University of Padova - Italy - Åbo...

P. Canu – Reacting Solids CACRE, Åbo Akademi, 2014

Reacting Solids – Applications

Prof. Paolo Canu University of Padova - Italy

Computer-Aided Chemical Reaction Engineering Course

Graduate School in Chemical Engineering (GSCE) Åbo Akademi - POKE Researchers network

May 2014


Contents

3. Applications

a) Non-porous solids

• TiO2 from TiCl4 b) Porous solids

• Direct reduction of Fe2O3 to Fe through SCM • Basket reactor • Shaft model

• Chemical Looping Combustion through SCM/CM


DRI Chemistry

Direct reduction

3 heterogeneous reactions of type

a F1 + b S1 → d F2 + e S2

F1= H2 and/or CO F2= H2O and/or CO2


DRI heterogeneous chemistry simplified (2 steps)

R1: Fe2O3 + H2 → 2FeO + H2O ΔHR = 46.6 kJ/mol

R2: FeO + H2 ↔ Fe + H2O ΔHR = 25.5 kJ/mol

R1: Fe2O3 + CO → 2FeO + CO2 ΔHR = 5.49 kJ/mol

R2: FeO + CO ↔ Fe + CO2 ΔHR = −15.7 kJ/mol

Note that wustite-iron is reversible


DRI chemistry - homogeneous reactions

Steam Reforming/ Methanation CH4 + H2O CO + 3H2 ΔHR,298 = 206.9 kJ/mol Water Gas Shift CO + H2O CO2 + H2 ΔHR,298 = −41.16 kJ/mol Methane Cracking CH4 → CS + 2H2 ΔHR,298 = 75.5 kJ/mol Coke Gasification CS + H2O → CO + H2 ΔHR,298 = 131.4 kJ/mol


DRI pellet model 1 - SCM

4 domains, 3 interfaces (frequently reduced to 3 of even 2 domains )


DRI pellet model 1

Assumptions (critical) in SCM approach

• Hematite is impervious

• Same diffusion rate in each solid phase, constant in time

• Constant porosity in each layer

• Reactive interfacees within porous shells

Advantages of SCM • At any time the state of the pellet

is summarized by the interface coordinates


DRI Reactor model

A. Gas is always flowing through a packed bed of solids

B. Solids can be:

• At rest (batch) → Test apparatus

• ‘Flowing’ → Shaft


DRI Test apparatus

A basket suspended on load cells (reaction looses weight significantly)

Approx dimensions D = 6 cm, L = 10 cm dp = 13 mm, ε=0.42, ρs = 3.4 t/m3

sol


DRI Gas momentum eq. porous bed at rest (Brinkman-type momentum equations)

u = surface (or apparent) velocity ε = bed porosity Q = (gas) mass production (H2 → H2O CO → CO2) k = permeability (from Ergun eq. - viscous and inertial terms)


DRI Gas species material balances

Maxwell-Stefan & T diffusion in (conservative) MBi

I = H2, CO, H2O, CO2, CH4, N2

( ) iiT

k kkkikii rw

TTD

ppwxxDw

tw

=

⋅+

∇−

∇−+∇−∇+

∂∂ ∑ ε

ρρρ u


DRI Maxwell-Stefan & T diffusion

DT [x 107 m2/s] = [-37.2 28.1 0.4 7.8 0.8] @ T =1000K and w=w°

[ ]

−−−−−−−−−−−−−−−−−−−−−

=× +

2

4

2

2

2

24222

24

0.25.14.28.16.67.15.20.23.6

9.15.18.53.21.8

5.6

10

NCHCO

OHCOH

NCHCOOHCOH

smikD


DRI BCs and ICs in test apparatus Solids

T=800°C c°= pure, dry, Hematite

Gas inside T=800°C

x°= H2 CO H2O CO2 CH4 N2 = [70 20 2 0.6 0 7]%

Gas IN

T=825°C+f(t) x°, v°


DRI Weight loss

Literature kinetics, adapted

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

00 50 100 150

Wei

ght l

oss (

g)

t (min)

DP_exp

DP_calc

0

10

20

30

40

50

60

70

80

0 100 200 300 400 500

Met

alliz

zatio

n %

|WL(g)|


DRI Temperature along the bed

Only qualitative agreement

(but TIN was varying)


