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Component Trapping with VLE Uncertainty: Principles, Design and Troubleshooting Paul M. Mathias, Henry Z. Kister, Bruce Parker, Lydia Narvaez, Thomas Schafer, and Alan Erickson Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02812 • Publication Date (Web): 14 Sep 2017 Downloaded from http://pubs.acs.org on September 29, 2017

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Industrial & Engineering Chemistry Research

Component Trapping with VLE Uncertainty: Principles, Design and Troubleshooting Paul M. Mathias,*1 Henry Z. Kister,1 Bruce Parker,2 Lydia Narvaez,3 Thomas Schafer,4 Alan Erickson4 1

2

3

Fluor Corporation, 3 Polaris Way, Aliso Viejo, CA 92698

Eli Lilly and Company, Lilly Corporate Center, Indianapolis, IN 46221

Fluor Daniel Caribbean, Inc., Suite 500 St. 2 No. 14 Metro Office Park, Guaynabo, Puerto Rico 00969 4

Koch Modular Process Systems, LLC, 45 Eisenhower Drive, Suite 350, Paramus, NJ 07652 *Corresponding author

CORRESPONDING AUTHOR EMAIL ADDRESS: [email protected] ABSTRACT : Intermediate components tend to accumulate near the middle of a distillation column in many chemical and petroleum separations. Their accumulation may lead to off-spec products, corrosion, plugging, or periodic cycling. The most common method of removing these intermediate components is by taking them out in one or more side draws. The addition of such side draws may not go far enough to achieve the desired product specs. If the side-draw approach fails, the expensive addition of a new tower may be required. The question of whether a side draw is sufficient to remove the accumulating intermediate components, or whether an additional column is needed, depends on the relative volatilities of the intermediate components at tower conditions. Often, there is a high degree of uncertainty in the model used for correlation of the phase equilibrium of these components. The Margules Uncertainty Analysis method is valuable in analyzing these situations and in guiding engineers to the rational solution. The case analyzed here is an acetonitrile + water separation tower with t-crotonaldehyde and propionitrile as the intermediate components. There are uncertainties in the correlation of the volatilities of these intermediate components in this system. In light of these uncertainties, our analysis addresses the question of whether the tight product specs can be achieved in one tower with a side draw or whether more than one tower is needed. The analysis shows that depending on the product specs and Acetonitrile (ACN) Purification, I&EC Research, September 2017 1 ACS Paragon Plus Environment


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the tolerance for a high reflux ratio, there would be situations where one can be certain that one tower will work, while in other cases more than one tower is needed to assure achievement of the required product specs. The analysis enables quantification of the risk of the single-column solution. KEYWORDS vapor-liquid equilibrium, phase-equilibrium uncertainty, azeotropic distillation, risk quantification

Acetonitrile (ACN) Purification, I&EC Research, September 2017 2 ACS Paragon Plus Environment

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Introduction This paper evaluates the options to purify an aqueous solution of ≈ 12 wt% acetonitrile (ACN) by distillation, and to recover about 90% of the ACN at the azeotropic composition (about 83 wt% at 1 atmosphere or 101.3 kPa). The separation is difficult due to intermediate components [propionitrile (PPN) and t-crotonaldehyde (T-CROTON)] that build-up in the distillation column. The solution options are a single column with a side draw, or a more complex flowsheet with multiple columns. An example of a multiple-column solution is to remove all of the water from the ACN, PPN and TCROTON via a pressure swing distillation, and then separate the dry ACN from the PPN and TCROTON. The multiple-column solution is the safe solution, but costs more than the single column with a side draw in terms of both capital cost and operating costs. Here we quantify the risk of the single-column solution by introducing uncertainty analysis into the process modeling. The problem of intermediate components in distillation is a general problem of component trapping that has been discussed extensively by Kister.1,2 In some cases, the top temperature is too cold and the bottom temperature is too high to allow these components to leave the column at the same rate as they enter. Having nowhere to go, these components accumulate in the column, which causes problems like off-spec products, flooding, cycling slugging, and corrosion. Cycling on a variable time period (typically with frequencies between two hours and two weeks) is a common symptom indicating unsteady-state component trapping. Proposed diagnoses of the problem include studying time variation of temperature profiles, taking internal samples, shooting gamma scans, and simulation studies. Solutions comprise raising or lowering the temperature (usually at the expense of recovery), taking side draws, or removing the problem components from the feed. Existing diagnoses and solutions have been discussed in detail by Kister.1,2 Here, for the first time, we apply uncertainty analysis to the problem caused by trapping of intermediate components in ACN purification. Modeling of separations by distillation requires gaining quantitative understanding of the uncertainties in the vapor-liquid equilibrium (VLE) and applying these uncertainties to the problem at hand. While many technologists have highlighted the need to recognize the impact of uncertainties in property models on process design and plant operability3,4,5,6,7 and several solutions have been suggested and evaluated in the literature,8,9,10,11,12,13,14 uncertainty analysis is scarcely used in chemical-engineering design practice. In fact, Kim et al.15 observed, “Its practical implementation in a variety of scientific and engineering fields has typically seen less emphasis than it deserves.” Mathias16 recognized that liquid-phase nonideality is a major source of phase-equilibrium uncertainty, and developed an intuitive and easy-to-apply uncertainty-analysis method based upon treating the mixture, for the purpose of Acetonitrile (ACN) Purification, I&EC Research, September 2017 3 ACS Paragon Plus Environment


