- System visualization. Triangular (three-component) and tetrahedral (four-component) RCMs are effective for displaying thermodynamic information.
- Evaluation of data. An RCM can be used to quickly check the thermodynamic consistency of complex experimental VLE data such as the existence of azeotropes, especially saddle ternary azeotropes, and can help guide an experimental program.
- Process synthesis. Construction of an RCM facilitates the evaluation of flow sheet concepts for new processes and retrofits.
- Process modeling. RCMs can aid in the understanding of a host of simulation issues, such as material balance, and composition and temperature profiles, and identification of infeasible or problematic column specifications that cause simulation convergence difficulties.
- Control analysis/design. Column balances and profiles can be analyzed to aid in control system design and operation.
- Process troubleshooting. RCMs can allow you to readily grasp many elements of separation system operation and malfunction, such as tracking trace impurities, with implications for corrosion and process specifications.
We;ll start with a brief primer on RCMs and then illustrate the principles with several practical examples. Unlike a binary x-y plot, relative volatility information is not presented, but a host of useful insights into all types of batch and continuous distillation operations can be garnered from studying the RCM of a multicomponent system.
What are RCMs?
The simplest form of distillation involves boiling a multicomponent liquid in a single-stage still pot. At equilibrium, the vapor generated in such a still pot is enriched in the more volatile components. If the vapor is withdrawn as formed, the liquid and vapor compositions change continuously over time.
The composition of the liquid remaining in the still pot becomes progressively less volatile and the temperature increases until the last drop is vaporized. A residue curve is a trace of this change in liquid composition for simple single-stage distillation with respect to time.
In addition, residue curves indicate the general behavior of continuous distillation columns operated at practical reflux ratios. An RCM is simply a collection of residue curves over the entire composition space, as shown in Figure 1 for the ethanol/water/benzene system at atmospheric pressure. [See Figure 1 and other figures by clicking on the Download Now button underneath this article.] All residue curves originate at low-boiling pure components or azeotropic compositions (often referred to as low-boiling nodes) and end at high-boiling compositions (high-boiling nodes). An RCM with more than one origin or terminus for residue curves has more than one distillation region.
For instance, the ethanol/ water/benzene system has three distillation regions. Intermediate boiling pure components and azeotropes that are not nodes are termed saddles. The pattern of boundaries, nodes and saddles of a given multicomponent system is related to the boiling points of the pure components and azeotropes and is readily definable mathematically. (Kiva et al. present a thorough review of the thermodynamic principles behind RCMs .)
Although 125 distinct RCMs are possible for three-component systems, only about 14 are commonly found (Figure 2). An RCM can be constructed from experimental data for many common systems or calculated with an equation-of-state or activity-coefficient expression, e.g., Wilson parameters or UNIFAC groups [2,3]. However, semiqualitative sketches based only on pure-component and azeotrope boiling-point data and approximate azeotrope compositions, if available, still can provide considerable information about a system. These data can be used to construct a qualitative RCM by the method presented in Perry;s Handbook . RCM sketches allow an engineer to quickly understand the existence and location of distillation boundaries, distillation regions and the feasible product regions for a given feed composition.
The overlayment of liquid/liquid phase-equilibrium data onto an RCM highlights heterogeneous azeotropic distillation possibilities (for example, Figure 4).
A single-feed distillation column can be designed with sufficient stages, reflux and material-balance control to produce a variety of different separations ranging from the direct mode operation (pure low-boiling node taken as distillate) to the indirect mode of operation (pure high-boiling node taken as bottoms). This range of operability results in a bowtie-shaped set of reachable compositions roughly bounded by the material balance lines corresponding to the sharpest direct and indirect separations.
No rigorous thermodynamic calculations are needed to construct the approximate bowtie region; so, it is particularly useful for early conceptual flow-sheet synthesis. The exact shape of the reachable composition space is further limited by the requirement that the distillate and bottoms lie on the same residue curve (i.e., in the same distillation region) and by the material balance constraint that distillate and bottoms be colinear with the feed. Figure 3 illustrates these principles. Except when highly curved, distillation boundaries act as barriers to single-feed distillations. Because saddles deflect residue curves, it is generally not possible to obtain a saddle product (pure component or azeotrope) from a simple single-feed column. (Doherty and Malone give a good review of the principles outlined above .)
