Multi-Component Mixtures

When oil and gas are produced simultaneously into a separator a certain amount (mass fraction) of each component (e.g. butane) will be in the vapour phase and the rest in the liquid phase. This can be described using phase diagrams (such as those described in section 4.2) which describe the behaviour of multi-component mixtures at various temperatures and pressures. However to determine how much of each component goes into the gas or liquid phase the equilibrium constants (or equilibrium vapour liquid ratios) K must be known. 

The type of treatment described here was originally introduced by Scott and Dullien [4], who confined attention to isothermal isobaric diffusion in binary mixtures. Similar equations were independently published shortly after by Rothfeld [5], and the method was later extended to multi-component mixtures by Silveston [6], Perhaps the most complete exposition is given by Mason and Evans [7],... 

Constant overhead composition, vaiying reflux. If it is desired to maintain a constant overhead composition in the case of a binaiy, the amount of reflux returned to the column must be constantly increased throughout the run. As time proceeds, the pot is gradually depleted of the hghter component. Finally, a point is reached at which the reflux ratio has attained a veiy high value. The receivers are then changed, the reflux is reduced, and an intermediate cut is taken as before. This technique can also be extended to a multi-component mixture. 

The effect of electrochemical sample treatment on the signal selectivity in multi-component mixtures is discussed. 

The curves show that the peak capacity increases with the column efficiency, which is much as one would expect, however the major factor that influences peak capacity is clearly the capacity ratio of the last eluted peak. It follows that any aspect of the chromatographic system that might limit the value of (k ) for the last peak will also limit the peak capacity. Davis and Giddings [15] have pointed out that the theoretical peak capacity is an exaggerated value of the true peak capacity. They claim that the individual (k ) values for each solute in a realistic multi-component mixture will have a statistically irregular distribution. As they very adroitly point out, the solutes in a real sample do not array themselves conveniently along the chromatogram four standard deviations apart to provide the maximum peak capacity. 

Note that this equation holds for any component in a multi-component mixture. The integral on the right-hand side can only be evaluated if the vapor mole fraction y is known as a function of the mole fraction Xr in the still. Assuming phase equilibrium between liquid and vapor in the still, the vapor mole fraction y x ) is defined by the equilibrium curve. Agitation of the liquid in tire still and low boilup rates tend to improve the validity of this assumption. 

CHEMCALC 1, Separations Calculations Gulf Publishing Company, Book Division P.O. Box 2608 Houston, TX 77252 Programs for use with multi-component mixtures to determine the conditions and compositions at the dew point and at the bubble point. 

HGSystem offers the most rigorous treatments of HF source-term and dispersion analysis a ailable for a public domain code. It provides modeling capabilities to other chemical species with complex thermodynamic behavior. It treats aerosols and multi-component mixtures, spillage of a liquid non-reactive compound from a pressurized vessel, efficient simulations of time-dependent... 

Crystallization-based separation of multi-component mixtures has widespread application. The technique consists of sequences of heating, cooling, evaporation, dilution, diluent addition and solid-liquid separation. Berry and Ng (1996, 1997), Cisternas and Rudd (1993), Dye and Ng (1995), Ng (1991) and Oyander etal. (1997) proposed various schemes based on the phase diagram. Cisternas (1999) presented an alternate network flow model for synthesizing crystallization-based separations for multi-component systems. The construction... 

Yu, A.B. and Standish, N., 1987. Porosity calculations of multi-component mixtures of spherical particles. Powder Technology, 52, 233-241. 

Unfortunately, exclusion chromatography has some inherent disadvantages that make its selection as the separation method of choice a little difficult. Although the separation is based on molecular size, which might be considered an ideal rationale, the total separation must be contained in the pore volume of the stationary phase. That is to say all the solutes must be eluted between the excluded volume and the dead volume, which is approximately half the column dead volume. In a 25 cm long, 4.6 mm i.d. column packed with silica gel, this means that all the solutes must be eluted in about 2 ml of mobile phase. It follows, that to achieve a reasonable separation of a multi-component mixture, the peaks must be very narrow and each occupy only a few microliters of mobile phase. Scott and Kucera (9) constructed a column 14 meters long and 1 mm i.d. packed with 5ja... 

