Extent of separation

By a combination of the two control handles, one can affect component specification in the product streams, but there is always some maximum possible extent of separation (value of Fenske ratio) in a given system. Nearly all control measures are designed to permit control of the two handles. It should be realized that column operation needs to be kept reasonably smooth, otherwise separation already achieved may in the following five minutes (or six hours) partially be undone by surging in the system. 

However, the resolution or extent of separation of any two peaks from a column is solely dependent upon both retention and column efficiency. 

For all of the general techniques of Figure 2, the separations are achieved by enhancing the rate of mass transfer by diffusion of certain species relative to mass transfer of all species by bulk movement within a particular phase. The driving force and direction of mass transfer by diffusion is governed by thermodynamics, with the usual limitations of equilibrium. Thus, both transport and thermodynamic considerations are crucial in separation operations. The rate of separation is governed by mass transfer, while the extent of separation is limited by thermodynamic equilibrium. Fluid mechanics also plays an important role, and applicable principles are included in other chapters. 

In laboratory analysis, the extent of separation is of major importance, i.e. is it thermodynamically possible to separate the components,... 

The extent of separation achieved between or amongst the product phases for each of the chemical species present in the feed depends on the exploitation of differences in molecular, thermodynamic and transport properties of the species in the different phases present. Some properties of importance are as below. 

The height of the column section is determined mainly by the number of stages or plates required which in turn depends on how easy or difficult the mixture is to separate, i.e. the extent of separation. If the boiling points of the components to be separated are close, then a large number of stages are required leading to a very tall column. The column height is limited, however, by factors such a wind conditions, etc. 

The height of a distillation column depends on the feed conditions, the product purity specifications and the extent of separation through the vapour-liquid equilibrium relationship, but also on the type of tray or packing used in the column as this affects the rate of separation. Column vendors will normally provide information on tray or packing efficiencies.9,10... 

The height of an absorption column depends on the feed conditions, the product purity specifications, the solvent used and the extent of separation through the absorption equilibrium relationship, but also on the rate of separation. If the rate of mass transfer of the gaseous component from the gas phase into the liquid phase is slow, then the column needs to be longer to ensure that the required amount is removed. The rate of mass transfer depends on the mass-transfer coefficient, normally denoted kG or k. The value of the mass-transfer coefficient depends on the components in the gas feed and on the solvent used and is often determined experimentally. The type of packing used in the column will also have an impact on the column height as for distillation. 

The extent of separation can be quantified in terms of the resolution obtained between two consecutive chromatographic peaks. This resolution can be expressed in terms of three elemental characteristics of chromatographic separation retention, selectivity and efficiency. The influence of each of these three factors on resolution will be discussed. 

The fact that resolution as defined by eqn.(4.1) can be related so elegantly to the fundamental parameters of the separation process (i.e. a, k and AT) is a great advantage for the use of resolution (RJ to quantify the extent of separation of a pair of chromatographic peaks. However, in opting for Rs we need to accept all characteristics... 

Should the criteria used to characterize the extent of separation ofa pair ofadjacent peaks in a chromatogram be affected by the relative peak heights ... 

The resolution between two peaks has been defined in chapter 1 and this definition has been reviewed in section 4.1.1. In this section we will define and investigate various other criteria that may be used to quantify the extent of separation between a pair of adjacent peaks in a chromatogram. We will refer to these criteria as elemental criteria . Later in this chapter the elemental criteria will serve as the basis of criteria for judging the extent of separation in entire chromatograms. 

Three definitions of peak-valley ratios are illustrated in figure 4.2. All of them express the extent of separation as some measure of the depth of the valley between two peaks divided by some measure of the peak height. The first criterion (P) measures the depth of the valley relative to the interpolated peak height as shown in figure 4.2.a. The corresponding expression is ... 

Figure 4.2 Three definitions for peak-valley ratios as elemental criteria to quantify the extent of separation between a pair of adjacent peaks in a chromatogram, (a) Peak-valley ratio (P eqn.4.3) according to Kaiser, (b) median peak-valley ratio (Pm eqn.4.4) according to Schupp and (c) (opposite page) the valley-to-top ratio (P eqn.4.5) according to Christophe. 

This figure applies to Gaussian peaks, but clearly, for peaks of other shapes there will also be some threshold value below which changes in the extent of separation will not be reflected in P. 

