1
J. D. HATFIELD, D. W. RINDT, and A. V. SLACK Tennessee Valley Authority, Wilson Dam, Ala.
Effect of basic process variables on
Phosphate Fertilizer Production Problem: To achieve accelerated phosphate conversion Research: Effect of basic process variables and additives Results: Correlations and empirical equations helpful in determining most economical conditions
ACIDULATION of phosphate rock with sulfuric acid to make superphosphate requires a curing period of several weeks for an acceptable degree of reaction. Interest in accelerating the reaction is reflected in a recent study of major reaction variables (74) and in work on a process for ammoniating superphosphate directly after denning (79). Quick curing of superphosphate by drying has also been studied ( 6 8 ,75). None of these studies, however, identified interrelationships and interactions between variables. The work described here was undertaken to determine quantitative effects of variables and their interactions and to investigate effects of various additives on reaction rate. Experimental
Design of Experiments. Tests were designed after Box's rotatable central composite method (2, 4). The five basic process variables-acid concentration and temperature, acid-rock ratio, and grade and particle size of rock-were varied in a partial factorial design, and additional tests were made a t the extremities of each variable and at the center of the design. Each test was run singly except for the one a t the center of the design, which was run six times to determine the standard deviation. Two series of tests were made ; the second was run after evaluation of data from the first series showed a need for some supplementary data. In addition to the study of these basic process variables, the effects of adding various materials to the reaction mixture were tested. Materials used were potassium chloride, ammonium nitrate, nitric acid, ammonium sulfate, urea, a surfactant, wet-process phosphoric acid, and superphosphoric acid. Additives could also have been treated as continuous variables, as were the basic variables, by testing a t various levels. However, a very large number of tests would have been required to give an experimental design such as that used for the basic variables. Therefore, the additives were treated as discrete variableseither present in a fixed amount or absent. Designs for discrete variables were partial factorials, by which evaluation of
main effects and all simple interactions with basic variables could be made. The three acids were substituted for a portion of the sulfuric acid a t an equivalence of 0.5 gram atoms of nitrogen and 2.0 gram atoms of phosphorus per gram atom of sulfur. Degree of substitution for nitric acid was 16.2570 of acid required; this is equivalent to the difference between acid-rock mole ratios of 1.00 and 1.14, which were the principal levels studied. Substitution of the two phosphoric acids was set arbitrarily a t 207,. Partial replacement with two of these acids has been studied previously (72, 78) but not under conditions which would give a good comparison of reaction rates for 1-hour and 4-hour periods. Curing temperature was also included as a variable as no attempt was made in the basic tests to hold the acidulate a t any particular temperature. Tests were carried out this way to avoid obscuring the effects of basic variables by artificial application of heat. Curing temperatures in large-scale operation, however. are somewhat higher than those obtained in laboratory tests (73, 76. 79). Therefore, application of external heat to produce a fixed curing temperature was studied as a discrete variable to get a factor by which small-scale tests could be extrapolated roughly to plant conditions. The temperature used, 225" F., appears to be a typical average den temperature. Materials. Potassium chloride was a commercial product guaranteed to contain not less than 60% potassium oxide. The ammonium nitrate (TVA plantgrade crystal) contained 33.5% nitrogen, and the ammonium sulfate, a commercial product. contained 21 .lo% nitrogen and 0.05y0 free sulfuric acid. h-itric acid, urea, and sulfuric acid were reagent-grade materials. The surfactant was an aliphatic polyoxyethylene product (nonionic type) which has been recommended (9, 70) for use in the manufacture of normal superphosphate. The wet-process phosphoric acid was a commercial product made from Florida pebble and contained 55% phosphorus pentoxide. Superphosphoric acid was macle a t TVA (77); it contained 76,3y0 phosphorus pentoxide, present as ortho-, pyro-, and polyphosphates in the ratios 48, 42, and 10, respectively.
