Differential adsorption bed

Macroscopic Methods Sorption Rate (12) IR spectroscopy (16, 17) Frequency response (20) Chromatography (12) ZLC (13) Differential adsorption bed (21) TAP reactor (22) Imaging (23) Membrane permeation (14,15) Effectiveness factor (18, 19) Tracer methods (12)... 

Although adsorbers are generally designed from laboratory data, the approximate performance can sometimes be predicted from equilibrium data and mass-transfer considerations. A mass balance on the solute for the flow of fluid through a differential adsorption-bed length, dz, over a differential-time duration, dt, gives... 

We now investigate the applicability of the heterogeneous model to the experimental data of light hydrocarbons onto activated carbon (Do, 1997). First we present the experimental methods from which the adsorption equilibrium data as well as kinetics data are collected. The method for kinetic measurement is the Differential Adsorption Bed (DAB) method, and the method for equilibrium measurement is the conventional volumetric method. The DAB method has been proven to be an useful and reliable means to collect the adsorption kinetics, and is described in the next section. 

Chapters 9 to 11 deal with the dynamic analysis of a single particle exposed to a constant bulk environment. The method of differential adsorption bed discussed in Chapter 11 is suitable for the application of the single particle analysis. A permeation method called the time lag method is useful for characterisation of diffusional flow, viscous flow and surface flow of pure gas through a single pellet (Chapter 12). The diffusion cell method either in steady state mode or transient mode is useful to characterize binary diffusional systems (Chapter 13). All these methods evolve around the analysis of a single particle and they complement each other in the characterization of diffusion and adsorption characteristics of a system. From the stand point of system set-up, the time lag and diffusion cell methods require a careful mounting of a particle or particles between two chambers and extreme care is exercised to avoid any gas by-passing the particle. 

After the few chapters on equilibria, we deal with kinetics of the various mass transport processes inside a porous particle. Conventional approaches as well as the new approach using Maxwell-Stefan equations are presented. Then the analysis of adsorption in a single particle is considered with emphasis on the role of solid structure. Next we cover the various methods to measure diffusivity, such as the Differential Adsorption Bed (DAB), the time lag, the diffusion cell, chromatography, and the batch adsorber methods. 

Mayfield, P.L.J., and Do, D.D., Measurement of the single-component adsorption kinetics of ethane, butane, and pentane onto activated carbon using a differential adsorption bed, Ind. Eng. Chem Res.. 30(6), 1262-1270 (1991). 

Equations (16), (20) and (22) each are a set of N simultaneous first order differential equations which can be integrated to give the mole fraction profile within the adsorption bed as a function of the dimensionless time x during the step... 

Adsorption beds are essentially transient, spatially distributed sterns, where the properties in the solid and gas phases varying over time in one or more spatial dimensions. The mathematical description of adsorption beds is usually described by a series of partial differential equations and a ebraic equatimis. In this paper, distinguishable features of the CSS model are briefly given. 

Huang, Y.H., et al.. Experimental study of binary equilibrium adsorption desorption of propane-propylene mixtures on 13X sieves by differential sorption bed system and investigation of their equilibrium expressions, Sep. Technol., 4(3), 156-166 (1994). 

However, the real point of Eq. 15.4-6 is not its accuracy but what it says about the adsorption zone. It says that the key to this zone is a quantity vjka), which is a close parallel to the length of unused bed / and to the height of transfer unit (HTU) used for differential adsorption and distillation ... 

Dyna.micPerforma.nce, Most models do not attempt to separate the equiUbrium behavior from the mass-transfer behavior. Rather they treat adsorption as one dynamic process with an overall dynamic response of the adsorbent bed to the feed stream. Although numerical solutions can be attempted for the rigorous partial differential equations, simplifying assumptions are often made to yield more manageable calculating techniques. 

Adsorbent drying systems are typicaHy operated in a regenerative mode with an adsorption half-cycle to remove water from the process stream and a desorption half-cycle to remove water from the adsorbent and to prepare it for another adsorption half-cycle (8,30,31). UsuaHy, two beds are employed to aHow for continuous processing. In most cases, some residual water remains on the adsorbent after the desorption half-cycle because complete removal is not economically practical. The difference between the amount of water removed during the adsorption and desorption half-cycle is termed the differential loading, which is the working capacity available for dehydration. 

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 differential equation of the second order Fickian model, requires two boundary conditions for its solution. The constant pattern pertains to a bed of infinite depth—in obtaining the solution we apply the downstream boundary condition cf — 0 as NPeC, —> < >. Breakthrough behavior presumes the existence of a bed outlet, and a boundary condition must be applied there. 

Reaction rates for the start-of-cycle reforming system are described by pseudo-monomolecular rates of change of the 13 kinetic lumps. That is, the rates of change of the lumps are represented by first-order mass action kinetics with the same adsorption isotherm applicable to each reaction step. Following the same format as Eq. (4), steady-state material balances for the hydrocarbon lumps are derived for a plug-flow, fixed bed catalytic reformer. A nondissociation, Langmuir-Hinshelwood adsorption model is employed. Steady-state material balances written over a differential fractional catalyst volume dv are the following ... 

