dp = characteristic length, e.g., size of packing element,
1 = extractant inlet end, outside column (2 = 1.0)
L
* = value at equilibrium with other phase
phase, LZT-1
Subscripts i = number of root of characteristic equation, and of corresponding coefficient in solutions for X and Y, Le. eq 13 and 14 j = X or Y phase x = X phase (feed) y = Yphase (extractant)
E, = effective longitudinal diffusion coefficient in the j t h F = extraction (stripping) factor, mU,/U,, dimensionless Ho, = height of an overall (“true”) transfer unit based on X phase, L kox = overall mass transfer coefficient based on X phase, LT-1 L = total length of contractor, L m = slope of equilibrium line, dcx/dcv,dimensionless No, = number of “true” overall transfer units based on X phase, dimensionless N o x p = number of overall “piston flow” transfer units based on X phase (with superscripts 0 and 1, as defined in Appendix), dimensionless P , = Peclet number for the j t h phase, U,dp/E,, d’imensionless q = intercept of straight equilibrium line on cx axis, ML-3 or (m0l)L-3 U, = superficial velocity of j t h phase, LT-1 X = generalized solute concentration in X (feed) phase, dimensionless Y = generalized solute concentration in Y (extractant) phase, dimensionless Z = z / L , fractional length within column, dimensionless z = length within column measured from X phase inlet,
L Greek Letters a , a’ = defined by eq 10 and 29, respectively p, p’, px‘, p,’ = defined by eq 11, 30, 35, and 39, respectively 7 , yx‘, yv‘, = defined by eq 12, 31, 36, and 40, respectively A,, A t ’ = roots of characteristic eq 15 and 28, respectively.
r‘,
Literature Cited Colburn, A. P., Trans. Amer. Inst. Chem. Eng., 35, 211 (1939). Eguchi, W., Nagata, S . . Chem. Eng. Jap.. 22, 218 (1958). Gayler, R . . Pratt, H. R. C., Trans. inst. Chem. Eng., 29, 110 (1951). Gayler. R.. Pratt. H. R. C., Trans. lnsf. Chem. Eng.,35, 267 (1957a). Gayler, R., Pratt, H. R. C.. Trans. Inst. Chem. Eng.. 35, 273 (1957b). Geankoplis. C. J., Hixson. A. N., Ind. Eng. Chem., 42, 1141 (1950). Geankoplis, C. J., Wells, P. J.. Hawk, E. L., Ind. Eng. Chem.. 43, 1848 (1951). Gier, T. E., Hougen, J. O., Ind. Eng. Chem.. 45, 1362 (1953) McMullen. A. K.. Miyauchi, T . . Vermeulen. T . , U.S. Atomic Energy Commission Rept., U.C.R.L. 3911, Suppl. (1958). Mecklenburgh. J. C., Hartland. S., I . Chem. E. Symp. Ser., No. 26, 115 (1967a). Mecklenburgh. J. C., Hartland. S., I . Chem. E. Symp. Ser.. No. 26, 121 (1967b). Mecklenburgh. J. C.. Hartland. S . , I . Chem. E. Symp. Ser.. No. 26, 130 (1967~). Miyauchi. T., U.S. Atomic Energy Commission Rept. U.C.R.L. 3911 (1957). Miyauchi, T., Vermeulen. T.. Ind. Eng. Chem.. Fundam.. 2, 113 (1963). Pratt. H. R. C., Ind. Chem.. 509 (1955). Pratt, H. R. C.. Ind. €ng. Chem., Fundam.. 10. 170 (1971). Rod, V.. Brit. Chem. Eng..9, 300 (1964). Sleicher, E. A..A.I.Ch.E. J.. 5 , 145 (1959). Stemerding, S., Zuiderweg. F. J., Chem. Eng. (London), CE156 (May 1963). Watson, J. S.. Cochran. H. D.. Ind. Eng. Chem., Process Des. Develop.. 10, 83 (1971).
