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  • 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: keMass Diffusivity: DabReaction 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: AB

    Components of Design Pellets (Ts, Cs)

    Mass Energy

    Effectiveness Factor [Fogler]

    Reactor (Ti, Ci) Mass Energy

    surfaceatratereactionratereactionactual

    =

    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, Tsr=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 d

    + =

    2

    2

    2 1exp 1 0d dd d

    + =

    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

    =

    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

    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!!

    = )exp(

    22

    s

    a

    e RTE

    aDR

    s

    s

    TTT )( max =

    RTEa

    =

    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/m3Ti=300K

    0)11(exp22

    =

    rr

    AB

    boar

    AB

    r

    TC

    DkS

    dzdC

    DU

    dzCd

    0)11(exp22

    =

    rr

    ib

    biar

    b

    pgr

    TC

    TkCSH

    dTk

    UCdz

    Td

    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. Ci Temperature 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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    Catalytic Pellet Reactor Under Uncer

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