
3 H8
in conjunction with a larger (and arguably a more physically
reasonable) value of . Nevertheless, Fig. 5 indicates that the
values of ECads
= 4.0 kcal/mol and = 1.7 are good estimates
3 H8
for reasonable description of experimental data. Based on these
results, the values of ECads
=4.0 kcal/mol and =1.7 are used
3 H8
in the remainder of this paper.
4. Effect of materials choice
4.1. Role of reactor wall thermal conductivity in stability
Figs. 6a and b show the critical values of heat loss coefficient for stable catalytic combustion as a function of wall thermal conductivity. Starting with a stable steady state solution
1104
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
120
1400
No spreader
100
Heat loss coefficient, h∞ (W/m2/K)
Wall temperature, Ts (K)
1200
1000
Cu spreader
800
Steel spreader
= 0.95
80
B
60
= 0.75
A
C
= 0.6
40
20
Catalytic region
0
600
1.0
2.0
3.0
4.0
Axial distance, x (cm)
5.0
6.0
Fig. 5. A comparison between experimental axial temperature profiles
(symbols) of Norton et al. (2006) and model predictions (lines) of
near-stoichiometric mixtures at an inlet flow rate of 2.0 SLPM. The reactor
was 6 cm long, with a gap size of 300 m separating the 790 m steel walls
and optional steel or copper thermal spreaders.
for certain sets of parameters, we perform a natural parameter
continuation by increasing the heat loss coefficient until a turning point is reached, beyond which the device quenches. Each
such turning point is represented with a symbol and the locus
(a two-parameter bifurcation diagram) of such critical points
delineates the region of stable self-sustained combustion (stable below each curve and not stable above). Fig. 6a plots stability curves for different fuel equivalence ratios at u0 = 0.5 m/s,
whereas Fig. 6b plots stability curves for different inlet velocities at = 0.75. A detailed discussion on the role of inlet
velocity on device stability (Fig. 6b) is deferred until the next
section.
The device stability increases on increasing the equivalence
ratio toward the stoichiometric point, as expected. The two
solid lines with circular symbols in Fig. 6a are the stability curves for = 0.75: open and filled circles representing
catalytic and homogeneous combustion, respectively. Clearly,
Pt-catalyzed single channel microburners are significantly more
stable than their homogeneous counterparts. Catalytic combustion can be sustained at large amounts of heat losses (either to
the surroundings or to an endothermic device integrated with the
microburner). For many operating conditions, a heat transfer
coefficient in the forced convection is entirely feasible, making
catalytic devices practically useful.
Our previous work revealed that the walls play a dual role
in determining the stability of homogeneous microburners:
they are responsible for heat losses as well as the heat recirculation via wall conduction required for preheating the
cold fuel–air stream to the ignition temperature (Kaisare
and Vlachos, 2006, Norton and Vlachos, 2003, 2004). In
100
u0=1 m/s
Heat loss coefficient, h∞ (W/m2/K)
0.0
= 0.75
Gas-phase
80
u0=2.5 m/s
u0=0.5 m/s
60
40
u0=5 m/s
20
0
10-1
100
101
Wall conductivity, ks (W/m/K)
102
Fig. 6. Critical values of heat loss coefficient for stable catalytic propane–air
combustion vs. wall thermal conductivity for (a) different equivalence ratios
at u0 = 0.5 m/s and (b) different inlet velocities at = 0.75. The symbols
denote turning points and the lines guide the eye. The filled symbols represent
stability limits for homogeneous (gas-phase) combustion. The letters (A, B,
and C) denote cases of three conductivities analyzed in Figs. 7 and 8.
homogeneous microburners, walls made with materials of
moderate thermal conductivities (such as ceramics, with ks ∼
2.10 W/m/K) provide maximum stability (see solid circles in
Fig. 6a). We have previously identified two modes of stability loss: microburner extinction at higher wall conductivities
(ks 10 W/m/K) due to greater heat losses, and flame blowout
at lower wall conductivities due to insufficient heat recirculation. In fact, homogeneous combustion is not sustainable
even in an adiabatic microburner at very low values of wall
conductivity.
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
1400
0.05
Lines: Gas Tg
1200
Temperature (K)
A:ks = 0.1 W/m/K
1000
0.04
0.03
0.02
0.01
0.1
Reaction rate (mol/m2/sec)
C3H8 mass fraction
Symbols: Wall Ts
0
800
1105
A: 0.1 W/m/K
0.08
0.06
rcat
0.04
B: 2 W/m/K
0.02
YC3H8
Ys,C3H8
rcat
0
C: 200 W/m/K
YC3H8
Ys,C3H8
600
C: ks = 200 W/m/K
0.0
B: ks = 2 W/m/K
400
rcat
0.2 0.4 0.6 0.8
Axial distance, x (cm)
1.0
YC3H8
0.0
0.2
0.4
0.6
Axial distance, x (cm)
0.8
1.0
Fig. 7. Axial profiles of wall (symbols) and gas (lines) temperatures near
extinction for the three different wall conductivities, corresponding to the
three cases marked in Fig. 6a. Temperature gradients near the entrance of the
reactor highlight the role of external heat transfer and its effect on stability.
Unlike the homogeneous case, catalytic combustion can be
sustained at very low values of wall conductivity. The overall
bell-like shape is still seen in Fig. 6a and the maximum appears to shift to higher wall thermal conductivity values with
decreasing equivalence ratio. As the wall conductivity increases
from low values, the reactor stability first increases, due to enhanced heat recirculation, and then decreases, due to higher heat
dissipation and heat losses through highly conducting walls.
