Ind. Eng. Chem. Res. 2001, 40, 3801-3805
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GENERAL RESEARCH Methanol Synthesis under Supercritical Conditions: Calculations of Equilibrium Conversions by Using the Soave-Redlich-Kwong Equation of State Jianguo Liu, Zhangfeng Qin, and Jianguo Wang* State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, P.O. Box 165, Taiyuan, Shanxi 030001, People’s Republic of China
The effects of the addition of several supercritical media on the equilibrium CO conversion in the methanol synthesis based on syngas under supercritical conditions were calculated by using the Soave-Redlich-Kwong equation of state. The results showed that the addition of proper solvents such as n-hexane and n-heptane could improve the CO conversion greatly under supercritical conditions. When using n-hexane, the favorite solvent mole fraction was 0.2-0.3, the optimum temperature was in the range of 473-483 K, and the pressure was above 8 MPa. Introduction Methanol, an important industrial chemical material, is produced on a large scale in the so-called “lowpressure” (50-100 bar) process from synthesis gas.1 However, the conversion of this formation process is limited by the thermodynamic equilibria and heat- and mass-transfer restraint, and its single-stage conversion is normally less than 10% (mol). Therefore, many efforts have been made to improve such a process in recent years, and one of the most important measures is by carrying out the synthesis reaction under a supercritical state.2 The laboratory and pilot experimental results of the Institute of Coal Chemistry, Chinese Academy of Sciences, have shown that, under supercritical conditions, the CO equilibrium conversion is improved and the heat- and mass-transfer efficiencies are enhanced greatly, and the single-stage conversion can be greater than 90% (mol). The reaction was operated at a temperature of around 473-483 K and a pressure of 8.5 MPa with n-hexane as a solvent.3 However, little literature has appeared so far on the effects of solvents on the methanol synthesis under supercritical conditions, and the further search for the optimum reaction conditions has certain blindness. Our efforts are therefore to find the basic rules which control the yield and the efficiency of methanol synthesis under supercritical conditions and offer suggestions to the further experimental works and industrial processes; such work will be certainly of great significance. To consider the reaction equilibrium at high pressure, the nonideality of the gas mixture must be corrected. The Soave-Redlich-Kwong (SRK) equation of state has been extensively used in calculating phase and reaction equilibria. Graaf et al.1 used it to calculate the chemical equilibria in methanol synthesis. They found that the chemical equilibria could be described very well by thermochemical data based on ideal gas behavior in combination with a correction for the nonideality of the gas mixture as predicted by the SRK equation of state.
In the present work, the system of methanol synthesis based on syngas was described by the SRK equation of state. The effects of the supercritical media (n-pentane, n-hexane, n-heptane, acetone, and nitrogen) on the CO conversion were investigated, and the operating conditions including the fraction of solvent, temperature, and pressure were optimized.
* To whom correspondence should be addressed. Phone: +86 351 4046092. Fax: +86 351 4041153. E-mail: iccjgw@ sxicc.ac.cn.
Using the heats of formation, entropies, and heat capacities of each component, the equilibrium constant K0 at different temperatures can be easily worked out.
