first principles 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 first principles multiscale modeling of heterogeneous catalytic reactors in OpenFOAM HPC enabling of OpenFOAM for CFD applications 25 March 2015

2 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Validation and examples 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)

3 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Validation and examples 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)

4 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

5 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

6 Chemical reactor design 1000 Temperature [ C] Flow [mmol/s] Axial length [mm] Axial length [mm]

7 Chemical reactor design [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 Dominant reaction mechanism: understanding & design H 2 H 2 O

8 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]

9 A multiscale phenomenon 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]

10 Catalysts at work (I) A

11 Catalysts at work (II) A Boundary layer 1 Film diffusion

12 Catalysts at work (III) A Boundary layer 1 Film diffusion Porous catalyst 2 Pore diffusion

13 Catalysts at work (IV) A Boundary layer 1 Film diffusion Porous catalyst 2 Pore diffusion Active sites A 3 4 Chemical reaction B Adsorption/ desorption

14 Catalysts at work (V) 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

15 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]

16 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]

Microkinetic modeling and transport Length [m] 10 0 10-3 Microkinetic modeling Complex geometries MESOSCALE MACROSCALE Reactor engineering and transport

17 Microkinetic modeling and transport Length [m] Microkinetic modeling Complex geometries MESOSCALE MACROSCALE Reactor engineering and transport phenomena CFD 10-6 Interplay among the chemical events MK/kMC 10-9 MICROSCALE Making and breaking of chemical bonds Electronic structure theory Time [s]

18 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]

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

20 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Validation and examples 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)

21 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

22 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 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 *

23 Boundary conditions Non-catalytic walls Catalytic walls 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* Adsorbed (surface) species

24 Numerical challenges (I) UU, TT, pp, ρρ, xx Dimensions of the system Proportional to the number of species Proportional to the number of cells

25 Numerical challenges (I) UU, TT, pp, ρρ, xx 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

Numerical challenges (I) UU, TT, pp, ρρ, xx Dimensions of the system Proportional to the number of species Proportional to the number of cells Stiffness Different temporal scales involved Different

26 Numerical challenges (I) UU, TT, pp, ρρ, xx 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 rr jj = AA jj TT ββ jj eeeeee EE aaaaaa,jj θθ ii RRRR NNNN ii=11 cc ii νν iiii

27 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

28 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Validation and examples 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)

29 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

Numerical solution Fully segregated algorithms Detailed kinetic schemes easy to implement and computationally efficient unfeasible when large, stiff kinetic mechanisms are used Complex

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

30 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

(surface) species Finite volume discretization After

transformed into an ODE system S = terms associated

heterogeneous reactions) ODE M = terms involving

31 Operator-splitting algorithm Stiff reaction terms gas-phase species PDE 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) ODE M = terms involving transport processes (convection and diffusion), non stiff and weakly non linear

32 Operator-splitting: an example (I) Chemistry = SS + MM Diffusion, convection...

33 Operator-splitting: an example (II) Chemistry = SS + MM Diffusion, convection... Operator-splitting scheme Chemical step = SS = MM Transport step

34 Operator-splitting: an example (III) Chemistry = SS + MM Diffusion, convection... Operator-splitting scheme Chemical step = SS = MM Transport step

35 Operator-splitting: an example (IV) Chemistry = SS + MM Diffusion, convection... Chemistry ti ti+1 ti+2 = SS ti ti+1 ti+2 ti ti+1 ti+2

36 Operator-splitting: an example (V) Chemistry = SS + MM Diffusion, convection... Chemistry ti ti+1 ti+2 = SS ti ti+1 ti+2 = MM Transport ti ti+1 ti+2

37 Operator-splitting: an example (VI) Chemistry = SS + MM Diffusion, convection... Chemistry ti ti+1 ti+2 = SS ti ti+1 ti+2 = MM Transport ti ti+1 ti+2

Operator-splitting in catalyticfoam (I) Catalytic wall Gas mixture Each computational cell behaves as a chemical reactor in the splittingoperator

38 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

39 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

number of adsorbed (surface) species Unknowns N = NG + 1 + NF NS

40 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

41 catalyticfoam structure

predictor) Properties evaluation Transport Eqs.

