Ind. Eng. C h e m . Res. 1990, 29, 867-875
867
Regression. In Statistical Package for Social Sciences, 2nd ed.; Nie, H. N., et al., Eds.; McGraw-Hill: New York, 1975.
Prediction of P205in the Product, Mining and Plant Control. Int. J . Min. Proc. 1985, 15, 219-230. Kim, J. Factor Analysis. In Statistical Package for Social Sciences,
Received for review January 15, 1990 Accepted January 18, 1990
2nd ed.; Nie, H. N., et al., Eds.; McGraw-Hill: New York, 1975. Kim, J.; Kohout, P. J. Multiple Regression Analysis. Sub Program
Filterability of Gypsum Crystallized in Phosphoric Acid Solution in the Presence of Ionic Impurities David Hasson* and Jonas Addai-Mensah Department of Chemical Engineering, Technion-Israel
Institute of Technology, Haifa 32000, Israel
John Metcalfe I M I ( T A M I ) , Institute for Research and Development Ltd., P.O. Box 313, Haifa 31002, Israel
There is poor understanding of the effect of phosphate rock impurities on the filtration characteristics of the gypsum slurry formed during H3P04production by the wet process, The present work studies the effects of Fe3+ and A13+ impurities on the filterability of gypsum produced in clean phosphoric acid solution. It is found that Fe3+ and A13+ exert similar effects a t the same molar concentration. At low concentrations, the impurities reduce the specific resistance of the filter cake and increase the average size of the gypsum crystals. At high impurity concentrations, the specific resistance of the filter cake increases and the average crystal size decreases. This result could perhaps explain the conflicting reports in the literature relating to the influence of Fe3+ and A13+ impurities on filterability of the gypsum slurry. habit. However, an increase of A1203concentration from 0.70% to 0.81% by weight showed a considerable reduction in crystal size. This phenomenon was more pronounced in a solution of 27.7% P,O, than in a solution of 32.3%
A difficulty encountered in wet process phosphoric acid production arises due to the presence of small but significant amounts of impurities in the phosphate rock, such as Fe3+, A13+, Mg2+,silicofluorides, and organic matter. These impurities can have large effects on the filterability of the gypsum crystals produced in the process, reducing the filtration capacity by a factor of as much as 4. Despite considerable work, carried out mostly with simulated phosphate rock solution, there is very little conclusive evidence regarding the effect of specific impurities on the filterability of calcium sulfate crystallizing in the system (Gilbert, 1966). Background information on the effect of single impurities could assist in interpreting plants results, but such data are sparse. The general objective of this research was to gain some basic insight on the effect of a single impurity, either Fe3+ or A13+,on calcium sulfate crystallizing in pure phosphoric acid solution. The effect of impurity concentration on both crystal size distribution and filter cake specific resistance was studied. Given the complexity of the phenomena studied, one of the aims of this research was to find out whether consistent results could be extracted from a relatively simple experimental system, enabling a systematic attack on the impurity effect problem.
p’2°5*
Adami and Ridge (1968) studied the properties of gypsum (CaS04.2H20)formed by hydration of the hemihydrate (CaSO4-0.5Hz0)in a medium containing 29.4% PzO, at temperatures between 35 and 60 O C . Under these experimental conditions, A1203and Fe203showed a clear beneficial effect. Instead of the poorly filterable elongated needles (500 pm long, 30 Fm wide) formed in a pure system, addition of 2% each of A1203,Fe203,and H F resulted in the crystallization of good filtration quality equiaxial grains (200 X 100 pm). In a pilot-plant study of a phosphate rock containing about 1% Si02, 0.04% Al, 0.21 % Fe203,0.53% MgO, and 2.55% F, Orenga (1983) examined the effect of the addition of an undisclosed amount of Alz03, He found an adverse effect. The filtration rate was significantly reduced (from 8.9 to 7.4 tons of P20,/(m2 day)). The A1203 shortened but did not widen the gypsum needles (length-to-width ratio reduced from 10:2 to 6:2). The maximum crystal size was reduced from 1400 to 600 km. In summarizing Fison’s experience on the effect of impurities, Robinson (1978) enumerates, among other desirable features of an “ideal” phosphate rock, the necessity of having “sufficient cationic impurities to produce rhombic-shaped dihydrate crystals”. However, he adds that “to achieve real progress in the future, the effects of impurities on crystal habit and growth need to be understood and quantified.” Summarizing such literature results, Becker’s (1983) monograph suggests that, in general, the presence of aluminum in phosphoric acid production has a positive influence on the crystal habitus, size, and, consequently, filterability. With regard to the presence of iron, Becker (1983) concludes that “nothing conclusive can be stated
Previous Work Gilbert’s (1966) photomicrographical study of gypsum crystallization in phosphoric acid demonstrates that commonly occurring impurities in phosphate rock can exert a major effect on the crystal size and habit and thus influence the filterability of the gypsum crystallized. Of special interest to this work are his results on the effects of iron and aluminum impurities on gypsum crystallization at 70 “ C . An increase of Fe203concentration from 0.94% to 1.03% by weight had no effect on the crystal size and
* To whom correspondence should be addressed. 0888-5885/90/2629-0867$02.50/0
~
1990 American Chemical Societv
