Matteo Maestri & Alberto Cuoci. Multiscale modeling of heterogeneous catalytic reactors in OpenFOAM

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1 Department of Energy & Department of Chemistry, Materials, and Chemical Engineering Matteo Maestri & Alberto Cuoci Multiscale modeling of heterogeneous catalytic reactors in OpenFOAM HPC enabling of OpenFOAM for CFD applications 6 April 2016 The catalyticfoam group The catalyticfoam Group Matteo Maestri heterogeneous catalysis, multiscale modeling, microkinetic modeling Alberto Cuoci CFD, numerical methods Stefano Rebughini (PhD Student) Hierarchical analysis of complex reacting systems, microchannel reactors Mauro Bracconi (PhD student) ISAT, complex geometries, metallic foams Former Students Sandro Goisis and Alessandra Osio Development of numerical methodology Giancarlo Gentile and Filippo Manelli Development of multi-region solver Tiziano Maffei Improvement of multi-region solver Salvatore Raffa Automatic generation of meshes for packed bed reactors 1

2 catalyticfoam project Chemical reactor engineering Catalytic reactor design: Important in chemical industry (~90% of industrial chemical processes are catalytic) Need for an accurate design to provide high yields ( ) Need for a deep understanding for advanced design 2

3 Chemical reactor engineering Catalytic reactor design: Important in chemical industry (~90% of industrial chemical processes are catalytic) Need for an accurate design to provide high yields ( ) Need for a deep understanding for advanced design A multiscale phenomenon 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] 3

4 Catalysts at work A B Boundary layer 1 7 Film diffusion Porous catalyst 2 6 Pore diffusion Active sites A Chemical reaction B Adsorption/ desorption Need of bridging between the scales Length [m] 10 0 MACROSCALE Reactor engineering and transport phenomena 10-3 MESOSCALE 10-6 Interplay among the chemical events 10-9 MICROSCALE Making and breaking of chemical bonds Intrinsic functionality Microkinetic analysis of complex chemical processes at surfaces, M. Maestri in New strategy for chemical synthesis and catalysis Wiley, Time [s] 4

5 A first-principles approach to CRE Length [m] 10 0 MACROSCALE Reactor engineering and transport phenomena CFD MESOSCALE Interplay among the chemical events MK/kMC 10-9 MICROSCALE Making and breaking of chemical bonds Electronic structure theory Time [s] Need of new numerical tools Length [m] 10 0 MACROSCALE Reactor engineering and transport phenomena MESOSCALE Interplay among the chemical events 10-9 MICROSCALE Making and breaking of chemical bond Development of a new solver Time [s] 5

6 Need of new numerical tools Length [m] 10 0 MACROSCALE CFD 10-3 MESOSCALE 10-6 MICROSCALE 10-9 Detailed kinetic mechanism Time [s] catalyticfoam structure 6

7 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Simulation with detailed kinetics: stiff ODE solvers and ISAT Validation and examples Annular reactor CPO of CH 4 on platinum gauze (complex 3D geometry) CPO of iso-octane (complex chemistry) Tubular reactor with Raschig rings (complex 3D geometry) Packed bed reactors for industrial applications (complex 3D geometry) Extensions KMC (Kinetic Monte Carlo) Catalysts at work A B Boundary layer 1 7 Film diffusion Porous catalyst 2 6 Pore diffusion Active sites A Chemical reaction B Adsorption/ desorption 7

8 Governing equations Catalytic wall Catalytic walls Adsorbed (surface) species Gas-phase continuity momentum gas-phase species gas-phase energy Boundary conditions Non-catalytic walls Catalytic walls 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* 8

9 Numerical challenges (I) U, T, p, ρ, x 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 r j = A j T β j exp E att,j θ i RT NC i=1 c i ν ij Numerical challenges (II) 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 segregated approaches are not feasible 9

10 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Simulation with detailed kinetics: stiff ODE solvers and ISAT Validation and examples Annular reactor CPO of CH 4 on platinum gauze (complex 3D geometry) CPO of iso-octane (complex chemistry) Tubular reactor with Raschig rings (complex 3D geometry) Packed bed reactors for industrial applications (complex 3D geometry) Extensions KMC (Kinetic Monte Carlo) Numerical solution Fully segregated algorithms Detailed kinetic schemes 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 10

