Diffusion resistance with complex reactions

In order to solve the mathematical model for the emulsion hquid membrane, the model parameters, i. e., external mass transfer coefficient (Km), effective diffu-sivity (D ff), and rate constant of the forward reaction (kj) can be estimated by well known procedures reported in the Hterature [72 - 74]. The external phase mass transfer coefficient can be calculated by the correlation of Calderback and Moo-Young [72] with reasonable accuracy. The value of the solute diffusivity (Da) required in the correlation can be calculated by the well-known Wilke-Chang correlation [73]. The value of the diffusivity of the complex involved in the procedure can also be estimated by Wilke-Chang correlation [73] and the internal phase mass transfer co-efficient (surfactant resistance) by the method developed by Gu et al. [75]. 

The problem is also more complex when heterogeneous catalysed reactions are considered. With porous catalyst pellets, reaction occurs at gas- or liquid-solid interfaces at the outer or inner sphere. When the reactants diffuse only slowly from the bulk phase to the exterior surface of the catalyst, gas or liquid film resistance must be taken into account. Pore diffusion resistance may be involved when the reactants move through the pores into the pellet. 

As the diffusion of reactants to form the activated complex occurs in series with chemical reaction, the total resistance for the generation of products may be written as the sum of diffusional and chemical resistances. Thus,... 

In the previous sections the concept of the effectiveness factor has been discussed. In this section it is discussed in further detail with the aim of extending the concept to industrially important complex reaction networks. The effectiveness factor is the most widely used man-made factor to account (in a condensed, one number manner) for the effect of different diffusional resistances on the actual (or apparent) rate of reaction for gas-solid catalytic systems. Although the use of the effectiveness factor concept in the simulation of catalytic reactors taxes the solution by extra computations, nevertheless it is a very useful tool to account for the complex interaction between the diffusion and reaction processes taking place within the system. Most of the published work (e.g. Weisz and Hicks, 1962 Aris, 1975a,b) deals with the effectiveness factor for the simple irreversible reaction,... 

Using artificial neural networks (ANN) the reaction system, including intrinsic reaction kinetics but also internal mass transfer resistances, is considered as a black-box and only input-output signals are analysed. With this approach the conversion rate of the i-th reactant into the j-th species can be expressed in a general form as a complex function, being a mathematical superposition of all above mentioned functional dependencies. This function includes also a contribution of the internal diffusion resistances. So each of the rate equations of Eq. 5 can be described with the following function based on the vanables which uniquely define the state of the system ... 

The results of simulations of TWC model with microkinetics and diffusion resistance within the washcoat enable the interpretation of the dynamics of surface coverages and overal reactions and can serve for the improvement of the washcoat design. It has been found that not only multiple steady states (hysteresis) but also various types of periodic and complex spatiotemporal concentration patterns can exist in the monolith. Thorough analysis of bifurcations and transitions among existing patterns is numerically demanding task due to dimension of the problem. 

While any number of complex mixtures of non-oxide ceramics can be formulated and studied with regard to their oxidation resistance, one hopes to obtain a material whose oxidation properties are dominated by the most protective oxide in the system. However, for this to occur, a continuous layer of this oxide must be formed in the scale, otherwise the oxidation rates are controlled by less protective oxides, gas phase diffusion, or the linear reaction rate of oxidant with the matrix. Only several systems of particular note will be discussed here. In the first of these systems. Si-containing material, e.g. SiC, additions are made to less... 

Transition metal complexes encapsulated in the channel of zeolites have received a lot of attention, due to their high catalytic activity, selectivity and stability in field of oxidation reactions. Generally, transition metal complex have only been immobilized in the classical large porous zeolites, such as X, Y[l-4], But the restricted sizes of the pores and cavities of the zeolites not only limit the maximum size of the complex which can be accommodated, but also impose resistance on the diffusion of substrates and products. Mesoporous molecular sieves, due to their high surface area and ordered pore structure, offer the potentiality as a good host for immobilizing transition complexes[5-7]. The previous reports are mainly about molecular sieves encapsulated mononuclear metal complex, whereas the reports about immobilization of heteronuclear metal complex in the host material are few. Here, we try to prepare MCM-41 loaded with binuclear Co(II)-La(III) complex with bis-salicylaldehyde ethylenediamine schiff base. 

Walter et al. [84] discussed several common experimental methods to estimate the influence of internal mass transfer resistances on the observed rates of heterogeneous catalytic reactions. For example, when the reaction temperature is varied, because the intrinsic reaction rate increases more strongly with temperature than the rate of diffusion, the influence of mass transfer becomes more important and the observed apparent activation energy decreases as the temperature increases effects of temperature on selectivity may be more complex. 

Chapter 3 dealt with the problem of the reaction kinetics for different gas-solid reactions, while chapter 5 dealt with the mass and heat transfer problems for porous as well as non-porous catalyst pellets. In chapter 5 different degrees of complexities and rigor were used. In chapter 5, the analysis started with the simplest case of non-porous catalyst pellets where the only mass and heat transfer Coefficients are those at the external surface which depend mainly on the flow conditions around the catalyst pellet and the properties of the reaction mixture. It was shown clearly that j-factor correlations are adequate for the estimation of the external mass and heat transfer coefficients (k, h) associated with these resistances. For the porous catalyst pellets different models with different degrees of rigor have been used, starting from the simplest case of Fickian diffusion with constant diffusivity, to the rigorous dusty gas model based on the Stefan-Maxwell equations for multicomp>onent diffusion. 

The assembly of such core-shell particles, both in two and three dimensions, further enables tailored complex structures to be created with new properties. The formation of even more complex structures can be accomplished by making use of the semipermeable nature of the silica shell. The slow diffusion of reagents through the shell allows selective core etching and chemical conversion to be effected. The kinetics of such reactions are controlled by the porosity and the thickness of the shell, so that the cores can be made resistant to almost any chemical reagent. 

---