A New Test System for Distillation Efficiency Experiments at Elevated

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

A New Test System for Distillation Efficiency Experiments at Elevated Liquid Viscosities: Vapor−Liquid Equilibrium and Liquid Viscosity Data for Cyclopentanol + Cyclohexanol Raj Ganesh Manivannan,† Sayeed Mohammad,† Ken McCarley,‡ Tony Cai,‡ and Clint Aichele*,† †

School of Chemical Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, United States Fractionation Research Incorporated, Stillwater, Oklahoma 74074, United States

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‡

ABSTRACT: Most of the distillation efficiency correlations that have been published thus far were developed or validated based on efficiency data at liquid viscosities less than 1 mPa·s. However, distillation with liquid viscosities greater than 1 mPa·s is encountered, in certain cases, in the chemical process industry. To study the effect of liquid viscosity on distillation efficiency at greater than 1 mPa·s, standardized test systems with elevated liquid viscosities at typical distillation conditions are required. To meet this objective, a new test system, cyclopentanol/ cyclohexanol, was chosen on the basis of a comprehensive set of search criteria. For this test system, vapor−liquid equilibrium data were collected from 2 to 101.3 kPa and modeled with the nonrandom two-liquid (NRTL) model. In addition, liquid viscosity data were measured from 303.15 to 373.15 K and modeled with the modified forms of the Andrade equations, in order to precisely represent the nonlinear dependence of liquid viscosity with temperature and composition. This test system will help study the effect of liquid viscosity on distillation efficiency from 1 to 5 mPa·s. Subsequent investigations on the effect of liquid viscosity on separation efficiency of distillation columns with trays are enabled. from polymeric solutions,14 distillation of products with suspended solids14 in food and pharmaceutical industries, mass transfer in viscous crude oil,15 separations involving ionic liquids,15 and vacuum distillation of bio-oil to obtain biofuels.16 To be able to accurately quantify the effect of liquid viscosity on distillation efficiency at greater than 1 mPa·s and to develop improved distillation efficiency correlations, distillation efficiency data at liquid viscosities greater than 1 mPa·s are required. This can be achieved only if we have standardized test systems with elevated liquid viscosities at typical distillation conditions. Researchers in the past have used glycerol/water to study the effect of liquid viscosity on separation efficiency, for absorption applications.17,18 However, the relative volatility (α) of glycerol/ water system is high, which will lead to a large variation in α over the height of the distillation column, and result in inaccuracies associated with the averaging of α required in the theoretical stage calculations using the Fenske equation.19 Böcker and Ronge20 used chlorobenzene/ethylbenzene with polybutadiene in different concentrations, and conducted distillation experiments to study the effect of viscosity on packed column efficiency. Bradtmöller and Scholl21 noted that the accumulation of a nonvolatile component (polybutadiene) added at the vapor−liquid interface would have increased the mass transfer resistance, and might have had an effect on the column

1. INTRODUCTION Distillation is the most widely used separation method in the chemical process industry with over 40 000 columns operating worldwide.1 The first step in designing a distillation column is the calculation of the number of theoretical stages. With the availability of rigorous models incorporated in the computeraided design packages, the theoretical stage calculation can be readily accomplished.2 The next step is to calculate the number of actual stages with the use of the distillation efficiency correlations. The accuracy of distillation efficiency correlations is an important factor in the design of distillation columns. An underprediction of distillation efficiency will lead to over design of columns which will result in an increase in capital cost. On the other hand, overprediction of efficiency will lead to under design of the columns with which the desired capacity and product purity may not be achieved. The variables that influence distillation efficiency can be classified into two main categories, the properties of the liquid mixture, and mechanical design of the column internals.3 One of the most important physical properties that influences distillation efficiency is liquid viscosity.3 This is mainly due to the strong inverse relationship between liquid diffusivity and viscosity.4,5 Most of the distillation efficiency correlations that have been published thus far were developed or validated based on efficiency data at liquid viscosities less than 1 mPa·s (1 mPa·s = 1 cP).3,6−13 However, distillation with liquid viscosities greater than 1 mPa·s is encountered, in certain cases, in the chemical process industry. Some examples are separations of monomers © XXXX American Chemical Society

Received: October 15, 2018 Accepted: December 18, 2018

A

DOI: 10.1021/acs.jced.8b00929 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Chemical Purity Specificationsa lot purity

NBP (before purification)

NBP (after purification)

component

source

mole fraction

T/K

T/K

NBP (NIST) T/K

cyclopentanol cyclohexanol cyclohexane n-heptane

Acros Organics Alfa Aesar Alfa Aesar VWR

0.998 0.998 0.999 0.996

412.96 433.55 353.82 370.97

413.38 433.73

413.53 433.93 353.85 371.51

a

Analysis method, gas chromatography; purification method, distillation; NBP, normal boiling point.

