Kinetic Study on Sodium Sulfate Synthesis by Reactive Crystallization

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Kinetic study on sodium sulfate synthesis by reactive crystallization Juan Carlos Ojeda Toro, Izabela Dobrosz-Gomez, and Miguel Ángel Gómez-García Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie504763q • Publication Date (Web): 09 Feb 2015 Downloaded from http://pubs.acs.org on February 9, 2015

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Industrial & Engineering Chemistry Research

Kinetic study on sodium sulfate synthesis by reactive crystallization Juan Carlos Ojeda Toro†, Izabela Dobrosz-Gómez‡, Miguel Ángel Gómez García†,* Grupo de Investigación en Procesos Reactivos Intensificados con Separación y Materiales Avanzados - PRISMA.

†

Departamento de Ingeniería Química, Facultad de Ingeniería y

Arquitectura. ‡Departamento de Física y Química, Facultad de Ciencias Exactas y Naturales. Universidad Nacional de Colombia, Sede Manizales. Campus La Nubia, km 9 vía al Aeropuerto la Nubia, Apartado Aéreo 127, Manizales, Caldas, Colombia tel./fax: (57) 6 8879300 - 55210/55129 * Corresponding author: [email protected] KEYWORDS: Reactive crystallization, sodium sulfate, kinetic, salting-out, antisolvent.

ABSTRACT

In this work, the kinetics of the reaction between sodium chloride and sulfuric acid, in aqueous solution and in the presence of ethanol as antisolvent, was studied as a function of each reactant concentration and temperature. The thermometric method was implemented to fit the experimental data obtained in an adiabatic batch reactor. The initial reaction rate methodology was applied to determine the order of reaction as well as the specific reaction rate constants. The reaction rate corresponded to an elementary reaction. Good agreement between experimental and simulation temperature profiles was achieved (AAD ca. 1.15%). The reactive crystallization process was found to be very selective to anhydrous Na2SO4, with yields higher than 95 wt. %.

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1. INTRODUCTION Sodium sulfate is the sodium salt of sulfuric acid. It is a white crystalline solid. When anhydrous, it is known as the mineral thenardite. Its decahydrate form, Na2SO4•10H2O, can be found naturally as the mineral mirabilite, also known as Glaubert salt in synthetic form. The heptahydrate one, Na2SO4•7H2O, can be transformed to mirabelite when cooled. Sodium sulfate is mainly used for the manufacture of detergents and in the Kraft process of paper pulping1. With an annual production of ca. 10 million tonnes, it is a major commodity chemical product. The total value of natural and synthetic sodium sulfate sold worldwide was estimated in $42 million in 2012. China remains the leading exporter and producer of natural and synthetic sodium sulfate in the world. About two-thirds of the world's production is from mirabilite and the remainder from by-products of chemical processes such as hydrochloric acid production2. Other chemical processes where sodium sulfate is the principal product include: (i) the Mannheim process, which involves the direct reaction of sodium chloride and sulfuric acid in a rotary furnace at 840°C, leading to obtain high purity sodium sulfate and hydrogen chloride gas; (ii) the Hargreaves process, which comprises sodium chloride, sulfur dioxide, oxygen, and water in a gas reaction at high temperatures; and (iii) the acid-base neutralization of sodium hydroxide and sulfuric acid to produce sodium sulfate and water. All these processes implicate high energy consumption in both reaction and separation steps3. The results of our previous work4 have envisioned that sodium sulfate can be obtained by reactive crystallization, a low energy consumption and environmentally friendly process. In this case, the reaction is carried out while the solid-liquid equilibrium of system (solubility) is altered by antisolvent agent addition5-7. Subsequently, a supersaturation driving force is generated and


