You can employ RCMs in a variety of ways, including:
- 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 If the vapor is withdrawn as formed, the liquid and vapor compositions change continuously over time.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 .)