Rate controlled process models pore diffusion

T iffusion in porous pellets is often the rate-limiting process in industrial adsorption or catalytic processes. Much useful work in this field has been done by Smith and coworkers (3, 5), but for molecular sieve pellets the situation is complicated by diffusion in the zeolite crystal itself, as well as through the pores formed between the crystals. Few studies have been made of zeolite crystal diffusion, but Barrer and Brook (1) reported some results on diffusion of simple gases in various cation-substituted mordenites, and Wilson (7) gives some indirect results from the study of separation of CO2 from air using a fixed bed of type 4A zeolite pellets. In the present work, results have been obtained by studying self-diffusion of CO2 in a single pellet of type 5A zeolite under controlled conditions. The experimental results were fitted satisfactorily by a very simplified model of the pellet structure, which made it possible to deduce approximate values of the self-diffusion coefficients for both pore and crystal diffusion. 

The foregoing survey was focused on situations where bnlk diffusion processes were rate determining. Such systems are amenable to analysis using an electrochemical approach. Other factors such as transport down pores or cracks, volatilization or melting of the oxide scale may occur and require different analyses but diffusion controlled processes may be mathematically modeled and correlated with the defect chemistry of the corrosion product. These limiting cases provide a guide to understanding the more complex phenomena frequently encountered. 

One can calculate the rates of internal and film diffusion if the pore diameter and process conditions are well defined. The temperature dependency of the rate can be presented in the form of an Arrhenius plot (i.e., log rate versus reciprocal temperature). Gasification rates can be divided into three zones, I, II, III, depending on various flow and diffusion condition. To determine the overall gasification rate in a gasifier when gas diffusion controls the overall rate, it is necessary to model the actual gasifier. 

In a number of adsorbents, the adsorbent particle is composed of a large number of microporous microparticles, with larger pores between them. If the dominant mass transfer resistance is within the microparticles, the adsorption process is controlled by the rate of micropore diffusion and the model is defined by the material balance on the microparticle level. For one-dimensional Fickian diffusion, it can be described by the following equation ... 

One of these proposed a non-equilibrium process in which the separation was controlled by differing rates of diffusion for different molecular masses [23]. Other workers have proposed a separation by flow mechanism [24, 25] in which the larger molecules are excluded from the surface of the gel particles and remain in the centre of the solvent channels and are thus eluted first. The original theory did not invoke a porous structure for the gel, but this was modified later. The mechanism bears resemblance to that proposed for hydrodynamic chromatography (see Chapter 10). A further model suggested that the pore size distribution of the gel was directly responsible for its ability to separate molecules by size, and that there is a one-to-one correspondence with size of pores and size of molecules [26]. All these theories have been critically reviewed in the book by Yau et al [6]. 

It is important to understand how the moisture moves to the drying surface during the falling-rate period, and two models have been used to describe the physical nature of this process, the diffusion theory and the capillary theory. In the diffusion theory, the rate of movement of water to the air interface is governed by rate equations similar to those for heat transfer, whilst in the capillary theory the forces controlling the movement of water are capillary in origin, arising from the minute pore spaces between the individual particles. 

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