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Apr 26, 2018 - Stripping crystallization (SC) was used to purify styrene (ST) from a liquid mixture of ST and ethylbenzene (EB). This new separation t...
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Cite This: Ind. Eng. Chem. Res. 2018, 57, 6759−6765

Purification of Styrene from a Styrene/Ethylbenzene Mixture by Stripping Crystallization Lie-Ding Shiau* Department of Chemical and Materials Engineering, Chang Gung University, Taoyuan, Taiwan R.O.C. Department of Urology, Chang Gung Memorial Hospital, Linkou, Taiwan R.O.C. ABSTRACT: Stripping crystallization (SC) was used to purify styrene (ST) from a liquid mixture of ST and ethylbenzene (EB). This new separation technology combines vaporization and crystallization to yield a crystalline product and a vaporous mixture from a liquid feed via three-phase equilibrium transformations. The three-phase equilibrium conditions for a liquid mixture determined by the thermodynamic calculations were adopted to direct the SC experiments. A unique apparatus was designed for SC experiments at low temperatures and pressures for a series of three-phase equilibrium conditions (from −33 °C and 9.0 Pa to −80 °C and 0.03 Pa). The experiments indicate that SC can be applied to the purification of ST from a liquid mixture of ST and EB with an initial ST concentration of 0.80−0.95.

1. INTRODUCTION Styrene (ST) is among the most important aromatic compounds; it is used extensively in the manufacture of polystyrene. The separation of ST from ethylbenzene (EB) is encountered during ST production via the catalytic dehydrogenation of EB. Because their boiling points are similar and because ST tends to polymerize quickly, it is rather complicated and energy-intensive to separate the two by conventional distillation.1 Alternative separation techniques such as membrane permeation,2−5 extractive distillation,6,7 adsorption to nanoporous materials,8,9 and extraction using the ionic liquids10 have been proposed in the literature. A new separation technology, stripping crystallization (SC), has been successfully developed to separate the mixed xylenes with similar boiling points.11−13 In principle, SC is performed at a triple-point condition where the liquid mixture is simultaneously vaporized and crystallized as a condition of the threephase equilibrium. Thus, at completion, the liquid mixture becomes a crystalline form of the major component after the vapor is condensed and removed. Unlike the solid−liquid equilibrium used in melt crystallization,14−23 SC uniquely requires no solid/liquid separation and no crystal washing, since no mother liquor is present with the crystals upon completion. The objective of this work was to investigate its feasibility in purifying ST from a liquid mixture of ST and EB.

Figure 1. Solid−liquid and vapor−liquid phase diagrams of styrene (ST, A component) and ethylbenzene (EB, B component) at normal pressure.

ST crystals can be produced when the temperature is between −100 °C and −30.6 °C when 0.16 < XA < 1. Note that Tm,A =

2. SC MODEL Figure 1 illustrates the solid−liquid and vapor−liquid phase diagrams of ST (A-component) and EB (B-component) at normal pressure. The eutectic point for the solid−liquid phase diagram lies where T = −100 °C and XA = 0.16, implying that © 2018 American Chemical Society

Received: Revised: Accepted: Published: 6759

February April 16, April 26, April 26,

7, 2018 2018 2018 2018 DOI: 10.1021/acs.iecr.8b00647 Ind. Eng. Chem. Res. 2018, 57, 6759−6765

Article

Industrial & Engineering Chemistry Research −30.6 °C. Generally, as pressure is reduced, the solid−liquid equilibrium temperature remains nearly constant, but the vapor−liquid equilibrium temperature decreases. Thus, for a given XA within the range, as pressure decreases, the solid− liquid equilibrium temperature coincides with the vapor−liquid equilibrium temperature, leading to a three-phase equilibrium that yields pure ST crystals and liquid and vapor phases of the remaining mixture. The SC process was simulated in a series of N equilibrium stage operations, as shown in Figure 2. Each stage was

(XA )n + (XB)n = 1

(4)

(YA )n + (YB)n = 1

(5)

Because the three-phase equilibrium transformation occurs in each stage, eqs 1−5 were simultaneously solved to determine the three-phase equilibrium condition in each stage. By definition, the phase rule is24−26 F=C+2−π

(6)

where F is degree of freedom, C is number of the component, and π is the number of phases. For the binary ST/EB liquid mixture, F = 1 because C = 2 and π = 3 at three-phase equilibrium. Therefore, if Tn is specified in each stage, eqs 1−5 constitute a set of equations that can be simultaneously solved for five unknown variables, Pn, (XA)n, (XB)n, (YA)n, and (YB)n for n = 1, 2, ..., N. Figure 3 shows P(T), XA(T), and YA(T) solved using eqs 1−5 to determine the three-phase equilibrium conditions for

