Effect of Phase-Equilibrium Uncertainties on the Separation of

Nov 16, 2016 - This paper has extended application of the Margules-based phase-equilibrium uncertainty method to a system exhibiting a heterogeneous a...
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Effect of Phase-Equilibrium Uncertainties on the Separation of Heterogeneous AzeotropesApplication to the Water + 1‑Butanol System Paul M. Mathias* Fluor Corporation, 3 Polaris Way, Aliso Viejo, California 92698, United States ABSTRACT: This paper extends application of the Margulesbased phase-equilibrium uncertainty method to a system exhibiting a heterogeneous azeotrope. The author developed the method in order to provide practicing engineers with an intuitive and easy-to-apply procedure to quantitatively relate process-design uncertainties to uncertainties in correlated physical properties, specifically nonideal phase equilibrium. The methodology was first applied to two case studies(1) a propylene−propane superfractionator for which small changes in correlated relative volatilities have a large effect on the design of the distillation column; and (2) a dehexanizer column that separates a mixture containing many close-boiling hydrocarbon componentsand demonstrated that the proposed method provides quantitative insight into the effect of property uncertainties for both these diverse process designs and helps to quantify the safety factors that need to be imposed upon the design. In a subsequent study, the methodology was applied to a distillation train that separates the acetone−chloroform−benzene ternary mixture, which contains one maximum-boiling azeotrope, and showed that the approach quantifies the effect of property uncertainties on utility consumption and also identifies limits on operating variables (specifically minimum recycle flow). In this paper, the Margules perturbation method is applied to the separation of the water + 1-butanol binary mixture. The application is complex because this binary exhibits liquid−liquid equilibrium and forms a minimum-boiling azeotrope, and the typical separation scheme includes a decanter as well as two distillation columns. Further, the chosen activity-coefficient model is unable to correlate the data within measurement uncertainty. Nevertheless, the methodology is demonstrated to provide useful quantitative estimates of the design uncertainty resulting from the combined measurement/model phase-equilibrium uncertainty.

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INTRODUCTION

To resolve the problem for the particular case of liquid-phase nonideality, Mathias9 developed an intuitive and easy-to-apply method based upon treating the mixture, for the purpose of activity-coefficient perturbation, as a set of pseudobinaries described by the Margules equation. Mathias first applied his method to two case studies9(1) a propylene−propane distillation column for which small changes in correlated relative volatilities have a large effect on the design of the distillation column; and (2) a dehexanizer column that separates a mixture containing many close-boiling hydrocarbon componentsand demonstrated that the proposed approach provides quantitative insight into the effect of property uncertainties for both these diverse process designs and helps to quantify the safety factors that need to be imposed upon the design. The results are consistent with the rules of thumb published by Fair10 in that the sensitivity of design to phase equilibrium increases as the relative volatility approaches unity,

Quantification of the uncertainty in measurements of physical properties is now recognized as essential by scientists and technologists in the chemical industry. In a forward to Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results,1 then-director of NIST, Dr. John W. Lyons, wrote, “It is generally agreed that the usefulness of measurement results, and thus much of the information that we provide as an institution is, to a large extent, determined by the quality of the statements of uncertainty that accompany them.” Five key journals in the field of thermodynamics (Journal of Chemical and Engineering Data, Journal of Chemical Thermodynamics, Fluid Phase Equilibria, Thermochimica Acta, and the International Journal of Thermophysics) have mandated reporting of combined uncertainties together with the experimental data tables.2−7 However, uncertainties in correlated physical properties are largely ignored in chemical process design. Kim et al.8 demonstrated the use of online resources to incorporate uncertainty analysis into chemical-engineering education, but observed, “Its practical implementation in a variety of scientific and engineering fields has typically seen less emphasis than it deserves.” © XXXX American Chemical Society

Special Issue: Proceedings of PPEPPD 2016 Received: June 29, 2016 Accepted: November 4, 2016

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activity coefficient, and this detailed data analysis is a key element of the perturbation scheme.

