Macrokinetics modeling

These aspects were carefully studied [29,46-48] and analyzed in several macrokinetic models. They are essential for choosing the methods indicated in Fig. 9.3 and constructing the suitable combination of reactor and operation conditions. In Fig. 9.3 the CVD/CVI methods are designated according to the methodology for how a gradient in the chemical potential of the reaction is applied. 

The main difference between metals and polymers is related to the fact that transitions from one state to another in polymers occur (as a result of changing of environmental conditions, primarily temperature) not as jumps but continuously. This leads to the absence of a clearly defined line or transition front. Additionally, because of die low heat and temperature conductivity of polymeric materials, a change in material properties may take place over a large volume,or even simultaneously throughout the whole mass of an article, although the local transition rates and degrees of conversion may be different. Thus it is necessary to develop a macrokinetic model of the transition. This model must describe the combined effects of non-stationary heat transfer and reaction kinetics and is used to determine the temperature and conversion fields. 

A macrokinetic model of the glyphosate reaction has been developed by Hu, et al. based on the primary reaction of PMIDA toward glyphosate and on the further oxidation of glyphosate to the undesired side product AMPA [4]. They concluded that an increase in the reaction temperature had an almost equal effect on the rate constant for the main reaction and the side reaction. The oxygen concentration also influenced both the main as well as the side reaction. However, a higher oxygen concentration accelerated the main reaction more compared with the side reaction under the reaction conditions. 

Above we have considered the general approaches and methods of non-linear analysis that have been used for studies of macrokinetic models of film systems. Some results are presented in Chap. 5. 

The choice to work with a macrokinetic model (i.e., an empirical equation) is made to simplify the kinetic parameters to be regressed. Because the WGS reaction has been discovered, many kinetic expressions have been developed and used. In general, either the Langmuir—Hinshelwood or the Eley—Rideal models have been used. In Table 1.1, most of the macrokinetic models are reported as an extract of a review of Smith, Loganathan, Shantha (2010). 

Macrokinetic models are stiU widely used for reactor design because they can be derived rather time- and cost-saving with an optimized set of experimental measurements (Deutschmann, 2011b). Even though the models are only valid in the limited range of conditions in which the kinetic data are derived for, they often fit their purpose in particular if the rate expressions reflect the molecular processes in some way and the rate-determining step is adequately taken into account. On the other hand, the microkinetic approach attempts to describe reactions using their most fundamental set... 

In summary, DFT calculation and microkinetic analysis-based macrokinetic modeling method is very helpful to understand the DHP chemistry and establish kinetic models with theoretical basis. But some discrepancy stiU exists between the experiments and the predictions based solely on energies determined by DFT calculations. For DHP, more data from theoretical calculation, surface science and kinetic experiments stiU need to be gathered for a more comprehensive microkinetic analysis and a more in-depth understanding of the kinetic behavior. With the development of nanotechnology, nanoparticles with specific structure properties can be routinely synthesized, which are ideal materials to probe the reaction... 

In a continuous reaction process, the true residence time of the reaction partners in the reactor plays a major role. It is governed by the residence time distribution characteristic of the reactor, which gives information on backmixing (macromixing) of the throughput. The principal objectives of studies into the macrokinetics of a process are to estimate the coefficients of a mathematical model of the process and to validate the model for adequacy. For this purpose, a pilot plant should provide the following ... 

There appears to be a more adequate approach when a local polarization characteristic is obtained as a result of analysis of the processes in the elementary cell and the local section of the electrode. This characteristic depends on the state transformation of the solid reagents and the concentrations of the electrolyte components. It further may be introduced into the equations describing the macrokinetic processes in an electrode, and may be used to model the behaviour of the system as a whole. 

Considering theoretically a copolymerization on the surface of a miniemulsion droplet, one should necessarily be aware of the fact that this process proceeds in the heterophase reaction system characterized by several spatial and time scales. Among the first ones are sizes of an individual block and macromolecules of the multiblock copolymer, the radius of a droplet of the miniemulsion and the reactor size. Taking into account the pronounced distinction in these scales, it is convenient examining the macrokinetics of interphase copolymerization to resort to the system approach, generally employed for the mathematical modeling of chemical reactions in heterophase systems [73]. 

In the washcoat, reaction rates are modeled via global reaction mechanisms. In such a global or macrokinetic reaction mechanism, several microkinetic adsorption, reaction and desorption steps are lumped together, reducing the overall number of kinetic parameters considerably. For some catalysts,... 

