Isothermal catalytic reaction

The global rate expression and the external effectiveness factor for an isothermal catalytic reaction... 

The flow directions (e.g., co-currcni, counter-current and flow-through) and flow patterns (e.g., plug flow, perfect mixing and fluidized bed) of feed, permeate and retentate streams in a membrane reactor can significantly affect the reaction conversion, yield and selectivity of the reaction involved in different ways. These variables have been widely investigated for both dense and porous membranes used to carry out various isothermal and non-isothermal catalytic reactions, particularly dehydrogenation and hydrogenation reactions. 

Rathousky and Hlavacek (1981) presented two mathematical models to illustrate the fact that the influence of adsorbed species on the rate of an isothermal catalytic reaction may lead to a complex dynamic pattern including multiplicity of steady states and oscillatory states. Multiple oscillations and horatian behavior can not be calculated from the models. Rathousky and Hlavacek (1982) studied CO oxidation on Pt/Al203 catalyst and observed changes in oscillations due to the variations in inlet temperature. For a narrow range they observed horatian behavior. Experiments show that interaction of two oscillatory processes cause horatian behavior. 

We may summarize by outlining a step-by-step procedure to analyze the driving forces and robustness of any isothermal catalytic reaction process ... 

Reactants must diffuse through the network of pores of a catalyst particle to reach the internal area, and the products must diffuse back. The optimum porosity of a catalyst particle is deterrnined by tradeoffs making the pores smaller increases the surface area and thereby increases the activity of the catalyst, but this gain is offset by the increased resistance to transport in the smaller pores increasing the pore volume to create larger pores for faster transport is compensated by a loss of physical strength. A simple quantitative development (46—48) follows for a first-order, isothermal, irreversible catalytic reaction in a spherical, porous catalyst particle. 

Adsorption of reactants on the surface of the catalyst is the first step in every reaction of heterogeneous catalysis. Flere we focus on gases reacting on solid catalysts. Although we will deal with the adsorption of gases in a separate chapter, we need to discuss the relationship between the coverage of a particular gas and its partial pressure above the surface. Such relations are called isotherms, and they form the basis of the kinetics of catalytic reactions. 

Empirical grey models based on non-isothermal experiments and tendency modelling will be discussed in more detail below. Identification of gross kinetics from non-isothermal data started in the 1940-ties and was mainly applied to fast gas-phase catalytic reactions with large heat effects. Reactor models for such reactions are mathematically isomorphical with those for batch reactors commonly used in fine chemicals manufacture. Hopefully, this technique can be successfully applied for fine chemistry processes. Tendency modelling is a modern technique developed at the end of 1980-ties. It has been designed for processing the data from (semi)batch reactors, also those run under non-isothermal conditions. 

The Langmuir adsorption isotherm provides a simple mechanistic picture of the adsorption process and gives rise to a relatively simple mathematical expression. It can also be used to obtain a crude estimate of specific surface areas. More important, from the viewpoint of the chemical engineer, it serves as a point of departure for formulating rate expressions for heterogeneous catalytic reactions. 

The Langmuir Equation for the Case Where Two or More Species May Adsorb. Adsorption isotherms for cases where more than one species may adsorb are of considerable significance when one is dealing with heterogeneous catalytic reactions. Reactants, products, and inert species may all adsorb on the catalyst surface. Consequently, it is useful to develop generalized Langmuir adsorption isotherms for multicomponent adsorption. If 0t represents the fraction of the sites occupied by species i, the fraction of the sites that is vacant is just 1 — 0 where the summation is taken over all species that can be adsorbed. The pseudo rate constants for adsorption and desorption may be expected to differ for each species, so they will be denoted by kt and k h respectively. 

Note the similarity of this expression to that for 9a, derived by the Langmuir adsorption isotherm. (ES)/(E0) plays a role analogous to 04, while S0 plays a role akin to the gas pressure. Although the expression is formally similar, we do not mean to imply that the two types of catalytic reactions proceed by similar molecular steps. 

The bench-scale unit for the study of catalytic reactions has been designed with features such as accessibility, isothermal operation, and catalyst pretreatment. The use for catalytic screening tests makes easy accessibility a necessity, while the study of kinetics prescribes isothermal operation. 