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activity-coefficient perturbation, as a set of pseudobinaries described by the Margules equation. The Margules perturbation method has been applied to several case studies, including propylene-propane superfractionator, where small changes in relative volatility and product purity have a large effect on design;16 a dehexanizer column that removes pentane and hexane from a heavier slate of components that are mostly aromatic and the system contains many components (≈ 60); 16 the “textbook problem” of acetone + benzene + chloroform separation, which revealed the relationship between uncertainty analysis and residue-curve analysis;17 the butanol + water separation, which demonstrated the extension to liquid-liquid equilibrium (LLE) and is a case where the thermodynamic model is inadequate;18 and ethyl acetate purification, which further revealed the relationship between uncertainty analysis and residue-curve, and showed the importance of fitting multicomponent data for complex systems.19 The Margules Uncertainty Analysis procedure used here follows that of the previous studies.16,17,18,19 The first step is detailed data regression to obtain the best model fit in the region of application (atmospheric pressure, 101.3 kPa), and quantitative estimation of the correlation uncertainties. This is an essential first step. The data regression is mainly applied to the quaternary system: water + ACN binary mixture, with PPN and T-CROTON at low concentration. In the second step, activity coefficients are varied within the process model to relate the confidence limits of the design to uncertainties of the correlated phase equilibria. The uncertainty analysis is only applied to T-CROTON as a representative intermediate component, since sufficient data are not available for PPN.

Margules-Based Activity-Coefficient Perturbation Scheme The perturbation scheme for the mixture nonideality has been published by Mathias,16 and hence is only briefly presented here. The approach uses the approximation that the perturbed activity coefficients can be guided by the Margules equation.

( )

( )

ln (γ i ) = ln γ im + ln γ ip

where

γ i is the activity coefficient of component i

(1)

after perturbation,

γ im is the activity coefficient calculated

by the chosen model (the “best” model in the region of interest should be used), and

γ ip represents the

perturbation obtained through the estimated model uncertainty. It should be emphasized that γ i is calculated m


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from the “best” activity-coefficient model, and is not in any way constrained by the pseudo-binary approximation.

γ ip is given by,

( ) = δ (1− x )

ln γ i

p

i

i

2

( )

 ln γ im  2  (1 − xi ) + ln γ im

( )

  

(2)

As previously noted,16 Equation 2 is phenomenological, but has desired characteristics. The value of

( )

ln γ ip is small when

γ im is close to unity (i.e., low departures from ideal behavior), and also is low

when the mole fraction of component i is close to unity. For components at concentrations close to infinite dilution and with activity coefficients significantly different from unity, the fractional change in

γ i resulting from the perturbation asymptotically approaches {exp(δi) – 1}. In order to apply the perturbation method, the value of δ i for each component must be related to the estimated uncertainty in its activity coefficient. This thorough data analysis is a necessary and important element of the perturbation scheme.

Correlation of VLE in the Water + ACN + PPN +T-CROTON System As in the previous uncertainty-analysis case studies,16,17,18,19 the perturbation scheme has been implemented as a user activity-coefficient model that adds the perturbation capability to the NRTL-RK property option in Aspen Plus V8.8. The NRTL-RK property option uses the NRTL activity-coefficient model20 and the Redlich-Kwong equation of state21 for the vapor phase. The pure-component properties come from the Aspen Plus V8.8 pure-component database. This study is at a pressure of 1 atm (101.3 kPa), the temperatures of interest are approximately 70-100 °C, and at these temperatures the correlations for the vapor pressures of these four compounds from the Aspen Plus database are expected to be accurate to better than 2 %. The reason for this confidence is that the Aspen Plus pure-component properties come from the DIPPR 801 database,22 and the correlated vapor pressures for the key components were checked against accepted DIPPR data in the 70-100 °C temperature range; no percentage deviations exceeded 2%. The Redlich-Kwong equation estimates 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, ≈1 atm. In addition, the vapor-phase fugacity coefficient appears in the vapor and liquid fugacities (in the liquid it converts the pure-component vapor pressure into the pure-liquid fugacity), and the two fugacity coefficients tend to cancel when all boiling points are similar. For this application, the phase-equilibrium uncertainty is largely determined by the uncertainties in the component activity coefficients. Acetonitrile (ACN) Purification, I&EC Research, September 2017 5 ACS Paragon Plus Environment


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The NRTL model has two temperature-dependent binary parameters ( α ijN and τij). α ijN is a symmetric binary parameter and τij is an asymmetric binary parameter,

τ ij = aij + bij / T + eij ln(T ) + f ij T

(3)

α ijN = cij + d ij (T − 273.15)

(4)

where, T is the temperature in Kelvin. The K-value of component i in a mixture (Ki) at vapor-liquid equilibrium (VLE) is defined to be the ratio of its vapor and liquid mole fractions at equilibrium, and the relative volatility between components i and j (αij) is the ratio of the two K-values. Ki ≡

αi j ≡

yi xi Ki Kj

(5)

(6)

