Macrokinetics

The objective of kinetic measurements is to discriminate between micro- and macrokinetics. 

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Reactors without the effect of macrokinetic properties are composed of elements that are either perfectly insulated from the viewpoint of... 

Chemical reactions obey the rules of chemical kinetics (see Chapter 2) and chemical thermodynamics, if they occur slowly and do not exhibit a significant heat of reaction in the homogeneous system (microkinetics). Thermodynamics, as reviewed in Chapter 3, has an essential role in the scale-up of reactors. It shows the form that rate equations must take in the limiting case where a reaction has attained equilibrium. Consistency is required thermodynamically before a rate equation achieves success over tlie entire range of conversion. Generally, chemical reactions do not depend on the theory of similarity rules. However, most industrial reactions occur under heterogeneous systems (e.g., liquid/solid, gas/solid, liquid/gas, and liquid/liquid), thereby generating enormous heat of reaction. Therefore, mass and heat transfer processes (macrokinetics) that are scale-dependent often accompany the chemical reaction. The path of such chemical reactions will be... 

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 ... 

MACROKINETICS OF ELECTROCHEMICAL PROCESSES (SYSTEMS WITH DISTRIBUTED PARAMETERS)... 

Electrochemical macrokinetics deals with the combined effects of polarization characteristics and of ohmic and diffusion factors on the current distribution and overall rate of electrochemical reactions in systems with distributed parameters. The term macrokinetics is used (mainly in Russian scientific publications) to distinguish these effects conveniently from effects arising at the molecular level. 

The macrokinetics of processes in gas-diffusion electrodes is analogous to that in liquid-phase electrodes. In calculations, one must take into account, however, that the electric current and the solute species will be carried only through that part of pore space which is electrolyte filled, whereas gas supply is accomplished primarily not by diffusion through the liquid but by flow in the gas channels. 

Macrokinetic Limitations in Electrodes with Disperse Catalyst... 

A quantitative investigation of the influence exerted by a substrate on the properties of disperse catalysts is hampered by the distorting effects of many other factors, particularly the macrokinetic limitations and the size effects mentioned in Section 28.5.4. 

Oxygen reduction can be accelerated by an application of electrodes with high surface area, e.g. the porous electrodes [9, 13]. The porous electrodes usually consist of catalysts, hydrophobic agent (polytetrafluoroethylene-PTFE) and conductive additive. Electrode kinetics on the porous electrodes is complicated by the mass and charge transfer in the pores and is called the macrokinetics of electrode processes . 

An analysis of the equations of macrokinetics of oxygen reduction on the porous hydrophobic electrodes gave some conclusions [15, 16] ... 

Chismadjev Yu.A., Markin V.S., Tarasevich M.R., Chirkov Yu.G. Macrokinetics of processes in porous electrodes. Moscow Nauka, 1971 (Russian). 

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. 

Ksenzhek O.S. Macrokinetics of Processes on Porous Electrodes. Electrochem. Acta. 1964 9 629-37. 

In order to estimate the region of this approximation applicability, it is necessary to examine macrokinetics of a polymeranalogous reaction with explicit allowance for the diffusion of a reagent Z into a globule. In this case, the profile of its constituent monomeric units will be fuzzy rather than stepwise (see Fig. 1). This brings up two questions. The first one is how this profile depends on kinetic and diffusion parameters of a reaction system. The second question is concerned with the effect of the profile shape on the statistical characteristics of the chemical structure of the products of a polymeranalogous reaction. A rigorous theory has been developed [22,23] which enables us to answer these questions. The main concepts of this theory are outlined in the subsequent Sections. 

The main macrokinetic problem to be solved for the description of this reaction is finding the evolution of the profile of concentrations Mi, M2 of monomeric units Mi, M2 inside a globule with radius R. By virtue of the spherical symmetry of the problem, concentration M is the same at all points of a globule located at identical distance r from its center. The same condition is apparently met by the concentrations of the second type units M2 = Mj0 - Mi and low-molecular reagent Z. Presuming monomeric units to... 

When considering the macrokinetics of PAR described by equations (Eq. 17), it is reasonable to focus on two limiting regimes. The first of these, the kinetically-controlled regime, takes place provided the rate of diffusion of molecules Z appreciably exceeds that of the chemical reaction. In this case, a uniform concentration Z = Ze should be established all over the globule after time interval t R2/D. Subsequently, during the interval t 1 /kZe, which is considerably larger than f[Pg.152]

Quite special is the consideration of the kinetically-controlled regime of the reaction in a globule. For this limiting macrokinetic regime probability... 

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]. 

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. 

Integration with the (micro) kinetics, in other words the kinetics of the pertinent free biocatalysts or of the immobilized biocatalysts including mass transfer, yields the overall reactor description or macrokinetics in later sections. In order to come up with these descriptions, a mass balance over the bioreactor should be drawn up (Figure 11.11). 

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 ... 

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. 

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... 

Sundmacher K, Hoffmann U. Macrokinetic analysis of MTBE synthesis in chemical potentials. Chem Eng Sci 1994 49 3077-3089. 

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