Multicomponent adsorption problems

Multicomponent pollutants in an aqueous environment and/or leachate of SWMs, which are COMs, usually consist of more than one pollutant in the exposed environment [1, 66-70]. Multicomponent adsorption involves competition among pollutants to occupy the limited adsorbent surface available and the interactions between different adsorbates. A number of models have been developed to predict multicomponent adsorption equilibria using data from SCS adsorption isotherms. For simple systems considerable success has been achieved but there is still no established method with universal proven applicability, and this problem remains as one of the more challenging obstacles to the development of improved methods of process design [34,71 - 76]. 

The problem of predicting multicomponent adsorption equilibria from single-component isotherm data has attracted considerable attention, and several more sophisticated approaches have been developed, including the ideal adsorbed solution theory and the vacancy solution theory. These theories provide useful quantitative correlations for a number of binary and ternary systems, although available experimental data are somewhat limited. A simpler but purely empirical approach is to use a modified form of isotherm expression based on Langmuir-Freundlich or loading ratio correlation equations ... 

The differences in critical molecular sizes of the different components involved in the multicomponent adsorption of large molecules give additional complexities in the problem of the pore network accessibility. Here we will briefly describe the influence of percolation phenomena and accessibility on binary adsorption. Further details of this are presented elsewhere [9,10]. 

The variety of activated carbons, carbon fiben, and carbon monoliths present on the market along with differences in the molecules to be adsorbed— removed causes that the choice of the adsorbents for a desired application becomes a difficult task. The capacities, for H2S, SO2, NO,., HCN, or VOCs removal depend on the type of carbon used (Fig. 21.3). The problem is even more complex when multicomponent adsorption is expected to occur and the regeneration options have to be considered. Usually carbon specifications... 

The issue of multicomponent adsorption still poses a fundamental problem to researchers working in the adsorption area. Many mathematical models have been proposed to address this problem, and there have been reviews such as those cited in this chapter. The choice of an appropriate model rests on the balance of simplicity and capability of the model as weU as the intended application of the model. For example, for quick calculation of the multicomponent equilibria of similar adsorbates (such as low-order paraffin gases), simple models such as the FastlAS and the extended Sips model are adequate. However, to study the influence of the porous structure of activated carbon on the adsorption equilibrium properties of nonpolar adsorbents, the MPSD model is complex enough, while still retaining some simplicity, to explain the effects of factors such as micropore size distribution and adsorbate molecular properties on the adsorption equilibria. 

In gravimetric adsorption measurements of pure gases adsorption of the gas on walls of tubes and vessels does not pose a problem as no mass balances of the gas are necessary. However, in multicomponent adsorption measurements it may influence the sorptive gas concentration to a certain extent, especially at low gas pressures and temperatures (T < 77K), and if- for example in a binary gas mixture -one component is strongly, the other only weakly adsorbed. Electropolishing of inner surfaces of all tubes and vessels, preferably made of stainless steel, can reduce this problem considerably. 

The linear equilibrium isotherm adsorption relationship (Eq. 11) requires a constant rate of adsorption, and is most often not physically valid because the ability of clay solid particles to absorb pollutants decreases as the adsorbed amount of pollutant increases, contrary to expectations from the liner model. If the rate of adsorption decreases rapidly as the concentration in the pore fluid increases, the simple Freundlich type model (Eqs. 8 and 9) must be extended to properly portray the adsorption relationship. Few models can faithfully portray the adsorption relationship for multicomponent COM-pollutant systems where some of the components are adsorbed and others are desorbed. It is therefore necessary to perform initial tests with the natural system to choose the adsorption model specific to the problem at hand. From leaching-column experimental data, using field materials (soil solids and COMs solutions), and model calibration, the following general function can be successfully applied [155] ... 