Theory The methanol synthesis reactions are given by the stoichiometric relationships
CO + 2H2 ) CH3OH
(1)
CO2 + H2 ) CO + H2O
(2)
The equilibrium constants of the two reactions are defined as follows:
K10 ) Kp,1Kφ,1(P0)2 )
( )( )( )
K20 ) Kp,1Kφ,1 )
xCH3OH
φCH3OH
xCOxH22
φCOφH22
eq
( )( xCOxH2O xCO2xH2
P0 P
(3)
eq
)
φCOφH2O
eq
2
φCO2φH2
(4)
eq
Here φi is the fugacity coefficient and xi the mole fraction of component i, respectively. The value of K0 can be calculated from the following thermodynamic relationships:
-∆rG0(T) ) RT ln K0(T) -∆rG0(T) -∆rG0(Tref) ) T Tref ∆rH0(T) ) ∆rH0(Tref) +
10.1021/ie0100479 CCC: $20.00 © 2001 American Chemical Society Published on Web 07/27/2001
∫T
T ref
(5)
∆rH0(T) T2
dT
∫TT ∆Cpo(T) dT ref
(6) (7)
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Ind. Eng. Chem. Res., Vol. 40, No. 17, 2001
Table 1. Heats of Formation (J·mol-1·K-1) and Entropies (J·mol-1·K-1) at 298 K and 101.325 kPa and the Parameters of Heat Capacity Equations Cp ) A + BT + CT2 + DT3 + ET4 (T in K and Cp in J·mol-1·K-1)7 gas
∆Hf0
S0
A
B × 103
C × 105
D × 108
E × 1012
H2 CO CH3OH CO2 H2O
0 -110.54 -201.17 -393.50 -241.80
130.57 197.54 239.70 213.69 188.72
25.399 29.556 40.046 27.437 33.933
20.178 -6.5807 -38.287 42.315 -8.4186
-3.8549 2.0130 24.529 -1.9555 2.9906
3.1880 -1.2227 -21.679 0.39968 -1.7825
-8.7585 2.2617 59.909 -0.29872 3.6934
The heats of formation and entropies and the heat capacities used in this work are listed in Table 1. To calculate the value of Kφ, the SRK equation of state is used. The SRK equation of state4 has the following form:
P)
aR RT v - b v(v + b)
(8)
where the quantity R is a function of temperature.
Ri ) [1 + mi(1 - Tri0.5)]2
(9)
Graboski and Daubert5 correlated mi with the Pitzer acentric factor
mi ) 0.48508 + 1.55171ωi - 0.15613ωi2
(10)
For the pure components, the constants ai and bi can be obtained from their critical properties.
ai ) 0.42747R2Tci2/Pci
(11)
bi ) 0.08664RTci/Pci
(12)
The critical parameters and acentric factor of each component used in this work are listed in Table 2. For mixtures the following mixing rules are used: N N
a)
∑ ∑xixjRijaij i)1 j)1
(13)
N
b)
xibi ∑ i)1
(14)
where the cross parameter is given by
Rijaij ) (RiRjaiaj)0.5(1 - Kij)
(15)
A ) RaP/R2T2
(16)
B ) bP/RT
(17)
Z ) Pv/RT
(18)
When
are assumed, the SRK equation (eq 8) can then be rewritten as
Z3 - Z2 - Z (A - B - B2) - AB ) 0
(19)
The fugacity coefficient of component i in the mixture is given by
ln φi ) bi(Z - 1)/b - ln(Z - B) N
xjRijaij/Ra - bi/b)(ln[1 + B/Z])/B ∑ j)1
A(2
(20)
Table 2. Critical Parameters Used in This Work7 gas
Tc/K
Pc/MPa
acentric factor
H2 CO CO2 H2O CH3OH N2 n-C5H12 n-C6H14 n-C7H16 CH3COCH3
33.18 132.92 304.19 647.13 512.58 126.10 469.65 507.43 540.26 508.20
1.313 3.499 7.382 22.055 8.096 3.394 3.369 3.012 2.736 4.702
-0.220 0.066 0.228 0.345 0.566 0.040 0.249 0.305 0.351 0.306
For the calculations, the compressibility factor Z could be obtained by solving eq 19. The largest root is used to evaluate gaseous-phase fugacity coefficients, while the smallest one is used to evaluate liquid-phase fugacity coefficients. The kij value can be obtained from cross second-virial coefficient data,6 but the equilibrium conversion values studied in this work are found to be insensitive to the changes of both kij and the mixing rule of the attractive parameter. This is due to the relatively low density of the mixtures at the conditions considered here and, consequently, the lower weight of the attractive part of the equation of state (eq 8), where the parameter a is the only one affected by kij. Therefore, in the present work all kij values are set to zero. After the fugacity coefficients of each component i are obtained, Kφ can be easily worked out. The equilibrium conversion can then be gained by solving eqs 3 and 4 simultaneously with the Newton-Raphson method. To make comparison with the experimental results in the literature,3 for all calculations, the reaction pressure is between 5.0 and 8.5 MPa and the temperature between 433 and 533 K. When using a solvent, the mole fractions of the reactant mixtures are initialized as follows: H2, 0.5517; CO, 0.1926; CO2, 0.0408; the solvent, 0.2149. In