Investigations into the Effects of the Cooling Rate on Stripping

Nov 2, 2012 - indicate that SC can be used to purify both PX from the PX-rich mixture and OX from the .... properties of PX and OX in Table 1 are adop...
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Investigations into the Effects of the Cooling Rate on Stripping Crystallization Lie-Ding Shiau* and Keng-Fu Liu Department of Chemical and Materials Engineering, Chang Gung University, Taoyuan, 33302 Taiwan, Republic of China ABSTRACT: This study investigates how the cooling rate affects the performance of stripping crystallization (SC) for purification of a p-xylene (PX)/o-xylene (OX) mixture to elucidate the rate process of three-phase equilibrium. A thermodynamic model is developed to simulate the three-phase equilibrium conditions during the batch SC operation. Experimental results indicate that SC can be used to purify both PX from the PX-rich mixture and OX from the OX-rich mixture. A slower cooling rate generally gives rise to a longer operating time, leading to a product with a higher purity and lower recovery ratio. We conclude that the three-phase equilibrium can be achieved quickly, even at a cooling rate of 0.50 °C/min. Importantly, the results of this study demonstrate that the proposed thermodynamic model can reliably determine the three-phase equilibrium conditions for the studied system.

1. INTRODUCTION Our laboratory has recently developed a new separation technology, stripping crystallization (SC), also referred to as distillative freezing, to separate mixtures with close boiling temperatures, including mixed xylenes,1−3 diethylbenzene isomers,4 and benzene/cyclohexane mixtures.5 While operated at a triple-point condition, in which the liquid mixture is vaporized and crystallized simultaneously because of three-phase equilibrium, SC combines distillation and crystallization to produce pure crystals by adequate control of the temperature and pressure. Generally, SC can be continued until the liquid phase is eliminated and only pure crystals remain in the final product. Therefore, in contrast to conventional crystallization, filtration or centrifugation is unnecessary to separate the solid crystals from the mother liquor because no mother liquor is present with the pure crystals. Additionally, crystal washing is unnecessary because no impurities are adhered to the crystal surfaces upon completion of the operation.1 A series of three-phase equilibrium conditions are attained by decreasing the temperature and reducing the pressure during the batch SC process.1 If a system can easily attain three-phase equilibrium, a faster cooling rate can be applied during the operation. However, if a system has difficulty in attaining three-phase equilibrium, a slower cooling rate must be adopted to ensure that three-phase equilibrium is achieved. This study investigates how the cooling rate affects the performance of SC for purification of a p-xylene (PX)/o-xylene (OX) mixture to elucidate the rate process of three-phase equilibrium. This helps to determine the time required for a system to achieve a series of three-phase equilibrium conditions during the SC operation. This information is essential in the design of an industrial SC process.

boundaries typically remain nearly unchanged, while the VLE boundaries are moved downward. Figure 1b illustrates the phase diagram at P = 582 Pa when the triple point of PX starts to occur at T = 13.3 °C (i.e., the VLE boundaries cross the SLE boundaries). Figure 1c illustrates the phase diagram at P = 60 Pa, which is lower than the triple-point pressure of PX. This figure also reveals a three-phase equilibrium state (points b, b′, and b″) with pure PX crystals, a liquid phase of mixtures, and a vapor phase of mixtures at T = −15.9 °C, XA = 0.45, and YA = 0.54. Figure 1d illustrates the phase diagram at P = 16 Pa, which is lower than the triple-point pressure of OX. This figure also reveals two three-phase equilibrium states. One is a three-phase state (points b, b′, and b″) with pure PX crystals, a liquid phase of mixtures, and a vapor phase of mixtures at T = −30.0 °C, XA = 0.29, and YA = 0.38 on the right-hand side of the figure. The other one is a three-phase state (points a, a′, and a″) with pure OX crystals, a liquid phase of mixtures, and a vapor phase of mixtures at T = −29.2 °C, XA = 0.10, and YA = 0.14 on the left-hand side of the figure. Thus, through control of the temperature and pressure, SC can be applied to produce both PX crystals from a mixture in the range of 0.24 < XA < 1 and also OX crystals from a mixture in the range of 0 < XA < 0.24. To apply SC in the binary PX/OX mixture, this study also develops a model to describe the heat- and mass-transfer phenomena occurring in the SC process. Figure 2 schematically depicts a batch SC process in a single vessel operated from t0 to tf for a chosen Δt. The batch SC process is simulated in a series of three-phase equilibrium operations. During the batch process, the vapor formed at time t − Δt is condensed to the liquid and removed, while the solid and liquid formed at time t − Δt remain in the vessel at time t. The entire process starts from the liquid mixture feed and is stopped at the eutectic temperature to avoid

2. SC MODEL The basic principles of the SC process are described in detail by Shiau et al.1 Figure 1a illustrates the solid−liquid equilibrium (SLE) boundaries and the vapor−liquid equilibrium (VLE) boundaries of PX (i.e., component A) and OX (i.e., component B) at a standard pressure. As the pressure is reduced, the SLE © 2012 American Chemical Society

