Pertti Koukkari20th Annual Users’ Meeting

GTT Technologies28.6. 2018

Comparing Mechanistic and Thermochemical

Modelling of Reaction Rate-Controlled

Multiphase Systems

Simulation of the Titanium(IV)Chloride Oxidizer

1. Motivation to calculate rate-controlled systems

2. Coupling of reaction matrix with stoichiometric formula matrix

3. Case example: TiO2 nanoparticle formation by TiCl4 oxidation

- detailed kinetic mechanism (DKM, West & al. 2007-2009)

- constrained Gibbs energy (CFE, by Koukkari & al. 1993 ⇒)

- comparison with experiment

4. Application in reactor simulation

5. Conclusions

CONTENTS OF PRESENTATION

PresenterPresentation NotesEnter speaker notes here.

Practical systems seldom reach complete equilibrium due to (slow) reaction kinetics

The reaction rate parameters of many suggested complex mechanisms are often less well known

mechanistic (DKM) modeling is a nearly impossible challenge for complex heterogeneous systems with many phases

⇒ it would be advantageous to include reaction rate restrictions to Gibbs energy minimization to allow for calculations of kinetically constrained reactors

MOTIVATION

PresenterPresentation NotesEnter speaker notes here.

𝑑𝑑𝐧𝐧 = 𝛖𝛖𝑑𝑑𝛏𝛏 ; 𝛏𝛏 = 𝛏𝛏 (𝑡𝑡)

MODELLING OF DYNAMIC MULTICOMPONENT SYSTEMS

Solve time course for amount of moles vs. extents of reaction (ξ):

In DKM, a group of ODE’s used and solved as a numerical initial value problem; parameters for all reaction rates required (e.g. CANTERA)

when solving min(G) for global minimum, the ξ’s are independent variables, but components are conserved by mass balance constraints

In constrained min(G) [CFE] the ξ = ξ(t) are solved from reaction rate equations to be used as additional conserved quantities

⇒ in CFE differential-algebraic (DA) approach is used, rate parameters applied for selected reactions only and a ‘timewise’ sequential min(G) is calculated (e.g. ChemSheet/ChemApp)

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*) Blomberg & Koukkari, Comput. Chem. Eng. 35 (2011) 1238-1251.Pajarre & al., Chem. Eng.Sci. 146 (2016) 244-258.Koukkari & Paiva, Chem.Eng.Sci 179 (2018), 227-242.

Constraints in the 2-component system:

2 components (α1, α 2 ) 4 species (α1, α 2, α3, α 4) 2 reactions (r1, r 2)

includes constraints for mass balances and reactions applies extents of reaction as additional constraints in min(G) number of constrained reactions can be chosen (0 ≤ r ≤ R)

Example of 2 reactions:

COUPLING OF REACTION AND CONSERVATION MATRICES

C(υ)

Reaction matrix Stoichiometricformula matrix

𝐂𝐂𝐓𝐓 =

1 0 𝛼𝛼10 1 𝛼𝛼21 2 𝛼𝛼31 3 𝛼𝛼4

𝐂𝐂(υ)𝐓𝐓 =

1 0 −1 0 𝛼𝛼10 1 0 0 𝛼𝛼21 2 0 0 𝛼𝛼31 3 0 1 𝛼𝛼40 0 1 0 𝑟𝑟10 0 0 1 𝑟𝑟2

Use row permutations(* in [I, υ] to convert υas constraints in C:

Formula matrixwith reaction constraints

⇔

r1 r2

⇒⇒⇒⇒⇒

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Superheated O2

TiCl4 -gasCooling water

ConeReactor & Coolingsections

TiO2 is formed as a nanoparticle suspension – used as the white pigment (> 5 Mt/yr) exothermic main reaction compensated by endothermic side reactions

(chlorine dissociation, TixOyClz formation) and efficient reactor cooling

Key reactions ∆H(1000 C)kJ/mol

TiCl4(g) + O2(g) ↔ TiO2 ↓ + 2Cl2(g) -175Cl2(g) ↔ 2Cl(g) +250

1600 C

500 C

900 ⇒ 1500 C

EXAMPLE: FLAME REACTOR FOR TiCl4 OXIDATION

.

