multiscale modeling and its application to catalyst design...

1

Dion Vlachos

Department of Chemical Engineering and Center for Catalytic Science and Technology

University of DelawareNewark, DE 19716

www.che.udel.edu/vlachos, [email protected]

Multiscale Modeling and its Application to Catalyst

Design and Portable Power Generation

Outline

Decentralized, future energy productionMiniaturization differs from scaling upMultiscale modelingApplication of multiscale modeling to

Development of detailed reaction mechanismsMicroreactor designProcess optimizationCatalyst designExperiment design

2

Outline



Down-scaling for future energy needs

• Distributed energy– On-board H2 production– Electric reliability– Local solutions, e.g., farms

based on biomass

• Portable energy (electronics)

Smart CarCourtesy: Ballard Power Systems

3

Outline



Large scale H2 production is industrially mature• Steady state operation• Reforming:

endothermic, heat transfer controlled

- Fixed bed catalytic reactors with Ni catalyst for syngas

ReformingWGS, PurificationFuel

+ Air

Hydrocarbon

Steam

Pure H2

• Large scale flames supply the heat- Half of NG is burned to CO2 and

H2O• Complex downstream processing WGS

and PROX or membrane separation/PSA• Slow (τ~1s); bulky SR: CH4 + H2O = CO + 3H2 + 206 kJ/mol

WGS: CO + H2O = CO2 + H2 - 41 kJ/mol

4

Steam reforming is a bulky process

Sehested, Cat. Today 111 (2006) 103

First example of on-board reforming

• GM unveiled the world's first gasoline fuel processor for fuel cell propulsion at the annual automotive management conference in Traverse City, Mich.

• The Gen III processor, packaged in a Chevrolet S-10 pickup, reforms 'clean' gasoline onboard, extracting a stream of hydrogen to send to the fuel cell stack.

5

Microsystems for transportation and portable applications

• Advantages– Process intensification

• High heat and mass transfer coefficients

• Multifunctionality

– Compactness– Inherently safe

• Scale out is feasible for portable (small scale) devices

10 0

10 1

10 2

10 3

10 4

10 -2 10 -1 10 0 10 1

Reactor diameter [mm]

.01 atm

1 atm

u=1 m/s

Mas

s tra

nsfe

r coe

ffici

ent,

k

Reactor diameter [mm]

101

102

103

104

10010-1 10110-2

1 atm

0.01 atm

v = 1 m/s

100

Smart CarCourtesy: Ballard Power Systems

Microscales impose challenges and offer opportunities1

Laminar flows - mixing?Small systems - enough catalyst?Reactors shake - no moveable partsNeed small pressure dropsTransient operation very common

Fast startup and shutdown require active catalyst and fast heat transferCatalyst deactivation can become a major issue

Fast chemistryDifferent systems’ engineering2

?Monolithic type reactors

Dynamics

New chemistry and catalysts

1 Norton et al., "Downsizing chemical processes for portable hydrogen production", in Microreactor Techn. Process Intensification, ACS Symp. Series 914, 179 (2005)

2 Mitsos et al., IECR 43, 74 (2004)

Flowsheets/Optimization

6

Outline



The multiscale simulation paradigm: A bottom-up ladder

CFDMesoscopic Theory/CGMC

KMC, DSMCLB, DPD, BD

MD, extended trajectory calc.

10-2

LengthScale (m)

Time Scale (s)

Quantum Mechanics

TST

Lab Scale

10-10

10-9

10-7

10-6

10-12 10-9 10-3 103

Downscaling or Top-down info traffic

Upscaling or Bottom-up info traffic

Reviews: Raimondeau and Vlachos, Chem. Eng. J. 90, 3 (2002);Chatterjee et al., Chem. Eng. Sci., ISCRE Issue (2004);Vlachos, Adv. Chem. Eng. . 30, 1 (2005)

• Previous work focused usually on a single scale and one way of information passingdeveloped structure-properties relations (molecular descriptors) without attention to processing

7

The Multiscale Simulation Paradigm: Predict macroscopic performance from first principles

CFDMesoscopic Theory

KM, DSMC, LB, DPD, BD

MD, atomistic MC

10-2

LengthScale (m)

