VaporâLiquid Equilibria for Water + Propylene Glycols Binary Systems

Article pubs.acs.org/jced

Vapor−Liquid Equilibria for Water + Propylene Glycols Binary Systems: Experimental Data and Regression Elena M. Fendu* and Florin Oprea Petroleum Processing and Environmental Engineering Department, Petroleum−Gas University, Bd. Bucureşti, 39 No., 100680, Ploieşti, Romania ABSTRACT: The vapor−liquid equilibria (VLE) data are essential for the design of distillation columns to separate propylene glycols mixtures, obtained via the hydrolysis of 1,2-epoxy propane. In this study there are reported data for four binary systems involved, such as water + propylene glycols. VLE data have been measured in the temperature range (295.15 to 460.15) K and pressure up to 34.529 kPa for the following binary systems: water +1,2-propanediol (monopropylene glycol, MPG), water +1-(2-hydroxypropoxy)propan-2-ol (dipropylene glycol, DPG), water +2-[2-(2-hydroxypropoxy)propoxy]propan1-ol (tripropylene glycol, TPG), and water +2-(2-[2-(2-hydroxypropoxy)propoxy]propoxy)propan-1-ol (tetrapropylene glycol, TePG). The equipment used was a static apparatus built in our laboratory. The only literature data available for these systems were for the water + MPG binary system. The experimental data obtained were correlated with the NRTL model. The results showed a fairly good agreement between the model and the experimental data with a maximum deviation in composition terms of 3%.

1. INTRODUCTION The propylene glycols mixture, obtained by the hydrolysis of 1,2-epoxy propane, contains water + 1,2-propanediol (monopropylene glycol, further abbreviated as MPG) + 1-(2hydroxypropoxy)propan-2-ol preponderant in mixtures isomers (dipropylene glycol, further abbreviated as DPG) + 2-[2-(2hydroxypropoxy)propoxy]propan-1-ol preponderant in mixtures isomers (tripropylene glycol, further abbreviated as TPG) + 2-(2[2-(2-hydroxypropoxy)propoxy]propoxy)propan-1-ol preponderant in mixtures isomers (tetrapropylene glycol, further abbreviated as TePG) and poly(propylene glycol). Propylene glycols have several applications, including use as detergents, antimicrobials, preservatives, antifreeze, as functional fluids, paints, plasticizers, in textile industry, for obtaining unsaturated polyester resins, cosmetics, pharmaceuticals, humectants, and dehydrating agents.1 For an advantageous separation of this mixture, using distillation columns, in terms of purity of components and operating conditions, we are elaborating a new industrial process.2 The synthesis and simulation of this process requires good thermodynamic models. We can obtain parameters of these models by using accurate vapor−liquid equilibrium experimental data for the binary systems implicated, water + propylene glycols and between propylene glycols.3 This paper presents the vapor−liquid equilibria (VLE) data for the binary systems water + MPG, water + DPG, water + TPG, and water + TePG in the temperature range (295.15 to 460.15) K and pressure up to 34.529 kPa. The VLE experimental data were determined at low pressures because the separation process proposed by us can operate only in these conditions. The only literature data available for these systems were for the mixture water + MPG.4 The VLE data were measured by using an © 2014 American Chemical Society

equilibrium apparatus, built in our laboratory, described in our previous work.3 The experimental data were regressed with PRO/II simulation software to obtain binary parameters for the nonrandom two-liquid (NRTL) activity coefficient model.4,5 In the simulation software database TePG was missing. For this reason we defined TePG as a new component by using the physical (vapor pressure and liquid density) and transport (liquid dynamic viscosity and surface tension) properties of TePG that were presented in our previous work.3

2. EXPERIMENTAL SECTION 2.1. Materials. Tetrapropylene glycol used for the experimental determination was separated in our laboratory from a sample of higher propylene glycols available from Dow Chemical Company. 3 The mono-, di- and tripropylene glycol as commercial products, having high purity, were used without further purification; distilled water was used throughout all experiments. The specifications of all propylene glycols that were used are presented in Table 1. The pressure was measured using a DPI 705 sensor with the measuring range between 0 and 0.35·105 Pa and the temperature was measured with VWR International, LLC, NIST traceable digital thermometers (± 0.05 % accuracy and 0.001 K resolution). 2.2. Apparatus and Procedure. The vapor−liquid equilibria experimental data of all binary systems in this study were realized using an equilibrium apparatus built in our Received: October 8, 2013 Accepted: February 14, 2014 Published: February 21, 2014 792

dx.doi.org/10.1021/je4009014 | J. Chem. Eng. Data 2014, 59, 792−801

Journal of Chemical & Engineering Data

Article

Table 1. Specifications of the Chemicals Used in Experimental Determinations

a

chemical name

source

initial mass fraction purity

purification method

final mass fraction purity

analysis method

monopropylene glycol dipropylene glycol tripropylene glycol tetrapropylene glycol

S.C. Oltchim S.A. Dow Chemical Dow Chemical Dow Chemical

0.9993 0.9989 0.9993 0.7551

none none none distillation

0.994

GCa

Gas−liquid chromatography.