.

. 51…67 reactions2007

OO2O3Cl Cl2ClO ClOO Cl2OTi TiClTiCl2TiCl3TiCl4TiOCl2 TiOCl3TiO2Cl2

TiO2Cl3 TiCl2OClTi2O2Cl3Ti2O2Cl4Ti2O2Cl5Ti2O2Cl6Ti2O3Cl2Ti2O3Cl3 Ti3O4Cl4TiO2Cl5TiO2Cl6.TiO2(s)

Gas

Solid

SYSTEM FOR DKM CALCULATIONS (TiCl4 OXIDATION)WEST 2007

TiCl4

TiCl3

TiO2Cl3

TiO2Cl2 TiOCl3

TiOCl2

Ti2O2Cl3Ti2O2Cl4

Ti3O4Cl4

System Overall reaction

Reaction mechanism

Richard H. West

Mechanistic (DKM) model:

*West &al., Ind. Eng. Chem. Res.46, (2007) 6147.Karlemo & al., Plasma Chem .& Plasma Proc. 16, (1996) 59.

6 thermal decomposition reactions, ∆H > 0 12 abstractions and disproportionations, ∆H < 0 18 oxidation reactions, ∆H < 0 8 Cl/O-chemistry reactions, ∆H >

West & al.2007

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

400 900 1400 1900 2400 2900

Mol

e fr

actio

n

Temperature (K)

Monomers

Chlorides

Dimers

Ti3O4Cl4(g)

Ti5O6Cl8(g)

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

400 800 1200 1600 2000 2400 2800

mol

e fr

actio

n

Temperature [K]

Cl(g) Cl2(g) Cl2O(g) ClO(g) ClO2(g) O(g) O2(g) O3(g) Ti(g) TiCl(g) TiCl2(g) TiCl3(g) TiCl4(g) Ti2Cl6(g) TiO2(g) TiOCl(g) TiOCl2(g) TiO2Cl2(g) TiO2Cl3(g) TiOCl3(g) Ti2O2Cl3(g) Ti2O2Cl4(g) Ti2O2Cl5(g) Ti2O2Cl6(g) Ti2O3Cl2(g) Ti2O3Cl3(g) Ti3O4Cl4(g) Ti5O6Cl8(g)

⇔

⇔

P. Koukkari &EduardoPaiva 2017

DKM West &al., 2007

O2

TiCl4

Cl2

Ti2O2Cl2

ClTiOCl2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 5 10

mol

e fr

actio

n

time [ms]

CFE Koukkari &Paiva 2016

[ ] [ ]

1410268

071

−⋅=

−=

−=

s.A

RTmol/kJ.expAk

;TiClkdt

TiCld4

4

TiCl4 conversionconstraint:

Data from Koukkari & LiukkonenInd.Eng.Chem.Res.,41 (2002) 2931.

O2 Cl2

TiCl4

Ti2O2Cl4

TiOCl2Cl

COMPARISON OF DKM AND CFE KINETIC CALCULATIONMAJOR SPECIES

With only gas phase included, the two models appear in close agreement

Kinetics of major gaseous species generally used for aerosol nanoparticlemodelling (studies on nucleation and population balance)

O2

Cl2

TiCl4

Ti2O2Cl4

TiOCl2 Cl

COMPARISON OF DKM AND CFE KINETIC CALCULATIONMAJOR SPECIES

mol

e fr

actio

n

time [ms]

Ti3O4Cl4

Ti2O3Cl3

TiO2Cl2x104

0

0.0005

0.001

0.0015

0.002

0.0025

0 1 2 3 4 5

mol

e fr

actio

n

Time [ms]

DKM results CFE results

minor species monotonically ascending in CFE (unless additional constraints areapplied)

(no experimental data for detailed kinetics exist)

COMPARISON OF DKM AND CFE KINETIC CALCULATIONMINOR SPECIES (SELECTION)

DKM and CFE give congruent results for the (gas phase) kinetics

How about model vs. experiments ?

