Transcript Slide 1
Application of reaction route graphs to microkinetic analysis and design of water-gas-shift catalysts Caitlin A. Callaghan, Ilie Fishtik and Ravindra Datta Fuel Cell Center Chemical Engineering Department Worcester Polytechnic Institute Worcester, MA Introduction First principles calculations are becoming indispensable Molecular rearrangements on surfaces can be “seen” Reaction energetic calculations are becoming more reliable Microkinetic models are becoming increasingly available What more can be done? Kinetics LHHW Approach Rate expressions derived based on RDS, QE, QSSA, MARI Fitted to data Basic mechanism and assumptions are generally arbitrary Microkinetic Approach Involves elementary reaction kinetics No simplifying assumptions made Arbitrary mechanism Substantial computational effort is required Opaque Reaction Route Graph Theory Powerful new tool in graphical and mathematical depiction of reaction mechanisms New method for mechanistic and kinetic interpretation “RR graph” differs from “Reaction Graphs” – Branches elementary reaction steps – Nodes multiple species, connectivity of elementary reaction steps Reaction Route Analysis, Reduction and Simplification – Enumeration of direct reaction routes – Dominant reaction routes via network analysis – RDS, QSSA, MARI assumptions based on a rigorous De Donder affinity analysis – Derivation of explicit and accurate rate expressions for dominant reaction routes RR Graphs A RR graph may be viewed as hikes through a mountain range: – Valleys are the energy levels of reactants and products – Elementary reaction is hike from one valley to adjacent valley – Trek over a mountain pass represents overcoming the energy barrier RR Graph Topology Overall Reaction Routes (ORRs): – a RR in which the desired OR is produced Empty Reaction Routes (ERRs): – a RR in which a zero OR is produced (a cycle) Intermediate Nodes (INs): – a node including ONLY the elementary reaction steps Terminal Nodes (TNs): – a node including the OR in addition to the elementary reaction steps Electrical Analogy Kirchhoff’s Current Law a b – Analogous to conservation of mass ra rb rc rd re 0 e c d Kirchhoff’s Voltage Law – Analogous to thermodynamic consistency Af + Ag Ah Ai 0 Ohm’s Law – Viewed in terms of the De Donder Relation r r s ln r A R r s r r r f g i h The WGSR Mechanism s 1: s 2: s 3: s 4: s 5: s6: s 7: s 8: s 9: s10: s11: s12: s13: s14 : s15 : s16: s17: On Cu(111) E A Elementary Reactions E A ΔH 0 0 5.3 15.3 5.5 25.4 10.7 0 15.5 0 1.4 4.0 29.0 26.3 1.3 0.9 14.6 106 106 4 1012 1013 6 1012 1013 1013 1013 1013 1013 1013 1013 1013 1013 1013 1013 1013 H2O + S H2OS CO + S COS CO2S CO2 + S HS + HS H2S + S H 2S H 2 + S H2OS + S OHS + HS COS + OS CO2S + S COS + OHS HCOOS + S OHS + S OS + HS COS + OHS CO2S + HS HCOOS + S CO2S + HS HCOOS + OS CO2S + OHS H2OS + OS 2OHS H2OS + HS OHS + H2S OHS + HS OS + H2S HCOOS + OHS CO2S + H2OS HCOOS + HS CO2S + H2S 13.6 12.0 0 12.8 0 1.6 28.0 20.4 20.7 22.5 3.5 0.9 0 0 4.0 26.8 14.2 1014 1014 106 1013 106 1013 1013 1013 1013 1013 1013 1013 1013 1013 1013 1013 1013 -13.6 -12.0 5.3 2.5 5.5 23.8 -17.3 -20.4 -5.2 -22.5 -2.1 3.1 29.0 26.3 -2.7 -25.9 0.4 a,b a,b a,b a a,b a a a a a a a a a a a a a - activation energies in kcal/mol (θ 0 limit) estimated according to Shustorovich & Sellers (1998) and coinciding with the estimations made in Ovesen, et al. (1996); pre-exponential factors from Dumesic, et al. (1993). b – pre-exponential factors adjusted so as to fit the thermodynamics of the overall reaction; The units of the pre-exponential factors are Pa-1s-1 for adsorption/desorption reactions and s-1 for surface reactions. Constructing the RR Graph 1. Select the shortest MINIMAL ORR OR = s1 + s2 + s3 + s5 + s10 + s14 s1 s2 s14 s10 s3 s5 s5 s3 s10 s14 s2 s1 Constructing the RR Graph 2. Add the shortest MINIMAL ERR to include all elementary reaction steps s712 –––ss12 s1717===000 4 ++ss8911 615 14 10 15 s11 s1 s2 s7 s3 s12 s8 s10 s14 s6 s5 s17 s9 s7 s4 s15 Only s13 and s16 s6 s14 s17 s5 are left to be included s15 s s9 4 s10 s8 s12 s3 s2 s11 s1 Constructing the RR Graph 3. Add remaining steps to fused RR graph s11 s1 s2 s13 s7 s5 s3 s17 s14 s6 s16 s13 – s14 + s15 = 0 s12 + s13 – s16 = 0 