Table 2. Experimental VLE Data for Temperature T, Pressure p with Standard Uncertainty u(p), and Mole Fraction x1 for the System Water (1) + Monopropylene Glycol (2)a T/K

a

p/kPa

u(p)/kPa

T/K

345.15 347.15 350.15 353.15 355.15

0.617 0.699 0.840 1.005 1.131

0.003 0.004 0.002 0.030 0.007

357.15 360.15 363.15 365.15 367.15

347.15 350.15 353.15 355.15

11.271 12.925 14.745 15.998

0.024 0.037 0.037 0.029

357.15 360.15 363.15 365.15

330.15 333.15 335.15 337.15

9.318 10.697 11.712 12.813

0.066 0.058 0.052 0.024

340.15 343.15 345.15 347.15

323.15 325.15 327.15 330.15

9.025 9.986 11.020 12.661

0.022 0.012 0.014 0.042

333.15 335.15 337.15 340.15

323.15 325.15 327.15 330.15

11.092 12.300 13.581 15.578

0.020 0.038 0.012 0.008

333.15 335.15 337.15 340.15

317.15 320.15 323.15 325.15

9.114 10.627 12.352 13.630

0.012 0.011 0.027 0.033

327.15 330.15 333.15 335.15

p/kPa x1 = 0.0000 1.270 1.506 1.781 1.987 2.214 x1 = 0.2710 17.208 19.141 21.614 23.607 x1 = 0.5030 14.690 16.873 18.472 20.206 x1 = 0.7012 14.530 15.909 17.466 20.026 x1 = 0.9018 17.704 19.422 21.614 24.873 x1 = 1.0000 15.020 17.332 19.940 21.859

u(p)/kPa

T/K

p/kPa

u(p)/kPa

0.019 0.029 0.032 0.070 0.012

370.15 373.15 375.15 377.15

2.596 3.034 3.361 3.718

0.010 0.019 0.010 0.003

0.062 0.029 0.012 0.046

367.15 370.15 373.15 375.15

25.383 28.064 31.259 33.619

0.060 0.059 0.039 0.022

0.058 0.036 0.031 0.027

350.15 353.15 355.15 360.15

22.916 25.779 27.876 34.149

0.039 0.049 0.041 0.036

0.070 0.013 0.027 0.025

343.15 345.15 347.15 350.15

22.888 24.977 27.234 30.963

0.046 0.021 0.055 0.027

0.011 0.012 0.020 0.014

343.15 345.15 347.15

28.318 30.853 33.518

0.024 0.028 0.032

0.021 0.024 0.044 0.022

337.15 340.15 343.15 345.15

23.932 27.354 31.181 33.976

0.025 0.024 0.021 0.022

Standard uncertainties u are u(T) = 0.01 K and u(x) = 0.0002.

U shaped tube did not vary. When the pressure of the system did not change for 30 min (it was then that the equilibrium state was considered attained) air was introduced/removed in/from the system until the level of liquid in the tube was the same in the two branches and the vapor pressure was measured.3 The final step was to determine the concentration of water in the sample using coulometric Karl Fischer titration with a Cou-Lo Aquamax KF Moisture Meter apparatus which had a precision of ±5 μg for sample between 1 μg to 1 mg. The sample for this analysis was taken exactly at the end of the experiment using the glass syringe. Three analyses were performed for each sample and the average value was considered as corresponding to the equilibrium. The values of water concentration in the mixtures determined with this analysis, performed at the end of the experiment, were consistent with the values determined by weight at the start of the

laboratory. The construction and operation of this static apparatus were described in detail in our previous work, in which the the vapor pressure of a pure component was determined.3 The experiments for measuring VLE data for the binary mixtures water + propylene glycols at a certain temperature were performed using the following procedure. The first step was to prepare the mixtures at laboratory conditions (101.3 kPa, 293.15 K) by mass6,7 using a Mettler Toledo AB204-S electronic balance accurate to 0.0001 g. The mixture sample of about 30 mL was introduced in the equilibrium cell and was cooled near the liquid nitrogen temperature and then was degassed with a vacuum pump. The equilibrium cell and the U-shaped tube were placed in a thermostatic oil bath, where the desired temperature was maintained within ± 0.05 K.3 In the next step the bath was maintained at that temperature, until the level of the manometric liquid in the two branches of the 793



