Mixture multicomponent

In this section we briefly discuss some of the important issues that arise when the kinetic gas theory is extended to gas mixtures. For a more detailed study of kinetic theory of mixtures the reader is referred to Hirschfelder et al. [39], Williams [104] (app D) and Ferziger and Kaper [28]. 

It is first necessary to generalize the definitions of the important functions. If we denote the chemical species in a gas mixture by s, then ng, mg, fg, Cg, Cs, Fs, etc. will in general be different for each species. 

The starting point for the kinetic theory of low density, non-reacting mixtures of mono-atomic gases is the knowledge of the distribution function /s(r,Cg,t). fs r,Cg,t) is defined in such a way that the quantity fs r,Cg,t) dcgdr represents the probable number of molecules of the s-th species which at the time t lie in a unit volume element dr about the point r and which have velocities within the range dCg about c. It is emphasized that denotes the molecular velocity of a species s with respect to a coordinate system fixed in space. 

The total number of molecules of species s per unit spatial volume yields  

The mean (number average) values of any function ipg cg) over all the molecules of a particular species, s, 3ueld  

An interesting investigation of the ternary mixture H2S + C02+CH4 was performed by Ng et al. (1985). Although much of this study was at temperatures below those of interest in acid gas injection, it provides data useful for testing phase-behavior prediction models. The multiphase equilibrium that Ng et al. observed for this mixture, including multiple critical points for a mixture of fixed composition, should be of interest to all engineers working with such mixtures. It demonstrates that the equilibria can be complex, even for relatively simple systems. 

As a final case, figure 3A.2 shows the pressure-temperature diagram (phase envelope) for the mixture containing 40.23% H2S, 9.88% COz, and 49.89% CH4, which is the mixture studied by Ng et al. (1985.) The data points on the plot are their data. 

this figure requires some explanation. Only the region greater than -15°C is shown. This limit was imposed for two reasons. First, this is the region of interest to acid gas injection. Second, at lower temperatures some of the unusual phase behavior mentioned earlier manifests. Although interesting, this phase behavior 

The curve and the data points shown in figure 3A.2 are all dew points, incipient liquid formation. The experimental critical temperature for this mixture is -16.9°C. Therefore, the plot presents the large retrograde region for this mixture. From the PR calculations, the cricondentherm is estimated to be 29°C. In this mixture, liquid can form at a temperature almost 45 Celsius degrees higher than the critical temperature. The cricondenbar is estimated to be 12.5 MPa. It is difficult to confirm the location of either the cricondenbar or the cricondentherm with the available experimental data. However, the PR fits the data, and thus it can be concluded that the estimation of these points is quite accurate as well. 

Lipscomb. 1954. Carbon Dioxide-Propane System , Ind. Eng. Chem., 46 2535-2536. 

The continuity equation for any component A of a mixture consisting of N components will now be set up. We will only consider substance A. At time t it will enter the volume V (t) and have a surface area /1(f). The discharge of substance A enlarges the volume represented in Fig. 3.2 by dV = wAi dA At, where wAi is the flow velocity of substance A. Transferring (3.16) to (3.17) and (3.18) means 

3 Convective heat and mass transfer. Single phase flow 

According to this equation the increase in substance A is made up of two parts from the increase inside the system and from the amount of substance A which flows out of the system. 

As this relationship also holds for V (t) fore we obtain 

This type of mass balance is known as a component continuity equation. It can be set up for each component. This means that there are as many of these equations as there are components. The summation over all the components leads to a continuity equation for the total mass, due to J2 k = 0, H Qk = 0 and 5Z 0KwKi = 0wi In place of the N component continuity equations for a system of N components, N — 1 component continuity equations along with the continuity equation for the total mass can be used. 

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Comprehensive data collection for more than 6000 binary and multicomponent mixtures at moderate pressures. Data correlation and consistency tests are given for each data set. 

For each binary combination in a multicomponent mixture, there are two adjustable parameters, t 2 21 turn,... 

As discussed in Chapter 2, for noncondensable components, the unsymmetric convention is used to normalize activity coefficients. For a noncondensable component i in a multicomponent mixture, we write the fugacity in the liquid phase... 

