Ind. Eng. Chem. Res. 1990,29,421-432
42 1
Separation System Synthesis: A Knowledge-Based Approach. 1. Liquid Mixture Separations Scott D. Barnicki and James R. Fair* Department of Chemical Engineering, The University
of
Texas at Austin, Austin, Texas 78712-1062
A description is given for a task-oriented, or problem decomposition, approach t o the selection and sequencing of methods for separating multicomponent liquid mixtures. The design knowledge of the expert is organized into a structured query system, the separation synthesis hierarchy (SSH). This hierarchy divides the overall separation synthesis problem into subproblems or “tasks”. These tasks can be solved essentially independently from each other. Each task consists of a series of ordered heuristics based on pure component properties and on process characteristics. In its current implementation, SSH is limited to the sequencing of multicomponent mixture separations using eight industrially significant separation methods: simple distillation, azeotropic/extractive distillation, liquid-liquid extraction, stripping, adsorption, membrane permeation, and crystallization. During the past 15 years, considerable effort has been expended on developing systematic methods for the sequencing of distillation columns. Evolutionary and ordered heuristic methods have been notably successful for this type of space search problem and require relatively little expert design knowledge (Nishida et al., 1981; Kelley, 1987). Although distillation is the mainstay of the separation industry, a considerable number of situations exist in which distillation is a poor choice. The more general industrial problem of separation synthesis, using a number of different separation methods, has received little attention. Such a knowledge-intensive problem is not suited to solution solely by the ordered heuristic methods developed thus far. This paper describes a task-oriented, or problem decomposition, approach to the selection and sequencing of separation methods for multicomponent liquid mixtures. The design expert’s knowledge is organized into a structured query system, the separation synthesis hierarchy (SSH). This hierarchy divides the overall separation synthesis problem into subproblems or “tasks”. Each task can be solved essentially independently from the other tasks. The separation synthesis hierarchy presented here is being developed explicitly for implementation in a knowledge-based expert system, the separation synthesis advisor (SSAD). SSAD is currently in the prototype stage of development. In its current implementation, SSAD is limited to the preliminary sequencing of multicomponent liquid mixtures using one of the following methods: (1) simple distillation, (2) azeotropic/extractive distillation, (3) liquid-liquid extraction, (4) stripping, (5) adsorption, (6) membrane permeation, and (7) melt crystallization. In this work, methods requiring an extraneous substance to effect the separation are called mass separating agent (MSA) processes. All methods on the list above except simple distillation and melt crystallization (and sometimes azeotropic distillation) are MSA processes. Both simple distillation and melt crystallization require only the addition or removal of energy. Mass separating agent processes are further divided into methods requiring physical solvents or entrainers (PSE processes-azeotropic/extractive distillation, liquid-liquid extraction, and stripping), and methods requiring solid-phase agents (SPA processes-adsorption and membrane permeation). The term azeotropic distillation is commonly used to refer to two different types of fractionation involving azeotropes. The first type relies on the azeotrope(s) inherently present in the mixture to effect the separation; only the addition of energy is required. The second type of azeotropic distillation is a PSE process. An extraneous 0888-5885/90/2629-0421$02.50/0
substance, called an entrainer, which forms an azeotrope with one or more components is added to the mixture. The fractionation of the resulting azeotrope(s) achieves the desired separation.
Problem Statement The development of an expert system for the synthesis of separation sequences is an interdisciplinary endeavor, combining aspects of both chemical engineering and artificial intelligence (AI). These two diverse fields contribute very different, but deeply interrelated, perspectives to the separation synthesis problem. In broad terms, the chemical engineering separation synthesis problem for liquid mixtures can be stated as follows: Given (1)an n-component liquid mixture, (2) physical property data on the mixture, (3) product specifications, and (4) a portfolio of potential separation techniques, find the method(s) and sequence(s) of separations that (1) produce the desired products with the desired purities, (2) result in minimum separation costs, and (3) result in a limited number of feasible, reliable process designs. The synthesis of separation sequences is a classical chemical engineering design problem. Such work has been done successfully for decades. However, due to the inherent uniqueness and complexity of each new design problem, a comprehensive and systematic approach to process synthesis has remained elusive; process design still resides in the domain of the “expert”. As such, the following questions remain largely unanswered: (1j What knowledge is needed to determine which separation techniques should be used and in what order they should be accomplished? (2) How does an expert organize this knowledge to make design decisions? The synthesis of separation sequences encompasses three basic categories of AI problem types: (1)space search, (2) selection, and (3) design. The space search problem arises from the need to efficiently and systematically explore the potential separation sequences. Parallel to the sequencing is the selection of a separation method for a given split in a multicomponent mixture. The need for short-cut process modeling and economic evaluation bring into play design problems. Moreover, the situation is further complicated by the need to manipulate a large data base of physical/chemical properties. The important questions from an AI/ knowledge engineering viewpoint are (1) can the searchselection-design problems be decoupled or decomposed into tractable subproblems and (2) what is the most effective way to represent and structure the separation design knowledge 0 1990 American Chemical Society