the case of no solvent, the mole fractions of the reactant mixtures are initialized as follows: H2, 0.7027; CO, 0.2453; CO2, 0.0520. In all cases, the H2/CO/CO2 ratio is fixed as 2.86:1:0.21. Results and Discussion 3.1. Effects of Supercritical Media. To investigate the effects of supercritical media on the equilibrium CO conversion, several solvents including nitrogen, acetone, n-pentane, n-hexane, and n-heptane with a mole fraction of 0.2149 are added into the reactant mixtures of methanol synthesis based on syngas. Figure 1 shows how the CO equilibrium conversions change with temperature in the presence/absence of solvents. It can be concluded that, compared with the case in the absence of solvent, the addition of nitrogen has a negative effect on the CO equilibrium conversions in the range of temperature examined. On the contrary, the CO equilibrium conversions can be enhanced greatly by the addition of n-hexane, especially n-heptane at the temperature of around 473 K. For n-pentane and acetone, however, the CO conversion is a little bit lower than
Ind. Eng. Chem. Res., Vol. 40, No. 17, 2001 3803
Figure 2. Effects of the solvent concentration on the CO equilibrium conversions in the methanol synthesis with n-hexane as the solvent: the reaction pressure is 8.5 MPa, the initial ratio of H2/CO/CO2 is fixed as 2.86:1:0.21, and the initial mole fraction of n-hexane is shown in the figure legend.
Figure 1. Comparison of CO equilibrium conversions in methanol synthesis with different solvents including nitrogen, acetone, n-pentane, n-hexane, and n-heptane: the reaction pressure is 8.5 MPa. In the presence of solvent, the mole fractions of the reactants mixtures are initialized as follows: H2, 0.5517; CO, 0.1926; CO2, 0.0408; the solvent, 0.2149. In the absence of solvent, the mole fractions of the reactant mixtures are initialized as follows: H2, 0.7027; CO, 0.2453; CO2, 0.0520.
that in the absence of solvent around 473 K. Table 3 is a comparison of K0, Kp, and Kφ values of reaction (1) at 8.5 MPa. It indicates that adding proper solvents will change the fugacity coefficient ratios Kφ greatly and through which the CO equilibrium conversion can then be improved. At 493.15 K and 8.5 MPa, the Kφ values of reaction (1) for the systems with nitrogen, no solvent, and with n-heptane are 0.6415, 0.4640, and 0.0412, respectively. As a result, the CO equilibrium conversions are increased from 90.1% to 95.8% and 98.5%. The methanol synthesis is a volume-reduced as well as an exothermic reaction. The CO equilibrium conversion will decrease with the temperature and increase with the pressure. With the addition of a new solvent, there will be two factors that affect the CO conversion simultaneously: the dilution effect and solvent effect. For the volume-reduced reaction, the dilution effect results in the decrease of reactants partial pressures and then the decrease of equilibrium conversion, like the case with nitrogen. However, with the addition of proper solvents such as n-hexane and n-heptane, the solvent effect will surpass the dilution effect and then improve the CO equilibrium conversion at certain temperatures and pressures. As shown in Figures 1 and 4, with the addition of n-hexane and at a pressure of 8.5 MPa, the solvent effect dominates the reaction and then improves the CO equilibrium conversion at a temperature below 495 K. At higher temperature, however, the dilution effect exceeds the solvent effect, and the addition of solvent is not favorable for the increase of equilibrium CO conversion in this case. With n-heptane, the same conclusion can be drawn. 3.2. Effects of Solvent Concentrations. To examine the effects of solvent concentration, different amounts of n-hexane with a mole fraction from 0.1 to 0.5 are added into the reactant mixture while the H2/CO/CO2 ratio is fixed as 2.86:1:0.21 and the pressure is set as 8.5 MPa. As shown in Figure 2, at a temperature below
Figure 3. Effects of temperature on the CO conversions in methanol synthesis at different pressures with n-hexane as a solvent. The mole fractions of the reactant mixtures are initialized as follows: H2, 0.5517; CO, 0.1926; CO2, 0.0408; n-hexane, 0.2149.
