Ind. Eng. Chem. Res. 1990, 29, 862-867
862
GENERAL RESEARCH Beneficiation Process. A Mathematical Model for Predicting Product Grade as a Function of Raw Material Composition: Mining and Plant Control I t h a m a r Z. Pelly Department of Geology and Mineralogy, Ben Gurion University of the Negeu, Beer Sheua, Israel A method is described t o predict the content of a desired element in the products of a beneficiation process as a function of the impurities in the raw material. The method shows one of the possibilities of utilizing factor analysis and regression analysis for routine industrial purposes. The method consists of (a) developing a n on-line multielement analysis, (b) finding the elemental and mineralogical relationships in the product, by factor analysis, (c) determining the independent variables, (d) finding t h e relationships between the concentrations of the impurity variables in the raw material and in the product, (e) and developing a linear model to predict the desired element’s content. T h e predictions can be used for mining and plant control. Examples from a phosphate beneficiation by calcination process are given. There are some considerations involved in building a model to predict the content of the desired element in the product of a beneficiation process as a function of the composition of the raw material. One aspect involves the experimental problems. The sampling for analysis in the plant is not continuous, and a sample may be taken, for instance, every 2 h. In addition, there is a long time lag (for example, 10 h) between feed and the appearance of the product from this feed so that a specific product sample cannot be attributed to a specific feed. Another aspect is that a great part of the impurities of the raw material may not remain in the product, being leached out during the beneficiation process. These problems prevent a simple prediction of the desired element’s content in the product based upon the impurities of the raw material. The aim of this study was to find a mineralogical description of the beneficiation process (based on a chemical analysis of the elements) and to build a model that would predict the product’s grade from the composition of the raw material. This requires the determination of the parameters needed for such a model and testing the model in the plant. Such a model is very important from two aspects: (1)mining planning (which is done a few years ahead) which necessitates processing of a large volume of analytical data; and (2) control of the plant operation, by comparing the product’s grade to the optimal grade that can be expected from the raw material, thus finding if the plant operates under optimum conditions. This has to be done by an on-line analysis and not by using static laboratory simulations, as the results may be different. The method does not consist of the development of new mathematical methods or equations. The aim is to draw attention to the possibility (and show the way) of utilizing the well-known techniques of factor analysis and regression analysis for routine industrial purposes. In this article, the general lines of the procedure will be drawn and examples from a phosphate beneficiation by calcination system will be given. The method can be applied to find raw mate0888-5885/90/2629-0862$02.50/0
rial-product correlations in various other systems. Coupled with on-line analysis of the influencing variables, this will provide a good method for controlling mining and plant operations. Experimental Section In the application of the model to the phosphate beneficiation process, the following methods were used. Analytical Data. The analytical data were obtained by simultaneous multielement (eight) analysis of raw material and products in the calcination plant of Negev Phosphates Ltd., Oron, Israel. The analysis was done by using an ARL 74000 XRF spectrometer. Details of sample homogenization (which has critical importance) and of the analysis are described elsewhere (Issahary and Pelly, 1982a, 1983). Because of the very large amount of analytical data, only means and standard deviations were used. H20, Ca(OH),, and COz were determined by a Stanton-Redcroft TG Model 750 thermoanalyser. It was found that these are not influencing variables in the phosphate beneficiation system. Calculations. For factor analysis, using SPSS procedures (Kim, 1975),standardized concentrations were used, i.e., Ci/ui, so that the variance of each element is 1 and the total variance is equal to the number of elements in the system. Regression analysis has been well described in the literature. The book by Draper and Smith (1981)was used as a guide. Multiregression analysis calculations were done by using SPSS procedures (Kim and Kohout, 1975), which also present partial regression coefficients, the F test, the significance of the regression coefficients in the partial equations, the F test for the regression equations and their significance, etc. The following rules were used: the model will be considered as predictive if F > F(p-1, n-p, 0.01), but will be considered explanatory only if F(p1, n-p, 0.05) < F < F(p-1, n-p, 0.01). Here F(r1, r2, a)is the critical value for the F distribution for r l and r2 degrees of free-
0 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 5 , 1990 863 dom and significance cy, n is the number of samples, and p is the number of variables.
