Determination of the Reaction Kinetic Parameters for Li2CO3

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Kinetics, Catalysis, and Reaction Engineering

Determination of the reaction kinetic parameters for Li2CO3 crystallization from Li2SO4 and Na2CO3 solutions using calorimetric measurements Paola Aguilar, and Teofilo A. Graber Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00227 • Publication Date (Web): 19 Mar 2018 Downloaded from http://pubs.acs.org on March 19, 2018

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Industrial & Engineering Chemistry Research

Determination of the reaction kinetic parameters for Li2CO3 crystallization from Li2SO4 and Na2CO3 solutions using calorimetric measurements Paola G. Aguilar a and Teófilo A. Grabera, b, c* a

Department of Chemical and Mineral Process Engineering, University of Antofagasta, Av. Universidad de Antofagasta 02800, Antofagasta, Chile b Centro Avanzado del Litio y Minerales Industriales. CELIMIN. Universidad de Antofagasta, Av. Universidad de Antofagasta, 02800, Antofagasta, Chile c Centro de Investigación Científico y Tecnológico para la Minería (CICITEM R10C1004). Sucre 220, of. 602. Antofagasta, Chile.

ABSTRACT In a reactive crystallization, the reaction rate influences on the supersaturation level, and thus on the crystallization process and product quality. This work aims to determine reaction kinetic parameters for the Li2CO3 crystallization from Li2SO4 and Na2CO3 solutions using a calorimetric method. Experimental tests were carried out in a reaction calorimeter, under isothermal conditions, at different temperatures (333, 343 and 353 K) and initial concentrations for both reactants (0.7, 0.92 and 1.05 mol/L). Reaction enthalpies and specific heat of mixtures were experimentally determined, as well as reaction rates from thermal conversion data. Further, kinetic parameters such as activation energy (56.8 kJ/mol), frequency factor (1.35∙108 L0.48/min mol0.48) and reaction orders were calculated. The contribution of this work is to provide useful kinetic data that are not reported in the scientific literature, which are critical in the modeling and control of reactive crystallization process for the Li2CO3 production from lithium sulfate sources. 1. INTRODUCTION Lithium carbonate is a white crystalline solid widely used in many applications as in rechargeable batteries, glasses, ceramics and pharmaceuticals, among others. 1–3 In the next years, the consumption of lithium carbonate will grow due to the increasing demand of electric batteries, which, according to some projections, will produce a shortage of Li2CO3 in 2020.4 For this reason, a sustained production of this resource is necessary to cover this increasingly demand. Li2CO3 is obtained from the exploitation and processing of ores, brines and lithium-clays. The processing of brines is, in general, less expensive and entails lower energy consumption than the treatment of ores and clays; however, the chemical composition of brines, particularly the Mg/Li ratio, determines the ease of lithium extraction. 5 The traditional Li2CO3 processing generally handles brines with low Mg/Li ratio, about 6:1, and it involves a concentration stage in evaporation ponds, where the brine with high content of lithium chloride and magnesium as impurity is obtained. Subsequently, it goes to a purification stage to remove the impurities and then Li2CO3 is crystallized by adding sodium carbonate to the concentrated lithium chloride solution. 6 However, this is not 1 ACS Paragon Plus Environment

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suitable for the processing of brines with high Mg/Li ratios, as is the case of the Uyuni Salar (Bolivia), where the ratio is around 20:1. It requires a greater quantity of reagents, mainly CaO and Na2CO3 for the magnesium removal, which results in an increase of the production cost and in the generation of large amounts of calcium sulfate as waste in the liming stage. During the evaporation stage, the Li concentration in the brine decreases because its precipitation as Li2SO4 salts, thus it is unlikely to obtain a brine with high concentration of lithium chloride, as occurs in the traditional process. 7–9 Regarding to the processing of brines with high Mg/Li, few scientific reports are available, which basically address the difficulties to recover lithium from these matrices. 8,10,11 In the same way, industrial studies have been slowly investigated. The state-owned mining company Corporación Minera de Bolivia (COMIBOL) developed an alternative pilot process to obtain Li2CO3 from brines with a Mg/Li ratio of 22:1 (Figure 1). The precipitation of Li2SO4 occurs when the brine exceeds a density of 1.3 g/mL and a concentration of lithium and potassium of 0.6% and 0.07%, respectively. 7,12,13

Figure 1. Flowsheet of Li2CO3 production from brines with high Mg/Li ratio in the Uyuni Salar, Bolivia (Data 12,13 from COMIBOL, 2013 ).

