First-principles based catalytic reaction engineering Matteo Maestri

Transcription

1 CECAM International Summer School Hot topic 4 First-principles based catalytic reaction engineering Matteo Maestri July 23, 2013 Conversationshaus - Norderney, Germany

2 Catalytic cycle Consists of the elementary steps through which the reactants convert to the products [CO] Rh + [OH] Rh + [H] Rh CO [CO 2 ] Rh +2[H] Rh [H] Rh +[OH] Rh + Rh RDS CO 2 [H 2 O] Rh + 2Rh H 2 H 2 O

3 E pluribus unum Result of the interplay among phenomena at different scales Microscale COOH*+* CO*+OH* CO*+OH* COOH*+* COOH*+* CO 2 *+H* CO 2 *+H* COOH*+* CO 2 * + H 2 O* COOH* + OH* COOH* + OH* CO 2 * + H 2 O* CO 2 *+H* HCOO** HCOO** CO 2 *+H* CO 2 * + OH* + * HCOO** + O* HCOO** + OH* CO 2 * + H 2 O* CH* + H* CH 2 * + * CH* + * C* + H* C* + H* CH* + * CH 3 * + O* CH 2 * + OH* CH 2 * + OH* CH 3 * + O* CH* + OH* CH 2 * + O* CH 2 * + O* CH* + OH* ~ 10 2 potential different coverages [CO 2 ] Rh +2[H] Rh CO 2 H 2 [CO] Rh + [OH] Rh + [H] Rh CO [H] Rh +[OH] Rh + Rh [H 2 O] Rh + 2Rh H 2 O RDS Temperature [ C] mmol/s Macroscale CH 4 T gas O2 T catalyst CO H 2 H 2 O CO Axial length [mm]

4 Need of bridging between the scales Length MACROSCALE Reactor engineering and transport phenomena MESOSCALE Interplay among the chemical events MICROSCALE making and breaking of chemical bonds INTRINSIC FUNCTIONALITY Time

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6 From a traditional approach to CRE Length MACROSCALE Reactor engineering and transport phenomena MESOSCALE Interplay among the chemical events MICROSCALE making and breaking of chemical bonds effective/simplified approaches Time

7 to a first-principles approach to CRE Length MACROSCALE Reactor engineering and transport phenomena CFD MESOSCALE Interplay among the chemical events MK/kMC MICROSCALE making and breaking of chemical bonds Electronic structure theory Time

8 Need of bridging between the scales Length M. Maestri in New strategy for chemical synthesis and catalysis, Wiley-VCH (2012) MACROSCALE Reactor engineering and transport phenomena CFD MESOSCALE Interplay among the chemical events MK/kMC MICROSCALE making and breaking of chemical bonds Electronic structure theory Time

9 Need of bridging between the scales Length MESOSCALE Interplay among the chemical events MACROSCALE Reactor engineering and transport phenomena MK CFD Complex geometries MICROSCALE making and breaking of chemical bonds Electronic structure theory Microkinetic modeling Time

10 Outline Length Methodology Show-cases MACROSCALE Reactor engineering and transport phenomena MESOSCALE Interplay among the chemical events MICROSCALE making and breaking of chemical bonds M. Maestri & A. Cuoci Time

11 Outline Length Methodology Show-cases MACROSCALE Reactor engineering and transport phenomena MESOSCALE Interplay among the chemical events MICROSCALE making and breaking of chemical bonds M. Maestri & A. Cuoci Time

12 Governing equations Catalytic wall Gas-phase ρ + ( ρv) = t 0 continuity T 2 ( ρv) + ( ρ vv) = p + µ ( v + v ) µ ( v) I + ρg t 3 momentum t ( ρω ) ( ρω v) ( ρω V ) + = +Ω hom k k k k k k = 1,..., NG mass NG NG ρ ˆ T hom C + ρcˆ v T = ( λ T) ρ ˆ C ω ˆ Ω, V H t hom P P P k k k k k k= 1 k= 1 energy

