Adsorption constant pattern

Kumar, R, Column dynamics for multicomponent adsorption Constant pattern formation, Sep. Sci. Technol., 21(10). 1039-1046(1986). 

The distance requited to approach the constant pattern limit decreases as the mass transfer resistance decreases and the nonlinearity of the equihbrium isotherm increases. However, when the isotherm is highly favorable, as in many adsorption processes, this distance may be very small, a few centimeters to perhaps a meter. 

Favorable and unfavorable equihbrium isotherms are normally defined, as in Figure 11, with respect to an increase in sorbate concentration. This is, of course, appropriate for an adsorption process, but if one is considering regeneration of a saturated column (desorption), the situation is reversed. An isotherm which is favorable for adsorption is unfavorable for desorption and vice versa. In most adsorption processes the adsorbent is selected to provide a favorable adsorption isotherm, so the adsorption step shows constant pattern behavior and proportionate pattern behavior is encountered in the desorption step. 

Adsorption Dynamics. An outline of approaches that have been taken to model mass-transfer rates in adsorbents has been given (see Adsorption). Detailed reviews of the extensive Hterature on the interrelated topics of modeling of mass-transfer rate processes in fixed-bed adsorbers, bed concentration profiles, and breakthrough curves include references 16 and 26. The related simple design concepts of WES, WUB, and LUB for constant-pattern adsorption are discussed later. 

Most dynamic adsorption data are obtained in the form of outlet concentrations as a function of time as shown in Figure 18a. The area iebai measures the removal of the adsorbate, as would the stoichiometric area idcai, and is used to calculate equiUbrium loading. For constant pattern adsorption, the breakthrough time and the stoichiometric time ( g), are used to calculate LUB as (1 — (107). This LUB concept is commonly used... 

FIG. 16-2 Limiting fixed-bed behavior simple wave for unfavorable isotherm (top), square-root spreading for linear isotherm (middle), and constant pattern for favorable isotherm (bottom). [From LeVan in Rodtigues et al. (eds.), Adsorption Science and Technology, Kluwer Academic Publishers, Dotdtecht, The Nethedands, 1989 reptinted withpeimission.]... 

Local equihbrium theory also pertains to adsorption with axial dispersion, since this mechanism does not disallow existence of equilibrium between stationary and fluid phases across the cross section of the bed [Rhee et al., Chem. Eng. ScL, 26, 1571 (1971)]. It is discussed below in further detail from the standpoint of the constant pattern. 

After eliminating /if or cf using the adsorption isotherm, Eq. (16-140) can be integrated directly to obtain the constant pattern. 

Breakthrough Behavior for Axial Dispersion Breakthrough behavior for adsorption with axial dispersion in a deep bed is not adequately described by the constant pattern profile for this mechanism. Equation (16-128), the partial different equation of the second order Ficldan model, requires two boundaiy conditions for its solution. The constant pattern pertains to a bed of infinite depth—in obtaining the solution we apply the downstream boundaiy condition cf 0 as oo. Breakthrough behavior presumes the existence of... 

Treatments of constant pattern behavior have been carried out for multicomponent adsorption [Vermeulen, Adv. in Chem. Eng., 2, 147 (1958) Vermeulen et., Ruthven, gen. refs. Rhee and Amundson, Chem. Eng. ScL, 29, 2049 (1974) Cooney and Lightfoot, Jnd. Eng. Chem. Fundam., 5, 25 (1966) Cooney and Strusi, Jnd. Eng. Chem. Fundam., 11, 123 (1972) Bradley and Sweed, AJChE Symp. Ser. No. 152, 71, 59 (1975)]. The behavior is such that coexisting compositions advance through the bed together at a uniform rate this is the coherence concept of Helfferich and coworkers [gen. refs.]. 

