Apparent Dissolution Kinetics of Diatomite in Alkaline Solution

CATALYSIS, KINETICS AND REACTION ENGINEERING Chinese Journal of Chemical Engineering, 21(7) 736—741 (2013) DOI: 10.1016/S1004-9541(13)60533-9

Apparent Dissolution Kinetics of Diatomite in Alkaline Solution* DU Gaoxiang (杜高翔)1,**, LÜ Guocheng (吕国诚)1 and HE Xuwen (何绪文)2 1 2

School of Materials Science and Technology, China University of Geosciences, Beijing 100083, China School of Chemical & Environmental Engineering, China University of Mining & Technology, Beijing 100083, China

Abstract The dissolution kinetics of diatomite in alkaline solution is the theoretical basis for the process optimization of alkali-diatomite reaction and its applications. In this study, the dissolution kinetics of diatomite in NaOH solution is investigated. The results indicate that the dissolution reaction fits well the unreacted shrinking core model for solid-liquid heterogeneous reactions. The apparent reaction order for NaOH is 2 and the apparent activation energy for the reaction (Ea) is 28.06 kJ·mol−1. The intra-particle diffusion through the sodium silicate layer is the rate-controlling step. When the dissolution reaction occurs at the interface of unreacted diatomite solid core, the diffusion in the trans-layer (the liquid film around the wetted particle) reduces the rate of whole dissolution process. Keywords diatomite, sodium hydroxide, dissolution kinetics

1

INTRODUCTION

Sodium silicate is usually prepared by reaction of quartz sands (SiO2) and sodium carbonates or sodium sulfates (Na2CO3 or Na2SO4) at high temperatures (above 1250 °C), in which high energy-consumption and the pollution are the main disadvantages in those conventional techniques [1]. In recent years, many new methods have been developed to produce sodium silicate by the reaction between amorphous silica materials, such as diatomite or opal, and alkaline solution, such as sodium hydroxide, to avoid the environmental and energy-consumption problems [2]. The modulus, which is the molar ratio of SiO2 to Na2O in sodium silicate, changes with the amounts of NaOH to SiO2 used and other reaction parameters. For different applications such as mould sands, adhesives, cementing materials, detergents and the preparation of precipitated silica, the demand on the modulus of sodium silicate varies [3-6]. The dissolution kinetics of diatomite in alkaline solutions is the theoretical basis for the process optimization of alkali-diatomite reactions and applications. The kinetic behavior between sodium hydroxide and quartz materials in aqueous solutions under different conditions has been reported by several groups. The kinetic order for OH− and the kinetic constant under hydrothermal conditions are 0.470±0.013 and 3.933×10−6 g·m2·s−1, respectively, when the reaction temperature, pressure and molar ratio of SiO2/Na2O are 220 °C, 2.7 MPa and 2, respectively [7-9]. The dissolution and precipitation kinetics of quartz or Table 1

amorphous silica in the alkaline solution under mild conditions with pH of 11-12 and temperature of 23-70 °C have been examined [10]. The kinetic model for dissolution of silica aerosol in NaOH solution have been investigated, with the concentration of silica aerosol in NaOH solution being 0.05-0.79 mol·L−1 at 15-56 °C [11], the dissolution activation energy is (80±6) kJ·mol−1 and the interfacial energy of coarselyand finely-dispersed samples are 0.09 and 0.24 J·m−2, respectively [12, 13]. Most studies on the topic focus on the dissolution kinetics of pure SiO2, such as quartz, in the alkaline solution. Here, we investigate the kinetics of diatomite dissolution in NaOH solution, propose a new dissolution model based on the analysis of experimental data, and obtain reaction rate equation under certain reaction conditions, in which the apparent reaction order and the apparent activation energy are evaluated and the main rate-controlling factors are to be determined. 2 2.1

EXPERIMENTAL Materials

Diatomite is obtained from Jilin Yuantong Mining Co., Ltd. (with particle size distribution of d50 = 7.73 μm and d97 = 17.57 μm), the chemical composition and mineral composition of which are shown in Table 1 and Fig. 1, respectively. XRD results show that the diatomite material consists of a large quantity of diatomite and a small quantity of quartz and clay. NaOH (solid, A.R.) is purchased from Beijing Chemical Plant.

