Reversible distillation

Now suppose N2 mols of pure liquid [2] are isothermally and reversibly distilled into Ni mols of pure liquid [1]. The change of free energy for distillation of 8N2 mols of [2] into a mixture over which the partial pressure is p2 is, as we have shown ... 

Complete thermodynamic analysis, based on reversible distillation, takes into account the effects of finite temperature and composition driving forces as well as nonuniform heat distribution and hydraulic resistance (Fonyo, 1974a,b). The effect of nonuniform heat distribution (i.e., adiabatic distillation) can be mitigated by the introduction of intercoolers/interheaters (Terranova and Westerberg, 1989 Dhole and Linnhoff. 1992). 

However, the liquid-vapor phase equilibrium field has other important characteristics that become apparent under other distillation modes, in particular, under reversible distillation and usual (adiabatic) distillation with finite reflux. 

The regions of reversible distillation and regions of the identical order of components are especially signihcant for the analysis of possible cases of separation by distillation. 

Figure 2.10. A thermodynamically reversible distillation (a) an infinite column with heat input and output (segments with arrows) at any cross-section of column, (b) a trajectory of reversible distillation. Segments with arrows, liquid-vapor tie-lines for certain cross-section of column (little circles).

The thermodynamically reversible distillation is a hypothetical process in an infinite column in which heat is fed in or removed to each tray at zero temperature differences, there are no heat losses, there is no pressure drop along the column length, and there is no nonequilibrium in aU points, including feed point and points of vapor supply from the reboiler and reflux from the condenser. 

For the reversible distillation, the following condition is implemented (the second law of thermodynamics) ... 

For the reversible distillation, the operation fine should coincide with the equilibrium line for the binary mixture in the McCabe-Thiele diagram. 

The scheme of the reversible process is shown in Fig. 2.10a. Figure 2.10b illustrates a trajectory of the reversible distillation for three-component ideal mixture. 

Figure 2.11. A location of pinches (shaded) in colnmn for adiabatic distillation at minimnm reflux and reversible distillation for equal product composition (a) first class of fractionation (R < and reversible distillation, (b) second class of fractionation (R = and partially reversible distillation.

For the adiabatic column in the first class of fractionation, the product compositions coincide with the product compositions for the reversible distillation (Fig. 

Generally speaking, for the first and second fractionation classes under the minimum reflux mode, the points of compositions in the zones of constant concentrations (i.e., stationary points of the trajectory bundles) should be arranged at the trajectories of reversible distillation built for the product points. It follows from the conditions of the material balance and the phase equilibrium in the zones of constant concentrations. Figure 2.11b illustrates the partially reversible process (it is reversible in the colunm parts that are from the constant concentration zones for the minimum reflux mode up to the column ends). 

In the case of the reflux ratio alteration and conservation of the product composition, the stationary points of trajectory bundle are traveling along the reversible distillation trajectories built for a given product, so the trajectories may be called lines of stationarity. Thus, the analysis of the reversible distillation trajectory arrangement in the concentration simplex is decisive in general geometric theory of distillation. 

The analysis of temperature alteration, as well as the vapor and liquid flows along the trajectory of the reversible distillation, is the basis of the methods for nonadiabatic distillation unit design the background for developing the new... 

If there is a reversible distillation process, then there should be also an opposite process, which may be called a process of the distilled flow mixing. 

Figure 2.15. (a) A column for the process that is opposite to the distillation process, (b) McCabe-Thiele diagram (operation hnes at infinite reflux, 1 at finite reflux, 2 at minimum reflux, 3 at reversible distillation, 4 at opposite process, 5 little circles, tray composition). 

The analysis of the thermodynamically reversible process of distillation for multicomponent azeotropic mixtures was made considerably later. Restrictions at sharp reversible distillation were revealed (Petlyuk, 1978), and trajectory bundles at sharp and nonsharp reversible distillation of three-component azeotropic mixtures were investigated (Petlyuk, Serafimov, Avet yan, Vinogradova, 1981a, 1981b). 

Restrictions at nonsharp reversible distillation of three-component azeotropic mixtures were studied by Poellmann and Blass (1994). 

Trajectories of adiabatic distillation at finite reflux for given product points should be located in concentration space in the region limited by trajectories at infinite reflux and by trajectories of reversible distillation (Petlyuk, 1979 Petlyuk Serafimov, 1983). 

As far as stationary points of trajectory bundles of distillation at finite reflux lay on trajectories of reversible distillation, these trajectories were also called the lines of stationarity (pinch lines, lines of fixed points) (Serafimov, Timofeev, Balashov, 1973a, 1973b). These lines were used to deal with important applied tasks connected with ordinary and extractive distillation under the condition of finite... 

Significance of reversible distillation theory consists in its application for analysis of evolution of trajectory bundles of real adiabatic distillation at any splits. Numerous practical applications of this theory concern creation of optimum separation flowsheets determination of optimum separation modes, which are close to the mode of minimum reflux and thermodynamic improvement of distillation processes by means of optimum intermediate input and output of heat. 

Equation (4.1) concerns not only reversible distillation process, but also any thermodynamically reversible process. For the distillation. 

The main peculiarity of thermodynamically reversible distillation process consists of the fact that flows of two different phases (vapor and liquid) found in any cross-section are in equilibrium, and flows found in the feed cross-section are of the same composition as feed flows. 

In addition, the product points should lie on the straight hne passing through the liquid-vapor tie-line of feeding. Hence, it follows that the maximum length of reversible distillation trajectory is achieved at the intersection of this straight line with the hyperfaces of concentration simplex that (hyperfaces) correspond to (n - 1)-component constituents C i of the initial mixture (sharp separation). 

Sharp and Nonsharp Reversible Distillation of Ideal Mixtures... 

Feasible sharp reversible distillation split of ideal mixtures can be presented as follows 1, 2,... (n - 1) 2,3... n. Therefore, at the reversible distillation, components 2, 3,... (n - 1) are distributed among the top and the bottom products. At nonsharp and semisharp reversible distillation, both products contain all the components or one of the products does not contain the lightest or the heaviest component. At nonsharp reversible distillation, product points lie in the same straight line as at sharp distillation but at some distance from the hyperfaces of the concentration simplex. 

The mode of sharp reversible distillation is the most interesting. As far as xon = 0, Eq. (4.6) for this mode for component n looks as follows ... 

Therefore, in an arbitrary cross-section of upper (lower) section at sharp reversible distillation the ratio of liquid and vapor flows is equal to the phase equihb-rium coefficient of the heaviest (lightest) component (i.e., the component absent in the product of the section). 

Column Sequence of Ideal Mixtures Reversible Distillation... 

Figure 4.3 shows the change of the liquid flow rate at the height of a binary reversible distillation column (the column height is characterized by the concentration of the light component) for sharp and nonsharp separation. It is typical of sharp separation that the input of heat and of cold, which is not equal to zero, is required at the ends of the column and, for nonsharp separation, this input makes an infinitesimal quantity. 

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