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the product (sodium sulfate) is precipitated in the reactive solution. Consequently, the reaction and separation can be performed in a single stage, and the high yield purity salt can be separated at low energy costs, in a simple-faster operation8. This paper is focused on the determination of a kinetic expression for the simultaneous sodium sulfate and hydrochloric acid production by sodium chloride and sulfuric acid reaction in aqueous solution, in the presence of an antisolvent. Considering the exothermic nature of this reaction, a thermometric experimental methodology was defined basing on the proposition of Nguyen et al. (2001)9. It allows to correlate the increase in temperature due to the enthalpy of reaction with reactive consumption. To ensure that the measured change in temperature is provoked only by the enthalpy of reaction, an adiabatic close system was used. The determined kinetic expression rate shows the relationship between the temperature variation and the reactive concentration changes, when the material and energy balances are coupled. 2. REACTION KINETIC FRAMEWORK 2.1. Antisolvent selection Sodium sulfate and hydrochloric acid can be obtained by sodium chloride and sulfuric acid reaction in aqueous phase (homogenous), in the presence of an antisolvent, as follows: antisolvent 2NaCl sln + H2SO4 sln  →Na2SO4(s) + 2HCl sln

( )

( )

( )

(1)

High solubility of sodium chloride (reactant) and low solubility of sodium sulfate (product) are the key features for antisolvent selection. Basing on the experimental data reported in the literature4, 10-12, it was found that ethanol and methanol present good properties as antisolvent for


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the case under study. However, for work security, health, and trade reasons, the ethanol was selected. 2.2 Adiabatic batch reactor model For an adiabatic batch reactor, the material balance can be presented in the following way:

dNi dt

( )

= νi −rA VR

(2)

where Ni is the number moles of species i, t is the time, ν i is the stoichiometric coefficient of species i, VR is the reactor volume, and -rA is the rate of disappearance of A (sodium chloride), which identify our specie basis of calculation. Similarly, the energy balance can be expressed as follows: dT ( −∆ H rxn ,A ( T ) ) ( − rA VR ) = dt ∑ N iCp i

(3)

where ∆Hrxn,A is the heat of reaction per mol of A and Cpi is the heat capacity of each species. The rate of disappearance of A, -rA, in the sodium chloride and sulfuric acid (B) reaction, might be given by a rate law as follows:

−rA = kCαACβB

(4)

Thus, in equation (4), the reaction is α and β order with respect to reactant A and B, respectively. Combining the material and energy balances, it is possible to obtain:


4

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dT −∆Hrxn,A ( T )  k ( T ) CαACβB  =    CA  dt Cpsln 0  

(5)

For the electrolytic system under study, the rate constant, k, must be expressed as a function of the temperature and feed concentration (sodium chloride):

(

k T,C A

0

−E   ) = A exp  RT 

(6)

( )+k

(7)

0

A0 = k c ln CA 1

0

c2

where E is the activation energy, and k c and k c are the kinetic constants. 1

2

Considering that the energy generated by reaction equals to the sensible energy absorbed by reactive mixture, it is possible to say that, Tf

Msln ∫ CpslndT = M0A ( −∆Hrxn,A )

(8)

T0

where Msln and MA0 represent the mass of the solution and initial mass of A, respectively. This equation can be expressed as follows: MslnCpsln ∆T = M0A ( −∆Hrxn,A )

(9)

assuming constant or mean heat capacities and heat of reaction. Finally, reorganizing equation (9), it is possible to obtain:

( −∆H rxn ,A ) = M s ln ∆T Cps ln

M 0A

(10)


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Thus, the ratio between reaction enthalpy and heat capacity can be calculated from experimental data (Msln, MA0, and ΔT of reaction). 3. EXPERIMENTAL SECTION 3.1. Chemicals. Sodium chloride (NaCl) and sulfuric acid (H2SO4) were used as reactants. All chemicals were supplied by Merck (Table 1). Deionized water (H2O) and ethanol (C2H6O) were used as solvent and antisolvent, respectively. Table 1. Chemicals used in the reactive system (NaCl-H2SO4-EtOH-H2O).

Chemical Name Sodium chloride Sulfuric acid Ethanol

Source

Initial Mass Fraction Purity

Purification Method

Final Mass Fraction Purity

Analysis Method

Merck

0.995

none

-

-

Merck Merck

0.97 0.998

none none

-

-

3.2. Apparatus. The experimental scheme, shown in Figure 1, was prepared for kinetic studies. It allows obtaining temperature vs. time data (in digital form). The experimental device includes: a jacketed injector which contains the sulfuric acid solution, an adiabatic batch reactor, a stirplate, a temperature sensor LM35-LabJack board U12, and a computer. A homemade interface, programmed in Matlab® software, was used to read and store the experimental data.