Received: Revised: Accepted: Published: 1716

July 5, 2012 October 22, 2012 November 1, 2012 November 2, 2012 dx.doi.org/10.1021/ie301776c | Ind. Eng. Chem. Res. 2013, 52, 1716−1722

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Figure 1. Phase diagrams of (a) PX and OX at P = 1.01 × 105 Pa, (b) PX and OX at P = 582 Pa, (c) PX and OX at P = 60 Pa, and (d) PX and OX at P = 16 Pa.

properties of PX and OX in Table 1 are adopted from DIPPR.6,7 The SLE of OX at time t is described by the van’t Hoff equation as8,9

cocrystallization. Notably, cocrystallization of OX and PX occurs when SC is operated below the eutectic point. When SC is applied to produce OX crystals from the liquid mixture feed, the process is always maintained at a threephase equilibrium state with pure OX crystals and a liquid phase and a vapor phase of mixtures. As OX crystals are gradually formed during the batch process, the liquid composition of OX decreases over time. The corresponding temperature and pressure for the three-phase equilibrium during the batch process are determined as follows. The physical

ln[(XB)t (γB)t ] =

ΔHm,B ⎛ 1 1 ⎞ ΔCp,B ⎛ Tm,B − Tt ⎞ ⎜⎜ − ⎟⎟ + ⎜ ⎟ Tt R ⎝ Tm,B Tt ⎠ R ⎝ ⎠ −

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ΔCp,B R

⎛ Tm,B ⎞ ln⎜ ⎟ ⎝ Tt ⎠

(1)

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Figure 2. Representation of a batch SC process in a single vessel operated from t0 to tf for a chosen Δt. The batch SC process is simulated in a series of three-phase equilibrium operations.

Table 1. Some Physical Properties for PX and OX6,7 property

PX

OX

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

106.167 138.37 13.26 581.55 1.711 × 104 4.276 × 104

106.167 144.43 −25.17 21.97 1.360 × 104 4.583 × 104

Notably, the total vapor condensed during the operation is equivalent to ∑ttf1ΔVt. Because some liquid may remain along with the final crystals at the end of SC, the simulated purity of the final product (XB,S), including the final crystals and the remaining liquid, is defined as XB,S =

Sf + Lf (XB)f Sf + Lf

(9)

The simulated recovery ratio of PX (RB,S) is defined as At pressures of 1 atm and less, the assumption of ideal gases introduces little error. Because SC is operated at low pressures ( 0.85. Each data point represents the average final purity of the product, XA,E, for three repetitive experiments determined by GC upon completion of the experiments. Each symbol of the data point refers to a specific cooling rate (● for 0.50 °C/min and ○ for 0.34 °C/min). The number in parentheses next to each data point represents the average experimental recovery ratio. According to Figure 4, the operating temperature ranges for XA,0 = 0.75, 0.80, 0.85, and 0.90 are 37.3, 39.7, 42.0, and 29.7 °C, respectively. Notably, the operating pressures are in the range of 100−600 Pa. The large operating temperature ranges lead to a long operating time. For instance, the operating time during the purification of PX from 6.9 to −35.1 °C is 84 min at the fastest cooling rate of 0.50 °C/min for XA,0 = 0.85, as opposed to only 8 min during the purification of OX from −31.1 to −35.1 °C at the fastest cooling rate of 0.50 °C/min for XB,0 = 0.85. Thus, the operating time during the purification of PX is generally longer than that during the purification of OX. Figure 8 indicates that, at cooling rates of 0.50 and 0.34 °C/min, XA,E is higher than XA,S for XA,0 = 0.75 and 0.80; in addition, XA,E is close to 1 for XA,0 = 0.85 and 0.90. This figure reveals that XA,E increases with a declining cooling rate for various feeds. However, RA,E decreases with decreasing cooling rates and is always lower than RA,S for various feeds. Similarly, the final PX crystals might contain OX for the reasons described above.

4. RESULTS AND DISCUSSION Batch SC experiments are performed first to produce OX crystals from the PX/OX mixture. The calculated P(T) in Figure 3 is

Figure 7. Comparison between XB,f and XB,S in the purification of OX for various feeds. The dotted line represents XB,S, the data point represents XB,f, and the number in parentheses next to each data point represents the average experimental recovery ratio. Each symbol of the data point refers to a specific cooling rate (● for 0.50 °C/min, ○ for 0.34 °C/min, ▲ for 0.22 °C/min, and Δ for 0.10 °C/min).

adopted to direct the operation regardless of various cooling rates. Figure 7 compares the experimental and simulation results for various feeds (90 g with XB,0 = 0.85, 0.90, 0.95, and 0.97). The dotted line represents XB,S calculated by eq 9, indicating that XB,S = 1 only for XB,0 > 0.97. Each data point represents the average final purity of the product, XB,E, for three repetitive experiments determined by GC upon completion of the experiments. Each symbol of the data point refers to a specific cooling rate (● for 0.50 °C/min, ○ for 0.34 °C/min, ▲ for 0.22 °C/min, and Δ for 0.10 °C/min). The number in parentheses next to each data point represents the average experimental recovery ratio. The 1720

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ACKNOWLEDGMENTS

The authors thank the Chang Gung Memorial Hospital and National Science Council of Taiwan for financially supporting this research.