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Table 3. Experimental VLE Data for Temperature T, Pressure p with Standard Uncertainty u(p), and Mole Fraction x1 for the System Water (1) + Dipropylene Glycol (2)a T/K

a

p/kPa

u(p)/kPa

T/K

365.15 367.15 370.15 373.15 375.15

0.406 0.453 0.532 0.623 0.692

0.006 0.006 0.006 0.008 0.013

377.15 380.15 383.15 385.15 387.15

335.15 340.15 345.15 350.15 355.15

4.015 4.925 5.995 7.248 8.706

0.012 0.008 0.007 0.014 0.016

360.15 365.15 370.15 375.15 380.15

330.15 333.15 335.15 337.15 340.15 343.15

5.821 6.603 7.150 7.716 8.603 9.536

0.015 0.017 0.021 0.016 0.016 0.022

345.15 350.15 352.15 355.15 358.15 360.15

320.15 323.15 325.15 327.15 330.15

5.971 6.915 7.594 8.348 9.555

0.016 0.013 0.016 0.017 0.016

333.15 335.15 337.15 340.15 345.15

317.15 320.15 323.15 325.15 327.15

6.915 8.108 9.466 10.432 11.468

0.015 0.015 0.016 0.019 0.019

330.15 333.15 335.15 337.15 340.15

327.15 330.15 333.15

13.6245 15.8299 18.2676

0.016 0.017 0.021

335.15 337.15 340.15

325.15 327.15 330.15

13.6300 15.0204 17.3320

0.012 0.015 0.021

333.15 335.15 337.15

p/kPa x1 = 0.0000 0.767 0.894 1.039 1.146 1.264 x1 = 0.1706 10.397 12.347 14.589 17.155 20.083 x1 = 0.3005 10.355 12.592 13.838 15.434 17.185 18.444 x1 = 0.5142 10.876 11.847 12.913 14.658 18.279 x1 = 0.7226 13.166 15.020 16.396 17.928 20.461 x1 = 0.9006 20.038 21.953 25.073 x1 = 1.0000 19.940 21.859 23.932

u(p)/kPa

T/K

p/kPa

u(p)/kPa

0.008 0.006 0.008 0.011 0.011

390.15 393.15 397.15

1.461 1.684 2.029

0.012 0.013 0.019

0.019 0.018 0.019 0.016 0.016

385.15 390.15 395.15

23.414 27.189 31.456

0.013 0.014 0.031

0.021 0.014 0.017 0.018 0.019 0.018

362.15 365.15 367.15 373.15 375.15

19.781 21.942 23.136 28.031 30.115

0.019 0.020 0.019 0.017 0.027

0.019 0.016 0.014 0.017 0.015

350.15 353.15 355.15

22.457 25.164 27.248

0.023 0.018 0.015

0.013 0.015 0.017 0.018 0.018

343.15 345.15 347.15

23.456 25.667 28.079

0.018 0.020 0.015

0.021 0.022 0.021

343.15 345.15 347.15

28.606 31.174 33.960

0.019 0.017 0.027

0.017 0.022 0.019

340.15 343.15 345.15

27.354 31.181 33.976

0.020 0.016 0.034


Table 2. The equilibrium data are known for this binary system.5 We made these measurements in order to compare the results with those from literature. In Tables 3, 4, and 5 are presented the p−T−x experimental VLE data and the standard uncertainties u(p) for the systems water + DPG in the temperature range (317.15 to 397.15.15) K, water + TPG in the temperature range (303.15 to 405.15) K, and water + TePG in the temperature range (295.15 to 460.15) K. For these three binary systems there are no data reported in the literature. The NRTL5 model was used to correlate the experimental results. This model is readily generalized to multicomponent mixtures without additional parameters.9 Experimental data correlation was carried out using PRO/II simulation software with default objective function (eq 1), number of iterations at 50, and tolerance of 0.000001.4 The objective function (S) represent the minimization of the sum of squares for the relative deviations.

experiment. This shows that the initial composition did not change by the degassing procedure. This procedure was repeated at least three times for each composition of each binary mixture. The ELV experimental data for water + MPG, water + DPG, water + TPG, and water + TePG were obtained in the temperature range (295.15 to 460.15) K and pressures up to 34.529 kPa for different compositions of binary mixtures but also for the pure component involved. The standard uncertainties8 for temperature and concentrations of water expressed as mole fraction were ± 0.01 K and ± 0.0002, respectively. We measured the vapor pressure three times for each value of concentration and temperature, and we reported the average value and the standard uncertainty8 for each average value.

