Single-entry separator

Figure 2.1.2. Some examples of the nature of contact between various feed and product streams, (a) Membrane separates air into two product streams in a single-entry separator, which is a silicone membrane permeator for air separation, (b) Limited contact between vapor and liquid products in a sieve plate (the separator) in a distillation column, (c) Complete contact between a feed scrubbing liquid stream introduced as drops in a spray and the product gas stream after scrubbing.

An open separator will have at least three streams coming in and out through three different surface areas Sj (see Section 2.5 for a different case). We adopt the convention that for a single-entry separator the subscript j will have values 1,2,..., k corresponding to k product streams, but j = /for the single feed stream. For a double-entry separator, the two feed streams are to be denoted hyj =/i and/2, respectively, while the k product streams will continue to have 7 = 1,2,..., k. 

Consider the steady state operation of the single-entry separator shown in Figure 2.1.1. Since there is no accumulation of mass inside the separator,... 

For a single-entry separator with two output streams, (2.1.22) and (2.1.23a) reduce to... 

Binary separation in a single-entry separator with or without recycle... 

We consider now the description of binary separation in a single-entry separator with only two product streams. Assume steady state operation without any chemical reaction. As in Chapter 1 with region 1 and species 1, we assume here arbitrarily that species 1 is lighter than species 2 and thaty = 1 refers to that product stream which is richer in the lighter species 1. If we had perfect separation, product stream y = 1 will have only species 1 and product stream y = 2 will have only species 2. To start with, consider only a nonrecycle separator. Such a separator is sometimes called a splitter (Figure 2.2.1a). 

If x,i 7 x,2 and both are different from Xyt the single-entry separator has achieved some separation. How much separation has been attained can be estimated by suitable descriptors, indices of separation. The simplest of these indices bear the name of specific separation processes where they are extensively used the desalination ratio Dr the solute rejection R and the decontamination factor Df. 

Figure 2.2.1. (a) Nonrecycle single-entry separator, (b) Single-entry separator with part oflightfraction recycled to feed stream, (c) Singleentry separator with part of heavy fraction recycled to the feed. 

The index the extent of separation, Wcis shown in Chapter 1 to reflect both the quality of the separated regions in terms of composition and the amount of recovery of a species in its designated region. For a single-entry separator, an appropriate definition of is as follows (see Rony (1970) and the efficiency formula 9 in Rietema (1957)) ... 

Note that Fn = 0i and y2i = 2. where 0i is the ith component cut For perfect separation in a single-entry separator and two product streams,... 

Obviously, a flash desalinator is an asymmetric single-entry separator. We have... 

It would appear from the preceding treatments that for a single-entry separator, the cut 6 is independent of o y, or 0(2 For any given separation process, the relation between a separation factor and the cut, can be derived only by detailed considerations of the separation mechanism operative in the separator. In general, the separation fatrtor is likely to depend on 6. These dependencies wiU be considered when individual separation processes are discussed in later chapters. 

Single-entry separator with a product recycle... 

For a binaiy mixture dilute in one species and being separated in a single-entry separator, there will therefore be a better separation with recycle of light fraction for constant 6, and... 

A recycle single-entry separator may have part of its tails stream recycled to the feed (flash distillation. Figure 2.2.1(c)). Examples of radioactive rare gas separation with various recycle arrangements are given in Ohno et al. (1977, 1978). See Problem 2.2.7. One aspect to be noted while comparing separators with or without recycle is that since 0 is constant, but the actual feed flow rate to the separator changes with recycle from that without recycle, the dimensions of the two separators will be different See, however. Problem 2.2.8. 

Unlike that far a single-entry separator, where = aj X 0(2 by definition, here. 

In general, jr (for example, in Figure 2.3.2(b), where the vapor from the top of the column is only partially condensed, the composition of the product vapor and the product liquid will be different the partial condenser is also a single-entry separator. However, with a total condenser, all vapor from the column top is condensed to liquid x = x ). But with a total condenser on the column, Wff2= 0, = 0, x = and R is the reflux... 

