Micropores diffusion

It arises solely because we continue Co describe micropore diffusion in terms of smooch macropore concentration fields and their gradients, even under reactive conditions where these no longer adequately describe Che actual concentration gradients in the micropores. 

Microphysiometers Microplant Micropollutants Micropore diffusion Microporite... 

The mesopores make some contribution to the adsorptive capacity, but thek main role is as conduits to provide access to the smaller micropores. Diffusion ia the mesopores may occur by several different mechanisms, as discussed below. The macropores make very Htde contribution to the adsorptive capacity, but they commonly provide a major contribution to the kinetics. Thek role is thus analogous to that of a super highway, aHowkig the adsorbate molecules to diffuse far kito a particle with a minimum of diffusional resistance. 

Fig. 6. Concentration profiles through an idealized biporous adsorbent particle showing some of the possible regimes. (1) + (a) rapid mass transfer, equihbrium throughout particle (1) + (b) micropore diffusion control with no significant macropore or external resistance (1) + (c) controlling resistance at the surface of the microparticles (2) + (a) macropore diffusion control with some external resistance and no resistance within the microparticle (2) + (b) all three resistances (micropore, macropore, and film) significant (2) + (c) diffusional resistance within the macroparticle and resistance at the surface of the...

Micropore Diffusion. In very small pores in which the pore diameter is not much greater than the molecular diameter the diffusing molecule never escapes from the force field of the pore wall. Under these conditions steric effects and the effects of nonuniformity in the potential field become dominant and the Knudsen mechanism no longer appHes. Diffusion occurs by an activated process involving jumps from site to site, just as in surface diffusion, and the diffusivity becomes strongly dependent on both temperature and concentration. 

D5 adsorbed-phase (sohd, surface, particle, or micropore) diffusion... 

Numerical values for solid diffusivities D,j in adsorbents are sparse and disperse. Moreover, they may be strongly dependent on the adsorbed phase concentration of solute. Hence, locally conducted experiments and interpretation must be used to a great extent. Summaries of available data for surface diffusivities in activated carbon and other adsorbent materials and for micropore diffusivities in zeolites are given in Ruthven, Yang, Suzuki, and Karger and Ruthven (gen. refs.). 

Micropore diffusion, 1 596, 597-599 Microporous catalysts, in bisphenol A manufacture, 14 420 Microporous metal membranes, 15 813t Microporous particles, apparent effective diffusivity and, 15 729-730 Microporous range, pore diameters within, 16 812... 

The rate of n-paraffin desorption generally controls the overall production rate (18, 19). The diffusion of n-paraffins in commercial 5A molecular sieves is reported to be controlled by either micropore diffusion or macropore diffusion, or both, depending on the molecular sieve crytal size and macropore size distribution of the adsorbent (20). A 5A molecular sieve adsorbent with smaller crystal size and optimum macropore size distribution would have a faster adsorption-desorption rate and, therefore, a higher effective capacity. 

The microporous diffusivity D, in the constricted form and assumed equal for A and B is given by... 

Micropore diffusion Diffusion within the small micropores of the adsorbent which are of a size comparable with the molecular diameter of the sorbate. Under these conditions the diffusing molecule never escapes from the force field of the solid surface and steric hindrance is important. For zeolites the terms micropore diffusion and intracrystalline diffusion are synonymous. Raffinate Product stream containing the less strongly adsorbed species. 

FIGURE 4 Schematic diagram of a biporous adsorbent pellet showing the three resistances to mass transfer (external fluid film, macropore diffusion, and micropore diffusion). R9 pellet radius rc crystal radius. 

Micropore diffusion is an activated process, and the temperature dependence can generally be correlated according to an Eyring equation,... 

Many practical adsorption processes involve multicomponent systems, so the problem of micropore diffusion in a mixed adsorbed phase is both practically and theoretically important. Major progress in understanding the interaction effects has been achieved by Krishna and his coworkers through the application of the Stefan-Maxwell approach. The diverse patterns of concentration dependence of diffusivity that have been observed for many systems can, in most cases, be understood on this basis. The reader is referred, for details, to the review articles cited in the bibliography. 

Observation of distinct, slow and fast electrode charging processes by the same research group [219], presumably not related to micropore diffusion or surface reactions involving OH and H+ ions, was interpreted using the same argument ... 

The control of the microkinetics, consisting of micropore diffusion, chemisorption, surface reaction, and desorption, is the task of the catalyst developer and is not discussed further here. If the catalyst is specified together with its microkinetic properties, then reaction conditions (feedstock concentrations, pressure, temperature, and residence time) can be found that lead to optimum yields. The reaction engineer must determine these conditions and ensure that they are maintained in an industrial reactor. 

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. 

The described treatment of mass transport presumes a simple, relatively uniform (monomodal) pore size distribution. As previously mentioned, many catalyst particles are formed by tableting or extruding finely powdered microporous materials and have a bidisperse porous structure. Mass transport in such catalysts is usually described in terms of two coefficients, a effective macropore diffusivity and an effective micropore diffusivity. 

Kinetics was determined by fitting the experimental uptake curves with a bidisperded model. Only molecular diffusion was considered for the transport in macropore. The micropore diffusion in CMS samples was expressed by a dual model of the following form [3,5] ... 

Sorption Kinetics. The adsorption and desorption data were analyzed in terms of a model based on the following main assumptions. Micropore diffusion within the sieve crystals is the rate-controlling process. Diffusion may be described by Fick s law for spherical particle geometry with a constant micropore diffusivity. The helium present in the system is inert and plays no direct role in the sorption or diffusion process. Sorption occurs under isothermal conditions. Sorption equilibrium is maintained at the crystal surface, which is subjected to a step change in gas composition. These assumptions lead to the following relation for the amount of ethane adsorbed or desorbed by a single particle as a function of time (Crank, 4). 

Figure 3. Arrhenius plot for experiments micropore diffusivity data...

The results in this study have demonstrated clearly that the rate of adsorption and desorption of ethane at low concentrations on 4A molecular sieves in the absence of binder is controlled by intracrystalline diffusion of the ethane. Furthermore, the diffusion process may be characterized by Pick s law and an effective diffusivity dependent only on temperature, and applicable to both adsorption and desorption. It may be expected, therefore, that such micropore diffusion also determines the rates of ethane sorption with commercial 4A pellets containing clay... 

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