However, in the study of thermodynamics and transport phenomena, the behavior of ideal gases and gas mixtures has historically provided a norm against which their more unruly brethren could be measured, and a signpost to the systematic treatment of departures from ideality. In view of the complexity of transport phenomena in multicomponent mixtures a thorough understanding of the behavior of ideal mixtures is certainly a prerequisite for any progress in understanding non-ideal systems. 

Maxwell obtained equation (4.7) for a single component gas by a momentum transfer argument, which we will now extend essentially unchanged to the case of a multicomponent mixture to obtain a corresponding boundary condition. The flux of gas molecules of species r incident on unit area of a wall bounding a semi-infinite, gas filled region is given by at low pressures, where n is the number of molecules of type r per... 

The creatmenc of the boundary conditions given here ts a generali2a-tion to multicomponent mixtures of a result originally obtained for a binary mixture by Kramers and Kistecnaker (25].These authors also obtained results equivalent to the binary special case of our equations (4.21) and (4.25), and integrated their equations to calculate the p.ressure drop which accompanies equimolar counterdiffusion in a capillary. Their results, and the important accompanying experimental measurements, will be discussed in Chapter 6 ... 

Though illustrated here by the Scott and Dullien flux relations, this is an example of a general principle which is often overlooked namely, an isobaric set of flux relations cannot, in general, be used to represent diffusion in the presence of chemical reactions. The reason for this is the existence of a relation between the species fluxes in isobaric systems (the Graham relation in the case of a binary mixture, or its extension (6.2) for multicomponent mixtures) which is inconsistent with the demands of stoichiometry. If the fluxes are to meet the constraints of stoichiometry, the pressure gradient must be left free to adjust itself accordingly. We shall return to this point in more detail in Chapter 11. 

In general, tests have tended to concentrate attention on the ability of a flux model to interpolate through the intermediate pressure range between Knudsen diffusion control and bulk diffusion control. What is also important, but seldom known at present, is whether a model predicts a composition dependence consistent with experiment for the matrix elements in equation (10.2). In multicomponent mixtures an enormous amount of experimental work would be needed to investigate this thoroughly, but it should be possible to supplement a systematic investigation of a flux model applied to binary systems with some limited experiments on particular multicomponent mixtures, as in the work of Hesse and Koder, and Remick and Geankoplia. Interpretation of such tests would be simplest and most direct if they were to be carried out with only small differences in composition between the two sides of the porous medium. Diffusion would then occur in a system of essentially uniform composition, so that flux measurements would provide values for the matrix elements in (10.2) at well-defined compositions. 

Fig. 3. Temperature—enthalpy representation of stream where A represents a pure component that is condensiag, eg, steam B and C represent streams having constant heat capacity, that are to be heated or cooled, respectively and D represents a multicomponent mixture that changes phase as it is...

Water Treatment. Several components must be treated simultaneously in a multicomponent mixture as available in wastewaters to prove the technology of heterogeneous photocatalysis. The formation and subsequent elimination of intermediates in the photooxidative process must be monitored, identifying all intermediates and final products. 

In considering the effect of mass transfer on the boiling of a multicomponent mixture, both the boiling mechanism and the driving force for transport must be examined (17—20). Moreover, the process is strongly influenced by the effects of convective flow on the boundary layer. In Reference 20 both effects have been taken into consideration to obtain a general correlation based on mechanistic reasoning that fits all available data within 15%. 

The objective ia any analytical procedure is to determine the composition of the sample (speciation) and the amounts of different species present (quantification). Spectroscopic techniques can both identify and quantify ia a single measurement. A wide range of compounds can be detected with high specificity, even ia multicomponent mixtures. Many spectroscopic methods are noninvasive, involving no sample collection, pretreatment, or contamination (see Nondestructive evaluation). Because only optical access to the sample is needed, instmments can be remotely situated for environmental and process monitoring (see Analytical METHODS Process control). Spectroscopy provides rapid real-time results, and is easily adaptable to continuous long-term monitoring. Spectra also carry information on sample conditions such as temperature and pressure. 