868 Ind. Eng. Chem. Res., Vol. 29. No. 5, 1990 Table I. Composition of Feed and Product Streams H2SO4 mol/I, w t 70 0.95 5.50
acid feed” calcium phosphate feed
H2S04 -___
total phosphate feed filtrate solution
mol/L 0.41 0.02
wt % 2.85 0.1
H3PO* Ca(H2P04h H*O mol/L wt % mol/L wt YO mol/L wt 70 density, g/cm3 9.88 57.30 34.80 37.10 1.69* 4.29 35.3 0.72 14.10 33.90 50.50 1.19 P205 dissolved Ca2+ ~H*O Fe3+ ~ 1 3 + mol/L wt 70 mol/L wt % mol/L wt YO mol/L wt 70 mol/L wt % 3.35 33.8 0.41 1.16 34.10 43.6 0-0.38 0-1.5 0-0.58 0-1.10 3.81 38.5 0.05 0.135 3.14 46.86 0 4 . 3 5 0-1.4 0-0.54 0-1.04
“Acid feed: 10-12 cm3/min. Calcium phosphate feed: 12-14 cm3/min. Total feed to reactor: 22-26 cm3/min. *Increased up to 1.75 g/cm3 in the presence of impurities
:1--3---
h
-
I
H L E I I I I l
L
j ‘2
1’
L-
J
dP,---Y
Figure 1. Experimental apparatus. SV, sulfuric acid feed (5-L glass vessel); CV, calcium phosphate feed (5-L glass vessel); H, thermostatic magnetic stirring hot plate; FP, variable-speed Masterflex peristaltic pump; FI, rotameter; C, 1-L glass vessel; A, agitator, 2100 rpm; W, thermostatically controlled water bath; F, Buchner filter, sintered glass covered with No. 1 Whatman filter paper, 3.0-cm i.d., 26.0 cm long; OV, overflow; FR, filtrate receiver (1-L graduated glass vessel); T, sodium hydroxide solution trap; M, mercury manometer; VP, Edward’s vacuum pump.
about its influence on crystallization.” In principle, impurities exert their effect on crystal size and habit through their influence on kinetics of nucleation and growth. A recognized approach for studying such kinetics is the population balance technique applied to MSMPR crystallizers. However, this has been applied only to a limited extent to the phosphoric acid impurity problem. Sikdar et al. (1980) using this approach have been able to extract convincing evidence on the effect of excess sulfate concentration on the crystal size of calcium sulfate hemihydrate.
Experimental Section A schematic diagram of the experimental system is shown in Figure 1. Two feeds, consisting of an acidified calcium phosphate solution and a sulfuric acid solution, were continuously metered to a 1-L glass vessel, acting as a reactor and as an MSMPR crystallizer. The reacting streams caused crystallization of gypsum, CaS0,.2H20. A funnel-shaped overflow (30-mm i.d.) maintained a reaction volume of 580 cm3. The filterability of the crystallized gypsum was examined by batch constantvacuum filtration of the slurry flowing out of the crystallizer. Reagent-grade materials were used. The impurity was added with the sulfuric acid feed. Ferric ion impurity was obtained by dissolving Fe2(S0J3.7H20in the sulfuric acid
feed solution. Similarly, aluminum impurity was obtained by dissolving A&(S04),.16H20 in the sulfuric acid feed. Table I summarizes the material balance of the system. All runs were carried out under the following nominally identical conditions in the reaction-crystallization volume: residence time, T = 24 min; temperature, T = 40 “C; phosphoric acid concentration = 38.5% by weight P205; gypsum slurry concentration = 4.7% by weight (70 g/L filtrate). Gypsum solubilities were evaluated by measuring calcium concentrations in filtrates allowed to stand overnight. The values obtained were substantially constant for all runs: 0.04 mol/L or 0.12% by weight. The typical residual calcium concentration in the fresh filtrate was 0.05 mol/L or 0.135% by weight. Thus, since the calcium feed concentration was 1.16% by weight (0.41 mol/L), the conversion in the reaction-crystallization volume was high, amounting to 95-9870. In the two systematic series of experiments carried out, the Fe3+impurity content was varied from 0 to 0.35 mol/L crystallizer solution (1.5% by weight based on crystallizer slurry) and the A13+ content was varied from 0 to 0.54 mol/L (1.1% by weight based on slurry). The technique adopted to ensure satisfactory reproducibility was as follows. A run was started by feeding pure reagents containing no impurity, the crystallizer containing the slurry of the previous run. An experiment consisted of four parts: (a) No impurity was dosed for 2-2.5 h (6 residence times). (b) Impurity was dosed through the sulfuric acid feed for 2-2.5 h. (c) No impurity was dosed for 2-2.5 h. (d) Impurity was dosed through the sulfuric acid feed for 2-2.5 h. At the end of each part of the experiment, prior to changing the feeds, a filtration test was carried out. The filtration test consisted of measuring the filtrate volume, at a vacuum of 15 mmHg, as a function of time (in steps of 10 cm3 until a volume of 250 cm3 was collected, about 20 min). Except in a few cases, reproducibility between duplicate runs was excellent, well within 5%. Plots of reciprocal flow rate t / V versus filtrate volume V gave good straight lines in all cases. The specific cake resistance a (m/ kg) was evaluated as usual, from the slope of such lines. The following analyses were made to check the material balance and characterize the physical properties of the slurry (Addai-Mensah, 1987): calcium content in feed and filtrate by EDTA titration; acidity and P205content in feeds and filtrate by strong base titration using mixed indicator detection; Fe3+and AP+ in acid feed and filtrate by atomic absorption; viscosity of the filtrate using a Canon-Fenske viscometer; densities of filtrate and of gypsum crystals by pyknometry; volume shape factor of crystals by the sieve method (Mullin, 1972). The chemical composition of gypsum filter cake samples was determined by EDS and the crystal morphology examined by SEM (Joel tJSM at kV = 20/25). The crystal
Ind. Eng. Chem. Res., Vol. 29, No. 5, 1990 869 I
1.45
I
I
I
I
I
I I
i 1
I .& ~
~
~
~
I
I
,
I
T ~
I
i
I
I 4-
0
0 1
0:
0 3
0.