Figure 2. Simulated SC operation where each stage is operated at a three-phase equilibrium condition.

simulated under three-phase equilibrium conditions, requiring that several equations be satisfied. As the three-phase equilibrium is reached in each stage n, the solid−liquid equilibrium between the ST crystals and the liquid mixture is described by the van’t Hoff equation24−26 ln(XA )n (γA )n =

ΔHm ,A ⎛ 1 1⎞ ⎜⎜ − ⎟⎟ R ⎝ Tm,A Tn ⎠

(1)

where ΔHm,A = 1.10 × 107 J/mol and Tm,A = −30.6 °C.27 Certain physical properties of ST and EB are shown in Table 1. Table 1. Certain Physical Properties of Styrene and Ethylbenzene1,27 property

styrene

ethylbenzene

molecular weight boiling point, °C melting point, °C triple point pressure, Pa (N/m2) heat of melting, J/mol heat of vaporization, J/mol

104.2 145.2 −30.6 10.6 1.10 × 107 4.71 × 107

106.2 136.2 −95.0 4.01 × 10−3 9.18 × 106 4.78 × 107

Figure 3. Three-phase equilibrium conditions for purifying ST from a liquid mixture of ST and EB.

the purification of ST from a liquid mixture of ST and EB. Thus, as the equilibrium temperature decreases, the corresponding pressure, P(T), and the corresponding liquid composition of ST, XA(T), decreases. Similarly, Figure 3 reveals that, as the fraction of ST in the mixture decreases, the corresponding temperature and pressure for the three-phase equilibrium decreases. As shown in Figure 2, the three-phase equilibrium transformation occurs in the liquid in each stage, leading to ST crystal formation amid vapors from the mixture and the remaining liquid phase. Sn and Ln represent the amount of crystalline ST and liquid mixture, respectively, remaining in stage n, and Vn represents the amount of vapor formed and removed in stage n. As the vapor formed in each stage is removed, the crystals and the liquid formed enter the next stage. The amount of liquid decreases, and the amount of the crystals increases; therefore, L0 > L1 > L2 > ... > LN, and S0 < S1 < S2 < ... < SN. In Figure 2, Sn−1 + Ln−1 represents the ST crystals and liquid entering stage n while Sn + Ln represents the

Additionally, the vapor−liquid equilibrium is described by24−26 (YA )n Pn = (XA )n (γA )n (PAsat)n

(2)

(XB)n (γB)n (PBsat)n

(3)

(YB)n Pn =

(PAsat)n

(PBsat)n

where and are the temperature-dependent saturated pressures in stage n for ST and EB, respectively.27 As shown in Table 1, three-phase equilibrium occurs at −30.6 °C and 10.6 Pa for pure ST. When XB < 1, the equilibrium temperature should be below −30.6 °C, and the pressure should be below 10.6 Pa. At low pressure, the assumption of ideal gases introduces little error. Aucejo et al.28 found that at 5 and 15 kPa, this binary mixture exhibits very few deviations from ideal behavior, and no azeotrope exists. For simplicity, an ideal liquid solution is assumed (i.e., (γA)n = 1 and (γB)n = 1, given that the structures of ST and EB are similar). Therefore, 6760

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Industrial & Engineering Chemistry Research ST crystals and liquid leaving stage n. The entire material balance in stage n is described by Sn − 1 + Ln − 1 = Sn + Ln + Vn

(7)

Because Vn−1 represents the vapor formed in stage n − 1 that is subsequently removed, it is not part of the equation for stage n. It is assumed that pure ST crystals are formed at each stage without EB as an impurity and that EB exists only in the liquid and vapor phases. In stage n, the material balance for EB is described by Ln − 1(XW,B)n − 1 = Ln(XW,B)n + Vn(YW,B)n

where (YW,B)n =

(XW,B)n = (YB)n MB . (YA )n MA + (YB)n MB

(XB)n MB (XA )n MA + (XB)n MB

(8)

and

Notably, (XW,B)n and (YW,B)n can

Figure 4. Schematic diagram of the experimental apparatus for SC with the features: (1) magnetic-driven motor, (2) rotating scraper, (3) sample container, (4) sample, (5) coolant jacket, (6) insulation wall, (7) turbo molecular pump, (8) mechanical pump, (9) thermocouple, (10) pressure gauge, (11) transparent cover, and (12) liquid nitrogen.