The highest allowed heat transfer coefficient occurs for more
insulating materials in catalytic microburners in comparison
to homogeneous ones. While the heat loss–heat recirculation
tradeoff is observed in the catalytic microburner as well, a clear
demarcation between extinction and blowout does not exist. The
lower effective activation energy for propane catalytic combustion results in a more spread-out reaction zone than the corresponding gas-phase counterpart. Blowout occurs because the
upstream cooling of the hot reaction zone by the incoming cold
feed progressively pushes the hotspot downstream until it exits
the reactor. Due to the lower ignition temperature of catalytic
combustion, the impact of upstream cooling is not as critical as
in the homogeneous case. Additionally, as discussed below, the
microburner is diffusion-limited at lower wall conductivity; the
effect of upstream cooling is, therefore, even less important.
4.2. Role of reactor wall thermal conductivity in performance:
hot spots and fuel conversion
In order to understand the stability discussed above and the
role of materials in performance, Fig. 7 compares the axial temperature profiles for the three cases, marked in Fig. 6a, which
differ in wall conductivity. Fig. 8 shows the corresponding
Ys,C3H8
Fig. 8. Propane mass fraction in bulk-gas (solid lines) and near the surface
(symbols), and catalytic reaction rate (dashed lines) at the extinction limits for
the three cases marked in Fig. 6a. The scales (depicted in the top, left corner)
are the same for all three graphs. The reactor becomes more mass transfer
limited at lower wall thermal conductivities. Nearly complete conversion
occurs only for very low conductivity materials for these conditions.
propane mass fractions and the surface reaction rates. At very
low wall thermal conductivities (case A), a localized hot spot
is observed and the reaction rates are much higher near this
hot spot. This is obviously an undesirable situation from the
thermal point of view. The wall temperature drops rapidly in
the post-reaction zone due to heat losses, resulting in quenching of surface reaction. Overall, nearly complete conversion of
propane is found (desirable) due to fast rates near the first half
of the reactor. As the wall conductivity increases (case B), the
maximum temperature at the hot spot decreases but some temperature non-uniformity is still observed. Increased axial heat
recirculation through the walls moves the reaction zone upstream, resulting in higher stability than case A. Upon further
increase of the wall thermal conductivity (case C), the maximum wall temperature drops further and the wall temperature
becomes uniform. The temperatures in this case are ideal for
coupling with energy generation devices, such as higher temperature thermoelectrics. The maximum surface reaction rate
is now much lower, which results in decreased stability (compare case C to B in Fig. 6a). The critical heat loss coefficient
is higher in case B than the other two cases; the last one-third
of the reactor goes unutilized, in spite of incomplete propane
conversion, due to low wall temperatures, as seen in Fig. 8B.
In contrast, the uniform wall temperature in case C allows the
entire length of the reactor to be utilized in propane conversion.
At intermediate wall conductivities (e.g., ks = 20 W/m/K), the
reactor behavior is qualitatively similar to the high wall conductivity case. In both cases B and C, propane conversion is
not complete.
Our simulations and experiments in Fig. 5 indicate that materials of high conductivity (metals and some ceramics) are
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
capable of eliminating hot spots and provide nearly isothermal
wall conditions despite running very fast combustion chemistry
under non-diluted conditions. This finding is an important one
for robust catalyst and reactor performance and for determining kinetics from experiments. A major difference of catalytic
microburners from homogeneous ones is that the much higher
allowed heat loss coefficients result in much lower device temperatures that are a prerequisite for long-term stability of catalytic and housing materials. Our results regarding the effect of
materials have obvious implications not only for microburners
but also for monoliths and scaled-out microdevices (the latter
operate more closely to adiabatic conditions than a single channel considered here, i.e., the effective heat loss coefficient is
much lower in an ensemble of microsystems).
80
Low
conversion
Heat loss coefficient, h∞ (W/m2/K)
1106
Conversion > 95%
60
40
Tmax < 1500 K
20
4.3. Operation diagram
Microburner stability is not the only one that determines the
choice of reactor design and operating conditions. We have
addressed this issue previously in integrated gas-phase microburners coupled with ammonia crackers producing hydrogen
(Deshmukh and Vlachos, 2005). High propane conversion and
low device temperature (to ensure material stability) are important performance factors. Propane conversion in excess of
95% and a maximum wall temperature of 1500 K are taken as
reasonable (albeit arbitrary) thresholds in this work.
Generally, both propane conversion and the maximum wall
temperature decrease as the heat loss coefficient increases along
a vertical operating line of Fig. 6. This is the case when the
microburner is exposed to lower environmental temperatures
or coupled to a strongly endothermic reaction or a thermoelectric element removing heat at an increasing rate. Conversely,
as the system becomes more adiabatic, such as in a monolith
or a scaled-out microchemical system, one gets the benefit of
higher fuel conversion at the risk of higher temperatures. Fig. 9
presents an operation map for u0 = 1 m/s and = 0.75. The
thick line represents the stability limit, with symbols denoting turning (quenching) points; the two thin lines represent
the contours of 95% propane conversion and of a maximum
wall temperature of 1500 K. The shaded region between the
two curves is the operation region that satisfies both combustion efficiency and material stability criteria. For higher heat
loss coefficients than the upper boundary, conversion drops; for
lower heat loss coefficients than the lower boundary, temperatures become too high. The operation region is very narrow
at low wall conductivities and expands significantly for ceramics (ks ∼ 2.10 W/m/K) and metals (ks ∼ 20 W/m/K and
higher).
Obviously, these boundaries can be manipulated for each
material by, for example, changing residence time and/or
equivalence ratio. Thus, the main lesson from this diagram is
the concept that should be considered in design rather than
the numbers themselves. The corresponding figures for higher
velocities and equivalence ratios are skipped for brevity. As a
summary, we have found that the operation region shrinks at
higher velocities, due to lower conversions, as well as at higher
equivalence ratios, due to material stability issues.