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Figure 1. The experimental scheme to obtain sodium sulfate by reactive crystallization 3.3. Procedure. Basing on sodium chloride and sodium sulfate solid-liquid phase equilibria, at room temperature, in water-ethanol solution (Figure 2), the ethanol-water mixture containing 50 wt. % was selected to perform the thermometric tests. At such composition of ethanol-water mixture, the solubility of NaCl is still relatively high and that of Na2SO4 extremely low (Figure 2). The experiments were performed according to the conditions presented in Table 2. Thus, each time, sodium chloride and sulfuric acid solutions were prepared and stored in a thermostatic bath, at selected temperature. Subsequently, they were fed to the adiabatic reactor and the jacketed injector, respectively. After a significant time needed for temperature stability in the reactor (delay time of at least 100 s), the sulfuric acid solution, at the same temperature as the temperature of the reactor, was injected to the sodium chloride solution, starting the reaction. As a result, a thermogram (temperature vs. time data) was obtained. Each test was carried out by triplicate, in order to avoid systematic errors and to determine the reproducibility of results.


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NaCl UNIQUAC ext. (Thomsen et al., 2004) Pihno & Macedo (1996) Na2SO4 UNIQUAC ext. (Thomsen et al., 2004)

6

Salt solubility (mol/kg solm)

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Seidell (1919) Ojeda et al., (2014) 4

2

0 0,0

0,2

0,4

0,6

0,8

1,0

wEtOH salt free

Figure 2. NaCl and Na2SO4 solubilities4,13,14 in water-ethanol mixtures at 25 °C Table 2. The experimental design for the kinetic study on sodium sulfate synthesis by reactive crystallization. Experiment I.1 I.2 I.3 I.4

CA0, M 0.50 0.75 1.00 1.25

T0, °C

Data type

1.50

25

T vs. t at different CA0

25

T vs. t at different CB0

1.00

II.1 II.2 II.3 II.4

CB0, M

1.47

1.50 2.00 3.00

16

III.1 III.2 III.3 III.4

1.47

1.50

20 25 30

T vs. t at different T0

* The experiments I and III were performed at sodium chloride saturation conditions (in ethanol/water mixed solvent at 25 °C). ** A=NaCl and B=H2SO4. *** Standard uncertainties (u) are: u(T0) = 0.1 °C, u(CA0) = 0.01, u(CB0) = 0.01


8

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4. RESULTS AND DISCUSSION 4.1. Reactivity tests The typical temperature-time variations obtained from batch experiments are shown in Figure 3. An increase in temperature was observed immediately after the H2SO4 injection into the reactor, reaching a maximum temperature and remaining stable for a considerable time. In all cases, the temperature rise was ca. 3°C. However, it slightly depended on the specific experimental conditions. All temperature data have a deviation ±5% approximately (thermograms). The solid products, synthetized in each experiment, were characterized by X-ray diffraction (XRD) using a RIGAKU-MINIFLEX II diffractometer. Sample diffractograms were compared to the available patterns from the Joint Committee on Powder Diffraction Standards (JCPDS)15,16. The following salts were included in the analysis: NaCl, Na2SO4, Na3H(SO4)2, NaHSO4, NaHSO3. NaH3(SO4)2, Na2S2O5, Na2S, and Na2S2O3. In all cases, the four main diffraction peaks corresponded only to the diffraction pattern of anhydrous Na2SO4 (thenardite, JCPDS: 37-1465), confirming the high selectivity of the reactive crystallization process. The product yield was measured for each test. It was defined as the percentual relation between the mass of sodium sulfate obtained experimentally and this expected stoichiometrically, for a certain amount of sodium chloride fed. The experimental mass (average value) and calculated yields are shown in Figure 4. In all cases, the obtained yields were higher than 95%. Furthermore, the tests carried out at sodium sulfate saturation conditions (experiments II.1 and III.1) presented the highest sodium sulfate yields. The yields reached in II.2. and III.3 experiments were identical. All yield measurement data have a deviation ±3% approximately.