Consider a single-entry separator used either for separating solid particles from a fluid or separating solid particles having sizes above a particular value from those having sizes below the particular value. Let u/Jy. be the total mass flow rate of solids in the feed fluid whose total volumetric flow rate is Qf. In such a separator, there are only two product streams, the overflow (/ = 1) and the underflow (/ = 2). The total mass flow rate of solids in the overflow and the underflow are, respectively, and u/Jj- The overflow is identified with essentially the carrier fluid and the finer particles, whereas the underflow is assumed to have most of the coarser particles and small amounts of carrier fluid. Figure 2.4.1 illustrates this for a hydrocyclone (Talbot, 1980). Sizes of various natural and industrial particles are shown in Figure 2.4.2. 

The fraction of particles in the range tp to tp + dtp could be based on the weight fraction of particles, or the number fraction of particles, etc. Suppose we assume that/(rp) dtp gives the weight fraction (and therefore the mass fraction) of particles in the size range tp to tp 4- dtp. Then a mass balance of all particles, as well as of particles in this size range, yields at steady state for the single-entry separator ... 

These quantities are thus analogous to those we have already defined for a size distributed particle population. Instead of particle size, we have a distribution variable r, which is intrinsic to a given chemical species. For example, for a flash vaporizer single-entry separator (Figure 2.4.7), the material balance for 1 mole of feed having a molecular weight density function off/(M) is... 

For a multicomponent chemical mixture being fed into a single-entry separator with only two product streams, existing methods of description involve amongst others separation factors for selected components. Some of these separation factors, namely a,>, (definition (1.6.6)), ay (definition (1.6.8)), etc., were introduced earlier with closed... 

Example 2.4.4 illustrates the selection of heavy key and light key components for the distillation process. Note also that one can analyze the separator as though there are only two components, the heavy key (i = 2) and the light key (i = 1). Of course, in such a case the total molar feed flow rate is to be reduced to [xy + X2 for a single-entry separator, where Xiyand X2/refer, respectively, to the actual mole fractions of species 1 and species 2 in the actual feed. Thus Xy + X2f< 1. But in the hypothetical binary system, define Xj and X2/Such that (Hengstebeck, 1961)... 

If a multicomponent feed stream is separated by a single-entry separator into more than two product streams, the description acquires much greater complexity. Very little is available in the literature for such cases. The best approach appears to be to concentrate on two specific species and the respective species-specific product streams. Perfect separation will then consist of each product stream containing only a specified species. The various indices defined for binary systems in this chapter may be used with due provisions for the distribution of each species in each product stream. 

In some separation processes, only one product stream comes out of a single-entry separator. Further, the molar flow rates of various species in this product stream as measured by a detector (Figure 2.5.1) vary with time in a manner useful for separation. 

Figure 2.5.1. Time-varying molar output rate of solute species in the single product stream from a single-entry separator.

Obtain the following relation between the separation factor afj, the heads separation factor a%, the cut 0 and Xii for a single-entry separator and a binary feed ... 

Consider the separation of a binary mixture in two single-entry separators connected together as shown in Figure 2.P.I. The tails stream from separator 2 is recycled back to the feed stream to separator 1. The mole firaction of the ith species in the jth stream of separator n is indicated by x rij (for n = 1,2). If these two separators are operated such that ... 

Consider a single-entry separator with a dilute feed solution of heavy species 2. If a fraction rf of the tails stream is recycled to the feed stream and the separator operates with the same values of 6, ajj and does the non-... 

Consider a single-entry separator for the separation of a binary mixture of species 1 and 2 (Figure 2.2.1(a)). We wish to compare its separation performance with that of a single-entry separator having a fraction t) of its light fraction recycled to the feed stream. The operational conditions are as follows ... 

The separative power SU of a single-entry separator for a binary feed stream is defined by Dirac in terms of a... 

Consider a single-entry separator separating two species g and h in the feed stream. The molar flow rates of species g and h in the feed stream are, respectively. Go and Ho. The corresponding molar flow rates of species g and h in stream 1 and stream 2 are, respectively, Gi, Hi and G2, H2. Stream 1 is the light fraction. The following quantities are defined as follows ... 

A second mode of feed introduction involves a constant flow rate of feed into the separator at a fixed separator location for a fixed period of time, after which feed flow is stopped for a certain amount of time feed flow is restarted after this pause. The start-stop is carried out cyclically for as many cycles as is feasible/desirable (Figure 6.1.10(a)). Fixed-bed processes in a single-entry separator described in Sections 7.1.1-7.1.3,... 

Large-scale devices in industry employ centrifugal forces to separate particles from a fluid or droplets from an immiscible continuous phase. Usually, these large devices are single-entry separators a multiphase feed stream enters... 

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