but in addition showed quantitatively how the design uncertainty increases with product purity. In a subsequent study, Mathias11 applied the methodology to a distillation train that separates the acetone−chloroform−benzene ternary mixture, which contains one maximum-boiling azeotrope, and showed that the approach quantifies the effect of property uncertainties on utility consumption and also identifies limits on operating variables (specifically minimum recycle flow). This study also illustrated the relationship between uncertainty analysis and residue-curve analysis; residue-curve analysis for this system has been illustrated by Wahnshafft and Westerberg.12 In this paper, the Margules perturbation method is applied to the separation of the water + 1-butanol binary mixture. This separation is often a part of processes to purify butanol produced by fermentation.13 The separation is complex because the binary mixture exhibits liquid−liquid equilibrium and forms a minimum-boiling azeotrope, and the typical separation scheme includes a decanter as well as two distillation columns. Further, the chosen activity-coefficient model (nonrandom two-liquid (NRTL)14) is unable to correlate the data within measurement uncertainty. Nevertheless, the methodology is demonstrated to provide useful quantitative estimates of the design uncertainty resulting from the combined measurement/ model phase-equilibrium uncertainty. The methodology used is analogous to that of the previous two studies.9,11 The first step is focused data regression to obtain the best model fit in the region of application and estimation of the correlation uncertainties. This is an essential first step. In the second step, activity coefficients are perturbed within the process model to relate the design uncertainties to the uncertainties of the correlated model.

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CORRELATION OF VAPOR−LIQUID−LIQUID EQUILIBRIUM IN THE 1-BUTANOL + WATER SYSTEM Similar to the previous applications by Mathias,9,11 the perturbation scheme has been implemented as a user activitycoefficient model in the NRTL-RK property option in Aspen Plus V8.6. The NRTL-RK property option uses the NRTL activity-coefficient model14 and the Redlich−Kwong equation of state15 for the vapor phase. The pure-component properties are from the Aspen Plus V8.6 database and these are expected to be accurate. The application here is at a pressure of 1 atm (101.325 kPa), the temperatures of interest are in the range 360−390 K, and at these temperatures the correlations for the vapor pressures of these two compounds from the Aspen Plus database are expected to be accurate to less than 1%. The basis for this confidence is that the Aspen Plus pure-component properties come from the DIPPR 801 database,16 and the correlated vapor pressures have been reported to be accurate to less than 1%. The Redlich−Kwong equation is used for the vapor-phase fugacity coefficient, but this thermodynamic quantity is expected to be close to unity and accurately predicted since the pressure of interest is low, approximately 1 atm. For this application, the phase-equilibrium uncertainty is dominated by the uncertainties in the component activity coefficients. The NRTL model has two temperature-dependent binary parameters (αij and τij). αij is a symmetric binary parameter and τij is an asymmetric binary parameter,

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MARGULES-BASED ACTIVITY-COEFFICIENT PERTURBATION SCHEME The perturbation scheme for the mixture nonideality has been published by Mathias,9,11 and hence is only summarized here. The approach uses the simplification that the perturbed activity coefficients can be guided by the Margules equation. ln(γi) = ln(γi m) + ln(γi p)

(3)

αij = cij + dij(T − 273.15)

(4)

The Data Regression System (DRS) in Aspen Plus V8.6 has been used to obtain optimum values of the NRTL parameters of pressures at about 1 atm (101.325 kPa), which corresponds to the temperature range of ≈360−390 K. Phase-equilibrium data were obtained from NIST-TDE,17 and the source clearly indicates that this is a well-studied system since a large number of data sets are available. Both vapor−liquid and liquid equilibrium data have been used in the data regression, and the final values of the binary parameters are presented in Table 1. Figure 1, which compares the fitted NRTL model to the reference correlation of Maczynski et al.18 for liquid−liquid

(1)

where γi is the effective activity coefficient of component i after perturbation, γm i is the activity coefficient calculated by the chosen model (the “best” model should be used), and γpi represents the perturbation obtained through the combined model uncertainty. It is emphasized that γm i is calculated from the chosen activity-coefficient model, and is not constrained by the pseudobinary approximation. γpi is given by ⎡ ⎤ |ln(γi )| ⎥ ln(γi p) = δi(1 − xi)2 ⎢ 2 m ⎢⎣ (1 − xi) + |ln(γi )| ⎥⎦

τij = aij + bij /T + eij ln(T ) + fij T

Table 1. NRTL Parameters for the 1-Butanol/Water Binary. See eqs 3 and 4 for a Description of the Parameters

m

(2)

