Phase-Separating Multi-Component Mixtures

In a binary mixture of A and B particles, phase separation can occur when there is an effective repulsion between A-B pairs. In the current model, this is achieved by introducing velocity-dependent multi-particle collisions between A and B particles. There are Nx and Mb particles of type A and B, respectively. In two dimensions, the system is coarse-grained into Lj of cells of a square lattice of Unear dimension L and lattice constant a. The generalization to three dimensions is straightforward. 

Collisions are defined in the same way as in the non-ideal model discussed in the previous section. Now, however, two types of collisions are possible for each pair of cells particles of type A in the first cell can undergo a collision with particles of type B in the second cell vice versa, particles of type B in the first cell can undergo a colUsion with particles of type A in the second cell. There are no A-A or B-B collisions, so that there is an effective repulsion between A-B pairs. The rules and probabilities for these colUsions are chosen in the same way as in the non-ideal single-component fluid described in [33,55]. For example, consider the collision of A particles in the first cell with the B particles in the second. The mean particle velocity of A particles in the first cell is ua = (1/1Vc,a) L,=i where the sum runs 

bu )/ Nc + Nc,b) is the parallel component of the mean velocity of the colliding particles. The perpendicular component remains unchanged. It is easy to verify that these rules conserve momentum and energy in the cell pairs. The collision of B particles in the first cell with A particles in the second is handled in a similar fashion. 

Because there are no A-A and B-B collisions, additional SRD collisions at the cell level are incorporated in order to mix particle momenta. The order of A-B and SRD collision is random, i.e., the SRD collision is performed first with a probability 1/2. If necessary, the viscosity can be tuned by not performing SRD collisions every time step. The results presented here were obtained using a SRD collision angle of a = 90°. 

The transport coefficients can be calculated in the same way as for the one-component non-ideal system. The resulting kinetic contribution to the viscosity is 

---

The effect of 31 stationary phases on the relative volatility of silicon tetrachloride and methylchlorosilanes has been examined398 on firebrick containing the various stationary phases. 2-Chloroethyl ether, ethyl chloroacetate and 1,1,3-trichloropropane were found suitable for separating 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. 

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... 

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... 

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. 

A computer algorithm has been developed for making multi-component mixture calculations to predict (a) thermodynamic properties of liquid and vapor phases (b) bubble point, dew point, and flash conditions (c) multiple flashes, condensations, compression, and expansion operations and (d) separations by distillation and absorption. 

The separation of a multi-component mixture into products with different compositions in a multistage process is governed by phase equilibrium relations and energy and material balances. It is not uncommon in simulation studies to require certain column product rates, compositions, or component recoveries to satisfy given specifications with no concern for conditions within the column. Such would be the case when downstream processing of the products is of primary interest. In these instances, one would be concerned only with overall component balances around the column but not necessarily with heat balances or equilibrium relations. Separation would thus be arbitrarily defined, and the problem would be to calculate product rates and compositions. The actual performance of the separation process is analyzed independently in all the following chapters. 

Sreedhar, B. and Seidel-Morgenstern, A. (2008) Preparative separation of multi-component mixtures using stationary phase gradients./. Chromatogr. A, 1215, 133-144. 

Hahn G. J., Shapiro S. S., Statistical Models in Engineering, Wiley, 1967. Sinaiski E. G., Separation of two-phase multi-component mixture in oil-gas field equipment, Nedra, Moscow, 1990 (in Russian). Gradshtejn I. S., Ryszik, Tables of Integrals, Sums, Series, and Products, Nauka, Moscow, 1971 (in Russian). Ruckenstein E., Condition for the Size Distribution of Aerosols to be Self-Preserving, f. Colloid Interface Sci., 1975, Vol. 50, No. 3, p. 508-518. 

All of the considered processes relate to the separation of multi-phase, multi-component media, hence the title of the book. It should be noted that in the preparation technology for the transportation of oil, natural gas, and gas condensates, the term separation is traditionally understood only as the process of segregation of either a condensate and water drops or of gas and gas bubbles (occluded gas) from an oil. The concept of separation used herein can mean any segregation of components in multi-component mixtures or of phases in multi-phase systems. 

For separation applications, it is important to measure adsorption in two- or multi-component mixtures. In these cases the compositions of both the adsorbed and the gas phase are needed to obtain a full description of the system. These can be obtained by measurement, or, if data on the single component adsorptions are available, the adsorption behaviour of the mixture can be simulated if the interaction parameters between the two adsorbates are known. 

Head-space gas chromatography is a modem tool for the measurement of vapor pressures in polymer solutions that is highly automated. Solutions need time to equilibrate, as is the case for all vapor pressure measurements. After equihbration of the solutions, quite a lot of data can be measured continuously with reliable precision. Solvent degassing is not necessary. Measurements require some experience with the equipment to obtain really thermodynamic equihbrium data. Calibration of the equipment with pure solvent vapor pressures may be necessary. HSGC can easily be extended to multi-component mixtures because it determines all components in the vapor phase separately. 

If it were possible to identify or quantitatively determine any element or compound by simple measurement no matter what its concentration or the complexity of the matrix, separation techniques would be of no value to the analytical chemist. Most procedures fall short of this ideal because of interference with the required measurement by other constituents of the sample. Many techniques for separating and concentrating the species of interest have thus been devised. Such techniques are aimed at exploiting differences in physico-chemical properties between the various components of a mixture. Volatility, solubility, charge, molecular size, shape and polarity are the most useful in this respect. A change of phase, as occurs during distillation, or the formation of a new phase, as in precipitation, can provide a simple means of isolating a desired component. Usually, however, more complex separation procedures are required for multi-component samples. Most depend on the selective transfer of materials between two immiscible phases. The most widely used techniques and the phase systems associated with them are summarized in Table 4.1. 

---