Isotherm column dynamics

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

The simplest adsorption equation is Henry s Law, that is, the loading is directly proportional to the sorbate partial pressure. X= KP This linear isotherm equation adequately describes some adsorbents and, in the limit of low coverage, it actually describes most sorbents. For adsorption that is truly described by Henry s Hnear relationship, the loadings are low, the adsorption is bound to be essenhaUy isothermal and there are several published analytical solutions to describe both batch kinetics and column dynamic behavior for such systems. 

Langmuir isotherm or model Simple mathematical representation of a favorable (type I) isotherm defined by Eq. (2) for a single component and Eq. (4) for a binary mixture. The separation factor for a Langmuir system is independent of concentration. This makes the expression particularly useful for modeling adsorption column dynamics in multicomponent systems. 

Unfortunately, the available experimental results suggest that the column saturation capacity is often not the same for the components of a binary mixture, so Eq. 4.5 does not account accurately for the competitive adsorption behavior of these components [48]. A simple approach was proposed to turn the difficulty (next subsection). Although it is applicable in some cases, more sophisticated models seem necessary. Numerous isotherm models have been suggested to solve this problem. Those resulting from the ideal adsorbed solution (IAS) theory developed by Myers and Prausnitz [49] are among the most accurate and versatile of them. Later, this theory was refined to accormt for the dependence of the activity coefficients of solutes in solution on their concentrations, leading to the real adsorption solution (RAS) theory. In most cases, however, the equations resulting from IAS and the RAS theories must be solved iteratively, which makes it inconvenient to incorporate those equations into the numerical calculations of column dynamics and in the prediction of elution band profiles. 

In the preceding chapter we restricted our consideration of adsorption column dynamics to isothermal or near isothermal systems containing no more than two components. Indeed, most of the discussion was further restricted to systems containing only one adsorbable species in an inert carrier or solvent. The distinguishing feature of such systems is that the concentration profile shows only a single transition or mass transfer zone. In many adsorption systems of practical interest the situation is more complicated because the column is run adiabatically rather than isothermally and there are commonly more than one adsorbable components present in the feed. In such systems the concentration profile comprises more than one mass transfer zone. 

EQUILIBRIUM THEORY OF ADSORPTION COLUMN DYNAMICS FOR ISOTHERMAL SYSTEMS... 

Some methods for pore structure analysis have been presented The adsorption of benzene and the evaluation of isotherms through the Dubinin - Radushkevich equation, the estimation of immersion heats in benzene, the adsorption of water at relative pressures of h=0.6 and 1.0, the size exclusion liquid chromatography with tracers of different molecular diameters and the one - point adsorption of nitrogen. Six active carbons are included in the investigations. It is not possible to obtain reliable values with the simple water adsorption method. The results obtained with other methods are compared with performances of adsorption of phenol from aqueous solutions as obtained from measuring equilibria and column dynamics. It is shown, that the rank of the results of pore structure analysis is the same as from the dynamic experiments. 

The results of these static measurements can then be used to rate the probable usefulness of different adsorbents. However, the isotherm results from static water solutions do not apply to dynamic column situations in which equilibrium conditions may not occur. A better approach is to generate frontal breakthrough curves that can then be used to estimate the use of different polymers for different solutes dissolved in water. Theoretical and experimental reports (97, 143, 181, 286, 319-321, 537) discuss details about affinity measurements. These details are not included in this review because affinity is discussed only qualitatively in the sections on Theoretical Considerations and Generalized Methodology. These qualitative discussions suggest that neutral polymers such as the styrene-divinylbenzenes are efficient for adsorbing neutral hydrophobic solutes from water solutions but have little affinity for polar and ionic solutes. If the polarity of the polymer is increased to that of the acrylates, the affinity for neutral hydrophobic components will suffer but the more polar solutes will be better adsorbed. In the absence of actual test results under dynamic column flow conditions, the simple likes adsorb likes concept is invoked. 

Proportionate Pattern Behavior. If the isotherm is unfavorable (as in Fig. 1,111), the stable dynamic situation leading to constant pattern behavior can never be achieved. The equilibrium adsorbed-phase concentration then lies above rather than below the actual adsorbed-phase profile. As the mass transfer zone progresses through the column it broadens, but the limiting situation, which is approached in a long column, is simply local equilibrium at all points (c = c ) and the profile therefore continues to... 