Stability limit
High temperatures
0
10-1
100
101
Wall conductivity, ks (W/m/K)
102
Fig. 9. Operation map for propane–air catalytic combustion on Pt at u0 =1 m/s
and = 0.75. Thin top and bottom lines are contours for 95% propane
conversion and maximum device temperature of 1500 K, respectively. The
shaded region is the operation region that satisfies both propane conversion
and material stability requirements.
4.4. Heat and mass transfer limitations
There are several ways to characterize external heat and mass
transfer limitations and their effect on microburner stability. A
simple one is to determine the difference between bulk and surface quantities (driving forces). The larger the difference, the
more important the corresponding transport limitation is. Our
results in Fig. 8 indicate that there are substantial mass transfer
limitations, especially in the reactor entrance despite the small
gap size. This is in part due to the fast combustion kinetics that
renders the system transport-limited. The microburner tends to
be mass transfer limited at lower conductivities, where temperatures and intrinsic reaction rates are higher, and shifts toward
surface reaction limited at higher wall conductivities, where
temperatures and intrinsic reaction rates are lower.
Transverse temperature gradients are seen in Fig. 7 for all
material conductivities, especially near the entrance. This indicates that the upstream compartment connected to the microreactors needs to be considered for quantitative modeling since
this will affect preheating of reactants. The relative difference
between the wall and fluid temperatures in Fig. 7 suggests that
heat transfer affects stability over the entire range of wall conductivities.
In order to isolate the roles of transverse heat and mass transfer, Fig. 10 compares the stability of the actual microburner to
two hypothetical cases of infinitely fast heat or mass transfer
(simulated by increasing either Nu or Sh number, respectively,
to a very large value of 105 ). Note that the vertical scale is
linear, so the effect of heat transfer is as important (or more)
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
than that of mass transfer at low wall conductivities. Transverse heat transfer affects stability over the entire range of wall
conductivities, but less so at intermediate wall conductivities.
Increasing the heat transfer rate decreases reactor stability because greater heat transfer is tantamount to increasing the heat
loss from the reactor walls to the fluid. Unlike gas-phase microburners, where the gas gets hot via combustion and heats
up the wall, in catalytic combustion the heat is released at the
wall and is transferred to the combustible mixture. As a result,
heat transfer occurs mainly from the wall to the gas (except
for small opposite gradients downstream; see Fig. 7) and heat
loss not only to the surroundings but also to the fluid itself is
important.
In contrast to heat transfer, increasing the mass transfer rate
increases reactor stability due to an increase in the effective
reaction rate. The effect is small at higher wall conductivities,
consistent with the gradients in mass fractions seen in Fig. 8. For
more insulating walls, mass transfer becomes more important;
320
Heat loss coefficient, h∞ (W/m2/K)
240
200
Sh = ∞
160
120
80
Actual
40
Nu = ∞
10-1
in the limiting case of Sh=∞ and ks =0.1 W/m/K, the reactor
is extremely stable because reactants diffuse “instantly” to the
catalytic surface and the hot reaction zone is isolated since the
heat released does not get axially dissipated.
Time scales analysis, shown in Table 3, was conducted to
obtain trends and better rationalize our results. The time scales
for diffusion (of heat or species) between bulk-gas and wall
and for reaction are given by
100
101
Wall conductivity, ks (W/m/K)
102
Fig. 10. Effect of transverse heat and mass transfer on stability. Inlet conditions: u0 = 0.5 m/s and = 0.75.
d2
4D
diffusion =
(13)
and
reaction =
Cg,C3 H8
rcat (T̄ , Yg,C3 H8 ).âg
,
(14)
respectively. We use only diffusivity for these approximate estimates since its value is similar to that of thermal diffusivity.
The catalytic reaction rate is computed using Eq. (11) assuming
no transverse transport resistances, i.e., at a weighted average
temperature:
T̄ =
280
1107
(bw s cs Ts + d/2c̄p Tg )
,
bw s cs + d/2c̄p
and bulk-gas conditions for propane and oxygen (Yg,k ). These
time scales as well as the residence time in the reactor are computed at a point located 1.5 mm from the reactor entrance. This
location is sufficiently downstream to allow preheating of the
reacting mixtures, but not too far downstream where the reaction has proceeded to completion. Note that the residence time
reported in Table 3 is lower than the residence time computed
at the reactor entrance because the velocity increases with increasing temperature and due to the volumetric increase caused
by the reaction.
The analysis indicates that the heat and mass diffusion time
scales are within an order of magnitude to the reaction time
scales, implying that close to the stability limits, there is a strong
interplay of kinetics and transport. It is expected that transport
limitations will be more severe away from extinction points
where chemistry is typically faster. In addition, two trends are
obvious: transport limitations become more important at lower
wall conductivities and faster flows. The latter aspect will be
discussed below. An important take-home message is that for
Table 3
Residence time, time scale of transverse diffusion, and reaction time scale computed at 1.5 mm from the reactor inlet for various cases marked with letters in
Figs. 6 and 11
Case
Residence time
diffusion
reaction
diffusion
reaction
A
B
C
ks = 0.1
ks = 2
ks = 200
5.4
6.9
8.4
0.9
1.3
1.8
0.1
0.6
3.7
8.5
2.1
0.5
D
E
F
u0 = 0.1
u0 = 1
u0 = 5
45
3.8
1.5
2.1
1.5
5.0
21
0.6
0.8
0.1
2.5
6.2
The time scales are in ms, the wall conductivity in W/m/K, and the inlet velocity in m/s. See main text for details.
1108
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
fast chemistries, such as catalytic combustion, transverse transport effects in microreactors may still be significant.