Chemical composition of diatomite (%, by mass)

SiO2

Al2O3

Fe2O3

TiO2

CaO

MgO

K2 O

Na2O

MnO2

P2O5

SO3

L.O.I

90.30

3.48

0.95

0.26

0.28

0.26

0.32

0.16

0.002

0.072

0.036

4.28

Received 2012-01-06, accepted 2012-09-07. * Supported by the National Natural Science Foundation of China (50674080). ** To whom correspondence should be addressed. E-mail: [email protected]

Chin. J. Chem. Eng., Vol. 21, No. 7, July 2013

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Figure 1 XRD pattern of diatomite

2.2

Assumptions for the reaction

(1) Reactants diffuse uniformly in the reaction system. Thus the solid content in the solution is low and the system is rigorously stirred throughout [14]. (2) The reaction stops as soon as the sample is removed from the reaction system. In order to quench the reaction, the removed samples are diluted with a quintuple volume of distilled water immediately at low temperature, then filtrated and washed under vacuum. (3) The chemical composition of the diatomite material is that of pure SiO2 since it consists mainly of SiO2 phase (Fig. 1). Thus the term “SiO2” instead of “diatomite” is used here as the analysis and calculation “variable” in most cases. 2.3

Method

In a typical reaction, 120 g of diatomite, 35 g of solid sodium hydroxide (in order to obtain completely reacted product, the modulus of sodium hydroxide is set to 4, a little larger than its theoretical modulus, 3) and 360 ml distilled water were mixed in a 1000 ml three-neck flask. All flasks were sealed by polytetrafluoroethylene plugs to prevent the solution from evaporation. The three-neck flask was immersed into a water bath at pre-set temperature and the system was kept stirring for 3 h. 30 ml of sample was transferred into a beaker with 150 ml of cold distilled water added every 25 min. The resultant mixture was filtrated on a piece of filter paper and then washed with distilled water until sodium ions can not be detected in the solution. The concentration of Na+ in the filtrate and the amount of the SiO2 precipitate obtained were analyzed. The apparent reaction order and apparent activation energy were calculated and the kinetic equation was established based on these data.

2.4

Instrument

DZK-4 thermostat water bath (Beijing Zhongxingweiye Instrument Co., Ltd.), 0.5 L vacuum pump (Beijing Zhongxingweiye Instrument Co., Ltd.), JB-300D type electronic stirrer (Shanghai Standard Model Plant), and S-3500N type Scanning Electron Microscope (Hitachi Corporation) were used in the experiments. 3 3.1

RESULTS AND DISCUSSION Reaction mechanism

The reaction between diatomite and sodium hydroxide is a liquid-solid multiphase reaction. This reaction can be expressed as Na2O·nSiO2+H2O (1) nSiO2(s) + 2NaOH(l) where n is the modulus of sodium silicate, which is the molar ratio of SiO2 to Na2O, ranging from 1 to 4. The molar ratio used in the experiment is generally set between 3.0 and 3.4 for preparing precipitated amorphous silica with large specific area, and at about 2.0 in the cases of mould sand binders and detergents [15, 16]. Naturally, diatomite is the debris of diatoms with regularly structured pore arrangement (Fig. 2). The diatomite particles have disc-like appearance with many holes inside as shown in Fig. 2 (a). The pore structure can be observed more clearly in Fig. 2 (b) and the pore diameter usually ranges from 100 nm to 200 nm. The diatomite particles are considered as solid particles in this paper since the resultant sodium silicate film is too viscous to allow the flowing of the reactant solution. In the dissolution, the surface of diatomite particles is gradually covered by a newly produced sodium silicate layer, which is so concentrated and viscous that it reduces the diffusion of sodium hydroxide species significantly. Hence, for a solid diatomite particle, the

