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On the effect of liquid mixing rate on primary crystal size during the gas-liquid precipitation of calcium carbonate
chrmicai Engineering Science, Rimed in Gmat Britain.
Vol.
47.
No.
1914,
pp. 3817-3624.
1992.
OaE-2509/92
$5.00+0.00
01992pergulmbLtd
OF LIQUID MIXING RATE ON P!RINARY CRYSTAL SIZE THE GAS-LIQUID PRECIPITATION OF CALAXUBI CARBONATE
ONTHEEFFECT
DURING
LG. Department University College
Jones,
J. Hostommi&
and Zhou Li2
of Chemical and Biochemical Engineering, London, Torrington Place, London WClE
1.
Permanent address: Institute of Inorganic Chemistry, of Sciences, Majakovskeho 24, Prague, CZECBOSLOVAKIA. Permanent address: Institute of 2. Coal Chemistry, Sciences, P.O. Box 165, Taiyuan, Shanxi, P.R. CHINA.
7JE,
Czechoslovak Chinese
UK. Academy
Academy
of
ABSTRACT An analysis based on gas-liquid mass transfer with chemical reaction coupled with equations describing the dynamic population balance model of crystallization and precipitation kinetics is used to predict the effect of liquid mixing rate on the transient mean crystal size of calcium carbonate precipitated in a small flat-interface gas-liquid reaction cell via the gaseous carbonation of lime water. Experimentally, small discrete calcite crystals (
Precipitation; crystal growth;
calcium carbonate; nucleation; mass
carbon dioxide; transfer.
carbonation;
Recently, precipitation involving three steps vfz. gas-liquid mass transfer, chemical reaction and crystallization was analyzed in terms of the coupled equations for the film theory of gas-liquid mass transfer with chemical of crystallization. reaction and the mass and population balances It was predicted that a reduction in the mass transfer resistance would increase the crystal size and this was subsequently mean supported qualitatively in preliminary experiments by measurement of crystal size distributions of precipitated calcium carbonate produced via the gaseous carbonation of lime-water in a reaction cell (Wachi and Jones. 1991a.b). This present study alms to extend the analysis of mass transfer with chemical reaction and precipitation and to compare directly for the first time the predicted dependence of crystal size on gas-liquid mass-transfer rate with the performance of the precipitation cell operated under similar conditions.
3817
3818
A. 0.
Maction
F13
JONESet al.
kinetics
liquid phase reaction is operated batch-wise with contact of a continuously flowing gaseous reactant through a gas-liquid interface of constant surface area. The carbonation reaction of lime water involves gas. llauld and solid phases. The overall reactfon scheme can be described by the
The
following
-ti0&:
COz(gl
9
=
(aql + OH- HCOi
COa(aql
(a)
HCO ;
(b1
+ OH- =
COS2- +
Ca2+ + C03'- =
CaCOs(s)
The rate of reaction r
k
=
Hz0
(cl (d)
(bl is given by (Astarita,
CCOzl[OH-I
(1)
Reaction (c) is reversible and instantaneous, in equilibrium at any time and at every place Crvstallization The number
the participating in the solution.
components
are
kinetics
rate of nucleation
.
C=k
1967):
P
-
‘3 K
and linear crystal growth
rate are given by:
!s
SP
(31
where n and g are the orders of nucleation the solubility product of calcite.
and growth
Film Theory Briefly, mass balances of reactants and product respectively by Wachi and Jones, 1991al:
respectively,
in the liquid
film
and &p
1s
are given
6A/6t
= DA(6aA/8x21
-
kAB
(41
6B/8t
= Ds (S2B/Sx2)
-
2kAB
(51
BC/Bt
= Dc(82C/Bx21
+ kAB
where B’
corresponding
P
G’
-
B’
(6)
mass based rate equations
= vJ,Lo”
G' =
-
f3pN(x,Ll(G/2)L2dL
(a
=
m/6
[@
-
x
of nucleation for sphere1
for sphere)
and growth
are: (71 (81
19731, the only reactants In thil approach (see eg. Juvekar and 5harma. considered in the kinetics scheme are COa (component AI. OH- ion (component Bl ion (component Cl formed by consumed both by reactions (bl and (cl. and &react@n (~1 and consumed by the precipitation reaction ld); the concentration Is assumed to be constant across the diffusion layer. of ca
F13 The
El&t
population
of the precipitated
balance
8N/8t + G(6N/BL)
of liquid mixinglrte011primarycrystal size
particles
3819
is given by:
- DP(a2N/ax2)
(91
In Eq. (91, it is assumed that particles are Brownian diffusion of the crystals within described by the Stokes-Einstein equation:
removed from the the liquid film
liquid which
film may
DP=k,T/C3qL, The
boundary
at x = 0. The
liquid
at x = 8,
(101 conditions
for
t>o:
Eqs.
