Leaching kinetics of ulexite in sodium hydrogen sulphate solutions

Journal of Industrial and Engineering Chemistry xxx (2014) xxx–xxx

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JIEC-1819; No. of Pages 7

Review

Leaching kinetics of ulexite in sodium hydrogen sulphate solutions

Erbil Kavcı, Turan Calban, Sabri Colak, Soner Kus lu *

Ataturk University, Engineering Faculty, Department of Chemical Engineering, 25240 Erzurum, Turkey

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2. Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.1. Experimental procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3. Results and analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.1. Dissolution reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.2. Effect of parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.3. Effect of reaction temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.4. Effect of concentration of sodium hydrogen sulphate solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.5. Effect of stirring speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.6. Effect of solid/liquid ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.7. Effect of ulexite particle size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

4. Kinetic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

5. Discussion and conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

A R T I C L E I N F O

Article history:

Received 13 November 2013

Accepted 25 December 2013

Available online xxx

Keywords:

Ulexite

Sodium hydrogen sulphate

Leaching kinetics

A B S T R A C T

The aim of this study was to investigate the dissolution kinetics of ulexite in sodium hydrogen sulphate

solutions in a mechanical agitation system and to declare an alternative reactant to produce boric acid.

Reaction temperature, concentration of sodium hydrogen sulphate solutions, stirring speed, solid/liquid

ratio and ulexite particle size were selected as parameters of the dissolution rate of ulexite. The

experimental results were successfully correlated by linear regression using Statistica program.

Dissolution curves were evaluated in order to test shrinking core models for solid-fluid systems. It was

observed that increase in the reaction temperature and decrease in the solid/liquid ratio cause an increase

in the dissolution rate of ulexite. The dissolution extent is highly increased with increase in the stirring

speed rate between 100 and 700 rpm experimental conditions. The activation energy was found to be

36.4 kJ/mol. The leaching of ulexite was controlled by diffusion through the ash or product layer. The rate

expression associated with the dissolution rate of ulexite depending on the parameters chosen may be

summarized as: 1–3(1 � X)2/3 + 2(1 � X) = 6.17 � C0.97� W1.17� D�1.72� (S/L)�0.66� e(�36.4/RT)�t.� 2014 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights

reserved.

Contents lists available at ScienceDirect

Journal of Industrial and Engineering Chemistry

jou r n al h o mep ag e: w ww .e lsev ier . co m / loc ate / j iec

1. Introduction

Boron was discovered by French chemists Jossep Gay-Lussacand Louis Thenard, and independently by British chemist Sir

* Corresponding author. Tel.: +90 442 231 45 86; fax: +90 442 231 45 44.

E-mail address: [email protected] (S. Kus lu).

Please cite this article in press as: E. Kavcı, et al., J. Ind. Eng. Chem.

1226-086X/$ – see front matter � 2014 The Korean Society of Industrial and Engineer

http://dx.doi.org/10.1016/j.jiec.2013.12.089

Humphry Davy in 1808. It is a hard, brittle semi-metallic element.Its atomic number is 5, its atomic weight is 10.81 A and it melts at2348 K.

Boron mineral beds are concentrated principally in Turkey, theUSA, Argentina, Russia, Kazakhstan, China, Bolivia, Peru and Chile.Turkey holds approximately 67% of global boron reserves with 883million tons of B2O3 [1]. Boron products are used in close to500 different areas including space and aeronautics, nuclear

(2014), http://dx.doi.org/10.1016/j.jiec.2013.12.089

ing Chemistry. Published by Elsevier B.V. All rights reserved.


mailto:[email protected]


http://www.sciencedirect.com/science/journal/1226086X

http://dx.doi.org/www.elsevier.com/locate/jiec


Nomenclature

b stoichiometric coefficient

C concentration of borax decahydrate solution

(mol m�3)

CAg concentration of A in the bulk solution (mol m�3)

D mean particle size (m)

De diffusion coefficient (m2 min�1)

EA activation energy (kJ kmol�1)

kd mass transfer coefficient (m min�1)

ks reaction rate constant for surface reaction

(mol min�1)

ko frequency or pre-exponential factor (min�1)

L amount of liquid (mL)

n mol number (mol)

r correlation coefficient (�)

R universal gas constant (kJ kmol�1)

R initial radius of a solid particle (m)

S amount of solid (g)

