Multicomponent Gas-Liquid Systems

The same result could have been obtained from the results of part 1 as (3.99 kmol H20/h)/ (34.0 kmol BDA/h). 

Gas-liquid processes that involve several components in each phase include many chemical reactions, distillation, and transfer of one or more species from a gas to a liquid (absorption or scrubbing) or vice versa (stripping). 

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. 

The best way to evaluate equilibrium compositions is from tabulated data. Perry s Chemical Engineers Handbook (see footnote 1), pp. 2-76 through 2-89, gives partial pressures of vapors over various liquid solutions. Example 6.4-1 illustrates the use of such data. 

A gas stream consisting of 100 Ib-mole/h of an S02-air mixture containing 45 mole% SO2 is contacted with liquid water in a continuous absorber at 30 C. The liquid leaving the absorber is analyzed and found to contain 2.00 g of SO2 per 100 g of H2O. Assuming that the gas and liquid streams leaving the absorber are in equilibrium at 30 C and 1 atm. calculate the fraction of the entering SO2 absorbed in the water and the required water feed rate. 

---

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. 

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. 

In this section we review the experimental studies that have been carried out with a view to testing models of multicomponent condensation. There is a great shortage of experimental data on mass transfer in multicomponent vapor (plus inert gas)-liquid systems. Most published works deal with absorption (or condensation or evaporation) of a single species in the presence of a nontransferring component. Thus, this review is necessarily brief. 

With the treatment of gases as individual groups, some binary (or multicomponent) gas-liquid mixtures are reduced to mixtures of only two groups. For example, the carbon dioxide and methanol mixture considered at the conclusion of this section is actually a molecular mixture because both molecules are treated as groups by the UNIFAC approach, Similarly, mixtures of carbon dioxide with benzene or with paraffinic hydrocarbon liquids contain only two groups. The results for such systems are remarkably successful, as will be discussed in this section. The description of mixtures with more than two groups is possible for some of the present models, and the results look promising (Apostolou et al. 1995). 

Table 5.4-3 summarizes the design equations and analytical relations between concentration, C/(, and batch time, t, or residence time, t, for a homogeneous reaction A —> products with simple reaction kinetics (Van Santen etal., 1999). Balance equations for multicomponent homogeneous systems for any reaction network and for gas-liquid and gas-liquid-solid systems are presented in Tables 5.4-7 and 5.4.8 at the end of Section 5.4.3. 

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. 

Discussion of the concepts and procedures involved in designing packed gas absorption systems shall first be confined to simple gas absorption processes without complications isothermal absorption of a solute from a mixture containing an inert gas into a nonvolatile solvent without chemical reaction. Gas and liquid are assumed to move through the packing in a plug-flow fashion. Deviations such as nonisothermal operation, multicomponent mass transfer effects, and departure from plug flow are treated in later sections. 

Athes et al. (2004) compared the data from three static headspace methodologies (VPC, PRV and LC-SH) for determining gas/liquid partition coefficients of two aroma compounds in hydroalcoholic, multicomponent solutions at infinit dilution. They found that PRV was a simpler method compared to VPC and LC-SH and that VPC and PRV were more accurate than LC-SH since errors due to gas leaks and adsorption in gastight syringes are avoided. They suggested that these issues could be responsible for significant bias (50% lower values) obtained when using the LC-SH method. Nevertheless, all three methods were able to find an effect of ethanol (up to 20%) on the release of aroma compounds from their model system (Fig. 8F.1). 

Figure 8 Multicomponent chemical equilibria in gas-solid-liquid systems within Mt. St. Helens (source Symonds and Reed, 1993).

Symonds R. B. and Reed M. H. (1993) Calculation of multicomponent chemical-equilibria in gas-solid- liquid systems- calculation methods, thermochemical data, and applications to studies of high-temperature volcanic gases with examples from Mount St-Helens. Am. J. Sci. 293(8), 758-864. 

Since thermodynamic nonidealities are of the essence for phase separation in liquid-liquid systems, and such nonidealities contribute to multicomponent interaction effects, it may be expected that liquid-liquid extraction would offer an important test of the theories presented in this book. Here, we present some experimental evidence to show the significance of interaction effects in liquid-liquid extraction. The evidence we present is largely based on experiments carried out in a modified Lewis batch extraction cell (Standart et al., 1975 Sethy and Cullinan, 1975 Cullinan and Ram, 1976 Krishna et al., 1985). The analysis we present here is due to Ej-ishna et al. (1985). The experimental system that will be used to demonstrate multicomponent interaction effects is glycerol(l)-water(2)-acetone(l) this system is of Type I. The analysis presented below is the liquid-liquid analog of the two bulb gas diffusion experiment considered in Section 5.4. 

The applicability of the multicomponent mass diffusion models to chemical reactor engineering is assessed in the following section. Emphasis is placed on the first principles in the derivation of the governing flux equations, the physical interpretations of the terms in the resulting models, the consistency with Pick s first law for binary systems, the relationships between the molar and mass based fluxes, and the consistent use of these multicomponent models describing non-ideal gas and liquid systems. 

The result obtained from the film theory is that the mass transfer coefficient is directly proportional to the diffusion coefficient. However, the experimental mass transfer data available in the literature [6], for gas-liquid interfaces, indicate that the mass transfer coefficient should rather be proportional with the square root of the diffusion coefficient. Therefore, in many situations the film theory doesn t give a sufficient picture of the mass transfer processes at the interfaces. Furthermore, the mass transfer coefficient dependencies upon variables like fluid viscosity and velocity are not well understood. These dependencies are thus often lumped into the correlations for the film thickness, 1. The film theory is inaccurate for most physical systems, but it is still a simple and useful method that is widely used calculating the interfacial mass transfer fluxes. It is also very useful for analysis of mass transfer with chemical reaction, as the physical mechanisms involved are very complex and the more sophisticated theories do not provide significantly better estimates of the fluxes. Even for the description of many multicomponent systems, the simplicity of the model can be an important advantage. 

Lemert, R. M., and K. P. Johnston. 1989. Solid-liquid-gas equilibria in multicomponent supercritical fluid systems. J. Fluid Phase Equil. 45 265-286. 

The dosing pump/vaporizer technique is essentially easier to handle and in many cases suitable for multicomponent gas mixtures. Here the liquid with a definite flow rate is metered into a system, analog to the proportioning system for the generation of calibration gases (see Figure 16-7). The substance is vaporized in the system and simultaneously mixed with the pro-... 

The following example illustrates the use of the above equations in computing the isothermal two-phase compressibility of multicomponent systems. Consider a three-component system in the two-phase gas-liquid region. The calculation of the drij i/dP) f terms is the major task of computing two-phase compressibility. The matrix representation of Eq. (3,74) for the three-component system is... 

One other textbook deserves a special mention. The book by G. Froment and K. Bischoff, Chemical Reactor Analysis and Design, aims not to be easy but elegant, introducing the reader directly to the advanced theories of reaction engineering and to the frontiers of research by including complex reaction networks, advanced models for catalytic systems, multicomponent diffusion, and the surface renewal theory for gas-liquid contact. The book is excellent for students who wish to become scientists in chemical reaction engineering. 

The ideal solution laws such as Raoult s law and Raoult s law corrected for gas law deviation are applicable to binary or multicomponent systems. They treat each component independently of any other component present t.e., the relationship between the mol fraction in the vapor and in the liquid for a given component depends only on the temperature and total pressure. In many cases, these simplified rules are not applicable, and there is interreaction between the various components. It would be particularly desirable to have a satisfactory theoretical approach to the problem of multicomponent vapor-liquid equilibria since the experimental determination for this... 

---