Effects of Impurities on CaSO4 Crystallization in the Ca(H2PO4)2

This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes.

Article Cite This: ACS Omega 2019, 4, 12702−12710

http://pubs.acs.org/journal/acsodf

Effects of Impurities on CaSO4 Crystallization in the Ca(H2PO4)2− H2SO4−H3PO4−H2O System Xinru Mu,† Ganyu Zhu,*,‡ Xu Li,§ Shaopeng Li,‡ Xiaokang Gong,§ Huiquan Li,‡,∥ and Guoxin Sun*,†

Downloaded via 79.110.25.245 on July 28, 2019 at 07:59:53 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

School of Chemistry and Chemical Engineering, Institute for Smart Materials & Engineering, University of Jinan, 336 Nanxinzhuang West Road, Jinan 250022, P. R. China ‡ Key Laboratory of Green Process and Engineering, National Engineering Laboratory for Hydrometallurgical Cleaner Production Technology, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China § Yidu Xingfa Chemical Company Limited, Yidu, Hubei 443311, China ∥ University of Chinese Academy of Sciences, Beijing 100049, China S Supporting Information *

ABSTRACT: Wet-process phosphoric acid is a fundamental process in the fertilizer industry. The influence of impurities on crystallization kinetics of CaSO4 was investigated in the Ca(H2PO4)2−H2SO4−H3PO4−H2O system using a mixed suspension mixed product removal crystallizer. Effects of Si, Al, Fe, Mg, K, and Na on crystal morphology and structure were examined in the highly acidic system through scanning electron microscopy and high-resolution transmission electron microscopy. Results show that the increase of Mg, K, and Na content facilitates crystal growth. Si, Al, and Fe are beneficial to CaSO4 crystal growth at a certain concentration range. Impurities also affect the crystal morphology, and the addition of Si, Fe, and Na promotes the formation of needle-like crystals compared with other impurities. X-ray diffraction results show that the preferred crystal growth direction is (020), and the interplanar spacing of the crystals is affected by the element radius of the impurities.

1. INTRODUCTION Phosphorus chemicals, which are widely used to produce fertilizers and composite functional materials containing phosphorous,1,2 are mainly produced from phosphate rock through wet-process phosphoric acid. Wet-process phosphoric acid is produced via the acidic decomposition of phosphate rock, and CaSO4 is also generated in this process as a byproduct. This process can be expressed by the following equation

To date, effects of impurities on CaSO4 crystallization have been widely investigated,11−16 and many researchers support that impurities can affect the nucleation, crystallization, morphologies, and filterability of gypsum crystals.17−21 The CaSO4 sizes with different impurities were investigated. Low K+ and Na+ concentrations increase the average diameter of the crystal, while the presence of Mg2+ and Cu2+ increases the crystal size.22 Trivalent ions, such as Al3+ and Fe3+, also increase the average diameter of the crystal at low concentrations because they have a high surface adsorption affinity. Anions, such as F−, can affect the gypsum crystal morphology and form sphere-shaped aggregates.23 CaSO4 crystallization kinetics was also studied. Wang24 measured the CaSO4·2H2O crystallization rate by the free Ca2+ and SO42− ion dissolution rate. Results showed that the silica colloid promotes the gypsum crystallization rate but exhibited an insignificant effect on the nucleation rate for all saturated conditions. Rabizadeh25 showed that Mg2+, Li+, and K+ were only adsorbed on the newly formed surfaces of the growing gypsum crystals, while Na+ was incorporated into the synthesized crystals. The nucleation and growth kinetics of

Ca5F(PO4 )3 + 5H 2SO4 + nH 2O → 3H3PO4 + HF + 5CaSO4 ·nH 2O

(1)

However, phosphate rock in China is almost medium-sized and low grade, with high impurity content. A part of the impurities dissolves into the liquid phase and affects the H3PO4 quality. By contrast, undissolved impurities stay in the solid phase and affect CaSO4 crystallization, thereby increasing the acid content in the solid phase. The acid in phosphogypsum may reduce the phosphorus pentoxide yield and extensively affect CaSO4 utilization in various industries.3−5 In several industrial processes, the crystallization of gypsum also leads to the blockage of pipes or filters and reduces production efficiency.6−10 Therefore, the influence of impurities on phosphogypsum crystallization needs to be investigated. © 2019 American Chemical Society