s12 s8 s10 s s4 9 s15 s15 s s9 4 s10 s8 s12 s3 s7 s13 s16 s6 s14 s17 s5 s2 s11 s1 Constructing the RR Graph 4. Balance the terminal nodes with the OR OR s1 s2 s14 s13 s15 s10 s11 s17 s4 s16 s9 s6 s8 s5 s3 s5 s2 s1 s8 s6 s7 s12 s12 s7 s3 s9 s4 s11 s10 OR s16 s17 s15 s13 s14 Microkinetics We may eliminate s13 and s16 from the RR graph; they are not kinetically significant steps This results in TWO symmetric sub-graphs; we only need one n 6 R15 R1 n1 R2 n2 R6 n3 R12 R17 R9 R4 R7 n5 R8 R11 R14 R10 n4 + Aoverall – n7 R3 n8 R5 Network Reduction Experimental Conditions R4 + R6 vs. R14 Space time = 1.80 s FEED: H2Oinlet = 0.10 n6 R15 R1 n1 R2 n2 R6 n3 R17 CO2 inlet = 0.00 R12 R9 R4 R11 R10 n4 Aoverall – H2 inlet = 0.00 R7 n5 R8 R14 + COinlet = 0.10 n7 R3 n8 R5 Network Reduction Experimental Conditions R4 + R6 vs. R14 Space time = 1.80 s 15 10 FEED: COinlet = 0.10 H2Oinlet = 0.10 CO2 inlet = 0.00 H2 inlet = 0.00 10 Resistance (rate-1) 10 R14 5 10 0 R4 + R 6 10 -5 10 273 373 473 573 Temperature (K) 673 773 873 Network Reduction Experimental Conditions Effect of R14 on Conversion Space time = 1.80 s FEED: 0.8 COinlet = 0.10 H2Oinlet = 0.10 0.7 CO2 inlet = 0.00 H2 inlet = 0.00 Conversion of CO 0.6 0.5 0.4 0.3 0.2 Complete M echanism M echanism without s 0.1 14 0 273 373 473 573 Temperature (K) 673 773 873 Network Reduction Experimental Conditions R4 + R11 vs. R17 Space time = 1.80 s FEED: H2Oinlet = 0.10 n6 R15 R1 n1 R2 n2 R6 n3 R17 CO2 inlet = 0.00 R12 R9 R4 n5 R8 R11 n4 Aoverall – H2 inlet = 0.00 R7 R10 + COinlet = 0.10 n7 R3 n8 R5 Network Reduction Experimental Conditions R4 + R11 vs. R17 Space time = 1.80 s 25 10 FEED: COinlet = 0.10 H2Oinlet = 0.10 20 CO2 inlet = 0.00 10 Resistance (rate-1) H2 inlet = 0.00 15 10 10 10 R17 5 10 0 R4 + R11 10 -5 10 273 373 473 573 Temperature (K) 673 773 873 Network Reduction Experimental Conditions Effect of R17 on Conversion Space time = 1.80 s 0.8 FEED: COinlet = 0.10 H2Oinlet = 0.10 0.7 CO2 inlet = 0.00 H2 inlet = 0.00 Conversion of CO 0.6 0.5 0.4 0.3 0.2 Complete M echanism M echanism without s 0.1 17 0 273 373 473 573 Temperature (K) 673 773 873 Network Reduction Experimental Conditions R9 + R12 vs. R11 Space time = 1.80 s FEED: H2Oinlet = 0.10 n6 R15 R1 n1 R2 n2 R6 n3 CO2 inlet = 0.00 R12 R9 R4 n5 R8 R11 n4 Aoverall – H2 inlet = 0.00 R7 R10 + COinlet = 0.10 n7 R3 n8 R5 Network Reduction Experimental Conditions R9 + R12 vs. R11 Space time = 1.80 s 25 10 FEED: COinlet = 0.10 H2Oinlet = 0.10 20 CO2 inlet = 0.00 10 Resistance (rate-1) H2 inlet = 0.00 15 10 10 10 R9 + R12 5 10 0 10 R11 -5 10 273 373 473 573 Temperature (K) 673 773 873 Network Reduction Experimental Conditions Effect of R9 and R12 on Conversion Space time = 1.80 s 0.8 FEED: COinlet = 0.10 H2Oinlet = 0.10 0.7 CO2 inlet = 0.00 H2 inlet = 0.00 Conversion of CO 0.6 0.5 0.4 0.3 0.2 0.1 0 273 Complete M echanism M echanism without s9 and s12 373 473 573 Temperature (K) 673 773 873 Network Reduction Experimental Conditions Space time = 1.80 s FEED: H2Oinlet = 0.10 n6 CO2 inlet = 0.00 H2 inlet = 0.00 R7 R15 R1 n1 R2 n2 R6 n3 n5 R8 R4 R11 R10 n4 + COinlet = 0.10 Aoverall – n7 R3 n8 R5 Reduced Rate Expression R6 n2 n3 R15 n6 R7 R11 n5 R8 n7 R10 Aoverall rOR k6 K1 PH2O θ02 k8 k10 K 2 PCO k15 PH1/2 2 K 4 K5 k 6 K6 k15 PH1/2 2 K 4 K5 1/ 2 where 0 1/ 2 k8 k10 K 2 PCO 1 1 K1 PH2O K 2 PCO PH1/22 K 4 K5 1/ 2 1 P CO2 PH 2 KPH2O PCO Assume that OHS is the QSS species. Microkinetic Model Simulation for Cu 1 Conversion of CO Experimental Conditions Space time = 1.80 s 0.8 FEED: COinlet = 0.10 H2Oinlet = 0.10 0.6 CO2 inlet = 0.00 H2 inlet = 0.00 0.4 Experiment 0.2 Equilibrium Simplified Model 0 0 100 200 300 400 Temperature (oC) 500 600 Conclusions Predicted kinetics can provide for reliable microkinetic models. Reaction network analysis is a useful tool for reduction, simplification and rationalization of the microkinetic model. Analogy between a reaction network and electrical network exists. The analogy between reaction routes and electrical circuits provides a useful interpretation of kinetics and mechanism Application of the proposed formalism to the analysis of the WGS reaction mechanism validated the reduced model developed earlier based solely on a numerical RR analysis.