Crystal Growth and Agglomeration of Calcium Sulfite Hemihydrate Crystals

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Crystal Growth and Agglomeration of Calcium Sulfite Hemihydrate Crystals

Clifford Y. Tai, and Pao-Chi Chen

Ind. Eng. Chem. Res., 1995, 34 (4), 1342-1351 • DOI: 10.1021/ie00043a040 Downloaded from http://pubs.acs.org on November 25, 2008

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1342 I n d . Eng. C h e m . Res. 1995,34, 1342-1351

Crystal Growth and Agglomeration of Calcium Sulfite Hemihydrate

Crystals

Clifford

Y.

Tai*

Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 1061 7, ROC Pao-Chi

Chen

Department of Chemical Engineering, Long-Hau Junior College, Tao-Yuan, Taiwan, ROC

Crystal growth and agglomeration of calcium sulfite hemihydrate crystals from solution were

studied by reacting Ca(OH)2 with NaHS03 in a pH-stat semibatch crystallizer. Single platelet

crystals and agglomerates of platelet crystals were produced in

the

pH range from 5.80 to 6.80.

The crystallization mechanism changed from primary nucleation to crystal growth in the progressive precipitation. Using the titration curves, the growth rate was calculated from the

titration rate at the final stage of operation. The crystal growth rates of calcium sulfite

hemihydrate crystals were found to obey the parabolic rate law in the low supersaturation range. Another point to be noted is that the precipitates of calcium sulfite hemihydrate in agitated suspensions have a tendency to form agglomerates. It was found that the degree of agglomeration

is a weak function of relative supersaturation and magma density, while the pH value is a key

factor t h a t affects the degree of agglomeration. Addition of EDTA also has a n effect on the agglomeration of calcium sulfite hemihydrates.

Introduction

Flue gas desulfurization (FGD) processes are most

commonly utilized to remove sulfur dioxide from stack

gases of coal- or oil-fired plants. Many FGD processes, including throwaway processes, gypsum processes, and regenerative processes, have been developed over the last 30 years, and several processes are being used successfully in full scale. In the simple slurry technol-

ogy, SO2 is absorbed by a slurry of limeflimestone to

form calcium sulfite crystals of acicular habit and its

strong agglomeration, requiring large clarifiers and

filters to dewater the sludge to make an acceptable

landfill. On the other hand, the double alkali processes

are being investigated to overcome the scaling, plugging,

erosion, and dewatering problems that have been as- sociated with the 1imeAimestone systems. Besides, high SO2 removal efficiencies and high limeflimestone utili- zations are easily achieved with alkaline sodium scrubbing solutions by simply adjusting the scrubber operating pH (Valencia, 1982).

In the lime dual-alkali process, the absorption of SO2 with chemical reaction in the scrubber is

Na2S0,

+

SO,

+

H 2 0

-

2NaHS0,

Then, the scrubber solution is pumped into a crystallizer

and reacts with Ca(OH)2 solution transported from a storage tank. The major reaction equation in the crystallizer is

2NaHS0,

+

Ca(OH),

-

CaS0,.1/2H20(s)

+

3/2H20

+

Na2S03 The clear solution, NaZS03 solution in the crystallizer, is repumped into the scrubber for reusing. The calcium salt of CaS0&2H20(s) was obtained with good settling and filtration characteristics in a pilot scale operation (LaMantia et al., 1975; Satriana, 1981).

Crystal morphology and size affect the dewatering process, including sedimentation and filtration, and they

are key factors leading to a successful operation of a

FGD process (Tseng and Rochelle, 1986; Dirksen and Ring, 1991). Crystal morphology could be modified by solution composition, additives, and solution pH, which also influence the crystal growth rate (Dirksen and Ring, 1991; Chen et al., 1992). The dewatering process proceeded more easily for crystals in platelet form as compared with crystals in acicular form (Ottmers, 1974; Phillips, 1978).

Agglomeration complicates the analysis of crystal size

distribution (CSD) when using the batch and MSMPR

crystallizer data. Several methods were proposed to

investigate the effect of agglomeration on the CSD, such

as agglomeration kernel functions (Beckman and Farmer,

1987; Hostomsky and Jones, 1991; Tavare and Garside,

1993) and the degree of agglomeration (Budz et al.,

1986; Sohnel and Mullin, 1992; Tai and Chen, 1994).