(41-(61
A = (p/iiIco , I
phase
is in batch
t>O:
and
BB/8x = 0,
operation.
8W8x
= 0.
6N/Bx
-DA(&W3x)
= Y(&uat
+ km)
-DBWB/UxI
= Y(UB/Bt
+ ZkABI
-Dc(8c/6x)
= V(X/at
(121
l!quld phase per unit gas-liquid film, 8. is defined by: (131
L
L=L:
0
L =oD: Initial at
values
t = 0:
(11)
+ G' + B' - kAB1 + G(aN/aL))
Assuming newly nucleated particles have an effective nucleus size for example, can be estimated from the Gibbs-Thomson equation 1991al. then Jones,
t>O, OSxS,
= 0
Therefore,
where Y Is the specific volume of the bulk surface area and the thickness of the liquid d = D/k
(91 are:
2
-DP(BN/i3x) = V
at
by be
N=J/G
LO.
Wachi
which, and (141
n
N=O
(15)
are:
A = 0.
B=B.
c - 0,
N=O
(16)
Solving these equations by a n&erical method. time courses of concentrations the size dlscretized number and C(t,~x). and density of B(t.xI A(t,xl, particles. N(t.x.LiI. are obtained. Molar particle density in the bulk at discretized diameter L1 is calculated as:
P(L/I
= orpL;N(b.Li,t)LI
(171
from which various distribution characteristics may the mass based mean bulk particle size is calculated I-ax
thereby
be evaluated. as follows:
For
example,
L-ax
facilitating
(181
a
simple
comparison
of
model
predictions
with
data.
in what follows the transient mean crystal size predicted in the Thus, solution bulk will be compared with experlmental data under similar operating the effect of liquid agitation rate (which affects the conditions and gas-liquid mass transfer coefficient) will be determined.
3820
F13
JONES et al.
A. G.
Simnlification. If the processes of reaction and crystallization in the diffusion layer adjacent to the liquid-gas interface are slow and can be neglected, the model is reduced to a description of gas absorption through a clear fllm with crystal precipitation only occuring in the bulk: dA/dt
= kL(Ai
- AI/V
- kAB,
dp/dt
= Jn,
dp,/dt
= JGP,_~+
At t=o, initial
dB/dt
= -2kAB,
.7&b
dC/dt
= kAB
-
(G/2)p._p/3 - a&,L;
(J=1,4)
(191
the moments of particle size distribution are equal condition for A, B and C is again given by Eq. (16).
to
zero
and
the
The numerical methods employed to solve the crystal film model were as described previously Wachi and Jones, 1991al. Briefly, both the coordinates of space within the liquid film and particle diameter were discretized int_g 90 The boundary of the maximum particle diameter was 45 xl0 m. equal lengths. The time division used was 0.1 sec. The computer used was the IBM RS/6000, Model 540 in the Bloomsbury Computing Consortium Timesharing System. Thermodynamic and kinetic parameters used in calculations were taken from the literature either directly for the CO2-Ca(OH12-HzO system or from similar CaCOs systems as available, or were estimated, while the gas-liquid mass transfer coefficient was determined as a function of stirring rate by a dimensionless correlation, as in Table 1. Unfortunately, relatively few kinetic data are directly available for gas-liquid precipitation. Rather more are available for liquid-liquid systems, but these are highly variable. It is interesting to note that Koutsoukos and Kontoyannis for example, (19841, report substantially higher calcium carbonate nucleation rates than Packter Kotaki and Tsuge (19901 report differing results for (19681 while liquid-liquid and gas-liquid precipitation of CaCO3. In order to make a quantitative prediction of the effect of gas-liquid mass transfer on crystal however, the kinetic data of Packter (1968) and Reddy and Nancollas size. (19711 were found to be of the more convenient form for the present use.
Table
1.