Residence time (s)
10
-1
5. Effect of inlet velocity
= 0.75
ks = 2
80
5.2. Heat and mass transfer limitations
As before, three critical points are marked in Fig. 11 for
analysis: (D) extinction at low inlet velocity due to insufficient
heat generation; (E) extinction at moderate inlet velocity due to
large heat losses; and (F) blowout due to insufficient residence
time. Fig. 12 shows temperature profiles and Fig. 13 shows
species profiles along with catalytic reaction rates. The amount
of chemical power input into the system depends linearly on
Heat loss coefficient, h∞ (W/m2/K)
5.1. Microburner stability limits
10-3
10-4
E
60
F
= 0.75
ks = 20
40
20
= 0.6
ks = 20
D
0
10-1
100
101
Inlet velocity, u0 (m/s)
102
Fig. 11. Critical values of heat loss coefficient for stable catalytic propane–air
combustion as a function of inlet velocity, u0 , or inlet-based residence time
for different values of wall thermal conductivity (in W/m/K) and equivalence
ratio. The letters denote cases analyzed in Figs. 12 and 13.
1100
F: u0=5 m/s
900
Temperature (K)
The inlet velocity affects both the residence time and the
power input into a microburner via controlling the feed flow
rate. As the inlet flow velocity increases, the residence time
decreases but the power input increases. As a result, a maximum in stability may be expected. The flow velocity has
indeed a profound effect on the stability of catalytic microburners, changing both the quantitative values and the qualitative
trends of the critical heat loss coefficient vs. wall conductivity
curves in Fig. 6b. The stability curves at lower velocities (e.g.,
u0 = 0.5 m/s) are bell-like shaped due to a tradeoff between
heat recirculation and heat dissipation, as described in the previous section. At higher velocities (e.g., u0 = 2.5 m/s), the stability curves are qualitatively different though. Specifically, at
higher velocities, the region of stable combustion monotonically increases with increasing wall thermal conductivity. The
residence time in the reactor is no longer sufficient for complete
propane combustion and the reaction zone shifts downstream
with increasing flow velocity. More conducting walls recirculate heat in the reactor and preheat the incoming gases, moving
the reaction zone upstream and increasing the effective reaction rate. Unlike lower velocities, there is now enough propane
feed to overcome the larger heat losses encountered at higher
wall conductivities. Overall, lower flow velocities are preferred
for low conductivity walls whereas an optimum velocity exists
for highly conductive walls.
Fig. 11 depicts the critical heat loss coefficient vs. inlet
velocity for different wall conductivities and equivalence ratios indicated. The inlet-based residence time is also indicated.
The leaner the propane–air mixture, the less stable the microburner is. Like the homogeneous case (Kaisare and Vlachos,
2006), these curves display a typical bell-like shape: loss of
microburner stability occurs due to low power input in the lowvelocity arm and to short residence time in the high-velocity
arm. At a fixed equivalence ratio, insulating walls (e.g., ks =
2 W/m/K) improve stability in the low-velocity arm, due to
lower heat dissipation, whereas more conducting walls (e.g.,
ks = 20 W/m/K) improve stability in the high velocity branch,
due to higher axial heat recirculation. Further increase of the
wall conductivity beyond ks = 20 W/m/K results only in a
marginal change of extinction limits (data not shown).
10-2
E: u0=1 m/s
700
D: u0=0.1 m/s
F: u0=5 m/s
500
Symbols: Wall T
Lines: Gas T
300
0.0
0.2
0.4
0.6
Axial distance, x (cm)
0.8
1.0
Fig. 12. Axial profiles of bulk-gas (lines) and wall (symbols) temperatures
for the three cases marked in Fig. 11 ( = 0.75, ks = 20 W/m/K). The
wall temperature increases with inlet velocity due to a higher amount of
fuel supplied per unit time. The bulk-gas temperature approaches the wall
temperature further upstream at lower velocities due to higher residence time.
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
0.03
0.02
0.01
Residence time (s)
rcat
10
1800
0.064
0.048
0.032
0.016
0
0
-1
10
-2
10-3
10-4
YC3H8
E: 1 m/s
rcat
Ys,C3H8
F: 5 m/s
YC3H8
D: 0.1 m/s
YC3H8
Ys,C3H8
0.0
0.2 0.4 0.6 0.8
Axial distance, x (cm)
Max. wall temperature (K)
0.04
0.08
Reaction rate (mol/m2/sec)
C3H8 mass fraction
0.05
1109
1500
1200
= 0.6
ks = 20
900
1.0
= 0.75; ks = 2
600
1
Ys,C3H8
rcat
the inlet velocity. Hence, at low inlet velocities (case D), the device temperature is low resulting in a low reaction rate. Under
these conditions, the gradients between bulk-gas and surface
propane mass fractions are small and the system is surface
reaction limited due to the slow chemistry (short diffusion
time compared to reaction time; see Table 3) resulting from low
surface temperatures. Due to high residence times, the fuel is
completely converted.
As the inlet velocity increases (case E), the temperature rises
owing to the higher power input, and the rate of catalytic reaction increases. For faster flows, the gradients between gas
and surface temperatures are substantial and the incoming cold
feed starts pushing the reaction zone downstream. In case E,
although the maximum in the reaction rate is downstream, it is
still well within the reactor and the reaction proceeds to completion. The higher power input results in increased stability,
and high heat losses are the primary cause of stability loss. At
a still higher velocity of u0 = 5 m/s (case F), the residence time
is lower than the diffusion time (see Table 3), resulting in poor
transverse mass transport and, thus, in incomplete propane conversion. The region of maximum reaction rate is pushed toward
the reactor exit; any further increase in the external heat loss
coefficient results in blow out of the reaction zone and quenching of the device.