In those studies, they found that the degree of ag-

glomeration was a function of relative supersaturation,

stirring speed, and solid concentration. In order to

characterize the changes in CSD, the parameters, such

as the total number of crystals, Nt, the number of large

crystals greater than some arbitrary size,

LO,

and the

mass-weighted average size, L4,3, are utilized to quantify

the degree of agglomeration (Hark1 et al., 1986). When the agglomeration occurs, a decrease in the total number of particles, an increase in the number of large particles, and hence an increase in the mass-weighted average size would be observed.

To study the crystal growth of sparingly soluble salts, such as calcium sulfide hemihydrate and calcium carbonate, unseeded experiments (Klepetsanis and Kout- soukos, 1989; Kralj et al., 1990) and seeded experiments (Christoffersen and Christoffersen, 1990; Tai et al., 1993) have been applied. In these experiments, the pH- stat apparatus is most commonly employed (Tseng and Rochelle, 1986; Christoffersen and Christoffersen, 1990; Tai et al., 1993). From the titration curve (Klepetsanis

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Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1343

Figure 1. pH-stat semibatch crystallization system: 1, pH and temperature indicator; 2, reagent bottle; 3, pumping system of reagent; 4, reagent deliver line; 5 , burette; 6, thermometer; 7, water bath; 8, crystallizer; 9, temperature controller; 10, motor; 11, glass electrode; 12, reference electrode; 13, thermocompensator; 14, axial-flow impeller; 15, rotameter; 16, sparging tube.

and Koutsoukos, 1989; Tai et al., 1993) and the concentration-time curve (Kazmlerczak et al., 19821, the growth rates can be calculated.

The aim of this work was t o search for the operating

conditions that would form the platelet crystals of

calcium sulfite hemihydrate and to determine the

growth mechanism of platelet CaSO&H20 using a pH-

stat apparatus. The Ca(OH)flaHSOdH20 reacting system was performed without seeding. The crystallization process began with an increase of primary nuclei followed by crystal growth. The growth rate of calcium sulfite hemihydrate was calculated from the titration curves using the method proposed in this work.

In addition, the degree of agglomeration of calcium

sulfite hemihydrate crystals was assessed and cor-

related with operating variables in order to have a

better understanding of the agglomeration mechanism.

Experimental Apparatus and Procedure

The crystallization system of the semibatch study of

calcium sulfite hemihydrate is shown in Figure 1. The acrylic plastic crystallizer was placed in a thermostated water bath at 25 "C. The diameter and height of the crystallizer are 120 and 140 mm, respectively. The

crystallizer is baMed with four longitudinal baffles, of

which the thickness is 10 mm each, at 90" spacing. The diameter of the stirrer, an axial-flow glass-made agita-

tor, is 50 mm. The stirring rate was set a t 400 rpm to

suspend, the crystals. One liter of supersaturated

solution of calcium sulfite was prepared by adding

calcium hydroxide solution to the sodium bisulfite

solution already in the crystallizer. Before operation,

the electrodes were standardized with buffers of pH 4.01

and 6.86, respectively. Subsequently, the solution was

adjusted to a desired pH value by adding 0.1 M NaOH

or 0.1 M HC1 solution. All the chemicals were extra pure reagent grade from Kokusan Chemical Works.

Nucleation was initiated by the introduction of a known

amount of titrant into the supersaturated solution, and the crystallization process changed t o crystal growth at the latter stage of operation. The pH was kept constant during operation using a pH-stat apparatus (Kyoto

Electronic AT 200) to control the amount of calcium

hydroxide solution added into the crystallizer. In order to prevent the oxidation of sulfite ion in the solution, sparging of nitrogen was continued during the precipitation operation. The operating variables were pH, solution concentration, and concentration of EDTA. To

Table 1. Operating Conditions and Crystal Properties in the Crystallization of Calcium Sulfite Hemihydrate Crvstals

Operating Conditions total sulfite concentration 40-80 mM total calcium concentration 2.80-3.75 mM concentration of EDTA 0-2.45 mM

temperature 25 "C

agitation rate 400 rpm

operating time 120-130 min

crystal habit platelet

crystal system orthorhombic

main peak strength

crystal density 1390 kg/m3

mass weight mean size BET specific surface area (SSA)

a t initial stage (TSO) a t initial stage (TCA)

pH range 5.8-6.8

Crystal Properties

2.62, 3.16, 3.81, 5.35, 5.56A 33.86-68.34 pm

0.32-1.40 m2/g

simulate the industrial scrubbing liquor composition

(LaMantia et al., 19751, the concentration of total sulfite

was kept in large excess. In addition, the operating pH

range, from 5.80 t o 6.80, was similar to that of the

scrubbing solution. All the operating conditions were listed in Table 1.