The reactive crystallization of Li2CO3 from lithium sulfate and sodium carbonate solutions occurs in the last carbonation stage of the alternative process developed by COMIBOL12,13, being one of the most important steps in the production chain (Fig. 1). On the other hand, this reactive crystallization system is also present in others processes, like in the lithiumsulfated minerals, such as: spodumene, lepidolite and amblygonite to obtain Li2CO3.14 Also, in the pyrometallurgical process of lithium clays that was recently developed by Western Lithium Company.15 Therefore, the reactive crystallization of Li2CO3 is a key method to harvest solid lithium, whether from brines, ores or clays. Reactive crystallization involves the interaction between reactants in solution that results in the supersaturation of the dissolved product, which leads the formation of crystal nuclei. In this type of crystallization, the reaction rate influences on the supersaturation level, and thus on the subsequent crystallization process and product quality. A fast supersaturation tends to produce fine particles, which are transferred to downstream stages and produce 2 ACS Paragon Plus Environment

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operational problems as low filtration rates, high retention of solvent or impurities, poor washing and slow drying; being these conditions are undesired for industrial scale production. 16–18 Due to the importance of the understanding the influence of the chemical reaction on the performance of the reactive crystallization processes, the reaction kinetics of different systems have been studied, through finding expressions that relate the reaction rate with operating variables such as temperature and concentration of species. 19 In this sense, Kralj et at.20 and Tavare et al.21 were the first authors to introduce the reaction and mass transfer as kinetic phenomena that influence the reactive crystallization. Kralj et at.20 reported kinetic parameters of reaction and growth for the precipitation of vaterite from aqueous solution, such as: rate constants, activation energy. On the other side, Tavare et al.21 studied the crystallization of silica by neutralization of sodium silicate with diluted sulfuric acid in a pilot-scale stirred reactor. The reaction rate constant was evaluated by the method of initial rates determined from the concentration profiles of the solution. On the other side, Yi et al.22 studied the reaction and crystallization kinetics of Li2CO3 from LiHCO3 solutions. The results showed that the reaction rate of this process is represented by a second order equation and the apparent activation energy was determined, concluding that the growth of Li2CO3 is mainly controlled by diffusion. Myasnikov et al.23 investigated the crystallization kinetic of calcium carbonate and magnesium hydroxide through mixing supersaturated solutions. Further, an empirical relationship for determining inductive time in homogenous nucleation of calcite is proposed, which is used to calculate the surface energy and the activation energy in a wide range of temperatures and supersaturations. López et al.24 determined the reaction kinetic between solutions of KCl and H2SO4 to obtain potassium sulfate crystals, using an adiabatic batch reactor. The initial rate method and a thermometric methodology were applied to find the reaction orders, activation energy and the specific reaction rate constant. Later, Ojeda et al.25 apply the thermometric method to determine the reaction kinetic parameters for the reactive crystallization of sodium sulfate from sodium chloride and sulfuric acid. Several researches about the reaction kinetic for different systems of reactive crystallization have been performed; however, studies related with the reaction kinetic between solutions of lithium sulfate and sodium carbonate to obtain lithium carbonate and sodium sulfate, as shows bellow chemical reaction, have not been investigated yet. Therefore, this work aims to determine a kinetic expression that relates the reaction rate between Li2SO4 and Na2CO3 solutions with the temperature and reactants concentration, using a calorimetric method, which is a technique that gives information about kinetic and thermodynamic aspects from heat and mass balances. 26 Some articles have been published regarding the application of the online calorimetry technique in different crystallization systems, such as the crystallization of calcium oxalate, adipic acid in water, and zeolite, among others. 27–29 ( ) + ( ) → () + ( )