Test Procedures. Levels of rock particle size and grade of rock were achieved by screening a sample of Florida pebble into tlvo portions as follows: Composition of Screened Portion, - 20 mesh P205 CaO
FetOa F
Si02 H20
22.9 32.6 1.8 1.1 2.5 32.7 0.8
B-
- 4 +20 mesh 33.1
47.0 1.6 0.7 3.6 8.6 1.1
The two rock fractions were mixed together in various ratios to obtain phosphorus pentoxide contents ranging from 29 to 33% in increments of 1%. Portions of these samples were crushed in a disk-type mill and ground in a ball mill to obtain samples ranging from 50 to 90% -200 mesh (wet screen analysis), in increments of 10%. Sulfuric acid of the proper concentration, amount, and temperature was placed in a kitchen-type mixer, and 400 grams of rock was added with the mixer operating. Mixing of acid and rock was continued for 2 minutes; sides of the bowl were scraped during this period to promote homogeneity. After the reacted material had remained a t room temperature in an open vessel for 1 hour, a sample was taken for chemical analyses. The remaining material then was placed in a loosely sealed glass jar arid kept a t 140" to 160" F. Additional samples were taken a t the end of 4 arid 24 hours. T h e acidulation procedure was modified to some extent in testing discrete variables. Curing temperature tests were made by placing the acidulated mixture in a n oven immediately after the 2-minute mixing period. Additives were studied with curing a t room temperature as in the basic procedure. Potassium chloride, ammonium nitrate, ammonium sulfate, and urea were added a t the end of the 2-minute mixing period, and mixing was continued for another 2 minutes. Acids and surfactant were added to the sulfuric acid prior to adding the rock. The standard Association of Official Agricultural Chemists procedure (7) was used in determining citrate-insoluble VOL. 51, NO. 5
M A Y 1959
677
0
70
I
I
/'
-
t
-
XY, x3, x o
is unknown, but the experimental design permits evaluation of coefficients of empirical polynomials quite readily. Similar evaluations have been made by other workers (3, 7 7) with very good results. Levels of the variables studied were coded (Table I) ; continuous variables are related to the coded variables as follows : Acid concentration, % = 70 10x1 Acid-rock mole ratio, (SO8 PzOs)/CaO = 1.07 0 . 0 7 ~ 2 (1) Particle size of rock, yo -200 mesh = 70 10x3 Acid temperature, O F. = 130 5 0 x 4 Discrete variables, xg through 2 1 4 , were considered as zero if absent or + 1 if present. Attempts to fit a polynomial in 21, X Z , x 3 , and xq to data for continuous variables showed that a cubic or perhaps a quartic form would be required to give a fit as good as the data. However, when the range of each variable was decreased somewhat, a quadratic of the form y = bo bixi 62x2 t 3 ~ 3 64x4 f
Table 1.
bl3xlx3
b3axs2
bl4xlx4 624~2x4
678
I
-
-
I
I
I
I
Coded Values of Variables Affecting Phosphorus Pentoxide Conversion Were Used in Evaluating Experimental Results
Variable
+
Table II.
Code
-2
-1
0
1
2
51
50 0.93 50 30 29
60 1.00 60 80 30
70 1.07 70 130 31
80 1.14 80 180 32
90 1.21 90 230 33
No No No No No No No No No
Yes Yes
2 2 2 3
54 55
X6 51
58
X¶ XI0
511 312 213 514
Yes Yes Yes
Yes Yes Yes Yes
Reaction of Phosphate Rock with Sulfuric Acid as Influenced by Continuous Variables
Conversion. .~~ . L% ~
XI
-1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1
1 -1 1 0 0 0
0 0 0
623~2x3
634~3x4
0 0
-2 2 0
2 3
-1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 0 0 0 0
-1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 0 0 0
0
-2 2 0 0 0
0 -2 2 0 0 0
0
0 0
54
-1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 0
0 -2 2 0 0 0
0
2 5c
-1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -2 2 0 0 0 0 0 0
0 0
0
0
0
0
Id
71.3 68.1 69.9 76.0 80.9 74.9 78.2 79.7 77.3 71.0 83.2 72.8 86.3 72.6 87.1 78.9 84.6 82.9 81.7 76.8 74.1 85.6 73.3 86.6 80.8 79.3 83.1'
46 85.5 71.3 86.5 76.1 91.7 79.5 97.6 84.9 90.1 68.5 94.6 74.8 93.2 75.8 99.4 82.4 92.1 90.7 92.2 79.1 82.3 94.8 80.6 92.4 89.9 82.4 90.30
I "
2nd Series*
-
24f
Id
4e
89.3 83.9 99.0 96.5 94.9 89.3 99.1 99.1 91.0 82.7 99.4 85.4 93.8 88.9 99.9 95.0 94.1 92.7 93.8 79.6 84.1 100.0 91.8 95.5 92.2 92.1 93. So
66.2 66.3 72.3 75.0 73.3 72.9 84.0 79.0 77.6 68.6 81.6 74.5 79.3 75.0 89.6 78.6
89.4 73.4 91.9 77.3 85.0 77.7 95.4 81.7 91.3 70.7 94.2 74.1 94.2 73.8 97.9 82.3
... ...
