Overall reaction kinetics

The overall reaction kinetics conesponding to these stages of surface adsorption followed by reaction can be represented by die equation... 

Bubble-column slurry operation is the most widely used suspended-bed operation for large-scale continuous processes. It has been the subject of a considerable number of investigations, and it may be noted in particular that many studies of the overall reaction kinetics in such operations have been published. 

In this section, only those studies, all of relatively recent date, that particularly emphasize the determination of rate-determining process steps and the application of the relatively advanced theoretical models discussed in Section IV will be reviewed. For earlier studies of overall reaction kinetics, the reader is referred to the publications of Hall et al. (HI) and Kolbel (K6). 

Future work in this area will involve the extension of these techniques to other temperatures in an effort to better characterize the overall reaction kinetics of these two processes. In addition, degree of cure obtained through isothermal DSC measurements will be compared with the fraction of acetylene consumed as measured by isothermal FTIR experiments for the same temperature and time. Also, the effect of the incorporation of metal fillers on the isomerization and crosslinking reactions will be addressed. 

In the quantitative development in Section 24.4 below, we assume the flow to be ideal, but more elaborate models are available for nonideal flow (Chapter 19 see also Kastanek et al., 1993, Chapter 5). Examples of types of tower reactors are illustrated schematically in Figure 24.1, and are discussed more fully below. An important consideration for the efficiency of gas-liquid contact is whether one phase (gas or liquid) is dispersed in the other as a continuous phase, or whether both phases are continuous. This is related to, and may be determined by, features of the overall reaction kinetics, such as rate-determining characteristics of mass transfer and intrinsic reaction. 

The overall reaction kinetics for substitution could easily be resolved into two stages, as described by these equations ... 

In the discussion of premixed turbulent flames, the case of infinitely fast mixing of reactants and products was introduced. Generally this concept is referred to as a stirred reactor. Many investigators have employed stirred reactor theory not only to describe turbulent flame phenomena, but also to determine overall reaction kinetic rates [23] and to understand stabilization in high-velocity streams [62], Stirred reactor theory is also important from a practical point of view because it predicts the maximum energy release rate possible in a fixed volume at a particular pressure. 

Figure 14. Simple model demonstrating how adsorption and surface diffusion can co-Urnit overall reaction kinetics, as explained in the text, (a) A semi-infinite surface establishes a uniform surface coverage Cao of adsorbate A via equilibrium of surface diffusion and adsorption/desorption of A from/to the surrounding gas. (b) Concentration profile of adsorbed species following a step (drop) in surface coverage at the origin, (c) Surface flux of species at the origin (A 4i(t)) as a function of time. Points marked with a solid circle ( ) correspond to the concentration profiles in b. (d) Surface flux of species at the origin (A 4i(ft>)) resulting from a steady periodic sinusoidal oscillation at frequency 0) of the concentration at the origin.

The modeling of RD processes is illustrated with the heterogenously catalyzed synthesis of methyl acetate and MTBE. The complex character of reactive distillation processes requires a detailed mathematical description of the interaction of mass transfer and chemical reaction and the dynamic column behavior. The most detailed model is based on a rigorous dynamic rate-based approach that takes into account diffusional interactions via the Maxwell-Stefan equations and overall reaction kinetics for the determination of the total conversion. All major influences of the column internals and the periphery can be considered by this approach. 

The rate-based models usually use the two-film theory and comprise the material and energy balances of a differential element of the two-phase volume in the packing (148). The classical two-film model shown in Figure 13 is extended here to consider the catalyst phase (Figure 33). A pseudo-homogeneous approach is chosen for the catalyzed reaction (see also Section 2.1), and the corresponding overall reaction kinetics is determined by fixed-bed experiments (34). This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid-solid interface as well as dififusional transport phenomena inside the porous catalyst. 

Not only are the series of reactions in iron/peroxide systems complex, but there are additional equilibrium processes that may effect the overall reaction kinetics and mechanisms. Some pertinent equilibrium steps are given below ... 

The foregoing discussion refers solely to intraparticle diffusivity (micropore diffusion) as distinct from interparticle effects (macropore diffusion). Since a practical zeolite catalyst will consist of composite particles, each containing a large number of individual zeolite crystals, it is important to make a clear distinction between these two types of diffusion. In some cases macropore diffusion may be important in determining the overall reaction kinetics but will obviously not introduce or affect shape selectivity in any way. 

Another major factor when considering whole-cell versus cell-free reactions are the overall reaction kinetics. Some enzymatic reactions utilize a complex multicomponent enzyme system. Reconstitution of the crude or purified enzyme components are not usually as effective in vitro as they are when they remain in the intracellular milieu. Whole cells have often been called little bags of enzymes. Although this is an oversimplification, it is a useful concept to consider. Whole cells sequester the enzyme components in a small but concentrated form, which is usually optimal for high efficiency. Whole cells also contain co-factors, including the systems that recycle them, and control pH and ionic strength. Altogether these factors combine to make whole cells a very useful form for the presentation and use of sensitive enzyme catalysts. 

Very stable intermediates reside near the equihbrium potential for adsorbed oxygen and hydroxyl, and coupled proton/electron transfer to and dominates the overall reaction kinetics. In step 3 of Eq. (4), hydrogen peroxide may also form instead of water, and this "associative" hydrogen peroxide mechanism is believed to dominate for most noble metals. 

Alternatively, the dynamics of trapping and detrapping of electrons localized in intra-bandgap states can control the overall reaction kinetics, which would not depend upon the sole interfacial electron transfer rate. 

For pyrolytic reactions, the variation of the molar concentration [A] of a substance during the pyrolysis is not always the most appropriate parameter to be monitored. The calculation of [A] can be a problem for many types of samples, and very frequently during pyrolysis, not only one decomposition process takes place. In this case, the overall reaction kinetics must be considered. A more convenient parameter for monitoring pyrolytic reactions is, for example, the sample weight. For a reaction of the first order, by multiplying equation (2) with the volume V and the molecular weight M of the substance A, (W = [A] V IW) we will have... 

Equations of the type indicated above can be used to describe the kinetics of a single chemical process or overall reaction kinetics. Measurements of the variation of W in time in isothermai conditions allows the calculation of the constant k and order n for which a best fit of the experimental data can be obtained. For different reaction orders, Arrhenius formula for k given by relation (5) is usually still applicable. Once the values for k and n are known for a given reaction, the reaction kinetics can be described in a wider range of conditions. 

The kinetics equation of the type described by rel. (2.3.35a) is commonly applied for describing the overall reaction kinetics during pyrolysis. However, this equation provides only an approximation when the process is not composed of a single reaction [15]. The pyrolysis of solid samples is usually a complicated process, and rel. (2.3.35a) may lead to erroneous results. The simpler relations valid for the kinetics in... 

The reaction chemistry of the rhodium-catalyzed methanol carbonylation process under Monsanto conditions has been investigated extensively [6-8, 10, 12, 21, 26-29] (cf Section 2.1.2.1.1). The overall reaction kinetics are first order in both rhodium catalyst and methyl iodide promoter. The reaction is zero order in methanol and zero order in carbon monoxide partial pressure above 2 atm (eq. (6)) [27]. The kinetics agree well with the basic mechanism common to the three carbonylation reactions (see Section 2.1.2.1.1 and Tables 1 and 2). 

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