13 Governing equations Non-catalytic walls ( ) ωk =0 inert T ( ) T = g tt, inert ργ ω = α Ω het, k = 1,..., NG k mix k catalytic cat k ( ) inert Catalytic walls NR het cat j j j = 1 het λ T = α H r catalytic ( ) = f tt, θi σ =Ω het cat i i = 1,..., NS t Adsorbed (surface) species Detailed microkinetic models COOH*+* CO*+OH* CO*+OH* COOH*+* COOH*+* CO 2 *+H* CO 2 *+H* COOH*+* CO 2 * + H 2 O* COOH* + OH* COOH* + OH* CO 2 * + H 2 O* CO 2 *+H* HCOO** HCOO** CO 2 *+H* CO 2 * + OH* + * HCOO** + O* HCOO** + OH* CO 2 * + H 2 O* CH* + H* CH 2 * + * CH* + * C* + H* C* + H* CH* + * CH 3 * + O* CH 2 * + OH* CH 2 * + OH* CH 3 * + O* CH* + OH* CH 2 * + O* CH 2 * + O* CH* + OH* M. Maestri, Microkinetic analysis of complex chemical processes at surface, in New strategy for chemical synthesis and catalysis, Wiley-VCH (2012)

14 Numerical challenges Dimensions of the system Proportional to the number of species Proportional to the number of cells Stiffness Different temporal scales involved Different spatial scales involved Non-linearity Source term non linear in concentrations and temperature Coverage dependence of activation energy

15 Numerical solution Detailed kinetic schemes Fully segregated algorithms easy to implement and computationally efficient unfeasible when large, stiff kinetic mechanisms are used Complex geometries Strong non linearity of reaction terms High stiffness Fully coupled algorithms all the processes and their interactions are considered simultaneously natural way to treat problems with multiple stiff processes the resulting system of equations can be extremely large and the computational cost prohibitive Operator-splitting methods usually avoid many costly matrix operations allow the best numerical method to be used for each type of term or process the resulting algorithms can be very complex and usually differ from term to term

16 Operator-splitting algorithm Reaction Diffusion, convection... Strang splitting scheme Z. Ren, S. B. Pope, Journal of Computational Physics, 2008 M. Maestri, A. Cuoci, Chemical Engineering Science, 96 (2013)

17 Reactor network Catalytic wall Gas mixture Each computational cell behaves as a chemical reactor in the splittingoperator algorithm (chemical step) Each reactor is described by a set of stiff ODE, which must be integrated on the time step Δt Batch reactor Batch reactor M. Maestri, A. Cuoci, Chemical Engineering Science, 96 (2013)

18 Reactor network Homogeneous reactions Catalytic wall Catalytic wall NF NF NG d hom 1 cat het cat het k k j Aj k, j k j Aj k, j dt V j 1 j 1 k 1 ˆ dt ˆ 1 C H A H ˆ H i, j het cat i, j i= 1,...,NS j=1,...,nf t NG NF NG hom hom cat het het ˆ hom P k k j j k, j k, j k dt k 1 V j 1 k 1 k=1,ng Homogeneous reactions NF NF NG d hom 1 cat het cat het k k j Aj k, j k j Aj k, j dt V j 1 j 1 k 1 ˆ dt ˆ 1 C H A H ˆ H i, j het cat i, j i= 1,...,NS j=1,...,nf t NG NF NG hom hom cat het het ˆ hom P k k j j k, j k, j k dt k 1 V j 1 k 1 k=1,ng

19 Operator-splitting algorithm ti ti+1 ti+2 ti ti+1 ti+2 ti ti+1 ti+2 The procedure is iterated on the next time step M. Maestri, A. Cuoci, Chemical Engineering Science, 96 (2013)

20 Jacobian matrix Global system N U N U N C N C Jacobian matrix: Sparse Unstructured Blocks

21 Source term Global system Source term Jacobian matrix: Sparse Diagonal

22 Transport term Global system Source term Transport term Jacobian matrix: Sparse Unstructured

23 Operator-splitting algorithm Global system Source term Transport term

24 Solution procedure Navier-Stokes Eqs. (PISO predictor) Main features: Reactor network (Strang predictor) Properties evaluation Transport Eqs. (Strang corrector) Pressure Eqn. Velocity correction (PISO corrector) Solution of the Navier-Stokes equations (laminar and turbulent regime) No limit to the number of species and reactions No limit in geometry

