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GENERAL RESEARCH Determination of the Optimum Conditions for the Dissolution of Colemanite in H3PO4 Solutions Murat Yes¸ ilyurt,*,† Sabri C ¸ olak,† Turan C ¸ alban,† and Yas¸ ar Genel‡ Department of Chemical Engineering, Atatu¨ rk University, 25240 Erzurum, Turkey, and Department of Chemistry, Faculty of Education, Yu¨ zu¨ ncu¨ Yıl University, 65080 Van, Turkey
The Taguchi method is an engineering design optimization methodology that improves the quality of existing products and processes and simultaneously reduces their costs very rapidly, with minimum engineering resources and development man hours. In this study, this method was utilized to investigate the effect of various parameters for determining the optimum dissolution conditions of colemanite (Ca2B6O11‚5H2O) in phosphoric acid solutions. The parameters investigated were the acid concentration, particle size, stirring speed, and reaction time. The most significant parameters affecting the solubility were the reaction time and particle size, whereas the acid concentration and stirring speed had a lesser effect. The optimum dissolution conditions were determined as follows: reaction time, 12 min; particle size, 2.4 mm; acid concentration, 2.7 M; stirring speed, 450 rpm; reaction temperature, 94 °C; solid-to-liquid ratio, 0.25. Under these conditions, it was found that boron extraction from colemanite ore was 100%. Introduction Turkey has the largest boron reserves in the world. Huge portions of Turkey’s commercially recoverable boron reserves are colemanite (Ca2B6O11‚5H2O), ulexite (NaCaB5O9‚8H2O), and tincal (Na2B4O7‚10H2O). Boron compounds are consumed in a very wide range of industrial applications such as in the production of glass, fibers, heat-resistant materials, material processing, nuclear reactors, detergents, etc.1 One of the mostused boron compounds is boric acid, which is mainly produced from the reaction of colemanite with sulfuric acid.2 The reaction is as follows:
Ca2B6O11‚5H2O(s) + 2H2SO4(aq) + 6H2O f 6H3BO3(aq) + 2CaSO4‚2H2O(s) (1) Gypsum is formed as a byproduct throughout the reaction. After filtration of gypsum, crystallization of boric acid in high purity and efficiency is a very crucial process. This process has some disadvantages such as sulfate contamination in the product and disposal of gypsum, which causes severe environmental problems.3 In this respect, the dissolution of colemanite with different reactives has drawn considerable attention. Various dissolution studies in aqueous water and acidic solutions have been found in the literature.4-6 In a study7 done on the dissolution kinetics of colemanite in H3PO4 solutions, the dissolution rate was found to be controlled by a surface chemical reaction with an activation energy of 53.91 kJ‚mol-1. In another study,8 dissolutions of colemanite, ulexite, inyoite, and hydroboracite in H3PO4 solutions were investigated, and it † ‡
Atatu¨rk University. Yu¨zu¨ncu¨ Yıl University.