Stoichacmetry and reaction equilibria. Homogeneous reactions kinetics. Mole balances batch, continuous-shn-ed tank and plug flow reactors. Collection and analysis of rate data. Catalytic reaction kinetics and isothermal catalytic radar desttpi. Diffusion effects. 

Truly isothermal operation of a tubular reactor may not be feasible in practice because of large enthalpies of reaction or poor heat transfer characteristics. Nor is it always desirable, as, for example, in the case of a reversible exothermic reaction (see Sect. 3.2.4). In an exothermic catalytic reaction, it may be necessary to provide adequate means for heat transfer to prevent the development of local hot-spots on which coking may occur and reduce the catalyst activity. An excessive temperature rise may also cause the catalyst particles to sinter, thereby reducing their surface area and causing an irreversible decrease in catalytic activity. 

In practice, of course, it is rare that the catalytic reactor employed for a particular process operates isothermally. More often than not, heat is generated by exothermic reactions (or absorbed by endothermic reactions) within the reactor. Consequently, it is necessary to consider what effect non-isothermal conditions have on catalytic selectivity. The influence which the simultaneous transfer of heat and mass has on the selectivity of catalytic reactions can be assessed from a mathematical model in which diffusion and chemical reactions of each component within the porous catalyst are represented by differential equations and in which heat released or absorbed by reaction is described by a heat balance equation. The boundary conditions ascribed to the problem depend on whether interparticle heat and mass transfer are considered important. To illustrate how the model is constructed, the case of two concurrent first-order reactions is considered. As pointed out in the last section, if conditions were isothermal, selectivity would not be affected by any change in diffusivity within the catalyst pellet. However, non-isothermal conditions do affect selectivity even when both competing reactions are of the same kinetic order. The conservation equations for each component are described by... 

One could think about measuring b directly in a separate adsorption experiment. However, it has been found that the adsorption thus measured has no quantitative relation to the adsorption leading to a catalytic reaction. Not only the amounts adsorbed, but even the shape of the isotherm and the sensitivity to poisoning or surface alterations are totally different. The reason is that the adsorption experiment measures the total surface under favorable conditions (B.E.T. method), whereas the catalysis takes place on a quantitatively entirely different active ... 

Because the catalytic reaction A R is highly exothermic with rate highly temperature-dependent, a long tubular flow reactor immersed in a trough of water, as shown in Fig. P18.39, is used to obtain essentially isothermal kinetic data. Pure A at 0°C and 1 atm flows through this tube at 10 cm / sec, and the stream composition is analyzed at various locations. 

Catalytic reactions were carried out in the isothermal glass batch reactor installed in a shaker and connected to a gasometrical burette. The reactor was equipped with two inlets one for catalyst, solvent, and substrate, and one for hydrogen feeding. The total volume of fluid phase is 32 mL. Hydrogen consumption was controlled by... 

Isothermal catalytic surface concentration and process rate for reaction order (n)... 

In general, if heterogeneous catalytic reactions are to be conducted isothermally, the reactor design must provide for heat flow to or from the particles of catalyst so as to keep the thermal gradients small. Otherwise, temperatures within the catalyst bed will be non-uniform. The differential reactor and the various forms of the gradientless reactors are advantageous in this regard. 

Carbon disulphide is produced in an isothermally operated packed tubular reactor at a pressure of 1 bar by the catalytic reaction between methane and sulphur. 

There are several aspects of thermal sensitivity and instability which are important to consider in relation to reactor design. When an exothermic catalytic reaction occurs in a non-isothermal reactor, for example, a small change in coolant temperature may, under certain circumstances, produce undesirable hotspots or regions of high temperature within the reactor. Similarly, it is of central importance to determine whether or not there is likely to be any set of operating conditions which may cause thermal instability in the sense that the reaction may either become extinguished or continue at a higher temperature level as a result of fluctuations in the feed condition. We will briefly examine these problems. 

Most of the critical effects in oxidation reactions over Pt metals were observed under isothermal conditions. Hence the complex dynamic behaviour can be directly due to the structure of the detailed catalytic reaction mechanism, specifically to the laws of physico-chemical processes in the "reaction medium-catalyst systems. The types and properties of mathematical models to describe critical effects are naturally dependent on those physico-chemical prerequisites on which these models are often based [4, 9], Let us describe the most important factors used in the literature to interpret critical effects. 

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