2014_12_sierra

OPTIMIZATION OF POTENTIALLY RUNAWAY REACTIONS CARRIED OUT IN PLUG FLOW REACTORS

Tesi di: Carlos Sierra (797299)

Scuola di Ingegneria Industriale e dell'Informazione

Corso di Laurea in Ingegneria della Prevenzione e della Sicurezza nell’Industria di Processo

Anno Accademico 2013 – 2014

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Tesi di Laurea Magistrale – Carlos Sierra

Introduction

• Plug flow reactors that are carrying out exothermic reactionscan generate, under certain operating conditions, anuncontrolled temperature increase (thermal runaway) that couldlead to the triggering of other more exothermic reactions, suchas decomposition reactions.

• Thermal runaway studies on continuous reactors are normallyheld for steady state operation, because all the dynamicchanges take place in a short period of time.

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Scope

• Identify possible thermal runaway conditions for steady and unsteady state operations in a plug flow reactor.

• Set a safety operation range for a case study of a high exothermic reaction.

• Perform a criterion for thermal runaway conditions during unsteady state operations.

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Structure of the work

Theory model

Steady state simulations

Unsteady state simulations

Identify differences and establish a criterion (if possible)

MATLAB

System solution

Equations for mass and energy balances

Solution methodAnalytical

Numerical

Results analysis

Problem definition Runaway in PFR in unsteady state

ODE/PDE

NOT possible

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Model assumptions:

• Constant diameter through all the reactor.• No radial variations of velocity, concentrations, temperature or

reaction rate. Perfect mixing in the radial direction.• Constant density along the reactor.• Constant inlet velocity, which is equal to the axial velocity.

Model Plug Flow Reactor (PFR)

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Unsteady State equations

Mass balance:

Dimensionless mass balance:

Energy balance:

Dimensionless energy balance:

Steady State equations: Neglected time dependent and diffusive terms

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Thermal runaway

It is defined as a situation where a temperature rise changes theconditions of a chemical reaction, in a way that causes a furtherincrease in temperature. This is a kind of uncontrolled positivefeedback.

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Parametric sensitivity

• Parametric sensitivity

• Normalized sensitivity

It is defined as the system behavior with respect to changes in itsinput parameters. By changing these values, the systemcharacteristics can achieve desired or undesired behaviors.

When a system operates in the parametrically sensitive region (theregion where small variations of a parameter make the systembecomes sensitive), its performance becomes unreliable andchanges with small variations in the parameters.

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Numerical solution

MATLAB solver

Steady state simulations Unsteady state simulations

ODE solver

Ordinary Differential Equation (ODE)

Partial Differential Equation (PDE)

Function ODE15S

PDE solver

Function PDEPE✔Useful in all cases ✘Not useful in all cases

Method of lines + Finite difference

✔Useful in all cases

PDE Toolbox not considered ✘Useful for one dependent variable system

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Equation characteristics

• Initial conditions:

• Empty reactor.• Reactor temperature equal to wall temperature

• Boundary conditions: Dankwerts type

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• Boundary conditions: Dankwerts type

No change

Smooth step change

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Method of lines

• Approximation of the spatial derivatives using finitedifferences.

Differentiation matrixes

Fornberg algorithm

Iteratively computing the weighting coefficients of finite differenceformulas of arbitrary order of accuracy on arbitrarily spacedspatial grids.

• Time integration of the resulting semi-discrete (discrete inspace, but continuous in time) ODE, using ODE MATLABsolvers.

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Method of lines vs PDEPE

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.10.20.30.40.50.60.70.80.9

11.1

z[-]

X[-

]

=0[-] =0.15[-] =0.3[-] =0.45[-] =0.6[-] =0.75[-] =0.9[-] =1.05[-] =1.2[-]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.10.20.30.40.50.60.70.80.9

11.1

z[-]

X[-

]

=0[-] =0.15[-] =0.3[-] =0.45[-] =0.6[-] =0.75[-] =0.9[-] =1.05[-] =1.2[-]

Solution for P_in = 1.5[kPa]

Solution for P_in = 2.0[kPa]0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

00.10.20.30.40.50.60.70.80.9

11.1

z[-]

X[-

]

=0[-] =0.15[-] =0.3[-] =0.45[-] =0.6[-] =0.75[-] =0.9[-] =1.05[-] =1.2[-]

Oscillation for P_in = 1.5[kPa]

Not possible solution for P_in = 2.0[kPa]

Method of lines PDEPE

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Case study

Naphthalene oxidation to phthalic Anhydride

It is a chemical intermediate in the production of plasticizers forpolyvinyl chloride (PVC).