T reaction temperature (K)

t reaction time (min)

t* reaction time for complete conversion (min)

X fractional conversion of B2O3 (�)

W stirring speed (rpm)

rB molar density of solid reactant (mol cm�3)

E. Kavcı et al. / Journal of Industrial and Engineering Chemistry xxx (2014) xxx–xxx2

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applications, military vehicles, fuels, electronics and communica-tions, agriculture, glass industry, chemicals and detergents, ceramicsand polymeric materials, nanotechnology, automotive and energysectors, metallurgy and construction. Boron compounds:

– are used in the production of cameras, lenses and binoculars toincrease durability,

– are used in all kinds of kitchen products to make our lives easier,– have properties that enhance flexibility and increase durability,– are used in the production of ink to reduce smudging,– are commonly used in the production of ceramics due to a

unique property of lowering the firing point of ceramics, as wellas strengthening the structure of ceramic slips,

– are used in the treatment of allergic reactions to environmentalevents,

– are used in skin foundation, lipstick and nail polish because oftheir durability enhancing properties, helping make-up lastlonger,

– are used in military armored vehicles plates and gun barrelsbecause of their material hardening properties,

– to be used in the production cell phones, modems and televisionsbecause of unique radiation blocking capabilities and highconductivity,

– are crucial for flight and space travel: they are used in rocketfuels and in the production of satellites, aeroplanes, helicoptersand hot-air balloons,

– are commonly used for hygiene in cleaning applications,detergents and other disinfectants because of their anti-bacterialand bleaching properties,

– are used in biological growth and control chemicals as well asfertilizers and pesticides.

Boron minerals have properties that keep food fresh for longerand preserve nutrients, and they are widely used in the foodand beverage industry. Borax decahydrate is used in cement


production; in the pharmaceuticals and cosmetics industries, inthe leather and textile industries, and in the glass industry; as wellas in pesticides and fungicides, fertilizers and fire-retardants.Boron is used in nuclear reactor control bars and neutron absorbersin fail-safes and for waste storage purposes in nuclear plants toprotect human life against harm. Boron oxide has a wide range ofuses especially in the glass industry, in antiseptics and cosmetics,in the fire fighting, soap and detergent, as well as coating sectors.

Boron does not occur in nature as a free element, but crudeborax exists as a mineral associated with clay and other impurities.There are over 200 naturally occuring boron containing mineralswith warying degrees of boroxide content (B2O3). Ores withconcentrations of calcium, sodium and magnesium elements aswell as hydrate compounds are economically more viable to mine[2]. The most commerically important and frequently tradedminerals (salts, known as borates) are tincal, colemanite, ulexiteand kernite. These ores are refined into pure chemical compoundsof commercial importance [3].

Ulexite’s chemical formula is Na2O�2CaO�5B2O3�16H2O. Boricacid is used as a source of B2O3 in many fused products and asstarting material in the preparation of many boron chemicals suchas boron phosphate, boron tri-halides, boron esters, boron carbide,organic boron salts and fluoroborates [4,5].

It has been known that the investigation of the dissolution ofulexite ore in various solutions has been studied for production ofboron compounds. There are many studies in the literatureconnected with the dissolution kinetics of ulexite in varioussolutions. A summary of these studies is as follows: Alkan andKocakerim studied it in water saturated by sulfur dioxide and theactivation energy was calculated as 58 kJ/mol [6]. Kocakerim et al.investigated it in water saturated with CO2 in low temperatures(17–35 8C) and the activation energy was found to be 51.7 kJ/mol[7]. Kunkul et al. studied it in ammonia solution saturated with CO2

and described the dissolution rate by a first-order pseudo-homogeneous reaction model and found the activation energyto be 55 kJ/mol [8]. Tekin et al. carried out experiments with it inammonium chloride solution and found the activation energy to be80 kJ/mol [9]. Tunc et al. investigated it in H2SO4 solution. Theyfound that increasing H3O+ acid concentration increased thedissolution rate, but increasing SO4

