Catalytic Pellet Reactor Under Uncertainty Design

Catalytic Pellet Reactor Under Uncertainty Catalytic Pellet Reactor Under Uncertainty DesignDesign

Final Presentation at the REU meeting Chicago, IL, Tuesday, Aug. 4th, 2005.

Presenter: Celia Xue

Advisors: Pf. LinningerDr. Libin Zhang

Laboratory for Product and Process Design, Department of Chemical Engineering, University of Illinois,

Chicago, IL 60607, U.S.A.

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MotivationMotivationFig.1: A Typical Configuration of a Pellet

Reactor• Catalytic Pellet Reactor

• Application:– Catalytic Converters in cars– Paraffin Dehydrogenation– Production of Sulfuric Acid

• Design Complication– Coupling of Heat and Mass

transfer phenomenon– Impact of uncertain parameters

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Design Under UncertaintyDesign Under UncertaintyProduct Conversion??

Effectiveness FactorDiffusion + Reaction

• Uncertain Parameter: – system performance / safety – output quality.

• Lack of understanding lead to:– Loss of Revenue– Unsafe Design (Hot Spot, Explosion

etc.)

• Why we want to study it?– Safety Condition – Guarantee product quality and

maximum profit.– Control over design

Pellet Reactor

Inlet Conditions:

Ci and Ti

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

80 00 90 00 10000 1 1000 12000Fb

P(Fb

)

???

Operational Uncertainty

Property UncertaintyHeat Conductivity: ke

Mass Diffusivity: Dab

Reaction rate: a

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MethodologyMethodology

• Case Study: Pellet Reactor Design– Develop Models

– Solve Models in MATLAB

– Analyze the system response

– Quantify impact of uncertain parameters: safety, quality

• Numerical Methods– 1st Order ODE:

» R-K Method (ode45)

– 2nd Order Differential Equation:

» Collocation Method

– Integration: » Adaptive Lobatto

Quadrature Integration (quadl)

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Case Study: Case Study: Catalytic Pellet ReactorCatalytic Pellet Reactor

• Catalytic Reaction:– SO2 (g)+1/2 O2(g) ↔SO3 (g)– 1st Order Heterogeneous

reaction: A→B

• Components of Design– Pellets (Ts, Cs)

» Mass» Energy

– Effectiveness Factor [Fogler]

– Reactor (Ti, Ci)» Mass» Energy

surfaceatratereactionratereactionactual

=η

Fig. 3: Pellet Control Volume Fig. 4: Reactor Control Volume

Fig.2: Expanded View of a Pellet Reactor

Control Volume

Inlet

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Pellet Profiles Pellet Profiles

• Steady State

Boundary Conditions:r=R: Cs, Ts

r=0: dCs/dz=0, dTs/dz=0

• Dynamic State

Initial Conditions:1. t=0: To=12. t=0: Co =Steady State result

Steady State Pellet Temperature Profile

Steady State Pellet Concentration Profile

22

2

2 1exp 1 0d dd dϕ ϕ γ ϕθ θ θ ζ

⎡ ⎤⎛ ⎞+ −Φ − =⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦2

2

2 1exp 1 0d dd dζ ζ β γ ϕθ θ θ ζ

⎡ ⎤⎛ ⎞+ − − =⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

di

Concentration

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

p

Temperature

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

0 0.5 1Time

Con

cent

ratio

n (C

/Co)

r=1

r=0.887

r=0.5

r=0.113

r=00

5

10

15

20

25

30

35

40

0 0.5 1Time

Tem

pera

ture

(T/T

o)

r=0

r=0.113

r=0.5

r=0.88

r=1

Dynamic Pellet Concentration Profile

Dynamic Pellet Temperature Profile

Radius Radius

Scal

ed C

once

ntra

tion

Scal

ed T

empe

ratu

re

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Pellet Sensitivity at Steady StatePellet Sensitivity at Steady State

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

0.E+00 2.E-05 4.E-05 6.E-05CAs (mol/m^3)

Effe

ctiv

ess

Fact

or

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1.10

1.12

250 450 650 850 1050Ts (K)

Effe

ctiv

ess

Fact

or

surfaceatratereactionratereactionactual

=η

Effectiveness factor vs. TsEffectiveness factor vs. CAs

Diffusion limitedSurface reaction limited

Nominal Values:

CAs=2.46E-6 mol/m3

Ts= 550K

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Effectiveness factor vs. Inlet conditions

θθξ

γθϕη d21

0

)11(exp)(3∫ ⎥⎦

⎤⎢⎣

⎡−=

Multiple Steady States for PelletsMultiple Steady States for Pellets

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0 0.2 0.4 0.6 0.8 10.50

0.55

0.60

0.65

0.70

0.75

Scal

ed C

once

ntra

tion

0 0.2 0.4 0.6 0.8 1.00

0.2

0.4

0.6

0.8

1.0

Scal

ed C

once

ntra

tion

0 0.2 0.4 0.6 0.8 10.955

0.960

0.965

0.970

0.975

0.980

Scal

ed C

once

ntra

tion

Reaction Condition:

•Thiele Modulus =0.430

•Beta=0.4

•Gamma=30

Importance:

--Initial Conditions

--One steady state may go to another!!