TiOCl(2) ClOCl(2)

Karlemo & al., Plasma Chem .& Plasma Proc. 16, (1996) 59.

PresenterPresentation NotesEnter speaker notes here.

Plug flow reactor measurements of TiCl4 consumption with various residence times (700-900 C)

⇒ effective rate constant 𝑘𝑘𝑒𝑒𝑒𝑒𝑒𝑒 = 𝐴𝐴⋅ 𝑒𝑒𝑒𝑒𝑒𝑒 (−𝐸𝐸𝑎𝑎/𝑅𝑅𝑇𝑇)

EXPERIMENTAL ARRHENIUS PLOT FOR TiCl4 CONSUMPTION

Pratsinis, J.Am.Ceram.Soc. 1990, 73, 7, 2158-62

−�𝑙𝑙𝑙𝑙 �𝑐𝑐𝑜𝑜𝑐𝑐𝑇𝑇

�𝑡𝑡� � = 𝑘𝑘𝑒𝑒𝑒𝑒𝑒𝑒

[TiCl4] data as co; ci = ci(t)

keff = f(T) ;independent of residence time

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Plug flow reactor measurements of TiCl4 consumption with various residence times (700-900 C)

⇒ effective rate constant 𝑘𝑘𝑒𝑒𝑒𝑒𝑒𝑒 = 𝐴𝐴⋅ 𝑒𝑒𝑒𝑒𝑒𝑒 (−𝐸𝐸𝑎𝑎/𝑅𝑅𝑇𝑇)

GAS PHASE MODELS CHECKED WITH EXPERIMENTARRHENIUS PLOT*

*Pratsinis, J.Am.Ceram.Soc. 1990, 73, 7, 2158-62

Increasing deviationwith increase of residence time (tr)

lines not coinciding[keff(t) not constant] ??

Gas phase CFE calculations cross-checked with experiment

−�𝑙𝑙𝑙𝑙 �𝑐𝑐𝑜𝑜𝑐𝑐𝑇𝑇

�𝑡𝑡� � = 𝑘𝑘𝑒𝑒𝑒𝑒𝑒𝑒

[TiCl4] data as co; ci = ci(t)

DKM West &al., 2008

DKM with TiO2(s)deposition rate

DKM gasreactions withoutTiO2(s)deposition

Experiments(Pratsinis & al. 1990)

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CFE Koukkari & Paiva 2017

CFE RESULTS WITH TiO2(s) FORMATION

(all residence times)

CFE _ DKM comparison

(all residence times)

TiO2(s) entered, 3 lines coinciding

TiO2(s) dormant

Experiments only followed TiCl4 concentrations in gas phase

⇒ TiO2(s) ’entered’ seems to be the necessary & sufficient condition for agreement withobservation

Use in reactor engineering & scale-up

PresenterPresentation NotesInterleaf option 1: Use interleaf if you want to separate sections in your presentationYou can use interleaf with one or two photos or without photos

Superheated O2

TiCl4 -gasCooling water

Cone

Flame reactor scale-up with the rate-constrained model

Reactor & Cooling sections

TiO2 is formed as a nanoparticle suspension – used as the white pigment (> 3 Mt/yr) exothermic main reaction compensated by endothermic side reactions

(chlorine dissociation, TixOyClz formation) and efficient reactor cooling

Reactor chemistry ∆H(1000 C)kJ/mol

TiCl4(g) + O2(g) ↔ TiO2 ↓ + 2Cl2(g) -175Cl2(g) ↔ 2Cl(g) +250

Objective: Perform reactor scale-up with good coupling ofthermochemistry and reaction kinetics and validate the model

Build-up of the industrial TiCl4-oxidiser model

Gibbs energy (’HSC’) data available for all species

Cooling media flow G = G (T, P,ni)

T=T(x), P=P(x)

v=v(x)x

Q=Q(x) ξr

TiCl4(g), T1

O2(g), T2

TQ

Sand(to removedeposits from reactor walls)

