Supporting Information for: Combined Steam Reforming of Methane and Formic Acid to Produce Syngas with an Adjustable H2:CO Ratio Ahmadreza Rahbari, Mahinder Ramdin, Leo J. P. van den Broeke, and Thijs J. H. Vlugt∗ Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628CB, Delft, The Netherlands E-mail:
[email protected]
1
Gibbs Free Energy of Components
The Gibbs free energy (or chemical potential) of each component at standard pressure (P ◦ = 1 bar) can be evaluated from its ideal gas partition function 1–4 " ◦
µ (T ) = −RT ln
q(V, T ) V
!
kB T P◦
#
(S1)
q(V, T )/V is the temperature dependent part of the ideal gas partition function, kB is the Boltzmann constant, P ◦ is the standard reference pressure which equals 1 bar, T is the absolute temperature and V = kB T /P ◦ . For a general case of a non-linear polyatomic
S1
molecule, the temperature dependent part of the ideal gas partition function equals 1,2,5,6 q(V, T ) = V
2πM kB T h2
3n−6 Y
×
j=1
!3/2
π 1/2 · σ
T3 Θrot,A Θrot,B Θrot,C
!
(S2)
1 · ge1 exp (D0 /kB T ) 1 − exp (−Θvib,j /T )
M is the mass of the molecule, h is the Planck constant, σ is the rotational symmetry number of the molecule, 7 Θrot,A , Θrot,B , Θrot,C are the characteristic rotational temperatures of the molecule, Θvib,j is the characteristic vibrational temperature of the normal mode j, ge1 is the degeneracy of the electronic ground state, and D0 is the atomization energy of the molecule at 0 K. For more details about computation of the ideal gas partition function, the reader is referred to the book by McQuarrie et al. 1 Eq. S2 is evaluated based on experimental data from the NIST database (used in this work) or the JANAF tables. 1,6,8 Alternatively, quantum mechanical ab initio packages e.g. Gaussian 9 can be used to evaluate the terms in Eq. S2. 1,3,4 Chemical potentials, µ◦ , of methane, water, carbon monoxide, hydrogen, carbon dioxide and Formic Acid (FA) are listed in table Section 3.
2
Gibbs free energy change and reaction enthalpy
For a general case of homogeneous gas phase chemical reaction, it is well-known that the Gibbs energy of reaction and the equilibrium constant are related to chemical potentials of reactants and products (at P ◦ ). For a multicomponent reacting mixture of S distinguishable
S2
components we have 1,10 ◦
∆Gr (T ) =
S X
◦
νi µi (T )
i=1
= −RT ln K(T ) = −RT ln
" S Y
q(V, T ) V
i=1
= −RT
S X
"
νi ln
i=1
!
q(V, T ) V
kB T P◦ !
#νi
kB T P◦
#
(S3)
νi is the stoichiometric coefficient of component i, and K(T ) is the equilibrium constant of the reaction. 1 The reaction enthalpy at standard pressure is calculated directly from the Gibbs-Helmholtz equation ∂∆G◦r /T ∂T
3
!