Equation 2 is phenomenological, but has desired characteristics. The value of ln(γpi ) is small when γm i is close to unity (i.e., always small departures from Raoult’s law), and also is low when the mole fraction of component i is close to unity. For components at low concentrations and with activity coefficients significantly different from unity, the fractional change in γi resulting from the perturbation approaches {exp(δi) − 1}. To apply the perturbation method, the value of δi for each component must be related to the estimated uncertainty in its B

parameter

value

a12 a21 b12 b21 c12 d12 e12 e21 f12 f 21

61.0602 197.0177 −3464.67 −9171.82 0.355367 0.001356 −8.58908 −28.5386 61.0602 197.0177 DOI: 10.1021/acs.jced.6b00546 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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phase, and we may similarly conclude that an uncertainty of 0.01 in mole fraction represents three standard deviations.

Figure 1. Liquid−liquid equilibrium in the 1-butanol + water system. Comparison of NRTL fit (parameters in eqs 3 and 4; dashed line) to the reference correlation of Maczynski et al.18 (solid line). Figure 3. Solubility of 1-butanol in the butanol-rich phase. The double line is the reference correlation,18 the solid line is the NRTL model, and the dashed lines show ±0.01 from the NRTL model. The experimental data are from Erichsen and Brennst,19 Prochazka, Suska, and Pick,20 Aoki and Moriyoshi,21 Moranglu et al.,22 and Zhang, Fu, and Zhang.23

equilibrium in the 1-butanol + water system, provides an indication of the accuracy range of the NRTL model. The model provides an accurate correlation in the temperature range 360−390 K, and this is considered to be adequate for the present application. However, the NRTL model is clearly inaccurate at lower and higher temperatures, particularly in the vicinity of the liquid−liquid critical temperature (402.4 K). Figure 2 provides more detail on the model uncertainty in the

We now attempt to relate the uncertainties in Figure 2 and Figure 3 to a single “universal” perturbation parameter,” δ0, in the Margules perturbation framework. δ LLE ‐ C4OH = −δ0 × 0.08

(5)

δ LLE ‐ H2O = −δ0 × 0.032

(6)

In eqs 5 and 6, δLLE‑C4OH and δLLE‑H2O represent the perturbation parameters for liquid−liquid equilibrium for 1butanol and water, respectively, in eq 2. Figure 4 shows the

Figure 2. Solubility of 1-butanol in the water-rich phase. The double line is the reference correlation,18 the solid line is the NRTL model, and the dashed lines show ±0.002 from the NRTL model. The experimental data are from Erichsen and Brennst,19 Prochazka, Suska, and Pick,20 Aoki and Moriyoshi,21 Moranglu et al.,22 and Zhang, Fu, and Zhang.23

Figure 4. Effect of perturbation parameter δ0 on the calculated mole fractions of 1-butanol in the water-rich and butanol-rich phases. The perturbations corresponding to eq 2 are defined by eqs 5 and 6. The double vertical line represents “full perturbation,” three standard deviations.

water-rich region by comparing the model calculations for 1butanol mole fraction to the experimental data of Erichsen and Brennst,19 Prochazka, Suska, and Pick,20 Aoki and Moriyoshi,21 Moranglu et al.,22 and Zhang, Fu, and Zhang.23 The dashed lines show ±0.002 in 1-butanol mole fraction from the NRTL model calculation. Visual inspection of the model deviations from the data and the reference correlation indicate that an uncertainty of 0.002 includes all the model deviations in the 350−370 K temperature range and by our reckoning may be considered to be three standard deviations (≥99% certainty). Figure 3 shows analogous comparisons for the butanol-rich

results of these calculations. It should be noted that conservative perturbations will reduce the extent of the liquid−liquid equilibrium (LLE) region, that is, increase the 1-butanol mole fraction in the water-region phase and decrease its concentration in the butanol-rich phase, and hence a value of δ0 = 1 in eqs 5 and 6 approximately represents three standard deviations in model predictions of LLE, as gleaned from Figure 2 and Figure 3. The coefficients of 0.08 and 0.032, respectively, C

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in eqs 5 and 6 were determined manually by a few repeated calculations. We now turn toward developing relations similar to eqs 5 and 6 for the vapor−liquid equilibrium (VLE) regions of the phase diagram. Figure 5 compares calculations for the Txy