11 After spatial discretization PDE Numerical solution Fully segregated algorithms Detailed kinetic schemes 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 catalyticfoam Operator-splitting algorithm Stiff reaction terms gas-phase species gas-phase energy adsorbed (surface) species Finite volume discretization After spatial discretization, the original PDE systems is transformed into an ODE system S = terms associated to the stiff processes (homogeneous and heterogeneous reactions) M = terms involving transport processes (convection and diffusion), non stiff and weakly non linear 11

12 Operator-splitting: an example Chemistry φ t = S + M Diffusion, convection... Operator-splitting scheme Chemical step φ t = S φ t = M Transport step Operator-splitting: an example Chemistry φ t = S + M Diffusion, convection... Chemistry φ t = S ti ti+1 ti+2 ti ti+1 ti+2 ti ti+1 ti+2 12

13 Operator-splitting: an example Chemistry φ t = S + M Diffusion, convection... Chemistry ti ti+1 ti+2 φ t = S ti ti+1 ti+2 φ t = M Transport ti ti+1 ti+2 Operator-splitting: an example Chemistry φ t = S + M Diffusion, convection... Chemistry ti ti+1 ti+2 φ t = S ti ti+1 ti+2 φ t = M Transport ti ti+1 ti+2 13

14 Operator-splitting in catalyticfoam (I) 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 Semi-batch reactor Batch reactor Operator-splitting in catalyticfoam (II) Homogeneous reactions Catalytic face Catalytic face NF = number of catalytic faces NG = number of gas-phase species NS = number of adsorbed (surface) species Equations: N = NG NF NS Semi-batch reactor Gas-phase species Gas-phase temperature Adsorbed species 14

15 Operator-splitting in catalyticfoam (III) Homogeneous reactions NF = number of catalytic faces NG = number of gas-phase species NS = number of adsorbed (surface) species Unknowns N = NG NF NS Batch reactor Gas-phase species Gas-phase temperature Adsorbed species catalyticfoam structure 15

16 Fraction of the total computaional time [%] Solution procedure Navier-Stokes Eqs. (PISO predictor) Reactor network (Strang predictor) Properties evaluation Transport Eqs. (Strang corrector) Pressure Eqn. Velocity correction (PISO corrector) Main features: Solution of the Navier-Stokes equations (laminar and turbulent regime) No limit to the number of species and reactions Non-isothermal conditions t i+1 = t i + t Where is the computational time spent? diffusion, convection φ t = M + S reaction Transport Step Chemical Step Most of the CPU Time (80-90%) is spent for the numerical integration of the ODE systems corresponding to the homogeneous and heterogeneous reactors 16

17 Where is the computational time spent? Reaction/Chemical step φ t = S semi-batch reactor describing composition and temperature reaction terms for both homogeneous and heterogeneous chemistry solving the reaction term is the bottleneck of the system stiff and highly-non linear solved with expensive implicit method need for speeding up the chemical term Reaction step = independent ODEs ODE ODE ODE ODE ODE ODE ODE ODE ODE ODE ODE ODE ODE ODE ODE ODE t 0 t n t n+1 t F 17

18 Stiff ODE solvers in catalyticfoam (I) Language Linear system solution Parallel Code available License OpenSMOKE++ C++ Direct No Yes Free DVODE FORTRAN Direct No Yes Free CVODE C Direct/Iterative Yes Yes Free DLSODE FORTRAN Direct No Yes Free DLSODA FORTRAN Direct No Yes Free RADAU5 FORTRAN Direct No Yes Free LIMEX4 FORTRAN Direct No Yes Free only for academic use MEBDF FORTRAN Direct No Yes Free Most of the CPU Time (80-90%) is spent for the numerical integration of the ODE systems corresponding to the homogeneous and heterogeneous reactors The best performances are obtained using the following solvers: OpenSMOKE++, CVODE, DVODE Performances of stiff ODE solvers: CPU time 78 species, 1325 reactions 90 species, 1363 reactions homogeneous heterogeneous OpenSMOKE++ OpenSMOKE++ OpenSMOKE++ Direct integration vs extrapolation ODE n ODE n+1 t n t n+1 18

19 Direct integration vs extrapolation ODE n ODE n+1 t n t n+1 ODE n ODE n+1 Direct integration vs extrapolation ODE n ODE n+1 t n t n+1 ODE n ODE n+1 ODE n ODE n+1 ODE n ODE n+1 ODE n ODE n+1 19