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2. EXPERIMENTAL SECTION 2.1. Materials. Lithium sulfate monohydrate (Li2SO4·H2O) at 99.0% purity and sodium carbonate (Na2CO3) at 99.9% purity were used as reactants, both reagents were supplied by Merck. Deionized water with conductivity lower than 0.054 mS/cm was used as solvent in the all experiments. The solutions were not filtered. 2.2. Apparatus. The experimental set up to determine the specific heat of the solutions and the reaction kinetic of Li2CO3 from Li2SO4 and Na2CO3 solutions is shown in Fig. 2. An automatic reaction calorimeter (RC1e, Mettler Toledo) designed to work at isothermal and adiabatic conditions, was used. The reactor is a 1 L-jacketed glass vessel equipped with a thermostat, a mechanic stirrer, a calibration heater, sensor of temperature and pH electrode. The reaction calorimeter is coupled to a computer and a controller of devices (RD10, Mettler Toledo). The temperature of Na2CO3 solution was controlled by a thermostatic bath (Schott-Gerate, model CT 52) and it was added by a peristaltic pump (Masterflex, Cole Parmer). All the solutions were prepared using an analytical balance (AX204, Mettler Toledo). The solutions densities were measured using a density meter (Anton Paar DSA 5000M), measuring range from 0 to 3 g/cm3, resolution 1∙10-6 g/cm3 coupled with a thermostat that has a precision of ±0.001 K.

Figure 2. Experimental set up. 1-Reaction Calorimeter RC1; 2- Mechanic Stirrer; 3-Cotroller RD10; 4- Thermostat; 5- Peristaltic Pump; 6- Jacketed reactor; 7- Thermostatic Bath; 8- Computer

2.2.1. Reaction Calorimeter (RC1, Mettler Toledo). The RC1 calorimeter works according to the heat flow and mass balance principles. The heat flow exchanged with the fluid of the jacket is continuously calculated by eq 1, and it depends on the temperature difference between the solution within the reactor ( ) and the jacket fluid ( ), as well as to the overall heat transfer coefficient () and the transfer surface. 4 ACS Paragon Plus Environment

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= −

(1)

The overall heat transfer coefficient, is specific to each reactor and reaction, and can be easily calculated at different stages of the reaction by a simple calibration. This type of calorimeter ensures rapid control of the reaction temperature, since heat transfer is very efficient. The produced heat flowrates as consequence of a chemical reaction or physical changes are calculated by mass and heat flow balances. Mass balance considers dosing of reactant or product withdrawal. The heat balance includes all the flows between the interior and surroundings of the reactor. Through this balance, the reaction heat flow ( ) can be calculated considering the heat through jacket ( ), the accumulation term (

), the heat flow caused by addition (!"" ) and the losses in the reactor lid ("" ) (eq 2).

= +

+ !"" + "" where

= $ %&

' '(

(2)

(3)

'$ (4) '( The specific heat of reaction mixture (%& ) can be determined by interpolation between the specific heat of the solution before and after reaction. The progress of the reaction was monitored by direct measure of − , which depended on the liquid composition. When the difference is constant, the reaction finishes. The initial time (() ) was established when the reaction heat flow was initially detected, and the final time ( corresponds as the time when the heat flow returned to a baseline. Both times were set after de experiment finished. The reaction enthalpy (∆ +), denoted as the global heat released of reaction (, ) by the calorimeter, can be calculated by integration of the heat flow rate during the reaction period (eq 5). !"" = %&!" ( − !"" )

./

, = ∆ + = - '( .)

(5)

The thermal conversion in time ( (0. ) is obtained dividing the reaction heat flow at a determined time by ∆ + (eq 6). If there was only one reaction to be analyzed, the thermal and analytical conversion should be similar, then the thermal conversion can be used instead of the analytical conversion (01)2 34 ). This is helpful, since the obtaining of thermal data is much easier than the analytical ones, because sampling and chemical analysis is not required, but may involve different levels of sophistication in the equipment (reaction calorimeter) and in the data treatment.

