Navigate Phase Equilibria via Residue Curve Maps

Reactions and Separations

Navigate Phase Equilibria via Residue Curve Maps These maps provide a rapid, graphical means to visualize the separation possibilities and constraints of azeotropic ternary systems. They also help check the soundness of models used to predict equilibrium data.

Waldo E. de Villiers, Raymond N. French and George J. Koplos, Shell Global Solutions (US) Inc.

R

esidue curve maps (RCMs) have attracted interest from the academic and conceptual engineering design communities. Despite their usefulness, RCMs have received little attention from practicing process engineers. In addition to being useful as a separation synthesis tool, RCMs can also be used by the practicing engineer to visualize and investigate vapor/liquid/liquid equilibrium (VL(L)E) issues affecting modeling of distillation and liquid/liquid extraction columns. [VL(L)E denotes systems that contain two liquid phases and a vapor phase in equilibrium]. Other areas of application are column troubleshooting and control analysis. This article reviews the physical significance and termiExperimentally:

Low-boiling Component

Vapor at y(ξ)

Residue at x(ξ)

Heat

Feed Composition High-boiling Component

Intermediate-boiling Component

■ Figure 1. RCMs, using experimental or generated data, show the composition of the residue of a simple batch distillation over time.

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nology of RCMs, and illustrates their use to evaluate the underlying thermodynamics of ternary systems. Four examples cover: using data outside their intended range; employing VLE calculations instead of VL(L)E; using parameter sets optimized to different regression objectives; and choosing the appropriate model for the vapor phase. Wasylkiewicz and Shethna (1) present additional examples of using RCMs for data evaluation. RCMs are readily generated using commercial process simulation software, such as Aspen Plus or DISTIL. A residue curve represents the composition of the residue of a simple batch distillation involving three components over time (Figure 1). Mathematically: dξi/dx = xi – yi

(1)

where ξ is a nonlinear time scale that spans the duration of the experiment, x and y are the familiar mole fractions in the liquid and vapor, respectively, and i is the ith component. By integrating forward and backward in time from different starting positions, a family of curves — the residue curve map, is obtained. The usefulness of RCMs lies in the fact that the composition profiles of continuous distillation columns approximate the composition trajectories of the residue curves (RCs). Fien and Liu (2) provide a more-detailed discussion of this relationship. Figure 2 presents the RCM terminology. Nodes represent the starting and end points of RCs and can be pure components, or binary or ternary azeotropes. The nodes and saddle points are used to

Stable Node (Pure Component)

Saddle Point

T

(Binary Azeotrope) define distillation boundaries and associated regions. Residue curves point toward increasDistillation Boundary ing temperature and decreasing volatility. or Separatrix In Figure 2, each region has a different heavy boiler or stable node. The feed and Residue Curve product compositions of a distillation column can be overlaid in a geometrically simple Saddle Point manner as a mass balance line. The product Unstable Node (Binary Azeotrope) (Light-Boiling flows can be determined using the inverseTernary Azeotrope) lever-arm rule. RCMs do not explicitly show Distillation relative volatility. A related construction using Boundary “distillation lines” is useful in this regard. Compared to using sets of individual binary diagrams (Figure 3), RCMs display the behavior of the entire ternary system in one Saddle Stable Node Stable Node composition space. Both binary VL(L)E and Point (Binary Distillation (Pure Component) (Pure Component) Azeotrope) Boundary ternary LLE data can be represented on RCMs (Figure 3). As summarized by Doherty and Malone (3): “The structure of the residue ■ Figure 2. Curves point toward increasing temperature and decreasing volatility, and reveal the curve map is the underlying thermodynamic presence of azeotropes and distillation boundaries. principle that governs the shape of composition profiles and consequently the products that can be obtained from a distillation.” This Ethanol structure, in turn, is determined by the underlying VL(L)E data.