Note that the superscript “N” has been added to the NRTL parameter α ijN (Eq. 4) in order to distinguish it from the relative volatility, α i j . The Data Regression System (DRS) in Aspen Plus V8.8 has been used to obtain optimum values of the NRTL binary parameters at pressures at about 1 atm (101.3 kPa), which corresponds to the temperature range of ≈ 70-100°C. Phase-equilibrium data were obtained from the NIST-TDE23 database, the Dortmund databank,24 and other sources, and also key VLE data have been measured as part of this effort. The water + ACN binary is a well-studied system since a large number of datasets are available, however, the four binaries consisting of PPN and T-CROTON with water and ACN have only a few data. In fact, systems with PPN are very poorly covered by data, and therefore this study has chosen to focus on the effect of T-CROTON as the representative intermediate component. Table 1 presents the 14 chemical species considered in the Aspen Plus simulation together with their normal boiling points. The table also shows the estimated infinite-dilution activity coefficients in water and ACN at a representative temperature of 75°C; these correlations/estimations are discussed in detail later in this paper. The last column of Table 1 designates components other than water and ACN as “light,” “heavy,” or “intermediate.” The “light” components (1-4) have normal boiling points lower than that of ACN. These components will have K-values greater than unity over the entire column, and hence will split predominately to the distillate in the distillation column. The “heavy” components (1014) have normal boiling points greater than that of water, and also are fairly ideal with water (infiniteAcetonitrile (ACN) Purification, I&EC Research, September 2017 6 ACS Paragon Plus Environment

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dilution activity coefficients close to unity). These “heavy” components will always have K-values less than unity, and therefore will principally split to the bottoms stream of the distillation column. The “intermediate” components have normal boiling points higher than that of ACN, and form nearly ideal mixtures with ACN, consequently their K-values are likely to be below unity at the top of the column (in the vicinity of the water + ACN azeotrope). Further, the “intermediate” components have tb values close to that of water and also water infinite-dilution activity coefficients significantly greater than unity (see Table 1), and therefore their K-values will be greater than unity at the bottom of the column. As a result, the intermediate components have K-values that cross unity and therefore tend to build-up in the column. Table 1. Components in the acetonitrile purification Aspen Plus model.

Component Name

tb/ °C

Component ID

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

21.0 39.8 49.0 52.7 81.6 88.7 97.4 100.0 102.5 117.9 124.4 128.0 221.2 239.4

ACETALD DCM PROPALD ACROLEIN ACN C-CROTON PPN WATER T-CROTON ACETACID MEOXYETH MORPHOL ACETAMID ACETMOR

Acetaldehyde Dichloromethane n-Propionaldehyde Acrolein Acetonitrile cis-Crotonaldehyde Propionitrile Water trans-Crotonaldehyde Acetic Acid 2-Methoxyethanol Morpholine Acetamide 4-Ethylmorpholine

γ∞ at 75°C in

Water 9.0 235.9 32.2 17.1 11.7 32.5 41.6 1.0 32.5 1.3 2.7 1.1 1.0 1.1

ACN 1.1 1.2 1.3 1.1 1.0 1.4 1.0 6.1 1.4 1.9 2.0 1.0 1.0 1.0

Impurity Category

Light Light Light Light Intermediate Intermediate Intermediate Heavy Heavy Heavy Heavy Heavy

Crotonaldehyde has two isomers, cis and trans. The study of McGreer and Page25 found that ciscrotonaldehyde (CAS Registry Number: 4170-30-3) is far less chemically favored than transcrotonaldehyde (CAS Registry Number: 123-73-9), by about 1:50. Hence, although cis-crotonaldehyde is available in the simulation file, its properties are not considered reliable, and crotonaldehyde has been treated as entirely the trans isomer (T-CROTON) It is clear that the system of primary interest to this study consists of 4 components: water, ACN, PPN and T-CROTON. For the other binary mixtures, the NRTL parameters were obtained by regressing data from NIST-TDE23 and other sources, or were estimated using the UNIFAC method.26 It is noted that Acetonitrile (ACN) Purification, I&EC Research, September 2017 7 ACS Paragon Plus Environment


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the phase behavior of the other components (1-4 and 10-14 in Table 1) have negligible effect on this study. Table 2 presents the NRTL parameters for the water + ACN + PPN + T-CROTON system. The water + ACN binary mixture is well covered by experimental VLE data. The binaries of water with PPN and T-CROTON are also covered by VLE and LLE data; it is noted that these two binaries have regions of liquid-liquid immiscibility, but the concentrations of PPN and T-CROTON in this process are too low to exceed their miscibility limit. No data were found in the literature for the other three binaries. Data for the water + ACN + T-CROTON ternary were measured as part of this project.27 The NRTL parameters for the ACN + PPN are estimated based upon UNIFAC predictions.26 Generally, UNIFAC predictions are not sufficiently accurate, so future measurement may be needed. The NRTL parameters for the PPN + T-CROTON binary have been defaulted to zero. UNIFAC estimations26 indicate that this is a fairly ideal system (infinite-dilution activity coefficients ≤ 1.2). Minor components have a negligible effect on overall mixture nonideality, and it was decided that the assumption of ideality is the preferred choice.

Table 2. NRTL parameters for the water + ACN + PPN + T-CROTON system. See Eqs. 3 and 4 for a description of the parameters. Parameters e12, e21, f12, f21, and d12 are always equal to zero.