be calculated directly from (XB)n and (YB)n by simultaneously solving eqs 1−5. The three-phase equilibrium transformation was seen to occur in the liquid very quickly in each stage, thus forming ST crystals, vapors, and the remaining liquid. Therefore, in each stage, the melting heat released upon forming ST crystals from the liquid was assumed to be quickly removed by the vaporization of some portion of the liquid. Therefore, in stage n, (Sn − Sn − 1)ΔHm,A = (Ln − 1 − Ln)ΔHV,A

based on Figure 3. Thus, a series of three-phase equilibrium transformations occurred in the liquid feed, leading to ST crystal formation amid vapors from the mixture and the remaining liquid. The experiments were ended when vaporization was no longer observed in the chamber. Upon completion, the ST crystals and the remaining liquid in the sample container were weighed, and the latter was analyzed by gas chromatography. A batch experiment was performed based on Figure 4 and is illustrated in Figure 5. Each stage corresponded to a threephase equilibrium condition at a given time, tn, during the batch experiment. The liquid mixture was injected into the sample container at t = 0. Once the initial three-phase equilibrium condition (T1, P1) was reached for the initial liquid feed at t1, the three-phase equilibrium transformation occurred in the liquid, leading to the formation of ST crystals, vapor, and the remaining liquid. A new three-phase equilibrium condition (T2, P2) was then reached for the remaining liquid at t2, and the three-phase equilibrium transformation occurred again in the remaining liquid. Subsequently, a series of three-phase equilibrium transformations occurred in the liquid feed at 0 < t < tf. At the conclusion of the batch experiment (tf), only the produced crystals and the remaining liquid could be found in the sample container. Thus, a batch experiment performed based on Figure 4 is consistent with the scheme illustrated in Figure 2, where the vapor formed in each stage was removed, and the produced crystals and remaining liquid in the sample container in each stage entered the next stage.

(9)

where Sn − Sn−1 represents the amount of ST crystals formed from the liquid in stage n, and Ln−1 − Ln represent the amount of the liquid vaporized in stage n. For simplicity, the heat of vaporization for the liquid mixture is assumed to be close to ΔHV,A because ΔHV,A ≅ ΔHV,B, as shown in Table 1. If the feed is a liquid mixture only, L0, with a known (Xw,B)0, enters the first stage in Figure 2, leading to S0 = 0. Equations 7−9 constitute a set of equations that can be solved simultaneously for three unknown variables, S1, L1, and V1. Subsequently, Sn, Ln, and Vn can be solved for n = 2, 3, ..., N using a similar approach. Because SN and LN represent the final amount of crystalline ST and the remaining liquid, respectively, upon completion, the total amount vapor formed and removed is ∑Nn=1Vn.

3. EXPERIMENTAL SECTION The experimental assembly consists of a sample container in a large chamber as shown in Figure 4. The entire chamber was fitted with a cooling jacket in which liquid nitrogen was injected to lower the chamber temperature. A mechanical vacuum pump and turbo molecular pump were used in series to lower the pressure in the chamber. A temperature probe was positioned at the center of the liquid feed, and a pressure gauge was connected to the chamber. Thus, the operating temperature and pressure could be adjusted mid-experiment. Crystallization and vaporization of the liquid sample during the three-phase transformation were observed in the chamber via transparent cover. At the beginning of each experiment, 50 g of liquid feed mixture with a known composition, (XA)0, prepared by mixing ST (Acros, > 99% purity) and EB (Tedia, > 99.7% purity), was injected into the sample container. Because liquid nitrogen was used to cool the jacket, the temperature of the liquid feed decreased gradually over time. Generally, the cooling rate began at 0.4 °C/min and gradually slowed in later stages. As temperature decreased, pressure was adjusted downward

4. RESULTS AND DISCUSSION In this work, ST was purified from a 50 g binary liquid mixture of ST and EB. The fraction of ST was (XW,A)0 = 0.95 for Feed 1, (XW,A)0 = 0.90 for Feed 2, (XW,A)0 = 0.85 for Feed 3, and (XW,A)0 = 0.80 for Feed 4. The temperature was determined using eq 1, for example, T0 = −33 °C for Feed 1. As shown in Table 2, Tn was specified in each stage by Tn−1 − Tn = ΔT and ΔT = 2 °C. Then, Pn, (XA)n, (XB)n, (YA)n, and (YB)n were determined in each stage by simultaneously solving eqs 1−5 for the three-phase equilibrium conditions. Subsequently, Sn, Ln, and Vn were determined in each stage by simultaneously solving eqs 7−9 for L0 = 50 g and S0 = 0. Results are shown in Table 2. Thus, the batch experiments for Feed 1 were performed based 6761

