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Reacting Solids
I- Overview
Prof. P. Canu
University of Padova - Italy
University of Liège - Laboratoire de Génie chimique
September 2011
Occurrence
L.D. Schmidt, The engineering of chemical reactions
More often than expected → need for a unique approach
P. Canu – Reacting Solids
Liège, Sept. 2011
Reactions
Tentative classification
Wen, IEC, 1968
to be updated with subsequent process (MEMS,..)
P. Canu – Reacting Solids
Liège, Sept. 2011
Reactions
A) 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.
P. Canu – Reacting Solids
Liège, Sept. 2011
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
P. Canu – Reacting Solids
Liège, Sept. 2011
Reactions
B) Solid → Fluid and Solids
P. Canu – Reacting Solids
Liège, Sept. 2011
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
P. Canu – Reacting Solids
Liège, Sept. 2011
Reactions
C) Fluid and Solid → Fluids
P. Canu – Reacting Solids
Liège, Sept. 2011
Reactions
C) Fluid and Solid → Fluids
P. Canu – Reacting Solids
Liège, Sept. 2011
Reactions
D) 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
P. Canu – Reacting Solids
Liège, Sept. 2011
Reactions
E) Fluid and Solid → Fluid and Solid
Quite general:
• Calcination of sulfides to make oxides
• reductions of metal oxides
• steam-iron process to produce hydrogen
P. Canu – Reacting Solids
Liège, Sept. 2011
Reactions
E) Fluid and Solid → Fluid and Solid
P. Canu – Reacting Solids
Liège, Sept. 2011
Reactions
F) Fluids → Solids
• CVD
• Crystallization
P. Canu – Reacting Solids
Liège, Sept. 2011
Reactions
in general
a F1 + b S1 → d F2 + e S2
Each species can be present or not
Stoichiometry is relevant (also for volumetric effects)
P. Canu – Reacting Solids
Liège, Sept. 2011
Kinetics
Mechanism 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 surface
s = adsorbed
b = in the bulk of the solid
P. Canu – Reacting Solids
Liège, Sept. 2011
Mass (& heat) transfer
additional processes, before and after reaction
(heterogeneous + homogeneous reactions)
P. Canu – Reacting Solids
Liège, Sept. 2011
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)
P. Canu – Reacting Solids
Liège, Sept. 2011
Kinetics
Simplified 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 surface
P. Canu – Reacting Solids
Liège, Sept. 2011
Kinetics
Simplified view – lev. 1
A(g/l) + b B (s) → ….
1.
one global reaction
2.
irreversible
3.
adsorption equilibrium (Hinshelwood type, single specie ads.)
CA
R” = superficial reaction rate ≈ k ' ' '
1  K AC A
Not pseudo-1st order anymore!
P. Canu – Reacting Solids
Liège, Sept. 2011
Kinetics
Detailed approach - adsorption mechanisms
AsH3(g) + Ga(s) → AsH3(s) + Ga(b)
Atomic Site
the reaction conserves sites
P. Canu – Reacting Solids
AsH3(g) + O(s) → AsH3(s)
Open Site
reaction conserves sites and elements
Liège, Sept. 2011
Kinetics
Detailed approach - surface-reaction mechanisms
It can be complex, if detailed
P. Canu – Reacting Solids
Liège, Sept. 2011
Solids geometry
Classification
1.
Irregular (grit, crystals, flocs, …)
2.
Films/slabs
3.
Particles
4.
Cylinders, pillars, extrudates,..
Approximation to the simplest, more regular shape
P. Canu – Reacting Solids
Liège, Sept. 2011
Solids geometry
Particles?
1.
Shape
2.
Size
