reacting solids i- overview prof. p. canu university of padova - italy university of liège -...

Reacting SolidsI- Overview

Prof. P. CanuUniversity of Padova - Italy

University of Liège - Laboratoire de Génie chimiqueSeptember 2011

Occurrence

More often than expected → need for a unique approach

P. Canu – Reacting Solids Liège, Sept. 2011

L.D. Schmidt, The engineering of chemical reactions

ReactionsTentative classification

Wen, IEC, 1968to be updated with subsequent process (MEMS,..)


ReactionsA) Solid → Fluid

• pyrolysis of carbonaceous materials• combustion of double-base propellants• thermal decomposition (explosions) of some organic or inorganic

compound, especially explosives, e.g.

Solid can decompose gradually from the outer surface to its center, giving off fluid products.

At T>>Tdecomp → reaction may occur at the surface as well as inside the solid.


Reactions B) Solid → Fluid and Solids

Typical: pyrolysis and thermal decomposition of organic and inorganic solid materials.

• pyrolysis of carbonaceous materials• calcination of carbonates• dehydration of hydroxides and hydrates• removal of crystalline water from crystalline compounds


ReactionsB) Solid → Fluid and Solids


Reactions C) Fluid and Solid → Fluids

• combustions and gasifications of carbonaceous materials • oxidation of other solid compounds• solids (metals) and ions in aqueous solutions• reaction in ion-exchange resins


Reactions C) Fluid and Solid → Fluids


ReactionsC) Fluid and Solid → Fluids


ReactionsD) Fluid and Solid → Solids

• nitrogenation of calcium carbide to produce cyanamide:

• rusting reaction of metals, e.g.

• chemisorptions of gas or liquid on solid adsorbents


ReactionsE) Fluid and Solid → Fluid and Solid

Quite general:

• Calcination of sulfides to make oxides• reductions of metal oxides• steam-iron process to produce hydrogen


ReactionsE) Fluid and Solid → Fluid and Solid


ReactionsF) Fluids → Solids

• CVD• Crystallization


Reactionsin general

a F1 + b S1 → d F2 + e S2

Each species can be present or not

Stoichiometry is relevant (also for volumetric effects)


KineticsMechanism of local interactions between fluids and solids

SiH4(g) + Si(s) → 2H2(g) + Si(s) + Si(b)

g = in the gas, in front of the surfaces = adsorbedb = in the bulk of the solid


Mass (& heat) transfer

additional processes, before and after reaction(heterogeneous + homogeneous reactions)


Mass transfer

Species:

• in the fluid, far away from the surface (bulk)

• in the fluid, ‘in front’ of the surface

• on the surface (adsorbed)

• in the solid (bulk)


KineticsSimplified view – lev. 0

A(g/l) + b B (s) → ….

1. one global reaction

2. irreversible

3. no adsorption (or Henry type)

R” = superficial reaction rate = k”(T) CB” CA≈ k’’’(T) CA

“ = per unit surface (e.g. 1/cm2)

CA = volumetric concentration in the fluid, in front of the surfaceP. Canu – Reacting Solids Liège, Sept.

2011

KineticsSimplified view – lev. 1

A(g/l) + b B (s) → ….

1. one global reaction

2. irreversible

3. adsorption equilibrium (Hinshelwood type, single specie ads.)

R” = superficial reaction rate ≈

Not pseudo-1st order anymore!

AA

A

CKCk

1'''


KineticsDetailed approach - adsorption mechanisms

AsH3(g) + Ga(s) → AsH3(s) + Ga(b) AsH3(g) + O(s) → AsH3(s)

Atomic Site Open Site the reaction conserves sites reaction conserves sites and

elements


Kinetics Detailed approach - surface-reaction mechanisms

It can be complex, if detailed


Solids geometryClassification

1. Irregular (grit, crystals, flocs, …)

2. Films/slabs

3. Particles

4. Cylinders, pillars, extrudates,..

Approximation to the simplest, more regular shape


Solids geometryParticles?

1. Shape

2. Size

Size and/or Shape distributions(→ need for Population Balance Equations)


Solids geometryEvolution in size

1. Dissolving (→) / growing (←) film l(t)

2. Dissolving (→) / growing (←) particle r(t)

Not all the reacting solids change their size (→ r(t) )P. Canu – Reacting Solids Liège, Sept.

