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.