DRI test apparatus: gas phase composition

Beginning: H2 reactivity largely underpredicted (see also H2O)

CO reactivity quite under predicted (see also CO2)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 50 100 150 200

Perc

entu

ale

volu

met

rica

(mol

are)

t (min)

H2

CO

H2O

H2_CFD

CO_CFD

H2O_CFD

H2

CO

H2O


DRI test apparatus: gas phase composition

• CO2 initial production well described; long term reactivity overestimated

• no CH4 prediction (need of methanation reaction in the chemistry)

0%

2%

4%

6%

8%

10%

12%

14%

0 50 100 150 200

Perc

entu

ale

volu

met

rica

(mol

are)

N2

CH4

CO2

N2_CFD

CH4_CFD

CO2_CFD

N2

CO2

CH4


DRI test apparatus - conclusion

• Convenient set-up for tuning kinetics more representative than TGAs

• Porous bed is a critical assumption (few particle diameters)

• Higlights significant gas phase reactions

• Temperature distribution critical


DRI Shaft (industrial)

Two critical issues:

1. Solids flow 2. Solids reactivity

SOLIDS


DRI Solids flow

How does a dense bed of particles move? Quite scarce theories/models!

We developed a wide-purpose, pseudo-thermal (Tg) model


Granular flow pseudo-thermal (Tg) model

Some qualitative predictions 1. solids in a drum

2. flow down the shaft


DRI Solids flow in the shaft

Steady-state solids flow and porosity in the shaft


DRI Gas configuration -1

REDUCING GAS

SOLIDS


DRI Gas velocity in the bed

• Compares well with experimental average

in the upper part • Stagnation in the bottom

EXP


DRI Gas composition (mass. frac.)

0 - 0.128 0 - 0.494

H2 CO CH4

0 - 0.108

H2O

0.019 - 0.570

CO2

0.212 - 0.445


DRI Gas composition

Compares well with expected results

Species x_calc (%) x_exp (%)

H2 51 48

CO 14 15

H2O 19

CO2 9

CH4 5

N2 2


DRI Solids composition (kmol/m3

sol)

Hem

0 - 33

Wus

0 - 44 18

Fe

0 - 50

C(s)

0 - 4 0 – 75 %

metallization


DRI Temperature (K)

On the axis:

model lacks cooling in the bottom

Tgas Tsolid

300 - 1350

700 300

800

850

900

950

1000

1050

1100

1150

1200

1250

0 10 20 30 40

T so

lid (K

)

Heigth (m)

TS exp

TS calc


DRI Gas configuration – 2

Cooling gas from bottom

SOLIDS

REDUCING GAS

SOLIDS COOLING GAS


DRI Gas velocity in the bed

No stagnation anymore in the bottom


DRI Gas composition (mass. frac.)

0 - 0.127

0 - 0.487

H2 CO CH4

0 - 0.585

H2O

0 - 0.662

CO2

0- 0.327


DRI Gas composition

Similarly to case 1, compares well with expected results

Specie x_calc (%) x_exp (%)

H2 50 48

CO 14 15

H2O 19

CO2 9

CH4 5

N2 3


DRI Solids composition (kmol/m3

sol)

metallization Hem

0 - 33

Wus

0 - 44 12

Fe

0 - 56

C(s)

0 - 7 0 – 84 %


DRI Temperature (K)

On the axis: evident cooling at the bottom

800

850

900

950

1000

1050

1100

1150

1200

1250

0 10 20 30 40

T so

lid (K

)

Height (m)

TS exp

TS calc

300 - 1350 310 770

300 740

Tgas Tsolid


DRI Conclusions

1. SCM allows simulating complex configurations

2. It allows interfacing with a CFD code (scalars=interface positions, need to be tracked)

3. Though instrinsically approximated/wrong, it can be tuned to experimental data

4. Need for more realistic pellet models


Application 2 Applying CM and comparing to SCM


CLC The concept

Solids carry oxygen to the fuel – combustion without air! Requires metals that reduce/oxydise easily (Fe, Cu, Ni, ..)