2011

Solids geometryInternal structure (porosity) – spherical particles

S1 (black) transforms in S2 (colorless)

• sharp reaction front?• r1 and r2 are equal?


Solids geometryInternal structure (porosity)

Reaction takes place within the porous solid


Solids geometryInternal structure (porosity) - film

S1 (black) transforms in S2 (colorless)

Reaction front? Changes in volume?


Solids porosity

impervious ← actual solids (porous) → perfectly permeable

easy difficult easy


MicrostructureGrain model

Solids are composites (with internal grains)

Concentrations vary within each grain and across the grains composite

→ particle model


ReactorsContacting mode

For each phase:

1. mixing/segregation?2. in-/outflow?


ReactorsIndustrial


Conclusions

1. Reactive solids are pervasive and growing

2. The field is even broader than expected,

3. A unified approach is sought

4. Porosity (internal structure) the keypoint


References

1. L.D. Schmidt, The Engineering of Chemical Reactions, Oxford Univ. Press, 2° Ed.

2. O. Levenspiel, Chemical Reaction Engineering, 3° Ed, Wiley, 1999

3. J. Szekely, J. W. Evans, and Hong Yong Sohn, Gas-solid reactions Academic Press, 1976.

4. Wen, C. Y., Ind. Eng. Chem., 60 (9), 34 (1968).


Reacting SolidsII – quantitative analysis



Non-Porous solids

Developed on ‘paper’


Reacting SolidsIII – application of SCM



The application chemistry

Direct reduction

3 heterogeneous reactions like

a F1 + b S1 → d F2 + e S2

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


The application chemistry

Homogeneous reactions can occur

H2O + CO = CO2 + H2 WGS

CH4 + H2O = CO + 3H2 SR/Methanation

CH4 = Cs + 2H2 Cracking


The application pellet model

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


The application pellet model

Assumptions (critical) in SCM approach• Hematite is impervious

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

• Constant porosity in each layer

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

is summarized by the interface coordinates

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


The application Reactor model

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

B. Solids can be:• At rest (batch) → test apparatus• ‘Flowing ‘ → Shaft


The application Test apparatus

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

Approx dimensions D = 6 cm, L = 10 cmpellet diameter: dp = 13 mm (=0.42)

rs = 3.4 t/m3sol



porous bed at rest (Brinkman-type momentum equations)

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



Maxwell-Stefan & T diffusion in (conservative) MBi (i=H2, CO, H2O, CO2, CH4, N2)

iiT

k kkkikii rw

TTD

ppwxxDw

tw

rrr u

DT [x 107 m2/s] == [-37.2 28.1 0.4 7.8 0.8]

@ T =100K 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



Initial contitions (t=0):Solids

T=800°Cc°= pure, dry, Hematite

Gas inside T=800°Cx°= H2 CO H2O CO2 CH4 N2

= [70 20 2 0.6 0 7]%

Gas INT=825°C+f(t)x°, v°


The application test apparatus:

Weight loss

Some tuning of the kinetics is required

0 50 100 150

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

DP_exp

DP_calc

t (min)

Wei

ght l

oss (

g)

0 50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

70

80

|WL(g)|

Met

alliz

zatio

n %


The application test apparatus:

Temperature along the bed

Only qualitative agreement (but TIN was varying)


The application test apparatus: gas phase composition

Beginning: H2 reactivity largely under predicted (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


The application test apparatus: gas phase composition

• CO2 instantaneous production well described; long term reactivity overestimated

• no CH4 prediction (lack of methanation reaction )

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


The application test apparatus

Convenient set-up for tuning kinetics


The application shaft (industrial)

Two critical issues:

1. Solids flow2. Solids reactivity

SOLIDS


The application Solids flow

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

Our pseudo-thermal (Tg) model

1. solids in a drum

2. flow down the shaft


The application Solids flow

Steady-state solids flow and porosity in the shaft(Artoni, Santomaso, Canu, PRE &CES)


The application Gas configuration -1

SOLIDS

REDUCING GAS

SOLIDS


The application Gas velocity in the bed

• Compares well with experimental average in the upper part

• Stagnation in the bottom

EXP


The application Gas composition (mass. frac.)

0 - 0.128

0 - 0.494

H2

CO CH4

0 - 0.108

H2O

0.019 - 0.570

CO2

0.212 - 0.445P. Canu – Reacting Solids Liège, Sept.

