Binary mixture separation

Equations (14-153) and (14-155) have been developed for binary mixture separations and hold for cases where the operating line and equilibrium line are straight. Thus, when there is curvature, the equations should be used for sections of the column where linearity can be assumed. When the equilibrium line and operating line have the same slope, HETP = Hog and Nog = 5. (theoretical stages). 

Figure 18.11 Plot of the maximum production rate in elution versus the retention factor of the less retained component of a binary mixture. Separation factor 1.2. Each data point gives the maximum production rate after optimization of the mobile phase velocity, the sample size, the particle size, and the column length. Reproduced with permission from A. Felinger and G. Guiochon,. Chromatogr., 591 (1992) 31 (Fig. 12).

An excellent example of the implementation of SCFF to obtain palmitic acid from a plant source is the work of Brunner and Machado [7,72]. They conducted a detailed analysis on the fractionation of fatty acids from palm fatty acid distillates (99 % FFA (mainly palmitic, oleic and linoleic acid), 0.9 % squalene and 0.1 tocopherol) starting with a phase equilibrium analysis through to pilot plant studies and experimental verification of the separation. They postulated, from the phase equilibrium studies, that squalene and palmitie acid would be preferentially extracted and verified their postulation experimentally. They also considered a pseudo-binary mixture separation where palmitic acid is to be separated from oleic and linoleic acid and showed, using separation factors that this is possible. On pilot plant scale they showed that such a separation is feasible and balanced yield and extraet quality. At their optimum conditions (373 K, 29 MPa, extract to raffinate ratio of 1.2) they obtained an extract where the palmitic acid content was enriched from 52.5 % in the feed to 74.4 % in the extract and the oleic and linoleic acid content enriched from 46.3 % in the feed to 59.0 % in the raffinate. Squalene was also enriched in the extraet Irom 0.6 % in the feed to 1.2 % in the... 

C. Vallieres, E. Favre, Vacuum versus sweeping gas operation for binary mixtures separation by dense membrane processes, J. Membr. ScL, 244, 17-23 (2004). 

Figure 10.1.5. (a) Distillation column with a reboiler and a total condenser for a binary mixture separation, (b) Separation of a binary mixture into two pure compounds by binary distillation McCabe-Thiele diagram. (After Humphrey and Keller (1997).)... 

W. Kujawski, Pervaporative removal of organics from water using hydrophobic membranes. Binary mixtures. Separation Science and Technology 35 (2000) 89-108. 

A2.5.4.1 LIQUID-LIQUID PHASE SEPARATION IN A SIMPLE BINARY MIXTURE... 

The previous seetion showed how the van der Waals equation was extended to binary mixtures. However, imieh of the early theoretieal treatment of binary mixtures ignored equation-of-state eflfeets (i.e. the eontributions of the expansion beyond the volume of a elose-paeked liquid) and implieitly avoided the distinetion between eonstant pressure and eonstant volume by putting the moleeules, assumed to be equal in size, into a kind of pseudo-lattiee. Figure A2.5.14 shows sohematieally an equimolar mixture of A and B, at a high temperature where the distribution is essentially random, and at a low temperature where the mixture has separated mto two virtually one-eomponent phases. 

Figure A2.5.14. Quasi-lattice representation of an equimolar binary mixture of A and B (a) randomly mixed at high temperature, and (b) phase separated at low temperature.

In both cases the late stages of kinetics show power law domain growth, the nature of which does not depend on the mitial state it depends on the nature of the fluctuating variable(s) which is (are) driving the phase separation process. Such a fluctuating variable is called the order parameter for a binary mixture, tlie order parameter o(r,0 is tlie relative concentration of one of the two species and its fluctuation around the mean value is 5e(/,t) = c(r,t) - c. In the disordered phase, the system s concentration is homogeneous and the order... 

Here we shall consider two simple cases one in which the order parameter is a non-conserved scalar variable and another in which it is a conserved scalar variable. The latter is exemplified by the binary mixture phase separation, and is treated here at much greater length. The fonner occurs in a variety of examples, including some order-disorder transitions and antrferromagnets. The example of the para-ferro transition is one in which the magnetization is a conserved quantity in the absence of an external magnetic field, but becomes non-conserved in its presence. 