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Industrial & Engineering Chemistry Research

Figure 5. Schematic diagram of a batch experiment, where each stage corresponds to a three-phase equilibrium condition at a given time: at t = 0, only a liquid mixture feed in the sample container; at 0 < t < tf, the three-phase equilibrium of ST crystals, vapors of the mixture, and remaining liquid; at tf, only ST crystals in the sample container.

Table 2. Results Based on the Thermodynamic Calculations for 50 g of Feed 1 with (XW,A)0 = 0.95 (T0 = −33 °C, ΔT = 2 °C)

Table 5. Results Based on the Thermodynamic Calculations for 50 g of Feed 4 with (XW,A)0 = 0.80 (T0 = −40 °C, ΔT = 8 °C)

n

T (°C)

P (Pa)

XA (−)

YA (−)

L (g)

S (g)

V (g)

n

T (°C)

P (Pa)

XA (−)

YA (−)

L (g)

S (g)

V (g)

0 1 2 3 4

−33 −35 −37 −39 −41

8.93 7.60 6.40 5.33 5.33

0.949 0.908 0.866 0.826 0.787

0.880 0.811 0.745 0.680 0.619

50 13.3 6.28 3.48 0.60

0 29.4 34.9 36.9 38.2

0 7.27 1.60 0.78 1.57

0 1 2 3 4 5

−40 −48 −56 −64 −72 −80

4.67 2.13 0.89 0.35 0.12 0.03

0.797 0.666 0.536 0.433 0.347 0.275

0.644 0.446 0.315 0.218 0.151 0.102

50 21.1 11.8 7.69 5.22 3.49

0 22.1 28.7 31.2 32.4 33.1

0 6.79 2.74 1.59 1.22 1.04

on the corresponding T and P in each stage shown in Table 2, where the final T and P were at N = 4, determined when vaporization was no longer observed. It should be noted in Table 2 that, as T decreased during an experiment, the corresponding P and XA for three-phase equilibrium decreased. Similarly, Tables 3−5 list the calculated results for three different feeds. These experiments were stopped when

vaporization was no longer observed, which was 60 min for Feed 1, 130 min for Feed 2, 190 min for Feed 3, and 250 min for Feed 4. As shown in Tables 2−5, no vaporization was observed from −33 °C and 8.9 Pa to −41 °C and 5.3 Pa within 60 min for Feed 1. This was also the case from −40 °C and 4.7 Pa to −80 °C and 0.03 Pa for 250 min for Feed 4. Thus, lower values for T and P were required with longer experimental times when (XW,A)0 was lower. For each feed, when the T and P values for the three-phase equilibrium (Tables 2−5) were reached for the first stage, the transformation occurred very quickly, a phenomenon consistent with the assumption developed for eq 9. Therefore, eqs 1−5 and eqs 7−9, developed based on the scheme in Figure 2, can be adopted to study three-phase equilibrium transformations for the batch experiments performed in Figure 4. The experimental recovery ratio of ST is defined as

Table 3. Results Based on the Thermodynamic Calculations for 50 g of Feed 2 with (XW,A)0 = 0.90 (T0 = −35 °C, ΔT = 4 °C) n

T (°C)

P (Pa)

XA (−)

YA (−)

L (g)

S (g)

V (g)

0 1 2 3 4 5

−35 −39 −43 −47 −51 −55

7.20 4.93 3.33 2.27 1.47 0.93

0.890 0.820 0.744 0.673 0.607 0.546

0.810 0.680 0.562 0.467 0.393 0.329

50 18.3 9.94 6.14 3.95 2.50

0 25.0 31.2 33.9 35.2 36.0

0 6.72 2.08 1.19 0.86 0.70

RE =

Table 4. Results Based on the Thermodynamic Calculations for 50 g of Feed 3 with (XW,A)0 = 0.85 (T0 = −38 °C, ΔT = 6 °C) n

T (°C)

P (Pa)

XA (−)

YA (−)

L (g)

S (g)

V (g)