The interface should cause no reduction in chromatographic performance. This is particularly important for the analysis of complex multi-component mixtures (although the specificity of the mass spectrometer may, in certain circumstances, compensate for some loss of performance - see Chapter 3). 

It is possible to carry out a chromatographic separation, collect all, or selected, fractions and then, after removal of the majority of the volatile solvent, transfer the analyte to the mass spectrometer by using the conventional inlet (probe) for solid analytes. The direct coupling of the two techniques is advantageous in many respects, including the speed of analysis, the convenience, particularly for the analysis of multi-component mixtures, the reduced possibility of sample loss, the ability to carry out accurate quantitation using isotopically labelled internal standards, and the ability to carry out certain tasks, such as the evaluation of peak purity, which would not otherwise be possible. 

Equilibrium data are thus necessary to estimate compositions of both extract and raffinate when the time of extraction is sufficiently long. Phase equilibria have been studied for many ternary systems and the data can be found in the open literature. However, the position of the envelope can be strongly affected by other components of the feed. Furthermore, the envelope line and the tie lines are a function of temperature. Therefore, they should be determined experimentally. The other shapes of the equilibrium line can be found in literature. Equilibria in multi-component mixtures cannot be presented in planar graphs. To deal with such systems lumping of consolutes has been done to describe the system as pseudo-ternary. This can, however, lead to considerable errors in the estimation of the composition of the phases. A more rigorous thermodynamic approach is needed to regress the experimental data on equilibria in these systems. 

The set of possible dependent properties and independent predictor variables, i.e. the number of possible applications of predictive modelling, is virtually boundless. A major application is in analytical chemistry, specifically the development and application of quantitative predictive calibration models, e.g. for the simultaneous determination of the concentrations of various analytes in a multi-component mixture where one may choose from a large arsenal of spectroscopic methods (e.g. UV, IR, NIR, XRF, NMR). The emerging field of process analysis,... 

It is very difficult to cool pure metals and other pure elements fast enough to form glasses. However, metallic alloys can often be converted into glasses, particularly if they contain a mixture of small and large atoms such as iron and boron, or they are multi-component mixtures of metals that crystallize into more than one intermetallic compound (i.e., eutectic compositions). Thus, covalent chemical interactions of the atoms are important because they stabilize liquids and thereby inhibit crystallization. 

Although laser ablation is clearly becoming more popular (as shown in Fig. 9.1), it is difficult to produce fully quantitative data because of problems in matrix matching between sample and standard (see below and Section 13.3). There are also likely to be variations in ablation efficiency in multi-component mixtures, leading to over- or under-representation of particular phases of the sample. It is also unlikely that all ablation products will enter the plasma in the elemental state, or that different particle sizes produced by ablation will have the same compositions. Ablation products may, therefore, not be truly representative of the sample (Morrison et al. 1995, Figg et al. 1998). Additionally, limits of detection for most elements are approximately... 

The SMB separates binary mixtures into the components or multi-component mixtures into two fractions. The latter option is especially attractive if chromatographic conditions can be defined under which the target molecule is the first or the last to elute in a multi-component mixture. Under such circumstances the SMB can be used without technical modifications. In other situations, two SMB systems have to be used in series. 

UNDERWOOD, A. J. V. J. Inst. Petroleum 32 (1946) 614. Fractional distillation of multi-component mixtures — calculation of minimum reflux ratio. 

A melt is a liquid or a liquid mixture at a temperature near its freezing point and melt crystallisation is the process of separating the components of a liquid mixture by cooling until crystallised solid is deposited from the liquid phase. Where the crystallisation process is used to separate, or partially separate, the components, the composition of the crystallised solid will differ from that of the liquid mixture from which it is deposited. The ease or difficulty of separating one component from a multi-component mixture by crystallisation may be represented by a phase diagram as shown in Figures 15.4 and 15.5, both of which depict binary systems — the former depicts a eutectic, and the latter a continuous series of solid solutions. These two systems behave quite differently on freezing since a eutectic system can deposit a pure component, whereas a solid solution can only deposit a mixture of components. 