Superscripts 0 = feed inlet end, outside column (2 = 0)
Received for review April 18, 1974 Accepted August 5.1974
Production of Crystalline Pyrophosphoric Acid and Its Salts Chung Y. Shen Detergent and Fine Chemicals Division. Monsanfo lndustrial Chemicak Company Monsanto Company, St. Louis, Missouri 63166
A process for producing high-purity, crystalline, free-flowing pyrophosphoric acid from a liquid condensed phosphoric acid was developed. Kinetic studies show that diffusion is the rate-controlling step. Variables such as temperature, acid concentration, and sojourn time were defined for optimum continuous crystallization of pyrophosphoric acid. The easily handleable acid was shown to be a versatile raw material for preparing potassium, calcium, and other pyrophsophates.
In our earlier publications, we reported that polyphosphates could be produced by selective extraction of a condensed phosphoric acid (Shen, 1967) or by direct reaction of a condensed phosphoric acid with sodium carbonate to form a fast dissolving, effervescent phosphate (Shen, 1968) which saves the energy otherwise required in producing polyphosphates by the conventional calcination of orthophosphates and simplifies the process. The condensed phosphoric acids have a Pz05 concentration above 80
Ind. Eng. Chem., Process Des. Develop., Vol. 14, No. 1, 1975
100% HsP04. Several condensed phosphoric acids have been commercially available for some time (Durgin, et al., 1937). The condensed phosphoric acids contain a mixture of phosphates of various chain lengths. The distribution of these phosphate species depends on the P205/HzO mole ratio (Parks and Van Wazer, 1957). The compositions of the commercially available condensed phosphoric acid and an acid with a P205 content equal to pyrophosphoric acid are shown in Table I.
Table I. Composition of Condensed Phosphoric Acids
Phospholeum
'2 H,PO, equiv
105
'7 P,O, Actual distribution,
76.1
Liquid pyrophosphoric acid
Tetraphosphoric acid
110.12 79.76
116.0 84.0
r~
P20, as
H jP0: HiPzO, H P Q,, H,,PlO,> Higher chain
49 42 8
17.2 42.5 25.0
1 -
10.5 4.8
Table 11. Apparent Heat of Solutions and Crystallization of Pyrophosphoric Acids - AH. kcallmol at 25°C Heat of
crystallHeat of solution ization HiP2OT-I HJP2OT-11 Liquid pyrophosphoric acid
8 . 1 jz0.2 6 . 8 L 0.2 11.7 * 0.2
3.6 1 0 . 2 4.9
f
0.2
-
3.8 12.0
12.4 12.1 59.7
The purpose of this work was to develop a process to produce a high-purity crystalline pyrophosphoric acid from a liquid pyrophosphoric acid and to produce pyrophosphate salts from the crystalline pyrophosphoric acid (Shen. 1967-1970). Tetrapotassium pyrophosphate is used as a liquid detergent builder and calcium pyrophosphate is used as a dentifrice polishing agent. The existence of pyrophosphoric acid in the crystalline state has been known for many years (Peligot, 1840). All known methods of preparation are essentially the same (Abbot, 1909; Giran, 1903; Kiehl and Claussen, 1935; and Malowan, 1950). The crystalline pyrophosphoric acid is obtained either by spontaneous crystallization or by induced crystallization with a small amount of seed crystals directly from a liquid pyrophosphoric acid. The procedure (Malowan, 1950) is slow and often yields crystals of low purity (85-9570) because of inferior analytical technique and the problem of occluded liquid phosphoric acids. The generally accepted melting point of crystalline pyrophosphoric acid (61°C) was found to be in error (Wakefield and Egan, 1962). They showed that the crystalline pyrophosphoric acid exists in two forms. The usual form is a lower melting (54.3"C) Form 1. There is a more stable, higher melting (71.5%) Form II which can be crystallized from the liquid pyrophosphoric acid. Crystalline pyrophosphoric acid is very hygroscopic, has appreciable heats of solution and neutralization (National Bureau of Standards, 1952), and tends to hydrolyze into orthophosphoric acid (Bunton and Chaimovich, 1965). These problem-properties are difficult to overcome because the crystalline pyrophosphoric acid prepared by earlier methods was in the form of large chunks. Unless large amounts of cold water are used to keep the temperature and concentration low to minimize hydrolysis during the dissolution step, pyrophosphoric acid is not the desired starting material for preparing pyrophosphates (Van Wazer, 19%). Consequently, crystalline pyrophosphoric acid was a laboratory curiosity and drew little attention. Another purpose of this work was to develop a process for producing a finely divided and easily handleable crystalline pyrophosphoric acid suitable for commercial use. Experimental Section Chemicals. The liquid pyrophosphoric acid used throughout this work was prepared by diluting an 84% Pz05 condensed phosphoric acid (See Table I) at one time produced by Monsanto Co. The acid was analyzed and found to contain no measurable impurities in excess of the ACS chemical grade specifications. The liquid pyrophosphoric acid followed closely the composition given in Table I, regardless of the type of starting material in making the liquid phosphoric acid.
