The simplest form of distillation involves boiling a multicomponent liquid mixture batchwise in a single-stage still pot. At any instant in time the vapor being generated and removed from the pot is assumed to be in equilibrium with the remaining liquid (assumed to be perfectly mixed) in the still. Because the vapor is richer in the more volatile components than the liquid, the composition and temperature of the liquid remaining in the still changes continuously over time and moves progressively toward less volatile compositions and higher temperatures until the last drop is vaporized. For some mixtures, this last composition is the highest-boiling pure component in the system. For other mixtures, this final composition may be a maximum-boiling azeotrope. For yet other systems, the final composition varies depending on the initial composition of the mixture charged to the still.
A residue curve is a tracing of this change in perfectly mixed liquid composition for simple single-stage batch distillation with respect to time. Arrows are sometimes added, pointing in the direction of increasing time, increasing temperature, and decreasing volatility. Because simple, batch distillation can be described mathematically by dxt /d £ = x, - yt for all i = 1, ...n (13-126)
where E, is a nonlinear time scale, residue curves may also be extrapolated backward in time to give more volatile compositions which would produce a residue equal to the specified initial composition. A residue curve map (RCM) is generated by varying the initial composition and extrapolating Eq. (13-126) both forward and backward in time [Doherty and Perkins, Chem. Eng. Sci., 33, 281 (1978)]. Unlike a binary y-x plot, relative-volatility information is not presented. Therefore, it is difficult to determine the ease of separation from a residue curve map alone.
Residue curve maps can be constructed for mixtures of any number of components, but can be pictured graphically only for up to four components. For a binary mixture, a T-x,y diagram suffices; the system is simple enough that vapor-phase information can be included without confusion. With a ternary mixture, liquid-phase compositions are plotted on a triangular diagram, similar to that used in liquidliquid extraction. Four-component systems can be plotted in a 3-dimensional tetrahedron. The vertices of the triangular diagram or tetrahedron represent the pure components. Any binary, ternary, and quaternary azeotropes are placed at the appropriate compositions on the edges and/or interior of the triangle and tetrahedron.
The simplest form of ternary RCM, as exemplified for the ideal normal-paraffin system of pentane-hexane-heptane, is illustrated in Fig. 13-58(2. using a right-triangle diagram. Maps for all other non-azeotropic ternary mixtures are qualitatively similar. Each of the infinite number of possible residue curves originates at the pentane vertex, travels toward and then away from the hexane vertex, and terminates at the heptane vertex.
The family of all residue curves that originate at one composition and terminate at another composition defines a region. Systems that do not involve azeotropes have only one region—the entire composition space. However, for many systems, not all residue curves originate or terminate at the same two compositions. Such systems will have more that one region. The demarcation between regions in which adjacent residue curves originate from different compositions or terminate at different compositions is called a separatrix. Separatrices are related to the existence of azeotropes. In the composition space for a binary system, the separatrix is a point (the azeotropic composition). With three components, the separatrix becomes a (generally curved) line, with four components the separatrix becomes a surface, and so on.
All pure components and azeotropes in a system lie on region boundaries. Within each region, the most volatile composition on the boundary (either a pure component or a minimum-boiling azeotrope and the origin of all residue curves) is called the low-boiling node. The least-volatile composition on the boundary (again either a pure component or a maximum-boiling azeotrope and the terminus of all residue curves) is called the high-boiling node. All other pure components and azeotropes are called intermediate-boiling saddles (because no residue curves originate or terminate at these compositions). Adjacent regions may share nodes and saddles. Pure components and azeotropes are labeled as nodes and saddles as a result of the boiling points of all of the components and azeotropes in a system. If one species is removed, the labeling of all remaining pure components and azeotropes, particularly those that were saddles, may change. Region-defining separatrices always originate or terminate at saddle azeotropes, but never at saddle-pure components. Saddle-ternary azeotropes are particularly interesting because they are less obvious to determine experimentally (being neither minimum-boiling nor maximum-boiling), and have only recently begun to be recorded in the literature. (Gmehling et al., Azeotropic Data, VCH Publishers, Deer-
FIG. 13-58 Residue curve maps. (a) Nonazeotropic pentane-hexane-heptane system.
field Beach, Florida, 1994). However, their presence in a mixture implies separatrices, which may have an important impact on the design of a separation system.
Both methylethylketone (MEK) and methylisopropylketone (MIPK) form minimum-boiling azeotropes with water (Fig. 13-58b). In this ternary system, a separatrix connects the binary azeotropes and divides the RCM into two regions. The high-boiling node of Region I is pure water, while the low-boiling node is the MEK-water azeotrope.