Parameter
values
used
in calculatione
Parameter k
1.0x10'
.n
k;s
8
mol-"
8.06x10-' -9
DA=DB==DC
2.2x10
H
3.46~10-~
K
lP
k L
0
kL
Source
0.00347
m3n-3s-1,
4.2
Packter,
n~ol-%n~~+~s-~,
2.0
Reddy
m2/s
1968
& Nancollas,
Capunder
& Coloini,
1971 1984
bar m3/mol mo12m-6
Plurnmer & Busenberg,
12.4
m3s-1mol-'
Astarita,
0.01
m
Gibbs-Thomson
Sh = 0.322
Re""Scl"
Hikita
&
1982
1967 estimate
Ishikawa,
1969
F13
Effect of liquid mixingrateon primarycrystal size
3821
BXPEZBIMENTAL The experimental apparatus used was again as described in detail previously (Uachi and Jones, 199lb). The rotation rate of the agitators in both liquid was controlled at the same speed in the range 100 to 400 rpm. and gas Initially, the vessel was partly filled with solution of calcium hydroxide Drug House) filtered through the 0.3~ membrane filter. (Analar grade: British Gaseous nitrogen and carbon dioxide were mixed and saturated with water, and introduced to the upper space of the mixed gas was the vessel. The temperature was maintained at 25 f 0.5OC. The suspension of the solution and precipitated solids were sampled from the bulk by a pipette for subsequent analysis. Particle size distribution was determined by a laser particle sizer (Model 3300: Malvern Instruments Ltdl. RESULTBAND
DISCWSIC?N
In the early stages of the experiments, corresponding to higher pH (11 to 12). practically all precipitated particles were formed in the vicinity of the and comprised separate gas-liquid interface calcite rhombs within the size range 2 to 5 w, whereas later, at lower pH (-101, agglomerates, typically larger than 10 pm, of individual calcite particles were predominant (Fig. 1). This phenomenon was observed at all stirring conditions. The size of single calcite crystals was generally larger than in the previous study (Wachi and 1991bl where Technical grade calcium hydroxide was used, presumably due Jones, to the presence of more impurities than in the Analar grade inducing more primary heterogeneous nucleation. In order to determine the effect of agitation (mass transfer1 on primary crystal growth, only data taken before onset of agglomeration will be considered here, latter the the being considered elsewhere (Jones et al.. 1992; Uachi and Jones, 19921. 10
8
100rpm
202 302 405
a
q
o~o
+
m X XDX X
6 X 0%
pm
m
m
m m -I-
+
++
+
+
*++ x
+ +
a
0
20
80
Effect of agitation rate on meen bulk particle Initial concentration of Ca(OH)a = 5.2 mol/m3, partial pressure of Co2 in the gas stream 0.25
100 size bar.
~CaCOs);
F13
A. G. JONESetuf.
3822
It Is apparent in Fig.. 1 that the mean bulk particle size during the early stages of particle formation increases with increasing stirrer speed confirming previous experimental observations (Wachi and Jones, 1991bl. The development of the mean bulk particle size as a function of time was modelled using the coupled equations for the gas-liquid mass transfer both with and without crystal precipitation in the liquid film at conditions corresponding to those used in the experiments (Table il. The results of these calculations are summarised in Table 2 and Fig. 2 and are discussed below. Table
2.
Comparison of bulk by the film theory Bulk Exp. data
Time mln
Agitator speed: Film thickness: 1 3 5 10 15 20
Mean
Crystal film
mean crystal sizes predicted models with experimental data.
Crystal
Exp. data
Clear film
100 rpm 193 p 0.6 1.2 1.6 2.3 2.9 3.6
0.7 1.4 2.5 3.4
Sizes
Crystal film
0.04 0.3 0.9 3.6 8.0 12.0
1.2 2.0 3.5 4.7 -
0.8 1.7 2.1 3.3 4.5 5.0
.
a
Clear film
Exp. data
200 rpm 119 @m
10
m --
crnQAml
400 66 0.06 0.5 1.4 5.9 11.4 13.7
1.8 2.9 5.1 6.2 -
.
experimental cry&al film clear film
0
0'
A’ t-6008
3
6 ::I-I::_:
2 m 5 P
m
m
4
2
0
0
200 agitation
Fig.
300 rate
Crystal film
400
(rpm)
2: Dependence of bulk crystal size on agitation experimental conditions as in Fig. 1.
rate
Clear film
rpm cun
1.1 1.9 2.7 4.8 5.2 5.5
0.09 0.9 2.4 9.2 13*4 14.7
F13
Effect of liquid mixing rate on primary crysul size
3823
The
data clearly support the predicted positive dependence of crystal size on agitation rate. Bulk mean crystal sizes predicted by the crystal film model also appear comparable with experiment although nean crystal sizes in the film are somewhat larger (not shown). Precipitation in the crystal film both enhances mass transfer and depletes bulk solute concentration. Thus. In the clear film model bulk crystal sizes are initially slightly sraller than those predicted by the crystal film model but quickly become much larger due to increased yield. Taken together, these data imply that while the initial mean crystal growth rate and mixing rate dependence of size are successfully predicted, the terminal crystal size is overestimated inplying an underestimation of the nucleation rates in this system by the kinetics adopted.
cONcLu8IoN8 The primary carbonation predictions
crystal size of calcium carbonate precipitated during of lime water increases with agitation rate consistent and is attributed to gas-liquid mass transfer effects.
