fluid solid operation content

1. Liuotuksen kinetiikka – sileiden pintojen karheus
Dissolution kinetics – the roughness of even
surfaces
Tapio Salmi and Henrik Grénman
Outotec 10.2.2012

2. Outline
 Background of solid-liquid reactions
 New methodology for solid-liquid kinetic
modeling
 Description of rough particles
 General product layer model
 Particle size distribution
 Conclusions

3. Milestones from ÅA perspective
 Lectures in chemical reaction engineering at ÅA in 70’s: Ready
formulae were presented for ideal surfaces for gas solid
reactions  students did not understand anything
 At undergraduate library: Denbigh-Turner Chemical reactor
theory – the ideal concepts logically explained
 Organic liquid-phase reaction kinetics [ideal non-porous
particles] (Tirronen et al. 1998)
 Cellulose substitution [completely porous particles] (Valtakari et
al. 2003)
 Zink leaching – old theory and experimental observations in
conflict (Heidi Markus (Bernas) et al. 2004)
 General theory of rough particles (Salmi et al. 2010)
 General theory for product layer model (Salmi et al. 2011)
 Particle size distribution (Grénman et al. 2011)

4. Solid-liquid reaction kinetics
• The aim is to develop a mathematical model for the
dissolution kinetics

5. Why modeling is useful?
 Modeling helps in effective process and equipment
design as well as control
 Empirical process development is slow in the long
run
 The optimum is often not achieved through empirical
development, at least in a reasonable time frame

6. What influences the kinetics
A
A + B → AB → C (l)
C
AB
• Reaction rate depends on
– Mass transfer
• External
• Internal (often neglected)
– Intrinsic kinetics (the “real”
chemical rates

7. Practical influence of mass transfer
 External mass transfer resistance can be overcome by
agitation
 It is important to recognize what you actually are
measuring

8. What influences the kinetics
 Reaction rate depends on
 Surface area of solid
 Morphological changes
 Reactive surface sites on solid
 Heterogeneous solids
 Possible phase transformations in solid phase
 Equilibrium considerations
 Complex chemistry in liquid phase

9. Traditional methodology
The conversion is followed by measuring the solid or liquid
phase
0
2
4
6
8
10
12
0 2 4 6 8 10
Tid (min)
Koncentration
(gram/liter)
50°C
80°C
Time
Concentration

10. Sphere Cylinder Slab
Shrinking particle
Shrinking core
Traditional hypothesis in modeling
solid-liquid reactions

11. nr g() f(cS) Type of model
1 -ln(1-) cS/c0S First-order kinetics
2 (1-)-1/2
- 1 (cS/c0S)3/2
Three-halves-order kinetics
3 (1-)-1
(cS/c0S)2
Second-order kinetics
4 1 - (1-)1/2
(cS/c0S)1/2 One-half-order kinetics; two-dimensional
advance of the reaction interface
5 1 - (1-)1/3
(cS/c0S)2/3
Two-thirds-order kinetics; three-
dimensional advance of the reaction
interface
6 1 - (1-)2/3
(cS/c0S)1/3
One-thirds-order kinetics; film diffusion
7 [1 - (1-)1/3
]2
(cS/c0S)2/3
/(1 - (cS/c0S)1/3
) Jander; three-dimensional
8 1 - 2/3 - (1-)2/3
(cS/c0S)1/3
/(1 - (cS/c0S)1/3
)
Crank-Ginstling-Brounshtein, mass transfer
across a nonporous product layer
9 [1/(1-)1/3
– 1]2
(cS/c0S)5/3
/(1 - (cS/c0S)1/3
)
Zhuravlev-Lesokhin-Tempelman, diffusion,
concentration of penetrating species varies
with 
10 [1 - (1-)1/2
]2
(cS/c0S)1/2
/(1 - (cS/c0S)1/2
) Jander; cylindrical diffusion
11 1/(1-)1/3
- 1 (cS/c0S)4/3 Dickinson, Heal, transfer across the
contacting area
12 1-3(1-)2/3
+2(1-) (cS/c0S)1/3
/(1 - (cS/c0S)1/3
)
Shrinking core, product layer (different
form of Crank-Ginstling-Brounshtein)

liquid
particles
solid
c
kA
dt
dc


Traditional kinetic modeling –
screening models from literature
• The kinetics depends on the
surface area (A) of the
particles
• Because of the difficulties
associated with measuring the
surface area on-line, the change is
often expressed with the help of
the conversion
• Experimental test plots are used to
determine the reaction mechanism
3
/
1
)
1
(
1 



kt

12. Surface area of solid phase
Mineral 1
Sphere
Cylinder
Mineral 2
Cracking
Steadily
increasing
porosity
0
5
10
15
20
25
0 20 40 60 80 100
Conversion (%)
Total
surface
area
(m
2
/L)
• The change in the total
surface area of the solid
depends strongly on the
morphology of the particles
• Models based on ideal
geometries can be inadequate
for modeling non-ideal cases
• The particle morphology can
be implemented into the
model with the help of a
shape factor