0. = 01)2 34

.

5. '( = 6 ∆ + 5

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(6)


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2.3. Procedure. 2.3.1. Determination of solution properties. It is necessary to know some physical properties of the fed solutions, as the density (7) and specific heat (%8 ), to perform the heat balance in the system and determine the reaction enthalpy. A density meter (DSA 5000M, Anton Paar) was used to measure the density, which was calibrated using air and deionized water as reference substances. The reported data represent the average of measurements conducted in triplicate. On the other hand, the specific heat of the solutions (%8 ) was determined by the standard method included in the reactor software (iControl RC1e 4.0, Metler Toledo), which consists in a heating of the solution at 0.3 K/min for 10 minutes. The method considers a preliminary calibration by the Joule effect is necessary to determine the term. 30 In addition, the heat capacity of sensors (8) ) introduced in the reactor are included (eq 7). .

- − '( = ($" %8 + 8) )∆

(7)

9

2.3.2. Study of the reaction kinetic of Li2CO3 from Li2SO4 and Na2CO3 solutions. Experimental tests were carried out under isothermal conditions, stirring at 300 rpm, with temperatures (:; .)< ) and reactants concentrations (%1)3 and %@ A3 ). Three test groups were performed in order to classify the effect of the variables on the conversion and to obtain the kinetic parameters. The first and second test groups were performed at different excess percentages of each reactant and at same reaction temperature; the third set was carried out at different temperatures, using an intermediate level of Na2CO3 excess (Table 1). For each experiment, 250 mL of lithium sulfate and sodium carbonate were prepared and kept at the nominal temperature. Temperature range of 333-353 K was applied for the study of Li2CO3 crystallization, since in an industrial level the Li2CO3 is obtained between this range, due to its solubility decreases as temperature increases. Table 1. Experimental design of the reaction tests between Li2SO4 and Na2CO3 solutions. Test

%1)3 (mol/L)

%@ A3 , (mol/L)

I.1 I.2

0.70 0.70

0.92

I.3

343

1.05

II.1

0.70

II.2

0.92

II.3

1.05

0.70

III.1 III.2

:; .)< , (K)

343 333

0.70

0.92

III.3

343 353


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At the beginning, the reaction temperature was set with the vessel empty. Then, when the set temperature was reached, the Li2SO4 solution was introduced into the reactor and its specific heat and overall heat transfer coefficient were determined by the standard method of the RC1e software. Subsequently, the solution of sodium carbonate was fed by using a peristaltic pump at 50 mL/min for 5 min. Once the reaction finished, i.e. when ( − ) was negligible, the specific heat of suspension and the overall heat transfer coefficient after reaction were determined. This information allowed estimating the reaction specific heat of mixture by interpolation between the specific heats before and after the reaction. Additionally, the reaction enthalpy and conversion were obtained and used to calculate the kinetic parameters as the reaction orders (B, $), activation energy (D ) and frequency factor (9 ). 3. REACTION KINETIC FRAMEWORK Reaction calorimeters controlled by computer (RC1, Mettler Toledo), offer possibilities for the continuous measurement of the chemical reaction progress.31 Therefore, reagent concentrations in function of time can be calculated from the conversion data acquired experimentally through this type of calorimetric reactors (eqs. 8-12). Equations for a semibatch reactor were used in the first five minutes, due to during this time the Na2CO3 solution is added to the reactor changing the volume of total solution (E. ) (eqs. 8-10). The feed flow of Na2CO3 solution (,), the volume of the initial solution Li2SO4 (E3 ) and the moles added along first five minutes of Na2CO3 (B@ 2 A3F !! ) are considered.

E. = E3 + ,( %1)2 34 = %@ 2 A3F =

(8)

° B1) 1 − 01)2 34 2 34

E.

(9)

° B@ 2 A3F !! − B1) 0 2 34 1)2 34

(10) E. After five minutes, the volume of total solution in the reactor was constant and equal to 0.5 L (EI ). So, the system behaves like a batch reactor from this time. Eqs. 11 and 12 were used to calculate the reagents concentrations in a batch regime.