The constant pattern concept has also been extended to circumstances with nonplug flows, with various degrees of rigor, including flow profiles in tubes [Sartory, Jnd. Eng. Chem. Fundam., 17, 97 (1978) Tereck et al., Jnd. Eng. Chem. Res., 26, 1222 (1987)], wall effects [Vortmeyer and Michael, Chem. Eng. ScL, 40, 2135 (1985)], channeling [LeVan and Vermeulen in Myers and Belfort (eds.). Fundamentals of Adsorption, Engineering Foundation, New York (1984), pp. 305-314, AJChE Symp. Ser No. 233, 80, 34 (1984)], networks [Aviles and LeVan, Chem. Eng. Sci., 46, 1935 (1991)], and general structures of constant cross section [RudisiU and LeVan, Jnd. Eng. Chem. Res., 29, 1054 (1991)]. 

In a typical pulse experiment, a pulse of known size, shape and composition is introduced to a reactor, preferably one with a simple flow pattern, either plug flow or well mixed. The response to the perturbation is then measured behind the reactor. A thermal conductivity detector can be used to compare the shape of the peaks before and after the reactor. This is usually done in the case of non-reacting systems, and moment analysis of the response curve can give information on diffusivities, mass transfer coefficients and adsorption constants. The typical pulse experiment in a reacting system traditionally uses GC analysis by leading the effluent from the reactor directly into a gas chromatographic column. This method yields conversions and selectivities for the total pulse, the time coordinate is lost. 

Abstract To design an adsorption cartridge, it is necessary to be able to predict the service life as a function of several parameters. This prediction needs a model of the breakthrough curve of the toxic from the activated carbon bed. The most popular equation is the Wheeler-Jonas equation. We study the properties of this equation and show that it satisfies the constant pattern behaviour of travelling adsorption fronts. We compare this equation with other models of chemical engineering, mainly the linear driving force (LDF) approximation. It is shown that the different models lead to a different service life. And thus it is very important to choose the proper model. The LDF model has more physical significance and is recommended in combination with Dubinin-Radushkevitch (DR) isotherm even if no analytical solution exists. A numerical solution of the system equation must be used. 

Very recently, experiments using new techniques have been performed by Lodewyckx et al. [4], X-ray microtomography coupled with image analysis allows visualising dynamic adsorption of organic vapour and water vapour on activated carbon. Figure 17.3 in [4] shows profiles inside the bed at different times. It is remarkable that the fronts seem to be of constant pattern shape. 

In a review paper, LeVan [7] studied constant pattern models for gas adsorption. The model is based on the differential mass balance for the solute ... 

LeVan MD (1989) Asymptotic fixed bed behavior proportionate and constant patterns. In Adsorption Science and Technology , vol 158, NATO-ASI Series. Kluwer, Amsterdam, pp 149-168... 

When the constant pattern of the adsorption zone holds and the amount of an adsorbed is much larger than its concentration in the feed solution, then the velocity of movement of the adsorption zone is given as follows ... 

The time required from the start of feeding to the break point can be estimated with the assumption of the constant pattern stated above. Thus, substitution of Equation 11.10 into Equation 11.6 gives the following equation for the rate of adsorption ... 

The packed density of the bed, the void fraction of the particle bed, and the density ofthe feed solution are 386 kg m , 0.5, and 1000 kg m , respectively. The averaged overall volumetric coefficient of mass transfer is 9.2 h , and a constant pattern of the adsorption zone can be assumed in this case. 

Length of Unused Bed. The constant pattern approximation provides the basis for a very useful and widely used design method based on the concept of the length of unused bed (LUB). In the design of a typical adsorption process the basic problem is to estimate the size of the absorber bed needed to remove a certain quantity of the adsorbable species from the feed stream, subject to a specified limit ((/) on the effluent concentration. The length of unused bed, which measures the capacity of the adsoibei which is lost as a result of the spread of the concentration profile, is defined by... 

Let us first focus on a nonreactive system with constant separation factors. Typical examples are distillation processes with constant relative volatilities or adsorption processes described by competitive Langmuir isotherms. For nonreactive systems with constant separation factors, the constant pattern waves and spreading waves are... 

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