3. RESULTS AND DISCUSSION The VLE experimental data for the binary system water + MPG for temperatures from (317.15 to 377.15) K are presented in 794



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Table 4. Experimental VLE Data for Temperature T, Pressure p with Standard Uncertainty u(p), and Mole Fraction x1 for the System Water (1) + Tripropylene Glycol (2)a

a

T/K

p/kPa

u(p)/kPa

T/K

x1 = 0.0000 340.15 350.15 355.15 360.15 370.15

0.019 0.040 0.055 0.076 0.141

0.001 0.002 0.003 0.003 0.003

375.15 377.15 380.15 385.15 390.15

330.15 335.15 340.15 345.15 350.15

3.066 3.889 4.893 6.110 7.573

0.010 0.008 0.008 0.011 0.010

355.15 360.15 365.15 370.15 375.15

310.15 313.15 315.15 317.15 320.17 323.15 325.15

1.474 1.776 1.927 2.136 2.542 3.006 3.331

0.006 0.010 0.014 0.014 0.010 0.010 0.012

327.15 330.15 333.15 335.15 337.15 340.15 350.15

310.15 313.15 315.15 317.15 320.15 323.15 325.15

3.160 3.749 4.176 4.643 5.405 6.217 6.806

0.004 0.002 0.002 0.001 0.003 0.003 0.006

327.15 330.15 333.15 335.15 337.15 340.15 343.15

303.15 305.15 307.15 310.15 313.15 315.15 317.15

3.080 3.461 3.863 4.560 5.343 5.985 6.649

0.006 0.005 0.002 0.002 0.002 0.003 0.003

320.15 323.15 325.15 327.15 330.15 333.15 335.15

307.15 310.15 313.15 315.15 317.15 320.15

4.690 5.604 6.649 7.411 8.271 9.674

0.002 0.012 0.012 0.012 0.012 0.013

323.15 325.15 327.15 330.15 333.15 335.15

305.15 307.15 310.15 313.15 315.15 317.15

4.761 5.326 6.284 7.386 8.211 9.114

0.001 0.002 0.013 0.013 0.014 0.015

320.15 323.15 325.15 327.15 330.15 333.15

p/kPa 0.189 0.212 0.251 0.330 0.430 x1 = 0.1753 9.322 11.399 13.852 16.731 20.092 x1 = 0.2365 3.656 4.202 4.806 5.235 5.688 6.684 10.189 x1 = 0.5006 7.477 8.574 9.935 11.072 12.190 13.896 15.866 x1 = 0.7020 7.792 9.065 10.023 11.078 12.819 14.767 16.247 x1 = 0.9001 11.263 12.460 13.799 15.997 18.456 20.274 x1 = 1.0000 10.627 12.352 13.630 15.020 17.332 19.940

u(p)/kPa

T/K

p/kPa

u(p)/kPa

0.003 0.006 0.005 0.003 0.004

395.15 400.15 405.15

0.556 0.714 0.909

0.003 0.003 0.005

0.016 0.017 0.018 0.017 0.018

380.15 385.15 390.15

23.997 28.510 33.703

0.019 0.018 0.017

0.018 0.011 0.009 0.017 0.010 0.009 0.012

360.15 363.15 370.15 373.15 375.15 377.15 380.15

15.523 17.725 23.192 25.177 26.825 29.054 32.780

0.017 0.019 0.019 0.011 0.018 0.022 0.028

0.003 0.017 0.016 0.013 0.013 0.015 0.013

345.15 347.15 350.15 353.15 357.15 360.15

17.166 18.537 20.934 23.727 28.095 31.442

0.012 0.014 0.014 0.015 0.018 0.029

0.013 0.014 0.019 0.010 0.016 0.016 0.019

337.15 340.15 343.15 345.15 347.15 350.15

17.825 20.393 23.266 25.388 27.597 31.265

0.022 0.030 0.019 0.022 0.029 0.028

0.014 0.018 0.020 0.021 0.023 0.012

337.15 340.15 343.15 345.15 347.15

22.200 25.399 29.044 31.776 34.529

0.019 0.016 0.023 0.023 0.023

0.016 0.018 0.016 0.017 0.023 0.022

335.15 337.15 340.15 343.15 345.15

21.859 23.932 27.354 31.181 33.976

0.015 0.021 0.018 0.029 0.027

Standard uncertainties u are u(T) = 0.01 K and u(x) = 0.0002. 2 ⎛ Picalc ⎞ ⎜ ⎟ S = ∑ ⎜1 − Piexpt ⎟⎠ i=1 ⎝ N

ln γi = (1)

∑j τjiGjixji ∑k Gkixk

+

∑ j

⎛ ∑ xτ G ⎞ ⎜⎜τij − k k kj kj ⎟⎟ ∑k Gkjxk ⎠ ∑k Gkjxk ⎝ xjGij

(2)

The NRTL parameters are presented in eqs 2 to 6 as they are available in the PRO II reference manual.4 The parameters of these equations were obtained by minimizing the objective function.