Size and/or Shape distributions
(→ need for Population Balance Equations)
P. Canu – Reacting Solids
Liège, Sept. 2011
Solids geometry
Evolution 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 geometry
Internal structure (porosity) – spherical particles
S1 (black) transforms in S2 (colorless)
•
•
P. Canu – Reacting Solids
sharp reaction front?
r1 and r2 are equal?
Liège, Sept. 2011
Solids geometry
Internal structure (porosity)
Reaction takes place within the porous solid
P. Canu – Reacting Solids
Liège, Sept. 2011
Solids geometry
Internal structure (porosity) - film
S1 (black) transforms in S2 (colorless)
Reaction front? Changes in volume?
P. Canu – Reacting Solids
Liège, Sept. 2011
Solids porosity
impervious
easy
P. Canu – Reacting Solids
←
actual solids (porous)
difficult
→
perfectly permeable
easy
Liège, Sept. 2011
Microstructure
Grain model
Solids are composites
(with internal grains)
Concentrations vary within each grain and across the grains composite
→ particle model
P. Canu – Reacting Solids
Liège, Sept. 2011
Reactors
Contacting mode
For each phase:
1.
2.
P. Canu – Reacting Solids
mixing/segregation?
in-/outflow?
Liège, Sept. 2011
Reactors
Industrial
P. Canu – Reacting Solids
Liège, Sept. 2011
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
P. Canu – Reacting Solids
Liège, Sept. 2011
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).
P. Canu – Reacting Solids
Liège, Sept. 2011
Reacting Solids
II – quantitative analysis
Prof. P. Canu
University of Padova - Italy
University of Liège - Laboratoire de Génie chimique
September 2011
Non-Porous solids
Developed on ‘paper’
P. Canu – Reacting Solids
Liège, Sept. 2011
Reacting Solids
III – application of SCM
Prof. P. Canu
University of Padova - Italy
University of Liège - Laboratoire de Génie chimique
September 2011
The application
chemistry
Direct reduction
3 heterogeneous reactions like
a F 1 + b S 1 → d F 2 + e S2
F1= H2 and/or CO
P. Canu – Reacting Solids
F2= H2O and/or CO2
Liège, Sept. 2011
The application
chemistry
Homogeneous reactions can occur
H2O + CO = CO2 + H2
WGS
CH4 + H2O = CO + 3H2
SR/Methanation
CH4 = Cs + 2H2
P. Canu – Reacting Solids
Cracking
Liège, Sept. 2011
The application
pellet model
4 domains, 3 interfaces → SCM
(frequently reduced to 3 of even 2 domains )
P. Canu – Reacting Solids
Liège, Sept. 2011
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
•
P. Canu – Reacting Solids
At any time the state of the pellet
is summarized by the interface coordinates
Liège, Sept. 2011
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
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Test apparatus
A basket suspended on loading cells
(reaction looses weight significantly)
Approx dimensions D = 6 cm, L = 10 cm
pellet diameter: dp = 13 mm (=0.42)
rs = 3.4 t/m3sol
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Test apparatus
porous bed at rest (Brinkman-type momentum equations)
u = surface (or apparent) velocity
 = bed porosity
Q = (gas) mass production (H2 → H2O CO → CO2)
k = permeability (from Ergun eq. - viscous and inertial terms)
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Test apparatus
Maxwell-Stefan & T diffusion in (conservative) MBi
(i=H2, CO, H2O, CO2, CH4, N2)