2� concentration reduced thedissolution rate due to the precipitation of a solid film of CaSO4

and/or CaSO4�2H2O [10]. Alkan et al. reported it in aqueous EDTAsolutions and its dissolution was expressed according to theunreacted shrinking core model with changing fluid phaseconcentration and calculated the activation energy to be35.95 kJ/mol [11]. Kunkul et al. studied it in ammonium sulfatesolutions. They described dissolution process by heterogeneousdiffusion control through the ash layer or product layer model andfound the activation energy to be 83.5 kJ/mol [12]. Alkan andDogan investigated it in oxalic acid solutions. The reaction rate wascontrolled by product layer diffusion and calculated the activationenergy as 59.8 kJ/mol [13]. Demirkıran and Kunkul studied it inperchloric acid solutions and found that the process was describedby the Avrami model and found the activation energy to be 19.2 kJ/mol [14]. Ekmekyapar et al. studied it in acetic acid solutions. Theyfound that the dissolution kinetics obeys a shrinking core modelwith the surface chemical reaction as the rate-controlling step. Theactivation energy was found to be 55.8 kJ/mol [15]. Demirkıraninvestigated it in the ammonium acetate solutions. The dissolutionrate fit the chemical reaction control model and the activationenergy was found to be 55.7 kJ/mol [16]. The dissolution kinetics ofulexite in ammonium nitrate solutions was investigated byDemirkıran in a batch reactor. It was determined that thedissolution rate fit the chemical reaction control model. Activationenergy was found to be 58 kJ/mol [17]. Dissolution kinetics ofulexite prepared under different calcination temperatures in



Table 1Chemical analysis of ulexite minerals.

Component CaO B2O3 Na2O H2O SiO2 and others

% 18.85 36.37 6.6 35.47 2.71

E. Kavcı et al. / Journal of Industrial and Engineering Chemistry xxx (2014) xxx–xxx 3

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ammonium chloride solutions was studied by Demirkıran andKunkul. They found that the rate fit to the second-order pseudo-homogeneous model and activation energy was found to be64.3 kJ/mol [18]. Gur studied the dissolution kinetics of calcineulexite in ammonium chloride solutions at high solid-to-liquidratios. Activation energy was found to be 84.04 kJ/mol and the ratefit the homogeneous reaction model [19].

Boric acid is industrially produced by a reaction betweenulexite and sulphuric acid solution. As sulphuric acid is a strongacid, the impurities in boron ore are dissolved. This case causesimpurities in boric acid solutions. The quality of boric acid isreduced. Therefore, weak acid solutions should be used forproduction of boric acid.

The aim of our study was to investigate the dissolution kineticsof ulexite in sodium hydrogen sulphate solutions in a mechanicalagitation system and also to declare an alternative reactant toproduce boric acid. There is no study reported in the literatureabout such a procedure. Investigation of the dissolution conditionsand the dissolution kinetics of ulexite in sodium hydrogen sulphatesolutions will be beneficial in solving some problems encounteredduring boric acid production. Therefore, the kinetic data of thereaction of ulexite with sodium hydrogen sulphate are veryimportant for industrial application.

The dissolution kinetics of ulexite in sodium hydrogen sulphatesolutions was examined according to the heterogeneous reactionmodels. In our study, reaction temperature, concentration ofsodium hydrogen sulphate solutions, stirring speed, solid/liquidratio and ulexite particle size were chosen as process parameters.

2. Materials and methods

The sample used in this research was hand-picked from theulexite mine at Bigadic-Balıkesir, Turkey. Leaching experimentswere conducted under atmospheric pressure conditions. Allreagents used in the experiments were prepared from analyticalgrade chemicals (Merck) and distilled water. A constant tempera-ture water circulator was used in combination with the reactor tomaintain the mixture in the reactor at a constant temperature. Theexperiments were carried out in a 500 mL spherical glass reactor.The reactor was equipped with a reflux condenser to preventevaporation during heating and a mechanical stirrer to obtain ahomogeneous suspension in the reactor. The mechanical agitationexperimental system is fairly common, so no illustration of itappears in this paper.

2.1. Experimental procedure

A typical experiment conducted was as follows: 300 mL ofsodium hydrogen sulphate solution was poured into the reactor.The solution was heated to the desired temperature, at which itwas kept constant. All experiments were carried out using923 mm size fractions, except in experiments where the effectof particle size on the reaction rate was investigated. After this,large quantity of solid ulexite was added to the solution in thereactor. Stirring of the solution was started immediatelythereafter. The duration of the treatment depended on theexperimental conditions. At definite time intervals, 1 mL samplesof the reacted solution were taken for the assay of B2O3 andanalyzed by potentiometric and titrimetric methods [20,21].Based on the B2O3 estimated, the degree of dissolution of ulexitewas determined as a function of time.