the gaseous with model
NOTATION
q
concentration of reactant A. o1gm3 A at gas-liquid interface, mol/m
A
5 B B
concentration initial value
BZ C
mass based nucleation rate. mol/m'/s concentration of liquid pt;oduct. mol/m' initial value of C, mol/m
c
Dl8 s
c
diffusivity
G G'
ii J
kn kB
B, mol/m3
of B, mol/m3
of A, B and
diffusivity DP’ diameter of d
F
of reactant
C,
of particles,
respectively, m2/s
stirrer, m space-averaged molar particle density. mol/m3 linear growth rate, m/s mass based growth rate, mol/m'/s exponent for growth rate, q. (31. -; acceln. Henry's Law constant, bar m /la01 number nucleation rate, #/s/a second order chemical reaction rate cop&ant. Boltsmann constant, 1.38 x 1O-21. kg-m /s'/lC
ktl
growth
rate
kL
liquid
phase
k
nucleation
rate
K:P L i
solubility
product
coordinate mass-based discretized
of particle diameter, m mean particle diameter, Eq. particle diameter. m
“T
constant, mass
effective
LO
diameter
of vessel,
speed
stirrer,
fs ii
of
Eq.
transfer
constant,
L
c
ma/s
nucleic
of
coefficient, Eq.
m/s
(2) carbonate,
(mol/m (181,
m
m #/s
exponent for nucleation rate, Eq. (21, population density of particles, i/m partial pressure of gas, bar gas constant, J/mol/K
-
to gravity,
la/mol/s
(31
calcium
diameter,
due
l
32 1
n/S2
A. G.
3824 t
X
time, s temperature, R specific volume of bulk distance from gas-liquid
Re
N,d2P,/CI
agitated
uLp/cI
suspended
W(PLD*)
liquid
phase
Schmidt
kLD'D,
liquid
phase
Sherwood
T V
Rer SC Sh Greek
8 PL
P p
FJ
liquid per interface,
liquid
Reynolds
particle
F13
JONES et al.
unit m
surface
area,
m
number
Reynolds
number
number number
letters volume to length shape factor, surface to length shape factor. thickness of liquid film, m density of liquid, kg/m: crystal density. mol/m viscosity. kg/m/s j-th moment of particle size distribution,
mJB3
REFERENCES
Mass transfer with chemical reaction, p.131. Elsevier, Astarita. G. (1967) Amsterdam. Capuder, E. and T. Koloini 119841. Gas hold-up and interfacial area in aerated suspensions of small particles_ Chem. Engng. Res. Des.. 42. 255-260. (1969). Physical absorption in agitated vessels Hikita, H. and H. Ishlkawa with a flat gas-liquid interface. Bull. Univ. Osaka Prefec., A18, 427-437. Y and H, Tsuge, 1990. Reactive crystallization of calciumcarbonate by Kotaki, gas-liquid and liquid reactions. Canad. J. Chem. Engng. a. 435-442. Kontoyannis, Precipitation of calcium Koutsoukos, P.G. and C.G. (19841. carbonate in aqueous solutions. J. Chem. Sot.. Faraday Trans., 80. 1181-92. Precipitation of calcium Jones, A.G., S. Wachi and C.-C. Delannoy (19921. In FluidfzatIon VII, Brisbane May 92. carbonate in a fluidized bed reactor. Juvekar. V.A. and MM. Sharma (1973). Absorption of CO2 in a suspension of lime. Chem. Engng. Sci., 28, 825-837. The precipitation of .sparingly. soluble alkaline-earth Packter, A. (19681. metal and lead salts: nucleation and growth orders during the induction period. J. Chem. Sot. (AI, 859-862. (19821. The solubilities of calcite, aragonite L.N. and E. Busenberg Plummer. and vaterite in COa-HzC solutions between 0 and 90°C and evaluation of the aqueous model for CaCO3-COa-H20. Geochim. Cosmochfaa. Acta.. 46. 1011-1040. (19711. The crystallization of calcium and G.H. Nancollas Reddy. M.M. exchange and kinetics. J. Collofd Interface Sci., x, carbonate: 1. Isotopic 166-172. chlorination of ethylene and and Morikawa, H., 1986. Liquid-phase Wachi, S. 1,2-dichloroethane. J. Chem. Engng. Japan 19, 437-443. Mass transfer with chemical reaction and Wachl. S. and A.G. Jones (1991al. precipitation. Chem. Engng. Sci.. 46, 1027-1033. Jones (199lbl. Effect of gas-liquid mass transfer on A.G. Wachi. S. and the batch precipitation of crystal size distribution during calcium Chem. Engng. Scf ., &, 3289-3293. carbonate. Wachi. S. and A-G. Jones (19921. Dynamic modelling of particle size and degree of agglomeration during precipitation. Chem. Engng. Scf., In press.