422 Ind. Eng. Chem. Res., Vol. 29. No. 3, 1990 STMT
smm
Selector
Dlstillatlon Designer
/
Membrane Selector
Adsorbent Selector
I
Adsorbent Selector
1 Designer Figure 1. Separation synthesis hierarchy.
for use in an expert system environment.
Task-Oriented Expert System Design In the past, a number of highly successful rule-based expert systems (e.g., DENDRAL, (Feigenbaum et al., 1971), and MYCIN (Buchanan and Shortliffe, 1984)) have been constructed. In a rule-based system, the knowledge base and the inference mechanisms are typically separate from each other. The rules themselves often do not explicitly indicate the order in which they should be used. Largescale rule-based systems usually resort to metarules, an implicit grouping of rules. Metarules guide the problem solving locally, by allowing specific rules to be used only under certain circumstances. The separation of knowledge and inference mechanisms promotes general, domain-independent programming but does not take advantage of the inherent structure of many problems. The task-oriented approach to expert system design represents a strategy of explicit knowledge organization (Chandrasekaran, 1986). This method is based on the following premises: (1)A complex problem can be decomposed in terms of “generic” problem types or “tasks”. A large problem may be composed of scores of interrelated tasks. ( 2 ) The domain knowledge is available to encode into blocks of knowledge, each of which solves a single task. (3) The tasks can be built into a structured hierarchy which solves the overall complex problem. A problem decomposed in this manner can be thought of as a group of “specialists” each working on a separate task. Higher level “managers” ensure that the hierarchy of specialists works toward resolution of the overall problem. Tasks at the upper levels of the hierarchy are more abstract in nature, while those at the lower levels are more concrete. This behavior is reflected in the expert who
focuses on broader issues in the problem and delays consideration of the low level details until much later. The task-oriented method has proven useful in malfunction diagnosis (Davis et al., 1987; Ramesh et al., 1988), equipment design (Myers et al., 1988), and equipment selection problems (Gandikota, 1988) in chemical engineering.
The Separation Synthesis Hierarchy The key to the task-oriented approach is problem decomposition and knowledge structuring. Expert process engineers are able to select and combine successfully independent process steps into a coherent problem solution. Clearly an extensive body of information on separation processes is available, albeit much of it in a form unsuitable for direct coding into tasks. The separation synthesis hierarchy represents our approach to problem decomposition and knowledge organization for separation synthesis. The hierarchy emulates the approach that an expert process engineer follows. It is based on interviews with expert designers and supplemented by information from the literature. Figure 1 presents the complete selection/sequencing hierarchy in its present form. Each block represents a clearly defined and essentially independent subtask of the overall separation selection and desequencing problem. The SSH consists of three types of task specialists. Each type of specialist deals with a specific task type: (1) manager-separation sequencing; (2) selector-separation method selection, MSA selection; (3) designer-separation equipment design. Previously published heuristic methods have dealt with a simplified version of one of these blocks, the liquid split manager. These methods deal almost exclusively with split sequencing.