Fortunately, the effects of most mobile-phase characteristics such as the nature and concentration of organic solvent or ionic additives the temperature, the pH, or the bioactivity and the relative retentiveness of a particular polypeptide or protein can be ascertained very readily from very small-scale batch test tube pilot experiments. Similarly, the influence of some sorbent variables, such as the effect of ligand composition, particle sizes, or pore diameter distribution can be ascertained from small-scale batch experiments. However, it is clear that the isothermal binding behavior of many polypeptides or proteins in static batch systems can vary significantly from what is observed in dynamic systems as usually practiced in a packed or expanded bed in column chromatographic systems. This behavior is not only related to issues of different accessibility of the polypeptides or proteins to the stationary phase surface area and hence different loading capacities, but also involves the complex relationships between diffusion kinetics and adsorption kinetics in the overall mass transport phenomenon. Thus, the more subtle effects associated with the influence of feedstock loading concentration on the... 

Figure 2. Capillary gas chromatogram of blended pineapple pulp volatiles obtained by dynamic headspace sampling. Temperature programmed from SOX (4 min isothermal) to 180X at 2X/min on a 60m X 0.32 mm i.d. DB-WAX column. The peak numbers correspond to the numbers in Table II.

Isotherms are normally developed to evaluate the capacity of the carbon for the adsorption of different contaminants. Data are obtained in batch tests, which determine the equilibrium relationship between the compound adsorbed on the carbon and that remaining in solution. The isotherms are used as screening tools to determine which carbon is suitable for a given application. Batch equilibrium tests are often complemented by dynamic column studies to determine system size requirements, contact time, and carbon usage rates [19]. Other parameters that are used to characterize activated carbons for water treatment include phenol number, an index of the ability to remove taste and odor, and molas.ses number, which correlates with the ability to adsorb higher molecular weight substances. However, these parameters still do not reflect performance in service, and they can only be considered as guidelines. 

The plate number characterizes the influence of fluid dynamics and mass transfer on the chromatogram for a given column but not the thermodynamic effects of nonlinear isotherms. Therefore this characterization is not applicable in the range of nonlinear chromatography. Consequently, the resolution is not defined as well. 

The study of a particular adsorption process requires the knowledge of equilibrium data and adsorption kinetics [4]. Equilibrium data are obtained firom adsorption isotherms and are used to evaluate the capacity of activated carbons to adsorb a particular molecule. They constitute the first experimental information that is generally used as a tool to discriminate among different activated carbons and thereby choose the most appropriate one for a particular application. Statistically, adsorption from dilute solutions is simple because the solvent can be interpreted as primitive, that is to say as a structureless continuum [3]. Therefore, all equations derived firom monolayer gas adsorption remain vafid. Some of these equations, such as the Langmuir and Dubinin—Astakhov, are widely used to determine the adsorption capacity of activated carbons. Batch equilibrium tests are often complemented by kinetics studies, to determine the external mass transfer resistance and the effective diffusion coefficient, and by dynamic column studies. These column studies are used to determine system size requirements, contact time, and carbon usage rates. These parameters can be obtained from the breakthrough curves. In this chapter, I shall deal mainly with equilibrium data in the adsorption of organic solutes. 

Fig. 10-5. Observed Mg effluent concentrations from undisturbed soil columns with a model-fitted curve determined using a two-site, nonequilibrium model where R = 2.11 was determined from a dynamic isotherm and / and a were best-fit (0.11 0.04 and 1.89 0.17 h , respectively) [from Jardine et al. (1988), with permission].

As mentioned earher, the plate theory has played a role in the development of chromatography. The concept of "plate" was originally proposed as a measmement of the performance of distillation processes. It is based upon the assumption that the column is divided into a number of zones called theoretical plates, that are treated as if there exists a perfect equilibrium between the gas and the Hquid phases within each plate. This assumption imphes that the distribution coefficient remains the same fi-om one plate to another plate, and is not affected by other sample components, and that the distribution isotherm is hnear. However, experimental evidences show that this is not true. Plate theory disregards that chromatography is a dynamic process of mass transfer, and it reveals httle about the factors affecting the values of the theoretical plate number. In principle, once a sample has been introduced, it enters the GC column as a narrow-width "band" or "zone" of its composite molecules. On the column, the band is further broadened by interaction of components with the stationary phase which retains some components more than others. Increasing... 

Experimental interest lies in the value of q that depends on the applied concentration, that is, where q =/(c), which thus describes the isotherm-of the adsorbate. Application of protein solution to the column produced an effluent profile of the type shown in Figure 5. The amount of protein adsorbed may be calculated by integrating the area between the void volume and the actual effluent profile (lateral diffusion, DM, does not modify the integrated area). A series of runs using different cG values thus establishes a dynamic isotherm. 

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