We conclude our analysis by noting that the variation from a
surface reaction limited regime to a mass transfer limited regime
on increasing the inlet velocity (keeping all other parameters
constant) is a unique feature of catalytic microcombustion (it
does not have an analogue in homogeneous microburners). Interestingly, even in 600-m gap reactors (nominal case studied
= 0.75; ks = 20
0.8
Propane conversion
Fig. 13. Axial profiles of propane mass fractions in the bulk-gas (solid lines)
and near the surface (symbols), and rates of catalytic reaction (dashed lines)
for the three cases marked in Fig. 11 ( = 0.75, ks = 20 W/m/K). Close to
the turning points, the reactor is kinetically limited at low inlet flow velocities
(case D) due to lower temperatures and diffusion limited at higher velocities
(cases E and F). The reaction zone gets blown out at high velocities (case F).
= 0.75
ks = 20
= 0.6; ks = 20
0.6
0.4
= 0.75, ks = 2
0.2
Symbols: Burner extinction
0
10-1
100
101
Inlet velocity, u0 (m/s)
102
Fig. 14. (a) Maximum wall temperature and (b) propane conversion vs.
inlet velocity or inlet-based residence time for different wall conductivities
(W/m/K) and fuel equivalence ratios. Symbols (whenever shown) represent
turning points for stable combustion. Propane breakthrough (conversion less
than 95%) is observed for an inlet velocity of u0 > 2 m/s due to insufficient
residence time. Shaded regions indicate an approximate range ensuring low
temperatures (a) and high conversions (b). In panel a, the shaded region, to
the left of the vertical dotted line, indicates the flow range within which both
requirements are met.
so far), transverse mass transfer limitations are significant
for fast chemistries under most operating conditions. This
observation has important ramifications for experimental burner
design, and possible extraction of reaction kinetics from data.
5.3. Microburner efficiency and operating temperatures
Fig. 14 shows the variations in the maximum wall temperature and propane conversion as a function of inlet velocity
for different equivalence ratios and wall thermal conductivities, at a fixed heat loss coefficient of h∞ = 20 W/m2 /K. This
corresponds to a horizontal operating line (at h∞ = 20) along
Fig. 11. The symbols (whenever shown) at the ends of the
curves indicate critical conditions beyond which operation is
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
6. Effect of reactor length
Changing the reactor length at a constant inlet velocity
changes the residence time as well as the total area available
for heat loss to the surroundings. The effect of heat loss was
dominant in homogeneous microburners, primarily because
the reaction zone was localized, resulting in longer reactors
exhibiting decreased stability (Kaisare and Vlachos, 2006). In
catalytic microburners, the reaction zone can possibly span
the entire length of the reactor (for example, see Fig. 13).
As a result, increasing the reactor length can potentially lead
to increased stability. In this section, we study the roles of
increased catalyst area and heat losses, because of increasing
reactor length, in microburner design.
6.1. Microburner stability
The effect of reactor length on stability curves of critical
heat loss coefficient vs. wall thermal conductivity is shown in
Fig. 15. In Fig. 15a, the inlet velocity and thus the power input
80
70
Heat loss coefficient, h∞ (W/m2/K)
impossible. Under most conditions, the temperature exhibits a
bell-like shape with an expected maximum. For fast flows, the
curves are close to each other, indicating that the limiting factor is the short residence time and the wall conduction time is
sufficiently large. On the other hand, on the left arm of Fig. 14a
(low flow velocities), the residence time is long and the conduction time scale is important: higher equivalence ratios and
lower conductivities lead to higher temperatures as expected.
The collapse of all three curves in Fig. 14b indicates that
the conversion depends mainly on residence time with the exception of the stability limits, i.e., the minimum and maximum
flow velocities delimiting stable operation. These limits depend
on composition and wall material. At low inlet flow velocities
(flat part of curves), as far as the flow provides enough heat to
cope with heat losses, the propane conversion is complete and
independent of the wall thermal conductivity, equivalence ratio, and residence time. The inlet residence time required for
95% fuel conversion is approximately 6 ms, corresponding to
an inlet velocity of ∼ 1.7 m/s. This requires that we should
primarily operate the catalytic combustor in the left branch of
the bell-curve of Fig. 11a. Since this branch corresponds to
the heat-loss-governed extinction of the microburner, insulating walls (e.g., ks = 2 W/m/K or lower) allow greater device
stability than conducting walls (ks = 20 W/m/K or higher).
However, the maximum wall temperatures in devices of insulating walls exceed the material stability threshold of 1500 K
due to hot spot formation.
The shaded regions in Figs. 14a and b are regions that satisfy the material stability limits and the combustion efficiency
requirements, respectively. The range of flow for which both
requirements are met is to the left of the vertical dotted line
in panel a. This operation window is approximate since it depends slightly on wall conductivity and equivalence ratio. The
operation window for the catalytic microburner of nominal dimensions is quite narrow. Hence, we next consider the effect
of microburner dimensions on its stability.
60
l = 1 cm
50
l = 2 cm
40
30
l = 4 cm
20
10
0
80
l = 2 cm
70
Heat loss coefficient, h∞ (W/m2/K)
1110
60
50
l = 1 cm
40
l = 4 cm
30
20
10
0
10-1
100
101
Wall conductivity, ks (W/m/K)
102
Fig. 15. Effect of reactor length on the critical heat loss coefficient for =0.75
at (a) a constant inlet velocity of u0 = 0.5 m/s and (b) a constant residence
time of 20 ms. As the reactor length varies, the residence time changes in
panel a and the power input changes in panel b.
into the system are kept constant as the length varies. Increasing
the reactor length has no effect on the stability of microburners
with highly insulating walls. At very low wall conductivities,
the temperature in the post-reaction zone drops significantly
due to heat losses and the chemistry is completed upstream
(see Figs. 7 and 8 and related discussion); increasing reactor
length causes no additional heat loss. As the wall conductivity
increases, the axial wall temperature becomes uniform and heat
losses occur through the entire reactor length. As a result, the
critical heat loss coefficient decreases on increasing the reactor
length for highly conducting materials, i.e., microburners made
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
6.2. Microburner efficiency and operating temperatures
The maximum wall temperature and propane conversion vary
with inlet velocity for a fixed heat loss coefficient and different
lengths as depicted in Fig. 17. These simulations correspond to
a horizontal operating line (at h∞ =20 W/m2 /K) along Fig. 16.