20 Direct integration vs extrapolation ODE n ODE n+1 t n t n+1 ODE n ODE n+1 Initial conditions at time t n are very similar ODE n ODE n+1 ODE n ODE n+1 ODE n ODE n+1 Direct integration vs extrapolation ODE n ODE n+1 t n t n+1 ODE n ODE n+1 Initial conditions at time t n are very similar ODE n ODE n+1 ODE n ODE n+1 We expect the solution at time t n+1 are very similar ODE n ODE n+1 20

21 Direct integration vs extrapolation ODE n ODE n+1 t n t n+1 ODE n ODE n+1 ODE n ODE n+1 ODE n ODE n+1 previous integrations to solve ODEs with Why do not exploit ODE n ODE n+1 similar initial conditions? ISAT: In Situ Adaptive Tabulation ODEs integrations are stored in a tree exploit stored information to well-approximate ODEs with similar initial conditions by means of linear interpolation error control through definition of a trusted approximation region (ROA) Extrapolation Approximation Reaction mapping f l x q = f x 0 + A 0 x q x 0 Mapping gradient Query point Tabulated point ROA Direct integration Fast and accurate approximation Pope, Comb. Theory Modeling, 1997 M. Bracconi, A. Cuoci and M. Maestri, submitted 21

22 Example: fixed bed of Rashig rings (I) 35 mm φ est = 5 mm φ int = 2 mm h = 3 mm Methane heterogeneous n cells fluid ~180,000 catalytic ~60, surface species 82 heterogeneous reactions OPERATING CONDITIONS CH 4 mass fraction O 2 mass fraction N 2 mass fraction Inlet temperature K Outlet Pressure 1.01 bar Flow velocity 1 m/s Example: fixed bed of Rashig rings (II) time: s Computational time without ISAT: 12.5 days on 4 cores 22

23 Example: fixed bed of Rashig rings (III) time: s Computational time with ISAT: 2 days on 4 cores Speed-up factor of 6 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Simulation with detailed kinetics: stiff ODE solvers and ISAT Validation and examples Annular reactor CPO of CH 4 on platinum gauze (complex 3D geometry) CPO of iso-octane (complex chemistry) Tubular reactor with Raschig rings (complex 3D geometry) Packed bed reactors for industrial applications (complex 3D geometry) Extensions KMC (Kinetic Monte Carlo) 23

24 Numerical tests The numerical tests have been performed by investigating the combustion of a fuel-rich H 2 over Rh catalyst in an annular reactor ( * ). Operating conditions Inner radius Outer radius Reactor length cm cm 1.5 cm H 2 mole fraction 0.04 (-) O 2 mole fraction 0.01 (-) N 2 mole fraction 0.95 (-) Pressure 1 atm Rh site density mol/cm 2 Catalytic surf. 5 cm -1 ( * ) M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. Vlachos, 2D detailed modeling of fuel-rich H 2 combustion over Rh/Al 2 O 3 catalyst, Chemical Engineering Science (2008) Numerical test Cylindrical symmetry 2D domain Low computational effort Meshes 2D Axisymmetric Mesh from 2,000 to 10,000 cells Centered (2 nd order) spatial discretization Implicit Euler time integration Max Courant number