τij = aij + 795

bij T

+

cij T2

(unit is K)

(3)



Article

Table 5. Experimental VLE Data for Temperature T, Pressure p with Standard Uncertainty u(p), and Mole Fraction x1 for the System Water (1) + Tetrapropylene Glycol (2)a T/K

a

p/kPa

u(p)/kPa

T/K

415.15 420.15 425.15 430.15 435.15

0.022 0.055 0.122 0.235 0.409

0.002 0.002 0.003 0.002 0.005

437.15 440.15 443.15 445.15 450.15

373.15 375.15 377.15 380.15 383.15

7.822 8.347 8.900 9.786 10.744

0.009 0.012 0.011 0.013 0.015

385.15 390.15 393.15 395.15 400.15

330.15 333.15 335.15 337.15 340.15 343.15 345.14 347.15 350.15

4.181 4.669 5.361 5.763 5.995 7.150 7.585 8.064 8.869

0.006 0.007 0.006 0.008 0.010 0.009 0.016 0.018 0.019

353.15 355.15 357.15 360.15 363.15 365.15 367.15 370.15 373.15

323.15 325.15 327.15 330.15 333.15 335.15

5.942 6.442 7.030 7.998 8.891 9.489

0.013 0.014 0.015 0.016 0.015 0.015

340.15 343.15 345.15 347.15 350.15 353.15

295.15 300.15 305.15 310.15 315.15 320.15

1.567 2.187 2.851 3.624 4.658 6.040

0.002 0.004 0.006 0.004 0.007 0.012

325.15 327.15 330.15 333.15 335.15 340.15

300.15 305.15 307.15 310.15 313.15 315.15

3.272 4.399 4.917 5.801 6.817 7.589

0.002 0.004 0.004 0.014 0.013 0.013

320.15 325.15 327.15 330.15 333.15 335.15

300.15 305.15 307.15 310.15 313.15 315.15

3.569 4.761 5.326 6.284 7.386 8.211

0.003 0.003 0.013 0.013 0.014 0.016

320.15 325.15 327.15 330.15 333.15 335.15

p/kPa x1 = 0.0000 0.498 0.653 0.836 0.972 1.366 x1 = 0.1422 11.425 13.281 14.509 15.378 17.737 x1 = 0.2992 9.794 10.49 11.328 12.863 14.375 15.344 16.280 17.716 19.327 x1 = 0.4976 11.448 13.004 14.201 15.496 17.509 19.534 x1 = 0.5934 7.858 8.383 9.324 10.62 11.53 14.69 x1 = 0.9104 9.782 12.596 13.906 16.181 18.690 20.518 x1 = 1.0000 10.627 13.630 15.020 17.332 19.940 21.859

u(p)/kPa

T/K

p/kPa

u(p)/kPa

0.003 0.003 0.002 0.002 0.003

455.15 457.15 460.15

1.835 2.043 2.377

0.006 0.004 0.008

0.013 0.019 0.019 0.011 0.015

405.15 410.15 415.15

20.384 23.345 26.648

0.016 0.014 0.012

0.019 0.012 0.016 0.019 0.013 0.018 0.011 0.015 0.015

375.15 377.15 380.15 383.15 385.15 387.15 390.15

20.665 22.232 24.522 27.045 29.053 30.329 33.010

0.020 0.018 0.014 0.026 0.027 0.034 0.034

0.019 0.013 0.013 0.015 0.013 0.017

355.15 357.15 360.15 363.15 365.15 367.15

20.883 22.232 24.343 26.683 28.544 30.688

0.014 0.015 0.016 0.015 0.019 0.028

0.016 0.014 0.014 0.017 0.015 0.016

343.15 345.15 347.15 350.15 353.15 355.15

15.791 17.285 18.482 20.564 23.197 24.672

0.015 0.015 0.012 0.015 0.020 0.014

0.012 0.017 0.013 0.010 0.013 0.015

337.15 340.15 343.15 345.15

22.509 25.059 29.088 31.890

0.015 0.018 0.030 0.032

0.017 0.017 0.010 0.019 0.014 0.018

337.15 340.15 343.15 345.15

23.932 27.354 31.181 33.976

0.016 0.018 0.023 0.027


τij = aij +

bij RT

+

cij 2 2

RT

(unit is kcal or kJ)