0 1 2 3 4 5 6

−38 −44 −50 −56 −62 −68 −74

5.87 3.33 1.73 0.91 0.44 0.20 0.09

0.848 0.737 0.633 0.541 0.460 0.390 0.330

0.710 0.536 0.407 0.315 0.239 0.180 0.137

50 19.5 10.9 6.90 4.53 2.95 1.82

0 23.7 29.9 32.5 33.8 34.5 34.9

0 6.83 2.34 1.44 1.06 0.86 0.73

Wf (X w,A )f L0(X w,A )0

(10)

where L0 is the initial weight of the mixed liquid feed, (Xw,A)0 denotes the initial purity of ST in the feed, Wf refers to the final weight of the product, including the crystals and the remaining liquid obtained at the end of the experiment, and (Xw,A)f represents the experimental purity of the postexperimental ST. As shown in Tables 2−5, some liquid remained with the crystals at the end of each calculation. The calculated purity of ST in the final product, including the final crystals and the remaining liquid, is defined as XW,A = 6762

SN + L N(X w,A )N SN + LN

(11) DOI: 10.1021/acs.iecr.8b00647 Ind. Eng. Chem. Res. 2018, 57, 6759−6765

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Industrial & Engineering Chemistry Research The calculated recovery ratio of ST is defined as RC =

SN + LN (X w,A )N L0(X w,A )0

(12)

where SN, LN, and (Xw,A)N denote the crystal, liquid, and weight fraction of ST in the final stage based on the thermodynamic calculations. For example, Feed 1 yielded SN = 38.2 g, LN = 0.6 g, and (XW,A)N = 0.78 in the last stage (N = 4), leading to XW,A = 0.997 and RC = 81% using eqs 11 and 12. Figures 6 and 7 show the calculated final product purity plotted against final operating temperature, XW,A(T). The

Figure 7. Comparison of experimental and calculated results for Feed 3 with (XW,A)0 = 0.85 and Feed 4 with (XW,A)0 = 0.80 (○ represents the initial purity for Feed 3, ⊗ represents the calculated final purity for Feed 3, and ● represents the experimental final purity for Feed 3; □ represents the initial purity for Feed 4, square with cross represents the calculated final purity for Feed 4, and ■ represents the experimental final purity for feed 4; and the number in the parentheses next to each data point represents the recovery ratio).

thermodynamic calculations suggest that Feed 4 can yield XW,A = 0.931 and RC = 85% performing SC from −40 °C and 4.7 Pa to −80 °C and 0.03 Pa. Two batch experiments yielded XW,A = 0.916−0.922 and RE = 66−69%. Final experimental purities were generally slightly lower than those predicted using the thermodynamic calculations, and RE is slightly lower than RC . Discrepancies between calculated and experimental results are attributed to (a) the assumption in the thermodynamic calculations that each stage is operated at the three-phase equilibrium; however, experimentally, this might not always be achieved; (b) liquid inclusion might occur during crystal growth experimentally; (c) some amount of liquid might not have been removed from the crystals when experiments were ended; and (d) the current three-phase equilibrium conditions are calculated based on the thermodynamic data at normal temperature and pressure, which might cause deviations in determination of the actual three-phase equilibrium conditions; if more reliable thermodynamic data at low temperatures and pressures are available, more accurate three-phase equilibrium conditions can be determined in the thermodynamic calculations to reduce discrepancies between calculated and experimental results.

Figure 6. Comparison of experimental and calculated results for Feed 1 with (XW,A)0 = 0.95 and Feed 2 with (XW,A)0 = 0.90 (○ represents the initial purity for Feed 1, ⊗ represents the calculated final purity for Feed 1, and ● represents the experimental final purity for Feed 1; □ represents the initial purity for Feed 2, square with cross represents the calculated final purity for Feed 2, and ■ represents the experimental final purity for Feed 2; and the number in the parentheses next to each data point represents the recovery ratio).

starting point for each curve represents feed purity and initial SC operating temperature; the ending point represents the calculated product purity and final SC operating temperature. The number in the parentheses next to the ending point of each curve represents RC. Also shown in Figures 6 and 7 are comparisons with experimental results. Each data point represents the experimental final purity of the product versus the final operating temperature for a given batch experiment as well as the operating pressure P(T) for the three-phase equilibrium. As shown in Figure 6, the thermodynamic calculations suggest that Feed 1 can yield XW,A = 0.997 and RC = 81% performing SC from −33 °C and 8.9 Pa to −41 °C and 5.3 Pa. Two batch experiments yielded XW,A = 0.970−0.976 and RE = 71−74%. The thermodynamic calculations suggest that Feed 2 can yield XW,A = 0.97 and RC = 83% performing SC from −35 °C and 7.2 Pa to −55 °C and 0.93 Pa. Two batch experiments yielded XW,A = 0.951−0.961 and RE = 71−73%. As shown in Figure 7, the thermodynamic calculations suggest that Feed 3 can yield XW,A = 0.967 and RC = 83% performing SC from −38 °C and 5.9 Pa to −74 °C and 0.09 Pa. Two batch experiments yielded XW,A = 0.945−0.953 and RE = 66−70%. The