Figure 6. 1-Butanol/water relative volatility in the water-rich region at 101.325 kPa. Comparison of model calculations to the data of Stockhardt,27 Smith and Bonner,28 Ellis and Garbett,24 Vega and Alvarez-Gonsales,29 Kharin, Perelygin, and Remizov,26 Kato, Konishi, and Hirata,30 Jin,31 Zong, Yang, and Zheng,32 Iwakabe and Kosuge,33 Gu, Wang, and Wu,34 and Lladosa et al.35 The dashed lines show perturbations with δC4OH of ±0.3 (δH2O = 0). Figure 5. Txy diagram of the water +1-butanol at 101.325 kPa. The diamond, square, and circular data points are from Ellis and Garbett,24 Orr and Coates,25 and Kharin, Perelygin, and Remizov,26 respectively. The solid and dashed lines are the liquid and vapor mole fractions, respectively, from the NRTL model. The thick solid horizontal line identifies the liquid−liquid region calculated by the NRTL model.

diagram of the binary system at 101.325 kPa to the data of Ellis and Garbett,24 Orr and Coates,25 and Kharin, Perelygin and Remizov,26 and suggests that the model provides an overall satisfactory description of the VLE data. However, as previously pointed out by Mathias,11 Txy diagrams are unable to provide quantitative uncertainty estimates, and for this purpose relative volatility charts are needed. The K-value of component i in a mixture (Ki) at vapor− liquid equilibrium is defined to be the ratio of the vapor and liquid mole fractions at equilibrium, and the relative volatility between components i and j (αij) is the ratio of the K-values. x Ki ≡ i yi (7)

αij ≡

Ki Kj

Figure 7. 1-Butanol/water relative volatility in the butanol-rich region at 101.325 kPa. Comparison of model calculations to the data of Stockhardt,27 Smith and Bonner,28 Ellis and Garbett,24 Vega and Alvarez-Gonsales,29 Kharin, Perelygin, and Remizov,26 Kato, Konishi, and Hirata,30 Jin,31 Zong, Yang, and Zheng,32 Iwakabe and Kosuge,33 Gu, Wang, and Wu,34 and Lladosa et al.35 The dashed lines show perturbations with δH2O of 0.5 and −0.3 (δC4OH = 0).

(8)

quantitatively capture the shape of the relative volatility curve with respect to 1-butanol mole fraction. Here, variation of δH2O between −0.3 and 0.5 (with δC4OH = 0) captures the bounds of the measured data. For this region, an increase in the butanol− water relative volatility is a conservative perturbation, and hence a perturbation of δH2O = −0.3 may be considered to represent three standard deviations since essentially all the measured data fall within these bounds. Note that the model bias is not relevant to the uncertainty analysis since it occurs in the region of reduced butanol−water relative volatility (away from unity), which makes the separation by distillation easier. The combined uncertainties (three standard deviations) of mole fractions in the liquid−liquid equilibrium calculations by the NRTL model in the water-rich and 1-butanol-rich regions are 0.002 out of 0.02 (10%) and 0.01 out of 0.357 (2.8%), respectively. The VLE (specifically relative-volatility) combined uncertainties are demonstrated through Figure 8, which shows base and perturbed activity coefficients calculated by the

Figure 6 compares relative volatilities from the model in the water-rich region at 101.325 kPa to the data of Stockhardt,27 Smith and Bonner,28 Ellis and Garbett,24 Vega and AlvarezGonsales,29 Kharin, Perelygin, and Remizov,26 Kato, Konishi, and Hirata,30 Jin,31 Zong, Yang, and Zheng,32 Iwakabe and Kosuge,33 Gu, Wang, and Wu,34 and Lladosa et al.35 The dashed lines in Figure 6 also show perturbations using eq 2 with δC4OH = ± 0.3, and δH2O = 0. It is noted that a conservative perturbation will reduce the butanol−water relative volatility, and in an analogous manner to the above LLE analysis, we conclude that a perturbation of δC4OH = −0.3 may be considered to represent three standard deviations since essentially all the measured data (≥99%) fall within these bounds. Figure 7 presents similar comparisons to those in Figure 6, but here for the butanol-rich region; the data sources are the same. Figure 7 clearly indicates that the NRTL model cannot D