Received: April 17, 2019 Accepted: July 2, 2019 Published: July 25, 2019 12702

DOI: 10.1021/acsomega.9b01114 ACS Omega 2019, 4, 12702−12710

ACS Omega

Article

Mg2+ are 5- to 10-fold lower than those of Li+, Na+, and K+ because Mg has higher ionic strength and hydration enthalpy than monovalent ions, thereby inhibiting the crystal growth. Meanwhile, additives have great effects on CaSO4 crystallization kinetics.26−30 Citric acid and 2-phosphonobutane1,2,4-tricarboxylic acid have a strong effect on the induction period of gypsum nucleation.23,27 Malic acids can change crystal morphology through the selective complexation with Ca active sites on the crystal planes.28 Phosphonate additives are very effective retardants for gypsum crystallization because the phosphonate group can be adsorbed onto the crystal surface to inhibit the crystal growth.29 Although previous researchers have achieved many accomplishments in terms of the effects of impurity ions on the shapes and size of CaSO4 crystals, these studies are based on a neutral CaCl2 aqueous solution, which is a two-phase solid−liquid system. The actual wet-process phosphoric acid is a strong acidic solid−liquid− solid three-phase reaction. Previous studies lacked a reference for the actual acid hydrolysis process. Hence, the particle size, morphology, and crystallization kinetics of CaSO4 with different impurities in a strong acid system must be investigated. In this work, the Ca(H2PO4)2−H2SO4−H3PO4−H2O system was established to simulate the acid hydrolysis process. A mixed suspension mixed product removal (MSMPR) crystallizer, which is widely used in crystallization research studies,31−33 was used to investigate the CaSO4 crystallization rates. The effects of impurities on CaSO4 particle size, morphology, and structure were analyzed using a laser particle size analyzer, a scanning electron microscope, and a highresolution transmission electron microscope. On the basis of the above studies, the influences of different impurities on the crystallization process and crystal structures of CaSO4 were determined. The results of this study may provide a reference for the control of CaSO4 crystallization in the wet-process phosphoric acid process.

Figure 1. Effect of residence time on the CaSO4 (a) particle size distribution (PSD) and (b) median size.

2. RESULTS AND DISCUSSION 2.1. Residence Time Determination. During the crystallization process, the crystal size, morphology, growth, and nucleation rate were closely related to the residence time in the crystallizer. Therefore, the effects of residence time on CaSO4 crystallization were first investigated. X-ray diffraction (XRD) results showed that the raw materials immediately reacted to form CaSO4 after pumping into the crystallizer (Figure S1). The crystallizer was operated to reach the steady state after 2.5−7τ (Figure S2). With the increase of residence time, the particles size first increased and then decreased, which is similar to d0.5 (Figure 1). The maximum median size of 59 μm was obtained at the residence time of 3 h. Then, it further decreased to 11 μm at the residence time of 5 h. Gypsum morphology is one of the most important factors affecting the filtration rate. The filtration characteristics are influenced by the crystal size.34 Therefore, the CaSO 4 morphologies at different residence times are shown in Figure 2. When the residence time was 3 h, the crystal was rodshaped, thick, and uniform compared with that of 2 h. However, the cluster crystals were formed at the residence time of 4 h. When the residence time further prolonged to 5 h, the crystal becomes mainly rod-shaped and irregular because of the collision between different particles. It may be explained by the reason that excessively long residence time causes secondary crystal nucleation according to the crystal nucleation process.

Figure 2. Effect of residence time on the CaSO4 morphology.

Therefore, 3 h was the optimal residence time for the crystallization process and was selected as the residence time in the kinetic experiments. 2.2. Crystallization Kinetic Parameter Determination. 2.2.1. Particle Size Distribution. The PSD results, which are shown in Figure S3, were used to calculate the CaSO4 crystallization kinetics. The impurities affect the crystal size and morphology in the crystallization process, which depends on the growth rate of different crystal faces.21,25 The average particle size of CaSO4 crystals increased with the increasing content of Si, Fe, Al, and K. For Al, Fe, and Mg elements, the particle size curve deviated to two peaks at high impurity content (Figure 3). The influence of Mg on the crystal size was minimal among these elements, and the particle size fluctuated at approximately 50 μm, which is consistent with the results reported in the literature.35 However, the increasing Na content reduced the crystal size. The median size of CaSO4 crystals gradually decreased from 12 to 7 μm. 2.2.2. Population Density Calculation. Population densities nL under different conditions were calculated through eq 6. 12703


ACS Omega

Article

Figure 3. Effects of Al3+ on the CaSO4 crystal PSD.

The typical relationship between ln (nL) and L is shown in Figure 4. The population density decreased rapidly in the

Figure 4. Relationship between the population density and particle size at the Al/Ca ratio of 0.1.

