Of multicomponent systems

Distillation Columns. Distillation is by far the most common separation technique in the chemical process industries. Tray and packed columns are employed as strippers, absorbers, and their combinations in a wide range of diverse appHcations. Although the components to be separated and distillation equipment may be different, the mathematical model of the material and energy balances and of the vapor—Hquid equiUbria are similar and equally appHcable to all distillation operations. Computation of multicomponent systems are extremely complex. Computers, right from their eadiest avadabihties, have been used for making plate-to-plate calculations. 

Hctivity Coefficients. Most activity coefficient property estimation methods are generally appHcable only to pure substances. Methods for properties of multicomponent systems are more complex and parameter fits usually rely on less experimental data. The primary group contribution methods of activity coefficient estimation are ASOG and UNIEAC. Of the two, UNIEAC has been fit to more combinations of groups and therefore can be appHed to a wider variety of compounds. Both methods are restricted to organic compounds and water. 

Only the Wilson, NRTL, and UNIQUAC equations are suited to the treatment of multicomponent systems. For such systems, the parameters are determined for pairs of species exactly as for binary systems. 

The shape of the coohng and warming curves in coiled-tube heat exchangers is affected by the pressure drop in both the tube and shell-sides of the heat exchanger. This is particularly important for two-phase flows of multicomponent systems. For example, an increase in pressure drop on the shellside causes boiling to occur at a higher temperature, while an increase in pressure drop on the tubeside will cause condensation to occur at a lower temperature. The net result is both a decrease in the effective temperature difference between the two streams and a requirement for additional heat transfer area to compensate for these losses. 

A simple example of the analysis of multicomponent systems will suffice for the present consideration, such as the calculation of the components in a gaseous mixture of oxygen, hydrogen and sulphur. As a first step, the Gibbs energy of formation of each potential compound, e.g. S2, H2S, SO, SO2, H2O etc. can be used to calculate the equilibrium constant for the formation of each compound from the atomic species of the elements. The total number of atoms of each element will therefore be distributed in the equilibrium mixture in proportion to these constants. Thus for hydrogen with a starting number of atoms and the final number of each species... 

Renon s techniques valuable for the complexities of multicomponent systems and in particular the solution by digital computer. 

The relative amounts of the individual components (or species) making up a mixture or solution can be expressed in a variety of ways, depending upon the system at hand. A volumetric, mass, or molar basis may be employed to represent the compositions of multicomponent systems. 

Burnham, Hower, and Jones18 have used an IBM Card Programmed Calculator for the calculation of the interaction coefficients needed in setting up the analysis of multicomponent systems by x-ray emission spectrography according to an earlier treatment of Sherman.19... 

During this period of intensive development of unit operations, other classical tools of chemical engineering analysis were introduced or were extensively developed. These included studies of the material and energy balance of processes and fundamental thermodynamic studies of multicomponent systems. 

McMillan, W. G. Mayer, J. E. (1945). The statistical thermodynamics of multicomponent systems. Journal of Chemical Physics, 13, 276-305. 

Another very important technique for fundamental consideration of multicomponent systems is low energy ion scattering (LEIS) [Taglauer and Heiland, 1980 Brongersma et al., 2007]. This is a unique tool in surface analysis, since it provides the ability to define the atomic composition of the topmost surface layer under UHV conditions. The signal does not interfere with the subsurface atomic layers, and therefore the results of LEIS analysis represent exclusively the response from the outer surface. In LEIS, a surface is used as a target that scatters a noble gas ion beam (He, Ne, ... 

In contrast to quantitative analyses, the results of qualitative tests and of identifications cannot be evaluated by means of mathematical statistics. Instead, information theory is a helpful tool to characterize qualitative analyses, in particular in case of multicomponent systems. 

In specialized studies, chemical measurements achieve particular importance by their temporal and spatial resolution. In process control, the momentary value is interesting only in such exceptional situations in which a warning or control limit is passed. Much more information is contained in the time function of an analytical system, y = f(t), or y = f(z, t), in case of multicomponent systems as shown in Fig. 3.11. 