Component 1

ACN

PPN

WATER

ACN

ACN

PPN

Component 2

WATER

WATER

TCROTON

PPN

TCROTON

TCROTON

a12

-2.34

-4.53

5.38

0

0

0

a21

2.39

2.99

-2.34

0

0

0

b12

1165.5

2041.1

-751.4

27.1

55.1

0

b21

-199.2

-9.9

914.6

-30.0

55.1

0

c12

0.45

0.41

0.3

0.3

0.3

0.3

Key comparisons of model results to experimental data are provided next in order to quantify the VLE uncertainties. Figure 1 compares the calculated relative volatility in the water + ACN binary at about 101.3 kPa to data from 9 sources, which are identified in Table 3. The model describes the data, including the azeotropic and both low-concentration regions, accurately, and there is no indication of model bias. The dashed lines in Figure 1 show ± 20% from the model calculation. It is noted that that the water + ACN binary is not a significant cause of design uncertainty, and hence no uncertainty perturbation has been applied to this binary. The water + ACN azeotrope at 101.3 kPa is at an ACN mole fraction of 0.70 (ACN mass fraction = 0.83). Acetonitrile (ACN) Purification, I&EC Research, September 2017 8 ACS Paragon Plus Environment

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Figure 2 compares model relative volatilities for the water + T-CROTON binary mixture to the data of Kil and Zadorskii,28 Mkrtchyan et al.,29 and Rudakovskaya;30 it is not clear what isomer of crotonaldehyde was used in these studies, and we have assumed it was T-CROTON, or at least predominantly T-CROTON. Figure 2 also shows how the calculated relative volatility of T-CROTON changes as its perturbation parameter is varied from -0.4 to +0.4. The model uncertainty is difficult to estimate since the data are highly scattered when the T-CROTON concentration is low, say its mole fraction is less than 0.02. If we ignore the data for x (T-CROTON) < 0.02, the estimate of the expanded uncertainty for δT-CROTON (two standard deviations or 95% probability) is 0.2. It should be noted that the higher T-CROTON mole fractions in Figure 2 are approaching the liquid-liquid solubility limit. The data of Stephenson31 indicates that the solubility of T-CROTON in water at 363 K is 0.047. Table 3. VLE datasets used for the water + acetonitrile binary mixture, and compared with the NRTL-RK model in Figure 1.

Dataset Number

Dataset ID

Reference

1

V0508-05

Pratt (1948)32

2

V0508-06

Pratt (1948)32

3

V0508-14

Maslin and Stoddard (1956)33

4

V0508-16

Blackford and York (1955)34

5

V0508-23

Volpicelli (1967)35

6

V0508-25

Sada et al. (1971)36

7

V0508-37

Han (1980)37

8

V0508-43

Acosta et al. (2002)38

9

V0508-46

Liu et al. (2014)39

Figure 3 presents comparisons between model and data27 for the K-value of T-CROTON at low concentration (effectively infinite dilution) in the water + ACN binary mixture at 1 atm (101.3 kPa). The dashed lines indicate ± 30% from the model calculations, and the dotted lines show perturbed model calculations with δ=0.5 and δ=-0.5. Most of the data points fall within the dashed lines, and this may be considered to be the 99% uncertainty (about 2.6 standard deviations) of the model K-values for T-CROTON. The dotted lines (perturbed model) are equivalent to the ± 30% lines at the water-rich end, but have a smaller variation at the ACN-rich end. Based upon studying the uncertainties in Figure 2 and Figure 3, we conclude that perturbations of δ = ±0.5 represent an expanded combined uncertainty (two standard deviations or 95% probability) in the T-CROTON K-value. It should be noted that these uncertainty estimates have some element of subjectivity, due to Type B uncertainties; Chirico et al.40 define these Type B uncertainties as “evaluated by scientific judgment based upon all available Acetonitrile (ACN) Purification, I&EC Research, September 2017 9 ACS Paragon Plus Environment


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information.” The vertical line in Figure 3 at 83 wt% shows the ACN + water azeotrope, which corresponds to the distillate composition from the column, and it is clear that both the model and experimental data indicate that the K-value of T-CROTON drops below unity before reaching the top of the column, which, of course, is the reason that T-CROTON is an intermediate component. Qureshi et al.41 reported experimental infinite-dilution activity coefficients for T-CROTON in water in the temperature range 25-60 °C. These data indicate that increases from 39 at 25 °C to 48

at 60 °C. The values seem to level-off at 60 °C, and hence the value at 75 °C may be lower than 48, but likely higher than the value of 32.5 reported in Table 3. The value of that from the present

model at 100 °C is 32.1, and this value provides good average agreement with the data of Kil and Zadorskii,28 Mkrtchyan et al.,29 and Rudakovskaya30 (Figure 2, x(T-CROTON) → 0), and the data of Parker27 (Figure 3, water-rich end). Hence, it seems that the data of Qureshi et al.41 are biased slightly high, and we use the other data for our uncertainty assessments. Figure 4, which shows the K-value of PPN and ± 30% perturbations (dashed lines), is analogous to Figure 3. While the calculated results are similar for PPN and T-CROTON, there are no experimental data available for PPN, and hence the perturbation studies here are limited to T-CROTON, with the expectation that they will be semi-quantitatively applicable to PPN. It is useful from a practical engineering viewpoint to convert the perturbation in δ to a confidence limit (CL). In the present case, we are only concerned about positive values of δ because negative values will result in an optimistic lower calculated concentration of T-CROTON in the distillate. Assuming that the model fit of the data is unbiased, δ = 0 will give a CL of 50%. If we further assume that the distribution of δ values follows a standard normal distribution, CL may be estimated as,

≈ √

/

(7)

where σδ is the standard deviation of δ, and its value is equal to 0.25 based upon the above analysis. Table 4 presents values of CL for selected values of δ obtained through a numerical approximation to Eq. 7 using Eq. 7.1.26 from Abramowitz and Stegun42 for the error function. Table 4. Calculated values of the confidence limit (CL) for selected values of δ. Note that σδ = 0.25.

