Concentration profiles desorption

At about 100 C, the desorption of radon from charcoal is rapid and efficient enough to fully regenerate a charcoal bed in a reasonable amount of time. The desorption concentration profile also features an inflection point (see Figure 3). Equation (4) can therefore also be applied to find an optimal temperature for the desorption process. 

Figure 8 shows how the intrapellet concentration profiles vary with time during the course of CO desorption. Both the gas-phase (solid lines) and surface (dotted lines) CO concentration profiles exhibit relatively mild gradients inside the pellet, in contrast to the steep profiles established during the adsorption process. This can be attributed to the fact that the intrinsic rate of desorption is slower than that of adsorption. 

Figure 8. Computed time variation of intrapellet concentration profiles during CO desorption. Key ----------------------, gas phase and----, surface.

The input data required for parameter determinations are the concentration profiles at all time steps. These data can be obtained from leaching cell experiments. Thus, for example, in the case of desorption analysis, the concentration of the absorbed pollutants considered in the hypothetical example, at all... 

Figure 14. Simple model demonstrating how adsorption and surface diffusion can co-Urnit overall reaction kinetics, as explained in the text, (a) A semi-infinite surface establishes a uniform surface coverage Cao of adsorbate A via equilibrium of surface diffusion and adsorption/desorption of A from/to the surrounding gas. (b) Concentration profile of adsorbed species following a step (drop) in surface coverage at the origin, (c) Surface flux of species at the origin (A 4i(t)) as a function of time. Points marked with a solid circle ( ) correspond to the concentration profiles in b. (d) Surface flux of species at the origin (A 4i(ft>)) resulting from a steady periodic sinusoidal oscillation at frequency 0) of the concentration at the origin.

The lumped pore model (often referred to as the POR model) was derived from the general rate model by ignoring two details of this model [5]. The first assumption made is that the adsorption-desorption process is very fast. The second assumption is that diffusion in the stagnant mobile phase is also very fast. This latter assumption leads to the consequence that there is no radial concentration gradient within a particle. Instead of the actual radial concentration profile across the porous particle, the model considers simply its average value. 

When a concentration profile is known to follow a theoretical equation and is fit by the equation, it is important to include "free data," which are natural constraints. For example, in desorption experiments, under the right conditions, the surface concentration is zero. Even if surface concentration cannot be directly measured, this free data point should be applied. Another example is that the fraction of mass loss or gain at time zero is zero. Hence, the linear fit between the fraction and square root of time should be forced through the (0, 0) point (Figure 3-30b). Although this seems a trivial issue, new practitioners may overlook it. 

Surface diffusion can be studied with a wide variety of methods using both macroscopic and microscopic techniques of great diversity.98 Basically three methods can be used. One measures the time dependence of the concentration profile of diffusing atoms, one the time correlation of the concentration fluctuations, or the fluctuations of the number of diffusion atoms within a specified area, and one the mean square displacement, or the second moment, of a diffusing atom. When macroscopic techniques are used to study surface diffusion, diffusion parameters are usually derived from the rate of change of the shape of a sharply structured microscopic object, or from the rate of advancement of a sharply defined boundary of an adsorption layer, produced either by using a shadowed deposition method or by fast pulsed-laser thermal desorption of an area covered with an adsorbed species. The derived diffusion parameters really describe the overall effect of many different atomic steps, such as the formation of adatoms from kink sites, ledge sites... 

This expression will predict the movement of a solute whose adsorption is in equilibrium with the surrounding strata. This equilibrium chromatographic motion will result in the migration of a band of activity whose concentration profile is gaussian and whose deviation will be a function of the hydrodynamic dispersion, T (due to statistical variations in path length) and absorptive dispersion T (due to statistical variations in the absorption and desorption process). While these dispersions are interactive and do not sum in a simple fashion they both depend on path length. 

The benefits obtained by integrating adsorption into regenerative heat exchange demonstrate the synergies available between these two related processes. Similar advantages accrue when heat regeneration is incorporated into adsorptive reactors, in which concentration profiles are manipulated to improve reactor performance through selective ad- and desorption of components in the reaction medium. 