Figure 1. VLE apparatus used in this work: Fischer Labodest VLE 602. The diagram was obtained from Iludest, the manufacturer of this unit, and it is used here with permission.

The pressure was measured using an absolute pressure sensor with a resolution of 0.01 kPa and a standard uncertainty of 0.012 kPa. A buffer vessel was used in the connection between the VLE apparatus and vacuum pump to increase the vapor volume so that the pressure fluctuations were minimized. The temperature was measured using a Pt-100 RTD with a resolution of 0.01 K and a standard uncertainty of 0.06 K. The experiments were isobaric. The operating procedure was based on the principle of the circulation method. A part of the liquid mixture was evaporated by an electrical immersion heater installed in the glass apparatus. The heater was covered with quartz glass surface. Since nucleation can be a problem, especially at deep vacuum and low temperature operations, the immersion heater had an antibumping surface finish. This helps avoid superheating of the boiling liquid and improves the accuracy of the data collection. The rising vapor carried a small number of liquid droplets, and there was a very intensive phase exchange in a capillary contact tube, called a Cottrell-pump. The vapor- liquid mixture was then separated into liquid and vapor in a separation chamber. The design of the separation chamber prevented the transport of liquid in the vapor phase, which was condensed in a separate condenser. Equilibrium was reached by constant recycling of the liquid phase, condensed vapor phase, and the mixing of recirculated flows in the mixing chamber. Equilibrium was confirmed by the constant value of vapor temperature for more than an hour. Once the experiment reached equilibrium, condensed vapor and liquid samples were taken. The corresponding equilibrium vapor temperature was also recorded. The collected liquid and condensed vapor samples were analyzed using a SRI 310 gas chromatograph (GC). The GC was used with a thermal conductivity detector and a Restek MXT1 capillary column of 0.53 mm inner diameter and 5 μm film

performance. In addition, they noted that, with the use of a polymer, the influence of local viscosity versus bulk viscosity on the change of mass transfer should have been considered.22,23 Onken and Artl24 have summarized the properties of the standard test systems for distillation. However, it does not include a test mixture that will have liquid viscosities above 1.5 mPa·s at typical distillation conditions.21 Recently, Bratmöller and Scholl,21 proposed a new test mixture, 2-methyl-2-butanol/2-methly-1-propanol (MB/MP), which can have liquid viscosities from 0.5 to 4 mPa·s by operating the distillation columns from 2 to 95 kPa (1 kPa = 0.01 bar).21,25 Although this is a useful test system, additional test systems are necessary for extending the upper limit of liquid viscosity and for decoupling the effect of liquid viscosity and relative volatility from surface tension. In this work, a comprehensive search was conducted and a new test system, cyclopentanol/cyclohexanol (CP/CH), was selected. To accurately analyze the data obtained from distillation efficiency experiments, the quantification of vapor− liquid equilibrium (VLE) and liquid viscosity data are necessary. Therefore, VLE and liquid viscosity data were measured for this new test system. The results, along with the methodology used for data collection and modeling, are presented in the following sections.

2. EXPERIMENTAL SECTION 2.1. Chemicals. The sources and purity specifications of the chemicals are shown in Table 1. 2.2. Experimental Setup. Vapor−liquid equilibrium data were measured using a Fischer Labodest VLE 602 apparatus manufactured by Iludest GmbH, Germany. The details of the apparatus are shown in Figure 1. B



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thickness. Helium was used as the carrier gas. The accuracy of the GC composition measurements was checked using cyclopentanol/cyclohexanol standard samples prepared gravimetrically. The absolute errors were within a mole fraction of 0.002. Each of the liquid and condensed vapor samples from the vapor−liquid equilibrium experiments were analyzed twice, and the average values are presented in this paper. As per the NIST guidelines for uncertainty calculations,26 the standard deviation of the mean was calculated for each composition measurement in mole fraction and the maximum value was reported as the standard uncertainty in composition measurements, u(x1) = u(y1) = 0.003. For the measurement of liquid viscosity, a Discovery Hybrid Rheometer (DHR-3 Rheometer) with Peltier temperature control and double concentric cylinder geometry was used. The temperature and viscosity were measured with a standard uncertainty of 0.1 K and 0.08 mPa·s, respectively. 2.3. Apparatus Validation. The VLE apparatus was validated by collecting binary VLE data for cyclohexane/nheptane (C6/C7) at 101.3 kPa and comparison with the published literature data. The VLE data set27 that had passed the most number of thermodynamic consistency tests for C6/C7 at 101.3 kPa was chosen from NIST TDE. The binary VLE data comparison for C6/C7 at 101.3 kPa is shown in Figure 2. The

Table 2. Parameters for SRK Method parametera

value

std. dev.

k12 = k21 Pc,1 Pc,2 Tc,1 Tc,2 ω1 ω2

−0.00154 4080 2740 553.8 540.2 0.208 0.349

0.00043

units kPa kPa K K

a

Subscripts 1 and 2 in Table 2 denote cyclohexane and n-heptane, respectively.