At lower inlet velocities, nearly complete propane conversion
is obtained for all the three reactor lengths. Due to the greater
heat losses, the temperatures are slightly lower in the longer
microburners, resulting in slight breakthrough (note the diamond in Fig. 17b). As the propane velocity increases, propane
breakthrough is observed for the shortest reactor, whereas the
longer reactors still exhibit complete propane conversion. On
the right branch of the graph, the reactor length plays a more
important role; however, conversions are incomplete.
Residence time (s)
-1
10-2
10
10-3
10-4
80
70
Heat loss coefficient, h∞ (W/m2/K)
of highly conducting walls exhibit substantially reduced stability the longer they are. This behavior is consistent with our
previous conclusion that larger heat losses through highly conducting walls are responsible for decreased microburner stability. Additional calculations for higher inlet flow velocities (e.g.,
5 m/s), where breakthrough may be expected, indicate that the
effect of reactor length is even less pronounced than that shown
in Fig. 15a (curves are closer together; data not shown) due to
a shift of the bell-like stability curves toward higher conductivities.
Fig. 15b shows the effect of reactor length at a constant
residence time of 20 ms. As the reactor length increases, so
does the inlet velocity. Thus, the total power input into the reactor increases and offsets the higher heat losses through the
longer reactor walls. The heat recirculation–heat loss tradeoff that results in a non-monotonic nature of the critical heat
loss vs. wall conductivity curve is observed in all cases under
these conditions. The optimal wall conductivity for maximum
stability—at which the effects of greater heat loss/dissipation
outweigh the effects of greater heat recirculation—shifts toward
a higher value as the reactor length is increased. The higher inlet
velocity in the longer reactors pushes the reaction zone downstream. This shift in the optimal wall conductivity originates
because a greater amount of heat recirculation is required to
preheat the cold incoming gases and keep the reaction zone
upstream. Consequently, at a constant residence time, shorter
reactors are more stable at lower wall conductivities, because
insulating walls do not provide sufficient heat recirculation to
stabilize higher velocity flows in the longer reactors. On the
other hand, longer reactors are more stable at higher wall conductivities, because the higher power input results in a higher
heat generation to counterbalance the increased heat losses that
are responsible for device extinction.
Finally, Fig. 16 shows that the shorter reactors are more
stable in the heat-loss-governed extinction branch of the critical
heat loss coefficient vs. inlet velocity curve. On the other hand,
longer reactors provide a longer residence time, and are more
stable in the right branch of the curve, wherein the residence
time is lower than the diffusion time scale. Overall, the effect
of reactor length on the heat loss–velocity stability graph is not
dramatic.
1111
60
50
40
30
20
l = 2 cm
l = 1 cm
l = 4 cm
10
ks = 20 W/m/K
0
10-1
100
101
Inlet velocity, u0 (m/s)
102
Fig. 16. Effect of reactor length on critical heat loss coefficient vs. inlet
velocity curves at a constant wall thermal conductivity of ks =20 W/m/K and
= 0.75. The inlet-based residence time is also shown on the top horizontal
axis.
The above results for different reactor lengths collapse on
a single curve when plotted vs. residence time, as shown in
Fig. 17c. The symbols (whenever shown) represent the critical
residence time for microburner quenching. The propane conversion is a strong function of the residence time. The range
of residence times that provide > 95% propane conversion
increases with increasing reactor length from 5–40 ms for a
1-cm-long reactor to 5–150 ms for a 4-cm-long reactor.
Similar trends of maximum wall temperature, propane
conversion, and reactor stability are also observed at lower values of equivalence ratio for different reactor lengths (data not
shown). Given that operation should happen on the left arm of
Fig. 16, our analysis suggests that there is no dramatic effect
of reactor length on performance. The optimum reactor length
depends on material (Fig. 15) with longer reactors exhibiting
a larger range of operation with complete propane conversion.
Materials stability becomes an issue at intermediate flow velocities (close to the maximum of Fig. 17a) due to higher wall
temperatures; however, the equivalence ratio can be adjusted
to achieve lower device temperatures.
7. Effect of gap size
According to Eq. (8), the heat and mass transfer coefficients
increase linearly with decreasing gap size. The former transport reduces and the latter increases microburner stability (see
Fig. 10). Additionally, as the gap size decreases, the power input decreases at a constant inlet velocity. Alternatively, for a
constant power input (i.e., a constant volumetric flow rate), the
1112
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
80
1800
l = 4 cm
l = 1 cm
l = 2 cm
900
ks = 20 W/m/K
h∞ = 20 W/m2/K
600
1
l = 2 cm
0.8
Propane conversion
Heat loss coefficient, h∞ (W/m2/K)
1200
d =1200 μm
60
d = 600 μm
50
40
d = 300 μm
30
20
d = 150 μm
10
l = 1 cm
0
1
l = 4 cm
120
0.6
0.8
0.6
0.4
100
0.4
l = 1 cm
l = 2 cm
l = 4 cm
0.2
0.2
0
10-1
0
10-1
0
1
10
10
10
Residence time (ms)
2
100
101
Inlet velocity, u0 (m/s)
102
Fig. 17. Effect of reactor length on (a) maximum wall temperature and (b)
propane conversion vs. inlet velocity. The inset (panel c) plots the propane
conversion vs. residence time for the three different reactor lengths. The
symbols represent critical turning points beyond which the burner quenches.