25 Kinetic schemes Heterogeneous kinetics 5 Species: Rh(s), H2O(s), H(s), OH(s), O(s) 18 Reactions 1. H2+2Rh(s)=>2H(s) 2. 2H(s)=>H2+2Rh(s) 3. O2+2Rh(s)=>2O(s) 4. 2O(s)=>O2+2Rh(s) 5. OH(s)+Rh(s)=>H(s)+O(s) 6. H(s)+O(s)=>OH(s)+Rh(s) 7. H2O(s)+Rh(s)=>H(s)+OH(s) 8. H(s)+OH(s)=>H2O(s)+Rh(s) 9. H2O(s)+O(s)=>2OH(s) 10. 2OH(s)=>H2O(s)+O(s) 11. OH+Rh(s)=>OH(s) 12. OH(s)=>OH+Rh(s) 13. H2O+Rh(s)=>H2O(s) 14. H2O(s)=>H2O+Rh(s) 15. H+Rh(s)=>H(s) 16. H(s)=>H+Rh(s) 17. O+Rh(s)=>O(s) 18. O(s)=>O+Rh(s) Microkinetic mechanism Maestri et al., 2008 Mhadeshwar and Vlachos, 2005 Homogeneous kinetics 10 Species 21 Reactions 1. H+O2=OH+O 2. O+H2=OH+H 3. H+O2+M=HO2+M 4. H+2O2=HO2+O2 5. OH+HO2=H2O+O2 6. H+HO2=2OH 7. O+HO2=O2+OH 8. 2OH=O+H2O 9. H2+M=2H+M 10. O2+M=2O+M 11. H+OH+M=H2O+M 12. H+HO2=H2+O HO2=H2O2+O OH+M=H2O2+M 15. O+OH+M=HO2+M 16. H+H2O=H2+OH 17. H2O2+H=H2O+OH 18. H2O2+H=H2+HO2 19. HO2+H2O=>H2O2+OH 20. OH+H2O2=>H2O+HO2 21. O+H2O2=>OH+HO2 PolimiH2 mechanism (Frassoldati et al., 2006) Main results Inert wall Inert wall (5 mm) cat 0 Catalytic wall (15 mm) Acat cat 1.50 A 480 axial cells H2 mole fraction O2 mole fraction H2O mole fraction 473K 773K 973K [0-0.04] [0-0.10] [0-0.05] 25

26 Validation Comparison with experimental measurements Flow rate of: Nl/min Nl/min Nl/min Inlet: H 2 = 0.04 O 2 = 0.01 N 2 = 0.95 Reactor: R in = cm R out = cm L = 1.5 cm ( * ) M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. Vlachos, 2D detailed modeling of fuel-rich H 2 combustion over Rh/Al 2 O 3 catalyst, Chemical Engineering Science (2008) Validation Comparison with experimental measurements Flow rate of: Nl/min Nl/min Nl/min Inlet: H 2 = 0.04 O 2 = 0.01 N 2 = 0.95 catalyticfoam Reactor: R in = cm R out = cm L = 1.5 cm ( * ) M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. Vlachos, 2D detailed modeling of fuel-rich H 2 combustion over Rh/Al 2 O 3 catalyst, Chemical Engineering Science (2008) 26

27 Validation Comparison with experimental measurements Flow rate of: Nl/min Nl/min Nl/min Inlet: H 2 = 0.04 O 2 = 0.01 N 2 = 0.95 Reactor: R in = cm R out = cm L = 1.5 cm catalyticfoam 2D FD code* ( * ) M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. Vlachos, 2D detailed modeling of fuel-rich H 2 combustion over Rh/Al 2 O 3 catalyst, Chemical Engineering Science (2008) Comparison with Ansys-FLUENT 13.0 Dynamic simulation Steady-state simulation Profiles of adsorbed H2O along the catalytic wall in at 473K at several times Profiles of adsorbed H2O along the catalytic wall in steady state conditions at different temperatures catalyticfoam Ansys-FLUENT

28 ISAT performances 1.564e e e e e e e e e e-01 CH4 time: 0.05 s time: 0.15 s Correct choice of tolerance is of paramount in ISAT in order to have accurate results A tolerance of 1e-4 is enough for correctly describing the steadystate behavior If the transient is of interest, lower tolerances are usually required 1.563e e e e e ISAT 5e-3 ISAT 2.5e-3 x [m] time: 0.4 s ISAT 8e-4 DI A speed-up factor of (depending on the operating conditions) was measured Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Simulation with detailed kinetics: stiff ODE solvers and ISAT Validation and examples Annular reactor CPO of CH 4 on platinum gauze (complex 3D geometry) CPO of iso-octane (complex chemistry) Tubular reactor with Raschig rings (complex 3D geometry) Packed bed reactors for industrial applications (complex 3D geometry) Extensions KMC (Kinetic Monte Carlo) 28

