Kinetics intra-particle diffusion model

Batch kinetic data on the removal of reactive dye from solution using thermally chaired dolomite have been well described by empirical external mass transfer and intra-particle diffusion models. It was found that external mass transfer and intra-particle diffusion had rate limiting effects on the removal process which were attributed to the relatively simple... 

The kinetic data for the adsorption of Hg(II) by the copolymer satisfactorily follow both the pseudo-second-order model (where linear plots of t vs t/qt) as well as intra-particle diffusion model (up to 3h after that data does not satisfy intra-particle diffusion model, indicating that adsorption in the beginning is diffusion controlled. The correlation coefficients (R ) and the rate constants for CJ-g-PAA are shown in Table 10.4. While the isotherm studies indicate unilayer... 

Three kinetic models, pseudo-first-order, pseudo-second-order, and intra-particle diffusion model are used to fit the experimental data The mathematical description of these models is given below. The conformity between data predicted by arty of these models and the experimental data is indicated by the correlation coefficient R. The model of higher values of R means that it successfully describes the adsorption kinetics. 

The shrinking-core model (SCM) is used in some cases to describe the kinetics of solid and semi-solids-extraction with a supercritical fluid [22,49,53] despite the facts that the seed geometry may be quite irregular, and that internal walls may strongly affect the diffusion. As will be seen with the SCM, the extraction depends on a few parameters. For plug-flow, the transport parameters are the solid-to-fluid mass-transfer coefficient and the intra-particle diffusivity. A third parameter appears when disperse-plug-flow is considered [39,53],... 

Ostrovskii and Bukhavtsova published several experimental and theoretical works on capillary condensation in catalytic reactions. Capillary condensation was found to accompany some gas-phase catalytic processes, in particular hydrotreating of jet fuel fractions [7]. The effects of gas-liquid interfacial surface, intra-particle diffusion, and of the ratio of gas to liquid reaction rates under conditions of capillary condensation were estimated [8]. The experimental study of /j-xylene hydrogenation on Pt/Si02 (as a model reaction) was carried out in order to demonstrate the influence of capillary condensation on reaction kinetics and process dynamics, and corresponding model was proposed [9]. Finally, the poisoning of the catalyst under capillary condensation was also considered [10]. 

The kinetic parameters of the reduction should take in consideration the mass balance for the reducing gas (reagent) on the surface and in the fluid gas. Much of the models, as seen above, do not take into account inter- and intra-particle diffusion effects, which can significantly modify the reduction profile. The conditions under which these effects can be neglected must be determined. 

The issue of bioavailability is further clouded by the physical characteristics of soil and the role of a possible mass transfer limitation. Soil constituents are not simply flat surfaces with free and equal access to all bacterial species. The formation of aggregates from sand-, silt-, and clay-sized particles results in stable structures which control microbial contact with the substrate (Figure 2.7). Discussion of sorption mechanisms and binding affinities must include the possible impact of intra-aggregate transport of the substrate. If the substrate is physically inaccessible to the microorganism then both desorption from soil constituents and diffusion to an accessible site are necessary. The impact of intra-aggregate diffusion on degradation kinetics has been modeled for y-hexachlorocyclohexane (Rijnaarts et al., 1990) and naphthalene (Mihelcic Luthy, 1991). 

Two model approaches are compared by simulating reactive transport of acenaphthene in a heterogeneous porous medium. In a Monte Carlo approach a Lagrangian onedimensional streamtube model is used to assess the transport behaviour at field scale for distances of up to 800 m. Aquifer properties are taken from results of field experiments characterising a test site in a shallow quaternary sand and gravel aquifer. The results of the streamtube model are compared to model results of a two-dimensional Eulerian model. Both models account for kinetic sorption, described as diffusive transport in intra-particle pores. 

A wastewater treatment technique has been investigated, for reactive dye removal, in batch kinetic systems. Results indicate that chatted dolomite has the potential to act as an adsorbent for the removal of reactive dye fiom aqueous solution. The effect of initial dye concentration, adsorbent mass liquid volume ratio, and agitation speed on removal have been deteimined with the experimental data mathematically described using empirical external mass transfer and intrai>article diffusion models. The experimental data show conformity with an adsorption process, with the removal rate heavily dependent on both external mass transfer and intra-particle diffesion. 

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