FIG. 13-58 (Continued ) Residue curve maps. (c) Ethanol-cyclohexane-water system containing four minimum-boiling azeotropes and three distillation regions.
In Region II, the high- and low-boiling nodes are MIPK and the MEK-water azeotrope, respectively. The more complicated cyclo-hexane-ethanol-water system (Fig. 13-58c) has three separatrices and three regions, all of which share the ternary azeotrope as the low-boiling node.
The liquid-composition profiles in continuous staged or packed distillation columns operating at infinite reflux and boilup are closely approximated by simple distillation-residue curves [Van Dongen and Doherty, Ind. Eng. Chem. Fundam., 24, 454 (1985)]. Residue curves are also indicative of many aspects of the general behavior of continuous columns operating at more practical reflux ratios. For example, to a first approximation, the composition of the distillate and bottoms of a single-feed, continuous distillation column lie on the same residue curve. Therefore, for systems with separatrices and multiple regions, distillation-composition profiles are constrained to lie in specific regions. The precise boundaries of these distillation regions are a function of reflux ratio, but they are closely approximated by the RCM separatrices. If a RCM separatrix exists in a system, a corresponding distillation boundary will also exist. Separatrices and distillation boundaries correspond exactly at all pure components and azeotropes.
Residue curves can be constructed from experimental data or can be calculated analytically if equation-of-state or activity-coefficient expressions are available (e.g., Wilson binary-interaction parameters, UNIFAC groups). However, considerable information on system behavior can still be deduced from a simple semi-qualitative sketch of the RCM separatrices or distillation boundaries based only on pure component and azeotrope boiling-point data and approximate azeotrope compositions. Rules for constructing such qualitative distillation region diagrams (DRD) are given by Foucher et al. [Ind. Eng. Chem. Res., 30, 760-772, 2364 (1991)]. For ternary systems containing no more than one ternary azeotrope, and no more than one binary azeotrope between each pair of components, 125 such DRD are mathematically possible, although only a dozen or so represent most systems commonly encountered in practice.
Figure 13.59 illustrates all of the 125 possible DRD for ternary systems. Azeotropes are schematically depicted generally to have equi-molar composition, distillation boundaries are shown as straight lines, and the arrows on the distillation boundaries indicate increasing temperature. These DRD are indexed in Table 13-16 according to a temperature-profile sequence of position numbers, defined in a keyed-triangular diagram at the bottom of the table, arranged by increasing the boiling point. Positions 1, 3, and 5 are the pure components in order of decreasing volatility. Positions 2, 4, and 6 are binary azeotropes at the positions shown in the keyed triangle, and position 7 is the ternary azeotrope. Azeotrope position numbers are deleted from the temperature profile if the corresponding azeotrope is known not to exist. It should be noted that not every conceivable temperature profile corresponds to a thermodynamically consistent system, and such combinations have been excluded from the index. As is evident from the index, some DRD are consistent with more than one temperature profile. Also, some temperature profiles are consistent with more than one DRD. In such cases, the correct diagram for a system must be determined from residue curves obtained from experimental or calculated data.
Schematic DRD shown in Fig. 13-59 are particularly useful in determining the implications of possibly unknown ternary saddle azeotropes by postulating position 7 at interior positions in the temperature profile. It should also be noted that some combinations of binary azeotropes require the existence of a ternary saddle azeotrope. As an example, consider the system acetone (56.4°C), chloroform (61.2°C), and methanol (64.7°C). Methanol forms minimum-boiling azeotropes with both acetone (54.6°C) and chloroform (53.5°C), and acetone-chloroform forms a maximum-boiling azeotrope (64.5°C). Experimentally there are no data for maximum or minimum-boiling ternary azeotropes. The temperature profile for this system is 461325, which from Table 13-16 is consistent with DRD 040 and DRD 042. However, Table 13-16 also indicates that the pure component and binary azeotrope data are consistent with three temperature profiles involving a ternary saddle azeotrope, namely 4671325, 4617325, and 4613725. All three of these temperature profiles correspond to DRD 107. Experimental residue curve trajectories for the acetone-
chloroform-methanol system, as shown in Fig. 13-60, suggest the existence of a ternary saddle azeotrope and DRD 107 as the correct approximation of the distillation regions. Ewell and Welch [Ind. Eng. Chem., 1224 (1945)] confirm such a ternary saddle at 57.5°C.
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