was found that dissolution of borates in H3PO4 solutions was in diffusional character. In a different study9 done on the extraction of boric acid with nitric acid from colemanite, optimum working conditions were found as the following: 94 °C reaction temperature, 0.25 g‚mL-1 solid-to-liquid ratio, 2.4-mm particle size, 2.2 M acid concentration, 500-rpm stirring speed, and 11-min reaction time. Under these optimum conditions, the boric acid extraction efficiency from colemanite was 99.66%. No study could be spotted by us about the determination of the optimum conditions for the boric acid extraction from colemanite by phosphoric acid solutions. Thus, the aim of the present study is to determine the optimum working conditions by using the Taguchi method. There are a wide range of applications for the Taguchi method, from chemistry to engineering and from microbiology to agriculture.10-15 There are many ways to design a test, but the most frequently used approach is a full factorial experiment. It is very time-consuming when there are many factors. To minimize the number of tests required, fractional factorial experiments (FFEs) were developed. FFEs use only a portion of the total possible combinations to estimate the effects of the main factors and the effects of some of the interactions. Taguchi developed a family of FFE matrices that could be utilized in various situations. These matrices reduce the experimental number but still obtain reasonably rich information. The conclusions can also be associated with a statistical level of confidence. In Taguchi’s methodology, all factors affecting the process quality can be divided into two types: control factors and noise factors. The control factors are those set by the manufacturer and are easily adjustable. These factors are most important in determining the quality of the product characteristics. The noise factors, on the other
10.1021/ie020823s CCC: $30.25 © 2005 American Chemical Society Published on Web 03/30/2005
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Table 1. Chemical Composition of Colemanite Ore Used in This Study main mineral
%
main mineral
%
B2O3 SiO2 Al2O3 CaO
44.05 3.98 0.77 24.85
Fe2O3 H2O others
0.36 23.65 2.34
hand, are those undesired variables that are difficult, impossible, or expensive to control, such as the ambient temperature, humidity, etc. The major steps of implementing the Taguchi method are (1) to identify the factors, (2) to identify the level of each factor, (3) to select an appropriate orthogonal array (OA), (4) to conduct the experiments, (5) to analyze the data and determine the optimal levels, and (6) to conduct the confirmation experiment. In data analysis, signal-to-noise ratios are used to allow control of the response as well as to reduce the variability about the response. Material and Methods The colemanite ore used in this study was obtained from Emet-Mine (Ku¨tahya, Turkey). The sample was crushed, ground, and then sieved by using ASTM standard sieves to obtain 2.4-, 3.8-, and 5.2-mm average size fractions. The chemical composition of the ore was determined by volumetric and gravimetric methods. Trace elements were analyzed by an atomic absorption spectrophotometer. The chemical composition of colemanite ore is given in Table 1. There was no definitive trend between the B2O3 content and particle size ranges. All of the other chemicals used in the experiments and analyses were purchased as reagent grade from Merck. The dissolution process of the mineral was carried out at atmospheric pressure in a 250-mL, three-necked, round-bottomed spherical glass reactor. A thermostat was used for controlling the reaction temperature and a digitally controlled mechanical stirrer was employed for mixing. To avoid the loss of the reactor contents by evaporation, a cooler was attached to the reactor. First 100 mL of a phosphoric acid solution at a given concentration was put into the reactor. When the reactor contents reached the desired temperature (94 °C, boiling point in Erzurum, Turkey), a predetermined amount of the ore (25 g) was added into the solution while the contents of the reactor was stirred at a determined speed. As soon as the process was finished, the contents were filtrated, and boron in the solution was analyzed by a spectrophotometric method.16 All designed experiments require that a certain number of combinations of factors and levels be tested to observe the results of those test conditions. The Taguchi approach relies on the assignment of factors in specific OAs to determine those test combinations. Orthogonality means that factors can be evaluated independently of one another; the effect of one factor does not bother the estimation of the effect of another factor. One provision of orthogonality is a balanced experiment: an equal number of samples under the various treatment conditions. Experimental parameters and their levels used are given in Table 2. The experimental design used was the OA9(34) orthogonal array, which is indicated in the heading of the array shown in Table 3, because it is the most suitable for the conditions being investigated for four parameters, each with three levels. The levels of parameters were determined by pre-