Within this general framework there have been many different systems modelled and the dynamical, statistical prefactors have been calculated. These are detailed in [42]. For a binary mixture, phase separating from an initially metastable state, the work of Langer and Schwartz [48] using die Langer theory [47] gives the micleation rate as... 

Another important class of materials which can be successfiilly described by mesoscopic and contimiiim models are amphiphilic systems. Amphiphilic molecules consist of two distinct entities that like different enviromnents. Lipid molecules, for instance, comprise a polar head that likes an aqueous enviromnent and one or two hydrocarbon tails that are strongly hydrophobic. Since the two entities are chemically joined together they cannot separate into macroscopically large phases. If these amphiphiles are added to a binary mixture (say, water and oil) they greatly promote the dispersion of one component into the other. At low amphiphile... 

SCHEME FOR THE SEPARATION OF SIMPLE BINARY MIXTURES OF ORGANIC COMPOUNDS... 

The use of a ternary mixture in the drying of a liquid (ethyl alcohol) has been described in Section 1,5 the following is an example of its application to the drying of a solid. Laevulose (fructose) is dissolved in warm absolute ethyl alcohol, benzene is added, and the mixture is fractionated. A ternary mixture, alcohol-benzene-water, b.p. 64°, distils first, and then the binary mixture, benzene-alcohol, b.p. 68-3°. The residual, dry alcoholic solution is partially distilled and the concentrated solution is allowed to crystallise the anhydrous sugar separates. 

For ideal solutions (7 = 1) of a binary mixture, the equation simplifies to the following, which appHes whether the separation is by distillation or by any other technique. 

Example Separation of 2-Propanol—Water. Consider the separation of a binary mixture of 60 mol % water and 40 mol % 2-propanol (or isopropyl alcohol (IPA)) into two products consisting of 2-propanol of 99.5 mol % purity and water with <100 ppm 2-propanol impurity. 

The Separation Stage. A fundamental quantity, a, exists in all stochastic separation processes, and is an index of the steady-state separation that can be attained in an element of the process equipment. The numerical value of a is developed for each process under consideration in the subsequent sections. The separation stage, which in a continuous separation process is called the transfer unit or equivalent theoretical plate, may be considered as a device separating a feed stream, or streams, into two product streams, often called heads and tails, or product and waste, such that the concentrations of the components in the two effluent streams are related by the quantity, d. For the case of the separation of a binary mixture this relationship is... 

For the case of separating a binary mixture, the following conventions are used. The concentrations of the streams are specified by the mol fraction of the desired component. The purpose of the separation process is usually to obtain one component of the mixture in an enriched form. If both components are desired, the choice of the desired component is an arbitrary one. The upflowing stream from the separation stage is the one in which the desired component is enriched, and by virtue of this convention, a is defined as a quantity the value of which is greater than unity. However, for the processes considered here, a exceeds unity by only a very small fraction, and the relationship between the concentrations leaving the stage can be written, without appreciable error, in the form... 

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) ... 

Favorable Vapoi Liquid Equilibria. The suitabiHty of distiUation as a separation method is strongly dependent on favorable vapor—Hquid equiHbria. The absolute value of the key relative volatiHties direcdy determines the ease and economics of a distillation. The energy requirements and the number of plates required for any given separation increase rapidly as the relative volatiHty becomes lower and approaches unity. For example given an ideal binary mixture having a 50 mol % feed and a distillate and bottoms requirement of 99.8% purity each, the minimum reflux and minimum number of theoretical plates for assumed relative volatiHties of 1.1,1.5, and 4, are... 

As an example, consider the residue curve map for the nonazeotropic mixture shown in Eigure 2. It has no distillation boundary so the mixture can be separated into pure components by either the dkect or indkect sequence (Eig. 4). In the dkect sequence the unstable node (light component, L) is taken overhead in the first column and the bottom stream is essentially a binary mixture of the intermediate, I, and heavy, H, components. In the binary I—H mixture, I has the lowest boiling temperature (an unstable node) so it is recovered as the distillate in the second column and the stable node, H, is the corresponding bottoms stream. The indkect sequence removes the stable node (heavy component) from the bottom of the first column and the overhead stream is an essentially binary L—I mixture. Then in the second column the unstable node, L, is taken overhead and I is recovered in the bottoms. 

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