At the end of operation, the slurry was filtered and the solids were dried in an oven a t 110 "C for at least 1 h. Particle morphology and solid composition were examined by SEM, IR spectroscopy, and X-ray powder diffraction. In addition, particle size distribution was analyzed by the Microtrac sizer. The calcium ion concentration was determined by EDTA potentiometric titration using a combined F-2002 calcium ion selective

electrode and a K-401 reference electrode connected to

a PHM 82 digital pH meter, all from the Radiometer

Co. The specific surface area of the grown crystals was determined by the multiple-point BET technique (Mi- cromeritics, 2100D). Besides, the titration curve ob-

tained automatically at the latter stage of operation was

employed to calculate the crystal growth rates.

Determination of Relative Supersaturation and Crystal Growth Rate

Toft (1984) is given by

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1344 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995

Table 2. Equilibrium Equations and.Stability Constants for the Ca(OH)2/NaHSOs System at 25 "C (Lowell, 1970)

Mass Balance Equations

TCA = [Ca2+]

+

[CaOH']

+

[CaSO,'] (2) TSO = [H,SO,l

+

[HSO,-l

+

[CaSO;] (3)

TNA = [Na']

+

[NaOH] (4)

TCI = [Cl-] ( 5 )

Mass Action Equations

pK, = -logy,' [H+l[OH-I = 14.00 ( 6 )

pKz = -log (yl'[H+l[HS03-l) y,[H,SO,] = 1.88

pK3 = -log ~ ' [ ~ ~= ~7.21 ~ ~ - ' ) = 3.39 = 1.37 pK, = -log pK5 = -log (y&a2'l[OH-l) [CaOH'l

pK6 = -log (y12[Na+l[OH-l) y,[NaOHl = -0.57

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pKsp = - l ~ g ( r ~ [ C a ~ + l [ S O , ~ - I ) = 6.61 (12)"

a The value was calculated from the data that were reported

where IP = (Ca2+)(S032-) and Ksp is the solubility

product. Using mass action equations, which are pre- sented in Table 2, and mass balance equations, the

concentrations of all species in solution were computed

from the measured pH, total calcium concentration, total sulfite concentration, and total sodium concentration by successively approximating the ionic strength (Nancollas, 1966). The ionic activity coefficients were estimated from the modified Debye-Huckel equation:

by Brewer (1982) in Flue Gas Desulfurization.

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logy, =

-AZ2(-)

f i

- 0.31

l + f i

where yz is the activity coefficient of the ion with charge

z and A is a constant.

The growth rate of Cas03 can be expressed as the

consumption rate of total sulfite concentration (TSO):

J

d[TSOl V dt --=-

-

d[CaSO:l+ d[H2S031 d[HS03-l + + dt - dt dt d[S032-l dt (14)

where J and V are molar growth rate and solution

volume, respectively. Because the change of total sulfite

concentration in the crystallizer is equal to the consumption of calcium concentration in the burette of the pH-stat apparatus and the total concentration of calcium ion in the crystallizer, the material balance

on the total calcium ion is

d[CaSO&)I dt (15)

Because the growth rate d[CaS03(s)l/dt is equal to the

consumption rate of TSO, i.e. d[TSOYdt, the molar

growth rate can be derived (see Appendix)

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and the growth rate per unit crystal surface area is defined as

(17)

where f is a constant and is calculated from the

concentration of ion species using eq A-19,

cb

is the

concentration of titrant, and dVddt is the titration rate,

which is the slope of the titration curve. In addition,

Mt and SSA are magma density and the corresponding

specific surface area of crystals, respectively.