With this background, we now can examine the practical use of RCMs.
Let;s begin with a fairly common occurrence: operational problems with an azeotropic distillation column/decanter system. The system in question is designed to produce dried ethanol using benzene as the entrainer. Figure 4 depicts the steady-state material balance. The desired product is 99.9 wt.% ethanol, with less than 10 ppm benzene. The ternary ethanol/water/benzene azeotrope is decanted, with the organic layer refluxed to the column to provide entrainer flow.
The column has always been difficult to operate and often cannot meet the tight benzene specifications of the product ethanol. Two very different temperature profiles have been observed between on-spec and off-spec operation. The column operation is stable with either profile. However, the normal control action of increasing reflux or boilup (vapor from the reboiler) does not correct off-spec operation in most cases. Often the problem appears and disappears suddenly but seems to be related to fluctuations in feed composition. Is there an explanation for this apparent multiple steady-state behavior?
The number of saddles in a particular distillation region can have significant impact on design, operability and control. In a distillation region with one saddle (a three-sided region), all residue curves track toward the solitary saddle. However, in a four-sided region with two nonadjacent saddles, some residue curves tend to track toward one saddle, while others track toward the other saddle (the residue curves labeled A and B in Figure 1).
The ethanol-drying column operates in one of three such four-sided regions of the ethanol/water/ benzene system. As shown in Figure 5, column profile A, the major impurity in the ethanol product is benzene. For curve B, water is the major impurity. With sufficient stages below the feed, the stripping profile will generally follow very closely to one edge of the diagram (either the benzene- or water-free edge).
A column operated to simultaneously take both the high- and low-boiling nodes as products has very few degrees of freedom from a material balance standpoint. Small fluctuations in reflux, boilup or feed composition can result in feasible operation on many different residue curves that originate and terminate at these compositions but still meet material balance constraints. Increasing reflux further constrains the distillate composition. The bottoms composition will have to swing with column disturbances. Depending upon the direction this shift takes, the trace impurity profile in the ethanol product may move from water to benzene or vice versa. This is especially true if the control strategy involves maintaining a constant temperature at a point in the column prone to wide fluctuations in composition and temperature (i.e., the stripping section). The control system may have a difficult time compensating for disturbances.
Increasing the boilup does nothing to shift from a stable, yet undesirable, composition profile. Sufficiently high boilup can be used to drive enough benzene out of the ethanol product to meet specs. However, the purity will be higher than the 99.9-wt.% target, with concomitant high steam usage. The better approach is to ensure that the stripping profile stays on the benzene-free edge of the diagram (Profile B).
Generally, it is better not to try to closely approach the compositions of the high- and low-boiling nodes at once but instead to enable the distillate composition to float more freely with feed and reflux. Allowing reflux of both phases from the decanter can add an important degree of freedom that helps to dampen variations in the feed composition.
Columns such as this are often difficult to model with a process simulator. Simulation algorithms frequently rely on perturbation of a variable, such as reflux, reboil or distillate-to-feed ratio, while checking for convergence of column enthalpy and material balance. The simulator may be close to a feasible solution but successive iterations may appear to be far apart, as the unconverged solution swings between different composition and temperature profiles. As with column operation, over-constraint by specifying excessive staging or reflux can exacerbate simulation convergence problems. Often if the simulation is difficult to converge, then the column probably won;t run well either.
It is tempting to add a few extra stages into a design when data are limited. However, overdesign of the rectifying section is not good practice for operation in a four-sided region. It also constrains the distillate composition and can lead to many of the same difficulties with column operation.
How does the ethanol-drying column fit into an overall azeotropic distillation scheme for producing dry ethanol? A good place to start the design process is by examining the topology of the RCM. As illustrated in Figure 1, there are three binary and one ternary minimum-boiling azeotropes. Only one of the binary azeotropes and the ternary azeotrope are heterogeneous. Each pure component is a high-boiling node in one of the three distillation regions. The ternary is the low-boiling node in all three regions. Many other potential entrainers for the ethanol/water system, such as n-hexane, cyclohexane, heptane, toluene, ethyl butyl ether and dipropyl ether, exhibit qualitatively similar RCMs.