x,

Using data outside their intended range Figure 4 shows a series of RCMs for the ternary system methyl ethyl ketone, acetone (which is dimethyl ketone), and water (MEK/DMK/water) calculated at 1 atm and 6 atm. This was carried out using a commercial process-simulation program. For the first three RCMs, the VLE data were predicted using the NRTL method with binary parameCyclohexane Water ters taken from one of two of the simulator databanks, noted here as either databank A or databank B. At 1 atm, the two data sets generated equivalent VLE predictions (only the RCM from databank A is shown). At 6 atm, the parameters from databank B predicted a shift in the VLE, but no change in the general features of the RCM. However, using the parameters from databank A predicted a change ■ Figure 3. Mapping VL(L)E data to the sides of an RCM. into a highly unusual, albeit permissible, topology. For comparison, the RCM predicted by the Dortmund-modified UNIFAC method (4) (an esbinary azeotrope for MEK/DMK, as well as a ternary sadtimation method based on group contributions) is shown dle azeotrope, which are highly suspicious. to agree qualitatively with that generated using the dataTo solve this quandary and test the parameters used bank B parameters. in the two databanks, predictions were made for the Without validation of the underlying binary VLE data, it three sets of binary pairs (Figures 5–10). These comparis not possible to select one set of parameters over the other. isons were generated using the binary-analysis feature However, the RCM predicted by the databank A includes a of the process simulator. T

x,

y

y

x, y

T

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Reactions and Separations Acetone

Water

Acetone

MEK

Water

MEK

Databank A @ 1 atm

Databank B @ 6 atm

Acetone

Acetone Similar

is considerable disagreement between the two. The A set predicts that the activity coefficient of water increases indefinitely with increasing temperature. In contrast, the B set predicts the opposite behavior, a decrease in the activity coefficient. Although, databank B appears to predict high-temperature behavior more reliably than the other set, a more in-depth comparison involving actual VLE data is warranted before validating the set for generating RCMs as a function of pressure.

DMK/MEK As a mixture of two ketones differing by only one carbon atom, this system Topology should behave nearly ideally. Figures 8 and Suspect 9 demonstrate that databank A predicts unrealistic behavior at a higher pressure of 6 Water MEK Water MEK atm — that is, DMK becomes less volatile Mod. UNIFAC @ 6 atm Databank A @ 6 atm than MEK in MEK-rich mixtures. The activity coefficient plot, Figure 10, provides ■ Figure 4. RCMs for MEK/DMK/water differ at 6 atm for two prediction methods. more information. The A parameters are MEK/water based on overfitting data for a single isobar, a pressure of MEK and water would be expected to form a highly non1 atm. By generating temperature-dependent parameters ideal binary mixture. For this pair, databases A and B both for an ideal system from such a narrow range of data, the gave nearly identical predictions of a heterogeneous azeotrope resulting fit extrapolates poorly. The resulting model pre(Table 1). A sensitive way of evaluating VLE models is to dicts activity coefficients well below 1, meaning large look at the predictions of activity coefficients at infinite dilunegative deviations from ideality. The B parameter set tion, γo, as a function of temperature. Both sets of parameters was fit to data over a much wider temperature range and, generated similar values (Table 2). These parameters were reas expected, predicts nearly ideal behavior, with activity gressed over a relatively narrow temperature range, correcoefficients close to 1. sponding to 1-atm isobaric data, and the activity coefficients at infinite dilution, γo, show the typical monotonic function Using VLE calculations instead of VL(L)E that is inversely proportional to temperature. In modeling distillation columns for systems capable of highly non-ideal behavior, one must address whether to DMK/water Figure 5 shows that the two-parameTable 1. Comparison of azeotrope predictions for the ter sets predict qualitatively similar binary mixture MEK/water. VLE at 1 atm, with databank A predictParameter Temperature, Pressure, No. of Azeotropic ing a somewhat more difficult separaSet °F (~°C) atm Liquid Composition, tion. In Figure 6, the B set predicts that xMEK Phases the increase in pressure makes the sepaA 164.4 (74) 1 2 0.6500 ration more difficult, while the general B 164.6 (74) 1 2 0.6488 shape of the binary diagram is the same. A 269.7 (132) 6 2 0.5451 B 269.9 (132) 6 2 0.5438 However, set A predicts the occurrence of a heterogeneous azeotrope at the higher pressure. It is unusual for such Table 2. Comparison of activity coefficients at infinite dilution for the binary mixture MEK/water. non-ideal behavior to appear as pressure and temperature increase. Figure 7 indiTemperature, °C Parameter Set A Parameter Set B γoDMK γoWater γoDMK γoWater cates the basis for this suspect prediction. Set B is based on data over a much 30 62 6.6 63 6.5 wider temperature range than databank 70 39 6.1 39 6.0 100 29 5.8 29 5.7 A. Interestingly, in the range where 130 22 5.5 23 5.4 both data sets overlap (20–95°C), there