The parameters are: ks = 20 W/m/K, h∞ = 20 W/m2 /K, and = 0.75.
Heat loss coefficient ,h∞ (W/m2/K)
Max. wall temperature (K)
70
1500
80
d = 600 μm [10 ms]
60
d = 1200 μm [20 ms]
40
d = 150 μm [2.5 ms]
20
0
10-1
inlet velocity increases and the residence time decreases with
decreasing gap size. In this section, we delineate these competing effects by investigating the role of gap size.
Fig. 18a shows stability curves for various gap sizes at a
fixed inlet velocity. Microburners of high wall conductivities are
more stable when they have wider gaps. Under these conditions
where heat loss through the conducting walls dominates, the
increased power input for the wider gaps, in conjunction with
the reduced heat transfer from the hot walls to the cold gases
dictate the effect of gap size on reactor stability. On the other
hand, at lower wall conductivities, narrower microburners are
more stable. In spite of the lower power input, the higher mass
transfer rates substantially improve the stability of reactors of
lower gap size.
Fig. 18b compares the microburner stability for the alternative strategy of keeping the inlet flow rate constant (which results also in a constant Reynolds number in the parallel plate
geometry). A width (third-dimension) of 1 cm is arbitrarily assumed to compute the flow rate. The narrower reactors operate
d = 300 μm
[5 ms]
100
101
Wall conductivity, ks (W/m/K)
102
Fig. 18. Locus of stability for different gap sizes for the same (a) inlet velocity
(u0 = 0.5 m/s) and (b) inlet flow rate (360 sccm for a burner 1-cm wide) with
= 0.75. The numbers in square brackets represent the respective inlet-based
residence times in ms. In (a), larger gap reactors are favorable at higher wall
conductivities due to both the larger power input and the reduced heat transfer
from the hot walls to the cold gases. Higher mass transfer renders smaller
gap size reactors more stable at low conductivities. At a fixed feed rate (panel
b), narrower reactors are favorable for most practical wall materials.
with lower residence times due to an increase in the inlet velocity. Analysis similar to that shown in Fig. 10 indicates that at
lower residence times, the effect of mass transfer is even more
profound even at high conductivities (not shown). The same
conclusion was reached from the time scale analysis shown in
Table 3 for the nominal sized reactor. While the time scales of
heat and mass transfer between the wall and the fluid decrease
with shrinking gap size, the time scale of heat loss to the surroundings remains unchanged. As a result, at very high wall
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
1800
Max. wall temperature (K)
gap size, indicating that the power input is the limiting factor
and diffusion is not critical. After the maximum temperature is
reached, the conversion starts dropping with further increase in
the flow rate. It is near the maximum temperature and on the
right arm where the gap size plays an important role. Specifically, the conversion significantly increases on reducing the gap
size to 300 m (or lower), as compared to the nominal reactor
size. Further decreasing the gap size provides only a moderate increase in the region of stable combustion (Fig. 18b) or
in the operation region (Fig. 19). Shrinking of reactor gap size
comes at the cost of increased pressure drop and higher operating temperatures. Based on the results presented here, gap sizes
in the range of 100.200 m are pragmatic choices for standalone catalytic microburners of propane on Pt, in contrast to
the 600.1000 m range for the homogeneous (non-catalytic)
counterparts (Kaisare and Vlachos, 2006).
150 μm
300 μm
1600
1400
1200 μm
600 μm
1200
1000
800
600
1
150 μm
300 μm
Propane conversion
0.8
1
0.6
0.4
600 μm
0
1200 μm
600 μm
1200 μm
0.2
0.2
8. Conclusions
0.8 300 μm
0.6
0.4
150 μm
101
102
100
Residence time (ms)
0
102
103
Flow rate
1113
104
(cm3/min)
Fig. 19. (a) Maximum wall temperature and (b) propane conversion vs. inlet
flow rate for various reactor gap sizes with ks =20 W/m/K, h∞ =20 W/m2 K,
and = 0.75 (a burner width of 1 cm is assumed to compute flow rates). The
symbols (whenever shown) denote critical points for microburner quenching.
Inset: propane conversion vs. inlet-based residence time for various gap sizes.
conductivities, the narrower gap sizes are more stable primarily due to the increase in the mass transfer rates. This trend
is intuitively expected to continue as the gap size decreases
further, until the diffusion time scale becomes much lower
than the intrinsic reaction time scale; any further decrease in
gap size would not affect the effective reaction rate. However,
Fig. 19a indicates that this may not exactly be the case since
upon reduction of the gap size, the temperature keeps increasing
(at sufficiently fast flows) and so does the intrinsic reaction rate
constant. At very low wall conductivities, on the other hand,
heat recirculation through the insulating walls is not enough to
prevent blowout due to higher velocities in the narrower microburners. As a result, a crossover is observed whereby wider
gaps are more stable.
The effect of reactor gap size on the maximum wall temperature and conversion vs. inlet flow rate is shown in Figs. 19a
and b. On the left arm of the curves, the residence time is
longer than the diffusion and reaction time scales; conversion is
nearly complete and the temperature keeps increasing linearly
with increasing flow rate. The curves are almost independent of
In this paper, we studied the stability and performance of
catalytic microreactors for exothermic reactions. In the first
part of the paper, a computationally efficient pseudo-2D model
was developed to study catalytic combustion and was applied
to propane–air mixtures in Pt-catalyzed microburners. The
catalytic reactions were described by a one-step kinetic model,
obtained recently by a posteriori reduction of a 104-reaction
microkinetic model. The transverse heat and mass transport
were described by Nusselt (Nu) and Sherwood (Sh) number correlations obtained using computational fluid dynamics
(CFD) simulations. Specific results of the first part are as
follows:
• The catalytic microburner can be divided into a preheating,
a reaction, and a post-reaction zone. The preheating and the
reaction zones often overlap.