Discussion Detailed descriptions of the theory, equations, and computational procedures of the factor analysis are readily available (Harman, 1976; Kim, 1975). Only aspects relevant to this study will be described here. Factor analysis can help to determine the degree to which one or more variables are part of a common phenomenon. Input may be raw data, a correlation matrix, or a factor matrix. The output is a matrix that includes the number of factors, the variables loading each factor, the loading (or contribution) of each variable on the factor, and the variance of dispersion of each variable among the different factors. The procedure can be controlled by specifying the number of factors to be extracted or the minimum value of an eigenvalue for which a factor will be extracted. After factor extraction, rotation can be done. The exact configuration of the factor structure is not unique, and one factor solution can be transformed into another by rotation. Among the various rotation types are the orthogonal varimax and the direct oblimin method of oblique rotation. There is no unique and generally accepted best solution, yet not all the types of factor solutions are equally meaningful. Each tells us something different about the structure of the data. It is necessary to choose the best rotational method to arrive at the solution that satisfies the research problem. Orthogonal (independent) factors are mathematically simpler to handle (but the division to different factors is not always clear enough). Rotation will have the effect of shifting the values in each group to the limits, close to one or to zero, so as to obtain a clearer picture. The oblique factors are empirically more realistic. There is no reason to favor one method over another, and the choice should be made on the basis of the particular needs of a given research problem. Some of the implications for chemical-mineralogical systems in industrial beneficiation processes are as follows: If chemical elements are the variables, clear correlations (if they exist) may be found even in a system of a large number of variables even if the same element appears in different factors. These factors may represent minerals or may be just correlations (e.g., several trace elements on a clay). If S O l and A1,0, are taken as an example, it may be found not only that there is a correlation (obtainable from a Pearson correlation matrix with perhaps no clear reason for the correlation) but that there are high loadings of these elements on two factors. There are no theoretical answers to questions such as the following: Do SiOz and A1,0, appear in two minerals (i.e., orthoclase and clay)? Can these factors be used as input for factor analysis, creating factors of factors (contrary to Davis’s (1973) view)? Will these new factors be indicators for mineral associations (i.e., a clay with sodium chloride)? Which rotation is best suited to show mineralogical correlations in a set of elemental anlysis? Are only negative correlations expected to arise from dilution in a closed system (i.e., the more clay present, the less apatite)? In the absence of theoretical decisions, it is necessary to estimate if the obtained factor solutions and their interpretations make sense compared with what is known about the beneficiation system-elements, minerals, the possibility of reactions among them, etc. If more information can be obtained from IR spectra or X-ray diffraction (and this is not always possible), the choice may be easier. Factor analysis will show correlations caused by chemical bonding and by interactions or reactions of minerals and will provide a guide to understanding the multiregression
analysis, which helps us find which are the independent variables and which can be described as linear combinations of the others. In contrast to procedures in social sciences, where common variance is desired, here reliable specific variability (i.e., without the error component) also is a meaningful result. If SiOz does not have any correlation, this can be an indication that silica appears as an independent mineral. If one wants to apply the method for calculating factors of analytical data, the results depend on the precision and accuracy of the chemical analysis. If the errors of the measurements are relatively large, they will be included in the statistical treatment and correlations and factors caused by these errors may be obtained. The total variance consists of the communality of the element and the component of the variance contributed by the analytical error (e:). If this error variance is subtracted from the total variance, a new criterion for the number of significant factors is obtained, i.e., the number of factors that explain only the variance caused by “real” concentrations, which is the only variance for which explanation is needed. The standardized analytical error variance for element i is e: = (AEi/aJ2,and for all n elements, the standardized analytical error variance of the system is n
n
X = L e i 2= i=l
.