81.4 78.6 70.6 84.3 68.2 85.2 81.4 73.6
Grade of rock = 33% PnOs(xb = 2 ) . Applies to first series tests only. Table I. e After 4 hours. f After 24 hours. Average of six independent runs.
1 hour.
INDUSTRIAL AND ENGINEERING CHEMISTRY
2 2
~
1st Series
Continuous Yariables (Coded)=
ba422
gave an adequate fit. Data omitted were those for 90% sulfuric acid, 0.93 acidulation ratio, 50% -200 mesh, and 30' F. acid temperature. Omitted levels were extreme values in the experimental design and were relatively ineffective in achieving high conversions.
I
A
Acid concn., % Acid-rock mole ratio, (SO8 PnOb)/CaO Particle size of rock, % -200 mesh Acid temp., ' F. Grade of rock, 70PZOS Curing at 225O F. Addn. of KCI Addn. of NHlNOa Substn. of " 0 3 Addn. of ( N H ~ ) ~ S O I Addn. of urea Addn. of surfactant Substn. of wet-process acid Substn. of superphosphoric acid
++ + + + ++ + + + +f + (2) b22Xz2
I
-
J I
Yalue of Variable When Its Coded Value Is
++ + + +
biixi2 61zx1xz
I
I
phosphorus pentoxide. To prevent the reaction from continuing in the sample for analysis, it was washed free of acid immediately after it was taken. Interpretation of Data. A description of the joint action of the continuous variables was obtained by developing empirical equations to fit the data; grade of rock was omitted because its effect was found to be minor. The function relating phosphorus pentoxide conversion ( y ) to the remaining continuous variables (XI, X Z , x3, and x q ) defines a response surface in five-dimensional space. T h e true functional form y = f(x1,
-
0
0
...
...
92.6 77.6 75.0 89.2 74.2 91.3 91.0 79.8
After
P H O S P H A T E FERTILIZER P R O D U C T I O N ACIDULATION RATIO. Increasing acidrock ratio increased conversion in most tests. The effect was most pronounced a t low acidulation ratios, with addition of ammonium nitrate or potassium chloride, and in 24-hour tests. An optimum ratio between 1.10 and 1.15 is predicted for many conditions in 1-hour tests. PARTICLESIZE OF ROCK. Decreasing the particle size of the rock increased conversion independently of other basic variables. The effect was more pronounced with coarser rock, for shorter times, and with presence of wet-process phosphoric acid. No maximum in conversion was noted for rock particle size within the range studied for 1-hour tests; in 4-hour tests, however, a maximum was obtained in the presence of ammonium nitrate. ACID TEMPERATURE. Acid temperature passed through an optimum level which depended greatly upon levels of other variables. Most important interactions were those with acid concentration and time. At low concentrations of acid, higher temperatures increased conversions in 1-hour tests, but this effect decreased with time. At higher acid concentrations, increasing the temperature had a deleterious effect on conversion, particularly in shorter times. The effect of acid temperature \vas less pronounced for curing a t 225’ F. than in basic tests; similarly, in the presence of ammonium nitrate and nitric acid the effect of temperature was reduced significantly. GRADEOF ROCK. Comparison of d.ita from the first and second series of tests (Table 11) showed a small but significant effect of grade of rock. An increase in conversion of 0.6 and 0.5% was obtained
Discussion of Results Test results are given in Tables I1 and 111. Data were evaluated by setting up regression equations, based on Equation 2, for each time level. Coefficients for equations were obtained by the method of least squares (Table 11’). Equation 2 could be used for discrete variables in most cases by calculating new values for coefficients ba through bd and using the same values for b l l through b 3 4 as those calculated for the continuous variable equation. However, for addition of ammonium nitrate and partial substitution of nitric acid, calculation of new coefficients for some of the second degree terms was necessary. Standard deviation for the six duplicate runs at the center of the experimental design was 1.8y! phosphate conversion. hIost of this variation occurred in sampling and chemical analysis. \’ariability calculated from the interaction of test series, time, and basic variables was 1.99. These two values for error were pooled to obtain a standard deviation of 1.92 associated Lvith 38 degrees of freedom. Goodness of fit of regression equations was established by analysis of variance. Linear and quadratic variances were highly significant in practically every case, while “lack of fit” was of the same order of magnitude as the error mean square. This indicates that the second degree model (Equation 2) may be used to predict conversions over the applicable ranges of the variables with precision similar to that of laboratory tests. Effects of Variables. Fixing three of the four continuous variables, x1 through x4, and substituting fixed coded values from Equation 1 into Equation 2 produces for the unfixed variable, x,:
Table 111.
