Multicomponent separation methods

Smith and Brinkley developed a method for determining the distribution of components in multicomponent separation processes. Their method is based on the solution of the finite-difference equations that can be written for multistage separation processes, and can be used for extraction and absorption processes, as well as distillation. Only the equations for distillation will be given here. The derivation of the equations is given by Smith and Brinkley (1960) and Smith (1963). For any component i (suffix i omitted in the equation for clarity)... 

Several different approaches have been taken to develop programs that are efficient in the use of computer time, and suitable for the full range of multicomponent separation processes that are used in the process industries. A design group will use those methods that are best suited to the processes that it normally handles. 

When all of the coefficients are known, this can be solved for the concentrations of component i in every stage. A straightforward method for solving a tridiagonal matrix is known as the Thomas algorithm to which references are made in Sec. 13.10, Basis for Computer Evaluation of Multicomponent Separations Specifications. ... 

S. H. Cheng and Y. A. Liu. Studies in chemical process design and synthesis 8. A simple heuristic method for systematic synthesis of initial sequences for sloppy multicomponent separations. I ECRes., 27 2304, 1988. 

Powers MF, Vickery DJ, Arehole A, Taylor R. A nonequilibrium-stage model of multicomponent separation processes—V. Computational methods for solving the model equations. Computers Chem Eng 1988 12 1229-1241. 

Simple separation sequences give rise to similar results. Thompson and King (1972) developed a formula for predicting the number of different structures which exist for simple separation sequences. A simple separator is one which splits a multicomponent mixture into two products, the two products having no common components. For such a problem the number of structures possible is (2(N-1)) Sn V((N-1) N ) where N is the number of components in the multicomponent mixture and S the number of different separation methods. The following table indicates the size of this problem. The two structures for Hs3 components (say A, B and C) and S 1 method (distillation) are 1) separate A from BC in the first column and then separate B from C in the second and 2) separate AB from C in the first and then A from B in the second. 

Sedimentation in an ultracentrifuge is a powerful means for separating biological particles and large macromolecules. Sedimentation is the only static field (Sc) method other than electrophoresis (in all of its various forms) commonly used for multicomponent separations. 

In comparing separation techniques, we generally find a striking difference in methods based on continuous (c) chemical potential profiles and those involving discontinuous (d or cd) profiles. There is, for example, a glaring contrast in instrumentation, applications, experimental techniques, and the capability for multicomponent separations between the two basic static systems, Sc (e.g., electrophoresis) and Sd (e.g., extraction). Similarly, there... 

Another approach, which is often used in combination with modelling methods, is the so-called threshold method. In many cases, it is possible to define for each response a part of the experimental domain where the response is at least adequate. By combining these areas, one may then find a set of conditions where all responses are adequate. This is for instance the approach followed when the solvent triangle (see Section 6.5) is applied for multicomponent separations. The quality of the separation of each successive pair of substances in the chromatogram is determined. A limit is imposed (e.g. resolution should be at least 1.5) and for each pair the area in the triangle is obtained where this is the case. The part of the triangle where the criterion is not reached is shaded and this is done for each pair (see Fig. 6.4). The triangles for each binary separation are then superimposed and the area, which stays blank after this operation, is the one where all separations yield acceptable results. 

Heuristic methods were developed by well-experienced engineers and researchers. The first attempt to develop a systematic heuristic approach for the synthesis of multicomponent separation sequences was made by Siirola and Rudd. Common example is hierarchical heuristic approach.Heuristic rules are applied at five design levels to generate and evaluate the alternatives using economic criteria. The hierarchical heuristic method emphasizes the strategy of decomposition and screening. It allows for a quick location of flowsheet structures that are often near ... 

Krishnamurthy, R. and Taylor, R., A Nonequilibrium Stage Model of Multicomponent Separation Processes. I—Model Development and Method of Solution, AIChE J, 31, 449-456 (1985a). 

For multicomponent separations, it is often necessary to estimate the minimum reflux ratio of a fractionating column. A method developed for this purpose by Underwood [10] requires the solution of the equation... 

Two approaches are available to solve the multicomponent separation problem the design method and the rating method. These methods have different input-output specifications, as shown in Table 12.3. 

Most of the common separation methods used in the chemical industry rely on a well-known observation when a multicomponent two-phase system is given sufficient ttmu to attain a statioenry state called equilibrium, the composition of one phase is different from thet of the other. It is this property of nature which eenbles separation of fluid mixtures by distillation, extraction, and other diffusions operations. For rational design of such operations it is necessary to heve a quantitative description of how a component distributes itself between two contacting phases. Phase-equilibrium thermodynamics, summarized here, provides a framework for establishing that description. 

It is often sufficient, and cestainfy expedient, to use approximate methods for estimating the stage requirements for a multicomponent separation. These methods proceed according to the following sequence ... 

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