range of small particle sizes, thereby indicating that the results in this range deviated from the MSMPR theory. The nonlinear part indicates the nonconstant crystal growth rates which are caused by the agglomeration of small CaSO4 particles.36 According to the relationship between ln (nL) and L, the growth rate, nucleation rate, and agglomeration kernel factor can be further calculated. 2.2.3. Crystallization Kinetic Correlation. Nucleation rate, growth rate, and agglomeration kernel were obtained using eqs 9−11, respectively. Impurities were divided into four categories according to the main group element, and their effects on the crystallization process were discussed. 2.2.3.1. Effect of Si. The effect of SiO2 on crystallization kinetics was studied by changing the molar ratio of silicon to calcium. With the increase of molar ratio as shown in Figure 5, the growth rate increased at low ratio but decreased at high ratio. The effect on nucleation rate was opposite to that on growth rate. Therefore, the growth rate and nucleation rate have extreme values in the investigated range of the Si/Ca ratio. When the Si/Ca ratio was 0.02, the maximum SiO2 growth rate was 3.44 × 10−19, and the minimum nucleation rate was 9.35 × 1015. With the increase of SiO2, the agglomeration kernel increased from 4.32 × 10−19 to 3.51 × 10−18. Combined with PSD results for different Si/Ca ratios, the increase of particle size at relatively low Si/Ca ratio may be due to the growth of the crystals. Then the agglomeration kernel increased rapidly with the Si/Ca ratio and played the dominant role for the increase of crystal size and peak separation of PSD spectra. 2.2.3.2. Effect of Al and Fe. Al and Fe have considerable effects on CaSO4 crystallization. As shown in Figure 6, the CaSO4 growth rate first increased with the increasing Al/Ca ratio or Fe/Ca ratio. The maximum growth rates of 5.53 ×

Figure 5. Effect of SiO2 on CaSO4 crystallization; (a) growth rate; (b) nucleation rate; and (c) agglomeration kernel.

10−19 and 2.61 × 10−19 were obtained at the Al/Ca ratio of 0.02 and the Fe/Ca ratio of 0.06, respectively. The effects of Fe and Al on CaSO4 crystallization were essentially the same. However, the growth rate with addition of Al was approximately twice higher than that with Fe, and the nucleation rate was 2 orders of magnitude larger than that with Fe. The growth rate began to decrease with increasing Al or Fe content at high Al/Ca ratio or Fe/Ca ratio. The reason may be due to the fact that the increase of the concentration of Al and Fe causes the attraction between Al3+ and Fe3+ ions and the SO42− anion in solution. This attraction reduces the collision probability of Ca2+ and SO42− ions and thus affects the crystal growth rate.37 Meanwhile, the adsorption of ions is proved as another reason to lead to the inhibition of crystal growth.38 With the increase of Al and Fe concentrations, the nucleation rate and agglomeration kernel first increased and then decreased. The agglomeration kernel decreased faster with the increase of Fe content than that of the Al content. It leads to the larger particle size of the crystal with the impurity of Al than that of Fe. 2.2.3.3. Effect of Mg. The effect of Mg2+ on CaSO4 crystal growth was investigated. As shown in Figure 7, the CaSO4 crystal growth rate gradually increased with increasing Mg content and achieved the maximum value of approximately 7.90 × 10−19. Then, the growth rate decreased slightly when 12704


ACS Omega

Article

Figure 6. Effects of Al and Fe on CaSO4 crystallization; (a) growth rate; (b) nucleation rate; and (c) agglomeration kernel. Figure 7. Effects of Mg on CaSO4 crystallization; (a) growth rate; (b) nucleation rate; and (c) agglomeration kernel.

the Mg/Ca ratio was larger than 0.1. The effect on the nucleation rate was opposite to the growth rate. It is attributed to the effects of impurities on ionic strength and supersaturation.39,40 Meanwhile, Mg is likely to be present as ions or charged complexes and affects the activities of Ca2+ and SO42−.14,41,42 As a result, the nucleation rate decreased from 1.10 × 1017 to 4.40 × 1016 with increasing Mg content. Guan43 also proposed that Mg2+ may adsorb on the active sites and delay nucleation at a relatively low supersaturation rate. With the increasing Mg concentration, the agglomeration kernel first decreased and then increased, but the fluctuation was small. 2.2.3.4. Effects of K and Na. The effects of alkali metals on CaSO4 crystallization rates are shown in Figure 8. With the increase in K/Ca ratio, the CaSO4 crystal growth rate increased from 6.74 × 10−19 to 8.66 × 10−19 and then decreased slightly. The improved crystal growth rate has been attributed to the reduction of interfacial energy.39 With the increase of K concentration, the nucleation rate first increased and then decreased. The aggregation kernel increased from 1.53 × 10−17 to 3.80 × 10−17 with the increase in K content. The CaSO4 crystal growth rate increased with increasing Na/Ca ratio. In addition, Na is more conducive in promoting the crystal growth than K. When the Na/Ca ratio was 0.1, the growth rate increased to 1.79 × 10−18, which agrees with the results reported by Cui.44 The addition of appropriate amount of Na was also proposed for the H2SO4 decomposition of phosphate rock to form superior crystals and to improve the P yield.