The H4Pz07-1 seeds used in kinetic runs were obtained by grinding products under dry nitrogen made from batch crystallization. The acid was analyzed by ion-exchange chromatography to be 99% pure (A.S.T.M.. 1964). The crystals were sized by screening (through a U. S. 20 mesh, but retained on a U. S. 50 mesh screen). The estimated surface area of the seeds was about 70 cmZ/g. The X-ray diffraction pattern of the acid agreed well with the ASTM card No. 3-0275. The melting point of the acid was very sharp a t 54.4 f 0.2"C, using a Fisher-John melting point apparatus from Fisher Scientific Co. The density of H4Pz07-1 crystals was determined to be 1.99 g/cc at 25". The apparent heat of crystallizations of 99+% pure H4Pz07-1 and -11 from liquid pyrophosphoric acid were determined from the difference between heats of solution for solid and liquid acid in cold water using a calibrated calorimeter equipped with a Beckmann thermometer. Using this approach, we assumed that the heats of reorganization for the acid species (Van Wazer, 1958) and the net difference of heat of hydrations of the acid species for the solid and liquid acids are negligible (Irani and Taulli, 1966) as reported. These values are given in Table 11. The heat of solution of H4Pz07-1 was very close to the value of 8.7 kcal/mol calculated from the heat of formation of crystalline and aqueous solution of H4PzO7 given in the National Bureau of Standards Circular (1952). Presumably the crystalline H4P207 used in the earlier work was mainly Form-I, with some occluded liquid to give the high value. The heat of crystallization of H4P207-I obtained in this work was nearly 50% larger than the 2.44 kcal/mol estimated by Giran (1903), but our value agreed well with the heat evolved from heat balances of our bench-scale operation. The starting H4Pz07-11 was prepared bydhe method described by Wakefield and Egan (1962). High-purity (99%+) H4Pz07-11 seeds were prepared by the same method as H4P~07-Idescribed above. The melting point of H4P207-11 was determined to be 71.5 f 0.2%. The X-ray diffraction pattern of the Form I1 acid as given in Table I11 is different from the reported data (Wakefield and Egan, 1962). This difference was resolved and Mr. .J. P. Smith of the Chemical Department, Tennessee Valley Authority, confirmed our results. The density of H4Pz07-11 was determined to be 2.04 g/cc a t 25".