29 CPO of methane over platinum gauze (I) Operating conditions Original gauze structure Detail of wire intersections Inlet temperature 600 K Inlet velocity 10 m/s Gauze temperature K CH 4 mole fraction (-) O 2 mole fraction (-) He mole fraction 0.80 (-) Pressure 1.3 bar Pt site density mol/cm 2 Catalytic surf. 5 cm -1 Computational domain R. Quiceno, J. Perez-Ramirez, J. Warnatz, O. Deutschmann, Modeling the high-temperature catalytic partial oxidation of methane over platinum gauze: detailed gas-phase and surface chemistries coupled with 3D flow simulations, Applied Catalysis A: General 303 (2006) CatalyticFOAM: Heterogeneus catalysis within OpenFOAM CPO of methane over platinum gauze (II) 3D computational mesh 140,000 cells 3,500 catalytic faces Symmetry planes Inlet Heterogeneous kinetics 11 Surface Species 36 Surface Reactions R. Quiceno, et al., Applied Catalysis A: General 303 (2006) Outlet Symmetry planes Homogeneous kinetics 25 Species Centered (2 nd order) spatial discretization Implicit Euler time integration Max Courant number Reactions E. Ranzi, et al., Progress in Energy Combustion Science, 38 (2012) CatalyticFOAM: Heterogeneus catalysis within OpenFOAM 29

30 CPO of methane over platinum gauze (III) T inlet = 600K T gauze = 1000K The temperature of the mixture becomes uniform at 2-3 wires diameters downstream the gauze 2 days of calculation on 12 cores Under the conditions used in these tests the homogeneous reactions are not relevant Simulations performed with and without the gasphase reactions exhibit very similar results The concentration of radical species in the gas phase is negligible CO and CO 2 are produced on the surface of the catalytic wires, with their maximal yield occurring at the crossing of the wires CatalyticFOAM: Heterogeneus catalysis within OpenFOAM CPO of methane over platinum gauze (IV) Comparison with experimental data CO selectivity O 2 conversion CH 4 conversion CH4 and O2 conversions are not temperature dependent The CO selectivity is strongly influenced by the gauze temperature Mass fraction of main adsorbed species (CO(s), OH(s), etc.) is maximum downstream, where the inlet mixture meet the catalyst wires CatalyticFOAM: Heterogeneus catalysis within OpenFOAM 30

31 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Simulation with detailed kinetics: stiff ODE solvers and ISAT Validation and examples Annular reactor CPO of CH 4 on platinum gauze (complex 3D geometry) CPO of iso-octane (complex chemistry) Tubular reactor with Raschig rings (complex 3D geometry) Packed bed reactors for industrial applications (complex 3D geometry) Extensions KMC (Kinetic Monte Carlo) CatalyticFOAM: Heterogeneus catalysis within OpenFOAM CPO of iso-octane over rhodium catalyst (I) Sketch of a single channel (circular section) reactants products Operating conditions Inlet temperature 1076 K Inlet velocity 0.90 m/s Wall temperature 1076 K ic 8 H 18 mole fraction (-) O 2 mole fraction (-) N 2 mole fraction 0.80 (-) Pressure 1 atm Rh site density mol/cm 2 Rhodium catalyst Heterogeneous kinetics 17 Surface Species 56 Surface Reactions Homogeneous kinetics 168 Species 5,400 Reactions Catalytic surf. 5 cm -1 M. Hartmann, L. Maier, H.D.Minh, O. Deutschmann, Catalytic partial oxidation of iso-octane over rhodium catalyst: an experimental, modeling and simulation study, Combustion and Flame 157 (2010) CatalyticFOAM: Heterogeneus catalysis within OpenFOAM 31

32 CPO of iso-octane over rhodium catalyst (II) catalyst Gas-phase main species 2D mesh (4,000 cells) 4 days of calculation on 12 cores ic8h18 CO CO2 H2O O The catalytic surface reaction is very fast in the entrance (first 1 mm) Strong back-diffusion of H2: importance of diffusion coefficients Strong radial gradient are present in the first mm of the reactor The concentration of ic8h18 and O2 on the surface is practically zero, which means that catalytic reactions are mass-transfer limited H mm CatalyticFOAM: Heterogeneus catalysis within OpenFOAM CPO of iso-octane over rhodium catalyst (III) CatalyticFOAM 2D mesh (5,000 cells) DETCHEM CHANNEL ic8h M. Hartmann, et al.,, Combustion and Flame 157 (2010) CatalyticFOAM: Heterogeneus catalysis within OpenFOAM 32