• The microburner walls play a dual role: they act as a net heat
source in the preheating/reaction zones, and as a net heat sink
in the post-reaction zone. This is similar to homogeneous
microburners with the exception that heat is generated in the
gas (homogeneous) or on the wall (catalytic).
• The Nu number varies as a function of axial distance in a
non-monotonic manner; a sharp discontinuity in Nu number
is associated with the change in the heat source–heat sink
behavior of the wall. The Nu number approaches the constant temperature asymptote of Nu∞ = 3.8 in the preheating/reaction zone, and the constant heat flux asymptote of
N u∞ = 4.15 in the post-reaction zone.
• The Sh number profile is monotonic, with an asymptote of
Sh∞ = 3.8.
• With constant values of N u = 4 and Sh = 3.8, our pseudo-2D
model was able to adequately capture the CFD results at a
significantly lower computational cost. The resulting model
was able to reasonably describe the temperature profiles observed in our prior experimental work.
The thermal conductivity of the reactor solid structure, inlet
velocity, and equivalence ratio have a strong influence on the
1114
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
burner operation. Specific results of this part of our work are:
• Like homogeneous burners, a tradeoff between increased
heat recirculation and heat loss is also observed in catalytic
microburners, resulting in an optimal wall conductivity for
which the critical value of the external heat loss coefficient
for microburner stability is maximum.
• The optimal value of the wall thermal conductivity increases
with increasing velocity. At very high velocities, the microburner stability increases monotonically with increasing
wall thermal conductivity and an optimum material for stability does not exist.
• Transverse mass transfer is more important at low wall conductivities, whereas heat transfer is more important at high
and low wall conductivities. Increasing the mass transfer rate
increases the stability, whereas increasing the heat transfer
rate from the wall to the fluid decreases the stability for the
entire range of wall conductivities.
• The microburner tends to be diffusion limited at low wall
conductivities and/or at high velocities, and surface reaction
limited at low velocities. At intermediate velocities, the diffusion and intrinsic reaction rate are of the same order of
magnitude.
• High wall conductivity results in lower device temperature,
due to better heat dissipation as well as lower conversion,
especially close to extinction.
• Although a lower equivalence ratio leads to a less stable
burner, it provides lower device temperatures, which are important to ensure materials stability.
• The microburner stability exhibits a bell-like shape with increasing inlet velocity; the left arm is controlled from low
power input, it exhibits complete conversion with lower temperatures and is the most desirable operation regime. The
right arm is dominated by low residence times and exhibits
fuel breakthrough.
Finally, we studied the effects of reactor length and gap size
on catalytic microcombustion. The results depend on whether
one keeps fixed the residence time or the power input as the
size varies. The main points are:
• For materials in the range of typical ceramics to highly conductive, longer reactors are more stable at a fixed residence
time and less stable at a constant power input. Smaller gap
sizes lead to enhanced stability for a fixed flow rate (power
input). The opposite is true for a constant residence time.
Higher pressure drops and wall temperatures should also be
considered in choosing a practical (small) gap size.
• For sufficiently low velocities, where conversion is complete (up to the maximum temperature), the effect of reactor
length is small, and the effect of gap size is insignificant.
Longer reactors and/or smaller gaps extend the flow rate region within which complete conversion is possible.
In closing, we note that operation of catalytic microreactors
is controlled via a large number of parameters, including materials, geometric (size), composition, the fuel itself (not studied
here), and flow conditions whose effect often exhibits opposite
trends resulting in optima. Both stability limits and performance characteristics are important and compound the multidimensional operation regime of these inherently complex
systems. A comparison with homogeneous combustion revealed that catalytic microburners are more stable, can operate
with much more insulating materials, and can operate with
lower wall temperatures. While in recent years reaction engineering has mainly focused on mass transfer and kinetics, it is
clear that heat transfer and heat management play a vital role
at small scales.
Notation
â
A0
bw
c̄p
cs
C
d
D
E
h
H
k
k ads
k des
kmt
l
M
Nu
rcat
rgas
s0
Sh
t
T
u
x
X
Y
surface area per unit volume, m2 /m3
pre-exponential factor, s−1
wall thickness, m
specific heat of gas, J/kg/K
specific heat of solid, J/kg/K
concentration, mol/cm3
gap size, m
diffusivity, m2 /s
activation energy, kcal/mol
coefficient of heat transfer/loss, W/m2 /K
heat of reaction, J/mol
thermal conductivity, W/m/K
adsorption rate constant, cm3 /mol/s
desorption rate constant, s−1
mass transfer coefficient, m/s
length, m
molecular weight, kg/mol
Nusselt number
surface reaction rate, mol/m2 /s
gas-phase reaction rate, mol/m3 /s
sticking coefficient
Sherwood number
time, (s)
temperature, K
velocity, m/s
axial coordinate, m
mole fraction
mass fraction
Greek letters
kj
temperature exponent
catalyst site density, mol/cm2
catalyst surface area factor
surface coverage
stoichiometric coefficient of species k in reaction j
density, kg/m3
time scale, (s)
equivalence ratio
Subscripts and superscripts
ads
cat
adsorption
catalyst
N.S. Kaisare et al. / Chemical Engineering Science 63 (2008) 1098 – 1116
cm
des
g
k
ref
s
0
∞
∗
cup-mixing average
desorption
gas phase
species index
reference conditions
solid wall, surface
inlet conditions
external/environmental conditions
vacancies
Acknowledgment
This work was supported by the NSF (CBET-0729701).
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