Table 3. Experimental and Calculated VLE Data for Cyclohexane + n-Heptanea P/kPa

Texpt/K

x1,expt

y1,expt

Tcalc/K

y1,calc

101.3 101.3 101.3 101.3 101.3 101.3 101.3 101.3 101.3 101.3 101.3

370.97 368.67 365.55 363.57 362.17 360.95 359.69 357.05 355.78 355.19 353.82

0 0.1192 0.2507 0.3498 0.418 0.515 0.5993 0.7535 0.8469 0.8804 1

0 0.1879 0.3711 0.4798 0.5543 0.634 0.7181 0.8263 0.9009 0.9236 1

371.59 368.68 365.77 363.78 362.50 360.79 359.41 357.12 355.86 355.43 353.97

0 0.1889 0.3644 0.4781 0.5488 0.6403 0.7127 0.8315 0.8974 0.9203 1

a

Standard uncertainties for pressure, temperature, and composition are u(P) = 0.01 kPa, u(T) = 0.01 K, and u(x1) = u(y1) = 0.003. The composition values are in mole fraction.

distillation column efficiency. To be able to use the Fenske equation, a binary test system has to obey certain rules.19,21,30 Therefore, those rules were considered, in addition to the requirements imposed by the experiments for quantifying the effect of liquid viscosity on distillation efficiency using lab-scale glass columns, to form the following comprehensive set of search criteria. 1. The system must be surface tension neutral. Zuiderwig31 classified the binary mixtures into positive, negative, and neutral test systems, based on the difference in surface tensions of the pure components in a mixture, at their boiling points. A component is said to be surface tension neutral, if the difference in surface tensions of the pure components in a mixture at their boiling points is less than 2 mN·m−1. These neutral test systems will not have a significant effect due to surface tension gradient on separation efficiency.32 Positive systems are those in which the high boiling component has a higher surface tension than the low boiling component, and the reflux increases in surface tension from top to bottom of the column. Positive systems enhance the interfacial area in the froth regime and increase the separation efficiency.33 Negative systems are those in which the low boiling component has a higher surface tension than the high boiling component, and the reflux decreases in surface tension from top to bottom of the column. Negative systems enhance the interfacial area in the spray regime and increase the separation efficiency.33 Therefore, both surface tension positive and negative systems must be avoided for quantifying the effect of liquid viscosity on distillation efficiency.

Figure 2. VLE data comparison for C6/C7 at 101.3 kPa

Soave−Redlich−Kwong (SRK) model28 was regressed using Aspen Plus V9 with the chosen literature data set for C6/C7 and the predictions are also shown in Figure 2. The binary interaction parameter (kij) obtained upon regression along with the critical properties (Pc, Tc) and acentric factors (ω) used in the model are given in Table 2. The average absolute deviations (AAD) for the predictions were 0.05% and 0.76% for temperature and composition, respectively. The VLE data collected in this work and the calculated temperature and vapor composition values for C6/C7 at 101.3 kPa are presented in Table 3.

3. RESULTS AND DISCUSSION 3.1. Selection of a New Viscous Test System. A comprehensive set of search criteria was used to come up with a test system that will be helpful in quantifying the effect of liquid viscosity on distillation efficiency at greater than 1 mPa·s. Often, distillation efficiency experiments are carried out at total reflux,29 and the Fenske equation19 is used for the calculation of C