I m o u r i t y C o n c e n t r a t i o n , nole/e
1 3
3
0 6
0.3
0.5
O.L
0.6
solution
Figure 3. Effect of impurity concentration on the density of the phosphoric acid solution.
size distribution was measured by using a Malvern laser diffraction particle sizer, dispersing the cake in a saturated CaS04.2H20solution with a 5-min ultrasonic pretreatment.
35 I
,
I
, a
30
Results The two systematic series of experiments, in which all the parameters except impurity concentration were held constant, showed the following effects of the impurity. Solution Density and Viscosity. It is well established that ionic impurities have a strong influence on the viscosity and density of phosphoric acid (Slack, 1968) for the following reason. In orthophosphoric acid, neighboring PO4 tetrahedra are held together by hydrogen bonds. Water tetrahedra, which are considerably larger, cause distortion of the PO4 lattice structure and reduce its rigidity. Hence, the solution viscosity and density are reduced. Ions such as A13+ and Fe3+polarize the surrounding molecules, which strengthens the hydrogen bonds and thus stabilizes the lattice structure. Therefore, an increase in viscosity and density is to be expected as the concentration of A13+ or Fe3+ increases. Figure 2, which shows the measured change in viscosity with impurity concentration, is in good agreement with the correlation given in Slack's (1968) book. The viscosity is doubled by the addition of about 0.5 mol/L of the impurity. Figure 3 shows the measured change in density with impurity concentration. The data show a somewhat larger change in density with impurity concentration than expected from the linear correlation in Slack's (1968) book and do not conform to a linear dependency. The change in density due to the presence of 0.5 mol/L impurity is about 5 % . Specific Resistance of Gypsum Cake. The most significant result in this study is given in Figure 4, which shows the change in the specific resistance of the gypsum cake with impurity concentration. It can be seen that there are consistent systematic effects due to the impurities.
0.2
I m p u r i t y concentration, nole/e
solution
Figure 2. Effect of impurity concentration on the viscosity of the phosphoric acid solution.
0.1
1
-I I
5-
--
0
01
:7icur
02
t y c31certrat
03
2 - ,
04
no'e
05
06
so ~ * 1 3 n
Figure 4. Effect of impurity concentration on the specific cake resistance of gypsum.
These effects are similar for both A13+ and Fe3+when the impurity concentrations are expressed on a molar basis. The striking feature is that the specific resistance decreases with increasing impurity concentration at low impurity levels but increases with augmenting impurity concentration at high impurity levels. The minimum specific
870 Ind. Eng. Chem. Res., Vol. 29, NO. 5 , 1990 Table 11. EDS Analysis of Gypsum Crystals impurity Fe3+ or Ai3+ P mol/L wt '70 atom wt atom wt solution slurrv % '70 o/c % 0 5.2 4.49 0 3.27 I) 2.84 0 Fe3+ 6.99 0.04 0.06 6.02 0.63 0.275 2.78 0.14 0.22 2.40 0.095 0.41 0.10 0.15 6.88 5.94 0.41 0.095 7.98 0.40 0.62 6.86 0.128 0.55 9.49 0.128 0.32 0.51 8.25 0.55 0.71 1.10 6.88 5.91 1.1 0.257 0 257 1.00 1.59 19.6 16.74 1.1
S atom
Ca ?k imp preciritated
atom Ca/ atom imp
atom S/ atom P 8.8 15.3
56.53 55.78 54.71 56.39 51.86 54.90 46.02
1.1 2.7 1.8 5.6 4.6 5.0 7.2
1270 359 490 127 145 70 41
6 16.8 6.4 5.1 4.6 6.2 2.0
51.99 56.53 58.92
4.6 4.8
88 75
atom
wt
'70
wt %
%
45.72 49.95
40.78 44.76
49.08 46.77
'70 54.73 52.39
42.08 46.84 43.95 40.75 43.92 42.92 39.33
37.39 41.60 39.20 36.13 39.39 38.09 35.65
50.89 50.24 49.08 50.87 46.27 49.49 40.61
45.63 39.91 37.31
40.99 35.0 33.04
46.30 50.79 53.22
~ 1 3 +
0.132 0.230 0.273
0.275 0.48 0.55
0.58 0.71
8.07 9.31 8.76
0.44 0.53
7.02 8.03 7.51
/
m p i r t l c0nientr.t
-
-
a n ,mole
Figure 5. Effect of impurity concentration on the relative filtration time.