Representatives of the subfamilies Omaliinae and Proteininae (omaliine group) possess an abdominal defensive gland reservoir that opens out between sternite 7 and 8 [ 120]. The multi-component mixtures contained in these glands are used for defence. In Omaliinae and Proteininae the secretion is characterized by mixtures of acids (e.g. 2-methylpropanoic acid, hexanoic acid, 2-octenoic acid, 2-methylbutanoic acid, 3-methylbutanoic acid, butyric acid, and tiglic acid), aldehydes (( )-2-hexenal, heptanal, octanal, nonanal), ketoaldehydes such as 4-oxo-2-hexenal 41 (Scheme 5), 6-methyl-5-hepten-2-one, alcohols (octanol, ( )-2-hexen-l-ol, 2-methylbutan-l-ol), alkanes (nonadecane), esters (2-methylbutyl tiglate 42, various propanoates, 2-hexenyl 3-methylbutanoate, 2-methylbutyl 2-methylbutanoate, octanoates,butanoates), and aromatic compounds (e.g. 2-phenethyl 3-methylbutanoate 43). Unusual compounds are 2-... 

Asafu-Adjaye EB, Yun Jl, Su SY. 1985. Multi-component mixture analysis using room-temperature phosphorimetry. Anal Chem 57 904-907. 

To describe the impact of the x-values distribution type on the relative precision of relaxation rate estimates, we shall use a phenomenological factor fd. We expect it to be independent of all the other factors, but dependent upon the type of relaxation rate quantity to be determined (for example, the fastest- or the slowest-relaxing component in a multi-component mixture). 

A number of more sophisticated curve resolution procedures for multi-component mixtures have been developed over the years. The most well-known of these procedures are IPCA [77], SIMPLISMA [78] and OPA-ALS [79]. All rely on an a priori estimate of the number of observable species present, most if not all rely on the concept of a pure wavelength i. e. a spectral window where only one component is present, and all have difficulties with trace components i. e. components whose spectral features are embedded in the signal noise. In practice, both the prior estimate of the number of observable species present and the need for pure wavelengths are very serious restrictions, especially for catalytic systems where so many species are simultaneously present. ... 

In 1983, Sasaki et al. obtained rough first approximations of the mid-infrared spectra of o-xylene, p-xylene and m-xylene from multi-component mixtures using entropy minimization [83-85] However, in order to do so, an a priori estimate of the number S of observable species present was again needed. The basic idea behind the approach was (i) the determination of the basis functions/eigenvectors V,xv associated with the data (three solutions were prepared) and (ii) the transformation of basis vectors into pure component spectral estimates by determining the elements of a transformation matrix TsXs- The simplex optimization method was used to optimize the nine elements of Tixi to achieve entropy minimization, and the normalized second derivative of the spectra was used as a measure of the probability distribution. 

The basic expressions for the mass fluxes and the equations of continuity for multi-component mixtures are given in Sec. II,B. For a -component mixture of ideal gases in a system in which there is no pressure diffusion, forced diffusion, or thermal diffusion, the fluxes are given by... 

Computer simulation can also be used for relief sizing (see Annex 4). This may be the only safe alternative in cases where physical properties are non-ideal, multiple reactions occur or there are significant continuing.feed streams or external heating. It will be necessary to choose a computer simulation package which can handle multi-component mixtures comprising both volatile and permanent gas components. 

For wide boiling multi-component mixtures, the Clausius-Clapeyron relationship, used in deriving equations (A8.5)-(A8.10), is invalid. The definitions of Omega can be rewritten without the use of the Clausius-Clapeyron relationship. For example, equation (A8.5) becomes . ... 

To ensure sufficient contact between the fibers and the matrix, it is desirable to use a liquid precursor with a low viscosity. Reactive liquids are usually preferred over thermoplastics due to the low viscosity of liquids relative to polymer melts. The reactive liquid is typically a multi-component mixture. The reactive liquid may contain a monomer and an activator, which will cause the monomer to polymerize into a solid polymer matrix. 

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