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2. The change in surface tension of the mixture with temperature must be minimal (less than 20%) over the range of operating conditions, in order to decouple the effect of liquid viscosity from surface tension on distillation efficiency. 3. The relative volatility (α) should not be too high; α in the range of 1.1 to 3 is desired. A high value of α will lead to a large variation in α over the column height. Therefore, averaging of α required in the Fenske equation becomes less accurate. Further, a higher α value means an easier separation. Therefore, only a few theoretical stages can be used for efficiency experiments, which makes the distillation efficiency measurements less accurate. 4. VLE of the test system must be close to ideal. This ensures a nearly constant value of α over the column height. 5. The system must have elevated liquid viscosities (greater than 1 mPa·s) at boiling temperatures. Unlike absorption, distillation experiments are carried out at saturation temperatures. Therefore, it is important to ensure that the test system shows liquid viscosities greater than 1 mPa·s at the boiling temperatures corresponding to P ≥ 2 kPa. 6. Boiling temperatures must be in the range of 303.15 to 453.15 K at 2 kPa ≤ P ≤ 101.3 kPa to enable lab-scale efficiency experiments using glass columns. 7. The test system must show a Newtonian flow behavior in order to avoid the rheological complexities involved with non-Newtonian fluids. 8. The system must be completely miscible over the entire range of composition and boiling temperatures. 9. Racemic systems must be avoided. 10. The system must be available at a high purity (≥99%) and reasonable price. 3.2. Pure Component Vapor Pressures. As described earlier in section 2.2, the vapor pressure and VLE data were measured using the Fischer Labodest VLE 602 apparatus. Since there was a large amount of pure component vapor pressure data available for cyclopentanol and cyclohexanol in the literature, the regressed parameters for the NIST Wagner liquid vapor pressure equation were readily available in NIST TDE (TDE version 10.0 and database version 10.2). Equation 1 was used for predicting the vapor pressure in Aspen Plus V9. The regressed parameters for eq 1 are given in Table 4. The experimental vapor

Table 5. Vapor Pressure Data for Cyclopentanol and Cyclohexanola

C1 C2 C3 C4 ln Pc Tc Tlower Tupper

cyclohexanol

−9.33592 7.148 −13.7301 4.26186 15.4079 619.459 255.6 619.459

−10.406 10.0838 −16.1197 3.0664 15.275 647.1 298.136 647.1

Pv,expt/kPa

326.43 355.30 370.27 398.02 413.38

2 10 20 60 101.3

341.68 372.00 387.67 417.16 433.73

2 10 20 60 101.3

((Pv,expt − Pv,calc)/Pv,expt)100

Pv,calc/kPa Cyclopentanol 2.043 9.891 19.802 59.732 100.881 Cyclohexanol 2.058 10.011 19.902 59.711 100.777

−2.14 1.09 0.99 0.45 0.43 −2.90 −0.11 0.49 0.48 0.54

a Standard uncertainties for pressure and temperature are u(P) = 0.01 kPa and u(T) = 0.01 K.

cyclopentanol and cyclohexanol. This is also indicative of the capability of the VLE apparatus used in this work to accurately measure binary phase equilibrium data. A comparison of the relative error values in vapor pressure predictions using eq 1 for the data from this work and the literature data34−36 are shown in Figure 3a,b. ln(Pv /Pa) = ln Pc/Pa +

C1(1 − Tr) + C 2(1 − Tr)1.5 + C3(1 − Tr)2.5 + C4(1 − Tr)5 Tr

(1) T , Pv = vapor pressure in Pa, Tc

for Tlower ≤ T ≤ Tupper, where Tr = Pc = critical pressure in Pa, T = temperature in K, Tc = critical temperature in K, Tr = reduced temperature, C1, C2, C3, C4 = model parameters, Tlower, Tupper = applicable lower and upper temperature limits of the correlation, respectively. 3.3. Vapor−Liquid Equilibrium: Data and Modeling. VLE data (T−x−y) were measured isobarically at four different pressures from 2 to 101.3 kPa. This pressure range was chosen as lab-scale glass distillation columns are often limited to conducting experiments in this range. Further, to achieve elevated liquid viscosities, the distillation columns need to be operated at low temperatures. Low operating temperatures are achieved by conducting the experiments at vacuum pressures. The lower limit for pressure was set to 2 kPa, as operating the distillation columns below 2 kPa is not a standard case.21 In addition, sampling becomes extremely difficult at P < 2 kPa. The experimental VLE data collected in this work are shown in Table 6. The vapor phase was assumed to exhibit ideal behavior due to low pressures, and the activity coefficients (γ1, γ2) shown in Table 6 were calculated using eq 2. yP γi = i xiPv (2)

Table 4. Parameters for NIST Wagner Vapor Pressure Equation cyclopentanol

Texpt/K

where P = total pressure in Pa, xi, yi = mole fractions of component i in liquid and vapor phases, respectively, Pv = vapor pressure in Pa, calculated using eq 1. The values of relative volatility, α, shown in Table 6, were calculated using eq 3. γ Pv,1 α= 1 γ2Pv,2 (3)

pressure data collected in this work, along with the calculated values using eq 1, are presented in Table 5. The small relative error values in Table 5 show that there is a good agreement between the vapor pressure data from this work and the values calculated using the regressed NIST Wagner equation. Therefore, eq 1 along with the parameters reported in Table 4 can be used for the calculation of pure component vapor pressures of D



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Table 6. Experimental VLE Data for Cyclopentanol + Cyclohexanola