CLC Chemistry (F=CO)

2 𝐹𝐹𝐹 +

12

𝐹2 → 𝐹𝐹2𝐹3 (𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑠𝑜𝐹𝑠)

𝐹𝐹2𝐹3 + 𝐶𝐹 → 2 𝐹𝐹𝐹 + 𝐶𝐹2 (𝑟𝐹𝑜𝑟𝑟𝑜𝑜𝑜𝑜 𝑤𝑜𝑜𝑤 𝐶𝐹)

Overall:

𝐶𝐹 + 12

𝐹2 → 𝐹2

Several cycles modify the solids structure


CLC Measurements

• Thermal Gravimetric Analysis (TGA)

• Pseudobrookite (Fe2TiO5) to Ilmenite (FeTiO3)

• H2 or CO as fuel (reducing agent)

• from weight to conversion:

𝑋𝑟𝑟𝑟(𝑜) = 𝑚𝑜𝑜−𝑚(𝑡)𝑚𝑜𝑜−𝑚𝑟𝑟𝑟

𝑚 𝑜 = � 𝑀𝑊𝑗 ∙ � 4𝜋𝑟2𝑟𝑗𝑠 𝑟, 𝑜 𝑜𝑟𝑟0

0

𝑁𝑁

𝑗=1


CLC Measurements

Pseudobrookite (200 µm) reduction by 15% CO, 20% CO2, 65% N2


CLC SCM - One interface

𝐹𝐹2𝐹3 + 𝐶𝐹 → 2 𝐹𝐹𝐹 + 𝐶𝐹2

Effect of T and %CO

Poor quantitative agreement (3 parameters, A, E, DCO) (unless kinetics is adjusted with conditions)

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

T = 873 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

0 1000 2000 3000 40000

0.2

0.4

0.6

0.8

1

T = 973 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

T = 1073 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

0 200 400 600 800 1000 12000

0.2

0.4

0.6

0.8

1

T = 1073 K xCO = 0.3000 xCO2 = 0.2000

t (s)

X

ExpCalc

ExpCalc

ExpCalc

ExpCalc


CLC SCM - Two interfaces

𝐹𝐹2𝐹3 +

13𝐶𝐹 →

23𝐹𝐹3𝐹4 +

13𝐶𝐹2


Effect of T and %CO

Better (6 parameters, A’s, E’s, DCO in both phases) only single reactions rates are adjusted to approximate the bending

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

T = 873 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

ExpCalc

0 1000 2000 3000 40000

0.2

0.4

0.6

0.8

1

T = 973 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

ExpCalc

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

T = 1073 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

ExpCalc 0 200 400 600 800 1000 1200

0

0.2

0.4

0.6

0.8

1

T = 1073 K xCO = 0.3000 xCO2 = 0.2000

t (s)

X

ExpCalc


CLC CM - Grain model


𝑅 = 𝐴 ∙ exp −𝐸𝑜𝑅𝑔𝑇

∙ 𝑟𝐶𝐶𝑔 ∙ 1 − 𝑋 2/3

Effective D is not adjusted (predictive)

Not an improvement (2 parameters, A, E)

Bending can be a restructuring of the solids surface

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

T = 873 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

ExpCalc

0 1000 2000 3000 40000

0.2

0.4

0.6

0.8

1

T = 973 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

ExpCalc

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

T = 1073 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

ExpCalc

0 200 400 600 800 1000 12000

0.2

0.4

0.6

0.8

1

T = 1073 K xCO = 0.3000 xCO2 = 0.2000

t (s)

X

ExpCalc


CLC CM - Grain model with sintering


𝑅 = 𝐴 ∙ exp −𝐸𝑜𝑅𝑔𝑇

∙ 𝑟𝐶𝐶𝑔 ∙ 1 − 𝑋 𝛼

α=sintering parameter

Quite good agreement for all cases (3 parameters, A, E, α) A surface modification mechanism appears crucial

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

T = 873 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

ExpCalc

0 1000 2000 3000 40000

0.2

0.4

0.6

0.8

1

T = 973 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

ExpCalc

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

T = 1073 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

ExpCalc

0 500 10000

0.2

0.4

0.6

0.8

1

T = 1073 K xCO = 0.3000 xCO2 = 0.2000

t (s)

