Article pubs.acs.org/IECR
Chemical Equilibria in Methanol Synthesis Including the Water−Gas Shift Reaction: A Critical Reassessment Geert H. Graaf† and Jozef G. M. Winkelman*,‡ †
Graaf Independent Energy Advice, Parklaan 4, 9724AL Groningen, The Netherlands Department of Chemical Engineering, ENTEG, University of Groningen, Nijenborgh 4, 9747AG Groningen, The Netherlands
‡
S Supporting Information *
ABSTRACT: A large number of experimental equilibrium constants for the reactions involved in methanol synthesis were collected or calculated from several literature sources. Equilibrium relationships were derived from basic thermochemical data and subsequently fitted to the experimental results by adapting only the Gibbs energy of formation values for CH3OH and CO. Very small changes of these parameters as compared to the original literature values were sufficient to obtain accurate relationships that adequately describe the experimental results.
When the heat capacities of the components (cp°) are known as fourth-order polynomial functions of temperature, the following relationship for Kp° results.
1. INTRODUCTION Methanol synthesis is a highly important industrial process governed by the following reversible reactions. A: CO + 2H 2 ⇔ CH3OH (1) B: CO2 + H 2 ⇔ CO + H 2O
(2)
C: CO2 + 3H 2 ⇔ CH3OH + H 2O
(3)
ln Kp° (T ) =
+ a6T 5 + a 7T ln T ]
2. THEORY Ideal gas equilibrium constants can be calculated with the use of the following equations. 1 ⎡ −ΔG°(Tref ) + ⎢ R⎣ Tref
ΔH °(T ) = ΔH °(Tref ) +
∫T
T
∫T
T
ref
⎤ ΔH °(T ) d T ⎥ ⎦ T2
Δcp°(T ) dT
ref
© 2016 American Chemical Society
(6)
Industrial methanol synthesis is carried out at elevated pressures (±100 bar). Therefore, corrections for nonideal gas behavior are necessary. Graaf et al.1,2 have shown that the Soave−Redlich−Kwong equation of state (SRK-EoS)3 is suitable for this purpose. Recently van Bennekom et al.4 have optimized an adapted version of the SRK-EoS as published by Mathias5 for the methanol synthesis system. Furthermore, we found that a better fit of experimental equilibrium constants results by using the H2-specific α-function as described by Graboski and Daubert.6 We have used this optimized and extended SRK-EoS version in our analysis. Despite the fact that accurate thermochemical information is available nowadays, it turns out that still no consistent information on the chemical equilibria in methanol synthesis exists in the open literature. In order to get a better understanding of this observation we have conducted a sensitivity analysis with respect to the derivation of equilibrium relationships based on eq 6 and thermochemical data from the literature. From this analysis we conclude that the accuracy of the heat capacity data is sufficient
At equilibrium conditions only two of these three reactions suffice to describe the equilibrium composition, provided that accurate equilibrium constants are available. However, a literature survey reveals that no clear picture exists on this important subject especially regarding the methanol formation reactions 1 and 3. To a lesser extent the same applies for the (reverse) water−gas shift reaction 2, but in this case the differences between equilibrium constants are much smaller. The purpose of this publication is twofold. First we will clarify why these differences between equilibrium constants exist. Second, we will present new relationships for the equilibrium constants of the reactions involved based on experimental information from an extensive literature survey and thorough analysis.