Figure 3. (a) Relative error values in vapor pressure for cyclopentanol; (b) relative error values in vapor pressure for cyclohexanol.

where subscripts 1 and 2 denote cyclopentanol and cyclohexanol, respectively. To calculate the values of relative volatility in a distillation experiment, at given values of T, x, and y, it is important to model the VLE data. Therefore, VLE data were modeled using the nonrandom two-liquid (NRTL) model.37 The NRTL model was regressed with the experimental data presented in Table 6, to obtain the binary interaction parameters. The regression was done in Aspen Plus V9 with maximum-likelihood objective function.38 This objective function, given in eq 4, was chosen as it minimizes an error function that contains all measured variables, unlike the least-squares method. In addition, the maximum-likelihood approach takes into account the errors involved in the measured data, by including variances in the objective function. The Britt−Leucke algorithm39 was used with a convergence tolerance of 1 × 10−4.

x1

y1

101.3 101.3 101.3 101.3 101.3 101.3 101.3 101.3 101.3 101.3 101.3 60 60 60 60 60 60 60 60 60 60 60 10 10 10 10 10 10 10 10 10 10 10 2 2 2 2 2 2 2 2 2 2 2

433.73 431.07 428.25 427.42 424.94 422.68 420.85 417.9 416.53 415.47 413.38 417.16 415.22 413.3 410.6 410 406.72 404.45 403.5 401.33 399.86 398.02 372 369.62 367.5 365.22 363.5 362.5 361.19 359.32 358.14 356.74 355.3 341.68 339.45 337.47 335.3 333.5 332.77 331.45 329.65 328.55 327.47 326.43

0.000 0.101 0.207 0.235 0.365 0.452 0.551 0.699 0.792 0.857 1.000 0 0.0794 0.1605 0.2666 0.3073 0.4512 0.5627 0.6371 0.7513 0.8695 1 0 0.1057 0.2041 0.3228 0.4264 0.4994 0.5669 0.6833 0.7625 0.8862 1 0 0.1011 0.1935 0.3189 0.4359 0.4936 0.5765 0.6851 0.7922 0.8452 1

0.000 0.188 0.357 0.389 0.533 0.643 0.726 0.840 0.888 0.924 1.000 0 0.1415 0.283 0.4551 0.4817 0.6526 0.7621 0.8007 0.8843 0.9342 1 0 0.2085 0.3662 0.5153 0.6381 0.6946 0.7576 0.8454 0.8854 0.9382 1 0 0.2199 0.375 0.5347 0.656 0.717 0.7839 0.858 0.9108 0.9293 1

γ1

γ2

α

1.089 1.096 1.076 1.024 1.068 1.046 1.044 1.019 1.013

0.984 0.963 0.974 0.969 0.922 0.917 0.883 0.931 0.955

2.056 2.125 2.066 1.984 2.184 2.158 2.251 2.087 2.027

0.999 1.051 1.112 1.041 1.072 1.085 1.040 1.051 1.011

1.000 0.978 0.935 0.961 0.914 0.853 0.892 0.819 0.938

1.911 2.064 2.298 2.095 2.285 2.490 2.288 2.530 2.131

1.025 1.024 1.010 1.025 0.998 1.019 1.030 1.023 0.998

0.988 0.984 0.988 0.947 0.963 0.943 0.904 0.950 1.149

2.229 2.253 2.230 2.372 2.280 2.388 2.534 2.406

1.002 0.997 0.975 0.970 0.976 0.987 1.011 0.991 1.011

0.962 0.967 0.973 0.971 0.931 0.924 0.916 0.936 1.068

2.506 2.501 2.454 2.468 2.599 2.665 2.777 2.678 2.407

Standard uncertainties for pressure, temperature, and composition are u(P) = 0.01 kPa, u(T) = 0.01 K, and u(x1) = u(y1) = 0.003.

l 2 2 o o ij Pi ,calc − Pi ,expt yz oijj Ti ,calc − Ti ,expt yzz jj zz F = ∑m + j z zz zz o jj ojjk σT σP i=1 o { k { o n

The adjustable parameters obtained upon regression are presented in Table 7. The nonrandomness parameter, αij, was assumed to be equal to 0.3. The NRTL model equations used in the regression are shown below.