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Figure 9. Separation train used to produce acetone, ethanol, and 1butanol from fermentation broth. The highlighted section identifies the subsection studied in this paper. Figure 8. Activity coefficients of water and 1-butanol corresponding to the Txy diagram at 101.325 kPa (Figure 5). The chart is plotted on a log−log scale to reveal results of interest. The two thick upper lines are the activity coefficients of water and 1-butanol, the infinite-dilution values of which are 55 and 4.7, respectively. The region of LLE is identified by the vertical lines and corresponds to 1-butanol mole fractions of 0.020 and 0.357. The two lower curves show perturbed activity coefficients with δCH4OH = δH2O = 0.3. The perturbation in the 1-butanol activity coefficient is approximately constant at −21%, and this is because the 1-butanol concentration is low. The perturbation in the water activity coefficient varies from −3.0% at the LLE boundary to −17% at infinite dilution.

wt % 1-butanol. The upstream distillation columns in Figure 9 remove most of the acetone, ethanol, and other components so that the feed to the highlighted section of the flowsheet contains about 20 mol % or 50.7 mass% 1-butanol, with the remainder mostly water. For the purposes of this study the concentrations of all species other than water and 1-butanol are assumed to be zero. The flowsheet to purify 1-butanol employs a decanter to separate the water-rich and butanol-rich phases. The two streams are purified in separate distillation columns each having a reboiler and no condenser, and with the feed to the top stage. The products from the columns are the bottoms products, and the distillates are recycled to the decanter. Both columns operate at 101.325 kPa (no allowance for pressure drop), and the bottoms products specifications are achieved by varying the respective reboiler duties. The column specifications are summarized in Table 2. The decanter is assumed to operate at 363.15 K and 101.325 kPa.

uncertainty model. Only negative perturbations are shown for the activity coefficients since these correspond to conservative changes, that is, more difficult separation by distillation. In the water-rich region, the uncertainty in the relative volatility is approximately constant at 21% since the mole-fraction range is very small. For the 1-butanol-rich region, the relative-volatility varies considerably since the saturated liquid phase has just 36 mol % 1-butanol. The uncertainty varies from a low of 3% at the LLE boundary to 17% at the pure 1-butanol end. This section has demonstrated how careful analysis may be used to quantitatively determine model phase-equilibrium uncertainties in a complex vapor−liquid−liquid equilibrium system. The uncertainties vary from a low of under 3% to a high of about 21%. The variability in uncertainties results from a combination of measurement uncertainties and model bias. Further, a local fit of the data is needed to reduce model uncertainties by focusing on the region of interest. However, detailed analysis and expert judgment can be used to determine property uncertainties, and these uncertainties are used in the next section to estimate design uncertainties.

Table 2. Specifications for Water Column (WA-COL) and 1Butanol Column (BOH-COL) parameter number of stages pressure/kPa specifications vary variable

WA-COL

BOH-COL

5

10

101.325 water purity of 99, 99.9, and 99.99 wt % reboiler duty

101.325 1-butanol purity of 99.9 wt % reboiler duty

Figure 10 shows the manner in which the activity-coefficient perturbations have been implemented. It is noted that three separate sets of perturbations have been used through the “multiple dataset” capability in Aspen Plus.36 The perturbations are controlled by a single perturbation parameter, δ0, and may be considered to be the cumulative (expanded) perturbation from all three process units (one decanter and two distillation columns). The operating costs are considered to be represented by the reboiler duties of the two distillation columns. Figure 11 presents the percentage change in total reboiler duties (sum of the reboiler duties in WA-COL and BOHCOL). The base value is 99 wt % water in stream PROD-WA with no perturbation (i.e., NRTL parameters in Table 1). The fractional increase in total reboiler duties varies approximately linearly with δ0, and for the base case (99 wt % water in stream PROD-WA), and the full perturbation, δ0= 1, results in a 12%