9


28

27

26

Test 1 Test 2 Test 3

27


T (°C)

T (°C)

26

25 25

0

100

200

300

400

500

0

100

200

t (s)

300

400

500

t (s)

(b)

(a) 24

23

22


T (°C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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21

20

0

100

200

300

400

500

t (s)

(c) Figure 3. Representative thermograms obtained by triplicate for the following experiments: (a) experiment I.4, (b) experiment II.1, and (c) experiment III.2


10

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6

100

5

80

Obtained Expected

3

60

40

Yield, %

4

Mass, g

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2 20

1 0

0

I.1

I.2

I.3

I.4 II.1 II.2 II.3 II.4 III.1 III.2 III.4

Experiment

Figure 4. Sodium sulfate mass and yield obtained in each experiment (the experiment conditions correspond to these presented in Table 2)

4.2. Numerical data analysis To determine the precise value of initial and final temperature (∆T = Tfinal - Tinitial) of reaction, for each experimental test of sodium sulfate synthesis, the initial rate method was used17,

18

.

Figure 5 shows the analysis of three representative experimental thermograms (experimental raw data are presented as circle markers in Figure 5a). It should be noted that only the rising part of each curve temperature vs. time corresponds to the chemical reaction. Thus, at first, the condition at which first derivate of temperature vs. time (dT/dt) equals to zero (prior to the maximum rate of temperature change, triangle markers in Figure 5b) allows to define the precise value of initial reaction temperature for each test (triangle markers in Figure 5a). Next, the maximum rate of temperature change can be determined as the maximum value of dT/dt vs. time curve (star marker in Figure 5b). Assuming that the initial rate of temperature change equals to its


11


maximum rate, a straight line can be traced between the initial and maximum temperature rate points (triangle and stars markers in Figure 5a, respectively). Then, the final reaction temperature value (square points in Figure 5a) will correspond to the intercept point between the extrapolation of the previously traced straight line (dotted line in Figure 5a) and the temperature profile. Consequently, the absolute initial and final temperatures were determined calculating the average value of each of them from three performed experiments. Thus, the temperature change, expressed as ΔT = Tfinal - Tinitial, for each experiment was determined; and the ratio -ΔHrxn,A/Cpsln for each experiment was calculated using equation (10). 0,15 27

Spline Correlation dT/dt=0 Maximum dT/dt Initial dT/dt Experimental Data

Experimental data Initial temperature of reaction Final temperature of reaction Correlation line for initial rate method Maximum rate of temperature change Spline Correlation

26

dT/dt

0,10

Temperature (°C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0,05

0,00

25

50

100

150

200

250

50

100

Time (s)

150

200

250

Time (s)

(a)

(b)

Figure 5. (a) Plot of temperature vs. time to define the initial and final temperatures of sodium sulfate synthesis. (b) Plot of the derivative of temperature with respect to time (dT/dt) vs. time to apply the initial rate method. The MatLab function spline was used to fit experimental data

Using a non-linear data fitting procedure (lsqnonlin available in MatLab®), the kinetic parameters in equation (5) were adjusted numerically. The obtained results are presented in Table 3. Thus, it is possible to say that the reaction order with respect to NaCl (α) and H2SO4 (β) corresponds with the stoichiometric coefficient of each species in the elementary reaction (as


12

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written). It is important to clarify that the fitted value of the parameter (-∆Hrxn,A/Cpsln) includes all the heat effects (enthalpy of reaction and heat of crystallization) responsible for the detected increase of temperature. The fitted value is in good agreement with the calculated one, basing on data reported in the literature19,

20

. The relative error between the values estimated by us

(7.93729) and the calculated one (7.7880 K) is 1.88%. Table 3. Kinetic parameters values fitted for the rate law expression of sodium sulfate synthesis. Parameter

Value

α

2.0 ± 0.01

β

1.0 ± 0.05

kc1 (L2/mol2s)

1.54495 × 10−5 ± 7.73 × 10−7

kc2 (L2/mol2s)

5.93663 × 10−2 ± 2.97 × 10−4

-E/R (K)

1.96809 ± 0.098

-ΔHrxn,A/Cpsln (K)

7.93729 ± 0.397

The quality of the correlation was calculated from the absolute average deviation (AAD) as follows:

AAD = 100 / N TD

N TD

∑

i =1

(x

calc i

)

− x exp / x exp i i

(11)

where xi represents the temperature datum, and NTD is the total number of temperature experimental points. For a total of 103 experimental data, the AAD was ca. 1.15%, confirming the goodness of fit. Similar conclusions can also be made basing on the analysis of Figure 6, where calculated and experimental data are compared (reactor batch calculations were performed using equations (2) and (3) and the adjusted kinetic parameters). The simulated temperature vs.