2|

o o o } o o o o ~

T/K

a

N

2 ij yi ,calc − yi ,expt yz ij xi ,calc − xi ,expt yz zz j z + jj zz + jjjj zz j z j z σ σ x y k { k {

P/kPa

Table 7. Regressed NRTL Model Parameters for CP/CH from 2 to 101.3 kPa

(4)

where N = number of data points, T = temperature, P = pressure, xi, yi = liquid and vapor mole fractions of component i, respectively, σT, σP, σx, σy = standard deviations in temperature, pressure, liquid, and vapor mole fractions, respectively. E

parameter

value

std. dev.

b12 b21

602.736 −400.482

76.886 33.122



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Figure 4. (a) T−x−y diagram of cyclopentanol + cyclohexanol at 101.3 kPa; (b) T−x−y diagram of cyclopentanol + cyclohexanol at 60 kPa; (c) T−x− y diagram of cyclopentanol + cyclohexanol at 10 kPa; (d) T−x−y diagram of cyclopentanol + cyclohexanol at 2 kPa.

ln γ1 =

ij

2 y i yz G21 τ12G12 zyzzzz zz + jjj z z j z z z j (x + x G )2 zzzz 1 12 {{ k x1 + x 2G21 { k 2

i

j j x 22jjjτ21jjj j j j k

2 ij i i yzyzz yz G12 τ21G21 j j zzzz zz + jjj ln γ2 = x12jjjτ12jjj jj zz jj j x 2 + x1G12 zz (x1 + x 2G21)2 z{zz k { k k {

AAD (%) = (5)

ij bij yz zz τij = jjj j T/K zz k {

(6)

Gij = exp( −αijτij)

(8)

(7)

|Texpt − Tcalc| Texpt

yexpt

100 (10)

The AAD in temperature and composition predictions were 0.05% and 2.66%, respectively. The data were also regressed with the Wilson model in Aspen Plus V9 and the parameters are given in Table 8. 3.4. Thermodynamic Consistency Tests. The thermodynamic consistency of the VLE data sets were checked using the Redlich−Kister test,40 Herington test,41 Van Ness test,42 and end point test. The results of the consistency tests are shown in Table 9. The Redlich−Kister and Herington tests are based on the Gibbs−Duhem (G-D) equation.43 The G-D equation used in these tests is shown in eq 11. Experimental activity coefficients were calculated using eq 2 and modeled using NRTL model eqs 5−8, as suggested by Kurihara et al.44 For isobaric experiments, dP = 0; therefore, the third term in eq 11 is eliminated. The Redlich−Kister test consists of only the first term, and has a criteria of D ≤ 2 for a data set to be thermodynamically consistent. The parameter D was determined using eq 12. Since the experiments were isobaric, all the data sets failed the Redlich−Kister test. This is indicative of the fact that the second term in the G-D equation is significant. Herington41 proposed an approximation, given in eq 13, for the second term in eq 11, and included it in the consistency test using the G-D equation. As shown in Table 9, all the data sets passed the Herington test.

where subscripts 1 and 2 denote cyclopentanol and cyclohexanol, respectively; γ1, γ2 = activity coefficients, x1, x2 = liquid mole fractions, τ12, τ21 = binary interaction parameters, G12, G21 = model parameters, α12 = α21 = nonrandomness parameter = 0.3. Figure 4 panels a−d, show the T−x−y data, along with the predictions using the regressed NRTL model. The comparison between the experimental and calculated temperature and vapor composition values at a given pressure and liquid composition can be seen more evidently in Figures 5a,b. The percentage average absolute deviations (AAD) were calculated using eqs 9 and 10. AAD (%) =

|yexpt − ycalc |

100 (9) F



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where γ1, γ2 = activity coefficients of more and less volatile components, respectively, x1 = mole fraction of more volatile component, Hex = excess enthalpy of mixing, R = gas constant, T = temperature, Vex = excess molar volume, P = pressure, T0, P0 = temperature and pressure when x1 = 0, T1, P1 = temperature and pressure when x1 = 1, A, B = positive and negative areas in ln (γ1/ γ2) vs x1 plot, respectively. D = 100 J=

∫T

T1

o

Table 8. Regressed Wilson Model Parameters for CP/CH from 2 to 101.3 kPa

∫0

value

Std. Dev.

b12 b21

−15.858 16.499

0 7.96

1

ij γ yz lnjjjj 1 zzzz dx1 − k γ2 {

where

∫0

1

∫T

T1

H ex dT + RT 2

∫P

P1

ij γ yz lnjjjj 1 zzzz dx1 = |A| − |B| k γ2 { o

O

(12)