Ind. Eng. Chem. Res., Vol. 29, No. 3, 1990 423 One of the heuristics that is repeatedly referred to in the literature (e.g., King, 1980; Rudd, 1973) states that the method of separation should be chosen first. In terms of the concepts used here, the heuristic states that all selection tasks should be done first, (i.e., all selector specialists should be at the top of the separation hierarchy). In most cases, this has meant that distillation is assumed to be the best method for all separations. The use of the method selection heuristic, in principle] greatly reduces the magnitude of the remaining separation synthesis problem. By eliminating the selection problem all at once, one is left with only a split sequencing problem. In other words, the selection and sequencing problems can be completely decoupled. However, we have found the method selection heuristic to be too restrictive. The selection and sequencing problems cannot be completely decoupled in this manner. Although one can gain some early insight into the most favorable separation method(s) for a given split, the final choice cannot be made until much later. This is especially true for methods requiring mass separation agents. A judgement on separation method cannot be made until a list of potential solvents or adsorbents is available. In turn, the choice of solvent/adsorbent is influenced by the composition of the mixture to which it is to be added. Thus, the method selection problem is dependent on both the solvent/adsorbent selection task and the split sequencing problem. The separation synthesis hierarchy reflects this observation; selection and sequencing tasks are distributed throughout. The form of the hierarchy is guided by two principles. First of all, calculations are done as little as possible. Most decisions in the upper levels of the hierarchy are based solely on qualitative relationships. Detailed quantitative information is used primarily for final comparisons at the level of the designer specialists. The second principle is that distillation is the benchmark separation method to which all other methods must be compared. Distillation should always be the first method considered for any separation. Moreover, when other methods give comparable results to distillation, the reliability and efficiency of distillation make it the likely choice. This is reflected in the hierarchy by the continued comparison to distillation. The following sections describe in more detail the structure of the tasks needed for the preliminary analysis of liquid mixtures.
Phase Separation Selector At the highest level of the hierarchy is the phase separation selector (Figure 2). The phase separation selector uses equilibrium data and normal boiling point informatior. to determine whether a liquid or gas separation system (or possibly both) is necessary. There are two purposes of this task. The first purpose of the task is to divide the input stream into substreams of low volatility components and of high volatility components reducing the magnitude of the sequencing problem. Although some components may distribute, two smaller, independent sequencing problems are created. These reduced problems will typically require considerably less effort to solve. Removal of one component from a multicomponent mixture will generally reduce the number of possible separation sequences by an order of magnitude or more. The second purpose of the task is to reduce the method selection problem. For gaseous mixtures, the number of potential separations is reduced to only four: absorption, adsorption, membrane permeation] and cryogenic distillation. Similarly for liquids, one need only consider simple
INPUT MIXTURE
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distillation, extractive/azeotropic distillation, liquid-liquid extraction, adsorption, membrane permeation, stripping, and crystallization. A simple example illustrates the utility of the phase separation task. Thompson and King (1972) developed an equation relating the number of components, N , to be separated by M potential separation methods to the number of possible sequences, S:
For a 6-component mixture using the 10 potential separation methods mentioned above, there are 4200 000 possible separation sequences. Now assume four components appear in each of the liquid and gas substreams (i.e., two nonkey components distribute to both the liquid and gas). Considering four potential separation methods for the gas mixture and eight methods for the liquid stream, the number of possible sequences is 320 and 2560, respectively. Thus, for this case, the number of possible sequences is reduced by 99.9%. The grouping of components into liquid and gas substreams is based on the relationship of the normal boiling point of a component to the pressure needed to perform a separation of that component by distillation. Theoretically, distillation can be used over the entire range that vapor and liquid phases coexist (i.e., from the freezing point to the critical point). However, in practice, distillation a t extremes of temperature and pressure are often prohibitively expensive. At these limits, other separation methods compete favorably with distillation.
424 Ind. Eng. Chem. Res., Vol. 29, No. 3, 1990 LIQUID MIXTURE
Table I . Distillation Conditions component group gas gas-liquid liquid
distillation normal bp pressure range, range, atm _T R p > -20 P > 25 -56 < TBP< 0.0 14.5 < P < 25 0.0 < T B p < 50.0 P < 14.5 7 u p > 50 P < 14.5
condenser type refrigeration partial total
L I
total
Gases are taken as those components with normal boiling points less than -20 "C. Distillations of such components typically require high pressures (greater than 25 atm) and refrigeration. Components that can be condensed by cooling water (normal boiling point of 50 "C or more) are considered to be liquids. Distillation pressures are usually less than 14.5 atm and total condensers can be used. Table I summarizes the distillation conditions for gases and liquids. Components with normal boiling points between -20 and 50 "C require further evaluation. These gas-liquid transition components may require either partial or total condensers with distillation pressures between 25 and 14.5 atm. At this point in the decision process, one cannot make a clear judgement on the appropriate separation method for transition compounds. It may be best to condense these components so as to use liquid separation methods. On the other hand, gas separations may be more economical. With the grouping of the components identified, the next step is to calculate adjacent relative volatilities at the input mixture temperature and pressure. In most cases, there will be at least one large adjacent relative volatility value between two components in the gas-liquid transition region. This will certainly be true if there are no transition compounds; the relative volatility between the least volatile gas and most volatile liquid will undoubtedly be large. The components with the largest adjacent relative volatilities in the gas-liquid transition region are chosen as the key components. The mixture is divided into gas and liquid streams by a simple equilibrium flash. The flash is conducted a t an appropriate temperature and pressure so that the split between the key components is reasonably sharp. (See Example 2: Purification of Acetic Acid.) The liquids with some gas-liquid transition compounds proceed to the liquid split manager. Similarly, the gases go to the gas split manager.