Vol.
47.
No.
1914,
pp. 3817-3624.
1992.
OaE-2509/92
$5.00+0.00
01992pergulmbLtd
OF LIQUID MIXING RATE ON P!RINARY CRYSTAL SIZE THE GAS-LIQUID PRECIPITATION OF CALAXUBI CARBONATE
ONTHEEFFECT
DURING
LG. Department University College
Jones,
J. Hostommi&
and Zhou Li2
of Chemical and Biochemical Engineering, London, Torrington Place, London WClE
1.
Permanent address: Institute of Inorganic Chemistry, of Sciences, Majakovskeho 24, Prague, CZECBOSLOVAKIA. Permanent address: Institute of 2. Coal Chemistry, Sciences, P.O. Box 165, Taiyuan, Shanxi, P.R. CHINA.
7JE,
Czechoslovak Chinese
UK. Academy
Academy
of
ABSTRACT An analysis based on gas-liquid mass transfer with chemical reaction coupled with equations describing the dynamic population balance model of crystallization and precipitation kinetics is used to predict the effect of liquid mixing rate on the transient mean crystal size of calcium carbonate precipitated in a small flat-interface gas-liquid reaction cell via the gaseous carbonation of lime water. Experimentally, small discrete calcite crystals (
Precipitation; crystal growth;
calcium carbonate; nucleation; mass
carbon dioxide; transfer.
carbonation;
Recently, precipitation involving three steps vfz. gas-liquid mass transfer, chemical reaction and crystallization was analyzed in terms of the coupled equations for the film theory of gas-liquid mass transfer with chemical of crystallization. reaction and the mass and population balances It was predicted that a reduction in the mass transfer resistance would increase the crystal size and this was subsequently mean supported qualitatively in preliminary experiments by measurement of crystal size distributions of precipitated calcium carbonate produced via the gaseous carbonation of lime-water in a reaction cell (Wachi and Jones. 1991a.b). This present study alms to extend the analysis of mass transfer with chemical reaction and precipitation and to compare directly for the first time the predicted dependence of crystal size on gas-liquid mass-transfer rate with the performance of the precipitation cell operated under similar conditions.
3817
3818
A. 0.
Maction
F13
JONESet al.
kinetics
liquid phase reaction is operated batch-wise with contact of a continuously flowing gaseous reactant through a gas-liquid interface of constant surface area. The carbonation reaction of lime water involves gas. llauld and solid phases. The overall reactfon scheme can be described by the
The
following
-ti0&:
COz(gl
9
=
(aql + OH- HCOi
COa(aql
(a)
HCO ;
(b1
+ OH- =
COS2- +
Ca2+ + C03'- =
CaCOs(s)
The rate of reaction r
k
=
Hz0
(cl (d)
(bl is given by (Astarita,
CCOzl[OH-I
(1)
Reaction (c) is reversible and instantaneous, in equilibrium at any time and at every place Crvstallization The number
the participating in the solution.
components
are
kinetics
rate of nucleation
.
C=k
1967):
P
-
‘3 K
and linear crystal growth
rate are given by:
!s
SP
(31
where n and g are the orders of nucleation the solubility product of calcite.
and growth
Film Theory Briefly, mass balances of reactants and product respectively by Wachi and Jones, 1991al:
respectively,
in the liquid
film
and &p
1s
are given
6A/6t
= DA(6aA/8x21
-
kAB
(41
6B/8t
= Ds (S2B/Sx2)
-
2kAB
(51
BC/Bt
= Dc(82C/Bx21
+ kAB
where B’
corresponding
P
G’
-
B’
(6)
mass based rate equations
= vJ,Lo”
G' =
-
f3pN(x,Ll(G/2)L2dL
(a
=
m/6
[@
-
x
of nucleation for sphere1
for sphere)
and growth
are: (71 (81
19731, the only reactants In thil approach (see eg. Juvekar and 5harma. considered in the kinetics scheme are COa (component AI. OH- ion (component Bl ion (component Cl formed by consumed both by reactions (bl and (cl. and &react@n (~1 and consumed by the precipitation reaction ld); the concentration Is assumed to be constant across the diffusion layer. of ca
F13 The
El&t
population
of the precipitated
balance
8N/8t + G(6N/BL)
of liquid mixinglrte011primarycrystal size
particles
3819
is given by:
- DP(a2N/ax2)
(91
In Eq. (91, it is assumed that particles are Brownian diffusion of the crystals within described by the Stokes-Einstein equation:
removed from the the liquid film
liquid which
film may
DP=k,T/C3qL, The
boundary
at x = 0. The
liquid
at x = 8,
(101 conditions
for
t>o:
Eqs.