Oppositely, the nucleation rate and the agglomeration kernel gradually decreased with increasing Na/Ca ratio. According to the effects of different impurities on crystallization kinetics, the favorable impurity contents for CaSO4 crystal growth can be concluded as follows: Si/Ca = 0.02, Al/Ca = 0.02, Fe/Ca = 0.06, Mg/Ca = 0.1, K/Ca = 0.08, and Na/Ca = 0.1. Under those conditions, the crystals prefer to form larger particles, which are beneficial for the industrial operations. 2.3. Effect of Impurities on the CaSO4 Crystal Morphology. Morphologies of CaSO4 crystals obtained in all conditions are shown in Figure S4, and typical morphologies of CaSO4 are shown in Figure 9. It is found that the impurities played an important role in crystal growth. Uneven and curved tips can be observed in the presence of different impurities. Scanning electron microscopy (SEM) images showed that Si and Na had a great influence on crystal morphology among the investigated impurities. The presence of Si and Na resulted in the formation of elongated needle-like crystals, which is similar to the morphology of calcium sulfate hemihydrate.10 However, XRD analysis showed that no phase transition occurred during the process. Different with the addition of Si, the crystals presented as needle-like clusters with the increase of Na content. 12705


ACS Omega

Article

crystal was transformed from rough to smooth, which suggested that the addition of Mg may lead to the formation of defective crystals. 2.4. Effect of Impurities on the Crystal Structures. The effects of different impurities on the CaSO4 crystal structure have been investigated through high-resolution transmission electron microscopy (HRTEM) and selected area electron diffraction pattern analyses (Figure 10).45 The crystal plane

Figure 10. Crystal growth face of CaSO4 with the addition of different impurities: (a) SiO2, (b) AlPO4, (c) MgO, and (d) NaOH.

directions of the CaSO4 crystal are both (020) and (002) according to the calculation of Crystal Maker software. According to the XRD results shown in Figure 11, the growth orientation of the CaSO4 crystal was (020) with the addition of different impurities. However, the main growth direction of CaSO4 with the addition of Si was opposite to those crystals with the addition of other impurities. The interplanar spacing of the crystals was calculated by Fourier transformation, and the effects of different impurities on the interplanar spacing of CaSO4 crystals were investigated. As shown in Figure 12, the interplanar spacing values of the crystal plane (020) were 3.3956, 3.4014, 3.4320, and 3.5651 Å,

Figure 8. Effects of K and Na on the CaSO4 crystallization; (a) growth rate; (b) nucleation rate; and (c) agglomeration kernel.

It is clearly visible that as the Al content increased, the shape of crystals transformed from elongated to short rods. The particles were small but with uniform size because of the gradual increase in the nucleation rate. However, crystals with rough surface and needle-like shape have been formed in the presence of Fe. In addition, Mg and K have weak effect on the crystal morphology. As the Mg content increased, the surface of the

Figure 9. Effect of impurities on the morphology of CaSO4 tips; (a) Si/Ca ratio was 0.02; (b) Al/Ca ratio was 0.02; (c) Fe/Ca ratio was 0.02; (d) Mg/Ca ratio was 0.02; (e) K/Ca ratio was 0.02; and (f) Na/Ca ratio was 0.023. 12706


ACS Omega

Article

Figure 11. (a) XRD pattern analysis of the products prepared with different impurities and (b) local magnification of peak position corresponding to the crystal plane (020).

= 0.1. The presence of impurities formed elongated crystals compared with crystals without impurities through the changes of growth, nucleation rates, and agglomeration kernels. In particular, Si, Fe, and Na exhibited the most significant influences on crystal morphology among the impurities. XRD results indicated that the preferred crystal growth orientation was (020), and SiO2 may significantly affect the growth rate of this crystal plane. The interplanar spacing of the (020) crystal plane is also changed with the atomic radius of impurities. The results can provide a reference for selective removal of different impurities and CaSO4 crystallization control in the wet-process phosphoric acid process.

4. MATERIALS AND METHODS 4.1. Materials. All chemicals used in the experiments were of analytical grade. In the actual production process, returning acid predecomposed the phosphate rock, which further facilitated the reaction with H2SO4 (Figure S6). The equations are as follows Figure 12. Effect of impurities on CaSO4 interplanar spacing.

Ca5F(PO4 )3 + 7H3PO4 → 5Ca(H 2PO4 )2 + HF

with the Si/Ca, Al/Ca, Mg/Ca, and Na/Ca ratio of 0.02, respectively. According to the XRD results shown in Figure 11, the distance between crystal planes (020) was 3.4955 Å (reference code 01-072-0503). The crystal plane spacing increased with the addition of Na and decreased with the other impurities. It may be attributed to different atomic radii of added impurities. Impurities with larger atomic radius had a larger interplanar spacing of CaSO4, and the results showed that impurities have been combined in CaSO4 (Figure S5). As shown in Figure 11b, the peak position of the curve deviated the (020) crystal plane to the right with the addition of Mg. It is suggested that Mg is easier to be adsorbed on the surface of the crystal than Na and others.25 The change of interplanar spacing of the (020) crystal plane indicates the substitution of Mg2+ for Ca2+ into the structure.40 However, the interplanar spacing with the adsorption of Mg is still closest with that of the reference value as the similarity properties between elements in the same main group.

