The 14th International Congress on Catalysis
New approach to kinetic description of partially-reversible catalytic processes: Kinetics of the CH3OH synthesis at Zn/Cu-containing catalysts as an example Victor E. Ostrovskiia, Elena A. Kadyshevichb a
Karpov Institute of Physical Chemistry, Vorontsovo Pole 10, Moscow, 105064 Russia;
[email protected] Obukhov Institute of Atmospheric Physics,Pyzhevsky 3, Moscow 109117, Russia *Victor E. Ostrovskii: Fax number: 007 (495) 917-2490, E-mail:
[email protected];
[email protected]
Abstract: This consideration relates to the theory of deductions of kinetic equations (KEs) for the heterogeneous catalytic processes having rate-determining steps. A principally new approach to correct consideration of the reversereaction contributions to the observable kinetics is given. It, being applied to the CH3OH synthesis at Cu/Zn-containing catalysts allows derivation of the improved KE well-describing the available kinetic data obtained at 0.1-15 MPa and 450-650 K, including those obtained near the equilibrium; it is shown that the KE can be applied for modeling of manyshelf reactors operating under industrial conditions. The CH3OH-decomposition KE is also deduced and verified.
Keywords: Kinetics of catalytic processes, Methanol-synthesis kinetics, Methanol-synthesis mechanism. 1. Introduction If source substances A, B, etc transform stationary into products L, M, etc, the gross-reaction (GrR) rate, r = r+ − r– = k+ f1 (PA, PB, … PL, PM, …) − k– f2 (PL, PM,…PA, PB,…),
(1)
where r+ and r–- are the rates of the direct and reverse reactions, respectively, k+ and k– are the rate constants, and PA, PB, etc and PL, PM, etc are the pressures. For about 80 years, the procedure of reverse-reaction consideration is based on the notion on the stoichiometric numbers (SNs) of RDSs; the "RDS stoichiometric number" (RDSSN) is the number (ν) of times that the RDS has to occur for the GrR to occur once. However, for any one GrR, ν-values obtained experimentally by different authors vary significantly1 and the theoretical basis for the RDSSN notion is questionable. First, ν-values are, most likely, conditions-dependent and have no physical meaning near the reaction equilibrium, because, under equilibrium, the GrR rates are zero and the direct and reverse rates for any reaction step are the same. Second, although, for any GrR, all stoichiometric equations (SEs) satisfying the requirement of the equality between the numbers of the atoms of each chemical element written to the right and to the left from the equality sign, are quite equivalent, the algebraic deductions based on the use of different SEs and any definite ν value lead to different kinetic equations (KEs). Meanwhile, real kinetics of any reaction should be independent of the set of coefficients chosen for the SE of a GrR. Thus, the problem of consideration of reverse-reaction contribution to the GrR kinetics is not solved. Its solution is given below.
2. Theoretical and Results We consider the common approach by the example of the methanol synthesis (MS). The chemadphases existing at the ZnO-component catalyzing the MS (Z (free ZnO), ZH2, ZCOH2, ZO, ZH2CO2, and ZCO2) and the RDS nature are revealed in2, where the reverse reaction is traditionally considered on the RDSSN basis. The new approach allows us to improve the KE of the MS and to make it theoretically correct. The RDS is
The 14th International Congress on Catalysis
H2 + Z CO2 ↔ Z H2CO2,
(2)
and the rate is determined by the equation, were the coverages by CO2 and H2CO2 should be specified: r = r+ − r− = k+3 PH2 θZCO2 − k−3 θZH2CO2.
(3)
If we have any catalytic GrR presented by an SE with an arbitrary set of stoichiometric coefficients and know a specified RDS for this reaction, this means that, according to the RDS definition, the entire reaction less the RDS is equilibrium (equilibrium equation, EqEq). To write this equilibrium in the form of chemical equation, we should specify the numerical factor (matching coefficient, η) by which we should multiply the RDS equation before its subtraction from the gross-reaction SE. It will be shown that η has a unique value, is of stoichiometric nature, and requires no experiments for its specification; the procedure for its specification for any GrR-RDS pair of equations will be given. Below, (4), (5), and (6) are the arbitrary SE for the MS, the RDS with the corresponding η-value found by us analytically, and the EqEq, respectively. _CO2 + 3 H2 = CH3OH + H2O 3 ZCO2 + 3 H2 ↔ 3 ZH2CO2 CO2 + 3 ZH2CO2 ≡ CH3OH + H2O + 3ZCO2
(4) (5) (6)
If the SE is written in the form 1/3 CO2 + H2 = 1/3 CH3OH + 1/3 H2O (the comparative example), we have η = 1 (ZCO2 + H2 ↔ ZH2CO2) and the EqEq is 1/3 CO2 + ZH2CO2 ≡ 1/3 CH3OH + 1/3 H2O + ZCO2. To deduce the kinetic equation, we use the following mechanistic set, where four equilibriums (the number of the chemadphases minus two), namely, (7), (8), (10), and (11) connect arbitrarily all chemadphases with each other or with the gas components and (12) is obtained by subtraction of (7)+(8)+(10)+(11) from (6): CO2 + Z ≡ ZCO2 H2 + Z ≡ ZH2 ZCO2 + H2 ↔ ZH2CO2 (η = 3) ZH2CO2 + Z ≡ ZO +ZH2CO CH3OH + 2 ZO ≡ H2 + H2O + CO2 + 2Z CO2 + 2 ZH2CO2 + ZH2 + ZH2CO ≡ 2 CH3OH + 2 ZCO2 + ZO + Z
(7) (8) (9) (10) (11) (12)
Solution (in the terms of gas concentrations and equilibrium constants) of the (7)–(12) set relative to θZCO2 and θZH2CO2 and substitution of the corresponding expressions into (3) give the KE considering the reverse reaction with no RDSSN notion. It is important that the above comparative example gives the same KE.
3. Discussion Successful applications of this approach to descriptions of available data on the methanol synthesis and decomposition at 0.1-15 MPa and 450-650 K and to reactor modeling are discussed. Equilibrium constants for the KE are estimated from our calorimetric data3 and are specified in the course of these calculations.
4. Conclusion A new approach to kinetic description and modeling of partially-reversible catalytic processes is developed.
References 1. S.W. Weller, Catal. Rev.-Sci. Eng., 34 (1992) 227. 2. V.E. Ostrovskii, Catal. Today, 77 (2002) 141. 3. V.E. Ostrovskii, Ind. Eng. Chem. Res. 43 (2004) 3113.
