Mass transfer with chemical reaction Isothermal effectiveness

2 Mass transfer with chemical reaction Isothermal effectiveness 

Since solid-catalyzed reactions occur on the surface of a catalyst, the greater the extent of surface available for adsorption of reactants, the higher is the rate of reaction. Hence, particularly in practical applications, it is desirable to disperse the active components on a support having small volume but hig surface area. This is achieved by using support materials with highly 

The quantitative treatment of the effects of concurrent mass transfer and chemical reaction within porous structures was started separately by Thiele in the United States, Damkohler in Germany, and Zeldovich in Russia and reported separately between 1937 and 1939 [4, 13]. These analyses were further developed by Wheeler, Weisz, Wicke, and Aris [13]. 

The most significant result of these studies is the internal effectiveness factor which links the intrinsic rate to the actually measured global rate and is also a measure of the efficacy with which the available surface area of the catalyst is utilized. The internal effectiveness factor is defined as 

Ca and T denote the surface concentration of A and the surface temperature at any point along the pore. The central problem in the quantitative analysis of the simultaneous diffusion-reaction problem is to find an expression for // as a function of the parameters involved  

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In this paper only isothermal simulations have been conducted to show the important features of the model to describe mass transfer with chemical reaction. In many industrial processes, distillation, reactive distillation and some absorption processes, heat effects play an important role and therefore cannot be neglected. These effects will be discussed in Part II. 

The general theoretical approach is to develop the mathematical equations for simultaneous mass transfer and chemical reaction, as the reactants and products difHise into and out of the porous catalyst. When reaction occurs simultaneously with mass transfer within a porous structure, a concentration gradient is established. Since interior surfaces are thus exposed to lower reactant concentrations than surfaces near the exterior, the overall reaction rate throughout the catalyst particle under isothermal conditions is less than it would be if there were no mass transfer limitations. As will be shown, the apparent activation energy, the catalyst selectivity, and other important observed characteristics of a reaction are also dependent upon the structure of the catalyst and the effective diffusivity of reactants and products (Charles and Thomas, 1963). 

A first-order chemical reaction occurs isothermally in a reactor packed with spherical catalyst pellets of radius R. If there is a resistance to mass transfer from the main fluid stream to the surface of the particle in addition to a resistance within the particle, show that the effectiveness factor for the pellet is given by ... 

A to products by considering mass transfer across the external surface of the catalyst. In the presence of multiple chemical reactions, where each iRy depends only on Ca, stoichiometry is not required. Furthermore, the thermal energy balance is not required when = 0 for each chemical reaction. In the presence of multiple chemical reactions where thermal energy effects must be considered becanse each AH j is not insignificant, methodologies beyond those discussed in this chapter must be employed to generate temperature and molar density profiles within catalytic pellets (see Aris, 1975, Chap. 5). In the absence of any complications associated with 0, one manipulates the steady-state mass transfer equation for reactant A with pseudo-homogeneous one-dimensional diffusion and multiple chemical reactions under isothermal conditions (see equation 27-14) ... 

Trickle-bed reactors, wherein gas and liquid reactants are contacted in a co-current down flow mode in the presence of heterogeneous catalysts, are used in a large number of industrial chemical processes. Being a multiphase catalytic reactor with complex hydrodynamics and mass transfer characteristics, the development of a generalized model for predicting the performance of such reactors is still a difficult task. However, due to its direct relevance to industrial-scale processes, several important aspects with respect to the influence of external and intraparticle mass transfer effects, partial wetting of catalyst particles and heat effects have been studied previously (Satterfield and Way (1972) Hanika et. al., (1975,1977,1981) Herskowitz and Mosseri (1983)). The previous work has mainly addressed the question of catalyst effectiveness under isothermal conditions and for simple kinetics. It is well known that most of the industrially important reactions represent complex reaction kinetics and very often multistep reactions. Very few attempts have been made on experimental verification of trickle-bed reactor models for multistep catalytic reactions in the previous work. 

This study considers the diffusion of n-pentane in the PS and PP sheet samples to be one-dimensional, isothermal, without chemical reaction, and with negligible effects of pressure on the total density of the system [6]. In addition, the phase volume change due to mass transfer is neglected. Hence, the sorption/desorption of n-pentane in PS and PP is governed by the following diffusion equation with the Cartesian coordinates ... 

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