500 K, the addition of n-hexane with a mole fraction of 0.2-0.5 improves the CO equilibrium conversion and the solvent effect dominates the reaction. At higher temperatures, the dilution effect surpasses the solvent effect, and then the more solvent is added, the more rapidly the CO equilibrium conversion decreases. Therefore, it can be concluded that the addition of n-hexane with a mole fraction of 0.2-0.3 will be favorable for the CO equilibrium conversion at a temperature below 500 K. 3.3. Effects of Temperature and Pressure. In the presence of 20% (mol) of n-hexane, the CO equilibrium conversions at different temperatures and pressures are shown in Figure 3. It can be seen that the CO equilibrium conversion decreases with temperature and increases with pressure, which can be easily understood because the methanol-generating reaction is a volumereduced reaction and an exothermic reaction. Moreover, there exist plateaus of higher equilibrium conversion at temperatures below 493 K when the pressures are higher than 8.0 MPa, which provide a suitable zone for carrying out the synthesis reaction.
Table 3. Comparison of K0, Kp, and KO Values of Reaction (1) at 8.5 MPa Kφ × 103
Kp
CO conversion
T/K
K0 × 102
N2
no solvent
n-C7H16
N2
no solvent
n-C7H16
N2
no solvent
n-C7H16
473.15 483.15 493.15 503.15
2.489 1.505 0.928 0.582
0.043 0.025 0.014 0.009
0.070 0.037 0.020 0.011
7.575 1.791 0.225 0.057
573.4 607.4 641.5 675.3
357.9 412.1 464.0 515.2
3.286 8.403 41.21 102.3
0.957 0.934 0.901 0.859
0.985 0.974 0.958 0.934
0.999 0.996 0.985 0.960
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Ind. Eng. Chem. Res., Vol. 40, No. 17, 2001
Figure 4. Comparison of CO conversions of methanol synthesis at different temperatures and pressures, with or without solvent n-hexane. With solvent, the mole fraction of the reactants mixtures are initialized as follows: H2, 0.5517; CO, 0.1926; CO2, 0.0408; n-hexane, 0.2149. Without solvent, the mole fraction of the reactant mixtures are initialized as follows: H2, 0.7027; CO, 0.2453; CO2, 0.0520.
equilibrium conversion is improved under supercritical conditions, this work is mainly focused on the effect of solvent on the CO equilibrium conversion in the methanol synthesis. It can be drawn from this work that the operating conditions, with the addition of 20-30 mol % n-hexane or n-heptane, at a temperature between 463 and 488 K and a pressure between 8.0 and 10.0 MPa, will be suitable for the methanol synthesis reaction. Fortunately, it is easy to find suitable catalysts at this reaction conditions. To reduce the cost of additional solvents, using mixed solvents such as a mixture of C6C7 is also possible. The researchers in the Institute of Coal Chemistry, Chinese Academy of Sciences, have carried out a series of laboratory and pilot experiments,3 and their results are well-consistent with the calculation in this work. Conclusions The system of methanol synthesis based on syngas was described by the SRK equation of state, and the CO equilibrium conversions in the presence/absence of solvents at different temperatures and different pressures were calculated. The results showed that the addition of proper solvents such as n-hexane and n-heptane could improve the CO conversions greatly under supercritical conditions. When using n-hexane, the favorite solvent fraction is 0.2-0.3, the optimum temperature is in the range of 470-490 K, and the pressure is above 8 MPa. Acknowledgment The authors are grateful for the financial support of the National Key Basic Research Program.