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time variations follow similar tendency to this observed from the experimental data. However, one can see that at lower temperatures (16 and 20 °C) curve fitting to experimental data presents more significant deviations (probably due to the presence of some phase non-idealities related to the crystallization process at low temperatures). The reaction mechanism and kinetics will be studied further as a function of the activities of the reactants (including the activities model previously determined by us for this system4) in order to involve intermediates and transitions states. This will lead to a greater understanding of how and why the reactive crystallization occurs, reducing the model deviation at low temperatures, and giving insights of better ways to perform the reaction. 5. CONCLUSIONS The feasibility of synthetizing sodium sulfate by reactive crystallization was demonstrated in an adiabatic laboratory batch reactor. The kinetics of the reaction was studied in a wide range of reactant concentrations and temperatures. The rate of reaction was monitored by measuring the temperature change as a function of time. The reaction rate corresponded to an elementary reaction. An excellent agreement between simulation and experimental results in the adiabatic batch reactor was achieved, with an absolute average deviation of ca. 1.15%. A high product yield was obtained during all experiments (> 95 wt. %). The characterization test (XRD) of the obtained salt confirmed its anhydrous nature and high purity.


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Experimental Data Reactor Simulation

27,0

1.00 M

28

Experimental Data Reactor Simulation 1.50 M

26,5

2.00 M 27

Temperature (°C)

Temperature (°C)

26,0

0.50 M

2.00 M

1.00 M

0.75 M

25,5

3.00 M 26

25,0

25

0

500

1000

1500

2000

0

500

1000

Time (s)

1500

2000

Time (s)

(a)

(b) 20

Experimental Data Reactor simulation 19

Temperature (°C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


16°C

20°C

25°C 30°C

18

17

16 0

500

1000

1500

2000

Time (s)

(c) Figure 6. Comparison between simulation and experimental temperature profiles obtained for: (a) Experiments I: Change in the NaCl concentration fed, (b) Experiments II: Change in the H2SO4 concentration fed; and (c) Experiments III: Change in feed temperature. All experimental conditions correspond to these included in Table 2.


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ACKNOWLEDGEMENTS The authors acknowledge the financial support of DIMA (Programa para la financiación de Semilleros de Investigación en Emprendimiento en la Universidad Nacional de Colombia Sede Manizales – 2012– código 17037) and COLCIENCIAS (Programa Jóvenes Investigadores e Innovadores Convocatoria 566 de 2012 - Convenio Especial de Cooperación No. 0729 de 2012). The Laboratorio de Materiales Nanoestructurados y Funcionales from Universidad Nacional de Colombia, Sede Manizales, is also aknowledged for its help in XDR measurements. REFERENCES (1)

Garrett, D. E. Sodium sulphate: Handbook of deposits, processing and use. First edition, Academic Press, San Diego, 2001.

(2)

minerals.usgs.gov,http://minerals.usgs.gov/minerals/pubs/commodity/sodium_sulfate/mc s-2013-nasul.pdf, accessed 6th November 2014.

(3)

Kent, J.; Riegel, E. Kent and Riegel’s Handbook of Industrial Chemistry and Biotechnology. Eleventh Edition, Vol. 1, Springer, 2007.

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Ojeda Toro, J.; Dobrosz-Gómez, I.; Gómez, M. Sodium sulfate solubility in (water + ethanol) mixed solvents in the presence of hydrochloric acid. Experimental measurements and modeling. Fluid Phase Equilib. 2014, 384, 106.

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Mostafa Nowee, S.; Abbas, A.; Romagnoli, J. Antisolvent crystallization: Model identification, experimental validation and dynamic simulation. Chem. Eng. Sci. 2008, 63, 5457.

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Sundmacher, K.; Kienle, A.; Seidel, A. Integrated Chemical Processes, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2005.


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Kinetic Study on Sodium Sulfate Synthesis by Reactive Crystallization

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