ln Kp°(T ) =
1 [a1 + a 2T + a3T 2 + a4T 3 + a5T 4 RT
(4)
Received: Revised: Accepted: Published:
(5) 5854
February April 14, April 28, April 28,
29, 2016 2016 2016 2016 DOI: 10.1021/acs.iecr.6b00815 Ind. Eng. Chem. Res. 2016, 55, 5854−5864
Article
Industrial & Engineering Chemistry Research
main cause for the observed differences in the calculated equilibrium constants. A similar overview for the water−gas shift reaction is presented in Table 2. Literature Kp2° values show less variation
and can not be the cause for the discrepancies. The accuracy of the ΔH°(Tref) and ΔG°(Tref) values however is a decisive factor for obtaining accurate equilibrium constants (as might be expected). Comparing thermochemical data from various sources7−12 reveals that the ΔG°(Tref) value for CH3OH shows the greatest variation. Consequently, the greatest uncertainty of the calculated Kp1° values is caused by this parameter. It turns out that the sensitivity of Kp1° for the ΔG°(Tref) value for reaction 1 is a factor 4 higher as compared to ΔH°(Tref), taking the different variations of the thermochemical parameters into account. Furthermore, the sensitivity of Kp1° for the ΔG°(Tref) value for CH3OH is a factor 3.5 higher relative to CO, again including the observed variations of these parameters. Haynes et al.8 present a ΔG°(Tref) value for methanol of −162.298 kJ/mol (T = 298.15 K; p = 1 bar). With this value and in combination with the other thermochemical basic data from the same source an ideal gas equilibrium constant for reaction 1 of 2.07 × 10−3 bar−2 is calculated at T = 523.15 K. Further calculations with ΔG°(Tref) values which are 0.5% lower or higher yield equilibrium constants of 2.88 × 10−3 and 1.50 × 10−3 bar−2 respectively. This clearly shows the enormous effect of very small changes in the ΔG°(Tref) value for methanol on the calculated equilibrium constants: the difference between the highest and lowest Kp1° value is almost a factor 2. The 0.5% change of the ΔG°(Tref) value for methanol leads to an average change of 33% of the Kp1° value. For the water−gas shift reaction a similar sensitivity analysis was conducted. Here we investigated the effect of a 0.2% change in the ΔG°(Tref) value for CO, because the other thermochemical data have higher accuracies. Based on the work of Haynes et al.8 a Kp2° value of 1.12 × 10−2 at T = 523.15 K results. ΔG°(Tref) values for CO which are either 0.2% lower or higher yield equilibrium constants of 1.25 × 10−2 and 1.00 × 10−2 respectively. Also in this case the sensitivity is very large: the average change in the Kp2° value is 11% due to a 0.2% change in the ΔG°(Tref) value for CO. Kp1° values from some literature relationships are presented in Table 1 together with the results of the sensitivity analysis.
Table 2. Kp2° Values of Several Authors Including the Sensitivity Results with Regard to ΔG°(Tref) for CO source 8
Haynes et al. Haynes et al.8 “plus”a Haynes et al.8 “minus”b Newsome16 Bissett17 Graaf et al.1 Singh and Saraf18 a b
Haynes et al.8 Haynes et al.8 “plus”a Haynes et al.8 “minus”b Cherednichenko13 Peter15 Graaf et al.1 Klier et al.14
Kp1° (200 °C) (bar−2) 2.22 1.60 3.08 2.45 2.06 1.74 1.67
× × × × × × ×
10−2 10−2 10−2 10−2 10−2 10−2 10−2
Kp1° (250 °C) (bar−2) 2.07 1.50 2.88 2.22 1.95 1.59 1.58
× × × × × × ×
10−3 10−3 10−3 10−3 10−3 10−3 10−3
× × × × × × ×
× × × × × × ×
10 10−3 10−3 10−3 10−3 10−3 10−3
Kp2° (250 °C) 1.12 1.00 1.25 1.20 1.17 1.17 1.10
× × × × × × ×
−2
10 10−2 10−2 10−2 10−2 10−2 10−2
Kp2° (300 °C) 2.46 2.20 2.75 2.58 2.58 2.58 2.43
× × × × × × ×
10−2 10−2 10−2 10−2 10−2 10−2 10−2
Plus means that a 0.2% higher ΔG°(Tref) value for CO is applied. Minus means that a 0.2% lower ΔG°(Tref) value for CO is applied.