AEi2
Ei=l giz
AEi was calculated by doing several determinations of element i in several samples of the same batch and finding the standard deviation. This value was standardized by dividing by the standard deviation for element i in the system for which factor analysis is done, ui. The percentage of the standardized analytical error out of the total variance of the system is Y = (X/n)100 (the variance of each element is 1). As an example of one phosphate system, (AEJ uJ2 was found to be 0.245 for the 11 elements determined. The relative analytical error variance will be Y = (0.425/11)100 = 3.9%. Accordingly, it is necessary to seek only a number of factors (eigenvectors) whose sum of eigevalues will be about (100 - Y ) % ,Le., for the example above, only 96% of the system’s variance. In some cases no real difference is obtained by this correction. The aim is not to get a minimal number of factors needed to describe the system (as in social studies) but to obtain a solution with minimum loadings with opposite signs on the same factor and in which all factors have significant loadings. Correlations will be able to disperse among a maximum number of factors so that, if correlations among the elements remain in the same factor, it will not be because of lack of space but because they have a real correlation. The usual way of presenting the interactions is the varimax rotated factor matrix (orthogonal). Though some correlations were seen in the resulting matrix (Issaharyand Pelly, 1981a),a much clearer picture of the correlations was obtained by using the direct oblimin method in which the factors are oblique factors and not independent (Harman, 1976). The factors obtained are given in Table I. The elements loading each factor make it possible to interpret each factor as a mineral, oxide, or mineralogical reaction. This method was chosen because of intuition (it cannot be proved) that factors of this method are devoid of dilution effects among elements. Trial and error showed that, when 6 is chosen in such a way that the direct oblimin criterion is close to zero (positive), there are few meaningful loadings on each factor, but these have a high value (Le., intermediate values become close to zero). This selection
864 Ind. Eng. Chem. Res., Vol. 29, No. 5 , 1990 Table I. Factor Pattern Matrix (Obliaue) gypsum clay factor 1 factor 2 0.12631 0.03401 0.043 48 0.071 15 0.075 64 1.16043 -0.268 70 0.684 31 0.051 74 0.064 75 0.987 43 -0.024 90 -0.094 47 -0.138 55 0.027 27 0.559 88 0.041 27 -0.007 20 -0.132 74 -0.137 35 -0.037 78 0.059 54
carbonization factor 3 -0.171 55 -0.085 40 0.033 30 -0.123 18 0.161 09 0.007 30 0.161 61 -0.042 79 0.847 26 0.059 50 0.315 72
portlandite factor 4 0.011 46 -0.018 79 -0.029 23 0.047 70 -0.040 83 -0.134 25 0.088 27 -0.572 70 -0.04502 -0.751 97 0.055 25
F5=? factor 5 -0.253 90 0.199 55 -0.037 26 0.17238 -0.053 57 -0.053 47 -0.236 75 0.070 63 0.009 77 -0.023 36 0.11269
0.866 14 -0.191 91 -0.12507 0.18371 -0.987 32 -0.025 27 0.11888 0.211 92 -0.024 22 -0.180 56 0.912 94
halite factor 7 -0.052 06 0.908 62 -0.076 02 -0.024 61 -0.032 19 -0.072 42 0.865 37 0.184 07 0.05091 -0.255 81 -0.089 84
Table 11. Factor Pattern Correlations clay gypsum factor 2 factor 1 factor 1 1.00000 -0.507 1 2 1.000 00 factor 2 -0.507 1 2 0.180 20 -0.155 77 factor 3 0.382 89 -0.478 05 factor 4 0.244 04 factor 5 0.010 86 0.875 63 -0.379 96 factor 6 0.609 06 9 088 00 factor 7
carbonization factor 3 0.18020 -0.155 77 1.ooo 00 0.279 63 -0.082 94 0.215 85 -0.105 06
portlandite factor 4 0.382 89 -0.47805 0.279 63 1.00000 -0.248 20 0.324 88 0.217 80
factor 5 0.010 86 0.244 04 -0.082 94 -0.248 20 1.ooo 00 -0.229 34 0.15860
apatite factor 6 0.875 63 -0.379 96 -0.21585 -0.324 88 -0.229 34 1.ooo 00 0.532 65
halite factor 7 0.609 06 0.08800 -0.105 06 0.217 80 0.15860 0.532 65 1.000 00
Table 111. Factors of Factors. Varimax Rotated Factor Matrix (after Rotation with Kaiser Normalization) factor 1 factor 2 factor 3 factor 4 -0.770 F1 clay _ _ _ 09 _ _-0.424 _ _ _69- 0.585 15 0.023 24 F2 CaSO, 0.25045 0.641 08 -0.065 50 0.31085 F3 carbonization -0.151 46 -0.33903 -0.107 14 -0.00485 aF4 portlandite 0.131 06 0.771 37 0.00063 -0.24051 F5 0.089 61 -0.024 33 0.086 06 0.581 85 F6 apatite 0.99041 0.058 12 0.225 23 0.257 22 0.12684 0.08441 0.13203 0.87339 F7 halite