Methods Kinetic studies on the crystallization of pyrophosphoric acid were carried out in a heavy-duty, half-gallon, jacketed, 316 stainless steel, sigma-blades mixer made by Baker-Perkins, Inc., Saginaw, Mich. (Riegel, 1953). The top of the mixer was fitted with a 316 stainless steel hood and a clear plastic lid. The mixer was purged with a small stream of dry nitrogen entering through the hood. Samples or feed could be withdrawn or added through a hole in the hood without exposure to the moisture-laden air. The temperature of the reacting material was controlled to floc by circulating cold or warm water through the Ind. Eng. Chern., Process Des. Develop., Vol. 14, No. 1, 1975
81
Table 111. X-Ray Diffraction Pattern of Phase-I1 (mp 71.5%) H4P& (Cu K a Wavelength = 1.54178) 20
d-spacing
I/I,
20
d-spacing
111,
16.15 16.56 18.35 18.65 19.40 20.90 21.60 22.30 23.08 23.50 25.30
5.49 5.35 4.83 4.75 4.58 4.25 4.11 3.98 3.85 3.78 3.51
21 22 80 30 80 5 5 5 60 22 50
3.30 3.22 3.16
70 100 15
3.03 2.96 2.74 2.65 2.63 2.55 2.40 2.32 2.27 2.20 2.15 2.07 2.03 1.96 1.92
a
27.00 27.60 28.30
29.3 30.2 32.4 33.7 34.3 35.3 37.5 38.8 39.7 41.0 42.0 43.8 44.5 46.3 47.3
5 30 13 18 5 5 5 5 8 5 5 5 1.0 10
jacket. Samples taken from the reaction mixture were quenched in ice-cooled dilute S a O H solution. The resulting solution was analyzed by the ion-exchange chromatographic method (ASTM. 1964). The precision of the . method for each phosphate species is about k 0 . 2 7 ~ Hydrolysis of the polyphosphate species during the solution step proved to be negligible. Good agreement was obtained between duplicated samples, and the assay of the pyrophosphate products was high. Furthermore, the disappearance of the ortho and higher chain phosphates served as a built-in check. The increase in the pyrophosphate fraction was found to agree with the corresponding decrease of the ortho- and higher-chain phosphates. The neutralized sample solutions were kept in a refrigerator a t 0°C before analyses. The sample was found to be stable at least a week as judged by the fact that there was no apparent decrease in the higher chain phosphate content. The sampling error was determined by analyzing duplicate samples and was found to be about & l % of the pyrophosphate content. Details of various preparative procedures of pyrophosphates accompany the results in subsequent sections. Crystalline Pyrophosphoric Acid Process Development Mechanism and Kinetics of the Formation of C r y s talline H4P207. The formation of crystals in liquid systems usually takes place in two steps (Nancollas and Purdie, 1964). The first is nucleation which corresponds to the production of new centers from which growth can occur, In the second, the nuclei grow as material from the nutrient medium which is deposited on them. This mechanism apparently fits the batch crystallization of pyrophosphoric acid as shown in Figure 1. The batch operation was carried out in the sigma-blades mixer and the time started when the freshly prepared acid a t the desired temperature was mixed with the known amount of seeds preequilibrated at the desired operating temperatures. The batch temperature was controlled t o &1"C as described previously. When the pyrophosphoric acid concentration is less than 50%. there is an induction period during which additional nuclei form. After the nuclei become large in number, the rate of pyrophosphate formation follows essentially a first-order mechanism. The relatively small change in the rate constant with temperature, as discussed later, indicates that the rate-controlling step is the diffusion of the liquid to the solid surface. The fact that the ratio of net ortho- and polvphosphate fractions remains relatively constant during the course of the conversion to crystalline pyrophosphate indicates that the 82
Ind. Eng. Chem., Process Des. Develop., Vol. 14, No. 1, 1975
80
m
v, 60 m .6.
i
0
E
*O
, \
ORTHO
1
HIGH POLY
0
,
0
,
,
M
A
,
,
100
,- , ? - - ! , , I ,
150
2w
TIME, MIN.
Figure 1. Typical batch crystallization of H4P207-I(test conditions = 10% H4Pz07-I seeds and 90% by weight of liquid pyrophosphoric acid; temperature = 30 & 1').