Field, K6ros and Noyes [13] suggested to use as the basic model for the Belousov-Zhabotinsky system a rather complicated set of chemical reactions with seven intermediate products. Its more global analysis based on macrokinetic stages and retaining still the principal features of this reaction [14] has led to the simplified scheme with three intermediate products only. This model called Oregonator [9, 15] is described by the following equations ... 

Macasek, F., Cech, R. 1984. Macrokinetics of radiolysis in systems with liquid-liquid partition of substrates. I - A general approach to mathematical models of simulated solvent extraction systems. Rad. Phys. Chem. 23(4) 473—479. 

The experimentally-determined effectiveness factor is determined as the ratio of the experimental macro reaction rate to the intrinsic reaction rate under the same interface (bulk) composition and temperature. Based on the experimental conditions of the macrokinetics, the predicted effectiveness factors of the methanation reaction and the WGSR are obtained by solving the above non-isothermal one-dimensional and two-dimensional reaction-diffusion models for the key components. Table 1 shows the calculated effectiveness factors and the experimental values. By... 

Macrokinetics is the description and analysis of the performance of the functional unit catalyst plus reagents plus reactor. It leads to formal activation barriers called apparent activation parameter representing the superposition of several elementary barriers with transport barriers. It further delivers formal reaction orders and rates as function of the process conditions. These data can be modeled with formal mechanisms of varying complexity. In any case, these data can well describe the system performance but cannot be used to deduce the reaction mechanism. 

The current status of the models of fluctuational and deformational preparation of the chemical reaction barrier is discussed in the Section 3. Section 4 is dedicated to the quantitative description of H-atom transfer reactions. Section 5 describes heavy-particle transfer models for solids, conceptually linked with developing notions about the mechanism of low-temperature solid-state chemical reactions. Section 6 is dedicated to the macrokinetic peculiarities of solid-state reactions in the region of the rate constant low-temperature plateau, in particular to the emergence of non-thermal critical effects determined by the development of energetic chains. 

In the recent years different numerical models for the conversion of wood in a packed bed have been presented, e. g, [3-6], Existing models mostly describe the as a porous media by an Eulerian approach, with the cons vation equations for the solid and the gas phase solved with the same mesh. This approach implies that heat and mass transfer can only be taken into account according to the dimensions of the bed but not within the particles itself. Temperature and species distributions are assumed to be homogenous over the fuel particles. Thus, the influence of the particle dimensions on the conversion process can only be captured by simplified assumptions or macrokinetic data. 

For modelling the drying process in wood, different approaches have been proposed in the past. In numerical models the description of the mass loss of water by a heterogeneous reaction, as introduced by [9], is advantageous with respect to numerical stability. However, the macrokinetic data used in this approach is specific to certain boundary conditions, which excludes this model from a general use. Thus, a different approach is chosen here. 

As can be seen from the given examples, a discretization of the particles is necessary for a general approach, in which the need for macrokinetic or empirical data is reduced. Therefore the separation of the packed bed into different particles as realised in the presented model seems necessary to capture the rate limiting parameters within the bed. 

This volume is including information about thermal and thermooxidative degradation of polyolefine nanocomposites, modeling of catalytic complexes in the oxidation reactions, modeling the kinetics of moisture adsorption by natural and synthetic polymers, new trends, achievements and developments on the effects of beam radiation, structural behaviour of composite materials, comparative evaluation of antioxidants properties, synthesis, properties and application of polymeric composites and nanocomposites, photodegradation and light stabilization of polymers, wear resistant composite polymeric materials, some macrokinetic phenomena, transport phenomena in polymer matrix, liquid crystals, flammability of polymeric materials and new flame retardants. 

Processes which take place within homogeneous liquids phases process are the preferred reaction systems for thermokinetic descriptions. In heterogeneous systems, which can be modelled with the help of macrokinetic formal rate laws, thermokinetic evaluation is possible, too, but only if additional information on the properties of the two phases is obtained in parallel. 

For the simulation of RD columns in which the chemical reactions take place at heterogeneous catalysts, it is important to keep in mind that a macrokinetic expression (5.55) has to be applied. Therefore, the microkinetic rate has to be combined with the mass transport processes inside the catalyst particles. For this purpose a model for the multicomponent diffusive transport has to be formulated and combined with the microkinetics based on the component mass balances. This has been done by several authors [50-53] by use of the generalized Maxwell-Stefan equations. 

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