Kinetics of Adsorption in a Vessel

When adsorption takes place with suspended adsorbent particles in a vessel, adsorbate is transported from the bulk fluid phase to the adsorption sites in the adsorbent particle In this type of situauon, changes in the amount adsorbed or concentration in the fluid phase can be predicted by solving the set of differential equations describing the mass balances in the particle, at the outer surface and between the paruclc and the fluid phase In this chapter the adsorption uptake relations are shown for several typical situations These are applicable to batch adsorption in a liquid stirred tank, batch measurement of gas adsorption by gravity method or by pressure method as shown in Fig 5 1 Also adsorption in a shallow bed is a typical example of application of the treatment for batch adsorption with continuous flow (Fig 5 2) 

Basic equations to describe adsorption uptake phenomena in vessels consist of a set of the following mass balance equations, a diffusion equation to descnbe the mass balance in a particle, mass balance at the surface of the particle, global mass balance in a vessel Mass balance at a point in the particle is given as 

Mass balance at the surface of the particle is given by introducing mass 

Fluid to particle mass transfer coefficient ki is determined from fluid dynamic conditions as well as diffusion property of the fluid. 

When adsorption occurs in the vessel with continuous flow of fluid, then the mass balance equation becomes 

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This book comprises 12 chapters covering an introduction, porous adsorbents, adsorption equilibrium, diffusion in porous particles, kinetics of adsorption in a vessel, kinetics of adsorption in a column (chromatographic analysis and breakthrough curves), heat effects, regeneration of spent adsorbent, chromatographic separation, pressure swing adsorption and adsorption for energy transport. The text comprises a blend of mathematical analysis and descriptions of plant and processes. Each chapter is fully referenced. 

Chapter S deals mainly with batch adsorption kinetics in a vessel. Determination of intraparticle diffusion parameters should be done with a simple kinetic system where no other rate processes are involved. For this purpose measurement of concentration change in the finite bath where adsorption takes place is the most effective method. Concentration change curves derived for nonlinear isotherm systems as well as for a linear isotherm system are presented for convenient determination of rate parameters. These discussions are also applicable to the analysis and design of adsorption operation in a vessel dr differential reactor. 

The static technique may be applied to follow the interfadal tension as a function of time (to follow the kinetics of adsorption) till equilibrium is reached. In this case, the plate is suspended from one arm of a microbalance and allowed to penetrate the upper liquid layer (usually the oil) until it touches the interface, or alternatively the whole vessel containing the two liquid layers is raised until the interface touches the plate. The increase in weight AW is given by the following equation,... 

Any detectable effect on the reaction or behavior of a particular system by the interior wall of the container or reaction vessel. Because proteins can form high-affinity complexes with glass and plastic surfaces, one must exercise caution in the choice of reaction kinetic conditions. Wall effects can be discerned if one determines catalytic activity under different conditions that minimize or maximize contact of the solution with the container. In principle, an enzyme-catalyzed reaction should proceed at the same rate if placed in a capillary or a culture tube however, contact with the wall is maximized in a capillary, and wall effects should be more prominent. Some investigators add bovine serum albumin to prevent adsorption of their enzyme onto the container s walls. 

There are only a few recent publications. Anshits et al. [29,30] have carried out adsorption studies with various Cu—O phases and determined kinetics at low pressure in a static system. One of their conclusions is that the kinetics of partial and complete oxidation are very different. The mechanism of the latter is supposed to be of the associative type, contrary to the redox mechanism of the partial oxidation. A kinetic study with a continuously stirred vessel (375—400°C, 1 atm) was carried out by Laksh-manan and Rouleau [185]. In contrast to the redox mechanism, a singlesite Langmuir—Hinshelwood model is proposed, for which the k values and activation energies are determined. 

The question of the ( -potential value at the electrolyte solution/air interface in the absence of a surfactant in the solution is very important. It can be considered a priori that it is not possible to obtain a foam film without a surfactant. In the consideration of the kinetics of thinning of microscopic horizontal foam films (Section 3.2) a necessary condition, according to Reynolds relation, is the adsorption of a surfactant at both film surfaces. A unique experiment has been performed [186] in which an equilibrium microscopic horizontal foam film (r = 100 pm) was obtained under very special conditions. A quartz measuring cell was employed. The solutions were prepared in quartz vessels which were purified from surface impurities by a specially developed technique. The strong effect of the surfactant on the rate of thinning and the initial film thickness permitted to control the solution purity with respect to surfactant traces. Hence, an equilibrium thick film with initial thickness of about 120 nm was produced (in the ideal case such a film should be obtained right away). Due to the small film size it was possible to produce thick (100 - 80 nm) equilibrium films without a surfactant. In many cases it ruptured when both surfaces of the biconcave drop contacted. Only very precise procedure led to formation of an equilibrium film. 

The reaction vessels for the kinetic studies were 4000-ml. resistant glass bottles, in which solutions were agitated with Teflon-coated stirring rods extending directly into the adsorbate solution and connected to synchronous motors operating at 1550 r.p.m. Previous kinetic studies in similar systems had shown that rate of adsorption is independent of stirring rate at rotations greater than a few hundred r.p.m. (8). Tempera-... 

Figure 4.15. Kinetics of the adsorption process of a gasmixture (CO2, CH4) with equilibrium sorptive gas concentrations (yco2 20 %mol, = 80 %mol). The upper curve (Am) indicates the total absolute mass, cp. (2.31), of CH4 and CO2 adsorbed as function of time. Data have been taken from the microbalance recordings. The lower curves show the time variation of the pressure and the temperature of the sorptive gas mixture inside the adsorption vessel. As can be seen adsorption equilibrium is approached asymptotically and realized - in technical terms - after approximately 4 hours.

Effective diffusivity can be evaluated in a single pellet (113,168,169) or in a stirred vessel (115,170,171) or in a packed bed (113). The method of moments is usually used in parameter estimation. The method of moments and the theory of chromatography were also used extensively by Smith and coworkers in packed bed systems (113) for estimation of adsorption rate constants, particle diffusivity (172) and kinetic constants (173). Use of... 

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