Reaction kinetics microscale model

The mathematical modeling of polymerization reactions can be classified into three levels microscale, mesoscale, and macroscale. In microscale modeling, polymerization kinetics and mechanisms are modeled on a molecular scale. The microscale model is represented by component population balances or rate equations and molecular weight moment equations. In mesoscale modeling, interfacial mass and heat transfer... 

The Reynolds number in microreaction systems usually ranges from 0.2 to 10. In contrast to the turbulent flow patterns that occur on the macroscale, viscous effects govern the behavior of fluids on the microscale and the flow is always laminar, resulting in a parabolic flow profile. In microfluidic reaction systems, where the characteristic length is usually greater than 10 pm, a continuum description can be used to predict the flow characteristics. This allows commercially written Navier-Stokes solvers such as FEMLAB and FLUENT to model liquid flows in microreaction channels. However, modeling gas flows may require one to take account of boundary sUp conditions (if 10 < Kn < 10 , where Kn is the Knudsen number) and compressibility (if the Mach number Ma is greater than 0.3). Microfluidic reaction systems can be modeled on the basis of the Navier-Stokes equation, in conjunction with convection-diffusion equations for heat and mass transfer, and reaction-kinetic equations. 

Despite the development of microscale modeling for reaction—diffusion in zeolite, the complex of MTO reaction mechanism impedes the application of microscale modeling to MTO process. Up to now, the reliable reaction kinetics based on element reactions in MTO process is still under development (van Speybroeck et al., 2014). However, a reduced or simplified microscale model could be applied. Basically, the diffusion effect is negligible if the crystal radius is small enough. Then mass equation, i.e., Eq. (1), could be simplified by neglecting the species ffux term. In this case, MTO processes over ZSM-5 and SAPO-34 catalyst could be simulated by use of the single-event kinetics by Alwahabi and Froment (2004a) as an input. 

In microscale model, the reaction kinetics is constructed on the basis of element reaction system, and usually could be obtained by quantum... 

It is meaningful to examine the relation between microscale model, mesoscale model, and micromodel. For reaction kinetics, microscale and mesoscale models adopt the same kinetics that based on element reaction system. For diffusion, mesoscale model embodies two diffusion mechanisms (one for micropores and another for mesopores and macropores), and microscale model considers one diffusion mechanism since it only has micropores. No diffusion was considered within the macropores. It is obvious that the mesoscale model possesses the same theoretical foundation as the microscale model, but its application scope has been enlarged compared to the microscale model. Therefore, it could be reliably used as a tool to derive some parameters, such as effective chemical kinetics and effective diffusion parameters, for macroscale model. In the section following, we discuss the method on how to link the microscale kinetics to the lumped macroscale kinetics via the mesoscale modeling approach. 

In this work, the MeOH kinetic model of Lee et al. [9] is adopted for the micro-channel fluid dynamics analysis. Pressure and concentration distributions are investigated and represented to provide the physico-chemical insight on the transport phenomena in the microscale flow chamber. The mass, momentum, and species equations were employed with kinetic equations that describe the chemical reaction characteristics to solve flow-field, methanol conversion rate, and species concentration variations along the micro-reformer channel. 

How are the smafl-to-microscale excesses of one enantiomer over the other, produced by any of the scenarios outlined above, capable of generating a final state of enantiomeric purity In 1953 Frank [16] developed a mathematical model for the autocatalytic random symmetry breaking of a racemic system. He proposed that the reaction of one enantiomer yielded a product that acted as a catalyst for the further production of more of itself and as an inhibitor for the production of its antipode. He showed that such a system is kinetically unstable, which implies that any random fluctuation producing a transient e.e. in the 50 50 population of the racemic... 

The mass transport effects under ultrasound have been modeled. They offer a number of benefits per se, for microscale analytical studies and macroscale syntheses, including lessened power requirements to run at constant current, the need for lower concentrations of electrolyte salts and scope for different solvent systems, with altered product distributions if reaction pathways involve different kinetic regimes. 

The mesoscale multiregion model discussed above may open a way to link the microscale kinetics to the macroscale kinetics. The macroscale kinetics derived from microscale kinetics at least ensures that the reaction mechanism at the microscale can be correctly reflected. As mentioned by Campbell (1994), knowing a mechanism can give an intelligent way to extrapolate kinetics to unknown conditions. As far as we know, there is no MTO macroscale kinetics at present derived direcdy from microscale kinetics. 

The first question that arises while modeling of processes in microreactors is whether the macroscopic description is still valid at the microscale. Basically, the contribution of microreactors concerns the microscale section of chemical engineering rather than chemical aspect of reactions, reaction mechanism, and kinetics. 

The novelty in the aforementioned studies is the use of a comprehensive numerical model for the investigation of catalytic microscale reactors which includes, for the first time in the literature, detailed heterogeneous and homogeneous chemical reaction mechanisms, two-dimensional treatment for both the gas and solid wall phases and surface radiation heat transfer, under both steady and transient (quasisteady) conditions. Moreover, a validated chemical kinetics model for the coupled catalytic and gas-phase combustion of propane (a fuel of particular interest for portable applications) is presented for the first time. 

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