Non-steady-state approach t o steady-state kinetics: cas e study of H2S oxidation by oxygen
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1 Boresov Institute of Catalysis From the SelectedWors of Andrey N Zagoruio December, 2003 Non-steady-state approach t o steady-state inetics: cas e study of H2S oxidation by oxygen Andrey N Zagoruio Vladimir V Morinsii, Boresov Institute of Catalysis Available at:
2 Non-steady steady-state state approach to steady-state state inetics: case study of H 2 S oxidation by oxygen Andrey N. Zagoruio,, Vladimir V. Morinsii Boresov Institute of Catalysis Pr.Lavrentieva,, 5, , Novosibirs, Russia, zagor@catalysis.ru ru Corresponding author
3 Approach idea Transient inetic models of catalytic reactions are usually used for development and simulation of nonstationary processes. At the same time it is possible to use transient models for description of steady- state regimes. Such approach may become reasonable when complicated reaction mechanism leads give no way for elaboration of algebraic c equations for reactions rates or in case of other complications.
4 Case study: H 2 S oxidation to sulfur The process may be described by a set of reactions: H 2 S + ½ O 2 1/n S n + H 2 O (1) H 2 S + 3/2 O 2 SO 2 + H 2 O (2) H 2 S + ½ SO 2 1.5/n S n + H 2 O (3) Thermodynamic analysis: reactions (1) and (2) are practically irreversible, reversible, while Claus reaction (3) may be significantly equilibrium limited, especially ecially at elevated temperature and reaction gas moisture. Catalyst Commercial V/Ti catalyst ICT produced by Katalizator Company, Novosibirs, Russia
5 Kinetic experiments The steady-state state inetics of reaction system (1-3) was studied experimentally using direct-flow lab setup. Kinetic experiments included variation of reaction temperature (in( range C) and reagents (H 2 S, O 2, SO 2, H 2 O) inlet concentrations. Special tests with different catalyst pellets size confirmed the achievement of pure inetic area (with no diffusion limitations). Additional experiments proved the ideal mixing regime in the reactor. Complication: it was impossible to measure sulfur vapors concentration in outlet stream it is impossible to correctly distinguish the individual rates of reactions (1-3) from experimental data
6 Theoretical basis for development of reaction inetic scheme Catalytic activity is provided by vanadia only, titania serves as support only; V 2 O 5 under reaction conditions quicly reduces, surface reduction/oxidation idation in the reaction are provided by V V 2 O 3 cycles; H 2 S is involved in reaction via interaction with oxidized site resulting in formation of sulfided site and water; sulfided site may desorb sulfur and turn into reduced site; sulfided site may interact with neighboring oxidized sites with formation n of SO 2 ; reduced site may be reoxidized by both O 2 (quicly) and SO 2 (slowly).
7 Hypothesis of reaction inetic scheme H 2 S + ZO ZS + H 2 O (4) ZS Z + 1/6 S 6 (5) ZS +2 ZO SO Z (6) Z + ½ O 2 ZO (7) where ZO corresponds to oxidized active site (surface V 2 O 4 ), ZS sulfided site (surface V 2 O 3 S) and Z reduced site (surface V 2 O 3 ). NB: this is not detailed reaction mechanism, just reaction stages s scheme! Nevertheless, this scheme qualitatively describes regularities of reactions and, furthermore, it is thermodynamically consistent, being able to describe d reversibility of Claus reaction, using usual equilibrium constant t approach
8 Kinetic model of reaction stages The rates of stages (4-7) may be expressed in terms of mass-action action law : 1 r1 = 1CH 2Sθ O θ SCH 2O P1 r r = θ 2 1/ S S 6 P2 = θ θ θ C θ C S O SO2 P3 r = C 1/ O2 θ (8) (9) (10) (11) where θ O, θ S and θ - surface concentrations (surface fractions) of ZO, ZS и Z respectively, i rate constants, рi equilibrium constants.
9 Rates for reaction mixture gaseous and surface components W H2S = - r 1 W S6 = r 2 W SO2 = r 3 (12) W O2 = -1/2 r 4 W H2O = r 1 θ 0 / τ = -r 1 2 r 3 + r 4 θ S / τ = r 1 r 2 r 3 (13) θ/ τ τ = r r 3 - r 4 Thermodynamic consistence of a model is provided by evident relationship 2 3 P1 P2 (14) P3 = 2 K where Kp equilibrium constant for Claus reaction. P
10 Elaboration of steady-state state model Conventional procedure: all rates for intermediate surface compounds θ i / τ should be made equal to zero to eliminate surface concentrations and to express reaction rates via gas concentrations only. Complications: third orders of surface concentrations in equation (10) such system cannot be resolved algebraically; the individual rates of reactions (1-3) cannot be separated because this reaction system contains intersection of participating substances; separate investigation of Claus reaction inetics (in absence of oxygen) is possible but it was found that oxygen strongly influences the catalyst surface state and, evidently, in presence of oxygen Claus reaction rate will be significantly different. Elaboration of usual steady-state inetic equations is impossible
11 Nonstationary approach to steady-state state inetics Idea: to use equations (8-14) as a transient inetic model to describe reaction rates. To obtain the steady-state solution it is necessary to numerically integrate surface rate expressions (13) starting from zero time to infinite time until the moment when all transient equations (13) become equal to zero. Such procedure gives the steady-state values of θ i corresponding to given set of gas concentrations and, therefore, gives the way to calculate reaction rates for individual components (equations (12)). The optimal values of rate and equilibrium constants may be then be defined by application of conventional minimization procedure using whole experimental array.
12 Data fitting results (a) (b) 0,03 1 Concentration diffrence 0,02 0,01 H2S O2 SO2 Selectivity 0,98 0,96 0,94 0, ,01 0,02 0,03 0,04 0,9 0 0,01 0,02 0,03 0,04 H2S concentration (mol.fraction) H2S concentration (mol.fractions) Results of experimental steady-state data description by non-steady-state model under variation of H2S inlet concentration: (a) - reaction rates (in terms of difference between inlet and outlet concentrations), (b) - selectivity of oxidation into sulfur. Lines model, points experiments.
13 Advantages of the proposed approach The proposed model provides adequate description both for cases of complete reaction system and Claus reaction performance only. It has good predictive force for such important reaction parameter as selectivity in a wide concentration and temperature range. It reflects observed reaction sophisticated regularities lie slight decrease of reaction rate and selectivity with rise of water vapors content etc. Obtained values of model parameters show correct behavior with variation of reaction temperature: rate constants are increasing and adsorption equilibrium constants are decreasing under temperature rise with character of changing closed to Arrhenius type. Model is physically and thermodynamically consistent.
14 Conclusion Non-steady-state inetic models may be used for treatment of steady-state inetic data in case when algebraic elaboration of steady-state inetic equations is impossible or complicated. The proposed approach includes numerical integration of time-dependent differential equations until achievement of steady-state, resulting in possibility to numerically obtain the rate values for separate reaction stages for given composition of reaction mixture. The obtained non-steady-state model may be then applied in simulation of catalyst pellets and catalyst beds in research and engineering purposes.
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