=− P
∆Hr◦ T2
(S4)
Peng-Robinson Equation of State
The Peng-Robinson Equation of State (PR-EoS) 11–13 is used to evaluate the fugacity coefficient of a component in a mixture. The PR-EoS is one of the most widely used cubic EoS in industry and academia due to its simplicity and ease of implementation. 14,15 The PR-EoS equals
P =
RT am − υm − bm υm (υm + bm ) + bm (υm − bm )
S3
(S5)
in which υm is the molar volume of the mixture per mole mixture. The mixture parameters am and bm are based on pure component parameters and van der Waals mixing rules: 16,17
am =
S X S X
(S6)
yi yj aij
i=1 j=1
bm =
S X
(S7)
y i bi
j=1
aij = (1 − kij ) (ai aj )1/2
(S8)
with yi the mole fraction of component i, kij is a Binary Interaction Parameter (BIP) 18,19 between components i and j. ai and bi are defined as 2 h i R2 Tc,i 1/2 2 1 + 0.37464 + 1.54226ωi − 0.26992ωi2 1 − Tr,i Pc,i 0.0778RTc,i bi = Pc,i
ai = 0.45724
(S9) (S10)
ωi the acentric factor of a pure component, 20,21 Tr,i = T /Tc,i the reduced temperature of component i at temperature T , and Tc,i and Pc,i are critical temperature and critical pressure of component i. 22 Critical parameters and acentric factors are provided in Section 3 The Fugacity coefficient of component i in a mixture is obtained from 16,17,23 2
bi Am ln ϕi = (Zm − 1) − ln (Zm − Bm ) − √ bm 2 2Bm
S P
yk aik
k=1
am
bi Zm + 2.414Bm − ln bm Zm − 0.414Bm
(S11) with ϕi the fugacity coefficient of component i, Zm the compressibility factor of the mixture, and Am and Bm are defined as
Am = am (T ) P /R2 T 2 , Bm = bm P /RT , Zm = P V /RT
S4
(S12)
Table S1: Gibbs free energy or µ◦ , in kJ · mol−1 , of carbon monoxide, water, carbon dioxide, hydrogen, formic acid and methane at P ◦ = 1 bar, based on Eqs. S1 and S2. T [K] 800 825 850 875 900 925 950 975 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500
µ◦CO -1229.8 -1235.5 -1241.2 -1246.9 -1252.7 -1258.5 -1264.3 -1270.1 -1276.0 -1287.7 -1299.6 -1311.5 -1323.5 -1335.5 -1347.7 -1359.9 -1372.1 -1384.5 -1396.8
µ◦H2 O -1068.9 -1074.5 -1080.1 -1085.8 -1091.5 -1097.2 -1102.9 -1108.7 -1114.5 -1126.2 -1138.0 -1149.8 -1161.8 -1173.9 -1186.0 -1198.3 -1210.6 -1223.0 -1235.5
µ◦CO2 -1771.9 -1778.4 -1784.9 -1791.4 -1798.0 -1804.6 -1811.3 -1818.0 -1824.7 -1838.2 -1851.9 -1865.7 -1879.6 -1893.6 -1907.8 -1922.0 -1936.4 -1950.9 -1965.4
S5
µ◦H2 µ◦HCOOH -536.1 -2212.9 -540.1 -2220.7 -544.1 -2228.5 -548.1 -2236.4 -552.2 -2244.3 -556.3 -2252.3 -560.4 -2260.3 -564.5 -2268.4 -568.6 -2276.6 -576.9 -2293.0 -585.3 -2309.7 -593.8 -2326.5 -602.3 -2343.5 -610.9 -2360.8 -619.6 -2378.2 -628.3 -2395.7 -637.0 -2413.5 -645.9 -2431.4 -654.7 -2449.5
µ◦CH4 -1793.5 -1799.3 -1805.2 -1811.2 -1817.2 -1823.2 -1829.3 -1835.4 -1841.6 -1854.1 -1866.7 -1879.6 -1892.6 -1905.8 -1919.1 -1932.6 -1946.2 -1960.0 -1973.9
Table S2: Critical temperatures (Tc ), pressures (Pc ), acentric factors (ω) of carbon monoxide, water carbon dioxide, hydrogen, formic acid and methane. 6,20,24 Component CO H2 O CO2 H2 HCOOH CH4
Tc /[K]
Pc /[bar]
ω
132 647 304 33 577 190
34 220 73 13 75 45
0.066 0.344 0.228 -0.219 0.445 0.012
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References (1) McQuarrie, D. A.; Simon, J. D. Physical Chemistry: A Molecular Approach, 1st ed.; University Science Books: Sausalito, California, 1997. (2) Hill, T. L. An Introduction to Statistical Thermodynamics, 1st ed.; Dover Publications Inc.: New York, USA, 2015. (3) Balaji, S. P.; Gangarapu, S.; Ramdin, M.; Torres-Knoop, A.; Zuilhof, H.; Goetheer, E. L.; Dubbeldam, D.; Vlugt, T. J. H. Simulating the reactions of CO2 in aqueous monoethanolamine solution by reaction ensemble Monte Carlo using the Continuous Fractional Component Method. J. Chem. Theory Comput. 2015, 11, 2661–2669. (4) Poursaeidesfahani, A.; Hens, R.; Rahbari, A.; Ramdin, M.; Dubbeldam, D.; Vlugt, T. J. H. Efficient application of Continuous Fractional Component Monte Carlo in the reaction ensemble. J. Chem. Theory Comput. 2017, 13, 4452–4466. (5) Matito-Martos, I.; Rahbari, A.; Martin-Calvo, A.; Dubbeldam, D.; Vlugt, T. J. H.; Calero, S. Adsorption equilibrium of nitrogen dioxide in porous materials. Phys. Chem. Chem. Phys. 2018, 20, 4189–4199. (6) Chase, M. W.; Curnutt, J.; Prophet, H.; McDonald, R.; Syverud, A. JANAF thermochemical tables, 1975 supplement. J. Phys. Chem. Ref. Data. 1975, 4, 1–176. (7) Cotton, A. F. Chemical applications of group theory, 3rd ed.; Wiley-Interscience: New York, USA, 1990. (8) Stone, E. Complex chemical equilibria: application of Newton-Raphson method to solve non-linear equations. J. Chem. Educ. 1966, 43, 241. (9) Frisch, M. J. et al. Gaussian 09, Revision C.02. Gaussian Inc. Wallingford CT, 2016.