Ulexite samples used in the experiments were obtained fromBandırma Borax Corporation, TURKEY. The ulexite ore sampleswere crushed, dried under vacuum and sieved with ASTM standardsieves to give fractions of average sizes 3873, 1844, 923 and461 mm for dissolution experiments. Chemical analysis of ulexite


samples used in the experiments is presented in Table 1. Eachexperiment was repeated twice, and the arithmetic average of theresults of the two experiments was used in the kinetic analysis.Homogeneity of the suspension was exactly obtained at a stirringspeed of 500 rpm. Because of this, stirring speed rate of 500 rpmwas used as constant value in all experiments to obtainhomogeneity in the batch reactor.

3. Results and analysis

3.1. Dissolution reactions

The reaction that takes place in the solution can be written asfollows [20,21]:

6NaHSO4ðaqÞ ! 6NaþðaqÞ þ 6HSO4�1ðaqÞ (1)

6HSO4�1ðaqÞ þ 6H2OðaqÞ $ 6H3OþðaqÞ þ 6SO4

�2ðaqÞ (2)

When ulexite is added to the sodium hydrogen sulphatesolutions, the reaction that takes place in the solution can bewritten as follows [20,21]:

Na2O � 2CaO � 5B2O3�16H2OðsÞ þ 6H3OþðaqÞ ! 2CaþðaqÞ þ 2Naþ

þ 10H3BO3ðaqÞ þ 2H2OðlÞ(3)

2Caþ2ðaqÞ þ 2SO4

�2ðaqÞ ! 2ðCaSO4�2H2OÞðsÞ (4)

4Naþ2ðaqÞ þ 4SO4

�2ðaqÞ ! 4Na2SO4ðaqÞ (5)

The total reaction is as follows:

Na2O � 2CaO � 5B2O3�16H2OðsÞ þ 6NaHSO4ðaqÞ! 2ðCaSO4�2H2OÞðsÞ þ 10H3BO3ðaqÞ þ 4Na2SO4ðaqÞ

(6)

As can be seen from the total reaction (6), CaSO4�2H2O, boricacid and sodium sulphate have been obtained. As known, ulexiteminerals can dissolve in sodium sulphate solutions.

3.2. Effect of parameters

Reaction temperature, concentration of sodium hydrogensulphate solutions, stirring speed, solid/liquid ratio and ulexiteparticle size were selected as process variables to investigate theireffects on the dissolution level of ulexite. Parameters chosen andtheir ranges are presented in Table 2. In the experiments, while theeffect of one parameter was studied, the values of other parametersshown with asterisks in Table 2 were kept constant. A quantity of300 mL of sodium hydrogen sulphate solutions was used and keptconstant in all experiments. Homogeneity of suspension in thereactor was obtained with a stirring speed of 700 rpm, keptconstant in all experiments. The data obtained were plotted in theform of time versus fractional conversion as appearing in Figs. 1–5.In these figures, the fractional conversion X is defined:

X ¼ Amount of dissolved B2O3 in the solution

Amount of B2O3 in the original sample: (7)

3.3. Effect of reaction temperature

Temperature is a factor of great importance for the leachingkinetics. The effect of reaction temperature was examined at 298,



Table 2Parameters chosen and their ranges.

Parameter Values

Stirring speed (rpm) 100, 200, 300, 500, 600, 700a

Reaction temperature (K) 298, 308a, 318, 328, 338, 343, 353

Solid/liquid ratio (g/mL) 1/50a, 1/25, 1/10,

Particle size (mm) 3873, 1844, 923a, 461

Concentration of sodium hydrogen

sulphate (mol L�1)

0.5, 1.0, 2.0a

Reaction time (min) 1, 2, 3, 4, 5, 7, 10

a While the effect of one parameter was studied, the values of the other

parameters were kept constant.

161514131211109876543210

t(min)

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

X (

B2O

3)

298 K

308 K

318 K

328 K

338 K

343 K

353 K

Fig. 1. Effect of reaction temperature on dissolution rate of ulexite.

2,62,42,22,01,81,61,41,21,00,80,60,40,20,0

t(min)

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

X(

B2O

3)

100 rpm

200 rpm

300 rpm

500 rpm

600 rpm

700 rpm

Fig. 3. Effect of stirring speed on dissolution rate of ulexite.