Results and Discussion

Solid Composition of Platelet Crystals. Twenty- one runs were conducted in this work. The precipitate produced a t given conditions was examined by IR spectroscopy and X-ray powder diffraction. In all runs, the IR spectra showed that the major band appeared at 990 cm-' which is a standard peak (Vandeberg, 1983)

for calcium sulfite hemihydrate. No trace of calcium

sulfate was found in this work. The X-ray diffraction pattern has also demonstrated that calcium sulfite hemihydrate was the only crystal present in the system

throughout the experiments. A typical spectrum of an

X-ray pattern is shown in Figure 2. The main peaks as indicated are close to the standard values for calcium sulfite hemihydrate (McClune, 1983).

The SEM photographs show that the crystals are

platelets and their agglomerates, which are presented

in Figure 3, in all runs. The platelet form of calcium

sulfite hemihydrate crystal was found in a supersaturated solution in which the total sulfite concentration

ranges from 40 t o 80 mM and the pH values were in

the range of 5.8-6.8. The result is similar to that

reported by Tseng and Rochelle (1986) where the morphology of calcium sulfite hemihydrate is a spherical agglomerate of thick platelet from a different reaction system, CaCldNazSOflz0, in the absence of sulfate.

Titration Curves and Induction Period. Upon mixing of the calcium hydroxide solution with the sodium bisulfite solution, the precipitation process

started within 20 min for most runs. As shown in

Figure 4, which shows the titration curves, the induction time varied from run t o run, about 8 min for runs 7 and

5 but no appreciable induction time for run 14. The

difference was caused by the starting supersaturation, which is higher for run 14. Such a result has been suggested by Mullin (1972). The titration curves for all

runs can be divided into two regions as indicated in

Figure 4, a faster titration rate followed by a slower one. The steep slope of the titration curve in the first region indicated the occurrence of spontaneous nucleation,

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Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1345

6 00

500

4

00

Y CJ

aJ

a;

2 0 0

1 0 0

0 I

N bo 4 -

io

- 2

10

20

30

40 Diffraction angle,

28

Figure 2. X-ray powder diffraction pattern of calcium sulfite hemihydrate crystals for run 2.

( C )

(a) (b)

Figure 3. SEM photographs of calcium sulfite hemihydrate crystals: (a) a mixture of platelets and agglomerates, (b) platelet crystal,

and (c) agglomerate crystal.

which was similar to that reported by Klepetsanis and The amount of titration volume a t the first region

Koutsoukos (1989) for the precipitation of calcium within 30 min for run 14 was higher than that for runs

sulfate dihydrate and Frhche and Heughebaert (1989) 5 and 7. The possible reason was that a large amount

for calcium phosphate precipitation. The spontaneous of nuclei was induced immediately for run 14 a t a high

nucleation stopped until the relative supersaturation supersaturation level (ai = 1.36) and the pH became

became a lower value where the crystal growth was lower due t o the consumption of reactants. Therefore,

prevailing. The primary nuclei produced in the crys- a compensation of more basic solution (titrant, Ca(OH)2

tallizer were utilized as the seed crystals for further solution) by the autotitrator was required to keep the

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1346 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 E c 5 0 . 0 2 5 6o

-

R u n n o . 5 a A A Run no. 7 , 0 ~ 0 . 8 8 0 0 0 R u n no. 5 , 0 ~ 0 . 9 9 o o o Run n o . 1 4 , D z 1 . 3 6 h A

E

-

4 0 - c 8 c

e

-

c '2 3 0 - \c 0 0 0 30 60 90 120 150 T i me (mi

n)

Figure 4. Titration curves of Ca(OH)2 a t different pH levels: curve A, pH = 6.20; curve B, pH = 6.50; and curve C, pH = 6.80.

other hand, fewer nuclei were induced at moderate

supersaturation for runs 5 and 7.

As a result, the consumptions of basic solution for the

two runs were smaller than that for run 14, but it was

enough to keep the pH constant. The second region of

the titration curves with a slower titration rate, which

is probably due to crystal growth, begins a t 30,70, and

80 min for runs 14, 5, and

7,

respectively. The crystal

growth process occurred at an early stage of operation

for

run

14 because excess nuclei with large surface areas

were induced to reduce the supersaturation to a lower

level, which was unable to cause nucleation. The final supersaturation was 0.05,0.34, and 0.46 for runs 14,5,

and

7,

respectively.