⎥⎦

⎤⎢⎣

⎡−=Φ )exp(

22

s

a

e RTE

aDR

s

s

TTT )( max −=β

RTEa

=γ

Steady state a

Unstable region b

Steady state c

Normalized Thiele Modulus

Radius Radius Radius

Concentration profiles for a single reaction condition

Multiplicity

Effe

ctiv

enes

s Fa

ctor

Steady State a

Unstable region b

Steady State c

Reactor ProfilesReactor ProfilesSteady State Concentration Profile Steady State Temperature ProfileSteady State:

Ci=1.6E-2 mol/m3

Ti=300K

0)11(exp2

2

=⎥⎦

⎤⎢⎣

⎡−−−

rr

AB

boar

AB

r

TC

DkS

dzdC

DU

dzCd

γρη

0)11(exp2

2

=⎥⎦

⎤⎢⎣

⎡−

∆−−

rr

ib

biar

b

pgr

TC

TkCSH

dTk

UCdz

Tdγ

ρηρ

Dynamic Temperature ProfileDynamic Concentration Profile

Dynamic State:Initial Condition: Steady State

Ci=1.6E-2*5 mol/m3

Ti=300K

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Reactor Safety: HotspotReactor Safety: Hotspot

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0 0.2 0.4 0.6 0.8 11

1.05

1.10

1.15

1.20

1.25

length of reactor

Scal

ed T

empe

ratu

re

Ti=300KTi=350KTi=400KTi=450K

0 0.2 0.4 0.6 0.8 11.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

length of reactor

Scal

ed T

empe

ratu

re

Ko=4.42E-10 m3/(m2*s)ko=4.42E-10*1.2ko=4.42E-10*0.8

0 0.2 0.4 0.6 0.8 11

1.5

2.0

2.5

length of reactor

Scal

ed T

empe

ratu

re

Ci=1E-2Ci=1E-2*0.5Ci=1E-2*0.2Ci=1E-2*2Ci=1E-2*5

• “Hotspot” [Froment.] :– Temperature Profile reach

a maximum– Very exothermic reaction

• Why “hotspot” happens?– Depletion of reactant– Cooling

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11.00

1.05

1.10

1.15

1.20

1.25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Temperature Profile Concentration Profile

Temperature Profile vs. CiTemperature Profile vs. Ti

Scal

ed T

empe

ratu

re

Scal

ed C

once

ntra

tion

Temperature Profile vs. ko

Length of Reactor Length of Reactor

Reactor Safety: MultiplicityReactor Safety: Multiplicity

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

5

10

15

20

25

Time

Sca

led

Tem

pera

ture

Steady State a

Unstable region b

Steady State c

Ideal Design Steady State c

Unsafe Design Steady State a

Normalized Thiele Modulus

Multiplicity for Pellets

Multiplicity for Reactor

• How does reactor respond to pellet multiplicity?

• By testing uncertainty in inlet conditions, we find unsafe design!

– Initial steady state (z=0.5)» Tr=1.2» Cr=0.7

– Disturbance: » Ti=300K» Ci=1E-2 mol/m3

Effe

ctiv

enes

s Fa

ctor

ConclusionConclusion

– Pellet steady/dynamic state profiles

– Multiplicity in pellets

– Reactor steady/dynamic state profiles

– Reactor “hotspot”

– Uncertainty analysis helps to prevent unsafe design!

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ReferencesReferences

• 1. Malcom, A,; Linninger, A.A; “Integrating Design ad Control: Dynamic Analysis of Flexible Operation.”http://viena.che.edu/research/designcontrol/DesigControl.pdf. [June 8, 2005.]

• 2. Fogler H. Scott, Elements of Chemical Reaction Engineering, 3rd Ed., Prentice Hall PTR, 1999.

• 3. Froment Gilbert F. and Bischoff Kenneth B. Chemical Reactor Analysis and Design, 2nd Ed. John Wiley & Sons, Inc., Canada, 1979.

• 4. Catalytic Pellet Reactor. http://jbrwww.che.wisc.edu/~jbraw/chemreacfun/ ch7/slides-masswrxn.pdf. [July 11th, 2005]

• 5. Perkins Victor and Gomez Javier Cruz. Assessment of Electricity Generation to 2011 Using Low Sulfur Fuel Oil in Mexico. http://www.iaee.org/documents/AssessmentofElectricityGenerationto2011UsingLowSulfurFuelOilinMexicoVictorBazC3A1nPerkinsJavierCruzGC3B3mez.pdf. [July 11th, 2005]

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AcknowledgementAcknowledgement

• NSF DMI 0328134 REU Supplement (Linninger) PI

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