25 catalyticfoam structure OpenFOAM Complex CFD Numerical library for stiff ODEs system (LSODE, RADAU5, CVODE, BzzMath, etc.) CFD code for reacting flows with heterogeneous reactions CatalyticSMOKE Surface microkinetics OpenSMOKE Complex gas-phase chemistry M. Maestri, A. Cuoci, Chemical Engineering Science, 96 (2013)

26 Outline Length Methodology Show-cases MACROSCALE Reactor engineering and transport phenomena MESOSCALE Interplay among the chemical events MICROSCALE making and breaking of chemical bonds M. Maestri & A. Cuoci Time

27 Show-case I: Rashig-ring bed 1.5 cm Inlet mixture 5 cm Rashig-ring: 1 cm 0.5 cm 0.2 cm Mesh generation in collaboration with Dr. S. Lipp BASF SE, DE

28 Show-case I: Rashig-ring bed Laminar flow (Re = 50) Inlet mixture Operating conditions Internal diameter 1.5 cm Total length 5 cm H 2 mole fraction 0.04 (-) O 2 mole fraction 0.01 (-) N 2 mole fraction 0.95 (-) Temperature K Inlet velocity 0.2 m/s C1 microkinetic model on Rh: 82 reaction steps 13 adsorbed species UBI-QEP and DFT refinement M. Maestri et al., AIChE J., 2009

29 Inlet mixture Show-case I: Rashig-ring bed

30 Show-case I: Rashig-ring bed Inlet mixture Flow-field

31 Show-case I: Rashig-ring bed Inlet mixture Flow-field recirculation u [m/s] By-pass zone

32 Show-case I: Rashig-ring bed Inlet mixture Gas-phase species

33 Show-case I: Rashig-ring bed Inlet mixture Gas-phase species

34 Show-case I: Rashig-ring bed Adsorbed species at the catalyst surface Inlet mixture

35 Show-case I: Rashig-ring bed Adsorbed species at the catalyst surface Inlet mixture zx zy

36 Show-case I: Rashig-ring bed Dynamics of the system

37 Show-case I: Rashig-ring bed Dynamics of the system

38 Show-case II: packed bed of spheres 4 mm Inlet mixture 10 mm Catalytic particle: 600 µm Mesh generation in collaboration with Prof. Freund Erlangen University, DE

39 Show-case II: packed bed of spheres 4 mm Inlet mixture 10 mm 3D Unstructured Mesh: ~2,000,000 cells Homogeneous reactors: ~1,000,000 Heterogeneous reactors: ~1,000,000

40 Show-case II: packed bed of spheres Laminar flow (Re = 20) Inlet mixture Operating conditions Inlet diameter 4 mm Total length 10 mm H 2 mole fraction 0.036(-) O 2 mole fraction 0.014(-) N 2 mole fraction 0.95 (-) Temperature 573 K Inlet velocity 1.7 m/s C1 microkinetic model on Rh: 82 reaction steps 13 adsorbed species UBI-QEP and DFT refinement M. Maestri et al., AIChE J., 2009

41 Show-case II: packed bed of spheres Flow-field Inlet mixture By-pass zone

42 Show-case II: packed bed of spheres Flow-field

43 Show-case II: packed bed of spheres y Gas-phase species x

44 A first-principles approach to CRE Length MACROSCALE Reactor engineering and transport phenomena CFD MESOSCALE Interplay among the chemical events In collaboration with: K. Reuter and S. Matera (TUM) kmc MICROSCALE making and breaking of chemical bonds MK M. Maestri & A. Cuoci Time

45 First-principles kinetic Monte Carlo Evaluate the statistical interplay of large number of elementary processes open non-equilibrium system need to explicitely follow the time evolution rare event dynamics Molecular Dynamics simulations unsuitable. Map on a lattice model Markov jump process description adsorbed O adsorbed CO bridge rows cus rows d dt P ( x,t )= y k ( x, y) P ( y, t) y k ( y, x) P ( x, t) Each site a has own entry in x denoting its adsorbate state x a Simulate trajectories x(t) (kinetic Monte Carlo) Image courtesy of Dr. S. Matera (TUM) K. Reuter and M. Scheffler, Phys. Rev. B 73, (2006)