δ

δ /σδ

CL/ %

0

0

50.0

0.1

0.4

65.5

0.2

0.8

78.8


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0.3

1.2

88.5

0.4

1.6

94.5

0.5

2.0

97.7

0.6

2.4

99.2

Two design studies have been conducted to evaluate the effect of T-CROTON VLE uncertainty on the performance of a single column, and these are described next.

Design Study 1 – Single Column with Side Draw Figure 5 depicts the single column with side draw used for the first set of design studies. The feed flow is 770 kg/hr and is an aqueous mixture containing 12 wt% ACN, and with minor impurities. The impurity levels of PPN and T-CROTON in the feed are 100 ppmw (parts per million by weight) and 20 ppmw, respectively. The column has 35 theoretical stages including a reboiler and a total condenser.43 The distillate-to-feed ratio is set at 0.13, which corresponds to ≈ 91% ACN recovery at the azeotropic composition. The calculated reflux ratio is varied to obtain a T-CROTON concentration in the distillate of 1 ppmw. The feed stage is varied from 12 to 24. The base case is the feed to stage 20, and for this case the calculated reflux ratio is 7.0. Figure 6 shows the vapor and liquid concentration profiles (weight fraction) for ACN, PPN and T-CROTON in the distillation column for the base case. The concentration of ACN rises with stages toward the condenser (here in decreasing stage number) and quickly reaches the water + ACN azeotropic concentration just a few stages above the feed stage. The concentration profiles of PPN and T-CROTON show the characteristics of intermediate components since they both have concentration peaks below the feed stage. Note that the concentration peak of TCROTON is about three orders of magnitude above the distillate and bottoms concentrations. The distillate and bottoms concentrations of PPN and T-CROTON are both small since most of these two components are removed in the side draw. Figure 7 emphasizes these points by showing the K-value profile of T-CROTON together with its concentration profile. Note also that the relative values of the vapor and liquid concentrations switch as the K-value moves from less than one at the top of the column (lower stage numbers) to greater than one at the bottom of the column. Figure 8 studies how the reflux ratio needs to be adjusted to attain the spec of 1 ppmw T-CROTON in the distillate as the perturbation parameter of T-CROTON (δ, Eq. 2) and the number of rectification stages are varied. Increasing the number of rectification stages is helpful in reducing the required reflux Acetonitrile (ACN) Purification, I&EC Research, September 2017 11 ACS Paragon Plus Environment


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ratio, and this can be inferred from Figure 6 (and directly seen in Figure 8) because the concentrations of PPN and T-CROTON decrease monotonically in the rectification section of the column, but the effect is relatively weak. On the other hand, increasing δ (increased activity coefficient and therefore K-value of T-CROTON) results in a strong increase in the required reflux ratio. Very large reflux ratios cause problems, for example requiring large-diameter columns and significant increases in reboiler duty, and are usually resisted in industrial process-design practice. Figure 8 also shows the confidence limits (CL) for each value of δ. Note that the confidence that -∞ ≤ δ ≤ 0.4 is 95%. Figure 9 studies the effect of the side-draw rate for the base case (Figure 5 with reflux ratio of 7.0 and feed to stage 20). It is clear that varying the draw rate has a strong effect on the concentration of TCROTON in the bottoms (because it changes the total amount of T-CROTON removed in the side draw), but it has only a weak effect on the concentration of T-CROTON in the distillate. Since the main goal here is to reduce the concentration of PPN and T-CROTON in the distillate, the next study is done without the side draw.

Design Study 2 – Single Column with no Side Draw Figure 10 presents the single column with no side draw used for the second set of design studies, and with the total number of stages increased from 35 to 40. Other design conditions are the same as in Figure 5. Figure 11 is qualitatively the same as Figure 8, which supports the conclusion that the side draw affects the bottoms concentration of T-CROTON, but has only a weak effect on the result we desire, which is minimizing the concentration of T-CROTON in the distillate. As with Figure 8, Figure 11 also shows the confidence limits (CL) for each value of δ. Figure 12 presents the results of a study where the reflux ratio has been fixed at 10.0, and the perturbation parameter (δ) and the number of rectification stages are varied. Similar to Figure 8, Figure 12 shows that it is beneficial to increase the number of rectification stages as this reduces the concentration of T-CROTON in the distillate. However, the significant result is that the concentration of T-CROTON in the distillate is a very strong function of the uncertainty in the VLE, specifically the T-CROTON K-value. As δ increases not only does the concentration of T-CROTON in the distillate increase beyond the target value (1 ppmw), but it can also exceed the feed concentration (20 ppmw), in effect concentrating undesired impurities in the product! The vertical lines in Figure 12 relate the VLE perturbation (δ) to the confidence limits. At the 50% confidence level (δ = 0; see Table 4), the spec of 1 ppmw T-Croton in the distillate is achieved even if Acetonitrile (ACN) Purification, I&EC Research, September 2017 12 ACS Paragon Plus Environment