Velocity correction (PISO corrector) Main

equations (laminar and turbulent regime) No

42 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 Isothermal and adiabatic conditions tt ii+11 = tt ii + tt

43 catalyticfoam.c while (runtime.run()) loop { #include "readtimecontrols.h" #include "readpisocontrols.h" #include "compressiblecourantno.h" #include "setdeltat.h" runtime++; #include "rhoeqn.h" Continuity equation for (label ocorr=1; ocorr <= noutercorr; ocorr++) { #include "UEqn.H" Momentum equations #include "chemistry.h" Chemical step #include "properties.h" #include "YEqn.H" #include "TEqn.H" Transport step } for (int corr=1; corr<=ncorr; corr++) { #include "peqn.h" } PISO loop } #include "write.h" Post-processing

Chemical step Loop over all the reactors { if reactor is catalytic { assembling ODE initial values (gas-phase species, temperature, adsorbed species) solving the ODE system } else { moving the

44 Chemical step Loop over all the reactors { if reactor is catalytic { assembling ODE initial values (gas-phase species, temperature, adsorbed species) solving the ODE system } else { moving the solution to OpenFOAM assembling ODE initial values (gas-phase species and temperature) solving the ODE system Numerical library for stiff ODE systems (OpenSMOKE++, CVODE, LSODE, etc.) } } moving the solution to OpenFOAM

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

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

45 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++

46 Details about the C++ implementation For each solver a common C++ interface was created Creation of ODE System objects ODESystem_BatchReactor_Homogeneous_DVODE *odesystemobject_homogeneous; odesystemobject_homogeneous = ODESystem_BatchReactor_Homogeneous_DVODE::GetInstance(); Creation of ODE System Solver OpenSMOKE::OpenSMOKE_DVODE<ODESystem_BatchReactor_Homogeneous_DVODE> ode_homogeneous(odesystemobject_homogeneous); Loop on every computational cell ode_homogeneous.setmaximumnumberofsteps(100000); ode_homogeneous.setanalyticaljacobian(false); ode_homogeneous.setabsolutetolerance(atol); ode_homogeneous.setrelativetolerance(rtol); ode_homogeneous.setinitialvalues(t0,y0); ode_homogeneous.solve(tf); ode_homogeneous.solution(yf);

47 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Validation and examples 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)

48 CPO of methane over platinum gauze (I) Operating conditions Inlet temperature Inlet velocity 600 K 10 m/s Original gauze structure Detail of wire intersections 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)

CPO of methane over platinum gauze (II) 3D computational mesh 140,000 cells 3,500 catalytic faces Inlet Heterogeneous kinetics 11 Surface Species 36 Surface Reactions Symmetry planes www.detchem.

49 CPO of methane over platinum gauze (II) 3D computational mesh 140,000 cells 3,500 catalytic faces Inlet Heterogeneous kinetics 11 Surface Species 36 Surface Reactions Symmetry planes 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)

CPO of methane over platinum gauze (III) T inlet = 600K T gauze =

diameters downstream the gauze 2 days of calculation on 12 cores Under

relevant Simulations performed with and without the gasphase reactions

the gas phase is negligible CO and CO 2 are produced on the surface of

50 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

$selectivity is strongly influenced by the gauze temperature Mass fraction of main adsorbed species (CO(s), OH(s), etc.$

51 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

52 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Validation and examples 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)

53 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)

54 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 The catalytic surface reaction is very fast in the entrance (first 1 mm) CO Strong back-diffusion of H2: importance of diffusion coefficients H2O O 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

55 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)

56 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Validation and examples 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)