It was considered a gas phase reaction.

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The gas-phase naphthalene oxidation to phthalic anhydride is a highly exothermic reaction. This reaction is carried out in multi-tubular reactors, cooled by molten salt that is passing around an external jacket. As a catalyst, V2O5 is used.

Case study

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Case study

Initial values for the studied input parameters:

• Inlet pressure• Inlet temperature• Wall temperature• Inlet velocity

• Steady state analysis:• Reactor temperature vs dimensionless reactor length.• Normalized sensitivity for each input parameter.

• Unsteady state:• Normalized sensitivity for each input parameter, for different

dimensionless times.• Ratio between maximum reactor temperature and inlet temperature

vs conversion at that temperature (topological diagram).

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7625

725

825

925

1025

1125

1225

1325

1425

z[-]T[

K]

Pin=1.5[kPa]

Pin=1.6[kPa]Pin=1.7[kPa]

Pin=1.8[kPa]

Pin=1.9[kPa]

Pin=2[kPa]Pin=2.1[kPa]

Pin=2.2[kPa]

Results Steady State Inlet Pressure

Maximum rate of change

High sensitivity

1.5 1.6 1.7 1.8 1.9 2 2.1 2.20

10

20

30

40

50

60

70

Pin[kPa]

S(T,

P in)

Pin

= 1.85, S[T,Pin

] = 58.6996

Increase inlet pressure

Increase maximum reactor temperature

Hot spot moving to the left

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Results Steady State Inlet Temperature

0 0.1 0.2 0.3 0.4 0.5600

700

800

900

1000

1100

1200

1300

z[-]T[

K]

Tin=620[K]Tin=630[K]

Tin=640[K]

Tin=650[K]


Tin=680[K]

Tin=690[K]

Tin=700[K]


620 630 640 650 660 670 680 690 700 710 7200

20406080

100120140160180200

Tin[K]

S(T,

T in)

Tin

= 675, S[T,Tin

] = 161.1574


High sensitivity

Increase inlet temperature



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Results Steady State Wall Temperature

0 0.1 0.2 0.3 0.4 0.5600

700

800

900

1000

1100

1200

1300

z[-]T[

K]

Tw =580[K]Tw =590[K]

Tw =600[K]

Tw =610[K]

Tw =620[K]

Tw =630[K]Tw =640[K]

Tw =650[K]

Tw =660[K]

Tw =670[K]Tw =680[K]

580 590 600 610 620 630 640 650 660 670 6800

20

40

60

80

100

120

Tw[K]

S(T,

T w)

Tw = 638, S[T,T

w] = 104.3867


High sensitivity

Increase wall temperature



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Results Steady State Inlet Velocity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1625

630

635

640

645

650

z[-]T[

K]

v0 =0.1[m/s]

v0 =0.3[m/s]v0 =0.5[m/s]

v0 =0.7[m/s]

v0 =0.9[m/s]

v0 =1.1[m/s]v0 =1.3[m/s]

v0 =1.5[m/s]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-1.5

-1

-0.5

0

0.5

1x 10-4

v0[m/s]

S(T,

v 0)

v0[m/s] = 0.78, S[T,v

0] = -9.1981e-05


Very low sensitivity

Increase inlet velocity

Constant maximum reactor temperature

Hot spot moving to the right

Values close to zero

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Results Unsteady State Inlet Pressure

1.5 1.6 1.7 1.8 1.9 2 2.1 2.20

40

80

120

160

200

Pin[kPa]

S(T,

P in)

=0.1[-] =0.2[-] =0.3[-] =0.4[-] =0.5[-] =0.6[-] =0.7[-] =0.8[-] =0.9[-] =1[-]


No high sensitivity before this point

Steady state

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Results Unsteady State Inlet Pressure

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

1.2

1.4

1.6

1.8

2

2.2

2.4

Xmax[-]