Crystal Size Distribution

and Degree

of Ag-

glomeration. The crystal size distribution data determined by the Microtrac particle size analyzer on the

volume basis were converted to weight intensities as

shown in Figures 5 and 6. A bimodal distribution was

observed at the final stage of operation. The first population peak appeared between 0 and 20 pm, while the size range of the second population peak was between 20 and 100 pm. Under different pH values and

EDTA concentrations, the change of CSD indicated the

occurrence of agglomeration. Evidence in Figure 3c

shows that the agglomerates are many small platelets growing out from a common center to form a spherelike particle and contain many internal void spaces. How- ever, parts of the agglomerates show multiple platelets growing out from one platelet, but not enough to form a sphere.

_m_0.005

_-

-

.- 0,

3

0.000,- Crystal size

( p m )

(a) 0.030

₁

-

0.020 Run no. 7 - . +.' U .5 0.010

E

.- 01 0.005 Q, 40 80 1 v 0.020 '5 0.015 .G 0.010

I

_m_0.005 c U

E

s

0.000

.-

0 ₄₀ ₈₀ ₁₂₀ Crystal size

(LG)

(C)

Figure 5. Effect of pH on the CSD a t the same concentration level with TSO = 40 mM and TCA = 3.75 mM: (a) run 3 with pH

= 5.80, (b) run 7 with pH = 6.20, and ( c ) run 5 with pH = 6.50.

difficult to estimate. Therefore, instead of the number-

based degree of agglomeration, the mass-based degree of agglomeration was utilized, which is defined as

weight of particles larger than 16 p m

P =

_{weight of product} (18)

The particle size larger than 16 pm was considered as agglomerate because the weight intensity was the

lowest around 16 pm in most of the cases in Figures 5

and 6. Meanwhile, the mean size, L4,3, was also used

to assess the degree of agglomeration as adopted by Budz et al. (1987) and Hartel et al. (1986). It was inferred that the degree of agglomeration was a function

of magma density, Mt, initial relative supersaturation,

ai, and pH value. From the data of

CSDs,

P and L4,3

were calculated and are listed in Table 3. Values of L?,3

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Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1347 *0.025 0.020 c v c

.-

2

0.01 5 Run no. 13 Crystal size (pm) (a)

2

0.030

_I

Crystal size

( p m )

( b ) Crystal size

(pm)

( 4

Figure 6. Influence of EDTA on the CSD a t pH = 6.80 and the same concentration with TSO = 40 mM and TCA = 3.75 mM: (a) run 13 with EDTA = 0 mM, (b) run 17 with EDTA = 1.50 mM, (c) run 18 with EDTA = 2.45 mM.

work. When agglomeration occurs, a decrease in the

total number of particles, N , and a n increase in the

number of large particles would be observed, while the

mass-weighted average size, L 4 , 3 , would be increased

with an increase in the number of large particles. Thus,

a smaller N or a larger L 4 , 3 indicates a strong ag-

glomeration behavior in the crystallization process.

A multiple linear regression analysis from the ag-

glomeration data gave the following correlations:

P = 0.6755ai0,0634Mto.0515 exp[0.0548 pH] (19)

and

L4,3

= 4.84960~.0695M~0453 exp[0.3746 pH1 (20)

The measured values, I'm,, and ( L 4 , 3 ) m e a , are compared

with the calculated values,

Peal

and ( L 4 , 3 ) c a l , as shown

1

.o

0.9 f

a

0.8

n 7 -..

0.7

0.8

0.9

1.0 Pca I.

(a)

70

60

n

E

2

U

$

50 n 2

3

v 4c

30

40 50

60

70 (L

4,3)ca1.

(N

m )

( b )

Figure 7. Calculated values vs measured values for P and L4,3

(a) using eq 19 for P and (b) using eq 20 for L4,3.

in Figure 7; most data points fall within f 1 0 % of the calculated values. The low values of the parameters in

these correlations show that the influence of supersatu-

ration and magma density on the degree of agglomeration is not great. This can be explained as follows. In the ranges of operating conditions, the changes in and Mt0.0453 are 1.05 for the former and 1.10 for the latter, while the changes in exp[0.0548 pH1 and exp-

L0.3746 pH1 are 1.06 and 1.45 for P and L 4 , 3 , respec-

tively. This indicated that the effects of ai and Mt on

the degree of agglomeration are not significant. On the other hand, the pH value is the most sensitive factor affecting the degree of agglomeration during the pre-

cipitation.