Level of Continuous Variables X
-1 +1 -1 +l -1 f1 -1 +1 -1 +l -1 +1
l
X
2
-1 -1
+1 fl -1 -1
fl fl -1 -1 +1 +1 -1 -1
X
3
-1 -1 -1 -1 +1 +1 +1 +1 -1 -1 -1 -1
X
4
-1 -1 -1 -1 -1
-1 -1 -1
+1 +1
+1
Reaction of Phosphate Rock with Sulfuric Acid a s Influenced by Discrete Variables
1’6
1
b
The coefficients b’o and b’, vary with fixed conditions as a result of grouping like terms in Equation 2 after substitutions are made; the coefficient bll is lisled in Table IV. Equation 3 describes the action of the particular variable, x,, a t fixed conditions of other variables. Effects of continuous variables, calculated from Equation 3, are shown in Figurc 1. Dotted portions of curves connect with experimental points not used in development of regression equations. Curves similar to those in Figure 1 may be drawn for other combinations of values for fixed variables. Effects of continuous variables in the presence of various discrete variables a t their fixed levels may also be described. Obviously, the effect of a particular variable will depend greatly upon the arbitrarily fixed values of other variables. Equation 2 and appropriate coeficients in Table IT7 permit evaluating these effects over a wide range of conditions. . ~ C I D CONCENTRATIOS. \Vith increasing concentration of acid, conversion passed through a maximum and then decreased. Optimum concentration varied with time, acid temperature, addition of potash, addition of ammonium nitrate, partial substitution with wet-process acid, and curing at 225’ F. Many of these interactions are probably due to the. effect of variables on the amount of liquid phase present during acidulation. Addition of potassium chloride or ammonium nitrate accentuated the effect of acid concentration, while it was less pronounced in mixtures containing wetprocess acid.
4
27
C
85.0 87.6 72.7 81.5 80.3 96.2 76.2 79.8 90.0 89.9 83.4 85.5 92.5 98.7 83.7 94.7 84.5 88.8 69.8 78.2 87.7 97.8 75.1 80.8 91.8 89.3 75.6 84.3 91.5 99.0 79.0 84.0
1
4
X8 -~
1
4
x9
1
110
4
1
70.3 74.1 78.0 87.4 84.5 87.1 69.8 76.6 98.2 93.2 99.4 96.3 97.5 70.5 90.9 76.1 92.6 84.3
93.3 91.9 92.7 84.3 99.3 84.9 93.7 96.3
-
Conversion, % ’ Discrete Variable“
85.6
90.1
4
73.4 80.3
1
x”
4
~- 2 1 2 1
4
1
70.6
87.9
66.8
xi4 ___-
1
4
84.8 68.5 87.1
67.7 68.8
71.1 82.0
77.0 86.0 77.3 85.3
79.8 81.4 74.8 75.9 79.1
93.3 98.1 85.4 82.0
4
76.9
75.3
78.0
77.1 75.7 88.6 73.6 79.5 97.7 79.9 94.5 76.6 96.6
80.4 83.9 78.0 79.5 71.9 76.7 72.1 71.2 76.0 89.7 69.3 85.3 83.1
88.3
66.4 78.1 76.4 83.0 92.2 98.7 90.6 96.9
+1 81.6 90.0 75.1 78.6 72.1 70.2 77.9 77.0 75.1 74.4 74.6 75.4 -1 4-1 + l 92.3 94.3 +l +1 +1 70.5 75.7 90.1 87.2 74.0 75.1 74.1 72.9 69.4 71.4 77.1 79.9 72.9 74.8 -1 fl + I + l 99.0 99.4 94.9 94.9 85.8 86.0 80.3 85.1 88.3 98.7 81.1 95.1 91.3 97.0 +l +l +1 fl 86.1 93.1 0 0 0 0 91.1 93.2 90.6 94.0 0 0 0 + 2 87.0 90.1 85.0 86.8 0 O f 2 0 90.4 91.6 91.2 95.3 0 + 2 0 0 93.4 99.6 96.7 99.2 2 0 0 0 91.8 96.3 97.4 93.8 a Table I. Grade of rock, x5, varied throughout tests but had only minor effect. After 1 hour. OAfter 4 hours.