4,54,03,53,02,52,01,51,00,50,0

t (min)

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

X (

B2O

3)

1/10 g/ml

1/25 g/ml

1/50 g/ml

Fig. 4. Effect of solid/liquid ratio on dissolution rate of ulexite.


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308, 318, 328, 338, 343 and 353 K. The dissolution curves obtainedare shown in Fig. 1. As can be shown from Fig. 1, the quantity ofulexite dissolved increases with increasing reaction temperature.The reaction rate constant is exponentially dependent on reactiontemperature.

3.4. Effect of concentration of sodium hydrogen sulphate solutions

In general, the leaching rate increases with increased concen-tration of reagent, but only up to a certain maximum level. Theeffect of concentration of sodium hydrogen sulphate solutions wasstudied by varying to 1.0, 1.5, 2.0 M. The dissolution curves aregiven in Fig. 2. It can be seen from Fig. 2 that the dissolution level of

4.54.03.53.02.52.01.51.00.50.0

t(min)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

X (

B2O

3)

0,5 M

1,0 M

2,0 M

Fig. 2. Effect of concentration of sodium hydrogen sulphate solutions on dissolution

rate of ulexite.


the process increases with increase in the concentration of sodiumhydrogen sulphate solutions until about 2 M.

3.5. Effect of stirring speed

The effect of stirring speed on the dissolution rate of ulexite wasinvestigated at 100, 200, 300, 500, 600 and 700 rpm. The changebetween stirring speed and conversion is presented in Fig. 3. It can

4,54,03,53,02,52,01,51,00,50,0

t(min)

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

X (

B2O

3 )

3,873 mm 1,844 mm

0,923 mm 0,461 mm

Fig. 5. Effect of particle size on dissolution rate of ulexite.



Table 3Integrated rate equations for the unreacted shrinking core model and the other models.

Rate-controlling step Rate equation

Surface chemical reaction t=t� ¼ ½1 � ð1 � XÞ1=3� t� ¼ rBR=bksCAg (7)

The film diffusion control t=t� ¼ XB t� ¼ rBR=3bkgCAg (8)

Diffusion control through the ash or product layer t=t� ¼ ½1 � 3ð1 � XBÞ2=3 þ 2ð1 � XBÞ� t� ¼ rBR2=6bDeCAg (9)

For the first-order pseudo-homogeneous model �ln(1 � X) = kt (10)

For the second-order pseudo-homogeneous model (1 � X)�1 = kt (11)

Avrami model �ln(1 � X) = ktm (12)

Table 4Values of t* and De obtained in the experimental system.

T (K) C (mol/L) W (rpm) S/L (g/ml) D (mm) t* (min) De

(m2/s)

298 1.0 700 0.02 0.923 33.78 1.68 � 10�10

308 1.0 700 0.02 0.923 22.83 2.48 � 10�10

318 1.0 700 0.02 0.923 16.44 3.45 � 10�10

328 1.0 700 0.02 0.923 6.58 8.63 � 10�10

338 1.0 700 0.02 0.923 5.28 1.07 � 10�9

343 1.0 700 0.02 0.923 4.83 1.17 � 10�9

353 1.0 700 0.02 0.923 4.29 1.32 � 10�9

308 0.5 700 0.02 0.923 32.78 3.46 � 10�10

308 1.0 700 0.02 0.923 13.90 4.08 � 10�10

308 2.0 700 0.02 0.923 8.68 3.27 � 10�10

308 1.0 100 0.02 0.923 147.05 3.86 � 10�11

308 1.0 200 0.02 0.923 60.24 9.43 � 10�11

308 1.0 300 0.02 0.923 30.58 1.85 � 10�10

308 1.0 500 0.02 0.923 21.09 2.69 � 10�10

308 1.0 600 0.02 0.923 18.48 3.07 � 10�10

308 1.0 700 0.02 0.923 13.96 4.06 � 10�10

308 1.0 700 0.02 0.923 13.64 4.16 � 10�10

308 1.0 700 0.04 0.923 22.67 2.50 � 10�10

308 1.0 700 0.1 0.923 39.84 1.42 � 10�10

308 1.0 700 0.02 0.461 8.35 1.69 � 10�10

308 1.0 700 0.02 0.923 14.32 3.96 � 10�10

308 1.0 700 0.02 1.844 74.07 3.06 � 10�10

308 1.0 700 0.02 3.873 277.77 3.60 � 10�10


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be seen from Fig. 3 that the dissolution level of the processincreases with increase in the stirring speed rate.