Table 2. Parameters and Their Values Studied in Experiments levels parameters A B C D E F
acid concentration (M) particle size (mm) stirring speed (rpm) reaction time (min) reaction temperature (°C) solid-to-liquid ratio (g‚mL-1)
1
2
3
2.5 5.2 300 3
2.7 3.7 450 6 fixed (94) fixed (0.25)
2.9 2.4 600 9
Table 3. Experimental Design Used dissolved B (%)
expt no 1 2 3 4 5 6 7 8 9
parameters and levels A B C D
first trial
second trial
mean
performance statistic for “larger is better” (θ)
1 1 1 2 2 2 3 3 3
61.00 87.68 95.77 87.76 75.17 97.06 80.19 94.60 82.90
63.39 89.50 95.82 89.65 73.27 98.55 85.19 90.10 81.18
62.20 88.59 95.80 88.71 72.22 97.81 82.69 92.35 82.04
35.87 38.95 39.63 38.96 37.17 39.81 38.34 39.30 38.28
1 2 3 1 2 3 1 2 3
1 2 3 2 3 1 3 1 2
1 2 3 3 1 2 2 3 1
experiments, and we attempted to start from their minimum levels. For example, the level of the acid concentration was started from 2.5 M, which was determined according to the total reaction (eq 12) and the solid-to-liquid ratio used. If it used less than this value, there will not be enough acid concentration to dissolve the solid determined according to the solid-toliquid ratio used. Also, we made an effort to study with maximum particle size and minimum reaction time and stirring speed because of the economy. On the other hand, because the aim of the process is to obtain much more boric acid extraction at one stage, levels of the reaction temperature and solid-to-liquid ratio were fixed at 94 °C (boiling point of water at 610 mmHg, in Erzurum, Turkey) and 0.25 g‚mL-1, respectively. The reasons for using the highest levels of these parameters are that the solubility of boric acid highly increases with temperature and the solution volume for ore used is kept at a minimum level in terms of transport costs. To observe the effects of noise sources on this process, each experimental trial was repeated twice under the same conditions at different times. Also, the order of experiments was made random in order to avoid noise sources that had not been considered initially that could take place during an experiment and affect the results in a negative way. The performance measure analysis developed by Taguchi was chosen as the optimization criterion. When there is a target value to be achieved for response, he recommends the use of the performance measure (θ), which estimates the inverse of the coefficient of variation. For practical purposes, when the desired characteristic for the response is “the larger, the better” (as, for example, in the case of maximum extraction), Taguchi recommends the use of
(∑ )
θ ) -10 log
1 n
1 y2
(2)
whereas when the response is “the smaller, the better” (as, for example, in the case of power losses, leakages, etc.), he recommends the use of
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θ ) -log
{n1∑y } 2
(3)
where n is the repetition of each experiment and y is the result of each experiment. Note that the minus sign in the above formulation is used by convention so that θ is always maximized. After analysis of the experimental result, an experimenter chooses the control factor’s optimal levels that minimize the variability and bring the mean response nearest to the target value. The prediction of the process performance under the optimal conditions is usually required. This method suggests a prediction formula based on individual differences between the average of the chosen factor levels and the overall mean. For example, suppose we are interested in estimating the average yield of a process on the basis of the results of an experiment that indicated that factors A and B are significant with optimal levels A(3) and B(4). The process average under the optimal levels can be estimated by
h 4 - M)β(B) (4) µ ) Mβ(M) + (A h 3 - M)β(A) + (B where µ ) process average, M ) grand average of all of the experimental results, β ) coefficient of the grand average (M) and each parameter (A and B) defined by 1 - 1/F(A,B) [F(A,B) ) the F ratio of each parameter (note that when it is F(M), then F(M) ) Cf/MSSe, with Cf representing the ratio of the sum of squares to the total number of all observations and MSSe the error variance)], A h 3 ) average yield at level A(3), and B h4 ) average yield at level B(4). Clearly, the estimate of the mean µ is only a point estimate based on the averages of results obtained from experiment. An experimenter would prefer to have a range of values within which the true average would be expected to fall with some confidence. The confidence interval (CI) is a maximum and minimum value between which the true average should fall at some stated percentages of confidence. When stating a confidence value for a CI, experimenters are simply stacking the odds in their favor that the true average will fall between the stated limits. There is a CI that Taguchi uses for predicting a confirmation experiment:
CI ) xF(1,dfe;R) MSSene-1
(5)
where dfe is the residual degrees of freedom, F(1,dfe;R) is the critical value from the F tables depending on 1 and dfe at level of signifance R, MSSe is the mean sum of squares for residual variance, and ne is the effective number of replications. The general formula for the effective number of replications is as follows:
ne )
N 1 + Σ(ED)
(6)
where N is the size of the experiment and Σ(ED) is the total effective number of degrees of freedom. For example, if parameter A is a k-level factor, then EDA ) k - 1. A confirmation experiment is the final step in the iteration of the design of the experiments. A confirmation experiment is performed by conducting a test using a specific combination of the factors and levels previously evaluated. The purpose of the confirmation experiment is to validate the conclusions drawn during the analysis phase. Because a FFE OA is used and
Table 4. Level Averages for Means and Performance Statistic Values for Each Level of the Parameters parameter
level
mean
performance statistic
A
1 2 3 1 2 3 1 2 3 1 2 3
82.1933 86.2442 85.6933 77.8633 84.3875 91.88 84.1167 86.4450 83.5692 72.1525 89.6950 92.2833
38.1478 38.6449 38.6391 37.7216 38.4727 39.2375 38.3259 38.7276 38.3782 37.1067 39.0300 39.2951
B C D
several factors contribute to the variation observed, it is likely that the best combination of factors and levels was not present in the OA test combinations. The confirmation experiment is highly recommended to verify the experimental conclusions and is interpreted in this manner. If the result of the confirmation experiment is within the limits of CI, then an experimenter believes that the significant factors as well as the appropriate levels for obtaining the desired result are properly chosen. If the result of the confirmation experiment is outside the limits of CI, then an experimenter selects the wrong factors or levels to control the results at a desired value or has excessive measurement error, necessitating further experimentation. Results and Discussion The following reactions probably occur during the dissolution of colemanite in H3PO4 solutions:
6H3PO4(aq) S 6H2PO4-(aq) + 6H+(aq)
(7)
6H2PO4-(aq) S 6HPO4-2(aq) + 6H+(aq)
(8)
2(2CaO‚3B2O3‚5H2O)(s) f 4Ca2+(aq) + 3B4O7-2(aq) + 9H2O + 2OH-(aq) (9) 3OH-(aq) + 3H+(aq) S 3H2O 3B4O7-2(aq) + 15H2O + 6H+ S 12H3BO3(aq)
(10) (11)
2CaO‚3B2O3‚5H2O(s) + 4H3PO4(aq) + 2H2O f 2Ca(H2PO4)2(aq) + 6H3BO3(aq) (12) The collected data for boric acid extraction were analyzed using the MINITAB computer software package program for the evaluation of the effect of each parameter on the optimization criteria. The results are given in Table 3, and on the basis of level averages (for θ), Table 4 can be constructed from Table 3. We try to explain it with an example. Let us look at Table 3, column D, which shows a variation of the performance statistics (θ) for the reaction time. Now let us try to determine the experimental conditions for the first data point. The reaction time for this point is at the first level (3 min) for this parameter. Now let us look at Table 3 and find the experiments for the first level of reaction time. It is seen that experiments for which the column reaction time is 1 are experiments with experiment numbers 1, 5, and 9. The mean of the performance statistics of these experiments is the mean of the first
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Table 5. ANOVA Analysis for the Dissolution Process parameters A B C D
acid concentration particle size stirring speed reaction time error total
df
SS
MSS
F ratio
Cr (%)
2 2 2 2 9 17
59.01 595.37 27.58 1442.88 32.61 2157.46
29.51 297.69 13.79 721.44 3.62
8.14 82.16 3.81 199.10
2.39 27.26 0.94 66.54
level of reaction time (D). This value is given in line D1 of Table 4. The experimental conditions for the second data point thus are the conditions of the experiments for which the column reaction time is 2, and so on. The optimal levels of these factors are the levels with the maximum performance statistics (θ), that is, with minimum variability. It is clear from performance measures and ANOVA (Tables 4 and 5) that factors reaction time and particle size, and to a lesser degree factors acid concentration and stirring speed, significantly effect the variation in the response. According to Taguchi, the use of the F ratios in an ANOVA analysis is only helpful for the qualitative evaluation of whether factorial effects exist. For quantitative evaluation, this something that can be achieved through the use of a contribution ratio (Cr). The contribution ratio of a main factor effect is its contribution (in percentage terms) to the total variability of the experimental results. The contribution ratio can be achieved by dividing the source’s net variation by SSTotal, which is given as follows:
CrA )
SSA - dfAMSSError × 100 SSTotal
It is clear from the Cr column of Table 5 that the highest contributors to the variability of the experimental results are reaction time and particle size, with the reaction time accounting for more than 66% of total variation. From Table 4, the optimal levels of these factors are acid concentration (2), particle size (3), stirring speed (2), and reaction time (3). If the experimental plan given in Table 3 is studied carefully, it can be seen that this combination of factor levels (2, 3, 2, and 3) was not one of the nine combinations tried in the experiment. This is to be expected because of the high fractionality of the experimental design used (9 out of 34 ) 81 possible combinations). Using Taguchi’s estimation formula based on the level averages and the associated β coefficients (using Tables 4 and 5), an estimate of the performance for µ under the optimal conditions is given by formula (4), which yields
h 3 - M)β(B) + µ ) Mβ(M) + (A h 2 - M)β(A) + (B (C2 - M)β(C) + (D3 - M)β(D) We can find M (mean of the experimental results) ) 84.71 with β(M) ) 1 - 1/F(M) where
F(M) )
Cf (61 + ... + 81.18)2/18 129164.96 ) ) ) MSSe 3.62 3.62 35680.93
and so
β(M) ) 1 -
1 =1 35680.93
Also from Table 5
β(A) ) 1 -
1 1 ) 0.877, β(B) ) 1 , 8.14 82.16 β(C) ) 0.737, β(D) ) 0.995
Therefore
µ ) 84.71 × 1 + (86.24 - 84.71)0.877 + (91.88 - 84.71)0.988 + (86.44 - 84.71)0.737 + (92.28 - 84.71)0.996 ) 101.935 The confidence limits on the above estimate can be calculated using formulas (5) and (6)
CI ) xF(1,dfe;R) MSSene-1 where F(1,dfe;R) ) F(1,9;5%) ) 5.12, MSSe ) 3.62, and ne ) 18/(1 + 2 + 2 + 2 + 2 ) 2).
xF(1,dfe;R) MSSene-1 ) x5.12 × 3.62 × 2 ) 6.09 The CI for the confirmation experiment is M + CI < M < M + CI ) 101.935 - 6.09 < 101.935 < 101.935 + 6.09. This means that the dissolution percentage of B can be given at the optimum working conditions between 95.845 and 100%. The average value of the dissolution made in the confirmation experiment at 95% confidence fell within the interval calculated (98.6 and 99.2%). However, because we want to reach the 100% extraction of boron (keeping all of the parameters at their optimum levels except for the reaction time), the level of the reaction time was increased one stage (12 min) and all of the boron in the ore was extracted at the end of this period. A successful confirmation experiment is defined as one where the average of these samples falls within the CI, it is evident that the factors and interactions used in the estimate of the mean are, in fact, controlling the result. If so, the experimental process may stop for all practical purposes because a satisfactory solution to the problem has been identified. Conclusions Designing processes and products so that they are insensitive to variation in conditions is known as robust design. In the Taguchi method, a process or product must be designed so that it is robust against potential causes of variability (noise factors) that may occur before, during, or after production. In this study, the results of the application of the Taguhi method assisted the determination of the optimum working conditions for the dissolution of colemanite in H3PO4 solutions. The most significant parameters affecting the solubility were the reaction time and particle size. The acid concentration and stirring speed had an effect at a lesser degree. The optimum conditions for B2O3 extraction from colemanite ore with H3PO4 solutions were determined as follows: reaction time, 12 min; particle size, 2.4 mm; acid concentration, 2.7 M; stirring speed, 450 rpm. Because the Taguchi method includes both design and factors affecting the variability, the conditions determined in a laboratory environment may be very useful for the production of H3BO3 at an industrial scale. In the production of boric acid by the reaction of colemanite with sulfuric acid, gypsum is formed as a
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byproduct. This process has disadvantages from the point of view of both sulfate contamination in the product and disposal of gypsum, which causes environmental problems. When the colemanite is treated with phosphoric acid, monocalcium phosphate is produced as a byproduct in the reaction. Because of the high solubility of monocalcium phosphate, when the leach solution is passed through a strong acid-cationic ion exchanger, the Ca2+ ions are swapped with H+ ions held on ionexchanger resins, and according to following reactions, H3PO4 can be produced and reused.