VOL. 5 1 , NO. 5
M A Y 1959
679
a l A - L L u 4030
80
i 30
180
230
\
I \
I
I
1
1
20 0
ACID TEMPERATURE, OF
Figure 2. Acid concentration and temperature have mutual influence on PnOs conversion, resulting in a unique maximum of conversion for fixed levels of other variables Time 4 hr. Acidulation ratio 1.07. Curing temp. 225' F.
Particle size of rock
for each 1% decrease in phosphorus pentoxide content for 1 hour and 4 hours, respectively. This relatively small effect was neglected in calculations involving other variables. TIME. Reaction rate between 1 hour and 24 hours decreased in a first order manner with respect to unreacted rock when acid concentration was SOYo or greater. At lower acid concentrations, reaction rate was influenced greatly by other variables. Greater increments of conversion were obtained between 1 hour and 24 hours when the rock was coarsest and the mixture overacidulated to the greatest extent. Interaction of time and acid temperature was such that beneficial effects of higher temperature a t shorter times were practically nonexistent in 24 hours. CURINGAT 225" F. Keeping products a t 225' F. increased conversion 6.1 and 4.0% in 1 hour and 4 hours, respectively, as compared to curing without application of heat. Conversion increases for 1 hour were much greater in dilute acid and at lower acid temperatures, and were perhaps slightly greater at lower acidulation ratios. Increases in 4 hours were greatest a t higher acid concentration. ADDITIONOF MATERIALS. Addition of potassium chloride (to give a 1 to 1 phosphorus pentoxide-potassium oxide ratio) caused an average increase in conversion of 4.6% in 1-hour tests. This effect was more pronounced with dilute acid and a t lower temperature. For 4hour tests, potassium chloride increased conversion a n average of 4.2%; increases were larger with coarser rock. Addition of ammonium nitrate (to give a 1 to 2 nitrogen-phosphorus pentoxide ratio) gave average increases of 10.2 and 6.8% conversion for 1- and 4-hour tests, respectively. Increases were greater
680
7070, - 2 0 0 mesh.
A C I D TEMPERATURE,
Figure 3. Effect of variation in acid concentration and conversion is changed by addition of temperature on PzO~ potassium chloride and change in levels of fixed conditions; contours of PzO6 conversion and location of optimum combination of variables are shifted Time 1 hr. Acidulation ratio 1.4. Particle size of rock SO%, -200 mesh. Curing o t room temp.
with dilute acid, a t lower temperatures, and under conditions of overacidulation for 1-hour tests. I n 4-hour tests, greatest increases occurred at higher concentrations and lower acid temperatures. Presence of ammonium sulfate in the acidulation mixture (nitrogen-phosphorus pentoxide ratio = 1 to 4) had no significant effect on conversion after 1 hour, but decreased conversion after 4 hours by 4.0%. Greatest decreases were with acids of low concentration. Addition of urea (nitrogen-phosphorus pentoxide = 1 to 4) decreased conversion 1.9 and 7.1% in 1 and 4 hours, respectively. Greatest decreases were associated with acids of low concentration and high temperature. Presence of 0.4 pound of nonionic surfactant per ton of superphosphate had no effect on conversion, and there were no significant interactions with other variables. During the mixing operation the surfactant appeared to permit gases to escape more readily; the product was more dense and was considerably wetter than corresponding acidulates made without a surfactant. SUBSTITUTION OF .ACIDS. Substitution of nitric acid for part of the sulfuric acid gave average increases in conversion of 11.5 and 5.4% in 1- and 4-hour tests, respectively. Both increases were greatest at lower temperatures. T h e 1hour increases were slightly greater for coarser rock, while 4-hour increases were greatest with high acid concentrations and at high acidulation ratios. Substitution of wet-process phosphoric acid resulted in a n average decrease of 1.670 in conversion in 1-hour tests. De-