Ca(H 2PO4 )2 · H 2O + H 2SO4 + nH 2O → 2H3PO4 + CaSO4 ·nH 2O

(2)

(3)

Therefore, the returning acid, which was prepared with H3PO4, H2SO4, and deionized H2O, was used for CaSO4 crystallization. The molar ratio of H2O, H3PO4, and H2SO4 is 1:0.1:0.01. Meanwhile, analytical grade Ca(H2PO4)2·H2O (≥92%; Aladdin Bio-Chem Technology Co. Ltd.) was directly used as the raw material and reacted with H2SO4 (95−98%; Beijing Chemical Works) and H3PO4 (≥85%; Xilong Scientific Co. Ltd.). To investigate the effect of impurities on the crystallization process, Mg, Si, Fe, Al, K, and Na were selected as impurities according to phosphate rock formation. The impurities were added in the forms of phosphates, oxides, or hydroxides. Using analytical grade AlPO4 [≥54% (Al2O3); TianJin GuangFu Fine Chemical Research Institute], SiO2 (≥99%; Sinopharm Chemical Reagent Co., Ltd.), MgO (≥98%; XiLong Scientific Co., Ltd.), Fe 2 O 3 (≥99%; Sinopharm Chemical Reagent Co., Ltd.), KOH (≥85%; XiLong Scientific Co., Ltd.), and NaOH (≥96%; Beijing Chemical Works). The effects of impurities in the reagents on the crystallization of calcium sulfate can be neglected. Different impurities were mixed with Ca(H2PO4)2·H2O, and the ratio of impurity elements to Ca is shown in Table 1. 4.2. Experimental Procedure. Experiments were carried out in a 2 L round-bottomed flask (Figure 13). The reaction temperature was 80 °C, and the system was stirred with a flat-

3. CONCLUSIONS The effects of impurities on CaSO4 crystallization were systematically investigated in a highly acidic system of Ca(H2PO4)2−H2SO4−H3PO4−H2O. The results showed that the optimum residence time for CaSO4 crystallization was 3 h. The CaSO4 crystal growth can be facilitated when the impurity contents in phosphate rock are as follows: Si/Ca = 0.02, Al/Ca = 0.02, Fe/Ca = 0.06, Mg/Ca = 0.1, K/Ca = 0.088, and Na/Ca 12707


ACS Omega

Article

volume. In addition, the rupture term (Bd − Dd) can be neglected. Thus, the equation can be simplified as follows

Table 1. Amounts of Impurities in Different Experiments Al/Ca

Si/Ca

Mg/Ca

Fe/Ca

K/Ca

Na/Ca

0.01 0.02 0.07 0.10 0.16

0.004 0.008 0.020 0.040 0.060

0.01 0.02 0.07 0.10 0.17

0.01 0.02 0.06 0.10 0.14

0.02 0.04 0.06 0.08 0.09

0.023 0.046 0.069 0.092 0.100

Gv dn n + = Ba − Da τ dL

(5)

where Gv is the crystal volume growth rate and n indicates the population density and is a function of particle volume as follows n=

ΔwM T ρC v ̅ Δv

(6)

According to the references, the agglomeration term (Ba − Da) can be represented by the following equations Ba =

1 2

∫0

Da = n(v)

bladed stirrer at a constant rate of 300 rpm. First, the returning acid and Ca(H2PO4)2·H2O were previously mixed in container 1 according to the liquid−solid ratio of 2:1(mass ratio), and the impurities were also added. H2SO4 and H2O were mixed in container 2. The solutions in containers 1 and 2 were pumped into the reactor at a certain rate through two peristaltic pumps. When the residence time (τ) was reached, the reaction solution was extracted by a peristaltic pump to keep a constant volume in the crystallization reactor. Samples were collected at the same time interval. The PSD of the sample was analyzed immediately, and a certain volume of suspension sample was filtered, washed, and dried. Suspension density (MT) was measured according to the quality of the dried sample and the volume of filtrate (for details on calculations, see the part of Section 4.3). The investigation was done in the context of a continuous steady-state crystallization process, and each experiment with different conditions should be kept for 8− 10τ. PSD was analyzed using a laser particle size analyzer (Mastersizer-2000). The morphologies of crystals were analyzed using SEM (JSM-7610F). Analysis of crystal structures was conducted on HRTEM (FEI talos-F200X), and the distribution of elements was analyzed by Super-EDS. The crystal form and preferential growth direction were also evaluated via XRD (Empyrean). 4.3. Kinetic Model Establishment. For an MSMPR crystallizer, Randolph and Larson46,47 proposed the following volume-based population balance equation

β=

B0 =

k

μi =

v

β(u , v)n(u)du

(8)

1 ijj μ2 2 yz jj 2 − zzz j τ jk μ1 μ0 zz{

(10)

μ2 μ0 2 2τμ12

(11)

∫0

∞

n(v)v i dv

(12)

where v is the crystal volume and n(v) is the crystal population density. We used the change in impurities to evaluate the effects they have on gypsum nucleation and growth.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.9b01114. XRD patterns of synthesized CaSO4 crystals; typical crystal size distribution of samples at different multiples of mean residence time; particle size change of CaSO4 crystals at different molar ratios: SiO2, Fe2O3, MgO, KOH, and NaOH; effect of impurities on the morphology of CaSO4: SiO2, AlPO4, Fe2O3, MgO, KOH, and NaOH; and images of impurities on the surface of the CaSO4 crystal: NaOH, MgO, AlPO4, and SiO2; Process flow chart of laboratory wet-process phosphoric acid (PDF)