2RH + Ca2+ f R2Ca + 2H+ 2H2PO4- + 2H+ f 2H3PO4 Therefore, this process is more advantageous than the sulfuric acid process in which gypsum is formed as a byproduct. Literature Cited (1) Garrett, D. E. Borates; Academic Press: San Diego, CA, 1998. (2) C¸ etin, E.; Erogˇlu, I˙ .; O ¨ zkar, S. Kinetics of Gypsum Formation and Growth during the Dissolution of Coleminite in Sulfuric Acid. J. Cryst. Growth 2001, 231, 559. (3) Davies, T. W.; C¸ olak, S.; Hooper, R. M. Boric Acid Production by the Calcination and Leaching of Powdered Colemanite. Powder Technol. 1991, 65, 433. (4) Ceyhun, I˙ .; Kocakerim, M. M.; Sarac¸ , H.; C¸ olak, S. Dissolution Kinetics of Colemanite in Chlorine Saturated Water. Theor. Found. Chem. Eng. 1999, 33, 253.
(5) Zdanovski, A. B.; Biktagirova, L. G. On the Mechanism of the Decomposition of Calcium Borates in H3BO3 Solutions. Zh. Prikl. Khim. 1967, 40, 2659. (6) Kocakerim, M. M.; Alkan, M. Dissolution Kinetics of Colemanite in SO2-Saturated Water. Hydrometallurgy 1998, 19, 385. (7) Temur, H.; Yartas¸ ı, A.; C¸ opur, M.; Kocakerim, M. M. The Kinetics of Dissolution of Colemanite in H3PO4 Solutions. Ind. Eng. Chem. Res. 2000, 39, 4114. (8) Imamutdinova, V. M. Rates of Dissolution of Native Borates in H3PO4 Solutions. Zh. Prikl. Khim. 1967, 40, 2596. (9) Yes¸ ilyurt, M. Determination of the Optimum Conditions for Boric Acid Extraction from Colemanite Ore in HNO3 Solutions. Chem. Eng. Process. 2004, 43, 1189. (10) Do¨nmez, B.; C¸ elik, C.; C¸ olak, S.; Yartas¸ ı, A. Dissolution Optimization of Copper from Anode Slime in H2SO4. Ind. Eng. Chem. Res. 1998, 37, 3382. (11) C¸ opur, M.; Pekdemir, T.; C ¸ elik, C.; C¸ olak, S. Determination of the Optimum Conditions for the Dissolution of Stibnite in HCl Solutions. Ind. Eng. Chem. Res. 1997, 36, 682. (12) Abalı, Y.; C¸ olak, S.; Yapıcı, S. The Optimization of the Dissolution of Phosphate Rock with Cl2-SO2 Gas Mixtures in Aqueous Medium. Hydrometallurgy 1997, 46, 27. (13) Ross, P. J. Taguchi Techniques for Quality Engineering; McGraw-Hill: New York, 1987. (14) Logothetis, N. Managing for Total Quality from Deming to Taguchi and SPC; Prentice Hall: Englewood Cliffs, NJ, 1992. (15) Roy, R. A Primer on the Taguchi Methods; Van Nostrand Reinhold: New York, 1990. (16) Greenberg, A. E.; Trussell, R. R.; Clesceri, L. S. Standard Methods for the Examination of water and wastewater; American Public Health Association: Washington, DC, 1985.
Received for review October 18, 2002 Revised manuscript received June 20, 2004 Accepted February 21, 2005 IE020823S