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UNCERTAINTY ANALYSIS FOR 1-BUTANOL + WATER SEPARATION van der Merwe et al.13 have discussed several schemes to purify the main products of butanol fermentation: acetone, ethanol, and 1-butanol. A common scheme is shown in Figure 9. van der Merwe et al.13 concluded that the simple scheme of Figure 9 is not optimum, and other flowsheets based upon extractive distillation, for example using 2-ethyl-1-hexanol as extractant, are superior in terms of energy consumption. However, we decided to use the base case for our uncertainty-analysis study since it is a well-studied design. A typical feed to the separation train contains about 0.4 wt % acetone, 0.2 wt % ethanol, and 1 E

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Figure 10. Graphic explaining how the perturbations have been implemented in Aspen Plus. Three separate perturbations have been implemented through the universal perturbation parameter δ0 and the “multiple dataset capability” in Aspen Plus.36

Figure 12. Percentage change in total reboiler duties (sum of the reboiler duties in WA-COL and BOH-COL). In this case the relative change in reboiler duties is based upon the same water purity in stream PROD-WA and δ0= 0.

Figure 11. Percentage change in total reboiler duties (sum of the reboiler duties in WA-COL and BOH-COL). In effect, the single perturbation variable is δ0, and a perturbation of 100% means δ0= 1. The base value is 99 wt % water in stream PROD-WA with no perturbation (NRTL parameter in Table 1).

increase in total reboiler duty. Increasing the water purity, to 99.9 and 99.99 wt %, causes increases of 2.7% and 6.5%, respectively, in the total reboiler duties with no property perturbation (δ0= 0), but the increase in water purity effectively causes a shift in the relative change. This result is clarified in Figure 12, which indicates that increasing the water purity from 99 wt % to 99.99 wt % (a decrease of 2 orders of magnitude in the 1-butanol concentration), only causes a relative increase in total reboiler duty from 12.0% to 13.5%. It is interesting and useful to understand the relative contributions of the three process units to the increase in total reboiler duties and these results are presented in Figure 13. The contribution from the water column (WA-COL) is relatively small and the contributions from the other two units (LL-SEP and BOH-COL) are approximately equal. As expected the contribution from WA-COL increases from 11% to 26% as the water purity in stream PROD-WA increases, from 99 wt % to 99.99 wt %. The trends of these results are, of course, expected; however, the benefit of the perturbation approach is that they can now be quantified.

Figure 13. Relative contributions of the three process units (decanter and two distillation columns) to the increase in total reboiler duties as a function of purity of the water product in stream PROD-WA for a full perturbation (δ0 = 1).

Finally, Figure 14 presents the change in reboiler duty for the water column (WA-COL) alone. The percentage increases are larger than those for the entire flowsheet, and this result follows F

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This work has demonstrated that the method is applicable to systems exhibiting LLE, has shown that the methodology may be applied to cases in which the model (here the NRTL activity-coefficient model) is clearly inadequate, and has sharpened insight into the effects of product purity on design uncertainty.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The author declares no competing financial interest.

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Figure 14. Percentage change in WA-COL reboiler duty. The relative change in reboiler duties is based upon the same water purity in stream PROD-WA and δ0 = 0.