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just 15 rectification stages are used. At the 79% confidence level (0.8 standard deviations or δ = 0.2; see Table 4) it will be possible to attain the 1 ppmw T-CROTON spec if the number of rectification stages is increased slightly above 25. However, at the 95% confidence level (1.6 standard deviations or δ = 0.4) not only will it be impossible to attain the T-CROTON spec of 1 ppmw, but the T-CROTON

concentration in the distillate will actually exceed the feed concentration – effectively concentrating the unwanted impurity in the product. Charts like Figure 12 are crucial to making rational design decisions. The uncertainty analysis presented here clearly indicates that the single-column solution is the risky option, and also quantifies the risk in terms of confidence limits.

Conclusions The purpose of this study is to apply the Margules Uncertainty Analysis method to an industrially important component-trapping case, i.e., purification of acetonitrile used as a solvent in the pharmaceutical industry. Small impurities of T-CROTON and PPN turn a simple distillation into a very challenging problem. The study first focused on the VLE correlation, and determined that the key uncertainty is the K-values of the intermediate components, PPN and T-CROTON. Since adequate Kvalue data are only available for T-CROTON, this component was chosen as the representative intermediate key component. The first set of studies indicated that the target of 1 ppmw T-CROTON in the distillate can be met, at least in the simulation model, but at a significant increase in reflux ratio if the T-Croton K-value is increased within the established uncertainty. The second set of studies concluded that increasing the K-value of T-CROTON within the established uncertainty caused a significant increase in the T-CROTON concentration in the distillate, and the product concentration could even exceed the feed concentration. In all cases, the perturbation in δ has been related to the confidence limit (CL). The single-column solution thus appears to be a risky choice, and the risk has been quantified so that rational design decisions can be made.



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List of Tables Table 1. Components in the acetonitrile purification Aspen Plus model. ................................................. 7 Table 2. NRTL parameters for the water + ACN + PPN + T-CROTON system. See Eqs. 3 and 4 for a description of the parameters. Parameters e12, e21, f12, f21, and d12 are always equal to zero. ................... 8 Table 3. VLE datasets used for the water + acetonitrile binary mixture, and compared with the NRTLRK model in Figure 1. ................................................................................................................................ 9 Table 4. Calculated values of the confidence limit (CL) for selected values of δ. Note that σδ = 0.25.. 10

List of Figures Figure 1. Water + ACN relative volatilities at about 101.3 kPa. Comparison of model calculations to 9 data sources See Table 3 for details. ......................................................................................................... 15 Figure 2. Water + t-crotonaldehyde relative volatilities at about 101.3 kPa. Comparison of model calculations to data of Kil,28 Mkrtchyan,29 and Rudakovskaya.30 The data are considered to be unreliable for x (T-CROTON) < 0.02......................................................................................................................... 16 Figure 3. Mass K-Value of T-CROTON at low concentration in water + ACN at 1 atm (101.3 kPa). Comparison of model calculations to Eli Lilly data.27 The dashed lines show ± 30% from the model results. The dotted lines are model calculations with δ = 0.5 and δ = -0.5. The vertical line indicates the water + ACN azeotrope. ........................................................................................................................... 17 Figure 4. Mass K-Value of PPN at low concentration in water + ACN at 1 atm (101.3 kPa). No ternary experimental data are available. The dashed lines show ± 30% from the model results. The vertical line indicates the water + ACN azeotrope. ...................................................................................................... 18 Figure 5. Single column with side draw used for perturbation studies-1. The column operates at 1 atm (101.3 kPa). ............................................................................................................................................... 19 Figure 6. Vapor and liquid concentration profiles for ACN, PPN and T-CROTON in the distillation column corresponding to Figure 5, and with feed to stage 20. ................................................................. 20 Figure 7. Mass-fraction and K-value profiles of T-CROTON in the base case. The specifications are the same as those in Figure 6. ................................................................................................................... 21 Figure 8. Effect of perturbation parameter (δ) and number of rectification stages on the reflux ratio required to meet the spec of 1 ppmw T-CROTON in the distillate. See Figure 5 for details. The percentage in brackets show the extent of the perturbations at the ACN-rich and water-rich ends; the water-rich end has the larger perturbation. The confidence limits (CL) are also shown for each of the three values of δ. ....................................................................................................................................... 22 Figure 9. Effect of modifying side-draw rate on the concentrations of T-CROTON in the bottoms (left axis) and the distillate (right axis). The feed is at stage 20 and the reflux ratio is fixed at 7.0. .............. 23 Figure 10. Single column used for perturbation studies-2. The difference from Figure 5 is that the side draw has been eliminated.......................................................................................................................... 24


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Figure 11. Repeat of study shown in Figure 8 with no side draw and total number of stages increased from 35 to 40 (See Figure 10). The percentages in brackets show the extent of the perturbations at the ACN-rich and water-rich ends; the water-rich end has the larger perturbation. The confidence limits (CL) are also shown for each of the three values of δ. ............................................................................. 25 Figure 12. Effect of perturbation parameter (δ) and number of rectification stages on concentration of T-CROTON in distillate. Referring to Figure 10, the reflux ratio is fixed at 10. The vertical lines show the 79% and 95% confidence limits (CL); other values of CL may be estimated using Table 4. ............ 26

Figure 1. Water + ACN relative volatilities at about 101.3 kPa. Comparison of model calculations to 9 data sources See Table 3 for details.