X

ExpCalc


CLC CM - Grain model with sintering (NR=2)

𝐹𝐹2𝐹3 +

13𝐶𝐹 →

23𝐹𝐹3𝐹4 +

13𝐶𝐹2


𝑅1 = 𝐴1 ∙ exp −

𝐸𝑜1𝑅𝑔𝑇

∙ 𝑟𝐶𝐶𝑔 ∙ 1− 𝑋𝐹𝑟2𝐶3 𝛼1

𝑅2 = 𝐴2 ∙ exp −𝐸𝑜2𝑅𝑔𝑇

∙ 𝑟𝐶𝐶𝑔 ∙ 1 − 𝑋𝐹𝑟3𝐶4 𝛼2

Even better agreement for all cases (6 parameters, A’s, E’s, α’s)

0 500 1000 1500 20000

0.5

1

T = 873 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

0 1000 2000 3000 40000

0.5

1

T = 973 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

0 500 1000 1500 20000

0.5

1

T = 1073 K xCO = 0.1500 xCO2 = 0.2000

t (s)

X

0 500 10000

0.5

1

T = 1073 K xCO = 0.3000 xCO2 = 0.2000

t (s)

X

ExpCalc

ExpCalc

ExpCalc

ExpCalc


CLC Models summary

Final values of objective function:

SCM 1 interface, 3 pars: SSE = 6.48

SCM 2 interfaces, 6 pars: SSE = 4.19

Distributed reactions, 4 pars: SSE = 2.12

Distributed reactions, 7 pars: SSE = 1.74

Distributed reaction model is always superior even with fewer parameters


CLC CM studies – diffusion model

– Binary Fick (no effect of inert) – Mixture averaged

– Stefan-Maxwell

+ complex



diffusive flux of CO with 3 diffusion models Not very different (diluted conditions)

0 0.2 0.4 0.6 0.8 1-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0x 10

-5

r/R

J*C

O (mol

/cm

2s)

FickM-AS-M



Particle conversion (rel diff.) with Fick’s law (using DBE as diffusion coefficient) and Stefan-Maxwell model for different values of inert molar fraction

0 0.2 0.4 0.6 0.8 1-40

-35

-30

-25

-20

-15

-10

-5

0

t/t*

e F %

xE = 0.01

xE = 0.25

xE = 0.50

xE = 0.75

xE = 0.99



Particle conversion (rel diff.) Mixture Averaged and Stefan-Maxwell model for different values of inert molar fraction

0 0.2 0.4 0.6 0.8 1-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

t/t*

e MA %

xE = 0.01

xE = 0.25

xE = 0.50

xE = 0.75

xE = 0.99


• Mathematically, a different surface area for solid reactant and product has the same effect as the change of equilibrium.

• a°FeO/a°Fe2O3 should be measured, not fitted

Effect of superficial areas of pure solids


• Molecular effective diffusion

𝐷𝑖𝑗𝐸,𝑚 = 𝒟𝑖𝑗𝜀𝜏

• Knudsen diffusion

𝐷𝑖𝐸,𝐾 = 𝐾 ∙ 𝑇𝑀𝑀𝑖

∙ 𝜀𝜏

• K depends on the pore diameter

Effects of solid structure on diffusion


• Porosity change: based on solid conversion 𝜀 = 1 − 𝜌𝐴

𝜌𝐼

𝜌𝐴 = ∑ 𝑟𝑗 ∙ 𝑀𝑊𝑗𝑁𝑁𝑗=1

𝜌𝐼 = ∑ 𝑦𝑗𝜌𝐼,𝑗

𝑁𝑁𝑗=1

−1

• Pore size: from a measured distribution

– Fraction of solid with different diffusion rates – Population balance equations (PBE)

Solid structure


Use of a pore size distribution (PSD)

• Discretization into classes

0 100 200 300 400 500 600 7000

0.05

0.1

0.15

0.2

0.25

pore diameter (A)

Rel

ativ

e fra

ctio

n

0 100 200 300 400 500 600 7000

1

2

3

4

5

6

7

8x 10

-3

pore diameter (A)

Rel

ativ

e fra

ctio

n


PBE equations

• Nclass equations for Nclass solid reactant classes • Equation for the i-th solid class:

• Equation for the gas:

• Global conversion:


Population balance solved

00.2

0.40.6

0.81

05

1015

20

0

1

2

3

x 10-4

r/r0class

c (m

ol/c

m3 )

00.2

0.40.6

0.81

05

1015

20

0

1

2

3

x 10-4

r/r0class

c (m

ol/c

m3 )

00.2

0.40.6

0.81

05

1015

20

0

1

2

3

x 10-4

r/r0class

c (m

ol/c

m3 )

00.2

0.40.6

0.81

05

1015

20

0

1

2

3

x 10-4

r/r0class

c (m

ol/c

m3 )

00.2

0.40.6

0.81

05

1015

20

0

1

2

3

x 10-4

r/r0class

c (m

ol/c

m3 )

00.2

0.40.6

0.81

05

1015

20

0

1

2

3

x 10-4

r/r0class

c (m

ol/c

m3 )

00.2

0.40.6

0.81

05

1015

20

0

1

2

3

x 10-4

r/r0class

c (m

ol/c

m3 )

00.2

0.40.6

0.81

05

1015

20

0

1

2

3

x 10-4

r/r0class

c (m

ol/c

m3 )


• A fraction of the solid cannot be reached via pores • Gas can still diffuse via the dense solid • Much lower diffusivity than molecular/knudsen • Possible simulations with PBE

Gas diffusion into dense solid


Sensitivity on SS diffusivity

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t (s)

X

ModelExp

1e-9

3e-10 3e-11

3e-12

3e-8

3e-9

3e-6 3e-7

+ Ds (cm2/s)

Properties of the reduction of CuO with CO


• In CLC, initial distribution of solid can be non uniform • Different solid phases reacting at different rates • Effects on conversion profiles

Effect of solid migration


Fe-Ti distributions in activated ilmenite

Core – shell structure

Fe-Ti non uniform distributions

*Adanez et al., Energy and Fuels, 2010


Reduction of ilmenite particle


• First order kinetics not always accurate • Adsorption resistances can be present • Change to a Langmuir kinetic rate

Effect of gas solid adsorption

𝑅 = 𝑘 ∙ 𝑟 ∙ 𝑜𝑟𝑟𝑟𝑟𝑡 ∙ 1 − 𝑋 𝛼

𝑅 = 𝑘 ∙ 𝐾 𝑟 𝑥𝑟𝑟𝑟𝑟𝑟

1+𝐾𝑟 𝑟𝑟𝑟𝑟𝑡1 − 𝑋 𝛼


Kinetics comparison: ilmenite reduction with H2

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

t (s)

X

T = 800 oC xH2 = 0.15 xCO

2 = 0.2

CalcExp

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

t (s)

X

T = 800 oC xH2 = 0.05 xCO

2 = 0.2

CalcExp

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

t (s)

X

T = 800 oC xH2 = 0.15 xCO

2 = 0.2

CalcExp

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

t (s)

X

T = 800 oC xH2 = 0.05 xCO

2 = 0.2

CalcExp

1st order kinetics

Langmuir kinetics


Application to the reactor scale

• Distributed reactions --> any single pellet has a concentration profile • No analytical solution

• Coupling with a 1-D reactor model is not difficult

– Bulk gas equations with production rates given by:

Ni = molar flux of i at the pellet surface Mi = molecular weight of i R = pellet radius np = number of pellets per unit volume


Model results (BVP)

0 0.2 0.4 0.60

1

2

3

4

5

6

7

8

9

10

xi

z (m

)

COCO2

N2

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03z

= 9.

9 m

Fe2O3

Fe3O4FeOFe

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

z =

5.0

m

0 0.2 0.4 0.6 0.8 10

0.02

0.04

z =

0.0

m

r/R

Solid out Gas in

Solid in gas out

Pellet conversion

Gas conversion


Conclusions

1. Diffused Reaction in a solids pellet allows for • Diffused reaction region (instead of sharp interfaces) • Simultaneous diffusion and reaction (instead of sequential) • Local sintering • Size reduction/enlargement • Any reaction rate expression

2. Easily applicable for solids of • a known displacement law • in a constant fluid environment

3. Sintering laws are quite uncertain and difficult to investigate experimentally

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