Multicomponent gas-phase systems

MULTICOMPONENT GAS-PHASE SYSTEMS 10.3.1. Molar flux in terms of effective diffuslvity 

For a multicomponent system, the bulk flow velocity up is given by  

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In this treatment only the ordinary and Knudsen diffusion mechanisms will be considered. Then, mass transport in isothermal, multicomponent gas phase systems is described by the following constitutive equation ... 

For a multicomponent gas phase system, the appropriate constitutive equations are Equations 1 written in terms of component concentrations. (The reaction mixture is assumed to be an ideal gas.) ... 

Equations (299) and (300) depict the input-output relationships for the concentrations and the temperature in each phase for a given continuous steady-flow dispersed system. Therefore, (299) and (300) can be used in predicting the input-output relationships for a multistage multicomponent gas-liquid system with several continuous stirred vessels in series. 

Chemical Equilibrium The chemical equilibrium approach is more complex computationally than applying the assumption of an infinitely fast reaction. The equilibrium composition of a multicomponent system is estimated by minimizing the Gibbs free energy of the system. For a gas-phase system with K chemical species, the total Gibbs free energy may be written as... 

If you apply the Gibbs phase rule to a multicomponent gas-liquid system at equilibrium, you will discover that the compositions of the two phases at a given temperature and pressure are not independent. Once the composition of one of the phases is specified (in terms of mole fractions. mass fractions, concentrations, or. for the vapor phase, partial pressures), the composition of the other phase is fixed and, in principle, can be determined from physical properties of the system components. 

The purpose of this chapter is to give a comprehensible overview of a few frequently used adsorption isotherms (Als) for single- and multicomponent gas adsorption systems. The adsorption isotherm (AI) is, in the sense of thermodynamics, the thermal equation of state [7.81] for the adsorbed phase, i. e. a function... 

B. J. Anderson, M. Z. Bazant, J. W. Tester, and B. L. Trout, J. Phys. Chem. B, 109, 8153 (2005). Application of the Cell Potential Method To Predict Phase Equilibria of Multicomponent Gas Hydrate Systems. 

For prediction of gas phase diffusion coefficients in multicomponent hydi ocarbon/nonKydi ocai bon gas systems, the method of Wilke shown in Eq. (2-154) is used. 

To derive an explicit expression of the rate of desorption we restrict ourselves to nondissociative adsorption, listing references to other systems— such as multicomponent and multilayer adsorbates with and without precursors—for which such a treatment has been given, later. We look at a situation where the gas phase pressure of a molecular species, P, is different from its value, P, which maintains an adsorbate at coverage 6. There is then an excess flux to re-establish equilibrium between gas phase and adsorbate so that we can write [7-10]... 

It is known that, in a water phase, immiscible liquids such as gasoline or other petroleum products may form multicomponent droplets of various forms and sizes, under dispersive conditions. These droplets are transported by convection and diffusion, which contributes to the contamination of fresh water systems. However, during droplet transport, more volatile substances partition to the gas phase at the droplet surface, leaving less volatile material that volatilizes more slowly. More volatile material still exists in the droplet interiors, and it tends to diffuse toward the surface because of concentration gradients created by prior volatilization. Different components in a droplet have different volatilization rates, which may vary significantly during droplet transport, and as a result, the contamination of fresh water is affected accordingly. 

The system of equations for gas phase was obtained by Favre averaging the system of multicomponent multiphase medium. The modified k-e model is used to describe the behavior of the gas phase. The generalization of this model will... 

It is not known whether high-pressure fluids are Newtonian fluids that behave according to the laws given by Eqns. (3.4-1), (3.4-2), and (3.4-3). With regards to diffusion problems, for example, the Fickian nature of diffusion may be rather the exception than the rule. The diffusivity often depends on solute concentration, not only in extraction with a supercritical gas [1] but also in ordinary low-pressure diffusion in the gas phase and in diffusion in a liquid in multicomponent systems and in porous media. 

V" kg Gas-phase mass transfer coefficient for multicomponent systems, same units as Icg... 

Reactive absorption processes present essentially a combination of transport phenomena and reactions taking place in a two-phase system with an interface. Because of their multicomponent nature, reactive absorption processes are affected by a complex thermodynamic and diffusional coupling which, in turn, is accompanied by simultaneous chemical reactions [14—16], Generally, the reaction has to be considered both in the bulk and in the film region. Modeling of hydrodynamics in gas-liquid contactors includes an appropriate description of axial dispersion, liquid hold-up and pressure drop. 

It should be noted that distribution coefficients Ki comprise both fugacities in the gas phase and activity coefficients in the liquid phase. These coefficients are determined by the three-parametric Electrolyte-NRTL method. The latter is based on the local composition concept and satisfactorily represents physical interactions of this multicomponent electrolyte system [46]. 

In the preceeding sections, development of the measurement technique and analysis of gas-phase characteristics in a slurry bubble column have been made along with some comparison of the experimental data with other correlations from the literature. Up to this point, analysis of gas-phase characteristics has included only single or binary liquid components. Recently, a large effect on gas holdup and bubble size has been observed for multicomponent liquid mixtures that contain small concentrations of surface-active species (24). In their study, mixtures of alcohols and water at alcohol concentrations less than 0.1 percent caused a dramatic increase in gas holdup (up to a factor of 2) and a decrease in bubble size (up to a factor of 4) compared to those observed for the water system. The authors think the effect is the result of- interaction between molecules of different species, leading to an enrichment of one species in the interface. Therefore, in multicomponent liquid mixtures, it is necessary to have knowledge of the presence of surface-active species as well as the physical properties of the fluid. 

It will he shown that the behavior of heterogeneous systems is influenced by the number of components it contains. A system which consists of a single, pure substance will behave differently from one which is made up of two or more components when the pressure and temperature are such that both a liquid phase and a gas phase are present. Consequently, the discussion of phase behavior will begin with a description of single-component systems. This will be followed by a description of two-component systems. Finally, multicomponent... 

When multicomponent gas and liquid phases are in equilibrium, a limited number of intensive system variables may be specified arbitrarily (the number is given by the Gibbs phase rule), and the remaining variables can then be determined using equilibrium relationships for the distribution of components between the two phases. In this section we define several such relationships and illustrate how they are used in the solution of material balance problems. 

A detailed example of a complex gas-phase equilibrium calculation is given by Smith, Van Ness, and Abbott [Introduction to Chemical Engineering Thermodynamics, 5th ed., Example 15.13, pp. 602-604 6th ed., Example 13.14, pp. 511-513 7th ed.. Example 13.14, pp. 527-528, McGraw-Hill, New York (1996, 2001, 2005)]. General application of the method to multicomponent, multiphase systems is treated by Iglesias-Silva et al. [Fluid Phase Equilih. 210 229-245 (2003)] and by Sotyan, Ghajar, and Gasem [Ind. Eng. Chem. Res. 42 3786-3801 (2003)/. 

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. 

It is interesting to note that although the transfer process is predominantly gas-phase mass transfer controlled, there is a finite contribution from the liquid-phase transfer resistance. In multicomponent distillation, it is our experience that it is not safe to ignore the liquid-phase resistance even when for similar operating conditions for a binary system, the liquid-phase resistance is negligible. 

Hofer (1983) has analyzed the influence of gas-phase dispersion on the tray efficiency for binary systems. Extend the analysis for multicomponent mixtures. Include some numerical calculations and write up your work in the form of a paper for possible publication in the AIChEJ. 

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