INDUSTRIAL AND ENGINEERING CHEMISTRY
OF:
Product nutrient ratio 0:l:l
creases were greatest with acids of lower concentration. I n 4-hour tests, adverse effect of phosphoric acid in tests with acid of low concentration was balanced by a beneficial effect from fine grinding of rock; average conversions were identical to those for tests in which sulfuric acid alone was employed. Substitution of superphosphoric acid gave a slight decrease in conversion in 1hour tests at lower acid temperatures, but this was balanced by a slight increase at higher temperature. h-o effect was noted in 4-hour tests. Response Surfaces. Equation 2 describes quadric response surfaces when fewer than three variables are fixed. Surfaces are three-, four-, and fivedimensional, respectively, when two, one, and no variables are fixed. Surfaces may or may not have unique maxima of phosphate conversion in applicable ranges of continuous variables. A few examples illustrate the nature of the conversion response to variations of continuous variables. COMBINED ACTIONO F T W O \'ARIABLES. When two of the continuous variables are fixed, Equation 2 becomes y
= b'o
+ b'ixi + b ' l x j
f 6,ixi2
+
bjjx'j f bijxixi
(4)
where xi and x i are independent variables that are not fixed. Coefficients 6 ' 0 , b'i and b'i vary with fixed conditions, and bii, b,,, and bii are values reported in Table IV. Examples of response surfaces obtained by fixing two variables are shown in Figures 2, 3, and 4. Curves were constructed by fixing phosphate conversion, y, in Equation 4 and plotting
P H O S P H A T E FERTILIZER P R O D U C T I O N resulting conic sections in two unfixed variables. Dotted lines are outside the region of study from which regression equations were derived. In Figures 2 and 3, contours of constant phosphate conversion are elliptic, and unique maxima are obtained. Optimum conditions for these systems are indicated by a (apex of the conic response surface) with calculated maximum conversion a t these conditions shown in parentheses. Optimum conditions were obtained by equating the partial derivatives, hy/dx, and dy/dx,, of Equation 4 to zero and solving the simultaneous equations in x , and x i . Maximum conversion was obtained by substituting coded optimum conditions of x , and x , into Equation 4. I n Figure 4, a unique maximum in conversion is not obtained. The surface is saddle-shaped with hyperbolic contours rather than ellipses. The calculation for a point of inflection gives the point a t the center of the saddle surface; this point is a maximum along one axis of the surface and a minimum along the other. A4similar surface is obtained for partial substitution of nitric acid. Numerous other response surfaces may be constructed for other fixed conditions by using this procedure. I n general, inclination of surface axes t o independent variable axes will be governed by the sign and magnitude of cross-product terms, x t y 7 , while the other terms determine the nature of the conic sections. Where no unique maximum is found,
i 0" * N
Figure 4. Ammonium nitrate produces a "saddlesha ped " surface w i t h no u n i q u e maximum
+
Table IV. Conditions Continuous variables Discrete variables Curing at 225' F. Addn. of KC1 NH4NOa ("4) nSO4 Urea Surfactant Substn. of "03
Wet-process acid Superphosphoric acid Continuous variables Discrete variables Curing at 225' F. Addn. of KC1 NHiNOi (NH4)zSO4 Urea Surfactant Substn. of "08
Wet-process acid Superphosphoric acid
bo
Time 1 hr. Acidulation ratio 1.07. Particle size of rock 70%, -200 mesh. Curing at roam temp. Product nutrient ratio 1 :2:0
I
80
a?
i 0
2F
70
I-
z w
0
E- --.
z
6
0
d
92
0
U
\
50
20
\
I30
80
30
I80
230
A C I D TEMPERATURE, O F
either saddle-shaped curves (Figure 4) are obtained, or conversion merely increases throughout the range of one of the variables studied. T h e latter usually occurs when particle size of rock is one of the unfixed variables.