The extension of this approach to artificial leaves based on titanates, niobates, tantalates, metal nitrides and phosphides, metal sulfides, and other transition metal oxides appears possible and useful in order to enhance the photocatalytic efficiency. In addition, the construction of multicomponent systems such as Ti02-CdS or MoS2-CdSe for overall water splitting could also lead to further improvements. This... 

Equation (10.8) can be readily generalized to multicomponent systems. The only difference is that the number of particles of species j in each of the two regions, Mj and Nu,j replace Nj and Nu, respectively. In simulations of multicomponent systems dilute in one component, it is possible that the number of particles of a species in one of the two regions becomes zero after a successful transfer out of that region. Equation (10.8) in this case is taken to imply that the probability of transfer out of an empty region is zero. 

In further studies, Zastavker et al. established that the formation of helical ribbons with two distinct pitch angles is a general phenomenon observed in a wide variety of multicomponent systems containing a sterol.162 High-pitch (54°) and low-pitch (11°) helices were observed in almost all of the... 

As is usually the case in the study of complicated reactions that involve a great many different species, more attention has been given to the analysis of reaction products and intermediates than to the problems of the investigation of the kinetics of possible elementary reaction steps. Analytical studies of the systems have been advanced by the development of techniques such as gas chromatography for the analysis of multicomponent systems and mass spectrometry for the detection of free radicals and other highly unstable species. Furthermore, since most... 

COMPARISON OF PREDICTED AND EXPERIMENTAL WATER CONTENTS OF MULTICOMPONENT SYSTEMS (From Reference 2)... 

Beegle, B. L. (1973). Stability analysis of multicomponent systems. S.M. Thesis, Massachusetts Institute of Technology, Cambridge. 

Bertrand G. L., Acree W. E. Jr., and Burchfield T. (1983). Thermodynamical excess properties of multicomponent systems Representation and estimation from binary mixing data. J. Solution. Chem., 12 327-340. 

Wood B. I (1987). Thermodynamics of multicomponent systems containing several solid solutions. In Reviews in Mineralogy, vol. 17, P. H. Ribbe (series ed.), Mineralogical Society of America. 

Most multicomponent systems undergo phase separation because of their positive mixing enthalpies coupled with low entropy of mixing. Morphological features have been central to the study of multicomponent systems, because domain sizes, shapes, and interfacial bonding characteristics determine the mechanical properties. A proper understanding of these features often allow synergistic behavior to be developed. 

Two different methods have been presented in this contribution for correlation and/or prediction of phase equilibria in ternary or mul> ticomponent systems. The first method, the clinogonial projection, has one disadvantage it is not based on concrete concepts of the system but assumes, to a certain extent, additivity of the properties of individiial components and attempts to express deviations from additivity of the properties of individual components and attempts to express deviations from additivity by using geometrical constructions. Hence this method, although simple and quick, needs not necessarily yield correct results in all the cases. For this reason, the other method based on the thermodynamic description of phase equilibria, reliably describes the behaviour of the system. Of cource, the theory of concentrated ionic solutions does not permit a priori calculation of the behaviour of the system from the thermodynamic properties of pure components however, if a satisfactory equation is obtained from the theory and is modified to express concrete systems by using few adjustable parameters, the results thus obtained are still substantially more reliable than results correlated merely on the basis of geometric similarity. Both of the methods shown here can be easily adapted for the description of multicomponent systems. 

It is obvious that studies of multicomponent systems will lead to a very large numbers of phases. However, by analyzing a typical system, some trends can be found that can be used as guidelines. 

There is no well developed theory which describes the sputtering of multicomponent systems (e.g., oxides), but some authors (sec, for example, Ref. 88) have assumed that the results of Sigmund s theory are valid and have applied reasonable values for the stopping power and binding energy to obtain results for various multi-component systems. 

The unary phase diagram is seldom used in solid state syntheses. However, the unary diagram forms the basis for the phase diagrams of multicomponent systems. Since there are no composition variables, the only externally controllable variables in a unary system are simply the temperature and pressure. For this... 

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