T max

/Tin

[-]

=0.3[-] =0.4[-] =0.5[-]Steady state

Safety region

Steady state limit

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Results Unsteady State Inlet Temperature

620 630 640 650 660 670 680 690 700 710 7200

50

100

150

200

250

Tin[K]

S(T,

T in)

=0.1[-] =0.2[-] =0.3[-] =0.4[-] =0.5[-] =0.6[-] =0.7[-] =0.8[-] =0.9[-] =1[-]


No high sensitivity before this point

Steady state

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Results Unsteady State Inlet Temperature

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

1.2

1.4

1.6

1.8

Xmax[-]

T max

/Tin

[-]

=0.1[-] =0.2[-] =0.3[-]Steady state

Safety region

Steady state limit

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Results Unsteady State Wall Temperature

580 590 600 610 620 630 640 650 660 670 6800

40

80

120

160

200

Tw[K]

S(T,

T w)

=0.1[-] =0.2[-] =0.3[-] =0.4[-] =0.5[-] =0.6[-] =0.7[-] =0.8[-] =0.9[-] =1[-]


No high sensitivity before this point Steady state

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Results Unsteady State Wall Temperature

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

1.2

1.4

1.6

1.8

2

Xmax[-]

T max

/Tin

[-]

=0.2[-] =0.3[-] =0.4[-]Steady state

Safety region

Steady state limit

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Results Unsteady State Inlet Velocity

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-15

-10

-5

0

5x 10-3

vin[m/s]

S(T,

T w)

=0.1[-] =0.2[-] =0.3[-] =0.4[-] =0.5[-] =0.6[-] =0.7[-] =0.8[-] =0.9[-] =1[-]

Values close to zeroNo maximum rate of change

Steady state

Inlet velocity is not relevant under this analysis

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Results Unsteady State Inlet Velocity

0 0.1 0.2 0.30.95

1

1.05

1.1

Xmax[-]

T max

/Tin

[-]

=0.2[-] =0.3[-] =0.4[-]Steady state

No safety region definitionInlet velocity is not relevant under this analysis

Points concentration No change in reactor behavior

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Conclusions

• The steady state case was the best approach from the point of view of safety.

• The unsteady state maximum temperature values were close to the steady state ones.

• In the unsteady state case the hot spots were moving along the reactor, without describing a relevant higher temperature compared to steady state case.

• A new concept is not provided for thermal runaway criterion in unsteady state operation.

• The inlet pressure, the inlet temperature and the wall temperature registered a visible peak sensitivity change over the selected range; for the inlet velocity there was not reported this behavior.

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Questions

Thanks for your attention!

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Unsteady State equations

Mass balance:

Energy balance:

Steady State equations: Neglected time dependent (accumulation) and diffusive terms

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Dimensionless quantities

Conversion:

Dimensionless temperature:

Dimensionless axial coordinate:

Dimensionless time:

Arrhenius number:

Damkohler number:

Stanton number:

Mass Peclet number:

Energy Peclet number:

Dimensionless adiabatic temperature rise:

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Steady State equations

Mass balance:

Dimensionless mass balance:

Energy balance:

Dimensionless energy balance:

Neglected time dependent and diffusive terms

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• Stiff equation:

PDE for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small. This is evident when the equation includes some terms that can lead to rapid variation in the solution.

T increasesexp() increases

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PDEPE solver

• Gibbs phenomena:Fourier series of a piecewise continuously differentiable behaves at a jump discontinuity: the n-th partial sum of the Fourier series has large oscillations near the jump, which might increase the maximum of the partial sum above that of the function itself.

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Slope limiters and numerical dissipation

Wouwer A, Saucez P, and Vilas C. Simulation of ODE/PDE models with MATLAB, OCTAVE and SCILAB: scientific and engineering applications. Springer, 2014.

A slope limiter could be useful for oscillation problems in second order approximations.Algorithm more complex, and possible numerical dissipation.

First order approx

Second order approx

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Further work

• Modelling of highly exothermic reactions with solvers as COMSOL multi physics (CFD interface), for better visualization of hot spot points and understanding of the overall behavior along the reactor in the dynamical operation condition.

• Calculations and model validation for reactions in solid and liquid phases.

2014_12_sierra

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