46 Linking the scales Continuum equations need boundary conditions for the mass fluxes j α at the surface: j α n Coupled problem: to determine the TOF with 1p-kMC the pressures at the surface are needed, but the pressure field depends on the TOF kmc too expensive for direct coupling to the flow solver Run kmc beforehand and interpolate (Modified Shepard) Very efficient Easily extendable to more complex geometries = v α M α TOF TOF(x cm -2 s -1 ) T s = 600K, p s (O₂)= 1atm kmc (raw) kmc (interpolation) 0.5 p s (CO) (atm) S. Matera and K. Reuter, Catal. Lett. 133, (2009); Phys. Rev. B 82, (2010). 50

47 Linking the scales Continuum equations need boundary conditions for the mass fluxes j α at the surface: j α n Coupled problem: to determine the TOF with 1p-kMC the pressures at the surface are needed, but the pressure field depends on the TOF kmc too expensive for direct coupling to the flow solver Run kmc beforehand and interpolate (Modified Shepard) Very efficient Easily extendable to more complex geometries = v α M α TOF TOF(x cm -2 s -1 ) T s = 600K, p s (O₂)= 1atm kmc (raw) kmc (interpolation) 0.5 p s (CO) (atm) S. Matera and K. Reuter, Catal. Lett. 133, (2009); Phys. Rev. B 82, (2010). 50

48 Linking the scales Continuum equations need boundary conditions for the mass fluxes j α at the surface: j α n = v α M α TOF Coupled problem: to determine the TOF with 1p-kMC the pressures at the surface are needed, but the pressure field depends on the TOF kmc too expensive for direct coupling to the flow solver Run kmc beforehand and interpolate (Modified Shepard) Very efficient Easily extendable to more complex geometries TOF(x cm -2 s -1 ) T s = 600K, p s (O₂)= 1atm kmc (raw) kmc (interpolation) 0.5 p s (CO) (atm) Karsten s tutorial this afternoon S. Matera and K. Reuter, Catal. Lett. 133, (2009); Phys. Rev. B 82, (2010). 50

49 Show-case: the reactor STM

50 Show-case: the reactor STM Rasmussen et al., Review of scientific instrument, 69 (1998) 3879 CO oxidation on Ru 2 O inlet CO + O 2 outlet Rate constants k(x,y) from DFT and harmonic Transition State Theory Model system: CO oxidation on RuO 2 (110) 2 types of sites, bridge and cus Operating conditions T: 600 K P: 1 atm Inlet: CO + O2 (66%, 34% Vol) Inlet velocity: 5 cm/s Catalytic Wall Catalyst: Ru 2 O K. Reuter and M. Scheffler, Phys. Rev. B 73, (2006) catalyticfoam (interpolated kmc)

51 Show-case: the reactor STM Rasmussen et al., Review of scientific instrument, 69 (1998) 3879 d = 2 mm inlet CO + O 2 outlet Operating conditions T: 600 K P: 1 atm Inlet: CO + O2 (66%, 34% Vol) Inlet velocity: 5 cm/s Catalytic Wall Catalyst: Ru 2 O Computational details Mesh: unstructured, ~90,000 cells Discretization: 2 nd order, centered Max time step: 10-4 s CPU time: ~2 s per time step

52 Results Stream lines Strong recirculations Catalytic Wall Catalyst: Ru 2 O

53 Conclusions & perspectives Efficient coupling between heterogeneous microkinetic models and computational fluid dynamics (complex and fundamental chemistry with complex and general geometries) Description of the solid phase (diffusion/conduction and reaction within the solid: assessment of internal mass transfer limitation) Implementation of the interpolated kmc methodology in catalyticfoam (in collaboration with K. Reuter/S. Matera, TUM) Multiscale framework for the first-principles analysis of catalytic processes

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55 M. Maestri & A. Cuoci Tiziano Maffei, G. Gentile, F. Manelli, S. Rebughini, S. Goisis, A. Osio, M. Calonaci, F. Furnari, B. Baran, Y. Niyazi

56 Thank you for your attention! Politecnico di Milano Raffaello, The school of Athens, 1509, Apostolic Palace, Roma