(41-(61
A = (p/iiIco , I
phase
is in batch
t>O:
and
BB/8x = 0,
operation.
8W8x
= 0.
6N/Bx
-DA(&W3x)
= Y(&uat
+ km)
-DBWB/UxI
= Y(UB/Bt
+ ZkABI
-Dc(8c/6x)
= V(X/at
(121
l!quld phase per unit gas-liquid film, 8. is defined by: (131
L
L=L:
0
L =oD: Initial at
values
t = 0:
(11)
+ G' + B' - kAB1 + G(aN/aL))
Assuming newly nucleated particles have an effective nucleus size for example, can be estimated from the Gibbs-Thomson equation 1991al. then Jones,
t>O, OSxS,
= 0
Therefore,
where Y Is the specific volume of the bulk surface area and the thickness of the liquid d = D/k
(91 are:
2
-DP(BN/i3x) = V
at
by be
N=J/G
LO.
Wachi
which, and (141
n
N=O
(15)
are:
A = 0.
B=B.
c - 0,
N=O
(16)
Solving these equations by a n&erical method. time courses of concentrations the size dlscretized number and C(t,~x). and density of B(t.xI A(t,xl, particles. N(t.x.LiI. are obtained. Molar particle density in the bulk at discretized diameter L1 is calculated as:
P(L/I
= orpL;N(b.Li,t)LI
(171
from which various distribution characteristics may the mass based mean bulk particle size is calculated I-ax
thereby
be evaluated. as follows:
For
example,
L-ax
facilitating
(181
a
simple
comparison
of
model
predictions
with
data.
in what follows the transient mean crystal size predicted in the Thus, solution bulk will be compared with experlmental data under similar operating the effect of liquid agitation rate (which affects the conditions and gas-liquid mass transfer coefficient) will be determined.
3820
F13
JONES et al.
A. G.
Simnlification. If the processes of reaction and crystallization in the diffusion layer adjacent to the liquid-gas interface are slow and can be neglected, the model is reduced to a description of gas absorption through a clear fllm with crystal precipitation only occuring in the bulk: dA/dt
= kL(Ai
- AI/V
- kAB,
dp/dt
= Jn,
dp,/dt
= JGP,_~+
At t=o, initial
dB/dt
= -2kAB,
.7&b
dC/dt
= kAB
-
(G/2)p._p/3 - a&,L;
(J=1,4)
(191
the moments of particle size distribution are equal condition for A, B and C is again given by Eq. (16).
to
zero
and
the
The numerical methods employed to solve the crystal film model were as described previously Wachi and Jones, 1991al. Briefly, both the coordinates of space within the liquid film and particle diameter were discretized int_g 90 The boundary of the maximum particle diameter was 45 xl0 m. equal lengths. The time division used was 0.1 sec. The computer used was the IBM RS/6000, Model 540 in the Bloomsbury Computing Consortium Timesharing System. Thermodynamic and kinetic parameters used in calculations were taken from the literature either directly for the CO2-Ca(OH12-HzO system or from similar CaCOs systems as available, or were estimated, while the gas-liquid mass transfer coefficient was determined as a function of stirring rate by a dimensionless correlation, as in Table 1. Unfortunately, relatively few kinetic data are directly available for gas-liquid precipitation. Rather more are available for liquid-liquid systems, but these are highly variable. It is interesting to note that Koutsoukos and Kontoyannis for example, (19841, report substantially higher calcium carbonate nucleation rates than Packter Kotaki and Tsuge (19901 report differing results for (19681 while liquid-liquid and gas-liquid precipitation of CaCO3. In order to make a quantitative prediction of the effect of gas-liquid mass transfer on crystal however, the kinetic data of Packter (1968) and Reddy and Nancollas size. (19711 were found to be of the more convenient form for the present use.
Table
1.