rate of reorganization of the liquid portion to maintain the equilibrium distribution is very fast in comparison with the rate of crvstallization. For the run shown in Figure 1, the induction period terminated a t about 60 min and the conversion was completed after about 180 min. The final product was shown to contain about 95.5% pyro- and 3.5% orthophosphates by ion-exchange analysis. The limited pyrophosphoric acid composition was due to the Pz05 content of the starting condensed phosphonic acid being lower than theory. Crystallization of the pyrophosphoric acid from a stirred bed containing a mixture of liquid and solid pyrophosphoric acids does not follow the usual model of crystallization involved in a solution or a melt. There is no apparent continuous phase, a t least for batches using a high level of crystalline pyrophosphoric acid seeds. The mixture may be considered to consist of many small dispersed crystallization systems. The size of the crystallization system probably is in the order of the actual flow units, which are dynamically dispersed by the mixing blades. Liquid and solids may exchange between those crystallization systems because of the mixing action. The apparent induction time, when a high level of seed is used, a t least in part includes the time required to distribute the solids to some degree of uniformity into each of the crystallization systems. Since the crystallization rate after the initial induction period, as shown later, is unaffected by the amount of seeds, it suggests that the diffusion through the viscous liquid pyrophosphoric acid is the controlling step. Should the deposition on the solid surface be the controlling rate step, the rate constant should be proportional to the total seed surface areas, and hence to the two-third power of the weight of the seed. This, however, is shown not to be the case. The initial pyrophosphate concentration WOin the test acid depends on the amount of seed crystals used and the acid concentration. There is a limit to the amount of pyrophosphate in the product W , a t infinite time when all available pyrophosphoric acid is crystallized because the starting acid concentration differs from the theoretical value of 79.6% P205. If the postulation that after the induction period the rate-determining step is controlled by diffusion, then the potential to overcome the diffusional resistance is proportional to W , - W where W is the pyrophosphate concentration a t any time t. The rate equation then can be derived as
h
Wt.%
TEMP,
k
50
30 30
0.050
D
o
50
50
0.068
1.0
KEY -
0.8 0.6
iEMp
KEY .
k . M1N-l
43OC
0.098
0
3OoC
0.077
t
2ooc
0.067
+
\t
2 & SEEDS 10 6.050
0.4 %
3
0.3
-." -
7 0.2 e
5
d Y C c Y
% z z
0.1
0.0
0.021 0
I 23
1 40
\
60
80
I 100
I
120
TIME, MIN
Figure 2. Effect of temperature on the crystallization of Form-I H4P207 with 50% by weight of seeds.
Plots of In [ ( W , - W)/(W_ - Wo)] against time t given in the subsequent section showed that after the initial induction period, the postulated linear relationship is followed. The induction period decreased with an increase of the amount of seeds as expected. The H4Pz07-I was confirmed to be a metastable phase. It converted nearly quantitatively to H4Pz07-11 when a small amount of H4P207-11 seed crystals were added in an equal weight mixture of H4Pz07-1 and liquid pyrophosphoric acid. The crystallized product, as shown by X-ray diffraction and melting point determinations, contained no H4Pz07-I. Effect of Temperature and Seed Crystals. Studies on the rate of crystallization were made in a stirred bed using a closely controlled crystal size of -10 i- 50 U. S. mesh as a function of seed level and temperature. The results are shown in Figures 2 and 3. Lower temperatures reduce the crystallization rate, contrary to a claim by Malowan (1950) that cooling the system enhances crystallization. Seed crystals decrease the induction time so that the induction period is reduced from over 60 min with 10% seeds to about 10-15 min in the presence of 50% seeds by weight. At temperatures of 2 to 5" below the melting point, the mass becomes tackier and the rate is reduced. The optimum temperature for crystallization of pyrophosphonic acid appears to be somewhere around 10°C below the melting point; thus for H4Pz07-1, the temperature will be 34-44°C and for H4Pz07-II, 50-60°C. From the straight line portion of the conversion of liquid pyrophosphoric acid to H4Pz07-I or -11 given in Figures 2 and 3, the apparent rate constants a t various tem-
0.02
0
20
I
I
40
00
I 80
I 103
120
TIhlE MIN.
Figure 3. Effect of temperature and seed level on the crystallization of Form-I1 H4P207.