Time Scale (s)

Quantum Mechanics

TST

Lab Scale

10-10

10-9

10-7

10-6

10-12 10-9 10-3 103



• Challenges- Phenomena and models are

strongly coupled- Develop bridges between

models of various scales to enable accurate, robust, efficient, seamless coupling*

Reviews: Raimondeau and Vlachos, Chem. Eng. J. 90, 3 (2002);Chatterjee et al., Chem. Eng. Sci. 59, 5559 (2004);Vlachos, Adv. Chem. Eng. 30, 1 (2005)

DFT/MD Coupling

Ludwig and Vlachos, Mol. Simul. (2004)* For noise control in hybrid siml, see work by

groups of Braatz, Christofides, Vlachos



KMC, DSMCLB, DPD,


10-2

LengthScale (m)

Time Scale (s)

Quantum Mechanics

TST

Lab Scale

10-10

10-9

10-7

10-6

10-12 10-9 10-3 103




• Direct multiscale simulation (hybrid, coarse graining) is possible for systems of moderate complexity

• It is plagued by computational cost for complex systems, such as chemical reactors

• Are all scales and phenomena important?

8

Hierarchical, multiscale model development

Aghalayam et al., AIChE J. 46, 2017 (2000)

Deshmukh et al., Int. J. Multiscale Comp. Eng. 2, 221-238 (2004)

Lower Level TheoryMicrokinetic model chemistry parameters

Semi-empirical techniques (BOC), TSTDensity functional theory, DFT-MD

Catalyst modelMean field approximationKinetic Monte Carlo

Fluid flow/TransportSimple reactor models (PFR, CSTR, transp. correlations)Computational Fluid Dynamics (CFD)

Hierarchical, multiscale model development

Aghalayam et al., AIChE J. 46, 2017 (2000)


Higher Level TheoryMicrokinetic model chemistry parameters

Semi-empirical techniques (BOC), TSTDensity functional theory, DFT-MD

Catalyst modelMean field approximationKinetic Monte Carlo

Fluid flow/TransportSimple reactor models (PFR, CSTR, transp. correlations)Computational Fluid Dynamics (CFD)

Feature identification toolbox enables hierarchical model development and reduction

Last theoretical level: Engineering models are needed for reactor optimization and control and for model-based catalyst design

9

Hierarchy enables rapid screening of chemistry, fuels, and catalysts

• Hierarchy adds a new dimension to multiscaling: at each scale, more than one model can be run

Semiempirical: UBI-QEP, TST

ab initio:DFT, TST, DFT-MD

Continuum/Mean-field: ODEs

Theor. parameter estimation

Catalyst & adsorbed phase description

Discrete: Kinetic Monte Carlo

Ideal: Fixed bed, CSTR, etc.

Reactor scaleComputational Fluid Dynamics

(CFD)

Hierarchy, accuracy, cost

Scale

Length

Time

Hierarchy

Outline



10

• Good hydrogen carrierHigh energy density Stored as a liquid (at 25 oC, 8 atm)One of the most widely produced chemicals (>100 metric tones/yr)- Haber-Bosch Process- Infrastructure is already set up

NH3 cracking for H2 production

3 2 22 NH N +3 H 46 /→ + kJ mol1 Deshmukh et al., Ind. Eng. Chem. Res. (2004)2 Ganley et al., AIChE J. (2004)

Meth

anol

Etha

nol

Meth

ane

Prop

ane

• Catalytic decomposition of pure NH3 on Ru1,2

– Slightly endothermic– Minimal downstream processing

0

5

10

15

20

25

30

% w

t

17.6%

Amm

onia

Octan

e

NH3 decomposition on Ru: 2NH3 =N2+3H2

• NH3 as a storage medium• ‘Pure’ H2 – No COx• A microkinetic model is

build using BOC and TST• Our microkinetic model

captures the trend• High N* coverages

196 µm x 84 µm x 1078 µm

Mhadeshwar et al., Cat. Letters 96, 13-22 (2004)

0

0.2

0.4

0.6

0.8

1

650 850 1050 1250T [K]

N*

Empty sites (*)

0

20

40

60

80

100

Expts. [Ganley et al.]