resistance is obtained in the range 0.15-0.25 mol/L impurity concentration. As the viscosity of the solution increases with the impurity concentration, this will reduce the filtration rate at a constant specific cake resistance. The net effect of the impurity concentration on filtration rate, and hence on filtration time, is represented by the product of specific cake resistance and viscosity. Figure 5 shows the variation of (cup)1 relative to that of the pure solution, (cup),,, as a function of impurity concentration. It represents essentially the effect of impurity concentration on the relative filtration times, tl/to. It is seen that the filtration time is initially reduced, reaching almost one-half that of pure solution at impurity levels around 0.15-0.25 mol/L. At the highest impurity levels, filtration time is more than 3 times longer. It is interesting to note that, in many cases, the Fe203 and Alto3 impurities in phosphate rocks are around 1% . Under typical conditions in wet process phosphoric acid reactors, this would lead to impurity levels in solution in the region close to the minimum of the curves in Figure 5. Thus, the apparently conflicting reports of the effect of the addition of Fe3+and AP+ to industrial phosphoric acid reactors may perhaps depend on whether the rock used gives an impurity concentration level that is below or above this minimum. In order to obtain supporting evidence on the effect of the impurity on the specific cake resistance and to eluci-
5.65 4.3 4.3
date the mechanism of the phenomena, additional examinations of the gypsum crystals were carried out. Information on the chemical composition of the crystals was obtained to examine the presence of impurities in the crysuds. Crystai shape factors and crystal size distributions were measured as they determine the specific cake resistance. Chemical Composition of the GyLsum Filter Cake. Table I1 presents the concentrations of Ca, S, P, Fe, and A1 measured in the gypsum crystals for each experiment using the technique of electron-dispersive spectroscopy (EDS). The technique has a low relative accuracy, and this is seen in the scatter in the data and the lack of an exact ionic balance. However, several trends can be discerned. The concentration of the impurity in the gypsum increases as the concentration of the impurity in the solution increases, although the amount absorbed in the crystal is small enough to leave the concentration in solution almost unchanged. The data show that the fractional concentration of the impurity in the crystal is not constant but increases with an increase of the impurity concentration in solution. Also the data indicate that the amount of coprecipitated phosphate increases as the impurity concentration in the solution increases. Crystal Morphology. Filtration characteristics are, in principle, governed by the size and shape of the particles since these parameters determine the filter cake porosity, but quantification is difficult. In the case of phosphate gypsum, it would appear that thick rhombic crystals or agglomerates give better filtration characteristics than thin plates or needles (Becker, 1983; Slack, 1968). SEM photographs of the gypsum crystals obtained in the presence of differing amounts of impurities are shown in Figures 6 and 7. Numerous such photographs give evidence that Fe3+and A13+impurities have a clear effect on the size, shape, and thickness of the crystals. The morphclogical observations of this study were in general agreement with those reported by Sarig et al. (1981) and Budz et al. (1986), who examined the effect of A13+ on gypsum morphology in an aqueous solution not containing phosphoric acid. Table 111shows the effect of impurities on the volume shape factor as measured by the sieve method. It is seen that the shape factor of 1.4 for gypsum produced from pure solution is reduced to a value in the range 0.9-1.2, in the presence of impurities. Since the sieve method characterizes the second linear dimension of the crystals, this indicates that Fe3+ and A13+ impurities tend to improve the thickness-to-length ratio of the crystals. Table I11 also shows that the change in shape is accompanied by a change in crystal density. The measured
Ind. Eng. Chem. Res., Vol. 29, No. 5, 1990 871 Table 111. Crystal Size Distribution and Crystal Properties at Different Levels of Impurity Concentration imp concn, mol/L 0
LIo,C Irm
L50: Pm
L90,C Irm
L3,2?