The ELV data for the water + MPG system exist in the PRO II database for the NRTL model with three parameters. For this reason the VLE experimental data for the water + MPG system are regressed using the NRTL model only with three parameters. The relative deviations in the liquid phase composition and in the pressure of the calculated data compared with the experimental one in each point are shown in Figures 1 and 2. In Table 6 are presented

(4)

Gij = exp( −αjiτij)

(5)

αji = αji′ + βji′T

(6) 796



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Figure 1. Relative deviations Δp/p = {p(calc) − p(expt)}/p(calc) of the calculated p(calc) with the NRTL model from those determined experimentally p(expt) for the system water (1) + monopropylene glycol (2) at different mole fraction of water x1. ■, x1 = 0.0000; □, x1 = 0.2710; ●, x1 = 0.5030; ○, x1 = 0.7012; ▲, x1 = 0.9018; and △, x1 = 1.0000.

Figure 3. T−x−y diagrams for the system water (1) + monopropylene glycol (2) at various pressures of (a) 5 kPa and (b) 15 kPa: , NRTL equation with parameters resulted from this study; ---, NRTL equation with parameters from PRO II database. Figure 2. Relative deviations Δx1/x1 = {x1(calc) − x1(expt)}/x1(calc) of the calculated x1(calc) with the NRTL model from those determined experimentally x1(expt) for the system water (1) + monopropylene glycol (2) at different mole fraction of water x1. □, x1 = 0.2710; ●, x1 = 0.5030; ○, x1 = 0.7012; and ▲, x1 = 0.9018.

The ELV experimental data for the other three binary systems, water + DPG, water + TPG, and water + TePG, are regressed using the NRTL model with three, five, and eight parameters. Because the regression results using NRTL with three and five parameters were very poor we decided to abandon these results and present only the NRTL with eight parameters. The binary interaction parameters of NRTL model resulting from the regression of experimental data for the three binary systems mentioned above are presented in Table 7. In Figures 4, 5, and 6 there are presented the relative deviations Δp/p between the calculated vapor pressures p(calc) with the NRTL model and those experimentally determined p(expt) at different mole

Table 6. Binary Interaction Parameters of the NRTL Model Existing in PRO II Database and Results by Correlating the Experimental Data for the System Water + MPG NRTL binary interaction parameters

water + MPG from PRO II database

water + MPG this study

bij bji αij′

583.2600 −376.5620 0.2926

221.5988 −97.5501 0.90874

Table 7. Binary Interaction Parameters of the NRTL Model for Three Binaries: Water + DPG, Water + TPG, Water + TePG

the binary interaction parameters of the NRTL model existing in the PRO II database and those results by correlating the experimental data from this study for the system water + MPG. We have calculated and plotted T−x−y curves at two different pressures using the two NRTL models presented for this mixture to compare and also to validate our entire procedure in order to determine vapor−liquid equilibria data for the binary systems involved in this work (Figure 3). From this figure it can be seen that for a constant pressure of 5 and 15 kPa dew point curves are overlapping for the two models and the bubble point curves traced with the two NRTL models show small differences. 797

NRTL binary interaction parameters

water + DPG

water + TPG

water + TePG

aij bij cij aji bji cji α′ij β′ij

−0.64596 55.42093 123404 −0.79661 −40.07079 86262.183 −0.73422 0.00787

0.22794 90.11773 46630.85 0.21153 −19.5187 −22491.6 0.90484 0.00695

−1.7637 −278.359 80719.02 −1.1991 −120.196 145422 −0.37169 0.00938



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Figure 7. Relative deviations Δx1/x1 = {x1(calc) − x1(expt)}/x1(calc) of the calculated x1(calc) with the NRTL model from those determined experimentally x1(expt) for the system water (1) + dipropylene glycol (2) at different mole fractions of water x1. □, x1 = 0.1706; ●, x1 = 0.3005; ○, x1 = 0.5142; ▲, x1 = 0.7226; and △, x1 = 0.9006.

Figure 4. Relative deviations Δp/p = {p(calc) − p(expt)}/p(calc)of the calculated p(calc) with the NRTL model from those determined experimental p(expt) for the system water (1) + dipropylene glycol (2) at different mole fractions of water x1. ■, x1 = 0.0000; □, x1 = 0.1706; ●, x1 = 0.3005; ○, x1 = 0.5142; ▲, x1 = 0.7226; △, x1 = 0.9006; and ◆, x1 = 1.0000.