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P = 6 atm

P = 1 atm 1

1 Databank A

y, DMK

y, DMK

Databank B

0.6

0.4

0.6

Databank B

0.4

0.2

0.2

0

Databank A

0.8

0.8

0 0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

x DMK

x, DMK

■ Figure 5. Vapor vs. liquid predictions for DMK/water at 1 atm are almost

■ Figure 6. DMK/water at 6 atm — databank A parameters incorrectly

the same for databanks A and B.

predict a more-difficult separation at the higher pressure.

ternary and all three binary azeotropes reasonably, but sigconsider two liquid phases in the calculations. The tradinificantly overpredicted the solubility of water in SBE-rich tional reluctance to enable more-complicated thermodymixtures. RCMs offer a convenient way to visualize the namic calculations has largely been overcome by the comtrade-offs implicit in using such restricted sets in a ternary puting power of modern process simulation programs, at composition space. least for steady-state simulations. However, VL(L)E calcuUsing the appropriate model for the vapor lations can be problematic in dynamic modeling and in some particularly difficult steady-state models. The situaBecause distillations for most chemical processes take tion is exacerbated by the limitations of the state-of-the-art place at “low” pressures, selecting the model to represent thermodynamic models to simultaneously represent multithe vapor phase fugacities usually has a minimal impact on component VLE and VL(L)E. VLE calculations. It is not uncommon for NRTL parameRCM analysis can be a useful screening tool to see the ters regressed using one model for the vapor phase (e.g., impact of VLE vs. VL(L)E calculations. In Figure 11, the the Redlich-Kwong equation of state) to be used in simulacomposition profiles for two simulations are plotted on an tions in which another model for the vapor phase (e.g., RCM. In one case, the thermodynamic calculations considideal) is specified. Such mixing and matching of parameered only VLE in the column, with VL(L)E allowed only in ters will generate incorrect VLE predictions for systems the condenser. In the second case, VL(L)E was enabled on all that are significantly non-ideal in the vapor phase. stages and resulted in a significantly different result. (Note: Figures 12 and 13 show RCMs for an aqueous mixture RR is the reflux ratio, and F, B and D are 100 the feed, bottom and distillate flowrates, "Suspect Extrapolation" respectively.) H2O Databank A DMK Databank B γo

Parameter sets optimized to different regression objectives As discussed above, it is often not possible to simultaneously represent vapor/liquid and vapor/liquid/liquid equilibria to a desired precision. Thus, it is not uncommon to have separate parameter sets optimized for either VLE or LLE, or some compromise between the two. An example of this was found with the system sec-butyl alcohol, di-secbutyl ether, and water (SBA/SBE/water). Using binary and ternary VL(L)E data from Kovach and Seider (5), an LLE-optimized parameter set represented the LLE behavior well, but failed to predict the SBA-SBE azeotrope. At the same time, a VLE-optimized set predicted the

10

DMK Databank A 230˚C

95˚C

20˚C

H2O Databank B 1 0.0019

0.0027

0.0035

1/T, K-1

■ Figure 7. DMK/water — databank B is based on a wider temperature range and gives truer predictions.

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Reactions and Separations

P = 6 atm

P = 1 atm 1

1 Ideal

Databank A

0.8

0.8

Ideal

y, DMK

y, DMK

Databank B 0.6 Databank A

0.4

Databank B 0.4

0.2

0.2

0

0.6

0 0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

x, DMK

x, DMK

■ Figure 8. DMK/MEK at 1 atm — Interaction parameters from databanks

■ Figure 9. DMK/MEK at 6 atm — databank A incorrectly predicts that

A and B are a reasonably close match.

DMK becomes less volatile at high MEK concentrations.

of formic and acetic acids, calculated using the same set of NRTL parameters but different models for the vapor phase. The NRTL parameters were regressed from binary data, using an association model to represent the complexation involving the carboxylic acids in the vapor phase. The RCM in Figure 12 was generated using the same association model for the vapor phase, and it correctly predicts the ternary maximum boiling azeotrope, as well as the one binary azeotrope (formic-acid/water) (6). Figure 13 was generated, assuming an ideal vapor phase, and it yields incorrect predictions. The ternary

Literature Cited

azeotrope is missing, and two binary azeotropes are shown (formic-acid/water and acetic-acid/water). Thus, inconsistent handling of the vapor phase produced an RCM missing a key feature for the separation design, the distillation boundary involving the ternary azeotrope. An RCM predicted using the Dortmund-modified UNIFAC model for the liquid phase with an ideal vapor phase will result in a very similar RCM to that shown in Figure 13. This suggests that the UNIFAC method can reasonably predict the liquid phase nonideality in carboxylic-acid/water mixtures, but it can-