L3.2,b
Irm
Irm
span
crystaI density, g/cm3
shape factor, fv
3.1 3.8
10.5 13.9
40.1 53.4
7.3 8.7
9 10.8
3.47 3.76
2.316 2.316
1.41
0.06 0.10 0.13 0.26 0.35
5.2 5.3 6.4 4.8 5.9
18.7 19.1 20.0 21.4 25.8
62.2 80.2 54.7 84.6 132.6
11.2 11.5 12.9 11.3 13.6
13.7 14.2 14.9 15.5 17.3
3.05 3.92 2.42 3.74 4.92
2.375 2.393 2.4 15 2.470 2.496
1.21 1.22 0.9s 0.89 0.86
0.13 0.20 0.21 0.23 0.27 0.54
5.0
20.5
96.1
11.5
13.5
4.45
6.8 7.4 5.3
24.3 22.4 15.2
79.2 63.6 34.1
14.7 15.1 10.2
17.6 17.3 13.1
2.98 2.51 1.89
2.363 2.390 2.397 2.410 2.460 2.501
1.12 1.28 1.02 1.21 1.12 1.20
Fe3+
~13+
a Surface mean diameter numerically evaluated according to eq 2. This value is plotted in Figures 8 and 9. bSurface mean diameter evaluated analytically from eq A13, assuming a bilinear distribution. Lm, and Lw are crystal sizes a t lo%, 50%, and 90% cumulative mass distribution, respectively.
a.
O.OM
Fe+3
b.
O.OM
Fe”
c.
*
0.06M
Fe
d.
0.10M
v- .
_
Fef3
AI +3 AI +3 AI +3
e.
0.13rq
f.
~ e ’ ’
0.261”
re’’
Figure 6. Effect of Fe3+ impurity concentration on gypsum habit. Figure 7. Effect of A13+ impurity concentration on gypsum habit.
crystal density of 2.32 g/cm3 in a pure solution agrees well with the literature value (Becker, 1983). It is seen that the crystal density systematically increases with the impurity concentration, up to a value of 2.5 g/cm3. Size Distribution. According to the Kozeny-Carman equation, the specific resistance of the filter cake is given by
k f 2 ( 1 - t) (1)
a= ~ ~ c ~ L 3 , 2 ~
where f is the ratio of area to volume shape factor, t is the
cake porosity, pc is the crystal density, and surface mean diameter:
L3.2
is the
” L It is therefore expected that the influence of impurities on a should be correspondingly reflected by the effect of impurities on the surface mean diameter. Table I11 presents the data extracted from the size distribution measurements. This table displays particle
872 Ind. Eng. Chem. Res., Vol. 29, No. 5 , 1990 Table IV. Analysis of Crystal Size Distribution Data According to the Bilinear Distribution
0 G
17.3 23.4
0.35 0.58
0.10 0.12
3.6 5.1
1.828
8.809
0.063 0.095 0.128 0.257 0.351
65.0 30.9 33.8 34.3 60.0
1.53 0.79 0.76 0.79 1.78
0.23 0.14 0.16 0.16 0.23
6.6 5.6 4.7 4.9 7.7
1.770 1.630 1.853 1.809 1.404
30.7 43.0 58.0 53.4
0.84 0.79 1.49 0,75
0.14 0.20 0.23 0.18
6.0 3.9 6.5 4.2
1.523 2.268 1.622 2.967
7.6
X
lo7
0.6767
0.3101
0.987
11.775 9.196 8.802 8.932 10.870
2.3 X 5.4 X 3.1 X 3.8 X 1.7 X
lo7 lo" lo7 lo7 lo7
1.065 0.5736 0.5400 0.6356 0.9437
0.0846 0.2808 0.2383 0.2768 0.2494
1.150 0.854 0.778 0.912 1.193
9.137 8.958 10.507 12.361
5.3 X 2.3 X 4.1 X 4.2 X
lo7 lo7 lo7 lo7
0.6752 0.7963 0.5862 0.9446
0.4096 0.1982 0.1321 0.0155
1.085 0.995 0.718 0.960
Fe3+
.
AI3+ 0.132 0.230 0.270 0.540
i
-.
t
I j
________-
I
0 1
3 .
0
~ e m' n~c e n t r a t > o r , ncle
3 u t 2p
Figure 8. Variation of specific cake resistance and surface mean crystal size with Fe3+ concentration.
sizes corresponding to cumulative mass distributions of 1070,5070,and 90%. It also gives values of the surface mean diameter L3,2and of the span of the distribution. The span is defined by span =
L90% - LlO%
01
(3)
L50%
The span appears to remain constant in the case of iron impurities and to decrease in the case of aluminum. An important finding is observed in the effect of impurities on the surface mean diameter, L3,2 It is seen from Figures 8 and 9 that, except for the point with 0.35 mol/L Fe3+,the variation of surface mean diameter correlates very well with the changes in the specific resistance. The initial decrease in a is accompanied by a systematic increase in average particle size, while the subsequent increase in a at high impurity levels is accompanied by a reduction in the particle size. This result represents independent supporting evidence for the existence of an optimal impurity level, giving a minimum filtration resistance. Further analysis of the crystal size distribution data, providing values for the apparent nucleation and growth rates, is given in the Appendix.