conversions obtained. Optimum combinations are found by treating partial derivatives of Equation 2 in the same way that derivatives of Equation 4 were treated in the preceding section. Figure 5 shows maximum 1-hour conCOMBINED ACTIONO F ALLVARIABLES. versions a t various levels of rock fineness. Combined action of all variables can be Curves are loci of apices of the response represented by calculating the optimum surfaces in four dimensions-namely, combination of three variables at various X I , XZ, x4 and y, when particle size of the levels of the fourth variable and then plotrock is fixed a t specific values. Curves for ting the fourth variable against maximum addition of ammonium nitrate and par-
Regression Coefficients of Equation 2 for Various Conditions"
82.80 -2.40 2.55 3.16
bii bzz b33 b44 1 Hour 2.15 -1.63 -0.86 -0.80 -2.88
88.91 -3.99 1.71 3.36
0.84
87.36 91.10 82.36 80.89 83.40
E
bi
-4.61 -4.03 -1.52 -1.71 -1.92
bz
2.54 3.51 2.68 2.13 3.06
b3
b4
3.57 1.58 2.62 -1.66 -1.60 -0.95 -1.26 3.19 1.57 2.99 1.28 2.30 1.65
90.59 -1.72 2.69 2.14 -0.83 81.24 -0.89 2.36 3.51 1.60 83.26 -2.12 2.22 2.58 3.01 90.30 -7.77 2.34 2.44
0.72
blz
'
b13
b14
0.37 -0.62 -2.06
bis
b24
bar
0.04 -0.04 -0.53
0.03
0.06 -1.04 -1.12 -2.98
-2.94 -1.05
4 Hours 0.23 -3.06 -0.44 -0.54
2.11
0.18
0.66 -1.61
0.67
0.13 -0.04
94.34 -6.26 2.53 2.23 -0.32 94.51 93.20 86.32 83.20 90.70
-7.82 -3.51 -5.02 -5.91 -7.67
1.57 2.66 2.24 2.30 3.22
1.61 0.82 2.66 3.20 1.79
-0.05 -1.28 -0.70 -0.55 -1.11 -0.18
0.47 -0.59
94.03 -0.38 4.38 1.82 -2.22 -0.37 -1.04 -0.71 90.52 -5.97 1.56 3.54 -0.36 90.17 -8.24 2.51 2.42 -0.09
24 Hours Continuous variables 93.80 -2.69 3.56 1.89 -1.10 -1.13 -0.02 -0.31 a When coefficients are not given, coefficients for continuous variables should be used.
0.08
-0.82
0.34
1.00
0.18
0.93 -1.16
VOL. 51, NO. 5
-0.44 -0.81
MAY 1959
0.34
681
'--I 98
s
96 Figure 5. Effect of rock fineness on
2 94
2
maximum conversion in one hour when other major variables are a t optimum c o n d i tions. Minor variables influence maximum conversion attainable
v)
92
> 90 0 "
88
a!!
5
86
5
;;
84
U
E
to evaluate effects of various quantities of these materials singly, together, and in combinations with various den temperaAs these materials are common tures. fertilizer materials, their use in increasing acidulation rate may be particularly attractive for integrating acidulation of rock with production of a complete fertilizer and eliminating storage or curing of superphosphate. Properties not studied are also quite important in acidulating phosphate rock. Use of optimum conditions determined in this study, or of additives which proved beneficial, would be predicated on acceptable results in regard to physical condition of the product, corrosiveness of mixtures, and fuming of reactants. Equations developed in this study should be helpful in further investigation of these problems.
82 Acknowledgment
80 I "
60
70
80
90
P A R T I C L E SIZE OF R O C K , % -200 MESH
tial substitution of nitric acid are not shown because calculated points of inflection are coordinates of "saddle" points. Maximum 1-hour conversions were considerably greater for curing at 225 F. and addition of potassium chloride than corresponding maxima for the basic procedure involving only continuous variables. Addition of superphosphoric acid and nonionic surfactant gave maxima somewhat similar to the basic procedure, while maxima were considerably lower for addition of ammonium sulfate, urea, and wet-process acid. I t would be useful to know the effect on conversion of altering two or more discrete variables simultaneously; for example, the combination of curing at 225" F. with either addition of potassium chloride or ammonium nitrate, or both, should result in rapid reaction of acid with rock. However, Equation 2 cannot be used for this because of probable interactions between discrete variables. T h e study would have had to be increased considerably in scope to identify such interactions. Table V.
VERIFICATION O F REGRESSION EQUAAdditional experimental tests were made to check some of the predicted conversions in optimum regions of various response surfaces (Table \'). Excellent agreement between experimental and calculated values was obtained in most cases. Average difference was somewhat less than experimental error; the equations are therefore considered satisfactory.