3.6. Effect of solid/liquid ratio

The effect of solid/liquid ratio on the dissolution rate of ulexitewas investigated by varying the ratio to 0.02, 0.04, 0.1 g/mL. Thedissolution curves are given in Fig. 4. It can be seen from Fig. 4 thatthe dissolution rate decreases with increasing solid/liquid ratio.This situation can be explained by the decrease in the number ofulexite particles per amount of solutions.

3.7. Effect of ulexite particle size

The effect of particle size was studied by treating five sizes offractions of this mineral, namely 3.873, 1.844, 0.923 and 0.461 mm.The dissolution curves are presented in Fig. 5. As can be seen fromFig. 5, as the particle size decreased the dissolution rates increasedbecause of increasing surface area.

4. Kinetic analysis

The solid-fluid heterogeneous reaction rate can be obtained fromthe heterogeneous reaction model. The experimental data wereanalyzed based on the unreacted shrinking core model to evaluatethe rate-controlling step [22,23]. The heterogeneous reaction modelgives rate equations for each control mechanisms. The step with thehighest resistance is the rate-controlling step. The model has beenused for solid–liquid heterogeneous systems in both analytical andnumerical methods. Integrated rate equations for the unreacted


shrinking-core model and the other models are shown in Table 3.According to the model, the kinetic data were treated by equations inTable 3. The application of the above models to the experimentaldata will help in determining the dissolution kinetics of the process.In the cases in which the chemical reaction is much faster than thediffusion, the leaching is said to be diffusion-controlled. The leachingmechanism often becomes diffusion controlled when, during theleaching, a porous product layer forms on the surface of the particleto be leached. The mechanism of diffusion controlled leaching ofspherical particle is often called the shrinking core model [22,23].Experimental data that fit the heterogeneous diffusion controlledash or product layer in the form of t/t* = 1–3(1 � X)2/3 + 2(1 � X).Diffusion coefficients (De) through product films for the system wereobtained from Eq. (9). Time for complete conversion (t*) and thediffusion coefficients (De) obtained in the experimental system arepresented in Table 4. The evidence for this proposal is as follows:Regression analysis has shown that experimental data correlate wellwith Eq. (9) in Table 3, which means that the dissolution is diffusioncontrolled ash or product layer. During the reaction, CaSO4�2H2Oprecipitates. Therefore, it may appear that the process is controlleddiffusion product or ash film. The regression coefficient was found tobe 0.987 as higher linearity. The variation of 1–3(1 � X)2/3 + 2(1 � X)with time (t) is plotted for reaction temperature, concentration ofsodium hydrogen sulphate solutions, stirring speed, solid/liquidratio and ulexite particle size in Figs. 6–10, respectively. Eq. (9) inTable 3 is the expression for diffusion controlled leaching accordingto the shrinking core model. As is evident from the equation, thereaction time for complete conversion is proportional to the squareof the radius of the particle. For diffusion controlled leaching, thereaction time for complete conversion is proportional to R2. Using



3,23,02,82,62,42,22,01,81,61,41,21,00,80,60,40,20,0

t (min)

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

1-3

(1-X

) 2

/3+

2(1

-X)

298 K r 2 =0,9985

308 K r 2 =0,9867

318 K r 2 =0,9766

328 K r 2 =0,9853

338 K r 2 =0,9963

343 K r 2 =0,9920

353 K r 2 =0,9948

Fig. 6. Variation of 1–3(1 � X)2/3 + 2(1 � X) with time for reaction temperatures.

4.54.03.53.02.52.01.51.00.50.0t (min.)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

1-3

(1-X

)2/3

+2

(1-X

)

1/10 g/ml r2 =0,9881

1/25 g/ml r2 =0,9811

1/50 g/ml r2 =0,9890

Fig. 9. Variation of 1–3(1 � X)2/3 + 2(1 � X) with time for solid/liquid ratio.

4.54.03.53.02.52.01.51.00.50.0t (min.)

0.0

0.1

0.2

0.3

0.4

0.5

1-3

(1-X

)2/

3 +2(

1-X

)

0,5 M r 2 =0,9918

1,0 M r 2 =0,9951

2,0 M r 2 =0,9918

Fig. 7. Variation of 1–3(1 � X)2/3 + 2(1 � X) with time for concentration of hydrogen

sodium sulphate solutions.