Although the multicomponent Langmuir equations account qualitatively for competitive adsorption of the mixture components, few real systems conform quantitatively to this simple model. For example, in real systems the separation factor is generally concentration dependent, and azeotrope formation (a = 1.0) and selectivity reversal (a varying from less than 1.0 to more than 1.0 over the composition range) are relatively common. Such behavior may limit the product purity attainable in a particular adsorption separation. It is sometimes possible to avoid such problems by introducing an additional component into the system which will modify the equilibrium behavior and eliminate the selectivity reversal. 

Many practical adsorption processes involve multicomponent systems, so the problem of micropore diffusion in a mixed adsorbed phase is both practically and theoretically important. Major progress in understanding the interaction effects has been achieved by Krishna and his coworkers through the application of the Stefan-Maxwell approach. The diverse patterns of concentration dependence of diffusivity that have been observed for many systems can, in most cases, be understood on this basis. The reader is referred, for details, to the review articles cited in the bibliography. 

For multicomponent systems, the expression for y here employed may be shown equivalent to that involved in the cluster diagram technique (6), which is currently being employed in a variety of problems. The present derivation shows that the starting expressions satisfy the thermodynamic consistency relation embodied by the adsorption isotherm. It is, however, important to observe that any direct application of these alternative rigorous approaches, which is of necessity of an approximate nature, leads to some violation of the complete internal equilibrium conditions. Similarly, calculations of surface tension which employ the adsorption equation as a starting point invariably violate mechanical equilibrium in some order of approximation. 

For the solution of sophisticated mathematical models of adsorption cycles including complex multicomponent equilibrium and rate expressions, two numerical methods are popular. These are finite difference methods and orthogonal collocation. The former vary in the manner in which distance variables are discretized, ranging from simple backward difference stage models (akin to the plate theory of chromatography) to more involved schemes exhibiting little numerical dispersion. Collocation methods are often thought to be faster computationally, but oscillations in the polynomial trial function can be a problem. The choice of best method is often the preference of the user. 

A division Into "adsorption from dilute solution" and "adsorption from binary (and multicomponent) mixtures covering the entire mole fraction scale" appears to be useful. For simplicity, we shall designate mixtures covering the entire mole fraction scale as binary mixtures, as opposed to dilute solutions. This distinction is a consequence of issues (1) - (3) above, and reflected in thermodynamic and statistical interpretations. For instance, in dilute solutions locating the Gibbs dividing plane is not a problem, but for a mixture in which one of the components cannot confidently be identified as the solvent, it is. 

Unfortunately, the study of phase equilibria in solution, e.g., liquid-solid adsorption, is not a highly popular area of research. Gas-solid adsorption and vapor-solution equilibria have been studied in far more detail, although most of the information available concerns the fate of single components in a diphasic system. Liquid-solid adsorption has benefited mainly from the extension of the concepts developed for gas phase properties to the case of dilute solutions. Multicomponent systems and the competition for interaction with the stationary phase are research areas that have barely been scratched. The problems are difficult. The development of preparative chromatography and its applications are changing this situation. 

All cases of practical importance in liquid chromatography deal with the separation of multicomponent feed mixtures. As shown in Chapter 2, the combination of the mass balance equations for the components of the feed, their isotherm equations, and a chromatography model that accounts for the kinetics of mass transfer between the two phases of the system permits the calculation of the individual band profiles of these compounds. To address this problem, we need first to understand, measure, and model the equilibrium isotherms of multicomponent mixtures. These equilibria are more complex than single-component ones, due to the competition between the different components for interaction with the stationary phase, a phenomenon that is imderstood but not yet predictable. We observe that the adsorption isotherms of the different compounds that are simultaneously present in a solution are almost always neither linear nor independent. In a finite-concentration solution, the amount of a component adsorbed at equilib-... 

The use of pattern recognition techniques in conjunction with sensor arrays constitutes a promising approach for multicomponent analysis and for improved selectivity [26]. Similarly, a smart sensor system that employs a temperature-controlled array of SAW sensors, automated sample preconcentration, and pattern recognition has been described [27], The proposed technology seems to offer a satisfactory solution for the problems associated with non-selective adsorption by coating materials. 