Parameter
values
used
in calculatione
Parameter k
1.0x10'
.n
k;s
8
mol-"
8.06x10-' -9
DA=DB==DC
2.2x10
H
3.46~10-~
K
lP
k L
0
kL
Source
0.00347
m3n-3s-1,
4.2
Packter,
n~ol-%n~~+~s-~,
2.0
Reddy
m2/s
1968
& Nancollas,
Capunder
& Coloini,
1971 1984
bar m3/mol mo12m-6
Plurnmer & Busenberg,
12.4
m3s-1mol-'
Astarita,
0.01
m
Gibbs-Thomson
Sh = 0.322
Re""Scl"
Hikita
&
1982
1967 estimate
Ishikawa,
1969
F13
Effect of liquid mixingrateon primarycrystal size
3821
BXPEZBIMENTAL The experimental apparatus used was again as described in detail previously (Uachi and Jones, 199lb). The rotation rate of the agitators in both liquid was controlled at the same speed in the range 100 to 400 rpm. and gas Initially, the vessel was partly filled with solution of calcium hydroxide Drug House) filtered through the 0.3~ membrane filter. (Analar grade: British Gaseous nitrogen and carbon dioxide were mixed and saturated with water, and introduced to the upper space of the mixed gas was the vessel. The temperature was maintained at 25 f 0.5OC. The suspension of the solution and precipitated solids were sampled from the bulk by a pipette for subsequent analysis. Particle size distribution was determined by a laser particle sizer (Model 3300: Malvern Instruments Ltdl. RESULTBAND
DISCWSIC?N
In the early stages of the experiments, corresponding to higher pH (11 to 12). practically all precipitated particles were formed in the vicinity of the and comprised separate gas-liquid interface calcite rhombs within the size range 2 to 5 w, whereas later, at lower pH (-101, agglomerates, typically larger than 10 pm, of individual calcite particles were predominant (Fig. 1). This phenomenon was observed at all stirring conditions. The size of single calcite crystals was generally larger than in the previous study (Wachi and 1991bl where Technical grade calcium hydroxide was used, presumably due Jones, to the presence of more impurities than in the Analar grade inducing more primary heterogeneous nucleation. In order to determine the effect of agitation (mass transfer1 on primary crystal growth, only data taken before onset of agglomeration will be considered here, latter the the being considered elsewhere (Jones et al.. 1992; Uachi and Jones, 19921. 10
8
100rpm
202 302 405
a
q
o~o
+
m X XDX X
6 X 0%
pm
m
m
m m -I-
+
++
+
+
*++ x
+ +
a
0
20
80
Effect of agitation rate on meen bulk particle Initial concentration of Ca(OH)a = 5.2 mol/m3, partial pressure of Co2 in the gas stream 0.25
100 size bar.
~CaCOs);
F13
A. G. JONESetuf.
3822
It Is apparent in Fig.. 1 that the mean bulk particle size during the early stages of particle formation increases with increasing stirrer speed confirming previous experimental observations (Wachi and Jones, 1991bl. The development of the mean bulk particle size as a function of time was modelled using the coupled equations for the gas-liquid mass transfer both with and without crystal precipitation in the liquid film at conditions corresponding to those used in the experiments (Table il. The results of these calculations are summarised in Table 2 and Fig. 2 and are discussed below. Table
2.
Comparison of bulk by the film theory Bulk Exp. data
Time mln
Agitator speed: Film thickness: 1 3 5 10 15 20
Mean
Crystal film
mean crystal sizes predicted models with experimental data.
Crystal
Exp. data
Clear film
100 rpm 193 p 0.6 1.2 1.6 2.3 2.9 3.6
0.7 1.4 2.5 3.4
Sizes
Crystal film
0.04 0.3 0.9 3.6 8.0 12.0
1.2 2.0 3.5 4.7 -
0.8 1.7 2.1 3.3 4.5 5.0
.
a
Clear film
Exp. data
200 rpm 119 @m
10
m --
crnQAml
400 66 0.06 0.5 1.4 5.9 11.4 13.7
1.8 2.9 5.1 6.2 -
.
experimental cry&al film clear film
0
0'
A’ t-6008
3
6 ::I-I::_:
2 m 5 P
m
m
4
2
0
0
200 agitation
Fig.
300 rate
Crystal film
400
(rpm)
2: Dependence of bulk crystal size on agitation experimental conditions as in Fig. 1.
rate
Clear film
rpm cun
1.1 1.9 2.7 4.8 5.2 5.5
0.09 0.9 2.4 9.2 13*4 14.7
F13
Effect of liquid mixing rate on primary crysul size
3823
The
data clearly support the predicted positive dependence of crystal size on agitation rate. Bulk mean crystal sizes predicted by the crystal film model also appear comparable with experiment although nean crystal sizes in the film are somewhat larger (not shown). Precipitation in the crystal film both enhances mass transfer and depletes bulk solute concentration. Thus. In the clear film model bulk crystal sizes are initially slightly sraller than those predicted by the crystal film model but quickly become much larger due to increased yield. Taken together, these data imply that while the initial mean crystal growth rate and mixing rate dependence of size are successfully predicted, the terminal crystal size is overestimated inplying an underestimation of the nucleation rates in this system by the kinetics adopted.
cONcLu8IoN8 The primary carbonation predictions
crystal size of calcium carbonate precipitated during of lime water increases with agitation rate consistent and is attributed to gas-liquid mass transfer effects.