4,54,03,53,02,52,01,51,00,50,0

t(min)

0,0

0,1

0,2

0,3

0,4

0,5

1-3

(1-X

) 2/3

+ 2

(1-X

)

3,873 mm r2= 0,9686

1,844 mm r2= 0,9972

0,923 mm r2= 0,9987

0,461 mm r2= 0,9468

Fig. 10. Variation of 1–3(1 � X)2/3 + 2(1 � X) with time for particle size of ulexite.

0,000008

0,000010

0,000012

0,000014

0,000016

R 2

(m

2)

r 2 =0,9981


G Model


the heterogeneous diffusion controlled through the ash or productlayer, the t* values were plotted versus R2. The high linearitybetween t* and R2 is shown in Fig. 11. The regression coefficient (r2)was found to be 0.9981. Otherwise, the regression coefficient (r2)between t* and R was found to be 0.9621. The Arrhenius plots of ln ks

versus 1/T were drawn to determine the activation energy of thereaction [22–25]. Arrhenius plots of ln ks versus 1/T are shown inFig. 12. From the slopes of the straight lines the activation energy of

300250200150100500

t *

0,000000

0,000002

0,000004

0,000006

Fig. 11. Linearity between t* and R2.

2.62.42.22.01.81.61.41.21.00.80.60.40.20.0

t(min)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

1-3

(1-X

) 2

/3+

2(1

-X)

100 rpm r 2 =0,9754

200 rpm r 2 =0,9887

300 rpm r 2 =0,9889

500 rpm r 2 =0,9965

600 rpm r 2 =0,9981

700 rpm r 2 =0,9970

Fig. 8. Variation of 1–3(1 � X)2/3 + 2(1 � X) with time for stirring speed.


the reaction is found to be 36.4 kJ/mol. It has been reported that theactivation energy of diffusion controlled through the ash or productlayer reactions is under 40 kJ/mol [26]. Similar results were found inthe literature [10–14]. Further, this value indicates that thedissolution rate of ulexite is a diffusion controlled through productor ash layer. The fact that the dissolution rate of ulexite is dependenton the stirring speed is shown by the fact that the control mechanismis diffusion controlled through the product or ash layer (Fig. 12).



3,43,33,23,13,02,92,8

1/T x 103

-13,0

-12,8

-12,6

-12,4

-12,2

-12,0

-11,8

-11,6

-11,4

-11,2

-11,0

-10,8

-10,6

lnk

r2 = 0,9531

Fig. 12. Arrhenius plot of the dissolution process.


G Model


The values were found by non-linear regression analyses(Statistica 7.0, non-linear estimation model, user-specified regres-sion-least squares, security value of %95, comparison value of1 � Exp(�6), and maximum iteration values of 1000) and theanalyses gave the model mathematically as follows:

1 � 3ð1 � XÞ2=3 þ 2ð1 � XÞ ¼ 6:17 � C0:97 � W1:17 � D�1:72

� ðS=LÞ�0:66 � eð�36:4=RTÞ � t (13)

5. Discussion and conclusion

The aim of the study was to investigate the dissolution kineticsof ulexite in sodium hydrogen sulphate solutions in a mechanicalagitation system and to declare an alternative reactant to produceboric acid. Based on the results obtained in this research, thefollowing conclusion may be drawn:

– The dissolution rate of ulexite increased with increase in reactiontemperature and decrease in the solid/liquid ratio.

– The dissolution extent highly increased with increase in thestirring speed rate between 100 and 700 rpm.

– The dissolution process follows a shrinking core model with theheterogeneous diffusion controlled through the ash or productlayer as the rate controlling step.

– The activation energy was found to be 36.4 kJ/mol.– Weak acid solutions such as sodium hydrogen sulphate solutions

should be used for production of boric acid. So that theimpurities in boric acid produced are reduced.


– The mathematical form of the model based on the parameterschosen was as follows:

1 � 3ð1 � XÞ2=3 þ 2ð1 � XÞ ¼ 6:17 � C0:97 � W1:17 � D�1:72

� ðS=LÞ�0:66 � eð�36:4=RTÞ � t

Acknowledgements

This work was financially supported by Ataturk UniversityResearch Council (Project No. 2012/101), to whom the authorswish to express their gratitude.

References

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Leaching kinetics of ulexite in sodium hydrogen sulphate solutions