Liquid Split Manager The next phase in the synthesis process involves a preliminary effort at split sequencing. The sequencing method emphasizes the use of distillation for as many splits as possible and the early use of distillation. The primary purpose of the liquid split manager (LSM) is to make the best distillation sequence possible out of those separations where simple distillation is the favored method. Separations that require mass separating agent processes or crystallization are deferred to a lower level manager. The four-step procedure is outlined below (see also Figure 3). (1)Identify product streams and product specifications. This ensures that no unnecessary separations are done. (2) Rank components in order of decreasing adjacent relative volatilities. Relative volatility gives a strong indication of the ease of separation and the favorability of simple distillation. (3) Identify all azeotropic mixtures that may interfere with product specification. Azeotropes require special processing considerations and should be dealt with when
Rank components by adjacent relative volatilities
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further information is available. (4) Perform splits in the order specified by a set of sequential heuristics. Each potential split is evaluated by one of the mixture selector specialists (see next section, Zeotropic/ Azeotropic Mixture Selectors). If simple distillation is the favored method, then the separation is performed, and the resulting substreams are analyzed further by the LSM. If simple distillation is inappropriate, the separation is not performed, but other potential separation methods are identified. The next split specified by the LSM is now checked for the applicability of simple distillation. The LSM is guided by the assumption that all simple distillations should be performed first. This is based on the premise that simple distillation, when suitable, is the easiest and most reliable method for multicomponent separations. The presence of nonkey components tends to complicate the design of MSA processes and crystallizers. Moreover, as mentioned previously, the removal of a component from the mixture reduces the number of possible sequences by an order of magnitude or more. Azeotropic separations are typically difficult to perform. They should be performed in the absence of other components if possible. It is important to identify these mixtures as early as possible. When data are available, the azeotropes can be easily identified. However, for cases when incomplete information is available, the potential of azeotrope formation can still be determined. The following set of five questions, in decreasing order of certainty, are used to indicate the likelihood of azeotropes. An affirmative response indicates unlikelihood. In other words, an answer of yes to question 1 is a stronger indication that azeotropes are not present than an answer of yes to question 5 .
Ind. Eng. Chem. Res., Vol. 29, No. 3, 1990 425 LIQUID SPLIT
(1)Are the components homologous or isomers of the same chemical family? (2) Is the difference in normal boiling points greater than 15 “C? (3) Are the components members of chemical families unlikely to form azeotropes? (4) Are the carbon numbers of the compounds greater than six? (5) Is the ratio of vapor pressures less than the infinite dilution activity coefficient?
p?%/p!& < %K
-1-NO
cns =
The first term is the number of minimum stages for distillation. The second and third terms penalize uneven distributions and overly large distillates. In essence, the CDS is a measure of the applicability of distillation. It must be emphasized that the split sequence specified at this point is preliminary. The LMS determines the best sequence for the separations that can be done by simple distillation. Separations requiring MSA methods or crystallization are identified. Sequencing of these separations is done at a lower level of the hierarchy.
Zeotropic/Azeotropic Mixture Selectors For each split selected by the LSM, one must determine a list of potential separation methods. This task is accomplished by one of three mixture selector specialists. The mixture selectors do not indicate a ranking of sepa-
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(This is a semiquantitative relationship, based on the assumptions that the binary solution is regular and the activity coefficient curves are symmetric (Martin, 1975)). Once the azeotropes have been identified, a list of ordered heuristics is used to obtain a preliminary split sequencing. The list of heuristics is based on the work of Nadgir and Liu (1983). Their list has been modified to account for azeotropes. The heuristics are applied sequentially. If a heuristic is inapplicable, the next one on the list is considered. (1) Remove corrosive and hazardous materials first. (2) Remove reactive components first. (3) Perform separations between azeotropes last. Azeotropic separations tend to be difficult, and they should be done in the absence of other components. (4) Perform difficult zeotropic (nonazeotropic) separations last, but before azeotropic separations. This is a modification of the heuristic of Rudd et al. (1973) and King (1980) stating that separations of low relative volatilities should be done in the absence of other components. (5) Remove components in order of decreasing percentage of the feed. If the relative volatility is reasonable, a component that is a large fraction of the feed should be removed first to decrease the size of later separation equipment. (6) Favor 50/50 splits. If feed percentages do not vary widely, favor sequences that give equimolar product and residue streams provided the relative volatility is reasonable. (7) All things being equal, perform the separation with the smallest coefficient of difficulty of separation (CDS) first (Nath and Motard, 1981). The CDS quantifies the last three heuristics:
1
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Figure 4. Zeotropic mixture selector.