02
03
04
05
06
-_ e "* Figure 9 Variation of specific cake resistance and surface mean crystal size with A13+ concentration. ,&
,n
e"--3-
on
&
I L
1-
Discussion This study has shown that in the low concentration range both A13+ and Fe3+ impurities seem to affect the crystal size distribution such that the average crystal size increases with impurity concentration. A t higher concentrations, the opposite trend is observed. The above trends are the result of the complex effect of the impurities on the rates of nucleation, growth, and possibly agglomeration of the precipitating crystals. Sarig and Mullin (1982) observed in an aqueous system of gypsum precipitation that A13+ increased the induction period at low concentration, signifying that the nucleation rate diminished. At high concentrations, A13+reduced the induction period, signifying that the nucleation rate increased. Their proposed explanation was based on the assumption that the retardation of the induction period was caused by fully hydrated aluminium species adsorbing on gypsum nuclei and blocking their growth, thus extending the induction period. The different effect of A13+ on the induction period a t higher concentrations was ascribed to the reduced hydration of the A13+ ions at high concentrations. In the present study, where A13+ was also observed to have a different effect at low and high concentration levels,
Ind. Eng. Chem. Res., Vol. 29, No. 5, 1990 873 Table V. Crystal Sampling from Different Zones of the Crystallizer imp concn of Llo, L,, Lgo, L3,2111 L3,Db Lc, 0.27 mol/LA13+ pm pm pm pm pm pm filter cake 6.65 20.2 55.3 13.4 17.3 32.0 top scoop 5.8 19.1 53 11.7 17.1 61.0 bottom scoop 8.4 24.8 67.8 17.0 18.5 45
span 2.41 2.47 2.39
GF:
GP;
pm/min 0.21 0.23 0.22
pm/min 0.70 1.49 0.71
no./ (gmin) 1.57 2.0 2.64
(Gr)p/
(GT)F 3.4 6.5 3.3
Surface mean diameter evaluated numerically according to eq 2. *Surface mean diameter evaluated according to eq A13, assuming a bilinear distribution. Calculated from G r assuming r = 24 min for all particle sizes.
Table VI. Kinetic Data of Calcium Sulfate Crystallization in Phosphoric Acid final slurry phase temp, P206 solids G, O C concn, wt % concn, wt % pm/min investigator crystallized 0.15-0.30 40.0 1.5/3.8 Amin and Larson (1968) hemihydrate 70 Sikdar et al. (1980) hemihydrate 70-90 40-50.0 20.0 0.05-0.20 Monaldi et al. (1982) Ben-Yosef et el. (1984) this work
gypsum gypsum gypsum
80-90 76 40
37 27/32 4.7
29.0 30.0 39.0
0.10
0.02-0.10 0.1-0.60
0.14-1.8
impurity
Bo,no./(g min) 1 X 106-1 X lo7 1 X 106-5 X lo7
3.0 X lo6 3 X 10'-3 X lo5 8 X lo7-13 X lo7 2 x 107-5 X lo7
1-3% So -: excess enhances B o phosphate rock phosphate rock no impurity with Fe3+,A13+
systematic approach used in this study, it should be possible to provide a hitherto lacking framework for assessing the effects of various impurities on gypsum filterability. 108
c
Acknowledgment This work forms part of a Master's Dissertation of J. A.M. Thanks are due to the Technion V.P.R. Fund-E. & J. Bishop Research Fund for their support.
Nomenclature .-
104
loo
t
a'
B o = nucleation rate, no./(g of crystals min) f = ratio, f A / f V
1 20
40
,
1
60
a0
100
Crystal size, t :uml
Figure 10. Typical result of semilogarithmic plot of population density data.
the above explanation seems unlikely, due to the presence of a concentrated phosphoric acid solution. Clearly, the mechanisms by which aluminum and iron affect gypsum crystallization are still poorly understood and require further investigation.
Conclusions This study examined the effect of both Fe3+ and A13+ impurities on gypsum filterability in a simple model system, and it was found that consistent systematic results can be observed. T h e effects of the impurities on the filterability of the gypsum were found to be remarkably different in the low and high impurity ranges. In the low impurity range, both A13+ and Fe3+ act to improve the filterability of the gypsum, while in the high concentration range the filterability is reduced. The PzO,losses in the crystal increase systematically with the impurity concentration. These results could perhaps explain the conflicting reports in the literature on whether Fe3+and A13+impurities improve the filterability of gypsum and Pz05recovery or whether they have a deleterious effect. By extending the
fA = area shape factor, dimensionless fv = volume shape factor, dimensionless G = crystal growth rate, pm/min k = constant in Kozeny-Carman equation, dimensionless L = size of crystal, pm L3,2= surface mean diameter, pm L, = cut size in bilinear distribution, pm N = nuclei formed per unit mass crystals per unit volume n = population density of crystals, no./(g of crystals pm) no = population density of embryo-size crystals, no./(g of crystals pm) 7" = temperature, "C t = time, min V = volume, cm3 W = cumulative undersize mass of crystals per unit volume slurry W , = total mass of crystals per unit volume of slurry x = L / G T , dimensionless size parameter Greek Letters cy = specific resistance of filter cake, m/kg t = porosity of filter cake, dimensionless g = viscosity, CP p = solution density, g/cm3 pc = crystal density, g/cm3 T = mean residence time, min Subscripts
F = fine particles P = coarse particles
Appendix. Analysis of the Size Distribution Data It has been shown that the change of average crystal size with impurity concentration corresponds well to the trend predicted by the effect of impurity on the filter cake resistance. It was therefore of interest to analyze further the
874 Ind. Eng. Chem. Res.. Vol. 29. No. 5 . 1990
crystal size distribution data by the population balance method as applied by previous workers (Amin and Larson, 1968; Sikdar et al., 1980; Monaldi et al., 1982; Ben-Yosef et al., 1984). The usual simplifying assumptions made are size-independent growth, absence of attrition and agglomeration processes, and ideal MSMPR conditions. With these assumptions, the number distribution of the crystals is given by (Mullin. 1972) dlnn dL
1 GT
where n = dN/dL is the population density of particles of size L . Equation A1 predicts a linear relation between In n and L, having a slope of 1/GT. The population density distribution, n(L), is calculated from measurements of the cumulative undersize mass distribution by n=-
1
d(W/WT)
f”PC3
(A21
dL
Figure 10 shows a typical result obtained in this work.