T − Tmin H ex dT = 150 max 2 Tmin RT

(13)

where Tmax, Tmin = maximum and minimum temperatures, respectively, at each pressure. The end point test checks the consistency between the end points of the VLE curve and vapor pressure measurements. Most of the vapor pressure measurements passed the end point test, except the two measurements at 2 kPa and one measurement at 10 kPa. It was reasonable to expect higher relative errors at deep vacuum VLE measurements, as controlling pressure was relatively difficult at deep vacuum, and small deviations in predictions can lead to relatively large errors. The Van Ness point-to-point test42 checks the capability of the regressed model to predict the vapor composition. As shown in Table 9, the regressed NRTL model was predicting the vapor compositions reasonably well, and passed the test at 2 and 10 kPa. Data sets at 0.6 and 1.01 bara failed the Van Ness test, but the absolute deviations were within 2%. Therefore, the regressed NRTL model from this work can be used for VLE predictions of CP/CH from 2 to 101.3 kPa. 3.5. Pure Component and Mixture Liquid Viscosities: Data and Modeling. Liquid viscosities were measured for the pure components and mixtures of the new test system to better quantify the effect of viscosity on distillation efficiency. Liquid viscosities were measured using a Discovery hybrid rheometer with double concentric cylinder geometry, as described earlier in section 2.2. The first step was to check whether the test system followed Newtonian flow behavior. This was done by measuring shear stress, at different values of shear rates. The shear rate was varied from 2 to 100 s−1, and the corresponding shear stress values were recorded. There was a linear relationship between the shear stress and shear rate, which confirmed the Newtonian flow behavior. Pure component and mixture liquid viscosity data were collected for cyclopentanol and cyclohexanol at a shear rate of 50 s−1, from 303.15 to 373.15 K. The experimentally measured liquid viscosity data are presented in Table 10. Liquid viscosity

Figure 5. (a) Parity plot for the temperature predictions using the NRTL model; (b) parity plot for the composition predictions using the NRTL model.

parameter

||A| − |B|| |A | + |B |

V ex dP = 0 RT

(11)

Table 9. Results of Thermodynamic Consistency Tests Redlich−Kister P/kPa

D/%

Herington

end point

|D − J|

2

10.12

3.17

10

11.21

4.27

60

9.63

2.41

101.3

8.23

0.83

pass criteria

D ≤ 2%

|D − J| < 10

(|Pexpt − Pcalc|/Pexpt)100 CH: 2.90 CP: 2.14 CH: 0.11 CP: 1.09 CH: 0.48 CP: 0.45 CH: 0.54 CP: 0.43 (|Pexpt − Pcalc|/Pexpt)100 < 1 G

Van Ness |ycalc − yexpt|100 0.71 0.76 2.00 1.28 |ycalc − yexpt|100 < 1 DOI: 10.1021/acs.jced.8b00929 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 10. Pure Component and Mixture Liquid Viscosity Data for Cyclopentanol (CP) and Cyclohexanol (CH)a liquid viscosity μ/mPa·s T/K 303.15 308.15 313.15 318.16 323.16 328.15 333.16 338.16 343.16 348.16 353.16 358.16 363.16 368.17 373.15

x1 = 0

x1 = 0.1

x1 = 0.3

x1 = 0.5

x1 = 0.7

x1 = 0.9

x1 = 1

33.66 25.52 19.50 15.04 11.84 9.48 7.60 6.08 4.98 4.08 3.40 2.86 2.47 2.15

34.92 27.86 21.32 16.48 12.92 10.27 8.26 6.73 5.54 4.61 3.88 3.29 2.81 2.44 2.13

23.18 19.17 15.13 11.96 9.64 7.91 6.48 5.40 4.51 3.85 3.29 2.83 2.46 2.13 1.89

16.54 13.78 11.11 9.04 7.41 6.14 5.14 4.34 3.70 3.17 2.73 2.37 2.08 1.85 1.63

12.51 10.67 8.78 7.20 6.01 5.11 4.28 3.65 3.14 2.75 2.38 2.08 1.84 1.61 1.46

9.20 7.88 6.57 5.49 4.65 3.96 3.39 2.92 2.54 2.23 1.96 1.74 1.55 1.40 1.25

8.20 6.85 5.76 4.87 4.17 3.58 3.08 2.68 2.35 2.07 1.82 1.61 1.43 1.28 1.18

a Viscosity values were measured at P = 102 kPa. Standard uncertainties for pressure, temperature, composition, and liquid viscosity are u(P) = 3 kPa, u(T) = 0.1 K, u(x1) = 0.001, and u(μ) = 0.08 mPa·s. The composition values are in mole fraction.