ration methods from most favored to least favored but rather an unordered list of all possible processes. The zeotropic selector is used for separations between nonazeotropic (zeotropic) components (Figures 4 and 6-8). The azeotropic selector is used for separations between azeotropic components (Figures 5-7 and 9). The gas-liquid transition selector determines whether a group of components identified as gas-liquid transition components by the phase separation selector should be condensed or vaporized (Le., determines whether gas or liquid separation methods should be used). This task will be described in a future paper. Qualitative information is still quite useful a t this level of analysis. The mixture selectors employ criteria based on pure component data, process characteristics, and whether azeotropes are present. The results of these simple comparisons generally reduce the number of potential separation methods to four or less. (A) Component Properties. ( 1 ) Relative Volatility. The relative volatility, a , between two components indicates the ease of separation by simple distillation. For a > 1.5, simple distillation is generally the most economical process (see below, Process Characteristics. (1)Separation Type, for a possible exception to this rule). If a < 1.1, distillation requires high refluxes and large numbers of stages. For these cases, distillation is ruled out. For the large gray area (1.1< a < 1.5),other separation methods may be competitive with simple distillation. No firm judgment can be made by these qualitative comparisons. (2) Slope of Vapor Pressure Curve. If the slopes of the vapor pressure curves of two components differ significantly within an acceptable temperature and pressure range, then the relative volatility can generally be altered, possibly to greater than 1.5. The “acceptable” temperature and pressure ranges will depend on available heating medium and cooling water temperatures and on the temperature sensitivity of the materials being processed. (3) Freezing Point Differences. Feasible crystallization processes typically require 20-30 “C differences in pure component freezing points. In addition, the freezing points should be at or above ambient temperatures if the added expense of refrigeration is to be avoided. (4) Chemical Family Similarity. Selective physical solvents for PSE processes will achieve separations only for chemically dissimilar components. Homologues of similar size and isomers in the same chemical family generally cannot be separated by PSE methods. Compounds of close molecular weight and shape in the same chemical family tend to exhibit similar physical properties and thus similar selectivity and solubility in solvents. As the size and shape differences increase, the physical properties may differ considerably, even for homologues. Typically, the boiling points of compounds of largely
426 Ind. Eng. Chem. Res., Vol. 29, No. 3, 1990
varying sizes in the same chemical family will be sufficiently different to allow the use of simple distillation. However, when simple distillation cannot be used for other reasons (e.g., temperature sensitivity of the compounds), PSE processes should not be eliminated as potential separation methods for chemically similar compounds of widely varying sizes. The effectiveness of a given membrane for a separation depends both on the diffusivity and solubility of the various components in the membrane. Solubility can be related roughly to the interaction between the functional groups in the membrane material and those of the components to be separated. The differences in solubilities of two given components will be significant only if the components themselves contain different functional groups. Thus, membrane permeation may be a feasible separation method if the components to be separated are in different chemical families. (5) Structure and Size Characteristics. Membrane permeation based on diffusion effects and molecular sieve adsorption both require structural and/or size differences between components to be separated. The effect of structure and size on selectivity can be especially dramatic for adsorption using zeolites and carbon molecular sieves. Certain sizes and shapes of molecules may be excluded completely from the micropores of the adsorbent due to the extremely narrow distribution of pore sizes. A number of industrially important bulk adsorptive separations are based on this molecular sieving effect, notably Union Carbide’s IsoSiv processes (Cusher, 1986) and certain Sorbex processes of UOP (Mowry, 1986). Even if the size and structural differences are insignificant, adsorption may still be a feasible alternative if polarities vary. (6) Polarity Differences. Commercial adsorbents can be divided into polar and nonpolar types. Polar adsorbents, such as silica gel, activated alumina, and zeolites, tend to bind the polar compounds in a mixture more strongly. Nonpolar adsorbents, such as activated carbon, are more useful for removing less polar materials from a mixture of more polar compounds. For both polar and nonpolar adsorbents, higher selectivity is achieved when there is a large difference in polarity between the desired adsorbates