2. Methods
Recent studies on gas-phase micro-burners and hydrogen production using
homogeneous combustion as an energy supply route have revealed the
feasibility of such an operation, on the one hand, but the
susceptibility of gaseous flames to radical and thermal quenching, on
the other, arising from confining flames in small devices [39, 40].
The high temperatures associated with homogeneous combustion also limit
the choice of materials for device fabrication. Given the small scales
of these devices and the large surface-area-to-volume ratios, catalytic
combustion appears to be a promising alternative to gaseous combustion.
Elimination of flames makes integration into compact devices easier. The
lower temperatures, compared to those in homogeneous combustion,
generated via catalytic combustion can significantly widen the operating
window of these micro-devices [41, 42]. Fuel-lean catalytic
operation can eliminate and carbon monoxide formation, without coking of
the catalyst. Even though catalytic combustion has been studied
intensively, both experimentally and theoretically accurate and reliable
rate expressions for the combustion of alkanes are not readily
available, but are highly desirable for design and optimization studies
of microchemical devices and possible homogeneous-heterogeneous hybrid
systems, namely thermally stabilized combustion [43, 44]. Surface
reaction rates have traditionally been modeled with one-step rate
expressions of a power-law form [45, 46]. Such rate expressions
provide no insight into the physics and their regime of applicability is
ill defined [47, 48]. As a result, the wide scatter in the
parameters is not surprising, making the usefulness of power-law rate
expressions questionable.
Langmuir-Hinshelwood type kinetic rate expressions are used to describe
reaction rates. An advantage of a Langmuir-Hinshelwood type kinetic rate
expression is that reaction orders could vary from positive to negative
as operating conditions change. The assumptions made in
Langmuir-Hinshelwood models rely mainly on intuition or at best on
limited knowledge of reaction energetics. Adequate description of
experimental data via a Langmuir-Hinshelwood model is typically
considered as validation of the assumptions made. If the model fails to
describe data, a different set of assumptions is made and the process is
repeated. This methodology does not necessarily guarantee that the
underlying assumptions are correct and that the derived rate expression
captures the physics of the reaction mechanism over a broad range of
conditions, which is typically delimited by the available experimental
data. Since the coverages of surface species vary considerably with
operating conditions and within the reactor itself, so do the
rate-determining step conditions. Microkinetic models that describe all
relevant elementary reaction pathways are needed to overcome the
limitations discussed above and provide insights into the mechanistic
pathways. A number of microkinetic models are available for simple fuels
on noble metal catalyst surfaces. The foremost challenge in microkinetic
model development is the estimation of kinetic parameters. Computational
fluid dynamics simulations using microkinetic models for design and
optimization are a central processing unit-intensive task. Hence,
reduced kinetic models and one-step rate expressions for the combustion
of small alkanes on noble metal surfaces are desirable. The quest for
better and more efficient catalysts for commercial processes is an
ongoing journey for the chemical industry. Tools such as high-throughput
screening using microreactors are being developed to this end, but
analysis of data from such experiments is challenging. A simple
theoretical model with a few catalyst-based parameters, which can be
estimated from first principles calculations or simple experiments, can
be valuable for catalyst screening.
The combustor pressure in this work is assumed to be constant. This
greatly simplifies the calculations because it means that the momentum
equation does not have to be solved. As a result, a relatively large
number of combustor configurations can be investigated in a reasonable
amount of time. While pressure loss in micro-channels can be an
important performance parameter because of its impact on the efficiency
of thermodynamic cycles, the losses associated with the optimum
combustor configurations identified here are less than a few percent.
Note, however, that pressure losses for combustor configurations away
from the optimum combustor configurations can be much larger and their
accurate determination will require inclusion of the momentum equation.
The use of silicon as a combustor material imposes two additional
constraints on the simulation. The first is that the equivalence ratio
be less than or equal to 0.6 so that the adiabatic flame temperature
remains below the melting point of silicon. The second is that the
temperature dependence of silicon’s thermal conductivity be included.
Silicon’s thermal conductivity changes by more than a factor of 6 over
the expected range of temperatures and is computed using a power law fit
to tabulated data. Six million evenly spaced cells are used to
discretize the gas flow path and structure. The cells are numerous
enough to capture gradients accurately no matter where the flame is
stabilized in the passage. The number of computational cells is kept
constant as the length of the combustor is reduced. Adequate resolution
is verified by checking that doubling the mesh size does not influence
the results of the computations. The reference length scale used here is
the reaction zone thickness associated with a freely propagating flame
that does not interact with a structure. The temperature profile used to
compute the reference length scale is determined by setting the Nusselt
number for heat transfer between the gas and the structure equal to
zero. The reference velocity is the laminar flame speed associated with
a freely propagating flame. It is also computed by setting the Nusselt
number equal to zero. Thermal coupling between the reacting gas and the
structure has important implications for the design of efficient, high
power density combustors. The overall efficiency of a micro-channel
combustor can be written as the product of a chemical efficiency and a
thermal efficiency.