Figure 5. Relative deviations Δp/p = {p(calc) − p(expt)}/p(calc) of the calculated p(calc) with the NRTL model from those determined experimentally p(expt) for the system water (1) + tripropylene glycol (2) at different mole fractions of water x1. ■, x1 = 0.0000; □, x1 = 0.1753; ●, x1 = 0.2365; ○, x1 = 0.5006; ▲, x1 = 0.7020; △, x1 = 0.9001; and ◆, x1 = 1.0000.

Figure 8. Relative deviations Δx1/x1 = {x1(calc) − x1(expt)}/x1(calc) of the calculated x1(calc) with the NRTL model from those determined experimentally x1(expt) for the system water (1) + tripropylene glycol (2) at different mole fractions of water x1. □, x1 = 0.1753; ●, x1 = 0.2365; ○, x1 = 0.5006; ▲, x1 = 0.7020; and △, x1 = 0.9001.

Figure 6. Relative deviations Δp/p = {p(calc) − p(expt)}/p(calc) of the calculated p(calc) with the NRTL model from those determined experimentally p(expt) for the system water (1) + tetrapropylene glycol (2) at different mole fractions of water x1. ■, x1 = 0.0000; □, x1 = 0.1422; ●, x1 = 0.2992; ○, x1 = 0.4976; ▲, x1 = 0.5934; △, x1 = 0.9104; and ◆, x1 = 1.0000.

Figure 9. Relative deviations Δx1/x1 = {x1(calc) − x1(expt)}/x1(calc) of the calculated x1(calc) with the NRTL model from those determined experimentally x1(expt) for the system water (1) + tetrapropylene glycol (2) at different mole fractions of water x1. □, x1 = 0.1422; ●, x1 = 0.2992; ○, x1 = 0.4976; ▲, x1 = 0.5934; and △, x1 = 0.9104. 798



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Figure 10. T−x−y diagrams for the system water (1) + dipropylene glycol (2) at various pressures of (a) 5 kPa, (b) 15 kPa, and (c) 30 kPa: , NRTL equation with parameters resulted from this study; ---, IDEAL model; ···, UNIFAC model.

Figure 11. T−x−y diagrams for the system water (1) + tripropylene glycol (2) at various pressures of (a) 5 kPa, (b) 15 kPa, and (c) 30 kPa: , NRTL equation with parameters resulted from this study; ---, IDEAL model; ···, UNIFAC model..

fractions of water for the systems water + DPG, water + TPG, and water + TePG, respectively. The highest values for the maximum and the average relative deviation Δp/p were recorded for the water + TePG system, 2.96 % and 1.04 %, respectively. The relative deviations Δx1/x1 of the calculated x1(calc) with the NRTL model from those determined experimentally x1(expt) at different mole fractions of water x1 for the systems water + DPG, water + TPG, and water + TePG, are presented in Figures 7, 8, and 9, respectively. The maximum relative deviation Δx1/x1 between these binary systems is 2.99 % for the water + TePG system. The values of the average relative deviations, in terms of

the concentration in the liquid phase for water in the binary systems, are in the range of (0.34 to 0.72) %. Generally, it can be seen that all these relative deviations have relatively small and acceptable values. For these three binary systems there are no data available in the literature regarding vapor−liquid equilibrium, for this reason we decided to compare the resulting data from this study with data calculated with IDEAL and UNIFAC (UNIquac Functional-group Activity Coefficients) models. We have chosen the IDEAL model for comparison even if the mixtures of real fluids did not form ideal solutions, it have been established that mixtures of similar liquids often exhibit behavior 799



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Figures 10, 11, and 12 show the T−x−y diagrams for the mixtures water + DPG, water + TPG, and water + TePG at three pressure values. These diagrams are useful in engineering practice, because they help the chemical engineers in the analysis of systems’ behavior. The bubble and dew point curves in these figures are traced using the UNIFAC model (dotted line), IDEAL model (dashed line), and NRTL model with parameters’ results from this study (the continuous line). As shown in the T−x−y diagrams, for the liquid phase (bubble point curves) there was an agreement between the NRTL model and IDEAL model, but not with UNIFAC model. The dew point curves traced with the three models were overlapping for the water + DPG and water + TPG binary mixtures. The binary system water + TePG for the vapor phase more sharply deviated from ideal behavior than the two other binary systems presented.