and the unadsorbed liquid. However, adsorption may still be a viable option if polarities are similar when size and structural differences are large. (7) Boiling Point Range. The boiling range of the component to be separated may indicate the favored method. For example, stripping is favored for separations of low boilers. Liquid-liquid extraction and extractive distillation are better for high boilers. (8) Temperature Sensitivity. Some components may decompose or react unfavorably at the temperature needed for distillation. Moreover, the freezing point of a component may be too high for distillation to be carried out at an acceptable temperature and pressure. Simple, extractive, or azeotropic distillation cannot be used for these separations. (B) Process Characteristics. ( 1 ) Separation Type (Bulk or Dilute). As the ratio of distillate to bottoms moves away from unity, other separation methods compete more favorably with distillation. In general, a dilute distillation is uneconomical. A separation is considered dilute when the total distillate or bottoms of a potential distillation operation is less than 5% of the feed. In addition, a large distillate-to-bottoms (D/B) ratio has a greater effect on the econimics of a distillation than a small D/B ratio. Mixtures composed of mostly low-value, low-boiling components to be separated from a small
amount (less than 10-1570) of a low-value, high-boiling component require large amounts of energy to vaporize the 85-9070 of the feed that will appear in the distillate. All forms of distillation (simple, extractive, and azeotropic) can be eliminated as potential methods for dilute separations. During the past 10 years, adsorption has gained a place as a bulk separation method in addition to its continued use as a dilute purification tool. Union Carbide’s vaporphase IsoSiv processes and UOP’s liquid-phase Sorbex technology have proven economical for the separation of what are considered here as liquid compounds (see phase separation selector for the definition of liquid compounds). Thus, adsorption is a potential method for both dilute and bulk separations. Membrane permeation can generally be used only for dilute liquid mixtures. No bulk liquid separations are done commercially. Melt crystallization is limited to bulk separations. The low reliability and low recovery typically associated with crystallization processes make its use as a dilute purification tool unfeasible. Liquid-liquid extraction and stripping can be used for either dilute or bulk separations if an appropriate solvent can be found. (2) Purity. In practice, both simple distillation and crystallization can achieve high-purity separations (99+ YO pure). The purity of the products obtained by PSE processes depends to a large extent on the solvent chosen. However, in principal, PSE processes can achieve highpurity separations if a selective solvent can be found. Adsorption is much the same. If a selective adsorbent can be found, high purity is possible. Membrane permeation, on the other hand, tends to give only an incremental increase in purity with each passage through the membrane. As a result, a high-purity product will not result from membrane permeation unless one resorts to a multistage scheme. Depending on the selectivity of the membrane, typically at least four stages are needed to achieve greater than 90% purity, with a correspondingly low recovery rate. Thus, if a high purity is essential, membrane permeation can be eliminated as a potential separation method. (3) Recovery. Recovery is defined here as the degree of separation obtained between product streams. In other words, a high recovery separation results in two high-purity products. As is the case with purity, simple distillation and PSE processes (with a selective solvent) can achieve high recovery separations. Adsorption recovery can be high for both bulk and dilute solutions, depending on the adsorbent. Bulk adsorptive separations using IsoSiv or Sorbex technology are claimed to have recoveries of 95-98% (Mowry, 1986; Cusher, 1986). Melt crystallization recovery is limited in practice by the presence of eutectic points. In all crystallization operations, only one pure component crystal can be obtained at a time. For simple systems, a second component will not crystallize until all of the first component is removed from solution. However, if the system in question forms a eutectic, the second component will begin to simultaneously crystallize at some intermediate composition (see Walas (1985) for a review of solid-phase thermodynamics). Although the two crystals can sometimes be separated by density differences, this is usually not a reasonable industrial option. Thus, the eutectic point represents a practical limit on the recovery of crystallization processes. The maximum fractional recovery, R , of a component can be related to the eutectic point composition: (4)
Ind. Eng. Chem. Res., Vol. 29, No. 3, 1990 427 Table 11. Special Processing Situations favored method condition a dilute solution (between 1% and 5%) of a high boiling, polar compound; distillation would require liquid-liquid extraction vaporization of large amounts of the feed a dilute solution (