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Chin. J. Chem. Eng., Vol. 21, No. 7, July 2013

(a) Morphology in low magnification

(b) Microstructure in high magnification

Figure 2 SEM images of diatomite particles

reaction process can be divided into several steps: the diffusion of sodium hydroxide from solution to the external surface of a wetted particle, referred to trans-layer diffusion; intra-particle diffusion (the diffusion through the sodium silicate layer) to the reaction interface; the chemical reaction at the interface and the diffusion of sodium silicate species into the main body of the solution, etc. Since the overall reaction rate is usually controlled by the slowest step, a crucial task is to find the rate-controlling factors. The shrinking unreacted core model is one of readily accessible theories to describe such solid-liquid multi-phase reaction. This model is used here to describe the diatomite dissolution in the alkaline solution, in which the total particle size is invariable while the reaction interface moves inward gradually. That is to say, the reaction proceeds gradually with the decrease of the solid core size and the increase of the thickness of resultant sodium silicate layer, with the diameter of the particle unchanged (Scheme 1).

Scheme 1 Dissolution model of a diatomite particle in NaOH solution

The diffusion rate of sodium hydroxide through the liquid (newly-formed sodium silicate) film to the diatomite surface is related to the diffusion resistance and the concentration gradient of sodium hydroxide in the hydraulic diameter of a wetted diatomite particle, which can be described by Fick’s first law [17], −dnNaOH /( S ⋅ dt ) = k1 ( cNaOH,L − cNaOH,S )

(2)

where dnNaOH/dt is the moles of NaOH passing through the liquid film around the wetted particle in a

time interval, S is the surface area of a diatomite particle, k1 is the diffusion rate constant, cNaOH,L and cNaOH,S are the molar concentrations of sodium hydroxide in the external and internal surfaces of the liquid film layer around a wetted diatomite particle (mol·L−1), respectively. However, the actual chemical reaction rate depends on the concentration of sodium hydroxide at the reaction interface, the concentration of the resulted sodium silicate and the reaction temperature, etc. The temperature effect on the dissolution rate is expressed by Arrhenius equation K = K 0 ⋅ e − E / RT

(3)

where K is a reaction rate constant, K0 represents the rate constant when E = 0, and E is the reaction activation energy. 3.2

Apparent reaction order

Due to the high viscosity of sodium silicate at low temperatures, the reaction is carried out at 70 °C and 90 °C. Samples were collected at 70 °C and 90 °C at an interval of 25 min and then the SiO2 content and Na+ concentration of the collected samples were measured. The experimental results are shown in Table 2. The modulus of sodium silicate varies with reaction time. The actual modulus of sodium silicate can be calculated by the amount of the residual sodium hydroxide. For the sake of convenience, all moduli are set to 4.0 in the calculation. The amounts of the reacted silica and sodium hydroxide at time t, denoted by subscript t, can be calculated as follows. mSiO2 ,t = cSiO2 ,filtrate,t ⋅ Vfiltrate,t ⋅ Vtotal / Va,t

(4)

where mSiO2 ,t is the mass of the reacted silica (g), cSiO2 ,filtrate,t is the concentration of SiO2 in the sample suspension (g·L−1), Vfiltrate,t is the volume of filtrate collected(L), Vtotal and Va,t are the total volume of the reaction mixture and the volume of the sample collected at time t, which are 0.552 L and 0.025 L, respectively.