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Figure 8. Comparison between XA,f and XA,S in the purification of PX for various feeds. The dotted line represents XA,S, the data point represents XA,f, and the number in parentheses next to each data point represents the average experimental recovery ratio. Each symbol of the data point refers to a specific cooling rate (● for 0.50 °C/min and ○ for 0.34 °C/min).

5. CONCLUSIONS This study investigates how the cooling rate affects the performance of SC for purification of a PX/OX mixture to elucidate the rate process of three-phase equilibrium. A thermodynamic model is also developed to simulate the three-phase equilibrium conditions during the batch SC operation. According to the model, the SC operating pressures for purifying OX are significantly lower than those for purifying PX. Moreover, the SC operating temperature range for purifying OX is smaller than that for purifying PX. The experimental results demonstrate the feasibility of using SC to purify both PX from the PX-rich mixture and OX from the OX-rich mixture. As predicted by the model, the experimental results confirm that purification of OX is more difficult than that of PX. A slower cooling rate generally increases the operating time, leading to a product with a higher purity and lower recovery ratio. The results demonstrate that the proposed model can accurately describe the heat- and mass-transfer phenomena in the SC process. We conclude that three-phase equilibrium can be achieved quickly for the studied system, even at a cooling rate of 0.50 °C/min. This fast equilibrium renders SC a short operation time in industrial applications. In contrast to conventional crystallization, the impurity is vaporized and no mother liquor is present at the end of SC. Consequently, filtration and crystal washing are unnecessary for the crystals finally obtained.

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NOTATION ΔCp,j = change in the heat capacity from the solid phase to the liquid phase for the jth component, J/mol·K ΔHm,j = heat of melting for the jth component (>0), J/mol ΔHV,j = heat of vaporization for jth component (>0), J/mol Lt = mass of the liquid in the vessel at time t, g P = pressure, Pa Psat j = saturated pressure of the liquid of the jth component, Pa R = ideal gas constant, 8.314 J/mol·K Rj,E = experimental recovery ratio of the jth component, dimensionless Rj,S = simulated recovery ratio of the jth component, dimensionless St = mass of the solid in the vessel at time t, g T = temperature, K Teu = eutectic temperature, K Tb,j = boiling temperature of the jth component, K Tm,j = melting temperature of the jth component, K t = time, min ΔVt = mass of the vapor leaving the vessel at time t, g W0 = initial weight of the liquid mixture feed, g Wf = final weight of the product, including the crystals and the remaining liquid, obtained at the end of the experiment, g (Xj)t = mole fraction of the jth component in the liquid phase at time t, dimensionless Xj,0 = mole fraction of the jth component in the liquid mixture feed, dimensionless Xj,E = experimental purity of the jth component in the final product measured by GC, dimensionless Xj,S = simulated purity of the jth component in the final product predicted by simulation, dimensionless (Yj)t = mole fraction of the jth component in the vapor phase at time t, dimensionless

Greek Letter

γj = activity coefficient of the jth component in the liquid phase, dimensionless Subscript

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0 = in the feed f = in the final product t = at time t

REFERENCES

(1) Shiau, L. D.; Wen, C. C.; Lin, B. S. Separation and Purification of pXylene from the Mixture of m-Xylene and p-Xylene by Distillative Freezing. Ind. Eng. Chem. Res. 2005, 44, 2258−2265. (2) Shiau, L. D.; Wen, C. C.; Lin, B. S. Application of Distillative Freezing in the Separation of o-Xylene and p-Xylene. AIChE J. 2006, 52, 1962−1967. (3) Shiau, L. D.; Wen, C. C.; Lin, B. S. Separation of p-Xylene from the Multicomponent Xylene System by Stripping Crystallization. AIChE J. 2008, 54, 337−342. (4) Shiau, L. D.; Liu, K. F.; Jang, S. M.; Wu, S. C. Separation of Diethylbenzene by Distillative Freezing. J. Chin. Inst. Chem. Eng. 2008, 39, 59−65. (5) Shiau, L. D.; Yu, C. C. Separation of the Benzene/Cyclohexane Mixture by Stripping crystallization. Sep. Purif. Technol. 2009, 66, 422− 426.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 011-886-3-2118800 ext. 5291. Fax: 011-886-3-2118700. Notes

The authors declare no competing financial interest. 1721

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(6) NIST Standard Reference Database 11: DIPPR data compilation of pure compound properties, version 5.0, sponsored by The Design Institute for Physical Property Data (DIPPR) of the American Institute of Chemical Engineers, 1985. (7) Kirk, R. E.; Othmer, D. F., Eds.; Encyclopedia of Chemical Technology; Wiley: New York, 1991. (8) Smith, J. M.; Van Ness, H. C.; Abbott, M. M. Introduction to Chemical Engineering Thermodynamics; McGraw-Hill Book Co.: Singapore, 2001. (9) Sandler, S. I. Chemical, Biochemical, and Engineering Thermodynamics, 4th ed.; John Wiley & Sons: Beijing, 2006.

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