Desorption from an oil-water multilaminate should be an accurate model for controlled release from liposomes and lipid multilayers and may be helpful to understand transport through naturally occurring biological laminates such as stratum corneum. Asymptotic solutions based upon simple assumptions about the concentration profile may also be used to understand the desorption properties. 

Figure 2. Concentration profiles in the penetration zone at t = r for forced desorption of CO,.

The experimental desorption concentration profiles were obtained in the same way as the experimental adsorption profiles. However, using the local equilibrium model to describe the process, only qualitatively results can be obtained. Mass transfer resistance has stronger effect on desorption in comparison to adsorption so its importance cannot be neglected in the modeling. 

Diffusion and sorption kinetics are critical for maintenance of sharp concentration profiles in fhe liquid and the beds. Complexation of metals to supported ligands is extremely sensitive to a variety of parameters, and the predominant presence of reactants at the upstream end and products at the downstream end may lead to imdesired variations in adsorption and desorption behavior. 

Figure 2-4 Typical concentration profiles of instantaneous reaction between the gas A and the reactant C, based on film theory, ids Diffusion controlled - slow reaction, (fcl kinetically controlled-slow reaction, (c) gas-film-controlled desorption - fast reaction, 0 liquid-film-controlled desorption-fast reaction, (e) liquid-film-controlled absorption -instantaneous reaction between A and C, (/) gas-film-controlled absorption-instantaneous reaction between A and C, (g) concentration profiles for A, B, and C for instantaneous reaction between A and C-both gas- and liquid-phase resistances are comparable.1 2...

Figure I shows NO and NO2 concentration profile obtained from temperature programmed desorption, (a) is ACF, (b) (f) as CACF, the ratio of KOH to ACF is 1 9, 1 4, 1 3, 1 2, and 1 1, respectively. CACF was increased adsorptivity with offers selective adsorptivity by KOH in NO, adsorption, and CACF (KOH ACF = 1 3) had an adsorptivity that was four times higher than that of ACF. However, excess impregnated KOH (1 2, 1 1) was deactivated by pore blocking. NO, desorption on CACF was mostly...

Figure 1. A. NO and B. NOj concentration profiles obtained from Temperature Programmed Desorption when the bed depths of NOx adsorbed BHAC are 1cm, 2cm, and 9cm.

For complete separation the desorption fronts of the two components must not exceed points 1 and 2 respectively, which are located one column downstream the desorbent and extract port. Since the concentration profile displayed in Fig. 7.16 demonstrates the situation at the end of a switching interval, all ports will move one column downstream in the very next moment. In the case were the desorption front of component B does exceed point 2, the extract stream, meant to withdraw the more retained component A only, will be polluted with B after the ports have been switched. The same applies to point 1. If component A is shifted into section IV the adsorbent will transfer it to the raffinate port and the raffinate will be polluted. For the adsorption fronts, components A and B must not violate points 3 and 4, respec-... 

Figure 7.21 shows the internal axial concentration profiles at the end of a switching interval for a system of linear isotherms and no competitive interaction of the two components. After switching all ports downstream in the direction of the liquid flow, the extract will be polluted with component B because the desorption front of B violates point 2 (Fig. 7.16). 

Only the desorption front of component B is influenced by the increased flow rate in section II - all other fronts are not influenced and remain at their initial position. The decrease in feed flow rate has an impact on the total height of the concentration plateaus, especially in section III. This procedure of shifting the fronts is also applicable for all other sections of the SMB process, to optimize the internal concentration profile according to Fig. 7.16 and improve the process performance with respect to purities, productivity and eluent consumption. 

Applying the same strategy as introduced for linear isotherms, an internal concentration profile as shown in Fig. 7.24 is obtained. Again only the flow rate in section II has been increased by decreasing both extract and feed flow rate. The desorption front of component B is again pushed in the correct direction. However, in this case a change of flow rate in section II does also effect the situation in other sections of... 

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