Q knk V

∫0

(7)

where μ0, μ1, and μ2 are the sum of the multiplication between the population density and particle volume of all particles at different moments and can be obtained as follows with different moments (i = 0, 1, 2).

d log V ∂(Gv n) ∂n + +n ∂τ ∂τ dτ

∑

β(u , v − u)n(u , t )n(v − u)du

The crystal growth rate Gv, nucleation rate B 0, and agglomeration kernel β were obtained by substituting eqs 5 and 6 into eq 3 and following the treatment proposed by Hulburt and Katz48,49 as follows μ Gv = 1 τμ0 (9)

Figure 13. MSMPR experimental apparatus; 1mixed acid tank; 2 Ca(H2PO4)2 storage tank; 3, 4, and 9metering pumps; 5 thermostat; 6crystallizer; 7blender; 8thermometer; 10 sampling tank.

= Ba − Da + Bd − Dd −

v

(4)

The moment transformation approach is adopted to solve eq 2. The growth rate was assumed to be independent of the particle 12708


ACS Omega

■

Article

(15) Feldmann, T.; Demopoulos, G. P. The Crystal Growth Kinetics of Alpha Calcium Sulfate Hemihydrate in Concentrated CaCl2−HCl Solutions. J. Cryst. Growth 2012, 351, 9−18. (16) Tang, N.; Zhang, Y. H.; Ren, C. L.; Cai, F.; Wang, J. N.; Ju, X. W. Study on Crystallization Process of Calcium Sulfate Dihydrate in Gypsum Type Brine System. J. Salt Chem. Ind. 2011, 40, 27−30. (17) Abdel-Aal, E. A.; Abdel-Ghafar, H. M.; El Anadouli, B. E. New Findings about Nucleation and Crystal Growth of Reverse Osmosis Desalination Scales with and Without Inhibitor. Cryst. Growth Des. 2015, 15, 5133−5137. (18) Hasson, D.; Addai-Mensah, J.; Metcalfe, J. Filterability of gypsum crystallized in phosphoric acid solution in the presence of ionic impurities. Ind. Eng. Chem. Res. 1990, 29, 867−875. (19) Fu, H.; Guan, B.; Jiang, G.; Yates, M. Z.; Wu, Z. Effect of Supersaturation on Competitive Nucleation of CaSO4 Phases in a Concentrated CaCl2 Solution. Cryst. Growth Des. 2012, 12, 1388− 1394. (20) Feldmann, T.; Demopoulos, G. P. Influence of Impurities on Crystallization Kinetics of Calcium Sulfate Dihydrate and Hemihydrate in Strong HCl-CaCl2 Solutions. Ind. Eng. Chem. Res. 2013, 52, 6540−6549. (21) Shukla, J.; Mehta, M. J.; Kumar, A. Effect of Ionic Liquid Additives on the Solubility Behavior and Morphology of Calcium Sulfate Dihydrate (Gypsum) in the Aqueous Sodium Chloride System and Physicochemical Solution Properties at 30 °C. J. Chem. Eng. Data 2018, 63, 2743−2752. (22) Mao, X.; Song, X.; Lu, G.; Sun, Y.; Xu, Y.; Yu, J. Effects of Metal Ions on Crystal Morphology and Size of Calcium Sulfate Whiskers in Aqueous HCl Solutions. Ind. Eng. Chem. Res. 2014, 53, 17625−17635. (23) Jun, L.; Wang, J. H.; Zhang, Y. X. Effects of the Impurities on the Habit of Gypsum in Wet-Process Phosphoric Acid. Ind. Eng. Chem. Res. 1997, 36, 2657−2661. (24) Wang, F.; Davis, T. E.; Tarabara, V. V. Crystallization of Calcium Sulfate Dihydrate in the Presence of Colloidal Silica. Ind. Eng. Chem. Res. 2010, 49, 11344−11350. (25) Rabizadeh, T.; Stawski, T. M.; Morgan, D. J.; Peacock, C. L.; Benning, L. G. The Effects of Inorganic Additives on the Nucleation and Growth Kinetics of Calcium Sulfate Dihydrate Crystals. Cryst. Growth Des. 2017, 17, 582−589. (26) Prisciandaro, M.; Lancia, A.; Musmarra, D. The Retarding Effect of Citric Acid on Calcium Sulfate Nucleation Kinetics. Ind. Eng. Chem. Res. 2003, 42, 6647−6652. (27) Prisciandaro, M.; Olivieri, E.; Lancia, A.; Musmarra, D. PBTC as an Antiscalant for Gypsum Precipitation: Interfacial Tension and Activation Energy Estimation. Ind. Eng. Chem. Res. 2012, 51, 12844− 12851. (28) Guan, Q.; Hu, Y.; Tang, H.; Sun, W.; Gao, Z. Preparation of αCaSO4·1/2H2O with Tunable Morphology from Flue Gas Desulphurization Gypsum Using Malic Acid as Modifier: A Theoretical and Experimental Study. J. Colloid Interface Sci. 2018, 530, 292−301. (29) Akyol, E.; Ö ner, M.; Barouda, E.; Demadis, K. D. Systematic Structural Determinants of the Effects of Tetraphosphonates on Gypsum Crystallization. Cryst. Growth Des. 2009, 9, 5145−5154. (30) Jiang, W.; Pan, H.; Tao, J.; Xu, X.; Tang, R. Dual Roles of Borax in Kinetics of Calcium Sulfate Dihydrate Formation. Langmuir 2007, 23, 5070−5076. (31) Park, K.; Kim, D. Y.; Yang, D. R. Operating Strategy for Continuous Multistage Mixed Suspension and Mixed Product Removal (MSMPR) Crystallization Processes Depending on Crystallization Kinetic Parameters. Ind. Eng. Chem. Res. 2016, 55, 7142− 7153. (32) Peng, Y.; Zhu, Z.; Braatz, R. D.; Myerson, A. S. Gypsum Crystallization during Phosphoric Acid Production: Modeling and Experiments Using the Mixed-Solvent-Electrolyte Thermodynamic Model. Ind. Eng. Chem. Res. 2015, 54, 7914−7924. (33) Polat, S.; Sayan, P.; Titiz Sargut, S. MSMPR tipi kristalizörde kalsiyum sülfat dihidrat kristalizasyonunun glutamik asit varlığında incelenmesi. J. Fac. Eng. Architect. Gaz. 2017, 32, 1121−1130.