It is seen that the data do not fit a line of constant slope. The data can, however, be approximated by two straight lines of different slopes, intersecting a t cut size L,. The
(A9j
For a perfect fit of the experimental points to the assumed bilinear distribution, the following material balance condition would be met exactly:
w?
-WF +-=1 WT
(A101
WT
The experimental data were analyzed by choosing several values of Lc, calculating no, (GT)F,and ( C T )for ~ each case by linear regression of the two lines, and evaluating W,/ W , and Wpl W , from eq A8 and A9. The values of L, and the ensuing parameters were those giving the minimum deviation from the mass balance equation, (A10). Table IV presents the results of the above analysis of the crystal size distributions obtained with various impurity concentrations. It is seen that the material balance constraint of eq A10 holds reasonably well, within 20%, thus justifying the use of the bilinear approximation. By use of the distribution parameters ( G T ) ~(G7Ip, , and L,, the surface mean diameters can be calculated as follows. For the range 0 < L < L,, holding the mass fraction wF/
WT,
results of this study were analyzed accordingly. Integration of eq A1 gives the following population density distributions for particles below and above size L,. respectively: For the size range L, < L < L,, holding the mass fraction WPlW,,
where The average surface mean diamter for the whole distribution is Thus, the semilogarithmic plot on n versus L allows evaluation of the parameters L,, ( G T ) ~( G, T ) ~and , no. The nucleation rate is given by
B o = nOGF
(A61
The validity of the approximation of the bilinear distribution defined above can be checked by the following material balance. The fractional mass of particles in the finer size range is given by
and the fractional mass in the coarser size range is given by
where
(A13) Values of the surface mean diameters calculated according to eq A13 are presented in Table 111. It is seen that the mean diameters based on the bilinear distribution have somewhat higher values than those evaluated by numerical integration. However, they show the same trends of the effect of impurity on mean particle size. One possible reason for the occurrence of the bilinear distribution could be the occurrence of classification in the crystallization vessel. In order to examine this possibility, an experiment was carried out where the crystal size distribution was measured from slurry samples scooped from the top and the bottom of the crystallization vessel and compared with the distribution obtained €om a filter cake sample. These results are shown in Table V. It can be
Ind. Eng. Chem. Res. 1990,29, 875-882
seen that there is no marked difference in the various crystal size distributions. The reason for the deviation of the data from the unilinear distribution predicted by the ideal MSMPR model is not clear. Such deviations are often observed in analyzing MSMPR data and have been explained as indicative of the occurrence of agglomeration (Budz et al., 1986) or size-dependent growth (Jancic and Garside, 1976). Table VI summarizes all published data on the apparent kinetics of gypsum and hemihydrate crystallization, derived assuming ideal MSMPR conditions (unilinear distribution). The results obtained in this study using a bilinear distribution yield somewhat larger values for the apparent growth rate and nucleation rate. Registry No. PO(OH)3, 7664-38-2; Fe3+, 20074-52-6; A P , 22537-23-1; gypsum, 13397-24-5.
Literature Cited Adami, A.; Ridge, M. J. Observations on Calcium Sulphate Dihydrate Formed in Media Rich in Phosphoric Acid: I. Precipitation of Calcium Sulphate Dihydrate. J . Appl. Chem. 1968, 18, 361-365. Addai-Mensah, J. Effect of Impurities of the Filterability of Gypsum Formed in Phosphoric Acid Solution. MSc. Dissertation, Technion, Haifa, Israel, 1987. Amin, A. B.; Larson, M. A. Crystallization of Calcium Sulfate from Phosphoric Acid. Ind. Eng. Chem. Process Des. Deu. 1968, 7, 133-137. Becker, P. Phosphates and Phosphoric Acid; Fertilizer Science and Technoloty Series; Marcel Decker Inc.: New York, 1983. Ben-Yosef, E.; Holdengraber, C.; Metcalfe, J.; Gryc, S. Factors Affecting the Filterability of Gypsum Obrained in a Bench Scale Continuous Unit for WPA. Abstract of Papers, 50th Israel Chemical Society Meeting; Jerusalem, Israel, 1984; p 198.