TIONS.
Conclusions
Reaction rate of phosphate rock and sulfuric acid has been expressed as a combination of effects of basic process variables. Response surfaces have been demonstrated, and the validity of estimating conditions for maximum conversion has been established. Additional study to link the empirically fitted surfaces Fvith the basic mechanism (5) is suggested. .4ddition of ammonium nitrate, nitric acid, or potassium chloride during acidulation gives a pronounced increase in rate of reaction. Additional study is needed
Comparison of Calculated and Experimental Conversions Particle
Conversion, 1 Hr. 4 Er. Discrete W Ratio Mesh" ' F. Variable Exptl. Calcd. Exptl. Calcd. 90.5 98.9 100.0 None 88.0 163 90 56 1.15 96.5 88.2 96.1 Curing at 225' F. 87.3 167 60 56 1.12 98.4 93.0 97.2 Curing at 225' F. 93.7 166 70 54 1.11 98.9 96.2 98.5 Curing at 225" F. 9 7 . 4 164 80 52 1.11 95.2 98.0 96.8 Curing at 225' F. 9 7 . 1 163 90 51 1.11 100.0 97.3 99.9 Addn. of KCl 96.1 180 80 50 1.14" 98.8 95.8 95.4 Addn. ",NO3 91.7 205a 70 55" 1.07O 99.4 99.4 97.4 80a Substn. of "08 97.1 70 60' 1.14a Levels of ' other variables are at calculated optinnuin values for 1-hour convera Fixed value. sions. Acid
Concn.,
682
Acid-
Size,
Mole
-200
Rock
7G
Acid Temp.,
INDUSTRIAL A N D ENGINEERING CHEMISTRY
T h e assistance of J. E. Tackett, Gail Barclay Colley, and Owen W. Livingston in experimental work is gratefully acknowledged. literature Cited
(1) Assoc. Offic. Agr. Chemists, Washington, D. C., "Official Methods of Analysis," p. 10, 1955. (2) Box, G. E. P., Biometrika 39, 49 (1952). (3) Box, G. E. P., Biometrics 10, No. 1, 16 11954). (4)' BOX; G. E. P., Wilson, K. B., J. ROY. Statistical SOC.13B. 1 11951). (5) Box, G. E. P., Youie, P. V., Biometrics 11, 287 (1955). ( 6 ) Bridger, G. L., Drobot, LV., J . Agr. Food Chem. 4,532 (1956). ( 7 ) Bridger, G. L., Kapusta, E. C., IND. ENG.CHEM.44, 1540 (1952). (8) Bridger, G. L., Kearns, 3. L., J . Agr. FoodChem. 4.527 11956). ( 9 ) Fox, E. J.; Batson, H. E., Jr., Breen, A. V., Ibid., 2, 618 (1954). (10) Fox, E. J., Hardesty, J. O., Kumagai, R., Farm Chem. 117, No. 9, 43 (1954). (11) Hader, R. J., Harward, M. E., Mason, D. D., Moore, D. P., Soil Sci. SOC.Am. Proc. 21, No. 1, 59 (1957). (12) McKnight, D., Anderson, J. F., Jr., Striplin, M. M., Jr., Hignett, T. P., J.Aer. Food Chem. 1. 162 11953). (13) Xzarshall, H. L.', Hendricks, S. B., Hill, W. L., IND.EXG.&EM. 32, 1631 i 1940) ,-_ .-,. (14) Nunn, R. J., Dee, T. P., J . Sci. Food Agr. 5 , 257 (1954). (15) Procter, J. T., Fertilizer SOC. Engl. ' Proc. NO. 7 (1949). (16) Siems, H. B., in "Fertilizer Technology and Resources," K. D Jacob, ed., vol. 111. D. 167. Academic Press. New York, 195i. 7) Striplin, M. M., Jr., McKnight, D., hiegar, G. H., J . Agr. Food Chem. 6, 298 (1958). 8) Yates, L. D., Nielsson, F. T., Fox, E. J., Magness, R. M., IND. ENG. CHEM.45, 681 (1953). 9) Young, R. D., Heil, F. G., J. Agr. Food Chem. 5,682 (1957). RECEIVED for review August 4, 1958 ACCEPTED January 5, 1959 Division of Fertilizer and Soil Chemistry, 132nd Meeting, ACS, New York, September 1957.