An obvious criterion by which to judge the extent of separation of chromatographic peaks, especially for the optimization of a quantitative analysis, is the fraction of the peak that is free of overlap from adjacent peaks. The definition for this so-called fractional overlap criterion is illustrated in figure 4.3. An equation to describe the fractional overlap is... 

Clearly, FO gives a good indication of the accuracy with which a peak can be quantitatively determined in a chromatogram. However, it is not the same as the error involved in quantitative analysis. The latter is affected not only by the extent of separation (reflected in FO), but also by the algorithms or programs used to establish the peak area. 

Characteristics of different elemental criteria for measuring the extent of separation of a pair of chromatographic peaks. 

Recommendations for the use of different elemental criteria for measuring the extent of separation of a pair of chromatographic peaks. The preferred criteria are given, while possible alternatives appear in brackets. 

A second major category of proposed criteria to express the extent of separation in an entire chromatogram is that in which the product is takerfof the values for all pairs of peaks of one of the elemental criteria defined before. Taking the products of these criteria is equivalent to taking the sum of the logarithms, for instance... 

Summary of product criteria proposed in the literature to express the extent of separation achieved in a chromatogram. 

Data for capacity factors, elemental criteria and for criteria judging the extent of separation in the entire chromatograms. Chromatograms are shown in figure 4.8. Criteria for pairs of peaks separation factor (S, eqn.4.15), resolution (Rs, eqn.4.14) and peak-valley ratio (P, eqn.4.10). 

We should add that while resolution and peak capacity are excellent criteria of merit for the separation of multicomponent mixtures into discrete zones, other criteria exist, some very general, for judging the efficacy of separation and purification in any separative operation (see Section 1.4). Various terms such as impurity ratio and purity index abound. Rony has developed a criterion termed the extent of separation [22]. Stewart, as well as de Clerk and Cloete, have shown that entropy can be formulated as a very general measure of separation power, as we might expect from the discussion of Section 1.6 [23,24]. An excellent discussion of separation indices, with an emphasis on non-Gaussian zones (below), is found in Dose and Guiochon [25]. 

There are a wide range of different grades of wastepaper available, depending on the source and the extent of separation. As the name implies, wastepaper designated as direct pulp substitutes is utilized with little treatment before reslushing in a hydrapulper. The direct pulp substitutes are the highest grade of wastepaper. 

From Eqs. (7-1) and (7-2), it follows that the separation factor is purely based on the compositions of the entering and exit streams regardless of their flows. Another measure of the separation efficiency of a membrane process is the extent of separation proposed by Rony [1968]. In the context of applying this index of separation efficiency between two comfionents, it is assumed that there is no difficulty in separating the third component Thus the segregation fractions, fiy, are obtained from the molar flow rates of the permeate and retentate streams on the basis of only two components. The extent of separation is defined as the absolute value of a determinant of a binary separation matrix consisting of the segregation fractions as follows ... 

Besides some measures of separation efficiency such as the separation factor and extent of separation defined above, some quantity indicative of the throughput rate of a membrane system is needed to compliment the permselectivity of the membrane. It is quite common and practical in the membrane technology to use a phenomenological expression to relate the permeate flux (Ja in the unit of cm (STP)/s-cm7) of a given gas (A) through the membrane to the driving force, the transmembrane pressure difference (Ap) as follows ... 

To measure the separation efficiency of a membrane reactor involving multiple reaction components, the extent of separation, briefly introduced in Chapter 7, was used to replace the more commonly used separation factor by Mohan and Govind [1988a]. This alternative index of separation performance is based on the flow quantities of the process streams involved while the separation factor is calculated from the compositions instead. The goals of a high conversion and a high separation sometimes contradict each other. The choice or, more often than not, compromise of the two goals depends, on one hand, on the downstream separation costs and, on the other, on the process parameters such as the ratio of the reactant permeation to reaction rate and the relative permeabilities of the reaction components. 

For those cases where the permeability of reactant A is in between those of the two products, B and C, both the conversion and extent of separation increase with increasing permeation rate or permeation to reaction rate ratio (Table 11.9). The corresponding optimal compressor load (recycle flow rate to feed flow rate) also increases with the rate ratio. The top (permeate) stream is enriched with the most permeable product (i.e., B) while the bottom (retentate) stream is enriched with the least permeable product (i.e., C). It is noted from Table 11.9 that the optimal compressor loads for achieving the highest conversion and extents of separation can be quite different and a decision needs to be made for the overall objective. 

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