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Chin. J. Chem. Eng., Vol. 21, No. 7, July 2013

Table 2 Reaction time /min

ex situ sample composition analysis Content of SiO2/g·L−1

Accumulative filtrated volume/ml

Concentration of Na2O in filtrate/g·L−1

70°C

90°C

70°C

90°C

70°C

90°C

25

448

452

1.79

3.52

2.88

2.36

50

420

375

3.28

6.78

3.25

2.96

75

389

370

4.68

7.62

3.88

2.91

100

470

355

4.43

8.09

3.00

2.90

125

430

384

3.55

7.59

3.50

2.61

150

425

392

5.99

8.24

3.63

2.75

Table 3

The relationship between concentration of unreacted NaOH and reaction time cNaOH,t/mol·L−1

(cNaOH,t)−1

ln(cNaOH,t)

Reaction time/min

70 °C

90 °C

70 °C

90 °C

70 °C

90 °C

0

1.54529

1.54529

0.43521

0.46068

0.64713

0.64713

25

1.27798

1.05420

0.24528

0.05278

0.78248

0.94859

50

1.08609

0.73727

0.08258

−0.30480

0.92073

1.35636

75

0.93845

0.64535

−0.0635

−0.43797

1.06559

1.54955

100

0.85126

0.57364

−0.16104

−0.55575

1.17474

1.74325

125

0.76842

0.52254

−0.26341

−0.64905

1.30137

1.91373

150

0.69671

0.50767

−0.36139

−0.67793

1.43533

1.96978

mNaOH,t = 2M NaOH ⋅ mSiO2 ,t

( 4M SiO ) 2

(5)

where mNaOH,t is the mass of sodium hydroxide consumed (g), MNaOH and M SiO2 are molecular mass of NaOH and SiO2, which are 39.997 and 60.0835 g·mol−1, respectively. The concentration (mol·L−1) of the remaining silica and sodium hydroxide in the residual reaction mixture at time t can be calculated as follows. cSiO2 ,t = ( mSiO2 ,0 − mSiO2 ,t ) (Vtotal ⋅ M SiO2 )

(6)

cNaOH,t = ( mNaOH,0 − mNaOH,t ) (Vtotal ⋅ M NaOH ) (7) where subscript 0 refers to the initial value. The relation between lncNaOH,t and reaction time t is linear when the apparent reaction order is 1, and the relation between (cNaOH)−1 and reaction time t is linear when the apparent reaction order is 2. The analysis results for the alkali-diatomite reaction are shown in Table 3.The relationship between the concentration of the remaining NaOH and reaction time is readily determined according to the data in Table 3. As shown in Fig. 3, the apparent reaction order for NaOH is 2. The apparent reaction rate is 2 −dcNaOH / dt = k ⋅ cNaOH, t

(8)

where k is a reaction rate constant, and cNaOH,t is the concentration of the unreacted NaOH in the solution at time t.

Figure 3 Determination of reaction order by data fitting ◇ 70 °C first order; △ 90 °C first order; ▲ 70 °C second order; ■ 90 °C second order; liner 90 °C second order; liner 70 °C second order

The value of k is 0.1306 at 70 °C and 0.2245 at 90 °C, determined by the slope of the fitting straight line as shown in Fig. 3. The apparent activation energy for this reaction (Ea) is from the following equation: ln ( KT2 / KT1 ) = Ea ⋅ (T2 − T1 ) ( RT2T1 ) (9) The value of Ea is calculated to be 28.06 kJ·mol−1. 3.3 Controlling factors and kinetic equation for the dissolution reaction

The alkali-diatomite particle reaction is explained

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Chin. J. Chem. Eng., Vol. 21, No. 7, July 2013 Table 4

Reaction time/min

Analysis on rate-controlling factor [1 − (1 − x)1/3]

x

[1+3(1 − x)2/3 − 2(1 − x)]

70 °C

90 °C

70 °C

90 °C

70 °C

90 °C

25

0.18355

0.36458

0.06536

0.14029

1.98775

1.94646

50

0.31531

0.58220

0.11861

0.25242

1.96117

1.84102

75

0.41669

0.64532

0.16446

0.29214

1.92779

1.79380

100

0.47656

0.69436

0.19409

0.32640

1.90159

1.74994

125

0.53344

0.72945

0.22440

0.35323

1.87150

1.71384

150

0.58268

0.73985

0.25271

0.36163

1.84069

1.70225

by the unreacted shrinking core model. If the diffusion of trans-liquid film is the rate-controlling factor, the kinetic equation [18] can be expressed as t =k⋅x (10) where t is the reaction time, x is the conversion of diatomite (SiO2) (%), and k is a constant, related to many factors such as surface area and diameter of particle, diffusion coefficient, and concentration of OH− in the system. If the dissolution reaction is the rate-controlling factor, the kinetic equation [18] can be written as t = k ⋅ [1 − (1 − x)1/ 3 ]