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MEK Databank B γo

1. Wasylkiewicz., S., and H. Shethna, “VLE Data Estimation for Synthesis of Separation Systems for Azeotropic Mixtures,” Paper 4e presented at AIChE Spring National Meeting, New Orleans, LA (Mar. 2002). 2. Fien, G. A. F., and Y. A. Liu, “Heuristic Synthesis and Shortcut Design of Separation Processes Using Residue Curve Maps, Ind. Eng. Chem. Res., 33, pp. 2505–2522 (1994). 3. Doherty, M. F., and M. F. Malone, “Conceptual Design of Distillation Systems,” McGrawHill, New York (2001). 4. Gmehling J., “The UNIFAC Consortium,” http://www.uni-oldenburg.de/tchemie/Consortium/ (2001). 5. Kovach, J. W., III, and W. D. Seider, “VaporLiquid and Liquid-Liquid-Equilibria for the System sec-Butyl Alcohol — Di-sec-Butyl Ether — Water,” J. Chem. Eng. Data, 32, 16 (1988). 6. Gmehling, J., et al., “Azeotropic Data — Part II,” VCH Publishers, New York, pp. 81, 92, 93, 291, 292, 1607 (1994).

1 DMK Databank B 153˚C

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56˚C

MEK Databank A DMK Databank A 0.1 0.0019

0.0027

0.0035

1/T, K-1

■ Figure 10. DMK/MEK binary — databank A overfits data from 1 atm and yields incorrect predictions when temperature varies.

70

79˚C

Ethanol

not compensate for the selection of the incorrect vapor phase model.

Conclusions Visual analysis of the structure or topology of an RCM can provide valuable insight into issues affecting the underlying VL(L)E data. RCMs are useful to screen binary parameters based on alternative databanks and regressions strategies. Because RCMs depict VL(L)E behavior in a ternary composition space, they can be more relevant than standard binary phase diagrams in assessing the utility of various parameter sets for distillation modeling. Not only are RCMs a useful (qualitative) tool for the practicing engineer involved with distillation analysis, but they also are a convenient bridge between practicing engineers and the thermodynamics

Column Profiles VLLE Condenser Only VLLE All Stages

Column Specs Same Feed RR = 10 F = 100 B = 71.6 D = 28.4

Cyclohexane

Water

■ Figure 11. Cyclohexane/water/ethanol — considering two liquid phases yields a column composition profile that differs significantly if only one phase is used. Acetic Acid

Acetic Acid

106.59 C

Formic Acid

106.90 C

Water

101.16 C

Formic Acid

Water

■ Figure 12. Formic-acid/acetic-acid/water — using NRTL plus an

■ Figure 13. Formic-acid/acetic-acid/water — here, NRTL plus an ideal

association model for the vapor phase yields correct predictions.

vapor-phase model do not predict what will actually happen.

WALDO E. DE VILLIERS is a distillation specialist in the Distillation Business Group of Shell Global Solutions (US) Inc. (Westhollow Technology Center, 3333 Highway 6 South, Houston, TX 77082-3101; Phone (281) 544-6074; Fax: (281) 544-8123; E-mail: [email protected]). He has 14 years of experience in process simulation, conceptual process development and process design at Shell and before that was with Sasol Technology. He has a BS and MS in chemical engineering from the Univ. of Stellenbosch, South Africa.

RAYMOND N. FRENCH is team leader for the engineering data and physical properties team in the Fluid Flow Business Group of Shell Global Solutions (US) Inc. (Phone: (281) 544-8382; Fax: (281) 544-7705; E-mail: [email protected]). He has 21 years of experience in applied thermodynamics and phase equilibria, particularly for process simulation. French has a BS in chemistry from Rensselaer Polytechnic Institute and a PhD in physical chemistry from the Univ. of Miami, Coral Gables, FL. He is a member of AIChE and ACS.

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GEORGE J. KOPLOS is a senior technical associate for the engineering data and physical properties team in the Fluid Flow Business Group of Shell Global Solutions (US) Inc. (Phone: (281) 544-7580; Fax: (281) 544-7705; E-mail: [email protected]). He has been with Shell for 24 years, the greater part of which he was involved with phase-equilibria experimentation. His current focus is on physical-property validation for process simulation. He has a BS Ed in biology from Southwest Texas State Univ.

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