Thermodynamic Equilibrium of Xylene Isomerization in the Liquid

This study deals with the thermodynamic equilibrium for xylene isomerization. ... led to the conclusion that the earlier available thermodynamic data ...
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Thermodynamic Equilibrium of Xylene Isomerization in the Liquid Phase Jonathan C. Gonçalves and Alírio E. Rodrigues* LSRELaboratory of Separation and Reaction Engineering, Departamento de Engenharia Química, Faculdade de Engenharia, Universidade do Porto, Rua do Dr. Roberto Frias, 4200-465 Porto, Portugal S Supporting Information *

ABSTRACT: This study deals with the thermodynamic equilibrium for xylene isomerization. Experiments performed by several researchers to calculate the equilibrium in the gas phase in the 1990s led to the conclusion that the earlier available thermodynamic data for xylenes, which were mainly based on experimental work performed in the 1940s, were in error. In this work a similar procedure was followed to determine the thermodynamic equilibrium for xylene isomerization in the liquid phase. By means of the thermodynamic functions at saturated conditions presented by the previously mentioned studies, the standard free energies of formation were calculated between 250 K and 550 K. Three different expressions were developed to calculate the equilibrium constants as a function of temperature.

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and Chirico et al.,4 highlighted the influence of the rotation of the methyl groups. Unfortunately, the aforementioned studies presented expressions for the equilibrium constants as a function of temperature only for the gas phase; this was probably due to the fact that xylene isomerization occurs industrially under gas phase conditions. However, in the past few years new trends in xylene production have focused on the use of xylene isomerization in the liquid phase driven by the environmental benefits of reduction of energy and pollution. Namely, the isomerization is separated in two stages: one in the liquid phase for xylenes and one in the gas phase for ethylbenzene.7,8 Moreover, research efforts are being made on process intensification by coupling xylenes isomerization and xylenes separation (both in the liquid phase) in a single unit using the simulated moving bed reactor (SMBR) technology.9,10 Following these new approaches, this work is intended to develop similar expressions of the equilibrium for xylene isomerization in the liquid phase based on the thermodynamic functions at saturated conditions presented by Chirico and coworkers.2−4

INTRODUCTION

Xylenes are aromatic hydrocarbons used as raw material for a variety of every day products. The most important is p-xylene (PX), which is produced based on two main operations, isomerization and separation. The isomerization reaction is limited by the thermodynamic equilibrium which results in a large recycle loop to achieve the desired amount of p-xylene. Because of the direct influence of the thermodynamic equilibrium in the process, accurate equilibrium values are of the most importance. Amelse1 carried out isomerization experiments over nonshape-selective and shape-selective catalysts and calculated the thermodynamic equilibrium of xylenes at 623 K and 673 K. On the basis of the results obtained, Amelse1 concluded that xylenes thermodynamic data were erroneous. According to Chirico et al.,2 available standard thermodynamic properties of formation (e.g., standard Gibbs free energy of formation) for the xylenes were the result of experimental work performed in the 1940s. Those experimental results were obtained only at one temperature, 298.15 K. p-Xylene has been studied extensively in the past in order to expand and improve the available data, but o-xylene (OX) and m-xylene (MX) have been left aside;2 this was probably due to the higher economic importance of p-xylene. Chirico and co-workers2−5 carried out experimental studies to measure calorimetric and physical properties used to determine standard Gibbs free energies of formation between 250 K and 550 K for the three xylenes and ethylbenzene. Furthermore, they developed expressions to evaluate the thermodynamic equilibrium which were in excellent agreement with the results of Amelse.1 Chirico and Steele6 concluded that the largest error was associated with the entropy of o-xylene in the liquid and gas phases. Both, Amelse1 © XXXX American Chemical Society

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EQUILIBRIUM IN THE LIQUID PHASE To obtain the standard Gibbs energy of formation to estimate the equilibrium constants in the liquid phase, the molar thermodynamic functions at saturation pressure (Ps) were extracted from the studies cited before, for temperatures between 250 K and 550 K (see Table S1 in the Supporting Information, SI). The saturation pressure was obtained from Received: February 26, 2013 Accepted: May 15, 2013