of the iteration criterion has to be based on intuition and mineralogical knowledge because there seems to be no other realistic criterion. Another matrix that can be obtained is the factor pattern correlation matrix-Table 11. This matrix shows the correlations among the factors. Factor-factor correlations can be used in this case, because the meaning of the factor correlations is known, i.e., correlations among minerals and not some superfactor (Davis, 1973). The correlation matrix is a symmetric square matrix, and the correlations can be used as input data for factor analysis. The solution this time was the Varimax method which gives independent (orthogonal) factors, loads most of the variance on the first factors, and does not give many factors that have only one loading. The result is a factor of factors matrix-Table 111. From the loading of minerals on each factor, mineral correlations can be seen clearly. It should be noted that, in a phosphate example, the determinant of the factor correlations matrix is zero. This shows that one of the factors, the sixth-apatite-as noted by the program printout is a linear combination of all the others, which is a very important conclusion. It must be stressed that the mineralogical correlations shown here may be true for this set of analyzed samples only. Other product systems, using phosphate raw material with a different composition, showed other correlations (such as calcium aluminates, etc.). But the important thing is that it seems that this method of finding the correlations can be used in totally different raw material-product industrial beneficiation systems. Factor analysis helps in choosing the influencing factors in the description of one parameter as a linear combination of the other components and in understanding why. Re-
apatite factor 6
gression analysis shows the exact quantitative relations and (using regression coefficients) helps to determine which are the influencing factors but does not provide the reasons why. In addition to building a linear model, regression analysis can be used to estimate the quantitative relations among the variables, aimed a t obtaining stoichiometric relations (Issahary and Pelly, 1981b). A problem arises: in the case of a highly significant correlation, which is the influencing parameter and which is the influenced parameter. Let us assume that among N variables there are two, j and i, having a meaningful correlation. The regression equation of j against the other measured parameters in the system will yield BO’$),which is the partial regression coefficient between j (dependent) and i (independent). But the regression of i against the other measured parameters will yield B(i;j),which is the partial regression coefficient of i (dependent) and j (independent). The F value will be the same in both cases, and a choice cannot be based on statistical considerations. In order to determine which is the independent variable, the following rule was used in this study: i is a function of j if I[B(j;i)]-ll > lB(i;j)l. A mixture containing small amounts of clay and quartz diluted with a large amount of a mineral devoid of silica and alumina (such as calcite) will be used as an example. A change in the alumina content will cause a change in the silica content, according to the clay stoichiometry, and a partial regression coefficient, B(SiO2;AlzO3),will be obtained. But, changes in the quartz content will cause only a small change in the alumina content (by dilution) and R(Al,O,;SiO,), a small number in absolute terms, will be obtained. In order to compare numbers of the same dimension, the reciprocal of B(Al20,;SiO2)will be used. so I [B(Al,03;Si02)]-11> !B(Si02;A1203)1.Accordingly, SiOz will be treated as a function of alumina; i.e., SiO, is influenced (dependent) by the influencing (independent) mineral A1,0,. Partial regression coefficients were used for several phosphate beneficiation systems to determine the independent variables and find an equation to describe the P,05 concentration in terms of the concentrations of the independent variables. The first step is to find the regression of each element against the other measured elements in the system. From these, the partial coefficients
Ind. Eng. Chem. Res., Vol. 29, No. 5, 1990 865 Table IV
so3
-1.008 1.005
-0.181 1 -0.037
-5.52 -27.0
Table V. Regression Data for a High Sulfate System (204 Samples) influencing variable j influenced variable i B(i;i) 10.2 CaO MgO pZ05
NazO
C1
so3
CaO A1203
CaO
SiOz
pZ05
SiOz CaO
so3 C1
so3 pZo5 so3
NazO CaO
-4.45 0.3151 -0.5043 -2.44 0.9811 6.70 1.722 -1.008 -2.187 -0.5954 1.005 0.4948 0.315 1.875
B(i;j)and B(j:i) are found. The next step is to decide which are the independent elements (P205is the dependent element)-Tables IV and V. From the tables, the following equation describing P20,as a function of the independent variables is obtained:
[P205]= 38.22 - 4.45[MgO]
+ 1.005[S03] - 1.008[Si02]