the gaseous with model
NOTATION
q
concentration of reactant A. o1gm3 A at gas-liquid interface, mol/m
A
5 B B
concentration initial value
BZ C
mass based nucleation rate. mol/m'/s concentration of liquid pt;oduct. mol/m' initial value of C, mol/m
c
Dl8 s
c
diffusivity
G G'
ii J
kn kB
B, mol/m3
of B, mol/m3
of A, B and
diffusivity DP’ diameter of d
F
of reactant
C,
of particles,
respectively, m2/s
stirrer, m space-averaged molar particle density. mol/m3 linear growth rate, m/s mass based growth rate, mol/m'/s exponent for growth rate, q. (31. -; acceln. Henry's Law constant, bar m /la01 number nucleation rate, #/s/a second order chemical reaction rate cop&ant. Boltsmann constant, 1.38 x 1O-21. kg-m /s'/lC
ktl
growth
rate
kL
liquid
phase
k
nucleation
rate
K:P L i
solubility
product
coordinate mass-based discretized
of particle diameter, m mean particle diameter, Eq. particle diameter. m
“T
constant, mass
effective
LO
diameter
of vessel,
speed
stirrer,
fs ii
of
Eq.
transfer
constant,
L
c
ma/s
nucleic
of
coefficient, Eq.
m/s
(2) carbonate,
(mol/m (181,
m
m #/s
exponent for nucleation rate, Eq. (21, population density of particles, i/m partial pressure of gas, bar gas constant, J/mol/K
-
to gravity,
la/mol/s
(31
calcium
diameter,
due
l
32 1
n/S2
A. G.
3824 t
X
time, s temperature, R specific volume of bulk distance from gas-liquid
Re
N,d2P,/CI
agitated
uLp/cI
suspended
W(PLD*)
liquid
phase
Schmidt
kLD'D,
liquid
phase
Sherwood
T V
Rer SC Sh Greek
8 PL
P p
FJ
liquid per interface,
liquid
Reynolds
particle
F13
JONES et al.
unit m
surface
area,
m
number
Reynolds
number
number number
letters volume to length shape factor, surface to length shape factor. thickness of liquid film, m density of liquid, kg/m: crystal density. mol/m viscosity. kg/m/s j-th moment of particle size distribution,
mJB3
REFERENCES
Mass transfer with chemical reaction, p.131. Elsevier, Astarita. G. (1967) Amsterdam. Capuder, E. and T. Koloini 119841. Gas hold-up and interfacial area in aerated suspensions of small particles_ Chem. Engng. Res. Des.. 42. 255-260. (1969). Physical absorption in agitated vessels Hikita, H. and H. Ishlkawa with a flat gas-liquid interface. Bull. Univ. Osaka Prefec., A18, 427-437. Y and H, Tsuge, 1990. Reactive crystallization of calciumcarbonate by Kotaki, gas-liquid and liquid reactions. Canad. J. Chem. Engng. a. 435-442. Kontoyannis, Precipitation of calcium Koutsoukos, P.G. and C.G. (19841. carbonate in aqueous solutions. J. Chem. Sot.. Faraday Trans., 80. 1181-92. Precipitation of calcium Jones, A.G., S. Wachi and C.-C. Delannoy (19921. In FluidfzatIon VII, Brisbane May 92. carbonate in a fluidized bed reactor. Juvekar. V.A. and MM. Sharma (1973). Absorption of CO2 in a suspension of lime. Chem. Engng. Sci., 28, 825-837. The precipitation of .sparingly. soluble alkaline-earth Packter, A. (19681. metal and lead salts: nucleation and growth orders during the induction period. J. Chem. Sot. (AI, 859-862. (19821. The solubilities of calcite, aragonite L.N. and E. Busenberg Plummer. and vaterite in COa-HzC solutions between 0 and 90°C and evaluation of the aqueous model for CaCO3-COa-H20. Geochim. Cosmochfaa. Acta.. 46. 1011-1040. (19711. The crystallization of calcium and G.H. Nancollas Reddy. M.M. exchange and kinetics. J. Collofd Interface Sci., x, carbonate: 1. Isotopic 166-172. chlorination of ethylene and and Morikawa, H., 1986. Liquid-phase Wachi, S. 1,2-dichloroethane. J. Chem. Engng. Japan 19, 437-443. Mass transfer with chemical reaction and Wachl. S. and A.G. Jones (1991al. precipitation. Chem. Engng. Sci.. 46, 1027-1033. Jones (199lbl. Effect of gas-liquid mass transfer on A.G. Wachi. S. and the batch precipitation of crystal size distribution during calcium Chem. Engng. Scf ., &, 3289-3293. carbonate. Wachi. S. and A-G. Jones (19921. Dynamic modelling of particle size and degree of agglomeration during precipitation. Chem. Engng. Scf., In press.