3. DERIVATION OF CHEMICAL EQUILIBRIUM CONSTANTS FROM EXPERIMENTAL LITERATURE DATA 3.1. Water−Gas Shift Reaction. First we will focus on the water−gas shift reaction, because our investigations showed that in several cases experimental equilibrium data from the literature for reaction 1 (methanol synthesis from CO/H2) could only be derived under the assumption that the equilibrium constant of the water−gas shift reaction is wellknown. Therefore, we first need to establish an accurate Kp2° relationship that can be used in further analysis. Literature data on experimental equilibrium data for the water− gas shift reaction can be divided in two categories. The first category consists of experimental results that were obtained with the purpose of obtaining experimental equilibrium data. The second category consists of catalytic activity testing results as a function of temperature or flow rate. In several cases these latter results contain data points at higher temperatures or lower flow rates where chemical equilibrium is closely approached. In Table 3 an overview is presented of literature sources for the first category. The Kp2° values were calculated from the experimental gas composition, pressure, and temperature correcting for nonideal gas behavior with the use of the Soave−Redlich−Kwong equation of state3 as adapted by Mathias5 using critical constants and acentric factors as presented by Poling et al.9 Binary interaction parameters were taken from van Bennekom et al.,4 except for hydrogen-containing binaries. In this case binary interaction parameters were set at zero values, because for H2 we used the SRK-adaptation as described by Graboski and Daubert.6 From a preliminary analysis we found that this approach for H2 results in a better fit of the experimental Kp°-data. The H2-specific
Kp1° (300 °C) (bar−2) 2.85 2.06 3.96 2.98 2.80 2.22 2.25
4.24 3.79 4.73 4.78 4.44 4.44 4.18
−3
as compared to the Kp1° results. Maximum Kp2° values are approximately 10% higher than the lowest values. However, also in this case the differences can be explained by very small changes in the ΔG°(Tref) value for (in this case) CO. From this analysis the conclusion seems justified that the differences between literature equilibrium relationships are caused by very small differences in the underlying basic thermochemical data and, most likely, the ΔG°(Tref) values for CH3OH and CO. The sensitivity for these basic data is very high. This also means that accurate experimental chemical equilibrium data may provide better estimates for these ΔG°(Tref) values.
Table 1. Kp1° Values of Several Authors Including the Sensitivity Results with Regard to ΔG°(Tref) for CH3OH source
Kp2° (200 °C)
10−4 10−4 10−4 10−4 10−4 10−4 10−4
Plus means that a 0.5% higher ΔG°(Tref) value for CH3OH is applied. Minus means that a 0.5% lower ΔG°(Tref) value for CH3OH is applied. a b
It shows that the differences between the various relationships are even smaller than the extremes of the sensitivity analysis. Consequently, it can be concluded that very small differences in the ΔG°(Tref) value for CH3OH can explain the differences between the various relationships, where the highest Kp1° values13 are approximately 40% higher as compared to the lowest values.14 This is further illustrated by the fact that Graaf et al.1 have used a ΔG°(Tref) value for CH3OH of −161.830 kJ mol−1 (0.3% higher relative to Haynes et al.8), which indeed turns out to be the 5855
DOI: 10.1021/acs.iecr.6b00815 Ind. Eng. Chem. Res. 2016, 55, 5854−5864
Article
Industrial & Engineering Chemistry Research
the reactor inlet stream is also determined by GC-measurements. The condensed methanol and water stream is not analyzed: the reactor exit mole fractions of methanol and water are calculated from material balances instead. Our analysis revealed that this approach leads to significant deviations of the material balances for carbon, hydrogen and oxygen (by comparing the calculated and the experimental dry gas composition). From a sensitivity analyis we conclude that it is not meaningful to derive both Kp1° and Kp2° values from Liu’s experimental data. However, we will show later in this paper that for most experiments it is possible to derive fairly accurate Kp1° values, if the mole fractions for water are calculated from a reliable Kp2° relationship. Figure 1 also shows that the results of Neumann and Köhler28 at higher temperatures are in good agreement with the Kp2° relationship derived from the work of Haynes et al.8 At lower temperatures (