The following model was obtained (Issahary and Pelly, 1982b) for one of the phosphate systems: [P,O5] = 38.40 - 4.5[Mg0] 2.45[A120J - 0.96[Si02] - 0.8[S03] The last equation is a model obtained for a specific tested system, but a model derived from one system (i) can be used in a general model for different systems (not too much different) of raw material used 0'). The general form for the model is E[ELX]; = CjBi
(1)
where E is the expectancy of element X in system j and C j is the vector of concentrations (or mean concentrations if a mean is wanted) of the independent variables (elements 1, ..., n ) in product system j ; i.e., C; = ([EL])',
[ELl];, [EL2];, ..., [ELn];)
This vector, Cj, includes [EL]!, which is the free term in the model derived from system i. For the example given above, [EL]! = 38.40, and C; = ([P205]p,[MgOIj, [Al2O3Ij, [SioZlj, [SO3lj)* Bi is the vector of regression of coefficients in system i, the system upon which the model is based:
The important thing is that B, and [EL]: taken from one system are used in a general model for all (not too much different) types of raw materials used and should be such that they should not cause a large error for different systems. In a regression equation like this, there should be a term, e, representing the error vector including both measurement errors and errors caused by lack of fit to the model. It we denote the expectancy of the error by E(c), then a condition for the accuracy of the model is E ( € )= 0; Le., the expectancy of the error is zero. It is important to repeat that the model is actually a regression equation derived from a specific data collection (i) in the plant, which may be a little different from that of the systems to be analyzed by the model 0'). The model described above predicts the desired element's grade in the product as a function of the impurities in the product. The important thing is, of course, to build a model predicting the desired element's grade in the product as a function of the composition of the raw material. As was mentioned above, there may be a long time lag between the feed and the appearance of the product so that a specific product sample cannot be attributed to a specific feed. Another aspect is that a part (or most) of the impurities in the raw material does not remain in the product but is leached out during the beneficiation process. These problems prevent a simple prediction of the content of the desired mineral in the product based on the impurities of the raw material. The method chosen was to find the relationships between the concentrations of the impurity variables in the raw material and their concentrations in the product and use these relationships to amend the linear model of the enriched mineral in the product as a function of the independent variables in the product. Only variables found to be independent in the product and for which a product-raw material correlation can be established can be used. As mentioned above, no direct raw material-product correlations of a specific sample can be found. These correlations must be found for the raw material-product system in question by a great number of analyses of raw material samples and product samples. There are several ways of describing the impurity in the product as a function of its concentration in the raw material: (1)We can predict the concentration of the impurity in the product by describing it as a linear function of its concentration in the raw material with reasonable error
GI* = G, + A
+ e,
where G,* is the concentration in the ith sample of the product, G, is the concentration in the ith sample of the raw material, A is a constant difference, and t, is an error associated with the G,* - GI couple. (2) With a large enough number of raw material samples, the mean of a large enough number of product samples can be expected and is equal to the expectancy of the impurity in the raw material, with or without deviation. The expectancy is E(G,*) = E(G,) + A (3) A nonlinear function is
where BELX(i) is the regression coefficient of element X in system i. For the example given above,
GI* = f ( G J +
6,
or a correlation modified into an approximate linear
866 Ind. Eng. Chem. Res., Vol. 29, No. 5 , 1990 Table VI. Empirical Test of the Model for Prediction of P,O, Content in the Product as a Function of Raw Material Composition _______ N,,no. of A’,, no. of [P,O,I, E[m], monthly SI,std dev measuremonthly s,,std __ dev measuremonth mean expectancy of E[m] ments mean of rp,o,i mrnts _. 1 32.96 0.61 156 32.95 0.66 229 33.46 0.57 298 2 33.42 0 52 225 12.1 J3.35 0.79 .3 33.36 0.49 52 33.45 0.58 257 3 33.36 0.42 115 33.13 0.49 109 d 33.19 0.62 5‘3 33.29 0 62 101’7 weighted 33.26 0 48 601 mean ________I____
~
.