$fraction 0.$ 100 (-) O 2 mole 056 (-) N 2

57 Tubular reactor with Raschig rings (I) Velocity Field [m/s] Inlet mixture Operating conditions Internal diameter 1 cm Total length 15 cm 3D Unstructured Mesh: ~250,000 cells Homogeneous reactors: 240,000 Heterogeneous reactors: 10,000 CH 4 mole fraction (-) O 2 mole fraction (-) N 2 mole fraction (-) Temperature K No homogeneous reactions! CPU time per heterogeneous reactor: 0.75 ms Residence time 0.15 s

Tubular reactor with Raschig rings (II) Rh(s)

$-4 10-9 ) Gas-phase species (mole fractions)$ microkinetic model on Rh 82 reaction steps 13

Maestri et al., AIChE J., 2009 CH4 (0.-0.

58 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 ( )

59 Tubular reactor with Raschig rings (III) Adsorbed species at the catalyst surface Inlet mixture

60 Tubular reactor with Raschig rings (IV) Dynamics of the system

61 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Validation and examples 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)

62 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

63 Global kinetic scheme Micro-kinetic model ssssssss 1 OO OO ssssssss 2 CC 2 HH 4 + CC 2 HH 4 ssssssss 3 OO + CC 2 HH 4 CC 2 HH 4 OO + ssssssss 4 CC 2 HH 4 OO CC 2 HH 4 OO + 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 rr = kk oooooooooooooo (PP OO2 ) nn (PP CC2 HH 4 ) mm kk oooooooooooooo = AAee EE aaaaaa RRRR

64 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

65 Isothermal simulations: 432 K The behaviour of the three packed beds is almost the same 3 days on 8 cores

66 Isothermal simulations: 550 K Spheres at high temperature can guarantee the higher conversion

67 Isothermal simulations C 2 H 4 Conversion vs Temperature 30 C 2 H 4 Conversion [%] 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 %

68 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

69 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Validation and examples 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)

70 Extension to kinetic Monte Carlo Length [m] 10 0 In collaboration with: K. Reuter and S. Matera (TUM) 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

71 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) K. Reuter and M. Scheffler, Phys. Rev. B 73, (2006)

72 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,

73 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)

74 An example: The reactor STM (II) 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

75 An example: The reactor STM (III) Steady-state results Strong recirculations

$An example: The reactor STM (IV) Dynamic results The CO mole fraction in$ $fraction 34% 50% 66% Initial conditions: CO + O2 (66%, 34% Vol) 0 1 2 3$

76 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 18% CO mole fraction 34% 50% 66% Initial conditions: CO + O2 (66%, 34% Vol) time [s]

77 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

78 An example: the catalytic gauze (II)

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

The catalyticfoam Group The catalyticfoam Group

modeling, microkinetic modeling Alberto Cuoci CFD,

Hierarchical analysis of complex reacting systems

geometries Former Students Sandro Goisis and

methodology Tiziano Maffei Improvement of

80 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 Mauro Bracconi (PhD student) ISAT, complex geometries Former Students Sandro Goisis and Alessandra Osio Development of numerical methodology Tiziano Maffei Improvement of multi-region solver Giancarlo Gentile and Filippo Manelli Development of multi-region solver

it/ Statistics since April 2013 Unique visitors: 2,500 Visits:

81 The catalyticfoam web-site The catalyticfoam code can be freely downloaded from our web site: Statistics since April 2013 Unique visitors: 2,500 Visits: 4,200 (~6 per day) Visits from 76 different countries About 200 registered users

82 Release - Policy The catalyticfoam software is fully compatible with OpenFOAM version 2.3.x. 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. Software is released under the L-GPL license through an independent webiste:

83 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., Rebughini, S., Gentile, G., Lipp, S., Cuoci, A., Maestri, M., Handling Contact Points in Reactive CFD Simulations of Heterogeneous Catalytic Fixed Bed Reactors, Submitted to Industrial & Engineering Chemistry Research (2015) T. Maffei, G. Gentile, F. Manelli, S. Lipp, M.Maestri, A.Cuoci, Multi-region approach in modeling gas-solid catalytic reactors, In preparation

84 Additional slides

85 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Extension to the multi-region modeling Validation and examples Annular reactor (simple chemistry) 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) Micro-channel reactors (Hierarchical analysis) Extensions KMC (Kinetic Monte Carlo) Conclusions and future works

diffusive flux to and from the catalytic surface.