wi
p 
u
T T
r
   r wi k Dik  xk  xk  wk    D
 r wi    ri
t
p 
T



H 2


6.5

8.1
4
2
Dik  10 m s  
5.8

 6.3
6.6




P. Canu – Reacting Solids
CO


2.3
1.5
2.0
1.8
H 2O CO2






1.9

2.5 1.7
2.4 1.5
CH 4





2.0
N2







H 2 
CO 

H 2O 
CO2 

CH 4 
N2 


DT [x 107 m2/s] =
= [-37.2 28.1 0.4 7.8 0.8]
@ T =100K and w=w°
Liège, Sept. 2011
The application
Test apparatus
Initial contitions (t=0):
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°
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
test apparatus:
Weight loss
t (min)
80
0
0
-100
50
100
DP_exp
Weight loss (g)
-150
-200
-250
-300
-350
-400
-450
-500
70
150
DP_calc
Metallizzation %
-50
60
50
40
30
20
10
0
0
100
200
300
400
500
|WL(g)|
Some tuning of the kinetics is required
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
test apparatus:
Temperature along the bed
Only qualitative agreement (but TIN was varying)
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
test apparatus: gas phase composition
100%
Percentuale volumetrica (molare)
90%
80%
H2
70%
H2
60%
CO
50%
H2O
40%
H2_CFD
30%
CO_CFD
CO
20%
H2O_CFD
10%
H2O
0%
0
50
100
150
200
t (min)
Beginning: H2
CO
P. Canu – Reacting Solids
reactivity largely under predicted (see also H2O)
reactivity quite under predicted (see also CO2)
Liège, Sept. 2011
The application
test apparatus: gas phase composition
14%
Percentuale volumetrica (molare)
12%
CO2
10%
N2
8%
CH4
N2
CO2
6%
N2_CFD
CH4_CFD
4%
CO2_CFD
2%
CH4
0%
0
50
100
150
200
• CO2 instantaneous production well described; long term reactivity overestimated
• no CH4 prediction (lack of methanation reaction )
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
test apparatus
Convenient set-up
for tuning kinetics
P. Canu – Reacting Solids
Liège, Sept. 2011
SOLIDS
The application
shaft (industrial)
Two critical issues:
1. Solids flow
2. Solids reactivity
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Solids flow
How does a dense bed of particles move?
Quite scarce theories/models!
Our pseudo-thermal (Tg) model
P. Canu – Reacting Solids
1.
solids in a drum
2.
flow down the shaft
Liège, Sept. 2011
The application
Solids flow
Steady-state solids flow
and porosity in the shaft
(Artoni, Santomaso, Canu, PRE &CES)
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Gas configuration -1
SOLIDS
REDUCING GAS
SOLIDS
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Gas velocity in the bed
EXP
• Compares well with experimental average in the upper part
• Stagnation in the bottom
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Gas composition (mass. frac.)
H2
CO
0 - 0.128
P. Canu – Reacting Solids
0 - 0.494
CH4
0 - 0.108
H2O
0.019 - 0.570
CO2
0.212 - 0.445
Liège, Sept. 2011
The application
Gas composition
Species
x_calc (%)
x_exp (%)
H2
51
48
CO
14
15
H2O
19
CO2
9
CH4
5
N2
2
Compares well with expected results
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Solids composition (kmol/m3sol)
Hem
Wus
0 - 33
P. Canu – Reacting Solids
18
0 - 44
Fe
0 - 50
C(s)
0-4
metallization
0 – 75 %
Liège, Sept. 2011
The application
Temperature (K)
700
300
On the axis:
model lacks cooling in the bottom
TS exp
1250
Tgas
Tsolid
TS calc
1200
1150
T solid (K)
1100
1050
1000
950
900
850
800
0
10
20
Heigth (m)
30
40
300 - 1350
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Gas configuration – 2
SOLIDS
REDUCING GAS
Cooling gas from bottom
COOLING GAS
P. Canu – Reacting Solids
SOLIDS
Liège, Sept. 2011
The application
Gas velocity in the bed
Non more stagnation in the bottom
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Gas composition (mass. frac.)
H2
CO
CH4
H2O
CO2
00.127
00.487
00.585
00.662
00.327
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Gas composition
Specie
x_calc (%)
x_exp (%)
H2
50
48
CO
14
15
H2O
19
CO2
9
CH4
5
N2
3
Similarly to case 1, compares well with expected results
