Binary countercurrent flow

A set of ternary mass transfer experiments was carried out by Toor and Sebulsky (1961b) and Modine (1963) in a wetted-wall column and also in a packed column. These authors measured the simultaneous rates of transfer between a vapor-gas mixture containing acetone, benzene, and nitrogen or helium, and a binary liquid mixture of acetone and benzene. Vapor and liquid streams were in cocurrent flow in the wetted-wall column and in countercurrent flow in the packed column. Their experimental results show that diffusional interaction effects were significant in the vapor phase, especially for the experiments with helium in the wetted wall column. 

Calculation of the degree of separation of a binary mixture in a membrane module for cocurrent or countercurrent flow patterns involves the numerical solution of a system of two nonlinear, coupled, ordinary differential equations (Walawender and Stem, 1972). For a given cut, the best separation is achieved with countercurrent flow, followed by crossflow, cocurrent flow, and perfect mixing, in that order. The crossflow case is considered to be a good, conservative estimate of module membrane performance (Seader and Henley, 2006). 

An ideal binary mixture can be separated into almost pure components in a separation column operated continuously with countercurrent flow. To separate a mixture of k components, k - 1 columns connected in series are needed. 

Figure 8.1.1. Type (1) system. Development of concentration profile for a binary gaseous system along the height of a vertical column of parallel plates having closed ends and subjected to thermal diffusion equilibrium and countercurrent flow of two regions by natural convection. Numbers in boxes in each Jigure represent mole % of lighter species (e.g. Hff. (After Grew and Ibbs (1952) and Powers (1962).)...

For ail species moving in a given direction in a coiumn, the solution of this equation wiii indicate that, at that coiumn exit, aii such species wiii appear/exist therefore multicomponent separation is not possibie. Oniy a binary separation is possible with one species moving in the opposite direction in the column and therefore available as a pure species. This is the primary reason why we will see that a countercurrent colutnn used for steady state processes such as distillation, absorption, extraction, crystallization, etc., separates a binary mixture only. For temany mixture separation, two columns are needed. Three columns are employed to separate a four-component mixture (see Chapter 9 for various schematics). However, if a feed sample injection is made, as in elution chromatography, into a mobile phase in countercurrent flow vis-k-vis another mobile phase, transient multicomponent separation would appear to be feasible. If pulse injection of one phctse containing feed is introduced countercurrent to the other phase, it may be possible to achieve a multi-component separation capability (as is tme for cocmrent flow, considered in Section 8.2). 

We have seen in Section 8.1.1.3 that continuous operation of a distillation column with countercurrent flow of vapor and liquid can separate a binary mixture only. If we have a multicomponent nonazeotropic mixture as feed, then only one of the two product streams can have one species with sufficient purity the other product stream will contain aU other species in quantities reflecting their feed concentration. This stream has to be fed to another distillation column that can produce two product streams, where each product stream will have sufficient purity with respect to one of the two remaining species for a ternary feed to the first distillation column. Similarly, if the feed to the first column has four components, in general, we will need three columns to obtain four product streams, each product stream being sufficiently purified in one of the species. In general, to separate n species in the feed by distillation in simple distillation columns of the type shown in Figure 8.1.19(b), we will need n - 1) distillation columns. 

A hypothetical moving-bed system and a Hquid-phase composition profile are shown in Figure 7. The adsorbent circulates continuously as a dense bed in a closed cycle and moves up the adsorbent chamber from bottom to top. Liquid streams flow down through the bed countercurrently to the soHd. The feed is assumed to be a binary mixture of A and B, with component A being adsorbed selectively. Feed is introduced to the bed as shown. 

Countercurrent and Cocurrent Plug Flows. The model equations for these flow patterns cannot be solved analytically. Oishi and coworkers first derived the general model eqnstions for a binary-component system with porous media.19 Walawenderand Stem,16 Blaisdell and Kammermeyer,1 and Pan and Habgood17 later reported solutions for similar membrane separators. The cocurrent-counteicurrent combiner inu flow pattern also lies been studied by Pen ned Habgood.17... 

In a countercurrent multistage section, the phases to be contacted enter a series of ideal or equilibrium stages from opposite ends. A contactor of this type is diagramatically represented by Fig. 8.1, which could be a series of stages in an absorption, a distillation, or an extraction column. Here L and V are the molal (or mass) flow rates of the heavier and lighter phases, and x,- and y,- the corresponding mole (or mass) fractions of component /, respectively. This chapter focuses on binary or pseudobinary systems so the subscript / is seldom required. Unless specifically stated, y and x will refer to mole (or mass) fractions of the lighter component in a binary mixture, or the species that is transferred between phases in three-component systems. 

The operating lines in Figure 13-9 are similar to those we found for binary flash distillatiom Both single-stage systems and cross-flow systems are arranged so that the two oudet streams are in equilibrium and on the operating line. This is not true of countercurrent systems. 

Consider a countercurrent gas permeator as well as a cocurrent gas permeator for the separation of a particular binary gas mixture at feed pressure Pf and permeate pressure Pp. Assume that there are no pressure drops on either the feed side or the permeate side. If the pressure ratio y 0, show that the separation achieved would be independent of the flow pattern. Assume a symmetric membrane with constant values of permeances. Will the situation be any different if we used the crossflow permeator of Section 7.2.1.1 ... 

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