86 Motivation In the original version of catalyticfoam the catalyst morphology is not detailed the presence of the catalyst was accounted for by as boundary condition imposing continuity between the reactive flux and the diffusive flux to and from the catalytic surface. This approach does not account for diffusive limitations in the solid phase or in general for the intrasolid transport phenomena Need of a Multi-Region Solver (gas phase + solid phases)

87 Microkinetic modeling and CFD A B Boundary layer 1 7 Film diffusion Porous catalyst 2 6 Pore diffusion Active sites A Chemical reaction B Adsorption/ desorption

88 Internal transport phenomena A B Boundary layer 1 7 Film diffusion Porous catalyst 2 6 Pore diffusion Active sites A Chemical reaction B Adsorption/ desorption

89 Internal transport phenomena A B Gas Phase Solid Phase 3 5 A 4 B

90 Multiple meshes for multiple regions

91 Multiple meshes for multiple regions Mesh 3: Solid Region 2 Mesh 1: Fluid Region Mesh 2: Solid Region 1

92 Multiple meshes for multiple regions Mesh 3: Solid Region 2 Mesh 1: Fluid Region Mesh 2: Solid Region 1 Multiple meshes Different properties for each region Separate governing equations on each cell

93 Linking the regions How to couple at the interface?

94 Linking the regions k OWN,I T OWN ( I ) T OWN,I = k = T NBR,I NBR,I T NBR( I ) How to couple at the interface? D OWN C C OWN OWN, I = D ( I ) NBR NBR( I ) = C NBR,I C

95 Linking the regions k OWN,I T OWN ( I ) T OWN,I = k = T NBR,I NBR,I T NBR( I ) D OWN C C T OWN I.OWN OWN, I = = D k T ΔOWN k Δ OWN OWN OWN OWN ( I ) NBR NBR( I ) = C NBR,I C k + k + Δ T Δ NBR NBR NBR NBR NBR C I.OWN = Mixed boundary conditions at the interface D C ΔOWN D Δ OWN OWN OWN OWN D + D + Δ NBR NBR NBR C Δ NBR NBR

96 Linking the regions k OWN,I T OWN ( I ) T OWN,I = k = T NBR,I NBR,I T NBR( I ) D OWN C C T OWN I.OWN OWN, I = = D ( I ) NBR NBR( I ) = C k OWN NBR,I T ΔOWN k Δ C OWN OWN OWN k + k + Δ T Δ NBR NBR NBR NBR Partitioned Approach NBR C I.OWN = Mixed boundary conditions at the interface D C ΔOWN D Δ OWN OWN OWN OWN D + D + Δ NBR NBR NBR C Δ NBR NBR 1) Solve in each zone with mixed BCs

97 Linking the regions k OWN,I T OWN ( I ) T OWN,I = k = T NBR,I NBR,I T NBR( I ) D OWN C C T OWN I.OWN OWN, I = = D ( I ) NBR NBR( I ) = C k OWN NBR,I T ΔOWN k Δ C OWN OWN OWN k + k + Δ T Δ NBR NBR NBR NBR Partitioned Approach NBR C I.OWN = Mixed boundary conditions at the interface D C ΔOWN D Δ OWN OWN OWN OWN D + D + Δ NBR NBR NBR C Δ NBR NBR 1) Solve in each zone with mixed BCs 2) Update interface values and solve in the neighboring region