As

shown in Figure 5, the CSD was a

function of pH a t the same solution concentration. It

was found that the bimodal CSD was significant and

disappeared gradually when the solution pH increased. In addition, the weight intensity of the large crystal size

was also increased with increasing solution pH.

This

was caused by agglomeration. The dependence of agglomeration on pH is probably due to the change of

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1348 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995

Table 3. Operating Variables, Growth Rates, and Agglomeration Parameters of Calcium Hemihydrate Crystals at Initial and Final Stages

80 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16

-

\"

- 0.46 14.25 0.98 1.11 1.40 18.18 0.36 0.44 2.92 1.22 5.53 0.56 5.54 0.62 6.01 0.40 6.82 0.58 5.03 0.42 7.64 0.32 5.44 0.41 1.80 1.24 1.78 1.20 2.54 - - - - - - - - - - - - - - - - - 0.89 43.12 0.94 51.79 0.74 33.86 0.95 59.60 0.91 47.98 0.84 49.83 0.91 42.40 - - - - - - - - - - - - - - - - - - - - - - 0.93 68.34 0.88 43.53 - - - - - - - - 0.93 61.30 0.84 36.08 0.92 44.66 - - - - - 26.91 2.78 81.30 5.91 43.47 36.59 25.37 -

-

- - - - - - - - - 33.13 53.68 - - - - 20.62 51.28 26.20 - - ~~~ ~ Mt SSA Rg(10") ~ ~ N I M ~ , ~( 1 0 - 4 ) b a solution compositions (mM)

runno. pH HzS03(x103) HS03- Ca2+ s03'- CaS03O Na+ u (kg/m3) (m2/g) (moL"idcm2) P @m) (no./kg) 5.80 1.77 36.26 0.56 14.16 3.18 44.95 0.88 - 1.71 6.50 1.78 1.69 5.80 8.24 7.87 6.80 1.02 0.98 6.50 1.83 1.70 6.00 5.26 4.72 6.20 3.43 3.15 6.20 3.31 3.30 6.20 3.31 3.07 6.50 1.78 1.66 6.00 5.13 4.64 6.50 1.75 1.61 6.80 0.98 0.93 6.20 3.32 3.13 6.00 13.12 12.83 35.32 36.24 34.87 37.19 35.77 37.20 36.14 37.19 35.19 37.19 34.02 37.19 34.78 36.24 33.86 36.24 34.28 36.25 34.34 36.24 33.47 36.24 33.83 35.64 34.43 36.24 34.73 76.23 75.59 0.16 0.57 0.16 1.19 1.20 0.26 0.06 0.42 0.19 0.90 0.63 0.67 0.38 0.91 0.48 0.91 0.40 0.57 0.27 1.23 0.65 0.56 0.34 0.36 0.07 0.91 0.32 0.90 0.34 13.67 14.22 13.52 2.63 2.51 32.21 31.03 14.59 13.61 4.22 3.78 6.89 6.34 6.65 6.11 6.65 6.19 14.22 13.27 4.11 0.72 14.03 12.86 30.97 2.96 6.68 6.31 10.38 10.19 0.87 3.18 0.86 1.61 1.58 2.53 0.56 2.38 1.07 1.89 1.25 2.12 1.16 2.84 1.44 2.84 1.23 3.18 1.44 2.52 1.27 3.19 1.87 3.31 0.65 2.83 0.99 2.84 1.07 43.85 46.87 46.01 39.96 38.98 47.10 46.22 45.32 43.70 39.94 37.73 43.54 41.66 39.97 38.27 39.96 38.57 47.01 45.37 40.12 37.98 39.94 38.14 56.02 53.63 41.99 40.82 86.03 81.74 0.50 0.15 1.32 - 0.20 0.39 0.64 - 0.62 0.05 1.06 - 0.31 0.99 - 0.34 0.27 0.77 - 0.44 0.23 0.88 - 0.46 0.25 1.17 - 0.54 0.32 1.21 - 0.43 0.34 1.30 - 0.55 0.33 1.04 - 0.44 0.29 1.30 - 0.77 0.30 1.36 - 0.05 0.43 1.17 - 0.28 0.36 1.18 - 0.34 0.38 -

a L 4 , 3 = JzL4n(L) dL/GL3n(L) dL which was evaluated by the numerical integration. N = J;n(L) dL which was evaluated by the numerical integration.