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: +86-10-82544830 (G.Z.). *E-mail: [email protected]. Phone: 0531-82767937 (G.S.). ORCID

Huiquan Li: 0000-0002-3702-3164 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by National Key Research and Development Program of China (no. 2017YFC0703200), National Natural Science Foundation of China (no. 51704272), China Postdoctoral Science Foundation (no. 2016LH0008), and Youth Innovation Promotion Association CAS.

■

REFERENCES

(1) Ashley, K.; Cordell, D.; Mavinic, D. A Brief History of Phosphorus: From the Philosopher’s Stone to Nutrient Recovery and Reuse. Chemosphere 2011, 84, 737−746. (2) Li, J. Y.; Qian, Y. M.; Wang, L.; He, X. M. Nitrogen-Doped Carbon for Red Phosphorous Based Anode Materials for Lithium Ion Batteries. Materials 2018, 11, 134. (3) Liu, H.; Bu, Y.; Nazari, A.; Sanjayan, J. G.; Shen, Z. Low Elastic Modulus and Expansive Well Cement System: The Application of Gypsum Microsphere. Constr. Build. Mater. 2016, 106, 27−34. (4) Gupta, K.; Singh, S.; Rao, M. S. R. Direct and Facile RoomTemperature Synthesis of Nanocrystalline Calcium Sulfate Dihydrate (Gypsum). Cryst. Growth Des. 2016, 16, 3256−3261. (5) Sebastian, L.; Martin, P.; Mihail, M.; Wolfgang, S.; Sergi, P.-R.; Wolfgang, T. Calcium Sulfate Nanoparticles with Unusual Dispersibility in Organic Solvents for Transparent Film Processing. Langmuir 2018, 34, 7096−7105. (6) Ossorio, M.; Van Driessche, A. E. S.; Pérez, P.; García-Ruiz, J. M. The Gypsum−Anhydrite Paradox Revisited. Chem. Geol. 2014, 386, 16−21. (7) Hoang, T. A.; Ang, M.; Rohl, A. L. Effects of Process Parameters on Gypsum Scale Formation in Pipes. Chem. Eng. Technol. 2011, 34, 1003−1009. (8) Rahardianto, A.; Shih, W.-Y.; Lee, R.-W.; Cohen, Y. Diagnostic Characterization of Gypsum Scale Formation and Control in RO Membrane Desalination of Brackish Water. J. Membr. Sci. 2006, 279, 655−668. (9) El-Shall, H.; Rashad, M. M.; Abdel-Aal, E. A. Effect of Phosphonate Additive on Crystallization of Gypsum in Phosphoric and Sulfuric Acid Medium. Cryst. Res. Technol. 2002, 37, 1264−1273. (10) Shukla, J.; Mehta, M. J.; Kumar, A. Effects of Aliphatic Alcohols on Solubility, Physicochemical Properties, and Morphology of Calcium Sulfate Dihydrate (Gypsum) in Aqueous Sodium Chloride Solution at 35 °C. J. Chem. Eng. Data 2019, 64, 536−544. (11) Amin, A. B.; Larson, M. A. Crystallization of Calcium Sulfate from Phosphoric Acid. Ind. Eng. Chem. Res. 1968, 7, 133−137. (12) Fu, H.; Jiang, G.; Wang, H.; Wu, Z.; Guan, B. SolutionMediated Transformation Kinetics of Calcium Sulfate Dihydrate to αCalcium Sulfate Hemihydrate in CaCl2 Solutions at Elevated Temperature. Ind. Eng. Chem. Res. 2013, 52, 17134−17139. (13) Hamdona, S. K.; Al Hadad, U. A. Crystallization of Calcium Sulfate Dihydrate in the Presence of Some Metal Ions. J. Cryst. Growth 2007, 299, 146−151. (14) Jiang, G.; Fu, H.; Savino, K.; Qian, J.; Wu, Z.; Guan, B. Nonlattice Cation-SO42− Ion Pairs in Calcium Sulfate Hemihydrate Nucleation. Cryst. Growth Des. 2013, 13, 5128−5134. 12709