PFR model

Ganley et al., AIChE J.2003

*NH*NH 33 ⇔+*H*NH**NH 23 +⇔+

*H*NH**NH 2 +⇔+*H*N**NH +⇔+*2N*2N 2 +⇔*2H*2H 2 +⇔

11

DFT is used to estimate lateral interactions


• DACAPO (solid-state electronic structure package by Hammer and coworkers*)

• 3-Layer slab of Ru(0001)

• 2 × 2 unit cell

• All layers are relaxed

• Plane wave cutoff = 350eV

• 18 k-points for surface Brillouin zone

• Generalized gradient approximation (PW-91)

* Hammer et al., DACAPO version 2.7 (CAMP, Technical University, Denmark)

90

100

110

120

130

0 0.25 0.5 0.75 1(N*+H*) coverage [ML]

DFT Calculations (this work)Linear fit Q

N (at H*=0)=128.2-33.3N*

N on Ru(0001) 3 layer slab

Linear fit QN (at N*=0.25)=120.1-6.2H*

N-N interactions

N-H interactions

Exps: Ganley et al., AIChE J. (2004)

DFT-retrained microkinetic model describes the experimental data well

• H-H and N-H interactions are small

• N-N interactions completely change the chemistry

• Extensive validation against UHV and high P data has been done

0

20

40

60

80

100

650 850 1050 1250

Expts. [Ganley et al.]

PFR modelwithout interactions

T [K]

PFR modelwith interactions

0

0.2

0.4

0.6

0.8

1

650 850 1050 1250T [K]

*

N* without interactions* without interactions

H*

N*

NH3*


12



KMC, DSMCLB, DPD,


10-2

LengthScale (m)

Time Scale (s)

Quantum Mechanics

TST

Lab Scale

10-10

10-9

10-7

10-6

10-12 10-9 10-3 103




• Typical objective- Mechanistic understanding- Reconcile large differences

in published data- Process optimization:

Process engineering

Outline



13

Computer-aided chemistry reduction• Sensitivity and Principal

Component Analyses – No a priori assumptions– Identification of important

reactions and species

• Small parameter asymptotics on species balances and site conservation– Simple algebra to derive a

rate expression2*N3

2N4N θPkθk 2*2 −=σ

2322 NNHNH -2 and 3 σ=σσ=σ0.5

HNH12104

1197

1

2N

4

3H

2

1NH

12

11

*

23223PP

kk2kkkk

kk

Pkk

Pkk

Pkk

1

1θ−++++

=ReducedModel

0

20

40

60

80

100

650 700 750 800 850 900 950

% N

H3 c

onve

rsio

n

Temperature [K]

ReducedModel

FullModel

FlowDirection

Mhadeshwar et al., Cat. Letters 96, 13 (2004)

µReactor is close to axial dispersion modelDeff vs. Geometric characteristics

• The method of homogenization is used that is based on separation of length scales

ξ1

ξ2

Ωf Ω1-Ωf

Γ

X0.50

0.25

0.00

Y

Post

PostUnit Cell

~ ( , )i ii o

u u xε ξ∞

=∑

, 1

( )m

iji j i j

u uDt x x=

∂ ∂ ∂=

∂ ∂ ∂∑ , 10

m

i iji j j

un Dx=∂

=∂∑

, 11

1 ( )[ ]f

meff k

ij is skk s s

D D dχξ δ ξξΩ=

∂= ∫ +Ω ∂∑

( ), 1 1

( ) ( ),m m

kij jk f

i j ji j j

D Dχξ ξ ξξ ξ ξ= =

⎛ ⎞∂ ∂ ∂= − ∈Ω⎜ ⎟⎜ ⎟∂ ∂ ∂⎝ ⎠

∑ ∑

, 1 1

m mk

i ij j jki j jj

n D n Dχξ= =∂

=∂∑ ∑

1L

ε =

14

Design and fab of microchemical systemsvia multiscale modeling

Contours of Velocity Magnitude

Norton et al., IECR 43, 4833 (2004)

catalyst

posts

Micromixer/reactor Hydrodynamically driven mixing

Top ViewCross Sectional View

Top ViewCross Sectional ViewCatalyst design

Microrxtr design

0

20

40

60

80

100

120

0 1 2 3 4 5 6

0 0.2 0.4 0.6 0.8 1

Pow

er o

utle

t (W

)