electrical charge on the crystal surface. At higher pH,

more HS03- ions are shifted t o

sCh2-,

thus giving a

higher relative supersaturation and reducing the amount

of HSO3- adsorbed on the crystal surface. The solutes

higher in supersaturation would induce more nuclei

which would give the ions more chances t o collide with

each other. Subsequently, the collision between crystals may begin t o create agglomerates, thus yielding more large agglomerates, because the electrical charge is neutralized with a decrease in calcium ion. Further evidence about the degree of agglomeration is that the L4,3, mass weight mean size, increased with decreasing NIMt, particle numbers per unit product of solid, as shown in Figure 8. The small particle numbers with a

large mean particle size, L4,3, were due to the ag-

glomeration of crystals (Hartel et al., 1986; Budz et al., 1987).

The addition of EDTA was found to be a factor that

influenced the CSD. Figure 6 illustrates the effect of

EDTA on the CSD at the same pH and initial solution concentration. A bimodal CSD was observed as the

concentration of EDTA increased. On the other hand,

the ratio NIMt increased with increasing EDTA as indicated in Figure 9. This evidence shows that the degree of agglomeration is attenuated by the addition of EDTA. Theoretically, one EDTA molecule chelates one calcium ion to reduce the free calcium ion in the

solution and thus to decrease the supersaturation.

Another possible reason is that the adsorption of anionic ion (EDTA) on the positively charged surfaces of calcium sulfite crystals affects the electrical potential of the salt nuclei. Once the nuclei are brought into contact by collision, the adsorbed EDTA might reduce the agglomeration rate by altering the electrical double layer (Dirksen and Ring, 1991).

n Y CSI \ 0 C v n

7

0

-

W c

z

\ Z 7 0 1

\

70

-

were calculated from the titration curves, by example,

shown in Figure 4. The titration curves in Figure 4 are

almost linear in the second region. The slopes obtained

for curves A, B, and C in the second region are 0.075,

0.036, and 0.034 mumin, respectively. These values

together with the values off and c b can be utilized to

calculate the molar growth rates using eq 16. Then, the molar growth rates of crystals per unit surface area of crystals, calculated by eq 17, are summarized in Table

(9)

Ind. Eng. Chem. Res., Vol. 34, No. 4,1995 1349 VzH20 at low supersaturation obeyed the parabolic rate

law, which is the same as that of many sparingly soluble

substances, including calcium carbonate, gypsum, calcium fluorite, and barium sulfate (Nielsen, 1984). A different result was reported by Ottmers (1974) and Phillips (1978) who found that the linear rate law was

observed for the crystal growth of CaSO&HzO. The

BCF theory states that the linear rate law occurs at higher relative supersaturation, while the parabolic rate

law occurs in most cases of lower relative supersatura-

tion. The different rate laws obtained in this work and

others may be due to different techniques and reactants

utilized in the experiments to determine the growth rate

data. 1 00

1

90

n

z

80 70 \ 0 C

-

60 O

Y-

s

c v \

z

/

O/

/6

/

01 1 I 1 I I

Conc.

of EDTA (mM)

0.0

0.5

1.0 1.5' 2.0 2.5

3.0

Figure 9. Effect of EDTA on the degree of agglomeration: 0 , TSO

= 80 mM and TCA = 3.75 mM; 0 , TSO = 40 mM and TCA = 3.75

mM. -7.0

-8.0

am

-9.0 0

-

-1 0.0 - 1 1

.o

-

This work 0

oono Tseng & Rochelle (1986)

0 0

0

8 -0.6

-0.4 -0.2 0.0 0.2

log

Of

Figure 10. Overall growth rate of calcium sulfite hemihydrate crystals at 25 "C: A, this work; 0, recalculated data from Figure

6 of Tseng and Rochelle (1986).

3. For sparingly soluble salts, the growth rate is usually

expressed as follows:

R,

=

kS

(21)

Generally, the growth data of calcium sulfite hemihy-

drate crystals are plotted as In R, vs In a. In order to

compare the data obtained from Tseng and Rochelle (19861, recalculation of supersaturation is required. The growth rate data of both works were plotted in Figure

10. In the supersaturation range under investigation,

a between 0.05 and 0.77, the linear plot gave n = 2.26

and lz = 3.68 x moVmin cm2. The data are quite

close to the values reported by Tseng and Rochelle (1986) in the low supersaturation range, where it obeys a parabolic rate law. The growth mechanism of CaS03.

