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

2
Tesi di Laurea Magistrale – Carlos Sierra
Introduction
• Plug flow reactors that are carrying out exothermic reactions
can generate, under certain operating conditions, an
uncontrolled temperature increase (thermal runaway) that could
lead to the triggering of other more exothermic reactions, such
as decomposition reactions.
• Thermal runaway studies on continuous reactors are normally
held for steady state operation, because all the dynamic
changes take place in a short period of time.

3
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.

4
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 method
Analytical
Numerical
Results analysis
Problem definition Runaway in PFR in unsteady state
ODE/PDE
NOT possible

5
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)

6
Unsteady State equations
Mass balance:
Dimensionless mass balance:
Energy balance:
Dimensionless energy balance:
Steady State equations: Neglected time dependent and diffusive terms

7
Thermal runaway
It is defined as a situation where a temperature rise changes the
conditions of a chemical reaction, in a way that causes a further
increase in temperature. This is a kind of uncontrolled positive
feedback.

8
Parametric sensitivity
• Parametric sensitivity
• Normalized sensitivity
It is defined as the system behavior with respect to changes in its
input parameters. By changing these values, the system
characteristics can achieve desired or undesired behaviors.
When a system operates in the parametrically sensitive region (the
region where small variations of a parameter make the system
becomes sensitive), its performance becomes unreliable and
changes with small variations in the parameters.

9
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

10
Equation characteristics
• Initial conditions:
• Empty reactor.
• Reactor temperature equal to wall temperature
• Boundary conditions: Dankwerts type

11
• Boundary conditions: Dankwerts type
No change
Smooth step
change

12
Method of lines
• Approximation of the spatial derivatives using finite
differences.
Differentiation matrixes
Fornberg algorithm
Iteratively computing the weighting coefficients of finite difference
formulas of arbitrary order of accuracy on arbitrarily spaced
spatial grids.
• Time integration of the resulting semi-discrete (discrete in
space, but continuous in time) ODE, using ODE MATLAB
solvers.

13
Method of lines vs PDEPE
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
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 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
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
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
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

14
Case study
Naphthalene oxidation to phthalic Anhydride
It is a chemical intermediate in the production of plasticizers for
polyvinyl chloride (PVC).
It was considered a gas phase reaction.

15
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

16
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).

17
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
625
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 2.2
0
10
20
30
40
50
60
70
Pin
[kPa]
S(T,Pin
)
P
in
= 1.85, S[T,P
in
] = 58.6996
Increase inlet
pressure
Increase maximum
reactor temperature
Hot spot moving to
the left

18
Results Steady State Inlet Temperature
0 0.1 0.2 0.3 0.4 0.5
600
700
800
900
1000
1100
1200
1300
z[-]
T[K]
Tin
=620[K]
Tin
=630[K]
Tin
=640[K]
Tin
=650[K]
Tin
=660[K]
Tin
=670[K]
Tin
=680[K]
Tin
=690[K]
Tin
=700[K]
Tin
=710[K]
Tin
=720[K]
620 630 640 650 660 670 680 690 700 710 720
0
20
40
60
80
100
120
140
160
180
200
Tin
[K]
S(T,Tin
)
T
in
= 675, S[T,T
in
] = 161.1574
Maximum rate of
change
High sensitivity
Increase inlet
temperature
Increase maximum
reactor temperature
Hot spot moving to
the left

19
Results Steady State Wall Temperature
0 0.1 0.2 0.3 0.4 0.5
600
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]
580 590 600 610 620 630 640 650 660 670 680
0
20
40
60
80
100
120
Tw
[K]
S(T,Tw
)
T
w
= 638, S[T,T
w
] = 104.3867
Maximum rate of
change
High sensitivity
Increase wall
temperature
Increase maximum
reactor temperature
Hot spot moving to
the left

20
Results Steady State Inlet Velocity
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
625
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
1
x 10
-4
v0
[m/s]
S(T,v0
)
v
0
[m/s] = 0.78, S[T,v
0
] = -9.1981e-05
Maximum rate of
change
Very low sensitivity
Increase inlet
velocity
Constant maximum
reactor temperature
Hot spot moving to
the right
Values close to zero

21
Results Unsteady State Inlet Pressure
1.5 1.6 1.7 1.8 1.9 2 2.1 2.2
0
40
80
120
160
200
Pin
[kPa]
S(T,Pin
)
 =0.1[-]
 =0.2[-]
 =0.3[-]
 =0.4[-]
 =0.5[-]
 =0.6[-]
 =0.7[-]
 =0.8[-]
 =0.9[-]
 =1[-]
Maximum rate of
change
No high sensitivity
before this point
Steady state

22
Results Unsteady State Inlet Pressure
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Xmax
[-]
Tmax
/Tin
[-]
 =0.3[-]
 =0.4[-]
 =0.5[-]
Steady state
Safety region
Steady state limit

23
Results Unsteady State Inlet Temperature
620 630 640 650 660 670 680 690 700 710 720
0
50
100
150
200
250
Tin
[K]
S(T,Tin
)
 =0.1[-]
 =0.2[-]
 =0.3[-]
 =0.4[-]
 =0.5[-]
 =0.6[-]
 =0.7[-]
 =0.8[-]
 =0.9[-]
 =1[-]
Maximum rate of
change
No high sensitivity
before this point
Steady state

24
Results Unsteady State Inlet Temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1
1.2
1.4
1.6
1.8
Xmax
[-]
Tmax
/Tin
[-]
 =0.1[-]
 =0.2[-]
 =0.3[-]
Steady state
Safety region
Steady state limit

25
Results Unsteady State Wall Temperature
580 590 600 610 620 630 640 650 660 670 680
0
40
80
120
160
200
Tw
[K]
S(T,Tw
)
 =0.1[-]
 =0.2[-]
 =0.3[-]
 =0.4[-]
 =0.5[-]
 =0.6[-]
 =0.7[-]
 =0.8[-]
 =0.9[-]
 =1[-]
Maximum rate of
change
No high sensitivity
before this point Steady state

26
Results Unsteady State Wall Temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1
1.2
1.4
1.6
1.8
2
Xmax
[-]
Tmax
/Tin
[-]
 =0.2[-]
 =0.3[-]
 =0.4[-]
Steady state
Safety region
Steady state limit

27
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
5
x 10
-3
vin
[m/s]
S(T,Tw
)
 =0.1[-]
 =0.2[-]
 =0.3[-]
 =0.4[-]
 =0.5[-]
 =0.6[-]
 =0.7[-]
 =0.8[-]
 =0.9[-]
 =1[-]
Values close to zero
No maximum rate of change
Steady state
Inlet velocity is not relevant under this analysis

28
Results Unsteady State Inlet Velocity
0 0.1 0.2 0.3
0.95
1
1.05
1.1
Xmax
[-]
Tmax
/Tin
[-]
 =0.2[-]
 =0.3[-]
 =0.4[-]
Steady state
No safety region
definition
Inlet velocity is not relevant under this analysis
Points concentration No change in reactor behavior

29
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.

30
Questions
Thanks for your attention!

31
Unsteady State equations
Mass balance:
Energy balance:
Steady State equations: Neglected time dependent (accumulation)
and diffusive terms

32
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:

33
Steady State equations
Mass
balance:
Dimensionless
mass balance:
Energy
balance:
Dimensionless
energy balance:
Neglected time dependent and diffusive terms

34
• 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 increases
exp() increases

35
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.

36
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

37
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

More Related Content

What's hot

Viewers also liked

Similar to 2014_12_Sierra

2014_12_Sierra