98 Linking the regions k OWN,I T OWN ( I ) T OWN,I = k = T NBR,I NBR,I T NBR( I ) D OWN C C T OWN I.OWN OWN, I = = D ( I ) NBR NBR( I ) = C k OWN NBR,I T ΔOWN k Δ C OWN OWN OWN k + k + Δ T Δ NBR NBR NBR NBR Partitioned Approach NBR C I.OWN = Mixed boundary conditions at the interface D C ΔOWN D Δ OWN OWN OWN OWN D + D + Δ NBR NBR NBR C Δ NBR NBR 1) Solve in each zone with mixed BCs 2) Update interface values and solve in the neighboring region 3) Iterate till convergence is reached

99 Coupling structure d Fluid Region ( ρmixyi ) = ( ρmixdmix,i ( Yi )) ( ΦYi ) dt d( ρmatc pt ) mix = ( k ( T )) C ( ΦT ) dt p with the mixed BCs on the interface: C T I,FLU I,FLU = = k D T ΔFLU k Δ FLU C ΔFLU D Δ FLU FLU FLU FLU FLU FLU FLU ksol T + ΔSOL ksol + Δ SOL SOL SOL DSOL C + ΔSOL DSOL + Δ SOL

100 Coupling structure d Solid Region ( ρmixyi ) = ρ D i ( Y ) T C dt d ( mix mix, i ) ( ρ c T ) I,SOL I,SOL mat dt = k p T ΔSOL k Δ SOL = SOL SOL SOL DSOL C ΔSOL = D Δ SOL SOL SOL ( k ( T )) with the mixed BCs on the interface: kflu T + ΔFLU kflu + Δ FLU DFLU C + ΔFLU DFLU + Δ FLU FLU FLU d Fluid Region ( ρmixyi ) = ( ρmixdmix,i ( Yi )) ( ΦYi ) dt d( ρmatc pt ) mix = ( k ( T )) C ( ΦT ) with the mixed BCs on the interface: C dt T I,FLU I,FLU = = k D T ΔFLU k Δ FLU C ΔFLU D Δ FLU FLU FLU FLU FLU FLU FLU ksol T + ΔSOL ksol + Δ SOL SOL p SOL DSOL C + ΔSOL DSOL + Δ SOL

Coupling structure d Solid Region ( ρmixyi ) = ρ D i ( Y ) dt d ( mix mix, i ) ( ρ c T ) mat dt p = ( k ( T

with the mixed BCs on the interface: with the mixed BCs on the interface: T I,SOL = k T ΔSOL k Δ SOL SOL SOL

I,SOL = DSOL C ΔSOL D Δ SOL SOL SOL DFLU C + ΔFLU DFLU + Δ FLU FLU C I,FLU = D C ΔFLU D Δ FLU FLU FLU FLU

k 1) T T abstolt T T ( k ) ( k 1) ( k ) ( k 1) Yi Yi abstoly Yi Yi i reltol T reltol Y Coupling Loop Solve

101 Coupling structure d Solid Region ( ρmixyi ) = ρ D i ( Y ) dt d ( mix mix, i ) ( ρ c T ) mat dt p = ( k ( T )) d Fluid Region ( ρmixyi ) = ( ρmixdmix,i ( Yi )) ( ΦYi ) dt d( ρmatc pt ) mix = ( k ( T )) C ( ΦT ) dt p with the mixed BCs on the interface: with the mixed BCs on the interface: T I,SOL = k T ΔSOL k Δ SOL SOL SOL SOL kflu T + ΔFLU kflu + Δ FLU FLU T I,FLU = k T ΔFLU k Δ FLU FLU FLU FLU ksol T + ΔSOL ksol + Δ SOL SOL C I,SOL = DSOL C ΔSOL D Δ SOL SOL SOL DFLU C + ΔFLU DFLU + Δ FLU FLU C I,FLU = D C ΔFLU D Δ FLU FLU FLU FLU DSOL C + ΔSOL DSOL + Δ SOL SOL Convergence Criteria Coupling Method ( k 1) T ( k 1) Y ( k ) ( k 1 ) ( k ) ( k 1) T T abstolt T T ( k ) ( k 1) ( k ) ( k 1) Yi Yi abstoly Yi Yi i reltol T reltol Y Coupling Loop Solve alternatively for every cell of the 2 coupled regions Check for convergence: if reached, proceed to next time step