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(10) Gmehling, J.; Kolbe, B.; Kleiber, M.; Rarey, J. Chemical Thermodynamics for Process Simulation, 1st ed.; Wiley-VCH Verlag & GmbH Co. KGaA.: Weinheim, Germany, 2012. (11) Peng, D.-Y.; Robinson, D. B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59–64. (12) Michelsen, M.; Mollerup, J. M. Thermodynamic Models: Fundamental & Computational Aspects, 2nd ed.; Tie-Line Publications: Holte, Denmark, 2007. (13) Kontogeorgis, G. M.; Folas, G. K. Thermodynamic Models for Industrial Applications: from Classical and Advanced Mixing Rules to Association Theories, 1st ed.; John Wiley & Sons: Wiltshire, Great Britain, 2009. (14) Meragawi, S. E.; Diamantonis, N. I.; Tsimpanogiannis, I. N.; Economou, I. G. Hydrate fluid phase equilibria modeling using PC-SAFT and Peng-Robinson equations of state. Fluid Phase Equilib. 2016, 413, 209–219. (15) Diamantonis, N. I.; Boulougouris, G. C.; Mansoor, E.; Tsangaris, D. M.; Economou, I. G. Evaluation of Cubic, SAFT, and PC-SAFT Equations of State for the Vapor-Liquid Equilibrium Modeling of CO2 Mixtures with Other Gases. Ind. Eng. Chem. Res. 2013, 52, 3933–3942. (16) Kwak, T.; Mansoori, G. A. Van der Waals mixing rules for cubic equations of state. Applications for supercritical fluid extraction modelling. Chem. Eng. Sci. 1986, 41, 1303–1309. (17) Lin, C.-T.; Daubert, T. E. Estimation of partial molar volume and fugacity coefficient of components in mixtures from the soave and Peng-Robinson equations of state. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 51–59.
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(18) Abudour, A. M.; Mohammad, S. A.; Jr., R. L. R.; Gasem, K. A. Predicting PR EOS binary interaction parameter using readily available molecular properties. Fluid Phase Equilib. 2017, 434, 130–140. (19) Abudour, A. M.; Mohammad, S. A.; Jr., R. L. R.; Gasem, K. A. Generalized binary interaction parameters for the Peng-Robinson equation of state. Fluid Phase Equilib. 2014, 383, 156–173. (20) Yaws, C. L. Thermophysical properties of chemicals and hydrocarbons, 2nd ed.; Gulf Professional Publishing: Oxford, UK, 2014. (21) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The properties of gases and liquids, 5th ed.; McGraw-Hill New York: New York, USA, 2001. (22) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST reference fluid thermodynamic and transport properties–REFPROP. NIST standard reference database 2002, 23, v7. (23) Walas, S. M. Phase Equilibria in Chemical Engineering; Butterworth-Heinemann: USA, 1985. (24) Chase, M. W. NIST-JANAF themochemical tables, fourth edition. J. Phys. Chem. Ref. Data 1998, 4, 1–1951.
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