Inlet fuel velocity (m/s)

Fuel flow rate (SLPM)

Max. poweroutput

Materials limit

Breakthroughlimit

Attainable regions in multifunctional microdevices

• Multifunctional devices provide millisecond operation• Adjustment of flow rates can provide variable power• Scaling out can supply transportation power levels

NH3 flow rate increases

3 8 2 2 2C H +5O 3CO +4H O→

3 2 22 N H N + 3 H→Wall

50 W

H2 maker:

18 kW

Kaisare et al., IECR (submitted)

15

Outline



Water-gas shift reaction on Pt: CO+H2O=CO2+H2

Thermodynamics1 is important but not sufficient:kinetics ‘corrects’ the WGS speed

0

20

40

60

80

100

473 573 673 773 873

CO

con

vers

ion

[%]

Full mech.

Equil.Experiments(Xue et al.)

A/V=150 cm-1

No coupling and literature mechs

Temperature [K]

1Mhadeshwar et al., J. Phys. Chem. B (2003)

16

Reactor Superstructure Optimization

• Modeled as n PFRs in series• Side feed and side draw from each reactor• Each PFR: same length and different temperature

• Gradient-based optimizer

Yk,f, mf

ms1

Side Feed (steam)

Feedl1, T1 l2, T2 ln, Tn

ms2 msnYk,s

md1 md2 mdn

Side Draw Output

Process optimization: Optimum temperature profile in the WGS reaction

• Total length:

• Inlet: 40 sccm feed (dry basis), with 18% CO

• Steam:

• Temperature constraints:

• All cases:– No split feed or side draw– All steam utilized– T constraints were inactive

2cmii

l =∑

, 40sccms ii

m ≤∑

373K 873KiT≤ ≤

450

500

550

600

650

700

750

2 4 6 8 10

Tem

pera

ture

, T

(K)

# of PFR

218 ppm

356 ppm

COout

= 1174 ppm

Vlachos et al., Compt. Chem. Eng. (2006)

17

Outline





KMC, DSMCLB, DPD,


10-2

LengthScale (m)

Time Scale (s)

Quantum Mechanics

TST

Lab Scale

10-10

10-9

10-7

10-6

10-12 10-9 10-3 103




• Typical objective- Mechanistic understanding- Reconcile large differences

in published data- Process optimization:

Process engineering

The multiscale simulation paradigm: A bottom up and top-down ladder

• Opportunity- Given a macroscopic

behavior, design materials and/or control nanoscale

- Product engineering

18

An example of catalyst optimization: NH3 decomposition

• Search is done on atomic descriptors while running the full chemistry model

• Libraries of computational information are created via DFT

• Models are built• Potential catalyst

candidates are identifiedHydrogen binding energy

Nitr

ogen

bin

ding

ene

rgy

Ammonia conversion (%) at 380 oC

Ulissi et al.

Outline



19

Maximizing information content of a model

• Parameters are uncertain• Often refined using statistically based experiments• We need to bridge first-principles modeling with systems

approaches in designing experiments

SA

NoYes

Guidelinesfor reactor design

Sort

Initial model

Refine hierarchically

the model

Identify exptal

conditions

ExptInformatics database (model based)

Model globally valid?

Models database

No Mod

el

Global search

Vlachos et al., Comp. Chem. Eng. 30, 1712 (2006)

Model-based design of experiments: Ensuring global accuracy of models

• Global Monte Carlo search in exptl parameter space (τ, P, T, compos., A/V)

• Local sensitivity analysis– Only a few model parameters are important

and can be extracted, but change in manipulated parameter space

• Sort by max NSC, RDS, MARI,…

(c)

(a)

(b)