33 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Simulation with detailed kinetics: stiff ODE solvers and ISAT Validation and examples Annular reactor CPO of CH 4 on platinum gauze (complex 3D geometry) CPO of iso-octane (complex chemistry) Tubular reactor with Raschig rings (complex 3D geometry) Packed bed reactors for industrial applications (complex 3D geometry) Extensions KMC (Kinetic Monte Carlo) CatalyticFOAM: Heterogeneus catalysis within OpenFOAM Tubular reactor with Raschig rings (I) Velocity Field [m/s] Inlet mixture Operating conditions Internal diameter 1 cm Total length 15 cm CH 4 mole fraction (-) O 2 mole fraction (-) N 2 mole fraction (-) Temperature K Residence time 0.15 s 3D Unstructured Mesh: ~250,000 cells Homogeneous reactors: 240,000 Heterogeneous reactors: 10,000 No homogeneous reactions! CPU time per heterogeneous reactor: 0.75 ms 33

34 Tubular reactor with Raschig rings (II) Rh(s) ( ) H(s) ( ) CO(s) ( ) CO2(s) ( ) Gas-phase species (mole fractions) Adsorbed species (mass fractions) C1 microkinetic model on Rh 82 reaction steps 13 adsorbed species UBI-QEP and DFT refinement M. Maestri et al., AIChE J., 2009 CH4 ( ) O2 ( ) H2O ( ) H2 ( ) Tubular reactor with Raschig rings (III) Adsorbed species at the catalyst surface Inlet mixture 34

35 Tubular reactor with Raschig rings (IV) Dynamics of the system Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Simulation with detailed kinetics: stiff ODE solvers and ISAT Validation and examples Annular reactor CPO of CH 4 on platinum gauze (complex 3D geometry) CPO of iso-octane (complex chemistry) Tubular reactor with Raschig rings (complex 3D geometry) Packed bed reactors for industrial applications (complex 3D geometry) Extensions KMC (Kinetic Monte Carlo) What s next? Complex domains relevant to industrial applications 35

36 Analysis of performances Investigated structures Cylinders Rings Spheres Same catalytic area A single element [m 2 ] N Sphere 1.13x Ring 1.88x Cylinder 1.57x cylinders 30 rings 50 spheres Global kinetic scheme Micro-kinetic model step 1 O O step 2 C 2 H 4 + C 2 H 4 step 3 O + C 2 H 4 C 2 H 4 O + step 4 C 2 H 4 O C 2 H 4 O + Global kinetic scheme KINETIC MODEL PARAMETERS A 9.85E5 1/(atm m 3 s) Eatt 15 Kcal/mol m 0.65 n 0.71 Suljo Linic and Mark A. Barteau, Construction of a reaction coordinate and a microkinetic model for ethylene epoxidation on silver from DFT calculations and surface science experiments, November 2002, Journal of catalyst, pag r = k overall (P O2 ) n (P C2 H 4 ) m k overall = Ae E att RT 36

37 Operating conditions OPERATING CONDITIONS C 2 H 4 Molar Fraction 35.0 % O 2 Molar Fraction 5.0 % CH 4 Molar Fraction 60.0 % Pressure 15 atm Temperature K Inlet Velocity 1 m/s Oxygen based process Methane as inert component Isothermal simulations at 432 K, 490 and 550 K Adiabatic simulations at 432 K Multiregion simulations at 490 K 73 Isothermal simulations: 432 K The behaviour of the three packed beds is almost the same 37

38 C 2 H 4 Conversion [%] Isothermal simulations: 550 K Spheres at high temperature can guarantee the higher conversion Isothermal simulations 30 C 2 H 4 Conversion vs Temperature Cylinder Sphere Ring Temperature [K] 432 K 490 K 550 K Cylinders 3.5 % 15. 5% 25.0 % Spheres 3.6 % 16.7 % 27.0 % Rings 3.5 % 14.1 % 22.8 % 76 38

39 Extension to multiregion Multiregion Mesh: the spheres have been meshed with the same level of refinement of the bulk phase - conformal mesh Adiabatic simulations Need to have very fine meshes close to the reactor wall Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Simulation with detailed kinetics: stiff ODE solvers and ISAT Validation and examples Annular reactor CPO of CH 4 on platinum gauze (complex 3D geometry) CPO of iso-octane (complex chemistry) Tubular reactor with Raschig rings (complex 3D geometry) Packed bed reactors for industrial applications (complex 3D geometry) Extensions KMC (Kinetic Monte Carlo) 39