(11)

where k is a reaction rate constant related to particle surface area and concentration of OH− on the reaction interface of particle. If the intra-particle diffusion rate, the diffusion rate of OH− passing through the sodium silicate layer, is the controlling factor, following equation [18] is obtained t = k ⋅ [1 + 3(1 − x) 2 / 3 − 2(1 − x)]

Figure 4 Relationship between the conversion of SiO2 and reaction time (1) ◇ 70 °C reaction rate; ■ 90 °C reaction rate; 70 °C liquid film diffusion rate; ▲ 90 °C liquid film diffusion rate; liner 90 °C liquid film diffusion rate; liner 70 °C liquid film diffusion rate; liner 90 °C reaction rate; liner 70 °C reaction rate

(12)

where k is the reaction rate constant. The rate-controlling factor and the apparent kinetic equation for the diatomite dissolution in the NaOH solution can be determined by comparing the linear relationship between functions x, [1 − (1 − x)1/ 3 ] and [1 + 3(1 − x)2 / 3 − 2(1 − x)] and reaction time t (the analyses are taken separately at 70 °C and 90 °C), as shown in Table 4, Figs. 4 and 5. The correlation coefficients indicate that the intra-particle diffusion and chemical reaction have almost the same influence on the apparent reaction rate, but the linear dependence of the former on reaction time t is better than that of later, so the intra-particle diffusion through the sodium silicate layer is the most significant rate-controlling factor in the reaction. Furthermore, the slopes of the regressed lines at 70 °C and 90 °C (Fig. 5) are −0.029 and −0.047, respectively, indicating that temperature also has obvious influence on the apparent reaction rate. From the above analysis, the kinetic equation of the diatomite dissolution in the NaOH solution can be written as

Figure 5 Relationship between the conversion of SiO2 and reaction time (2) ▲ 70 °C inner diffusion rate; ■ 90 °C inner diffusion rate; liner 70 °C inner diffusion rate; liner 90 °C inner diffusion rate

⎡1 + 3 (1 − xSiO ) − 2 (1 − xSiO ) ⎤ = k ⋅ t (13) 2 2 ⎦ ⎣ where xSiO2 is the conversion of diatomite (SiO2) at reaction time t, k is a dimensionless constant for the apparent reaction rate equation and related to reaction temperature, particle size, shape, etc. 2/3

Chin. J. Chem. Eng., Vol. 21, No. 7, July 2013

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CONCLUSIONS 4

The diatomite dissolution behavior in the NaOH solution fits the unreacted shrinking core model for the solid-liquid multiphase reaction under the mild conditions (ambient pressure and low temperature) in diluted, uniformly stirred solutions. The apparent reaction order for this reaction is 2, its apparent reaction 2 rate can be expressed as −dcNaOH / dt = k ⋅ cNaOH, t , and its apparent activation energy (Ea) is 28.06 kJ·mol−1. The intra-particle diffusion of NaOH species through the sodium silicate film on the surface of a wetted diatomite particle and the chemical reaction at the interface of unreacted solid core control the overall rate of the dissolution reaction. However, the intra-particle diffusion rate is the most significant rate-controlling factor. The dissolution rate equation for the conversion of diatomite (SiO2) (or the yield of sodium silicate) is ⎡1 + 3 (1 − xSiO )2 / 3 − 2 (1 − xSiO ) ⎤ = k ⋅ t , where k is a 2 2 ⎦ ⎣ dimensionless constant related to particle size, shape and reaction temperature. ACKNOWLEDGEMENTS

The authors are grateful to Prof. Libing Liao and Prof. Shuilin Zheng for their proofreading and advice on the manuscript.

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