Rectification equilibrium stages

When it is desired to compute, with rigorous methods, actual rather than equilibrium stages, Eqs. (13-69) and (13-94) can be modified to include the Murphree vapor-phase efficiency T ij, defined by Eq. (13-29). This is particularly desirable for multistage operations involving feeds containing components of a wide range ol volatility and/or concentration, in which only a rectification (absorption) or stripping action is provided and all components are not sharply separated. In those cases, the use of a different Murphree efficiency for each component and each tray may be necessary to compute recovery accurately. 

The number of actual equilibrium stages determines the number of flashes that will occur. The more stages, the more complete the split, but the taller and more costly the tower. Most condensate stabilizers will normally contain approximately five theoretical stages. In a refluxed tower, the section above the feed is known as the rectification section, while the section below the feed is known as the stripping section. The rectification section normally contains about two equilibrium stages above the feed, and the stripping section normally contains three equilibrium stages. 

The feasibility of the above setup can be evaluated by simulation with Aspen Plus [19]. The RD column is built-up as a reboiled stripper followed by a condenser and a three-phase flash, with organic phase refluxed to column. The result is that only 3 to 5 reactive equilibrium stages are necessary to achieve over 99% conversion. The stripping zone may be limited at 2-3 stages, while the rectification zone has 1-2 stages. 

For a binary system with a single equilibrium stage, i.e., a reboiled stillpot with no rectification column, the mass balance is given by the Rayleigh equation ... 

Simulation of multicomponent rectification is based on the so-called MESH equations (M = material balances, E = equilibrium, S = summation of mole fractions, H = heat balance) formulated for a single equilibrium stage (Fig. 5.2-33) as follows ... 

The equipment for continuous distillation can only separate one stage in the equilibrium diagram. Countercurrent distillation, also called rectification, has found widespread application with normal pressure and coarse vacuum distillation when complex mixtures or components with small relative volatility factor are to be separated. The fundamentals are discussed above (2.1.3.3.2) the technical side will be dealt with here [41-45]. 

If the mutual solubility of the two phases is negligible, the theoretical number of stages can be determined by means of a staircase diagram (steps between balance lines and equilibrium curves), in a similar manner to rectification or absorption. In this case, too, it is more convenient to work with loadings X,Y than with molar fractions x,y... 

In Fig. 9.4-3 the three adsorbent streams are bronght together and mixed with the result that they have the loading X. This loading can be found by the rule of balances or the mixing rale This rale is at first applied on the mass streams 5ri and S,2 and then on the binary mixture (4i + r2) and S s. The approach to equilibrium in a stage can be expressed by a stage efficiency, compare the sections on absorption, extraction, and rectification. This efficiency is mainly dependent on the residence time in relation to a characteristic diffusion time, see later. 

In absorption and extraction processes, the assumption of phase equilibrium of the phases leaving the stage is less valid than in rectification processes. The exact calculation for a counterflow column using the theory of separation stages is generally carried out for rectification processes. The following discussion of a system of nonlinear equations, based on the column model, is particularly valid for rectification, but this may be applied to all other counterflow processes. Before the equation system can be formulated the variables used to describe the state of the counterflow system must be expressed. According to the column model in Fig. 1-60 they are... 

In some cases a partial condenser is used, as in Fig. 9.19. Here a saturated vapor distillate D is withdrawn, and the condensate provides the reflux. This is frequently done when the pressure required for complete condensation of the vapor G, at reasonable condenser temperatures, would be too large. The A is plotted at an abscissa yj, corresponding to the composition of the withdrawn distillate. Assuming that an equilibrium condensation is realized, reflux Lq is at the end of the tie line C. <7, is located by the construction line Lq A, etc. In the lower diagram, the line MN solves the equilibrium-condensation problem (compare Fig. 9.14). The reflux ratio R = Lq/D = line A )(7,/line (7,Z.o, by application of Eq. (9.65). It is seen that the equilibrium partial condenser provides one equilibrium tray s worth of rectification. However, it is safest not to rely on such complete enrichment by the condenser but instead to provide trays in the tower equivalent to all the stages required. 

The investigations of Stage and Bose [65] carried out in laboratoiy rectification columns show that the thickness of the wall film fluctuates and does not reach equilibrium state. The difference between the results of Weisman [64] and of Stage tmd Bose [65] is explained [66] with condensation of the vapour on the column wall. 

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