102 Multi-region solver architecture Solve Solid for each time step... Solve Fluid

103 Multi-region solver architecture Solve Solid for each time step... Solve Fluid Continuity Equation PISO predictor-corrector loop Navier-stokes Equations Pressure Corrector

104 Multi-region solver architecture Solve Solid for each time step... Solve Fluid Continuity Equation Mass Transfer Equation Heat Transfer Equation Fluid Chemistry Homogeneous reactions Update Fluid Properties PISO predictor-corrector loop Navier-stokes Equations Pressure Corrector

105 Multi-region solver architecture Solve Solid for each time step... Solve Fluid Continuity Equation Mass Transfer Equation Mass Transfer Equation Heat Transfer Equation Solid Chemistry Homogeneous and heterogeneous reactions Site species conservation Heat Transfer Equation Fluid Chemistry Homogeneous reactions Update Fluid Properties PISO predictor-corrector loop Update Solid Properties Navier-stokes Equations Pressure Corrector

Equation Heat Transfer Equation Solid Chemistry Homogeneous and heterogeneous reactions Site species conservation Heat

106 Multi-region solver architecture Solve Solid for each time step... Solve Fluid Coupling loop convergence check Continuity Equation Mass Transfer Equation Coupling Loop Mass Transfer Equation Heat Transfer Equation Solid Chemistry Homogeneous and heterogeneous reactions Site species conservation Heat Transfer Equation Fluid Chemistry Homogeneous reactions Update Fluid Properties PISO predictor-corrector loop Update Solid Properties Coupling Loop Navier-stokes Equations Pressure Corrector multiregion

107 Validation with analytical solution dc = r dr dr 1 d 2 A A, eff 2 r kc r A C A = C As, r sinh φ R r sinh R ( φ ) Φ = 0.5 Φ = 1 Φ = 2 A B Φ = 5 Φ = 10 Φ = 20

108 Outline Introduction and motivation Development of the catalyticfoam solver for the OpenFOAM framework Governing equations Numerical methodology Extension to the multi-region modeling Validation and examples Annular reactor (simple chemistry) 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) Micro-channel reactors (Hierarchical analysis) Extensions KMC (Kinetic Monte Carlo) Conclusions and future works

109 Micro-channel technology (I) Development and intensification of processes which involve high exothermic reactions Improved heat transfer in the honeycomb matrix Improved mass transfer in the packed bed channel

110 Micro-channel technology (II) How unconventional geometry influences the mass transfer in microchannel reactors? Can literature correlations (developed for industrial reactors) describe mass transfer phenomena in micro-channel reactors?

111 Micro-channel reactor generation Two-step Monte Carlo process based on the algorithm of Soppe [1] H. J. Freund, Erlangen Universität, DE Soppe, W., Computer simulation of random packing of hard spheres. Powerd Techol., : p

diameter [m] 300 x 10-6 600 x 10-6 Reactor length [m]

112 Investigated micro-channel reactors 300 μm spheres 600 μm spheres Green channel Blue channel Particle diameter [m] 300 x x 10-6 Reactor length [m] 12.5 x x 10-3 Tube diameter [m] 4 x x 10-3

Pressure drops: 600 μm (blue channel) Pressure drops [bar/m] 25 20 15 10 5 Foumeny equation Eisfeld equation Ergun equation This work 600 μm spheres

113 Pressure drops: 600 μm (blue channel) Pressure drops [bar/m] Foumeny equation Eisfeld equation Ergun equation This work 600 μm spheres Particle Reynolds number Re = ρvd µ Particle Reynolds number N = D D Tube Particle Tube-to-particle diameter ratio describes wall effects