%1)2 34 = %@ 2 A3F =

° B1) 1 − 01)2 34 2 34

EI

(11)

° ° B@ − B1) 0 2 A3F 2 34 1)2 34

(12) EI It is important to clarify that the equations presented above (eqs. 8-12) consider lithium sulfate as the limiting reagent. In the same way, similar expresions were deduced for the case where the limiting reagent is sodium carbonate. On the other hand, all chemical reaction are governed by a rate law or rate equation, which is an algebraic expression that is in function of reagents properties (species concentrations) and reaction conditions (temperature, presion or catalyst type). The reaction rate is 7 ACS Paragon Plus Environment


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independent of the type of reactor (e.g., batch or continuous flow). 32 Therefore, in this work, the kinetic parameters of reaction were determined only from data acquired after five minutes that reaction started, when the system is operated under batch conditions. According to the mass balance equation for a batch reactor, the Li2SO4 reaction rates (−J1)2 34 ) can be determined if the variation of Li2SO4 concentration with respect to time K

! L62MN4 !.

O is known (eq 13). Hence, the concentration-time data were fitted to an nth-order

gauss equation and this equation was subsequently derivate with respect the time to !

determine the L62MN4 . This procedure was performed with a programed routine in MatLab software.

!.

−

'%1)2 34 = −J1)2 34 '(

(13)

Also the rate of disappearance of Li2SO4, −J1)2 34 , in the reaction between Li2SO4 and Na2CO3, might be given by the power law model (eq 14). In this model the rate law is the product of concentration of the individual reacting species, each of which is raised to a power. These exponents $ and B are the reacion orders with respect to Li2SO4 and Na2CO3, respectively. For the most laboratory and industrial reactions, the rate coeficient (P) depends only on temperature according to the Arrhenius equation (eq 15), where −D is Activation energy, 9 is frequency factor and Q is gas constant (8.3143∙10-3 kJ/mol K). Therefore, combining these equations (eqs. 14 and 15) was obtained an overall expression that relates the reaction rate between Li2SO4 and Na2CO3 solutions with the temperature and reactants concentration (eq 16).

−J1)2 34 = P%1)2 34 R %@ 2 A3F < P() = 9 S −J1)2 34 = 9 S

K

TUV O :W

TU K VO :W %1) 3 < %@ A3 R 2 4 2 F

(14) (15)

(16)

Experimental data of the reaction rates and the reactants concentrations determined at different temperatures (333, 343, 353 K) and excess percentages of Li2SO4 and Na2CO3 were correlated to the eq 16. Therefore, kinetic parameters ($, B, 9 B' D ) for the quaternary reactive system Li+, Na+//CO32-, SO42--H2O were calculated applying a nonlinear least-squares analysis. The quality of the correlation was calculated from the sum of the squared differences (X ) of experimental and calculated reaction rate (eq 17), where J) ;Y8 and J) represent the experimental and calculated reaction rate, respectively, is the total number of tests and Z is the number of parameters to be determined. 32

@

X =[ 4. RESULTS AND DISCUSSION

)\]

(J) ;Y8 − J) )

−Z 8

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(17)

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4.1. Physical properties of fed solutions. The density and specific heat of the fed solutions at the reactor are shown in Table 2, which were determined at different temperatures and molar concentrations. As expected, at higher temperatures the density slightly decreased for both Li2SO4 and Na2CO3 solutions, similar trend is reported by Cartón33, where densities of aqueous lithium sulfate solutions over the concentration range from 0.4 to 3.2 mol/kg H2O were obtained at different temperatures, from 283 to 323 K. On the other hand, at constant temperature, the specific heat decreases as the solution concentrations increase. This behavior can be explained as follows, for aqueous solutions of electrolytes, the main contribution to the specific heat comes from the water molecular structure and its vibrational frequency; thus, as greater number of electrolytes dissolved in the water, more water molecules will leave the structure and will be retained in the hydration sphere that surrounds the electrolyte, diminishing the specific heat. 34 Table 2. Experimental density (^) and specific heat (_` ) of Li2SO4 and Na2CO3 solutions at different temperatures and molar concentrations (a). TReaction (K) 333 343