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Table 1. Entropy (S0) and Enthalpy (H0 − H0(Tr)) of Reference Elements at Reference Temperature Tr = 298.15 K and standard pressure P0 = 100 kPa from Chase11

the (2,4) form of the Wagner equation as it was done by Chirico and co-workers:2−4 ⎛ Ps ⎞ 1 ln⎜ ⎟ = {A(1 − Tr) + B(1 − Tr)1.5 + C(1 − Tr)2 P T ⎝ c⎠ r + D(1 − Tr)4 }

graphite (C) T

(1)

K

where Tr = T/Tc, Pc is the critical pressure, and Tc is the critical temperature. The required equation parameters (A, B, C, and D), Pc, Tc, and some other required properties, of each species, are presented in Table S2 in the SI. Based on the values presented in Table S1 in the SI, the enthalpy (H) and entropy (S) in the standard state (i.e., at P0) were calculated at each temperature using Maxwell relations:

⎛ ∂S ⎞ ⎛ ∂V ⎞ ⎜ ⎟ = −⎜ ⎟ ⎝ ∂P ⎠T ⎝ ∂T ⎠ P

(2)

⎛ ∂H ⎞ ⎛ ∂V ⎞ ⎜ ⎟ = V − T⎜ ⎟ ⎝ ∂P ⎠T ⎝ ∂T ⎠ P

(3)

200 250 298.15 300 350 400 450 500 600

dV ΔP dT

T/K 250 260 280 298.15 300 320 340 360 380 400 420 440 460 480 500 520 540 550

(4)

⎛ dV ⎞ ΔH = ⎜V − T ⎟ΔP ⎝ dT ⎠

(5)

where ΔP = P − P . Following the procedure of Chirico and co-workers,2−4 molar volumes were obtained by means of the molecular weight (M) and the densities (ρ) calculated with a form of the corresponding-states equation of Riedel: 0

s

⎛ ρ T⎞ = 1 + 0.85⎜1 − ⎟ + (1.6916 + 0.9845ω) ρc Tc ⎠ ⎝ 1/3 ⎛ T⎞ ⎜1 − ⎟ Tc ⎠ ⎝

+ [H 0(T ) − H 0(298.15)]compound (7)

The Gibbs energy of formation was calculated with the enthalpy of formation and the entropies of the reference elements:11 Δf G 0(T ) = Δf H 0(T ) − T {S 0(T )compound −

∑ S 0(T )elements }

S

−1

J·mol K

−1· −1

kJ·mol

−0.665 −0.369 0 0.016 0.487 1.039 1.667 2.365 3.943

3.082 4.394 5.740 5.793 7.242 8.713 10.191 11.662 14.533

0

H0 − H0(Tr)

J·mol K

kJ·mol−1

119.412 125.640 130.680 130.858 135.325 139.216 142.656 145.737 151.077

−2.774 −1.378 0 0.053 1.502 2.959 4.420 5.882 8.811

p-xylene 42.672 43.098 43.882 44.526 44.589 45.225 45.801 46.320 46.792 47.218 47.604 47.954 48.271 48.559 48.822 49.062 49.282 49.384

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.019 0.018 0.018 0.017 0.017 0.017 0.017 0.016 0.016 0.016 0.016 0.016 0.016 0.015 0.015 0.015 0.015 0.015

m-xylene 41.615 42.050 42.867 43.537 43.601 44.264 44.861 45.403 45.892 46.336 46.737 47.11 47.43 47.74 48.01 48.25 48.48 48.60

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.019 0.018 0.018 0.017 0.017 0.017 0.017 0.016 0.016 0.016 0.016 0.14 0.14 0.14 0.14 0.14 0.14 0.14

o-xylene 42.866 43.296 44.088 44.732 44.795 45.430 46.002 46.518 46.983 47.404 47.783 48.13 48.44 48.72 48.98 49.21 49.42 49.53

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.019 0.018 0.018 0.017 0.017 0.017 0.017 0.016 0.016 0.016 0.016 0.14 0.14 0.14 0.14 0.14 0.14 0.14

molar volume was not taken into account since it was negligible compared to that of enthalpy and entropy. Ethylbenzene cannot be converted in the liquid phase because its isomerization to xylenes goes through naphthenes intermediates, which requires the presence of hydrogen. Nevertheless isomerization of xylenes can be carried out in the liquid phase over acid catalysts.9,10 Because of the aforementioned fact, the ethylbenzene was not taken into account in the thermodynamic equilibrium in the liquid phase. The equilibrium constants were defined for each isomer pair, according to the reaction scheme in Figure 1, as follows:

Δf H 0(T ) = Δf H 0(298.15)

∑ [H 0(T ) − H 0(298.15)]elements

−1· −1

0

(6)

Once the thermodynamic functions were obtained in the standard state for each temperature, the formation functions were calculated. Enthalpies of formation include the enthalpies of the reference elements:11

−

hydrogen (H2)

H − H (Tr) 0

Table 2. Gibbs Energy of Formation (ΔfG0/RT) of Xylene Species in the Liquid Phase

Integrating within the pressure range and assuming no variation of molar volume (V) in the liquid phase due to pressure, the following relations were obtained: ΔS = −

S

0

(8)

XOX /XMX = K1 = exp( −ΔR1G 0 /(RT ))

(9)

XMX /XPX = K 2 = exp( −ΔR 2 G 0 /(RT ))

(10)

XPX /XOX = K3 = exp( −ΔR 3G 0 /(RT ))

(11)

Three expressions of the form ln K = f(1/T) were obtained for each equilibrium constant through weighted least-squares regression; the F-test was used in order to determine the order of the polynomial and the significance of each parameter:12

The enthalpies and entropies of the elements were obtained from Chase11 and are shown in Table 1. Table 2 presents the Gibbs energy of formation for each xylene species with the corresponding uncertainty; error associated to pressure and B

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Table 3. Equilibrium Product Distribution (mol %) Based on the Equilibrium Constants from eqs 12 to 14a T/K 250 300 350 400 450 500 550

Figure 1. Reaction scheme for xylene isomerization. PX = p-xylene, MX = m-xylene, OX = o-xylene. K1 = OX/MX, K2 = MX/PX, K3 = PX/OX. The triangular scheme adds to the mechanism the direct conversion between o- and p-xylene in order to account for the influence of intracrystalline mass-transfer resistance.13

2 R adj = 0.9996

2 Radj = 0.9989

2 Radj = 0.9964

1.1 1.2 1.2 1.2 1.3 1.3 1.3

61.3 59.7 58.2 56.9 55.8 54.9 54.2

± ± ± ± ± ± ±

2.3 2.4 2.5 2.6 2.7 2.8 2.8

17.5 18.1 18.8 19.6 20.2 20.8 21.3

± ± ± ± ± ± ±

1.0 1.0 1.1 1.2 1.2 1.3 1.3

et al.14 carried out experiments on xylene isomerization in the liquid phase; they used the equilibrium constants within the kinetic parameters; however, they did not show the actual values. Chirico and Steele6 only reported isomerization equilibrium in the liquid phase at T = 323 K: (58.9 ± 2.9) % of m-xylene, (18.3 ± 1.7) % of o-xylene, and (22.8 ± 2.4) % of p-xylene. Using the expressions obtained in this study the following equilibrium distribution was obtained: (59.0 ± 2.4) % of m-xylene, (18.4 ± 1.1) % of o-xylene, and (22.6 ± 1.2) % of p-xylene. The aforementioned values show excellent agreement among themselves.

(12)

(13)

ln K3 = −29500±600(T /K)−2 + 197±4(T /K)−1 − 0.122±0.005;

± ± ± ± ± ± ±

o-xylene

Uncertainties of equilibrium constants from eqs 12 to 14 are calculated based on prediction of new values of the fitted curves and combined in quadrature to obtain the uncertainties within the product distribution.

ln K 2 = −8700±1800(T /K)−2 + 175±12 (T /K)−1 + 0.500±0.018;

21.2 22.2 23.0 23.5 24.0 24.3 24.5

m-xylene

a

ln K1 = 4190000±130000(T /K)−3 − 259±4(T /K)−1 − 0.486±0.008;

p-xylene

(14)

The curves obtained by eqs 12 to 14 are depicted in Figure 2. The product distribution in thermodynamic equilibrium for the

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CONCLUSIONS Three expressions were developed to determine the thermodynamic equilibrium constants for xylene isomerization in the liquid phase between 250 and 550 K. A simple procedure was followed based on published thermodynamic functions at saturation pressure.

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ASSOCIATED CONTENT

* Supporting Information S

Tables with published information of molar thermodynamic functions at saturation pressure (Table S1) and other properties and equation parameters (Table S2) used to determine the Gibbs energy of formation for each xylene species. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

Financial support from Fundaçaõ para a Ciência e Tecnologia (Ministry of Science and Technology of Portugal) through the Ph.D. scholarship SFRH/BD/74402/2010 is gratefully acknowledged.