peratures were estimated. The calculated activation energies under these test conditions were about 3.5 kcal/mol for both H4Pz07-1 and -11 crystallization steps and are in agreement with that expected for a reaction controlled by diffusion. This value is also in the same order as that found in the formation of pyrophosphate from orthophosphate in solutions (Schmulback, et al., 1960). The reaction rate for formation of H4P207-11 is somewhat lower than for H4P207-1. This may explain why H4P207-I is usually formed when there is no H4P207-II seed present. Effect of Acid Concentration. Pure pyrophosphoric acid contains 79.76% P205. If a product of crystalline pyrophosphoric acid of 98% purity is desired, the allowable acid concentration variation is from 79.61 to 79.93% Pz05. This narrow range would be a potential problem in commercial-scale production. A wide range of acid concentration can result in difficulties in crystallization. considering that either ortho- or high-polyphosphoric acid i; a fairly good solvent for pyrophosphoric acid. Indeed, it is extremely difficult to crystallize an acid containing about 82% PzOs. To study the effect of acid concentration, the P z 0 5 content of the liquid pyrophosphoric acid was varied from 78.95% (equivalent to a maximum purity of 88.95% H4P207) to 80.40% (equivalent to a maximum purity of 92.86% H4P207). At the extremes of these acid concentrations, even though the induction time was notably lengthened, the crystallization rate was not significantly changed based on the normalized scale [ ( W , - W)/ ( W , - W O ) ]described previously. Since the induction time disappears in these runs with a very large amount of seeds, the crystallization rate is not expected to change with the concentration covering the range of 78.95 to 80.40Yc P205. Effect of Using an Inert Solvent Carrier. In several runs a mixture containing 2040% carbon tetrachloride by Ind. Eng. Ghern., Process Des. Develop., Vol. 14, No. 1, 1975
83
Table IV. Continuous Crystallization of H4P207-11 a t 3O0Ca -
~~~~
Table V. Calcium Ammonium Pyrophosphates
Average feed acid rate, g/min 1
Sojourn time, min Calculated pyrophosphate content i n product b y eq 5 Actual pyrophosphate content, mol % Bed appearance
2
900
450
3 300
4 225
5 180
6 150
99
96
96
95
94
93
98
97
97
96
95
93
Free-flowing Slightly Balling sand-like wet and and fluffy somewhat sticky a Conditions: average amount of bed acid = 900 g; feed acid concentration = 79.7690 P205. weight was used. At the 20% level, the product was a freeflowing powder which slows little tendency to cake. The relatively high vapor pressure of carbon tetrachloride also prevented the acid from absorbing moisture. This could eliminate the need of a very dry atmosphere which is required for handling crystalline pyrophosphoric acid to prevent it from caking. At the 50% level, the product was a slurry which could be handled easily. Both types of products were found to be stable after two years of storage. There was no apparent reaction between CC14 and the acid based on 31P nmr spectra. The use of carbon tetrachloride increases the induction time of the crystallization process for the acids containing low amounts of seeds. This effect is expected, since the inert solvent disperses the acid into many small droplets. Therefore, the effect of any seed crystal is limited to the droplet only, rather than the entire mass in the case without the solvent. There is essentially no change in total crystallization time with the use of a solvent in batches with a large amount of seeds. Continuous Crystallization Process. In the continuous crystallization, the liquid acid was continuously fed at one end of the crystallizer while an equal amount of product was withdrawn from the opposite end of the sigma-blade mixer. Although the process is very simple, a high degree of crystallinity is required if free-flowing solid acid is to be obtained. This can be shown by the following theoretical analyses and supporting test results. Under steady state, the material balance around a complete mixing reactor gives
where F is the feed rate, W,, WI, and WZ are the concentration of pyrophosphate a t infinite time of reaction, and at inlet and outlet of the crystallizer, respectively, h is the reaction rate constant based on eq 1, and Q is the total material in the crystallizer. Since the sojourn time, 0 = Q / F , eq 3 gives
w, =
TI:,
-
LV, 1
-
w, 81:
(4)
Using a 79.76% PzOs liquid pyrophosphoric acid, WI and WL are 42 and 100, respectively. and a t 30°C, the k value is 0.05 min-I for H4Pz07-11. Equation 4 thus becomes
w2=
100
-
(5)
The product quality, Wz, calculated from eq 5 agrees well with the observed values a t various feed rates as shown in Table IV. At a feed rate above 4 g/min, the bed 84
Reactants, mol
Ind. Eng. Chem., Process Des. Develop., Vol. 1 4 , No. 1, 1975
Temp,
H4P207
CaO
-11
NH,
H,O
"C
Products"
1 2 1.5 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1.7 1.7 1.7 1.7 1.7 3.0 0.85 1.7 1.7 1.7 1.7 1.7
30 36 36 30 30 41 33 20-56 20 56 36 36