13. 0
R
V
A
a
P
P

Reaction rate:
Shape
factor:
Reaction rate:
• The morphology can be flexibly implemented with the help of a
shape factor (a)
New methodology for general
shapes
Geometry Shape factor
(a)
x=
1/a
1-x
Slab 1 1 0
Cylinder 2 ½ 1/2
Sphere 3 1/3 2/3
Rough,
porous
p
a
r
t
i
c
l
e
high value 0 1

liquid
particles
solid
c
kA
dt
dc



liquid
x
particles
solid
c
kc
dt
dc 

 1

14.  Detailed considerations give a
relation
between area (A),
specific surface area (σ),
amount of solid (n),
initial amount of solid(n0),
and molar mass (M);
a=shape factor
a
a
n
Mn
A /
1
1
/
1
0

 
Geometry Shape factor
(a)
x=
1/a
1-x
Slab 1 1 0
Cylinder 2 ½ 1/2
Sphere 3 1/3 2/3
Rough,
porous particle
high value 0 1
Often kinetics is
closer to first order!
The roughness is
always there, σ=1
m2/g is not a
perfect sphere!

15. New methodology
 The solid-liquid reaction mechanism should be
considered from chemical principles, exactly like in
organic chemistry!
)
(
1
liquid
x
particle
prod
c
f
kc
dt
dc 

Solid
contribution
Liquid
contributio
n

16. The dissolution of zink with ferric iron
ZnS(s) + Fe3+ ↔ I1 (I)
I1+ Fe3+ ↔ I2 (II)
I2 ↔ S(s) + 2 Fe2+ + Zn2+ (III)
________________________________________________
ZnS(s) + 2Fe3+ ↔ S(s) + 2 Fe2+ + Zn2+
The mechanism gave the following rate expression
D
K
c
c
c
k
r ZnII
FeII
FeIII )
/
(
2
2



17. The dissolution of zink with ferric iron
0
0.05
0.1
0.15
0.2
0 25 50 75 100 125 150
Time (min)
Fe
3+
(mol/L)
75°C
85°C
95°C
The reaction order is not 2/3 but clearly higher!
Wrong reaction order in the kinetic model is the worst mistake!

18. General product layer model

19. General product layer model in a nutshell
0
)
)
1
(
( 2
2



dr
dc
r
a
dr
c
d
D i
i
ei
*)
(
1
Li
b
Li
Li
a
ei
i c
c
k
CR
D
N 



 
)
/
)(
)
/
)(
/
)
2
(
1
(
1
(
)
(
)
2
(
2
R
r
R
r
Bi
a
R
c
c
D
a
N a
Mi
s
Li
b
Li
ei
i 







)
(
1
s
Li
k
ik
S
k
i c
R
A
N 



0
)
(
)
/
)(
)
/
)(
/
)
2
(
1
(
1
(
)
(
)
2
(
1
2










s
Li
k
ik
S
k
a
Mi
s
Li
b
Li
ei
c
R
R
r
R
r
Bi
a
R
c
c
D
a

A
R
dt
dn
k
ik
S
k
i




1
r
c
c
x
M
dt
dc x
j
x
j
j
j
j 

1
0
0


r
c
c
x
M
dt
dc x
j
x
j
j
i
i 

1
0
0


)
( LiS
c
f
r 

20. Comparison of shrinking particle
and product layer model

21. Effect of shape factor

22. Particle size distribution
VC = standard deviation / mean particle
size
• If the particle size distribution deviates significantly from the Gaussian
distribution, erroneous conclusions can be drawn about the reaction
mechanism
VC=0
VC=1.
2
VC=1.
5
VC=0
Shrinking sphere

23. Implementing the particle size
distribution into modeling
Total surface area in reactor
0
1
2
3
4
5
0 20 40 60 80 100
% dissolved
m²
/
100
ml
6 M
4 M
2 M
• Gibbsite is rough/porous and cracks during dissolution
• The surface area goes through a maximum, non-ideal
behavior