5. CONCLUSIONS SC was successfully used to purify ST from a liquid mixture of ST and EB. The three-phase equilibrium conditions for the liquid mixture determined by the thermodynamic calculations are adopted to direct the SC experiments. Based on the thermodynamic calculations, a series of three-phase equilibrium conditions were achieved in SC experiments by lowering the temperature and pressure of the liquid mixture initially containing ST at a concentration of 0.80−0.95, leading to the formation of ST crystals, vapors of the mixture, and remaining 6763

DOI: 10.1021/acs.iecr.8b00647 Ind. Eng. Chem. Res. 2018, 57, 6759−6765

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Industrial & Engineering Chemistry Research Xi = mole fraction of component i in dimensionless Xw,i = weight fraction of component i in dimensionless Yi = mole fraction of component i in dimensionless Yw,i = weight fraction of component i in dimensionless

liquid. A unique apparatus was designed for SC experiments, and it was operated at low temperature and pressure for a series of three-phase equilibrium conditions (from −33 °C and 9.0 Pa to −80 °C and 0.03 Pa). Experimental results indicate that when the initial ST concentration was lower, the final temperature and pressure had to be lower, and operating time had to be longer for purification. Experimental purity of ST ranged from 0.916 to 0.976, and the recovery ratio was 66% to 74%. Both are slightly lower than predicted by the thermodynamic calculations. The major concern for the SC operation is a portion of ST is lost through the vapor stream of each stage. To minimize the loss of ST in the vapor, the vaporized mixture can be recycled for continuous operation or mixed with the feed in next batch for batch operation. Because no chemicals need to be added, SC is a clean separation technology. In essence, it can be continued until the liquid phase is completely eliminated, and only pure crystals remain. Compared to conventional crystallization, neither a solid/liquid separation nor crystal washing is required because no mother liquor adheres to the crystal surfaces upon completion. Therefore, SC is a potential method for purifying ST from a liquid mixture of ST and EB. In spite of the advantages of SC described above, the major difficulty for industrial operation lies in the costly requirements of SC operated under the extremely low temperatures and pressures. It is the current research task in our laboratory to improve the recovery ratio and the final purity of ST without the extremely operating conditions.

■

liquid phase, liquid phase, vapor phase, vapor phase,

Greek letters

γi = activity coefficient of component i in liquid phase, dimensionless Subscript

■

0 = in the feed n = in stage n f = in the final stage

REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*(Tel.) 011-886-3-2118800, ext. 5291; (fax) 011-886-32118700; (e-mail) [email protected]. ORCID

Lie-Ding Shiau: 0000-0002-2959-8523 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author would like to thank Chang Gung Memorial Hospital (CMRPD2F0081) and Ministry of Science and Technology of Taiwan (MOST103-2221-E-182-067-MY3) for financial support of this research. The author also expresses his gratitude to Tze-Chi Liu and Keng-Fu Liu for their experimental work.

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NOTATION ΔHm,i = heat of melting for component i (>0), J/mol ΔHV,i = heat of vaporization for component i (>0), J/mol Ln = mass of the liquid phase out of stage n, g Mi = molecular weight of component i, g/mol P = pressure, Pa Psat i = saturated pressure for the liquid of component i, Pa R = ideal gas constant, 8.314 J/(mol K) RC = calculated recovery ratio, dimensionless RE = experimental recovery ratio, dimensionless Sn = mass of the solid phase out of stage n, g T = temperature, K Teu = eutectic temperature, K Tm,i = melting temperature of component i, K Ttri,i = triple-point temperature of component i, K Vn = mass of the vapor phase out of stage n, g 6764

DOI: 10.1021/acs.iecr.8b00647 Ind. Eng. Chem. Res. 2018, 57, 6759−6765

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DOI: 10.1021/acs.iecr.8b00647 Ind. Eng. Chem. Res. 2018, 57, 6759−6765