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Figure 2. Water + t-crotonaldehyde relative volatilities at about 101.3 kPa. Comparison of model calculations to data of Kil,28 Mkrtchyan,29 and Rudakovskaya.30 The data are considered to be unreliable for x (T-CROTON) < 0.02.


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Figure 3. Mass K-Value of T-CROTON at low concentration in water + ACN at 1 atm (101.3 kPa). Comparison of model calculations to Eli Lilly data.27 The dashed lines show ± 30% from the model results. The dotted lines are model calculations with δ = 0.5 and δ = -0.5. The vertical line indicates the water + ACN azeotrope.



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Figure 4. Mass K-Value of PPN at low concentration in water + ACN at 1 atm (101.3 kPa). No ternary experimental data are available. The dashed lines show ± 30% from the model results. The vertical line indicates the water + ACN azeotrope.


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Figure 5. Single column with side draw used for perturbation studies-1. The column operates at 1 atm (101.3 kPa).



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Figure 6. Vapor and liquid concentration profiles for ACN, PPN and T-CROTON in the distillation column corresponding to Figure 5, and with feed to stage 20.


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Figure 7. Mass-fraction and K-value profiles of T-CROTON in the base case. The specifications are the same as those in Figure 6.



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Figure 8. Effect of perturbation parameter (δ δ) and number of rectification stages on the reflux ratio required to meet the spec of 1 ppmw T-CROTON in the distillate. See Figure 5 for details. The percentage in brackets show the extent of the perturbations at the ACN-rich and water-rich ends; the water-rich end has the larger perturbation. The confidence limits (CL) are also shown for each of the three values of δ.


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Figure 9. Effect of modifying side-draw rate on the concentrations of T-CROTON in the bottoms (left axis) and the distillate (right axis). The feed is at stage 20 and the reflux ratio is fixed at 7.0.



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Figure 10. Single column used for perturbation studies-2. The difference from Figure 5 is that the side draw has been eliminated.


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Figure 11. Repeat of study shown in Figure 8 with no side draw and total number of stages increased from 35 to 40 (See Figure 10). The percentages in brackets show the extent of the perturbations at the ACN-rich and water-rich ends; the water-rich end has the larger perturbation. The confidence limits (CL) are also shown for each of the three values of δ.



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Figure 12. Effect of perturbation parameter (δ δ) and number of rectification stages on concentration of T-CROTON in distillate. Referring to Figure 10, the reflux ratio is fixed at 10. The vertical lines show the 79% and 95% confidence limits (CL); other values of CL may be estimated using Table 4.


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TOC Graphic



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[3] Streich, M.; Kistenmacher, H. Hydrocarb. Proc., 1979, 58, 237-241.

Property Inaccuracies Influence Low Temperature Designs,

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[8] Zeck, S. Thermodynamics in Process Development in the Chemical Industry - Importance, Benefits, Current State and Future Development, Fluid Phase Equilib., 1991, 70, 125–140 [9] Macchietto, S.; Maduabeuke, G,; Szcepanski, R. Exact Determination of Process Sensitivity to Physical Properties, Fluid Phase Equilib., 1986, 29, 59-67. [10] Reed, M. E.; Whiting, W. B., Sensitivity and Uncertainty of Process Designs to Thermodynamic Model Parameters: A Monte Carlo Approach, Chem. Eng. Commun. 1993, 124, 39–48. [11] Whiting, W. B. Effects of Uncertainties in Thermodynamic Data and Models on Process Calculations, J. Chem. Eng. Data, 1996, 41, 935–941. [12] Whiting, W. B.; Vasquez, V. R.; Meerschaert, M. M. Techniques for Assessing the Effects of Uncertainties in Thermodynamic Models and Data, Fluid Phase Equilib. 1999, 158–160, 627–641. [13] Xin, Y.; Whiting, W. B. Case Studies of Computer-Aided Design Sensitivity to Thermodynamic Data and Models, Ind. Eng. Chem. Res. 2000, 39, 2998–3006. [14] Whiting, W. B.; Vasquez, V. R.; Meerschaert, M. M. Techniques for Assessing the Effects of Uncertainties in Thermodynamic Model and Data, AIChE J., 1997, 43, 440–447. [15] 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. [16] 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. [17] Mathias, P. M. Effect of VLE Uncertainties on the Design of Separation Sequences by Distillation – Study of the Benzene-Chloroform-Acetone System. Fluid Phase Equilib., 2016, 408, 265-272.


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[18] Mathias, P. M. Effect of Phase-Equilibrium Uncertainties on the Separation of Heterogeneous Azeotropes – Application to the Water/1-Butanol System. J. Chem. Eng. Data, 2016, 61, 4077-4084. [19] Mathias, P. M.; Kister, H. Z. Effect of Phase-Equilibrium Uncertainties on Ethyl Acetate Purification, published in J. Chem. Eng. Data, 2017, http://dx.doi.org/10.1021/acs.jced.7b00172. Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J., 1968, 14, 135-144.