The chemical efficiency is defined as the ratio of the total heat
evolved in the reaction to the total heat available if the reaction is
to go to completion. In this work, this is equivalent to the fraction of
the fuel that gets consumed before the mixture exits the micro-channel.
The thermal efficiency is defined as the ratio of the total heat
actually delivered to the flow exiting the channel divided by the total
heat evolved by the reaction. This is computed from the axial
temperature profile through the micro-channel, the heat loss to the
environment, and the mass flow rate. The power density is defined the
energy release rate due to combustion divided by the combustor volume. A
catalyst is deposited on the inner surfaces of the combustor with
particular attention to the areas of highest interaction with combustion
gases, not the flame or reactants. For catalyst effectiveness, it is
important that the catalyst be located within the combustion zone on the
combustor wall in areas that are not blanketed by film cooling air. As
the combustion zone and film cooling within the combustion zone are
altered due to different operational conditions, it may be necessary to
coat the entire combustor to assure that the catalyst at any given time
is in an effective area. Backside cooled liner walls are preferred since
such systems do not flow significant cool air on the flame tube side of
the wall where the catalyst is applied. While a lean, pre-mixed
combustor that does not utilize film cooling is ideal for this design, a
total elimination of film cooling is not required. It is critical that
if film cooling is employed, that the operational non-film cooled area,
that is the area of the combustor not film cooled at an operational
condition where nitrogen oxides or carbon monoxide reduction is desired.
In addition, it is critical to this design that catalyst cooling,
generally accomplished by backside cooling of the combustor wall onto
which the catalyst is applied, be engineered such that the catalyst is
maintained at an effective operating temperature. This temperature is at
a minimum the threshold light-off temperature for the particular
catalyst interacting with the particular fuel. Typical precious metal
catalysts have minimum operating temperatures of approximately 400 °C.
Thus, with metal liners it is desirable to place the catalyst on a
thermal barrier inner coating which lines the inner surfaces of the
flame tube or combustor liner. The catalyst can be applied directly to
ceramic combustor liners if so equipped.
Catalytically-supported thermal combustion is achieved by contacting at
least a portion of the carbonaceous fuel intimately admixed with air
with a solid oxidation catalyst having an operating temperature
substantially above the instantaneous auto-ignition temperature of the
fuel-air admixture. At least a portion of the fuel is combusted under
essentially adiabatic conditions. Combustion is characterized by the use
of a fuel-air admixture having an adiabatic flame temperature
substantially above the instantaneous auto-ignition temperature of the
admixture but below a temperature that would result in any substantial
formation of oxides of nitrogen. The adiabatic flame temperature is
determined at catalyst inlet conditions. The resulting effluent is
characterized by high thermal energy useful for generating power and by
low amounts of atmospheric pollutants. Where desired, combustible fuel
components, for example, un-combusted fuel or intermediate combustion
products contained in the effluent from the catalytic zone, or fuel-air
admixture which has not passed through a catalytic zone, may be
combusted in a thermal zone following the catalytic zone. Sustained
catalytically-supported, thermal combustion occurs at a substantially
lower temperature than in conventional adiabatic thermal combustion and
therefore it is possible to operate without formation of significant
amounts of nitrogen oxides. Combustion is no longer limited by mass
transfer as in the case of conventional catalytic combustion, and at the
specified operating temperatures the reaction rate is substantially
increased beyond the mass transfer limitation. Such high reaction rates
permit high fuel space velocities which normally are not obtainable in
catalytic reactions. The adiabatic flame temperature of fuel-air
admixtures at any set of conditions is established by the ratio of fuel
to air. The admixtures utilized are generally within the inflammable
range or are fuel-lean outside of the inflammable range, but there may
be instances of a fuel-air admixture having no clearly defined
inflammable range but nevertheless having a theoretical adiabatic flame
temperature within the operating conditions. The proportions of the fuel
and air charged to the combustion zone are typically such that there is
a stoichiometric excess of oxygen based on complete conversion of the
fuel to carbon dioxide and water. The term instantaneous auto-ignition
temperature for a fuel-air admixture as used herein is defined to mean
that the temperature at which the ignition lag of the fuel-air mixture
entering the catalyst is negligible relative to the residence time in
the combustion zone of the mixture undergoing combustion. The catalyst
surface and the gas layer near the catalyst surface are above a
temperature at which thermal combustion occurs at a rate higher than the
catalytic rate, and the temperature of the catalyst surface is above the
instantaneous autoignition temperature of the fuel-air admixture. The
fuel molecules entering this layer spontaneously burn without transport
to the catalyst surface. As combustion progresses, the layer becomes
deeper. The total gas is ultimately raised to a temperature at which
thermal reactions occur in the entire gas stream rather than only near
the surface of the catalyst.