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Budz, J.; Jonas, A. G.; Mullin, J. W. Effect of Selected Impurities on the Continuous Precipitation of Calcium Sulphate (Gypsum). J . Chem. Technol. Biotechnol. 1986, 36, 153-161. Gilbert, R. L., Jr. Crystallization of Gypsum in Wet Process Phosphoric Acid. Ind. Eng. Chem. Process Des. Deu. 1966,5, 388-391. Jancic, S.; Garside, J. A. New Technique for Accurate Crystal Size Distribution in an MSMPR Crystallizer. In Industrial Crystallization; Mullin, J. W., Ed.; Plenum Press: New York, 1976; pp 363-372. Monaldi,, R.; Barbera, A.; Socci, F.; Venturino, G. Revamping and Energy Cost Reduction Obtained in one of Montedison's Phosphoric Acid Plants with Low Investment Cost. Presented at the IFA Technical Conference, 1982; Paper TA/82/8, 32 pp. Mullin, J. W. Crystallization, 2nd ed.; Butterworth: London, 1972. Orenga, M. Production of Phosphoric Acid from Phaloborwa Rock from the Pilot Studies to Experience of the Industrial Plants of Rhone Poulenc. Presented a t the IFA Seminar, Raw Materials in South Africa, Johannesburg, 1983; Part 111, pp 45-55. Robinson, N. Fisons' Experience on the Effect of Phosphate Rock Impurities on Phosphoric Acid Plant Performance. Presented a t the ISMA Technical and Economic Conference, Orlando, FL, 1978; Paper TA/78/8, 16 pp. Sarig, S.; Mullin, J. W. Effect of Trace Impurities on Calcium Sulphate Precipitation. J . Chem. Technol. Biotechnol. 1982, 32, 525-531. Sarig, S.; Kahana, F.; Epstein, J. A.; Stern, S. The Effect of Aluminum and Silicate Ions on Calcium Sulphate Dihydrate Precipitation in Steady State Systems. Scanning Electron Microsc. 1981, 4 , 253-257. Sikdar, K. S.; Ore, F.; Moore, J. H. Crystallization of Calcium Sulfate Hemihydrate in Reagent Grade Phosphoric Acid. AIChE Symp. Ser. 1980, 76 (No. 193), 82-89. Slack, A. V. Phosphoric Acid; Fertilizer Science and Technology Series; Marcel Decker: New York, 1968; Part I. Received for review October 24, 1989 Accepted December 1, 1989
Group-Contribution Flory Equation of State for Vapor-Liquid Equilibria in Mixtures with Polymers Fei Chen, Aage Fredenslund,* and Peter Rasmussen Znstitut for Kemiteknik, The Technical University of Denmark, DK-2800 Lyngby, Denmark
The equation of state presented in this work is a group-contribution extension of a slightly modified form of the Flory equation. The equation is similar to, but simpler than, the Holten-Andersen model. A new correlation for the degree of freedom parameter, C, has been introduced. T h e energy interaction parameters are based on group-group interactions, and also the C parameters are calculated by using the group-contribution approach. Results from correlation and prediction of pure-component liquid-phase properties and of vapor-liquid equilibria of mixtures with only solvents and of mixtures with solvents and polymers are presented. T h e results show that, although the parameters have been determined mostly from experimental information on normal boiling components and mixtures of these, the new equation of state is able to predict vapor-liquid equilibria for a large variety of mixtures of polymers and solvents over a wide range of temperatures with good accuracy.
Background In general, pure fluids have different free volumes, i.e., different degrees of thermal expansion compared with the hard-core liquid volumes. When liquids with different free volumes are mixed, these differences contribute to the excess functions. Differences in free volumes are not taken into account in conventional theories of liquid mixtures. They explicitly or implicitly assume all liquids to have the same configurational structure. For mixtures with components of low molar mass, this assumption apparently leads to acceptable results. In mixtures involving a polymer, however, the free volume dissimilarities may be significant. A thorough discussion of this point is found in Elbro et al. (1989). It has been shown by Delmas et al.
(1962) that the free volume differences are responsible for the occurrence of lower critical solution temperatures (LCSTs) of polymer solutions at sufficiently high temperatures. Treatment of these effects requires a model where density, besides temperature and composition, enters as a variable; in other words, an equation of state is needed. To develop an equation of state for liquids and liquid mixtures, it is convenient to start with the generalized van der Waals canonical partition function (Sandler, 1985). For a pure fluid, it is, 2 = (l/n!)(Vr/A3)"(q,,,)n exp(-E/PkT)n (1) where n is the number of molecules in the total volume
0888-5885/90/ 2629-0875$O2.50/0 0 1990 American Chemical Society