Because of the distillation boundary between Regions I and II, a single distillation from the indicated feed composition (Figure 4) cannot provide pure ethanol. Instead, obtaining both high purity and high recovery of ethanol requires a more complicated distillation sequence. Pure water is in the reachable composition space for any arbitrary column feedpoint in Region II. Pure ethanol is obtainable only in the composition space where ethanol is a high-boiling node (i.e., Region I). Exploitation of liquid/liquid equilibrium allows us to cross over the distillation boundary between Regions I, II and III to generate a benzene-rich stream. A convenient distillate composition in the two-phase LLE region is the ternary azeotrope, which is the low-boiling node in all distillation regions. The organic layer formed from the ternary azeotrope is in Region III, whereas the aqueous layer is in Region II. The organic layer can be mixed with the feed to produce a composition in Region I.
Now let;s put these facts together to generate one possible flow sheet alternative (Figure 4). Assume for the moment that the benzene-rich organic layer resulting from phase separation of the ternary azeotrope is available and is combined with the feed composition. The resulting mixture composition lies within Region I. This mixture can be distilled to give pure ethanol as the bottoms product (indirect split) and a composition close to the ternary azeotrope as the distillate. Once separated into organic and aqueous phases, we have regenerated the benzene-rich entrainer composition.
Distillation of the aqueous layer gives pure water as the bottoms product (indirect split) and a distillate composition close to a point on the feed-entrainer mixing balance line. The distillate from the water column can be combined with the original feed and the mixing balance adjusted accordingly. Although material balances must be confirmed by more detailed calculations, we have completed the design of the conceptual flow sheet. Other distillation sequences are possible. (A number of references [6, 7, 8, 9, 10] detail systematic methods of synthesizing distillation-based flow sheets using RCMs.)
Evaluation of data
Let;s explore the use of p-xylene as an entrainer for the separation of water and acetic acid by azeotropic distillation. Literature data indicate the water/p-xylene and acetic acid/p-xylene form minimum-boiling binary azeotropes and the water/acetic acid is pinched but non-azeotropic. No information could be found on the existence of a ternary azeotrope. This, of course, does not mean that one does not exist. Using the method of sketching RCMs found in Perry;s Handbook, 7th Edition , leads to the identification of three RCMs that are thermodynamically feasible for a system with binary minimum-boiling azeotropes between the highest-boiling pure component and each of the other two components. With this information, a simple experiment can be performed to determine which RCM is correct.
If no ternary azeotrope exists (Figure 6a), the p-xylene/water azeotrope will be the initial distillate no matter what composition is charged to the still pot because the p-xylene/water azeotrope is the low-boiling node in each distillation region. If a minimum-boiling ternary azeotrope exists (Figure 6b), it will be the initial distillate for any composition charged to the still, as the ternary azeotrope is again the low-boiling node for both distillation regions. If a saddle azeotrope exists (Figure 6c), the composition of the distillate will depend upon the composition charged to the still pot. For two regions the water/p-xylene azeotrope is the low-boiling node, while the p-xylene acetic acid azeotrope is the low-boiling node for the other two regions.
A ternary mixture consisting of 10 wt.% p-xylene, 10 wt.% acetic acid and 80 wt.% water (chosen arbitrarily) was charged to a still pot equipped with a 1-in. inner diameter 3 3-in. tall vacuum-jacketed packed column with a timed reflux head set to 6:1 reflux ratio. The mixture was fractionated batch-wise until p-xylene was exhausted from the still pot. All distillate cuts formed two liquid phases upon standing. The table gives the overall composition of the distillate cuts and final still pot composition.
For cuts 2-6, the data are consistent with the existence of a heterogeneous minimum-boiling ternary azeotrope, boiling point of 91°C, composition of roughly 1.5 wt.% acetic acid, 36 wt.% water and the remainder p-xylene. Therefore, Figure 6b is the correct qualitative RCM for this system. This experiment also gave information about the boiling point of the azeotrope, the composition of the two phases formed by the azeotropic mixture and the density of the two phases. Activity-coefficient parameters can be estimated directly from the single azeotropic point .
A powerful tool
These examples have touched upon a few applications of RCMs in process synthesis, modeling, control and operation. Although some of the more academic research in this area can seem rather esoteric, the basic principles are quite simple. With a little practice, RCM analysis can become second nature and will be one of the first tools you turn to when tackling a complex distillation problem.
Scott D. Barnicki is a research associate for Eastman Chemical Co., Kingsport, Tenn.
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