40 Extension to kinetic Monte Carlo Length [m] 10 0 S. Matera, M. Maestri, A. Cuoci, K. Reuter, ACS Catal., 2014 MACROSCALE Reactor engineering and transport phenomena CFD MESOSCALE Interplay among the chemical events MK/kMC 10-9 MICROSCALE Making and breaking of chemical bonds Electronic structure theory Time [s] 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 )= k (x, y) P ( y,t) k ( y, x) P (x,t) y y Each site a has own entry in x denoting its adsorbate state x a Simulate trajectories x(t) (kinetic Monte Carlo) S. Matera, M. Maestri, A. Cuoci, K. Reuter, ACS Catal.,

41 Effective bridging between the scales Continuum equations need boundary conditions for the mass fluxes j α at the surface: j α n = v α M α TOF T s = 600K, p s (O₂)= 1atm 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 ) 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 An example: The reactor STM (I) The Reactor STM CO oxidation on Ru 2 O 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 K. Reuter and M. Scheffler, Phys. Rev. B 73, (2006) Rasmussen, Hendriksen, Zeijlemaker, Ficke, Frenken, The Reactor STM: A scanning tunneling microscope for investigation of catalytic surfaces at semi-industrial reaction conditions, Review of Scientific Instruments, 69(11), (1998) S. Matera, M. Maestri, A. Cuoci, K. Reuter, ACS Catal.,

42 An example: The reactor STM (II) d = 2 mm outlet inlet CO + O 2 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 An example: The reactor STM (III) Steady-state results Strong recirculations 42

43 An example: The reactor STM (IV) Dynamic results The CO mole fraction in the inlet stream increases during the time Operating conditions T: 600 K P: 1 atm Inlet: CO + O2 (66%, 34% Vol) Inlet velocity: 5 cm/s CO mole fraction 50% 34% 18% 66% Initial conditions: CO + O2 (66%, 34% Vol) time [s] An example: the catalytic gauze (I) Rate constants k(x,y) from DFT and harmonic Transition State Theory Model system: CO oxidation on Pd(100): Original gauze structure Detail of wire intersections Computational domain 43

44 An example: the catalytic gauze (II) An example: the catalytic gauze (III) DFT kmc CFD 44

45 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Simulation with detailed kinetics: stiff ODE solvers and ISAT Validation and examples Annular reactor CPO of CH 4 on platinum gauze (complex 3D geometry) CPO of iso-octane (complex chemistry) Tubular reactor with Raschig rings (complex 3D geometry) Packed bed reactors for industrial applications (complex 3D geometry) Extensions KMC (Kinetic Monte Carlo) Overall HPC peformances Packed-bed of spheres 2 Mio Cells 45

46 Publications Publications on international journals M.Maestri, A.Cuoci, Coupling CFD with detailed microkinetic modeling in heterogeneous catalysis, Chemical Engineering Science 96(7), pp (2013) DOI: /j.ces Matera, S., Maestri, M., Cuoci, A., Reuter, K., Predictive-quality surface reaction chemistry in real reactor models: Integrating first-principles kinetic monte carlo simulations into computational fluid dynamics, ACS Catalysis 4(11), pp (2014) DOI: /cs501154e Maffei, T., Gentile, G., Rebughini, S., Bracconi, M., Manelli, F., Lipp, S., Cuoci, A., Maestri, M., A multiregion operator-splitting CFD approach for coupling microkinetic modeling with internal porous transport in heterogeneous catalytic reactors, Chemical Engineering Journal, 283, pp (2016) DOI: /j.cej Rebughini, S., Cuoci, A., Maestri, M., Hierarchical analysis of the gas-to-particle heat and mass transfer in micro packed bed reactors, Chemical Engineering Journal, In press, DOI: /j.cej Rebughini, S., Cuoci, A., Maestri, M., Handling contact points in reactive CFD simulations of heterogeneous catalytic fixed bed reactors, Chemical Engineering Science, 141, pp (2016) DOI: /j.ces Bracconi, M, Cuoci A., Maestri, M., In-situ adaptive tabulation for CFD operator-splitting based simulations of heterogeneous reactors, submitted The catalyticfoam software is fully compatible with OpenFOAM version 3.0. Nevertheless, it is not approved or endorsed by ESI/OpenCFD, the producer of the OpenFOAM software and owner of the OPENFOAM and OpenCFD trade marks. 46