24. Implementing the particle size
distribution into modeling

SP
k
x
E 
)
(
2
)
( 
SP
k
x
Var 
)
(
)
( 1
SP
k
x
k
k
e
x
x
f SP







 



0
1
)
( dt
e
t
k t
k
SP
SP
• The Gamma distribution is fitted to the fresh particle size distribution
and
the distribution is divided into fractions
• The shape parameter (k) and the scale parameter (θ) are kept
constant

25. Implementing the particle size
distribution into modeling
0 20 40 60 80 100 120 140 160 180
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Diameter (μm)
Frequency
(counts/min)
time
a
i
t
i X
r
r 0
,
, 
tP
i
tP
r
tP
r
r
aV
A i
i
,
,
, 
0
R
V
A
a
P
P

• A new radius is calculated for each fraction and each fraction is
summed to
obtain the new surface area in the reactor
• The new surface area is implemented into to rate equation





 1
0
0
0
X
V
V
m
m
c
c t
t
t

26. The fit of the model and
sensitivity analysis
2 3 4 5 6 7 8 9 10 11 12
0
1000
2000
3000
4000
5000
6000
7000
8000
shape factor
Obj.
function
0.8 0.9 1 1.1 1.2 1.3
x 105
300
400
500
600
700
800
900
1000
1100
Obj.
function
0 0.1 0.2 0.3 0.4 0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10 4
k0 (1/(min m2))
Obj.
function
Ea (J/mol)
0 5 10 15 20 25 30 35
0
20
40
60
80
Time (min)
Concentration
(g/L)
0 10 20 30 40
0
20
40
60
80
Time (min)
Concentration
(g/L)

27. Selection of the experimental system and equipment
Kinetic investigations Structural investigations
Mass- and heat transfer studies
Ideas on the reaction mechanism including structural changes of the solid
Derivations (and simplification) of rate equations
Model verification by numerical simulations and additional experiments
Estimation of kinetic and mass transfer parameters

28. Conclusions
 Modeling is an important tool in developing new
processes as well as optimizing existing ones
 Solid-liquid reactions are in general more difficult to
model than homogeneous reactions
 Traditional modeling procedures have potholes, which
can severely influence the outcome
 Care should be taken in drawing the right conclusions
about the reaction mechanisms

29. Things to consider in modeling
 Some important factors:
1. Be sure about what you actually are measuring
2. Evaluate if the particle size distribution needs to be taken
into account (VC<0.3)
3. If the morphology is not ideal use a shape factor to
describe the change in surface area (surface area,
density and conversion measurements needed)
4. Use sensitivity analysis to see if your parameter values
are well defined

30. Some relevant publications
 Salmi, Tapio; Grénman, Henrik; Waerna, Johan; Murzin, Dmitry Yu. Revisiting
shrinking particle and product layer models for fluid-solid reactions - From ideal
surfaces to real surfaces.Chemical Engineering and
Processing 2011, 50(10), 1076-1084.
 Salmi, Tapio; Grénman, Henrik; Bernas, Heidi; Wärnå, Johan; Murzin, Dmitry Yu.
Mechanistic Modelling of Kinetics and Mass Transfer for a Solid-liquid System:
Leaching of Zinc with Ferric Iron. Chemical Engineering Science 2010, 65(15),
4460-4471.
 Grénman, Henrik; Salmi, Tapio; Murzin, Dmitry Yu.; Addai-Mensah, Jonas. The
Dissolution Kinetics of Gibbsite in Sodium Hydroxide at Ambient Pressure.
Industrial & Engineering Chemistry Research 2010, 49(6), 2600-2607.
 Grénman, Henrik; Salmi, Tapio; Murzin, Dmitry Yu.; Addai-Mensah, Jonas.
Dissolution of Boehmite in Sodium Hydroxide at Ambient Pressure: Kinetics and
Modelling. Hydrometallurgy 2010, 102(1-4), 22-30.
 Grénman, Henrik; Ingves, Malin; Wärnå, Johan; Corander, Jukka; Murzin, Dmitry
Yu.; Salmi, Tapio. Common potholes in modeling solid-liquid reactions – methods
for avoiding them. Chemical Engineering Science (2011), 66(20), 4459-4467.
 Grénman, Henrik; Salmi, Tapio; Murzin, Dmitry Yu.. Solid-liquid reaction kinetics
– experimental aspects and model development. Rev Chem Eng 27 (2011): 53–
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