Mixture liquid viscosity i μ y i μ y i μ y lnjjj m zzz = x1 lnjjj 1 zzz + x 2 lnjjj 2 zzz k Pa·s { k Pa·s { k Pa·s { 2 2 + k12x1x 2 + m12x1 x 2

experiments at greater than 373.15 K started showing oscillations in the viscosity measurements due to the vaporization of the liquid sample and the formation of two phases, as experiments were done at atmospheric pressure. Therefore, liquid viscosity data at greater than 373.15 K are not presented in this paper and were not included in the regression. Equations 14−17 were used to model the nonlinear dependence of viscosity with temperature and composition. These are modified forms of the Andrade liquid viscosity equations which are available in Aspen Plus V9. The Andrade-type equations have been widely used in the literature to model liquid viscosity.45−48 The parameters in eqs 14−17 were regressed with the experimentally measured liquid viscosity data. The regressed parameter values are presented in Table 11.

ij b yz j z k12 = a12 + jjj T12 zzz jj zz k K {

jij d zyz m12 = c12 + jjj T12 zzz jj zz k K {

Ai Bi Ci Ai Bi Ci a12 b12 c12 d12

value Cyclopentanol −69.534 5814.604 7.971 Cyclohexanol −123.321 10000.000 15.260 Mixture 2.769 −931.257 −1.248 262.447

(16)

(17)

where μm = mixture liquid viscosity in Pa·s, T = temperature in K, x1, x2 = liquid mole fractions of cyclopentanol and cyclohexanol, respectively, k12, m12 = model parameters Figure 6 shows a plot of viscosity predictions using eqs 14−17, at boiling temperatures corresponding to P > 2 kPa, along with

Table 11. Regressed Parameters for Equations 14−17 parameter

(15)

std. dev. 6.933 342.675 1.018 0.519 0.000 0.089 0.856 288.596 3.924 1322.618

Pure component liquid viscosity

ij B yz i μ y iT y j z lnjjj i zzz = Ai + jjj Ti zzz + Ci lnjjj zzz j z j z kK { k Pa·s { kK{

(14)

where μi = pure component liquid viscosity for component i in Pa·s; T = temperature in K; Ai, Bi, Ci = model parameters.

Figure 6. Experimentally measured and predicted liquid viscosities of cyclopentanol and cyclohexanol at different compositions (mole %) and temperatures. H



Article

conditions. Therefore, this test system can serve as a good candidate to investigate the effect of liquid viscosity on distillation efficiency at liquid viscosities greater than 1 mPa·s.

the experimentally measured data. The average absolute deviations (AAD) in predictions for the range of conditions (T = 303.15 to 373.15 K) shown in Table 10 were 0.48, 1.50, and 1.37%, for pure CP, pure CH, and CP/CH respectively. Therefore, eqs 14−17 can be used along with the regressed parameters presented in Table 11 for calculating the liquid viscosities of pure components and CP/CH mixtures at different compositions and temperatures. To show the composition relationship of mixture viscosity more evidently, the difference (excess viscosity) between the measured mixture viscosity and mixture viscosity calculated using the simple mixing rule and pure component viscosities, was calculated using eq 18 at different temperatures and shown in Figure 7. Figure 7 also includes excess viscosity values

4. CONCLUSIONS A new test system (cyclopentanol/cyclohexanol) was selected based on a comprehensive set of search criteria to quantify the effect of liquid viscosity on distillation efficiency. Vapor−liquid equilibrium data were experimentally measured from 2 to 101.3 kPa and modeled using the nonrandom two-liquid (NRTL) model. Liquid viscosity data were also measured from 303.15 to 373.15 K and modeled using the modified forms of Andrade liquid viscosity equations. The effect of liquid viscosity on distillation efficiency can be accurately quantified from 1 to 5 cP using this newly developed test system, as there are minimal changes in other physical properties, such as surface tension. The efficiency quantification with this test system will provide the possibility of evaluating the validity of existing distillation efficiency correlations at greater than 1 mPa·s, thereby extending the applicability of existing correlations for higher viscosities.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel. No.: 405-744-9110. ORCID

Clint Aichele: 0000-0002-4414-2380 Funding

The authors would like to thank Fractionation Research Inc. (FRI) for funding this work. Notes

The authors declare no competing financial interest.

■ ■

Figure 7. Excess viscosity values for cyclopentanol and cyclohexanol over the full concentration range and at different temperatures.

ACKNOWLEDGMENTS The authors would like to acknowledge Ashwin Kumar Yegya Raman for his help with measuring liquid viscosity data.

calculated over the full composition range and at the corresponding temperatures using eqs 14−17 and 19. Δμexpt = μm ,expt − (x1μ1,expt + x 2μ2,expt )

(18)

Δμcalc = μm ,calc − (x1μ1,calc + x 2μ2,calc )

(19)

Table 12 shows the values of liquid viscosity, relative volatility, and surface tension, at pressure values of 2 and 20 kPa and the Table 12. Physical Property Values for an Equimolar Mixture of CP/CH at 20 and 2 kPa pressure, P/kPa

20

2

boiling temperature, T/K liquid viscosity, μ/mPa·s relative volatility, α surface tension, σ/mN m−1

377.39 1.48 2.23 24.88

332.06 5.4 2.62 29.51

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