ACS Omega

Article

(34) Rashad, M. M.; Mahmoud, M. H. H.; Ibrahim, I. A.; Abdel-Aal, E. A. Crystallization of Calcium Sulfate Dihydrate under Simulated Conditions of Phosphoric Acid Production in the Presence of Aluminum and Magnesium Ions. J. Cryst. Growth 2004, 267, 372− 379. (35) Liu, T. H.; Dou, Y.; Fang, Y.; Cui, P.; Shen, H.; Zheng, Z. Y.; Liu, R. Influence of Al3+, Na+ and Mg2+ on Crystallization of Calcium Sulfate Dihydrate. CIESC J. 2016, 67, 296−301. (36) Zhu, G.; Li, H.; Li, S.; Hou, X.; Xu, D.; Lin, R.; Tang, Q. Crystallization Behavior and Kinetics of Calcium Carbonate in Highly Alkaline and Supersaturated System. J. Cryst. Growth 2015, 428, 16− 23. (37) Yang, L.; Cao, J.; Luo, T. Effect of Mg2+, Al3+, and Fe3+ Ions on Crystallization of Type a Hemi-hydrated Calcium Sulfate under Simulated Conditions of Hemi-hydrate Process of Phosphoric Acid. J. Cryst. Growth 2018, 486, 30−37. (38) Kubota, N.; Otosaka, H.; Doki, N.; Yokota, M.; Sato, A. Effect of Lead(II) Impurity on the Growth of Sodium Chloride Crystals. J. Cryst. Growth 2000, 220, 135−139. (39) Yang, L.; Wu, Z.; Guan, B.; Fu, H.; Ye, Q. Growth Rate of αCalcium Sulfate Hemihydrate in K−Ca−Mg−Cl−H2O Systems at Elevated Temperature. J. Cryst. Growth 2009, 311, 4518−4524. (40) Ahmed, S. B.; Tlili, M. M.; Amami, M.; Ben Amor, M. Gypsum Precipitation Kinetics and Solubility in the NaCl−MgCl2−CaSO4− H2O System. Ind. Eng. Chem. Res. 2014, 53, 9554−9560. (41) Elgquist, B.; Wedborg, M. Stability Constants of NaSO4−, MgSO4, MgF+, MgCl+ ion Pairs at the Ionic Strength of Seawater by Potentiometry. Mar. Chem. 1978, 6, 243−252. (42) Leaist, D. G.; Goldik, J. Diffusion and Ion Association in Concentrated Solutions of Aqueous Lithium, Sodium, and Potassium Sulfates. J. Solution Chem. 2001, 30, 103−118. (43) Guan, B.; Yang, L.; Wu, Z. Effect of Mg2+ Ions on the Nucleation Kinetics of Calcium Sulfate in Concentrated Calcium Chloride Solutions. Ind. Eng. Chem. Res. 2010, 49, 5569−5574. (44) Cui, Y. S. Effect of Adding K+, Na+ ,Cu2+ and Zn2+ in Phosphate Rock on Phosphate Rock Decomposition. IM & P. 2007, 36, 1−2. (45) Jiang, W.; Gao, Z. Y.; Sun, W.; Gao, J. D.; Hu, Y. H. A Density Functional Theory Study on the Effect of Lattice Impurities on the Electronic Structures and Reactivity of Fluorite. Minerals 2017, 7, 160. (46) Larson, A. B. Theory of Particulate Processes; Randolph, A. D.; Larson, M. A., Eds.; Academic Press: New York, 1971; Chapter 3, pp 47−49. (47) McCoy, B. J. A Population Balance Framework for Nucleation, Growth, and Aggregation. Chem. Eng. Sci. 2002, 57, 2279−2285. (48) Costa, C. B. B.; Maciel, M. R. W.; Filho, R. M. Considerations on the Crystallization Modeling: Population Balance Solution. Comput. Chem. Eng. 2007, 31, 206−218. (49) Hulburt, H. M.; Katz, S. Some Problems in Particle Technology: A Statistical Mechanical Formulation. Chem. Eng. Sci. 1964, 19, 555−574.

12710


Effects of Impurities on CaSO4 Crystallization in the Ca(H2PO4)2

Recommend Documents