function (in the case, for instance, when the computer in the analytical instrument has only linear functions) is GI* = KG, + 1‘+ E,‘ where K is a constant and ti’ is an error including both measurement errors and the deviation of the line for G,* from the curve for GI*. The line chosen should be such that for the c o m m o n working range tL’ will be minimal. At the extremes-very high and very low concentrationsthere will be consistent errors. (4) The impurity concentration in the product cannot be predicted; only a mean value can be expected, without regard t o the content in the raw material
E(G,”)= constant As an example, for the impurities of the phosphate beneficiation system described above, it was found that the first scheme describes the alumina correlations, the second scheme describes the silica correlations, the third scheme describes the sulfate correlations, and the fourth scheme describes the MgO correlations (Issahary and Pelly, 1982b). In order to find a model for predicting the content of the desired element in the product as a function of the impurities of the raw material, we have to combine raw material-product impurity correlations with the general model (eq 1)which predicts the desired element’s content in the product as a function of the impurities in the product. We obtain E[ELX], = GjBi + AjB, where B, is the chosen vector of coefficients based upon system i, G, is the vector of impurity concentrations in the raw material, A, is the vector of constant deviations (raw material-product relations, schemes 1-4), and E[ELX], is the expectancy of element ( X ) concentration in the product obtained from a raw material with a composition 1. This model can be simplified for practical use: each regression line passes through the mean point, so we can substitute the values of the mean point of a large enough system in eq 2 and calculate A,B,, add it to the constant [ELI: in vector GI, and use this number in eq 2. -4s an example for a phosphate beneficiation process, where P,05 in the product as a function of raw material impurities was determined, the expectancies of P205and their standard deviations and the measured concentrations of P205in the product and their standard deviations were calculated-Table VI. The significance of the differences and the standard deviations between the predicted and measured values were calculated (Issahary and Pelly, 1985). A modification of the equation is described (Issahary and Pelly. 1985) in order to predict the Pz05grade in the product after preliminary washing of the raw material (to get rid of clays) as a function of the composition of the unit n s h t d raw material (or by another modification-as a function of the impurities of the ionshed raw material).
i
“2
This case, by the way, shows the importance of factor analysis even without a regression analysis model. Factor analysis studies showed that by calcination without pretreatment (for a high sulfate raw material) about 88% of the apatite variance is determined by a clay correlation. It was found that silica and alumina (by binding Ca) cause (by dilution) a great reduction in P,05 content, and with a preliminary washing, to get rid of the clays, a higher P205 grade was obtained. Application. Linear models developed by the method described above can be used (and are used) for mining control. Geologists can map the ore strata according to the predicted element’s content in the product (with or without preliminary washing). This mining planning can be done a long time ahead. Another use of the model, coupled with on-line analysis, is to estimate the efficiency of the plant’s operation. If the desired element’s content in the product is equal to the predicted value, the plant operates efficiently. If it’s concentration is lower than the predicted, the reason should be sought in one of the plant stages. If it’s content is lower than desired, the reason should be sought in the raw material or the preliminary washing stage. The application of this model allows ar. unequivocal determination of where the problem is-the grade of the feed to the kiln or in the plant, from the kiln on. This is a great operational advantage since without such a technique cases of low product grade can cause numerous problems (even leading to stopping of production) by seeking the cause in the plant’s operations. The mathematical treatment of finding the influencing parameters and the degree of their influence by factor analysis and regression analysis was applied to phosphate beneficiation. It can be applied to find raw materialproduct correlations in other systems also. Coupled with on-line analysis of the influencing variables, this will provide a good method for controlling plant operation. Literature Cited Davis, J. C. Statistics and Data Analysis in Geology: John Wiley and Sons, Inc.: New York, 1973; Chapter 7; p 517. Draper, N. R.; Smith, H. Applied Regression Analysis; John Wiley and Sons, Inc.: New York, 1981. Harman, H. H. Modern Factor Analysis, 3rd ed.; The University of Chicago Press: Chicago, 1976. Issahary, D.; Pelly, I. A Factor Analysis Study of Phosphate Beneficiation by Calcination. Anal. Chin. Acta 1981a, 133, 359-367. Issahary, D.; Pelly, I. A Regression Analysis Study of Phosphate Beneficiation by Calcination. Anal. Chim. Acta 1981b, 133, 369-3’78. Issahary, D.; Peily, I. Simultaneus Multielement Analysis of Phosphates by X-Ray Fluorescence. X-Ray Spectrom. 1982a, 11,8-12. Issahary, D.: Pelly, I. Prediction of the Phosphorus Pentoxide in the Product as a Function of Raw Material Composition. Anal. Chim. Acta 1982b, 138, 183-190. Issahary, D.; Pelly, I. Simultaneous Multielement Analysis of Phosphates by X-Ray Fluorescence. X-Ray Spectrom. 1983, 12, 50. Issahary. D.: Pelly. I. Phosphate Beneficiation h v Calcination.
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., e t 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
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1990 A m e r i c a n C h e m i c a l Societv