Conclusion

The semibatch precipitation of calcium sulfite hemi-

hydrate from aqueous solution is successfully conducted

in a pH-stat apparatus t o study the degree of ag-

glomeration and crystal growth of calcium sulfite hemihydrate. The precipitates were platelets and their

agglomerates in all runs under the operating conditions

listed in Table 1. The crystal growth kinetics was found

to obey the parabolic rate law, in agreement with BCF

theory at lower relative supersaturation. The effect of relative supersaturation and magma density on the degree of agglomeration is not significant at the final stage of operation, while the pH factor has a significant

effect. Besides, the addition of EDTA is also a factor

that affects the degree of agglomeration.

Nomenclature

A = area, m2

cb

= concentration of Ca(OH)2 added from burette,

f = constant in eq 16

fi

= constant defined in Appendix A

I = ionic strength, kmoVm3

IP = ionic product

J = molar growth rate, mol/min

lz = growth rate constant, mol/min cm2

Ki = stability constant in Table 2

Ksp = solubility product

L4,3 = mass weight mean size, pm

Mt = magma density, kg/m3

n = population density, no./pm m3

nb = molar number of Ca(OH)2 added from burette,

N = total particle numbers, n0./m3

R,

= growth rate per unit area, mol/min cm2

SSA = specific surface area, m2/g

TCA = total calcium ion concentration, kmol/m3

TCI = total chloride ion concentration, km01/m3

TNA = total sodium ion concentration, km01/m3

TSO = total sulfite ion concentration, km01/m3

t = time, min

V = volume of solution, m3

VI, = volume of Ca(OH)2 added from burette, mL

yz = activity coefficient of an ion with charge 2

2 = charge number

km01/m3

mol

Appendix A

Derivation of Eq 17 for Estimating Crystal Growth Rate. From eqs 7-9 in Table 2, the following

(10)

1360 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 relationships are obtained:

2 [ ~ a 2 + ~ [ ~ ~ : - ~

[ C ~ S O ~ ~ I = y2 (A-3)

KO0

We substitute the above equations into eq 3 to give

where

and

The growth rate of calcium sulfite hemihydrate is equal

to the consumption of

TSO:

d[CaS03(s)l

-

d[TSO] dt dt d[CaSO,'] + d[HzS031 d[HS03-l

+

-

+ dt - dt dt

Equation A-7 is substituted into eq 15 to give

-

1 dn,

-

d[Ca2+] d[CaSO:l d[CaOH+l

V

dt dt + dt + dt From eq 10, we have [Cazfl[OH-1

+

-yz (A-9) [CaOH

1 -

K5

Then, [CaS03°1, [S032-l, [H2S031, and [CaOH+l in eq

A-8 were eliminated by using eqs A-1-A-3 and A-9. The

resultant equation is

1 dn, dLHSO3-I d[Ca2+l (A-10)

V dt = f 3 dt

+

f 4 3 -

Y12rH+l

2[CaZ+b,2) (A-ll)

f 3 =

(

1+-

KO0 KO0

and

The electroneutrality of nonreacting components in the crystallizer is

d[S03'-1 d[HSOJ d[CaZf] + d[CaOH+]

dt

+

dt dt dt

When eqs A-2 and A-9 are substituted into eq A-13, the following relationship is obtained:

= 2 -(A-13) (A-14) d[HSO,-I d[CaZf] dt = f 5 7 where

Substituting eq A-14 into eqs A-4 and A-10 to eliminate

d[HSOs-Ydt, we obtain the following equations:

and

V

dt

Compare eqs A-16 and A-17 to give

dnb

J=f-

dt where f=- flf5

+

fz fd5

+

f4

The molar growth rate per unit area is E = - =

J

f d n b

-

g A A d t (A-18) (A-19) (A-20) Appendix

B

Calculation of

KP

of CaSO&HzO at 298 K. The solubility product of calcium sulfite hemihydrate crystals was obtained from thermal data reported by Brewer. The reaction equation is

(W298/RT) (B-2) where

(11)

Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1351

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Received for review March 28, 1994

Revised manuscript received December 30, 1994 Accepted J a n u a r y 13, 1995@

IE940207Z @ Abstract published i n Advance A C S Abstracts, March 15, 1995.