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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. [21]

[22] Rowley, R. L.; Wilding, W. V.; Oscarson, J. L.; Yang, Y.; Zundel, N. A. DIPPR® Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY, 2010. [23] 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. TDE is also available online at http://trc.nist.gov/tde.html. [24] Onken U.; Rarey-Nies J.; Gmehling J. The Dortmund Data Bank: A Computerized System for Retrieval, Correlation, and Prediction of Thermodynamic Properties of Mixtures. Int. J. Thermophys., 2005, 739-747. DDB is also available online at http://www.ddbst.com/ddb.html. [25]

McGreer, D. E.; Page, B. D. cis-Crotonaldehyde and Related Compounds. Can. J. Chem., 1969, 47, 866-867. [26] UNIFAC is an estimation method based upon group contributions. Several UNIFAC models are available in Aspen Plus V8.8. In the present study, since mainly approximate estimations are required, the base UNIFAC model has been used. Fredenslund, Aa.; Gmehling, J.; and Rasmussen, P. VaporLiquid Equilibria Using UNIFAC, A group-Contribution Method, 3rd Impression, Elsevier, Amsterdam, 1977. [27] Parker, B. Data measured in Eli Lilly Corporate Center Laboratory, August, 2016. [28] Kil, T. A.; Zadorskii, V. M. Liquid-Vapor Equilibrium for the Crotonaldehyde + Water System. Khim. Khim. Tekhnol., 1969, 217-21. [29] Mkrtchyan, R. V.; Tatevosyan, A. V.; Barsegyan, V. L.; Khachatryan, S. S.; Karamyan, D. R.; Voskanyan, P. S. Rectification of Vinyl Acetate. Prom-st Arm., 1977, 38-39. [30] Rudakovskaya, T. S.; Kondrateva, L. G.; Barmintseva, E. M.; Timofeev, V. S. Phase Equilibria in System Involving Crotonaldehyde. Fiz.-Khim. Osn. Rektifikatsii, 1970, 180-191, Lvov, Ed., MITKhT: Moscow [31] Stephenson, R. M. Mutual Solubility of Water and Aldehydes. J. Chem. Eng. Data, 1993, 38, 630-633. [32] Pratt, H. R. C. Continuous Purification and Azeotropic Dehydration of Acetonitrile Produced by the Catalytic Acetic Acid-Ammonia Reaction. Trans. Inst. Chem. Eng., 1947, 25, 43-68 [33] Maslan, F. D.; Stoddard, E. A. J. Acetonitrile + Water Liquid-Vapor Equilibrium. Phys. Chem., 1956, 60, 1146-1147. Acetonitrile (ACN) Purification, I&EC Research, September 2017 29 ACS Paragon Plus Environment


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[34] Blackford, D. S.; York, R. J. Vapor-Liquid Equilibria of the System Acrylonitrile-AcetonitrileWater. Chem. Eng. Data, 1965, 10, 313318. [35] Volpicelli, G. Liquid-Vapor and Liquid-Liquid Equilibriums of Acrylonitrile with Acetonitrile and Water. Chim. Ind. (Milan, Italy), 1967, 49, 720-730 [36] Sada, E.; Ohno, T.; Kito, S. Salt Effect in Vapour-Liquid Equilibrium for Acetonitrile + Water System. Kagaku Kogaku, 1971, 35, 372-5 [37] Han, S. Studies on VLE of Acrylontrile-Acetonitrile-Water System. Huaxue Gongcheng, 1980, 3, 22-44. [38] Acosta, J.; Arce, A.; Rodil, E.; Soto, A. A Thermodynamic Study on Binary and Ternary Mixtures of Acetonitrile, Water and Butyl Acetate. Fluid Phase Equilib., 2002, 203, 83-98. [39] Liu, H.; Cui, X.; Zhang, Y.; Feng, T.; Yang, Z. Isobaric Vapor–Liquid Equilibrium of Ethanenitrile + Water + 1,2-Ethanediol + 1-Ethyl-3-methylimidazoliumchloride. Fluid Phase Equilib, 2014, 378, 13-20. [40] Chirico, R. D.; Frenkel M.; Diky, V.; Marsh, K. N.; Wilhoit R. C. ThermoML - An XML-Based Approach for Storage and Exchange of Experimental and Critically Evaluated Thermophysical and Thermochemical Property Data. 2. Uncertainties. J. Chem. Eng. Data, 2003, 48, 1344-1359. [41] Qureshi M.S.; Uusi-Kyyny P.; Richon D.; Nikiforow K.; Alopaeus V. Measurement of Activity Coefficient at Infinite Dilution for Some Bio-oil Components in Water and Mass Transfer Study of Bubbles in the Dilutor. Fluid Phase Equilib., 2015, 392, 1-11. [42] Abramowitz, M.; Stegun, I. A. Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables; Dover Publications, Inc., New York, 1964. [43] Note that a total condenser does not function as a distillation stage since no fractionation occurs (see Figure 5 and Figure 10). However, it is counted as a stage in Aspen Plus, and this convention has been retained.


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