Tphe breakthrough curve for a fixed-bed adsorption column may be pre-dieted theoretically from the solution of the appropriate mass-transfer rate equation subject to the boundary conditions imposed by the differential fluid phase mass balance for an element of the column. For molecular sieve adsorbents this problem is complicated by the nonlinearity of the equilibrium isotherm which leads to nonlinearities both in the differential equations and in the boundary conditions. This paper summarizes the principal conclusions reached from a recent numerical solution of this problem (1). The approximations involved in the analysis are realistic for many practical systems, and the validity of the theory is confirmed by comparison with experiment. 

A three-bed adsorption unit is illustrated in Figure 15.16. It is used to dry the feed to a distillation column with a top temperature of —70°F thus a water dewpoint of —90°F is required. One of the vessels always is on regeneration and cooling down, and the other two in series on adsorption, with the more recently reactivated one downstream. A bleed off the process stream is diverted to use as regenerant. After the gas leaves the vessel being regenerated, the water is condensed out by cooling and the gas returns to the process downstream of a control valve that maintains a 10 psi differential. 

In most adsorption processes the adsorbent is contacted with fluid in a packed bed. An understanding of the dynamic behavior of such systems is therefore needed for rational process design and optimization. What is required is a mathematical model which allows the effluent concentration to be predicted for any defined change in the feed concentration or flow rate to the bed. The flow pattern can generally be represented adequately by the axial dispersed plug-flow model, according to which a mass balance for an element of the column yields, for the basic differential equation governing llie dynamic behavior,... 

Since the mobile phase is moving on a dry bed, several other undesirable effects occur. The adsorption of the first liquid (at the front) on the stationary phase is exothermic, causing the front to have a higher temperature than the rest of the system. Since the temperature of the system is not usually controlled but is allowed to assume the ambient value, some evaporation may occur at the solvent front. If the solvent is composed of a mixture of liquids, preferential evaporation of the most volatile one will cause a slight change in the solvent composition. In fact, the adsorption of a mixed mobile phase will probably also cause some changes in composition because the most polar component will be preferentially sorbed. The situation can become so severe that solvent demixing can occur. At best, a mixed solvent mobile phase is probably not uniform across the planar bed, and some temperature differentials probably exist as well. 

The total acidity deterioration and the acidity strength distribution of a catalyst prepared from a H-ZSM-5 zeolite has been studied in the MTG process carried out in catalytic chamber and in an isothermal fixed bed integral reactor. The acidity deterioration has been related to coke deposition. The evolution of the acidic structure and of coke deposition has been analysed in situ, by diffuse reflectance FTIR in a catalytic chamber. The effect of operating conditions (time on stream and temperature) on acidity deterioration, coke deposition and coke nature has been studied from experiments in a fixed integral reactor. The technique for studying acidity yields a reproducible measurement of total acidity and acidity strength distribution of the catalyst deactivated by coke. The NH3 adsorption-desorption is measured by combination of scanning differential calorimetry and the FTIR analysis of the products desorbed. 

If a sound theoretical adsorption wave expression could be applied to this problem, it would not only greatly reduce the number of experiments necessary to define completely the geometry of the bed, but could also be useful in the elucidation of the mechanism of adsorption of various gases on different types of adsorbents, from which information could be derived for their improvement or to indicate when the adsorbent has attained its maximum efficiency. Theoretical treatment of the problem has been made by various investigators (73,74,75). However, these workers did not have sufficient experimental data to support their views. The problem of adsorption by charcoal was treated by Wicke (76) and a number of useful differential equations derived. However, a real... 

In order to minimize external (bed) diffusion resistance and maximize the heat transfer rate it is desirable to use a very small adsorbent sample with the crystals spread as thinly as possible over the balance pan or within the containing vessel. To minimize the effect of non-linearities, such as the strong concentration dependence of the diffusivity, measurements should be made differentially over small concentration changes. Variation of the step size and comparison of adsorption and desorption curves provide simple tests for linearity of the system. The large differences between adsorption and desorption diffusivities, reported in some of the earlier work, have been shown to be due to the concentration dependence of the diffusivity(8) and in differential measurements under similar conditions no such anomaly was observed. 

Horstmann and Chase [35] have used the mass transfer parameters determined in stirred tank experiments to simulate the breakthrough curves of affinity chromatography experiments. Numerical methods using different computer packages were carried out to solve the differential equations of the stirred tank adsorption and to predict the performances of a packed bed chromatographic column. 

The operating conditions needed for adsorption rate measurements differ considerably from the requirements of the preparative packed bed operation mode. Kinetic mass transfer effects will increase as the flow rate is increased and the column capacity decreased. Furthermore, the major problem is to differentiate between a diffusion rate-limited process and the kinetic-limited one. The contribution of the diffusional mass transfer to the overall adsorption process will be reduced by using an immunoadsorbent with a low density of binding sites immobilized on a nonporous support. 

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