( )

oi

o

w

o

ii

o

gao

hddd

dhd

TThdQ

1ln2

+⋅

+⋅

−⋅⋅⋅=

λ

πTiCl4(g) + O2(g) → TiO2 ↓ + Cl2(g) (I)

Cl2(g) ↔ 2Cl(g) (II)

Reaction ∆HkJ.mol-1

∆GkJ.mol-1

Reaction rate equation * EakJ.mol-1

As-1

A’(dm3.mol-1)½.s-1

(I) -175.4 -104.1 [ ] [ ]( )[ ]424 TiClO'dTiCld kk

t+−= ~ 71 8.26⋅104 1.4⋅105

(II) 250.3 98.2 assumed equilibrium - - -

*TiCl4 consumption rate measured by Pratsinis & al., 1990

Choice of independent measurables for model validation:

VALIDATION OF NON-ISOTHERMAL SCALE-UP CALCULATIONS

direct temperature measurement(2 plug flow reactors)

00.10.20.30.40.50.60.70.80.9

1

CONE RT1 RT2 CT1 CT2-3 CT4-5 CT6-7 CT8

Q /

Qm

ax

Model Meas. heat transfer measurement from

the tubular reactor

Koukkari P., Penttilä K. and Keegel, M.: Coupled Thermodynamic and Kinetic Models for High-Temperature Processes, 10th International IUPAC Conference on High Temperature Materials Chemistry, Part I , Forscungszentrum Julich, 2000, 253-256.

CFE scale-up performed for 2 industrial pigment producers(US & NL)

plant historical trends fordirect & indirect checks

1 Feed inlet pressure2 Sand separator pressure3 Reactor tube heat rmvd4 Cooling tube heat rmvd

1

23

4

Immaterial constraints can be introduced to Gibbs energy minimization to allow the calculation of kinetically controlled systems

reaction matrix serves as basis for new constraints for reaction extents

stoichiometric matrix includes all reactions

⇒ CFE provides a viable and robust alternative for mechanistic kinetic studies in complex multi-component – multi-phase systems; has also small number of kinetic parameters

Assuming local chemical equilibrium (LCE) with TiO2(s) formation agrees with plug flow experiments – encourages more research on CFE/LCE method of multiphase systems

CONCLUSIONS

PresenterPresentation NotesEnter speaker notes here.

Published applications of the G(ξ) [Ratemix*] method

Methanation Extent of methanation reactions TiO2 production Oxidation of TiCl4 in furnace Combustion In-line PCC production

Post-flame NOX generation Precipitation of CaCO3

Clinker formation in cement kilns Phase equilibria during steel solidification

Formation of C2,3S-phases & free lime (cement making) Paraequilibrium phase diagrams

*Ratemix is a trademark of VTT

Methanation

Extent of methanation reactions

TiO2 production

Oxidation of TiCl4 in furnace

Combustion

In-line PCC production

Post-flame NOX generation

Precipitation of CaCO3

Clinker formation in cement kilns

Phase equilibria during steel solidification

Formation of C2,3S-phases & free lime (cement making)

Paraequilibrium phase diagrams

Methanation

Exten

t

of methanation reactions

TiO

2

production

Oxidation of TiCl

4

in furnace

Combustion

In

-

line PCC production

Post

-

flame NO

X

generation

Precipitation of CaCO

3

Clinker formation in cement kilns

Phase equilibria during steel

solidification

Formation of C

2,3

S

-

phases & free lime

(cement making)

Paraequilibrium phase diagrams

Methanation Extent of methanation reactions

TiO

2

production Oxidation of TiCl

4

in furnace

Combustion

In-line PCC production

Post-flame NO

X

generation

Precipitation of CaCO

3

Clinker formation in cement kilns

Phase equilibria during steel

solidification

Formation of C

2,3

S-phases & free lime (cement making)

Paraequilibrium phase diagrams

Thank you for your attention !

PresenterPresentation NotesInterleaf option 1: Use interleaf if you want to separate sections in your presentationYou can use interleaf with one or two photos or without photos

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