Figure 2. Equilibrium constants Ki as a function of temperature according to eqs 12 to 14: ◆, i = 1; ▲, i = 2; ■, i = 3. Error bars are larger for temperatures above 440 K due to the increase in the uncertainty of the saturation functions of m-xylene and o-xylene.

Notes

The authors declare no competing financial interest.

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three xylenes was calculated by linear combination of two of the equilibrium constants defined by eqs 9 to 11, and the material balance (∑Xi = 1). The obtained product distribution for several temperatures is presented in Table 3. Unfortunately, there are very few references of thermodynamic equilibrium for xylene isomerization in the liquid phase in the literature. For instance, Cappellazzo et al.13 and Norman

REFERENCES

(1) Amelse, J. A. In The Influence of Diffusion Limitations on Xylene Isomerization, Proceedings from the Ninth International Zeolite Conference, Montreal, 1992; Ballmoos, R. v.; Higgins, J. B.; Treacy, M. M. J., Eds.; Butterworth-Heinemann: Oxford, 1993; pp 457−465. (2) Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A.; Steele, W. V. Thermodynamic Equilibria in Xylene Isomerization. 1. The C

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Thermodynamic Properties of p-Xylene. J. Chem. Eng. Data 1997, 42 (2), 248−261. (3) Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A.; Reynolds, J. W.; Steele, W. V. Thermodynamic Equilibria in Xylene Isomerization. 2. The Thermodynamic Properties of m-Xylene. J. Chem. Eng. Data 1997, 42 (3), 475−487. (4) Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A.; Cowell, A. B.; Reynolds, J. W.; Steele, W. V. Thermodynamic Equilibria in Xylene Isomerization. 3. The Thermodynamic Properties of o-Xylene. J. Chem. Eng. Data 1997, 42 (4), 758−771. (5) Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A.; Steele, W. V. Thermodynamic Equilibria in Xylene Isomerization. 4. The Thermodynamic Properties of Ethylbenzene. J. Chem. Eng. Data 1997, 42 (4), 772−783. (6) Chirico, R. D.; Steele, W. V. Thermodynamic Equilibria in Xylene Isomerization. 5. Xylene Isomerization Equilibria from Thermodynamic Studies and Reconciliation of Calculated and Experimental Product Distributions. J. Chem. Eng. Data 1997, 42 (4), 784−790. (7) Mohr, G. D. Xylene Isomerization. U.S. Patent 6,770,792 B2, Aug. 3, 2004. (8) Abrevaya, H.; Marte, J. C.; Wilson, S. T.; Koster, S. C.; Bauer, J. E.; Sinkler, W.; Wilson, B. A.; Jacobsen, L. L. Hydrocarbon Conversion Using an Improved Molecular Sieve. U.S. Patent 8,304,593 B2, Nov. 6, 2012. (9) Minceva, M.; Gomes, P. S.; Meshko, V.; Rodrigues, A. E. Simulated moving bed reactor for isomerization and separation of pxylene. Chem. Eng. J. 2008, 140 (1−3), 305−323. (10) Bergeot, G.; Leinekugel-Le-Cocq, D.; Wolff, L.; Muhr, L.; Bailly, M. Intensification of Paraxylene Production Using a Simulated Moving Bed Reactor. OGSTRevue d’IFP Energies nouvelles 2010, 65 (5), 721−733. (11) Chase, M. W. J., NIST-JANAF Thermochemical Tables, 4th ed.; American Inst. of Physics: Maryland, 1998. (12) Montgomery, D. C.; Runger, G. C. Applied Statistics and Probability for Engineers: John Wiley & Sons Incorporated: New York, 2005. (13) Cappellazzo, O.; Cao, G.; Messina, G.; Morbidelli, M. Kinetics of Shape-Selective Xylene Isomerization over a ZSM-5 Catalyst. Ind. Eng. Chem. Res. 1991, 30 (10), 2280−2287. (14) Norman, G. H.; Shigemura, D. S.; Hopper, J. R. Isomerization of Xylene over Hydrogen Modernite. A Comprehensive Model. Ind. Eng. Chem. Res. 1976, 15 (1), 41−45.

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