P. Canu – Reacting Solids
Liège, Sept. 2011
The application
Solids composition (kmol/m3sol)
Hem
0 - 33
P. Canu – Reacting Solids
Wus
12
0 - 44
Fe
0 - 56
C(s)
0-7
metallization
0 – 84 %
Liège, Sept. 2011
The application
300
740
Temperature (K)
Tgas
On the axis:
Tsolid
evident cooling in the bottom
1250
TS exp
1200
TS calc
1150
T solid (K)
1100
1050
1000
950
900
850
800
0
10
20
Height (m)
30
40
310
P. Canu – Reacting Solids
300 - 1350
770
Liège, Sept. 2011
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
P. Canu – Reacting Solids
Liège, Sept. 2011
Reacting Solids
IV –reacting porous solids
Prof. P. Canu
University of Padova - Italy
University of Liège - Laboratoire de Génie chimique
September 2011
The physical picture
solid conversion
Issues
• Reaction across the solid
• Diffused interface
• Variable volume
P. Canu – Reacting Solids
Liège, Sept. 2011
The physical picture
Approches
→ Volumetric reaction models
P. Canu – Reacting Solids
Liège, Sept. 2011
The diffused reaction
Model eqs.
Gas (c)
PSSA and equimolarity
(or large volum. flow rate) reduce it to
Solid (c’)
u accounts for shrinking/enlargment
P. Canu – Reacting Solids
Liège, Sept. 2011
The diffused reaction
Model eqs.
Effective diffusivities
Di,eff = f(Di , )
Local variation of porosity
ai = aio xibi
ai = surface of i-solid/volume
bi = sintering exponent
Some information from BET measurements
P. Canu – Reacting Solids
Liège, Sept. 2011
The diffused reaction
Model solution
Coupled PDEs
Unknown functions:
•
•
•
•
c(t,r)
c’(t,r)
MOL (discretize on r, integrate on t)
(othogonal) collocations
Finite differences
…
P. Canu – Reacting Solids
Liège, Sept. 2011
The diffused reaction
Model solution
Discretization in space (100 grid points) - Integration in time
Profiles(t) at literature parameters
P. Canu – Reacting Solids
Liège, Sept. 2011
The diffused reaction
Model solution
Average mass fraction in pellet
1
Fe2O3
Fe3O4
0.9
FeO
Fe
0.8
0.7
X
0.6
0.5
0.4
0.3
0.2
0.1
0
0
500
1000
1500
2000
2500
3000
3500
t (s)
P. Canu – Reacting Solids
Liège, Sept. 2011
The diffused reaction
Model solution
0.015
0.03
c
(mol/cm3)
0.01
Magn
0.02
0.015
c
Hemat
(mol/cm3)
0.025
0.005
0.01
0.005
0
0
0.1
0
0
0.2
500
0.3
1000
1500
0.4
2000
0
0
0.5
2500
3000
0.2
500
1000
0.6
3500
t (s)
Hematite
0.4
1500
2000
2500
0.6
3000
r (cm)
→
3500
4000
0.8
r (cm)
t (s)
Magnetite
Fast transients in time; never sharp in space
SCM?
P. Canu – Reacting Solids
Liège, Sept. 2011
The diffused reaction
c
0.05
0.05
0.04
0.04
0.03
(mol/cm3)
0.06
Fe
0.03
0.02
c
Wus
(mol/cm3)
Model solution
0
0.01
0.2
0.01
0
0.4
-0.01
0
0
0.1
0.2
-0.01
0
0
0.02
0.3
500
0.4
1000
1500
500
1000
1500
0.6
2000
2500
3000
0.5
2000
2500
0.6
3000
3500
3500
4000
0.8
r (cm)
4000
0.7
r (cm)
t (s)
t (s)
Wustite
→
Iron
Slow kinetics; even smoother in space
SCM?
P. Canu – Reacting Solids
Liège, Sept. 2011
The diffused reaction
Model solution
0.7
1
0.6
0.9
0.8
0.5
0.7
0.4
Magn
X
0.5
X
Hemat
0.6
0.3
0.4
0.2
0.3
0.2
0.1
0.1
0
0
0
0.1
0.2
0.3
0.4
r (cm)
Hematite
0.5
0.6
0.7
→
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
r (cm)
Magnetite
Distributed reaction
SCM?
P. Canu – Reacting Solids
Liège, Sept. 2011
The diffused reaction
Model solution
0.7
0.9
0.8
0.6
0.7
0.5
0.6
0.4
Iron
X
0.4
X
Wust
0.5
0.3
0.3
0.2
0.2
0.1
0.1
0
0
-0.1
-0.1
0
0.1
0.4
0.3
0.2
r (cm)
Wustite
0.5
0.6
0.7
0
→
0.1
0.2
0.3
0.4
0.5
0.6
0.7
r (cm)
Iron
even smoother in space
SCM?
P. Canu – Reacting Solids
Liège, Sept. 2011
The diffused reaction
Model solution
Step-like profiles require much larger
reaction/diffusion rates
P. Canu – Reacting Solids
Liège, Sept. 2011
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
P. Canu – Reacting Solids
Liège, Sept. 2011
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).
P. Canu – Reacting Solids
Liège, Sept. 2011