2011

The application 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


The application Solids composition (kmol/m3

sol)

Hem

0 - 33

Wus

0 - 4418

Fe

0 - 50

C(s)

0 - 4 0 – 75 %

metallization


The application Temperature (K)

On the axis:model lacks cooling in the bottom

Tgas Tsolid

300 - 1350

700

300

0 5 10 15 20 25 30 35 40800

850

900

950

1000

1050

1100

1150

1200

1250 TS exp

TS calc

Heigth (m)

T so

lid (K

)


The application Gas configuration – 2

Cooling gas from bottom

SOLIDS

REDUCING GAS

SOLIDSCOOLING GAS


The application Gas velocity in the bed

Non more stagnation in the bottom


The application Gas composition (mass. frac.)

0 - 0.127

0 - 0.487

H2

CO CH40 - 0.585

H2O0 - 0.662

CO20- 0.327


The application 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


The application Solids composition (kmol/m3

sol)

metallizationHem

0 - 33

Wus

0 - 4412

Fe

0 - 56

C(s)

0 - 7 0 – 84 %


The application Temperature (K)

On the axis:evident cooling in the bottom

0 5 10 15 20 25 30 35 40800

850

900

950

1000

1050

1100

1150

1200

1250 TS expTS calc

Height (m)

T so

lid (K

)

300 - 1350

310

770

300

740


Tgas Tsolid

Conclusions

1. SCM allows simulating complex configuration

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


Reacting SolidsIV –reacting porous solids



The physical picturesolid conversion

Issues• Reaction across the solid• Diffused interface• Variable volume


The physical pictureApproches

→ Volumetric reaction models


The diffused reactionModel eqs.

Gas (c)

PSSA and equimolarity (or large volum. flow rate) reduce it to

Solid (c’)

u accounts for shrinking/enlargment


The diffused reactionModel eqs.

Effective diffusivities Di,eff = f(Di , )

Local variation of porosityai = aio xi

bi

ai = surface of i-solid/volume

bi = sintering exponentSome information from BET measurements


The diffused reactionModel solution

Coupled PDEs

Unknown functions: c(t,r) c’(t,r)

• MOL (discretize on r, integrate on t)• (othogonal) collocations• Finite differences• …



Discretization in space (100 grid points) - Integration in time

Profiles(t) at literature parameters



Average mass fraction in pellet

0 500 1000 1500 2000 2500 3000 35000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t (s)

X

Fe2O3

Fe3O4

FeOFe



Hematite → Magnetite

Fast transients in time; never sharp in space

SCM?

00.1

0.20.3

0.40.5

0.6

0500

10001500

20002500

30003500

0

0.005

0.01

0.015

0.02

0.025

0.03

r (cm)

t (s)

c Hem

at (m

ol/c

m3)

0

0.2

0.4

0.6

0.8

0 5001000 1500 2000

2500 3000 35004000

0

0.005

0.01

0.015

r (cm)

t (s)

c Mag

n (mol

/cm

3)



Wustite → Iron

Slow kinetics; even smoother in space

SCM?

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0500

10001500

20002500

30003500

4000

-0.01

0

0.01

0.02

0.03

0.04

0.05

r (cm)

t (s)

c Fe (m

ol/c

m3)

0

0.2

0.4

0.6

0.8

0 500 1000 1500 2000 2500 3000 3500 4000

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

r (cm)

t (s)

c Wus

(mol

/cm

3)



Hematite → Magnetite

Distributed reaction SCM?

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

r (cm)

X Hem

at

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

r (cm)X M

agn



Wustite → Iron

even smoother in space

SCM?

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

r (cm)

X Wus

t

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

r (cm)X Iro

n



Step-like profiles require much larger reaction/diffusion rates


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


References

1. S.P. Trushenski, K. Li, W.O. Philboork, Metallurgical Transaction , 5, 1149, (1974)

2. Ishida M, and Wen, C. Y., Chem. Eng. Sci., 26, 1031 (1971).

3. O. Levenspiel, Chemical Reaction Engineering, 3° Ed, Wiley, 1999

4. J. Szekely, J. W. Evans, and Hong Yong Sohn, Gas-solid reactions Academic Press, 1976.

5. Wen, C. Y., Ind. Eng. Chem., 60 (9), 34 (1968).


reacting solids i- overview prof. p. canu university of padova - italy university of liège -...

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