A 4-component mixture candicidin D shown ia Figure 1 is the primary component. Multicomponent mixture. 

The most recendy developed model is called UNIQUAC (21). Comparisons of measured VLE and predicted values from the Van Laar, Wilson, NRTL, and UNIQUAC models, as well as an older model, are available (3,22). Thousands of comparisons have been made, and Reference 3, which covers the Dortmund Data Base, available for purchase and use with standard computers, should be consulted by anyone considering the measurement or prediction of VLE. The predictive VLE models can be accommodated to multicomponent systems through the use of certain combining rules. These rules require the determination of parameters for all possible binary pairs in the multicomponent mixture. It is possible to use more than one model in determining binary pair data for a given mixture (23). 

Simple analytical methods are available for determining minimum stages and minimum reflux ratio. Although developed for binary mixtures, they can often be applied to multicomponent mixtures if the two key components are used. These are the components between which the specification separation must be made frequendy the heavy key is the component with a maximum allowable composition in the distillate and the light key is the component with a maximum allowable specification in the bottoms. On this basis, minimum stages may be calculated by means of the Fenske relationship (34) ... 

Errors, when tested against binary and multicomponent mixtures of both hydrocarbons and nonhydrocarbon gas mixtures, average about 3 percent. 

Multicomponent Mixtures No simple, practical estimation methods have been developed for predicting multicomponent hquid-diffusion coefficients. Several theories have been developed, but the necessity for extensive activity data, pure component and mixture volumes, mixture viscosity data, and tracer and binaiy diffusion coefficients have significantly limited the utihty of the theories (see Reid et al.). 

The generalized Stefan-Maxwell equations using binary diffusion coefficients are not easily applicable to hquids since the coefficients are so dependent on conditions. That is, in hquids, each Dy can be strongly composition dependent in binary mixtures and, moreover, the binaiy is strongly affected in a multicomponent mixture. Thus, the convenience of writing multicomponent flux equations in terms of binary coefficients is lost. Conversely, they apply to gas mixtures because each is practically independent of composition by itself and in a multicomponent mixture (see Taylor and Krishna for details). 

Lejfler-Cullinan They extended their binaiy relation to an arbi-traiy multicomponent mixture, as follows ... 

When multicomponent mixtures are to be separated into three or more products, sequences of simple distillation columns of the type shown in Fig. 13-1 are commonly used. For example, if aternaiy mixture is to be separated into three relatively pure products, either of the two sequences in Fig. 13-4 can be used. In the direct sequence, shown in Fig. 13-4, all products but the heaviest are removed one by one as distillates. The reverse is true for the indirect sequence, shown in Fig. 13-4 7. The number of possible sequences of simple distillation columns increases rapidly with the number of products. Thus, although only the 2 sequences shown in Fig. 13-4 are possible for a mixture separated into 3 products, 14 different sequences, one of which is shown in Fig. 13-5, can be synthesized when 5 products are to be obtained. 

The sequencing of distillation columns and other types of equipment for the separation of multicomponent mixtures has received much attention in recent years. Although one separator of complex design can sometimes be devised to produce more than two produc ts, more... 

Feed analyses in terms of component concentrations are usually not available for complex hydrocarbon mixtures with a final normal boihng point above about 38°C (100°F) (/i-pentane). One method of haudhug such a feed is to break it down into pseudo components (narrow-boihng fractions) and then estimate the mole fraction and value for each such component. Edmister [2nd. Eng. Chem., 47,1685 (1955)] and Maxwell (Data Book on Hydrocarbons, Van Nostrand, Princeton, N.J., 1958) give charts that are useful for this estimation. Once values are available, the calculation proceeds as described above for multicomponent mixtures. Another approach to complex mixtures is to obtain an American Society for Testing and Materials (ASTM) or true-boihng point (TBP) cui ve for the mixture and then use empirical correlations to con-strucl the atmospheric-pressure eqiiihbrium-flash cui ve (EF 0, which can then be corrected to the desired operating pressure. A discussion of this method and the necessary charts are presented in a later subsection entitled Tetroleum and Complex-Mixture Distillation. ... 

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