4. CONCLUSIONS Measurements of the vapor−liquid equilibria for the binary systems water + MPG, water + DPG, water + TPG, and water + TePG in the temperature range (295.15 to 460.15) K and pressures up to 34.529 kPa were carried out using a equilibrium apparatus built in our laboratory. The VLE experimental data were correlated with the NRTL model. The small values of the relative deviations for liquid phase composition and for pressure showed a good agreement between experimental and calculated data. The study of water + the MPG system, for which there are data, validated our entire procedure to determine vapor−liquid equilibria data. For the other three binary systems, water + DPG, water + TPG, and water + TePG, for which there are no data in the literature, we compared the results data from the NRTL model based on experimental data with data calculated with IDEAL and UNIFAC models. We concluded that the behavior of the binary systems studied is close to ideal, and that the UNIFAC model does not accurately predict the vapor−liquid equilibrium. The results of our studies encouraged us to extend our work for propylene glycols binary systems to obtain valuable thermodynamic models for vapor−liquid equilibria. The VLE data reported in this study are sufficiently accurate for the design of a new industrial process to separate propylene glycols.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +40244 576 211. Fax: +40244 575847. E-mail: emfendu@ upg-ploiesti.ro. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank Dow Chemical Company for the sample material and Mr. Alexandru Pană, Head of Quality Control Department, S. C. Oltchim S. A. Râmnicu Vâlcea, Romania, for technical assistance.

Figure 12. T−x−y diagrams for the system water (1) + tetrapropylene glycol (2) at various pressures of (a) 5 kPa, (b) 15 kPa, and (c) 30 kPa: , NRTL equation with parameters resulted from this study; ---, IDEAL model; ···, UNIFAC model.

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close to ideality.10 The UNIFAC model is a group contribution model, based on the UNIQUAC (UNIversal QUAsi-Chemical) equation, very widely used to predict vapor−liquid equilibrium systems when experimental data are not available.11,12 We used UNIFAC modified Lyngby model to calculated ELV data for the binary systems involved because the accuracy of this model was improved by incorporating a temperature-dependent form for the binary group energy interaction parameter.4 Researchers at Lyngby developed a three-parameter temperature dependent form for the binary interaction parameter.13

REFERENCES

(1) Martin, A. E.; Murphy, F. H. Glycols Propylene Glycols, 1994. The Dow Chemical Company. http://www.dow.com/PublishedLiterature/ dh_006e/0901b8038006e13c.pdf (accessed Oct 24, 2012). (2) Oprea, F.; Fendu, E. M.; Nicolae M. Separation process of propylene glycols from the mixture obtained at propylene oxide hydrolysis. Romanian Pat. Appl. A/00076, 2013. (3) Fendu, E. M.; Oprea, F. Vapor Pressure, Density, Viscosity, and Surface Tension of Tetrapropylene Glycol. J. Chem. Eng. Data 2013, 58, 2898−2903.

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(4) Simulation Software PRO/II of SimSci-Esscor, version 9.1; Invensys Systems, Inc.: South Lake Forest, CA, 2012. (5) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135−144. (6) Ramsauer, B.; Neueder, R.; Kunz, W. Isobaric vapour−liquid equilibria of binary 1-propoxy-2-propanol mixtures with water and alcohols at reduced pressure. Fluid Phase Equilib. 2008, 272, 84−92. (7) Holguín, A. R.; Rodríguez, G. A.; Cristancho, D. M.; Delgado, D. R.; Martínez, F. Solution thermodynamics of indomethacin in propylene glycol + water mixtures. Fluid Phase Equilib. 2012, 314, 134−139. (8) Taylor, B. N.; Kuyatt, C. E. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results. NISTTechnical Note 1297, 1994 ed.; National Institute of Standards and Technology: Gaithersburg MD, 1994. (9) Prausnitz, J. M.; Tavares, F. W. Thermodynamics of fluid-phase equilibria for standard chemical engineering operations. AIChE J. 2004, 50, 739−761. (10) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; Prentice Hall PTR: NJ, 1999; pp 194−196. (11) Seader, J. D.; Henly, E. J. Separation Process Principles; John Wiley & Sons, Inc.: New York, 1998; pp 79−81. (12) Sheikholeslamzadeh, E.; Rohani, S. Vapour−liquid and vapour− liquid−liquid equilibrium modeling for binary, ternary, and quaternary systems of solvents. Fluid Phase Equilib. 2012, 333, 97−105. (13) Larsen, B. L.; Rasmussen, P.; Fredenslund, A. A modified UNIFAC group contribution model for prediction of phase equilibria and heats of mixing. Ind. Eng. Chem. Res. 1987, 26, 2274−2286.

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VaporâLiquid Equilibria for Water + Propylene Glycols Binary Systems

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