Figure 5. Effects of the mixed solvent (n-hexane and n-heptane) concentration on the CO equilibrium conversions in the methanol synthesis: the reaction pressure is 8.5 MPa, the initial ratio of H2/CO/CO2/solvent is fixed as 0.5517:0.1926:0.0408:0.2149, and the mole fraction of mixture solvents (n-hexane and n-heptane) is fixed as 0.3. The value of x is the fraction of hexane in the mixed solvent.
Figure 4 is a comparison of the CO equilibrium conversions in the presence and absence of n-hexane at different temperatures and pressures. It is found that the addition of n-hexane may have positive or negative effects on the CO conversion depending on the temperature and pressure, which can be explained again by the dilution effect and solvent effect. Because the solvent effect surpasses the dilution effect at higher pressure and lower temperature, the CO equilibrium conversion can be improved by the addition of n-hexane at higher pressure and lower temperature. The CO conversion is enhanced greatly at a pressure above 8.0 MPa and a temperature below 490 K. 3.4. Effects of the Mixed Solvent (n-Hexane and n-Heptane) Concentrations. The effects of mixed solvent (n-hexane and n-heptane) concentrations on the equilibrium CO conversion were also investigated. As shown in Figure 5, the CO equilibrium conversion can be enhanced by the addition of a mixed solvent of n-hexane and n-heptane, and it increases with the n-heptane concentration in the mixed solvent. This proves that the use of a proper mixed solvent such as industrial solvent oil is feasible to reduce the cost of solvent in such a process. 3.5. About the Synthesis of Methanol under Supercritical Conditions. Although the heat- and mass-transfer efficiencies can be enhanced and the CO
Nomenclature a ) constant in the SRK equation b ) constant in the SRK equation Kij ) interaction parameter in the SRK equation K0 ) equilibrium constant Kp ) equilibrium constant based on partial pressure Kφ ) fugacity coefficient ratio mi ) parameter in SRK equation P ) pressure [MPa] Pc ) critical pressure [MPa] R ) gas constant [J‚K-1‚mol-1] T ) temperature [K] Tc ) critical temperature [K] Tr ) reduced temperature v ) specific volume [m3] xi ) mole fraction i Z ) compressibility factor ) Pv/RT Greek Letters ∆rCp ) specific heat change [J‚K-1‚mol-1] ∆rH ) enthalpy change [J‚mol-1] ∆rG ) Gibbs energy change [J‚mol-1] R ) temperature-dependent parameter in the SRK equation φi ) fugacity coefficient of i ω ) acentric factor Superscript ) classical
o
Subscripts c ) critical eq ) at equilibrium i ) pure component i
Ind. Eng. Chem. Res., Vol. 40, No. 17, 2001 3805 ij ) binary parameter for components i and j ref ) reference 1 ) methanol synthesis reaction (1) 2 ) water gas shift reaction (2)
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(4) Soave, G. Equilibrium constants from a modified RedlichKwong equation of state. Chem. Eng. Sci. 1972, 27, 1197. (5) Graboski, M. S.; Daubert, T. E. A modified Soave equation of state for phase equilibrium calculations. 1. Hydrocarbon system. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 443. (6) Chueh, P. L.; Prausnitz, J. M. Vapor-Liquid equilibrium at high pressures. Vapor-Phase fugacity coefficients in nonpolar and quantum-gas mixtures. Ind. Eng. Chem. Fundam. 1967, 6, 492. (7) Yaws, C. L. Chemical Properties Handbook; McGraw-Hill Book Co.: Beijing, 1999.
Received for review January 12, 2001 Accepted May 29, 2001 IE0100479