To calculate thermodynamic equilibrium in multicomponent systems, the so-called optimization method and the non-linear equation method are used, both discussed in [69]. In practice, however, kinetic problems have also to be considered. A heterogeneous process consists of various occurrences such as diffusion of the starting materials to the surface, adsorption of these materials there, chemical reactions at the surface, desorption of the by-products from the surface and their diffusion away. These single occurrences are sequential and the slowest one determines the rate of the whole process. Temperature has to be considered. At lower substrate temperatures surface processes are often rate controlling. According to the Arrhenius equation, the rate is exponentially dependent on temperature ... 

The main problem in the thermodynamic theory of penetration is to determine the dependence of the adsorption of a soluble surfactant on its bulk concentration for any given (constant) adsorption of the insoluble surfactant (surface concentration), and the onset of the surface pressure jump in mixed monolayers, caused by the adsorption of a soluble surfactant in the presence of the insoluble component. There exist several main theoretical approaches to the description of the penetration thermodynamics. One is based on the Gibbs adsorption equation for multicomponent monolayers [143-146], Another approach, initially proposed by Pethica... 

The study of protein adsorption by FT-IR has not been a single project instead it has involved a series of research steps that are generally outlined in flowsheet format in Figure 1. This perspective demonstrates the need to solve certain technical problems before more advanced, and more technically interesting, experiments can be performed and/or interpreted. For example, just as it is necessary to develop appropriate flow cells before kinetic data can be acquired, so also must the approaches to the analysis of protein mixtures from their infrared spectra be learned before software can be optimized for multicomponent analysis. 

Even though these isotherms presumably account for nonuniform surfaces, they have primarily been developed for single adsorbing components. Thus, the rational extensions to interactions in multicomponent systems is not yet possible, as with the Langmuir isotherm. This latter point is important for our further applications, and so we essentially use only the Langmuir isotherms for developing kinetic rate expressions. However, not all adsorption data can be represented by a Langmuir isotherm, and this is still an unresolved problem in catalytic kinetics. 

The processes discussed in this chapter demonstrate the great variety of phase equilibrium that can arise beyond the basic vapor-liquid problems discussed in most of the previous chapters. Many other systems could be included The adsorption of gases onto solids (used in the removal of pollutants from air), the distribution of detergents in water/oil systems, the wetting of solid surface by a liquid, the formation of an electrochemical cell when two metals make contact are all examples of multiphase/multicomponent equilibrium. They all share one important common element their equilibrium state is determined by the requirement that the chemical potential of any species must be the same in any phase where the species can be found. These problems are beyond the scope of this book. The important point is this The mathematical development of equilibrium (Chapter 10) is extremely powerful and encompasses any system whose behavior is dominated by equilibrium. 

Adsorption kinetics of a single particle (activated carbon type) is dealt with in Chapter 9, where we show a number of adsorption / desorption problems for a single particle. Mathematical models are presented, and their parameters are carefully identified and explained. We first start with simple examples such as adsorption of one component in a single particle under isothermal conditions. This simple example will bring out many important features that an adsorption engineer will need to know, such as the dependence of adsorption kinetics behaviour on many important parameters such as particle size, bulk concentration, temperature, pressure, pore size and adsorption affinity. We then discuss the complexity in the dealing with multicomponent systems whereby governing equations are usually coupled nonlinear differential equations. The only tool to solve these equations is... 

We have discussed in the last two chapters about the various transport mechanisms (diffusive and viscous flows) within a porous particle (Chapter 7) and the systematic approach of Stefan-Maxwell in solving multicomponent problems (Chapter 8). The role of diffusion in adsorption processes is important in the sense that in almost every adsorption process diffusion is the rate limiting step owing to the fact that the intrinsic adsorption rate is usually much faster than the diffusion rate. This rate controlling step has been recognized by McBain almost a century ago (McBain, 1919). This has prompted much research in adsorption to study the diffusion process and how this diffusional resistance can be minimized as the smaller is the time scale of adsorption the better is the performance of a process. 

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