-8 -4 0 4 8

Rea

ctio

n

NH2*+* NH*+H*

N2+2* 2N*

NSC

NH3*+* NH

2*+H*

H2+2* 2H*

2H* H2+2*

2N* N2+2*

NH*+* N*+H*N*+H* NH*+*

NH*+H* NH2*+*

NH2*+H* NH

3*+*

NH3* NH

3+*

NH3+* NH

3*

-15 -10 -5 0 10 15

Rea

ctio

n

NH2*+* NH*+H*

N2+2* 2N*

NSC

NH3*+* NH 2*+H*

H2+2* 2H*2H* H 2+2*

2N* N 2+2*NH*+* N*+H*

N*+H* NH*+*

NH*+H* NH 2*+*

NH2*+H* NH 3*+*

NH3* NH 3+*NH3+* NH 3*

-0.5

0

0.5

1

1.5

2

0 20 40 60 80 100Ammonia conversion [%]

NH3*+*=NH2

*+H*

|NSC

|

731 0.3 2.0 1541 0.02 0.50 0.48

Vlachos et al., Comp. Chem. Eng., 30, 1712 (2006)

20

Normalized parameter sensitivity vs. conversion (CSTR)

NH2*+*=NH*+H* is the most sensitive reaction

H2

NH3

N2

RDS R2RDS R3 RDS R4

D Optimal

E Optimal

A OptimalRDS R1

RDS R5 RDS R6

500600

700800

900

0

1

2

3

4

50

5000

10000

15000

Sur

face

are

a / v

olum

e (1

/cm

)

Residence time (s) T (K)

RDS R5RDS R3

RDS R4E Optimal

A Optimal

RDS R1RDS R6D Optimal

RDS R2

Optimal statistical and physics-aided designsCompared D, A, E and physics-aided designs

Inlet composition space – no clear pattern

Optimum at relatively low temperature, intermediate cat. surface area/reactor volume

Prasad and Vlachos, Ind. Eng. Chem. Res. (submitted)

21

D optimal metric

Kinetic relevance –D Optimality and partial equilibrium (PE)

High values of the det. of the Fisher info matrix correlate with fewer reactions in PE and farther from equil.

Non PE

PE|PEI|: NH2 *+*=NH*+H* |PE

I|: N2+2

*=2N*


Partial equil. index:PEI=rf/(rf+rb)

0

0.2

0.4

0.6

0.8

1

3 4 5 6

Highest det(FIM)Mid-value det(FIM)Lowest det(FIM)

Prob

abili

ty

No. of reactions in partial equilibrium

Approach to overall equilibrium

Kinetic relevance –D Optimality and sensitivity coefficients

D optimal metric

High values of the Fisher information matrix correlate with larger normalized sensitivity coefficients of the sensitive reactions

Opt.

Equil.

|NSC|: NH2 *+*=NH*+H* |NS

C|: N 2+

2*=2N

*


22

Is a Single Optimal Point Good Enough?The D optimal response surface is highly nonlinear

You must be very close to the optimal point to ensure optimality

Experimental constraints may make this unachievable

Representative cross-section of D optimal response surface

D optimal metric vs. distance from optimal point


0

0.05

0.1

0.15

0.2

0.25

0.3

-20 -15 -10 -5 0 5

1%10%20%

Dis

tribu

tion

log(det(FIM))

Identifying regions (clusters) of D-optimal data using informatics tools

Clusters are identified using ‘partitioning among medoids’


23

Assessment of Informatics Approach

Sample anywhere within clusters (experimental flexibility)

Substantial improvement over single optimal points

Distribution of D optimal metric within optimal region and in entire parameter space

Prasad and Vlachos

0

0.05

0.1

0.15

0.2

0.25

-20 -15 -10 -5 0 5

Full ensembleWithin first D optimal region

Dis

tribu

tion

log(det(FIM))

Proof of concept via experiments

• 44 new experiments conducted in optimal region

• Varied– Temperature– Catalyst amount– Inlet composition

• Good agreement of model prediction and data

Karim, Prasad, and Vlachos (in preparation)

0

20

40

60

80

100

0 20 40 60 80 100

Con

vers

ion

% (e

xper

imen

t)

Conversion, % (model)

24

Summary and future directionsFuture energy generation will happen at much smaller scalesDownscaling is different even at the

multiscale modeling and its application to catalyst design...

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