114 Pressure drops: a comparison 10 Pressure drops [mbar/m] μm spheres Pressure drops in the reactor with 600 μm sphere diameter are controlled by wall effects Pay attention: same tube-to-particle diameter ratio of the previous microchannel reactor studied Pressure drops [bar/m] Ergun equation Eisfeld equation This work 300 μm spheres Pressure drops in micro-channel reactor with 300 μm sphere diameter are high and wall effects are negligible Reynolds number

$Mass transfer coefficient (I) Value Unit dimension Temperature 653 K Out let pressure 101325 Pa Inlet molar fraction Nitrogen (N 2 ) 0.95 Oxygen (O 2 ) 0.014 Hydrogen (H 2 ) 0.$

115 Mass transfer coefficient (I) Value Unit dimension Temperature 653 K Out let pressure Pa Inlet molar fraction Nitrogen (N 2 ) 0.95 Oxygen (O 2 ) Hydrogen (H 2 ) Irreversible first-order kinetics model at the catalytic wall (Da 100) Identical condition within each channel Isothermal condition Laminar flow ( 10 < Re < 90 ) Characteristic length: D Particle Mass transfer regime

116 Mass transfer coefficient (II) 1,8 Mass transfer coefficient [m/s] 1,2 0,6 Micro-channel: 300 μm Micro-channel: 600 μm Mass transfer coefficient estimated with Integral Mass Balance (IMB) method: K mat, i v ( ) uin ln 1 χ = al 0, Reynolds number The mass transfer coefficient is higher for the micro-channel reactor with the sphere diameter of 300 μm

117 Sherwood number: 600 μm 18 Sherwood Yoshida et al. Wakao and Funazkri Micro-channel: 600 μm J m Yoshida et al. [2] = 0.91 Re 0.51 ψ Sh Reynolds number Wakao and Funazkri [1] Re = + Sc Schmidt number: µ Sc = ρ D i Particle Reynolds number: Re Re = ρvdparticle = µ Yoshida Reynolds number: ρvd Particle 6 µ (1 ε) Wakao, N. and T. Funazkri, Effect of fluid dispersion coefficients on particle-to-fluid mass transfer coefficients in packed beds: Correlation of sherwood numbers. Chemical Engineering Science, (10): p Yoshida, F., D. Ramaswami, and O.A. Hougen, Temperatures and partial pressures at the surfaces of catalyst particles. ALChE Journal, (1): p

118 Why the difference? Sherwood Yoshida et al. Micro-channel: 600 μm Packed bed: 6 mm This comparisons shows that the different Sherwood number depends on the tube-to-particle diameter ratio N = D D Tube Particle Reynolds number and NOT on microdimensions Particle diameter [m] Tube diameter [m] Tube-to-particle diameter ratio Micro-channel 600 x x Conventional packed bed 6 x x

119 Why the difference? Sherwood Yoshida et al. Micro-channel: 300 μm Micro-channel: 600 μm The Sherwood number depends on the tube-to-particle diameter ratio N = D D Tube Particle Reynolds number Particle diameter [m] Tube diameter [m] Tube-to-particle diameter ratio Micro-channel 600 x x Micro-channel 300 x x

coefficient is reduced by wall effects also in the micro-channel with 300 μm Mass transfer

120 Wall effects 600 μm sphere diameter 300 μm sphere diameter The higher mass transfer coefficient for micro-channel with 300 μm depends on the lower influence of the wall effects The mass transfer coefficient is reduced by wall effects also in the micro-channel with 300 μm Mass transfer coefficient [m/s] 1,8 1,2 0,6 0, Reynolds number Micro-channel: 300 μm Micro-channel: 600 μm

First-principles based catalytic reaction engineering Matteo Maestri

CECAM International Summer School Hot topic 4 First-principles based catalytic reaction engineering Matteo Maestri July 23, 2013 Conversationshaus - Norderney, Germany Catalytic cycle Consists of the elementary