REFERENCES

(1) Taylor, B. N; Kuyatt, C. E. Guidelines for the Evaluation and Expression of Uncertainty in NIST Measurement Results; NIST Technical Note 1297; National Institute of Standards and Technology: Gaithersburg, MD, 1994. (2) Chirico, R. D.; De Loos, T. W.; Gmehling, J.; Goodwin, A. R. H.; Gupta, S.; Haynes, W. M.; Marsh, K. N.; Rives, V.; Olson, J.; Spencer, C.; Brennecke, J. F.; Trusler, J. P. M. Guidelines for Reporting of Phase Equilibrium Measurements (IUPAC Recommendations 2012). Pure Appl. Chem. 2012, 84, 1785−1813. (3) Brennecke, J. F.; Goodwin, A. R. H.; Mathias, P.; Wu, J. New Procedures for Articles Reporting Thermophysical Properties. J. Chem. Eng. Data 2011, 56, 4279−4279. (4) Weir, R. D.; Trusler, J. P. M.; Pádua, A. New Procedures for Articles Reporting Thermophysical Properties. J. Chem. Thermodyn. 2011, 43, 1305−1305. (5) Cummings, P. T.; de Loos, Th. W.; O’Connell, J. P. New Procedures for Articles Reporting Thermophysical Properties. Fluid Phase Equilib. 2011, 307, iv−iv. (6) Rives, V.; Schick, C.; Vyazovkin, S. New Procedures for Articles Reporting Thermophysical Properties. Thermochim. Acta 2011, 521, 1−1. (7) Haynes, W. M.; Friend, D. G.; Mandelis, A. Editorial: New Procedures for Articles Reporting Experimental Thermophysical Property Data. Int. J. Thermophys. 2011, 32, 1999−2000. (8) Kim, S. H.; Kang, J. W.; Kroenlein, K.; Magee, J. W.; Diky, V.; Frenkel, M. Online Resources in Chemical Engineering Education: Impact of the Uncertainty Concept from Thermophysical Properties. Chem. Eng. Educat. 2013, 47, 48−57. (9) Mathias, P. M. Sensitivity of Process Design to Phase Equilibrium − A New Perturbation Method Based Upon the Margules Equation. J. Chem. Eng. Data 2014, 59, 1006−1015. (10) Fair, J. R. Advanced Process Engineering. AIChE Monograph Series 1980, 76, 5−41. (11) Mathias, P. M. Effect of VLE Uncertainties on the Design of Separation Sequences by Distillation − Study of the BenzeneChloroform-Acetone System. Fluid Phase Equilib. 2016, 408, 265−272. (12) Westerberg, A. W.; Wahnschafft, O. Synthesis of DistillationBased Separation Processes. Adv. Chem. Eng. 1996, 23, 63−170. (13) van der Merwe, A. B.; Cheng, H.; Görgens, J. F.; Knoetze, J. H. Comparison of Energy Efficiency and Economics of Process Designs for Biobutanol Production from Sugarcane Molasses. Fuel 2013, 105, 451−458. (14) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135−144. (15) Redlich, O.; Kwong, J. N. S. On the Thermodynamics of Solutions. V An Equation of State. Fugacities of Gaseous Solutions. Chem. Rev. 1949, 44, 233−244. (16) DIPPR. http://www.aiche.org/dippr (accessed May 20, 2016). (17) Frenkel, M.; Chirico, R. D.; Diky, V.; Yan, X.; Dong, Q.; Muzny, C. ThermoData Engine (TDE): Software Implementation of the Dynamic Data Evaluation Concept. J. Chem. Inf. Model. 2005, 45, 816−838.

because the uncertainty in relative volatility for the water-rich region is high (Figure 6 and Figure 8), but again the effect of increased water purity is weak as the relative change in total reboiler duty only increases from 28% to 34% as the water purity in stream PROD-WA rises from 99 wt % to 99.99 wt %. The results of the sensitivity study may be summarized as follows: 1. The overall process uncertainties are remarkably low in spite of the data uncertainty (especially for VLE in the water-rich region, Figure 6 and Figure 8) and the model inadequacy (Figure 1 and Figure 7). It is clear that good data and a careful fit of the relevant data do give beneficial results in terms of desirable low uncertainty. 2. The NRTL model is not capable of fitting the entire range of the VLLE data simultaneously. This identifies a need for improved activity-coefficient models. However, a “local fit” of the data overcomes this deficiency and enables accurate process designs in practice. 3. The present analysis sharpens insights into the effect of product purity on design uncertainty. Increase in the water purity by 2 orders of magnitude has only a weak effect on the relative uncertainty, and this is because the relative volatilities in the two distillation columns are sufficiently different from unity. This result is in sharp contrast to the propane−propylene splitter9 (relative volatility at the propylene-rich end ≈1.1) where the product purity strongly increases the sensitivity of the design uncertainty to uncertainties in the phase equilibrium. 4. The uncertainty analysis has the capability to identify the separate contributions to the uncertainty. It is thus possible to identify whether the data in specific regions may need to be improved. Here, improved accuracy is needed for the VLE data in the water-rich region if the overall uncertainty needs to be reduced.

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CONCLUSIONS This paper has extended application of the Margules-based phase-equilibrium uncertainty method to a system exhibiting a heterogeneous azeotrope. As in the previous two applications of this series,9,11 the essential first step in the process is to collect, fit, and analyze the available data to quantitatively estimate data/model uncertainties. Each paper of this series has identified new insights and benefits of uncertainty analysis. G

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DOI: 10.1021/acs.jced.6b00546 J. Chem. Eng. Data XXXX, XXX, XXX−XXX