Solution Li2SO4 Na2CO3 Li2SO4

Na2CO3

353

Li2SO4 Na2CO3

%(mol/L) 0.70 0.92 0.70 0.92 1.05 0.70 0.92 1.05 0.70 0.92

ρ(g/ cm )

1.04589 ± 0.00003 1.07293 ± 0.00009 1.04171 ± 0.00001 1.05956 ± 0.00001 1.07076 ± 0.00010 1.04224 ± 0.00005 1.06914 ± 0.00018 1.07957 ± 0.00006 1.03750 ± 0.00002 1.06520 ± 0.00013

cj ( J/g K) 3.87 ± 0.04 4.01 ± 0.01 4.16 ± 0.03 3.87 ± 0.02 3.80 ± 0.01 4.17 ± 0.04 4.03 ± 0.03 3.48 ± 0.03 4.41 ± 0.01 4.11 ± 0.01

4.2. Reaction enthalpy and Specific Heats of reaction mixture. Specific heats of reaction mixture and reaction enthalpies were experimentally determined for the reaction between lithium sulfate and sodium carbonate solutions (Table 3). Positives enthalpies were observed for all tests, indicating that the reaction is endothermic, absorbing heat of the surroundings; the system temperature along reaction falls. Figure 3 shows the reaction heat flow ( ) and the reaction total mass ($ ) against time at 343 K, for the experiment without excess reagent, i.e. 0.7 mol/L Li2SO4 and 0.7 mol/L Na2CO3. A fluctuation of the at the beginning was observed, provoked by the initial contact of the solutions. Moreover $ increased constantly up to 500 g during the first five minutes, which was the time assigned to feed the reactor. The area between and baseline (dashed) represents the global heat produced by the reaction, which can to be assimilated to the reaction enthalpy (∆ +), due to the reaction was performed under constant pressure (eq 5). According to Ojeda,25 the values of reaction enthalpy and specific heats of reaction mixture involve all the heat effects, enthalpy of reaction and heat of crystallization. 9 ACS Paragon Plus Environment


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Figure 3. Reaction heat flows ( ) and mass of the reacting mixture ($ ) for the experiment without excess reagent at 343 K.

Reaction enthalpies (∆ +R ) and specific heats (%& ) at different temperatures (333, 343, 353 K) for the reaction between 0.7 mol/L Li2SO4 and 0.92 mol/L Na2CO3 are presented in Table 3. As expected, at higher temperatures the reaction enthalpies are greater. Since it is an endothermic reaction, the increase of the temperature favors the reaction and causes that it absorbs more energy from the surroundings. Figure 4 shows that higher global reaction heats (denoted by the dashed areas) were obtained at higher temperatures. The reaction time increases as the temperature decreases. Table 3. Reaction Enthalpy and specific heat of mixing at different temperatures, for 0.7 mol/L Li2SO4 and 0.92 mol/L Na2CO3 TReaction (K)

∆ +R (kJ/mol)

%& (kJ/g K)

tReaction (min)

333

17.25 ± 0.31

3.99 ± 0.04

37.17 ± 0.23

343

20.13 ± 0.50

4.09 ± 0.04

28.20 ± 0.21

353

32.67 ± 0.42

4.35 ± 0.01

20.18 ± 0.41

In this work, the reaction enthalpy and the specific heat were determined separately by the calorimetric method, unlike other studies, as in Ojeda,25 where only the ratio between reaction enthalpy and specific heat (∆ +R /%& ) was calculated from experimental data of temperature in an adiabatic reactor by the thermometric method for the reactive system (NaCl-H2SO4-EtOH-H2O). Thermodynamic properties data reported by Wagman35 are used to calculate the reaction enthalpy for the studied system at 298 K. In order to obtain the ∆ +R at higher temperatures, the heat capacity data is extrapolated by the Criss-Cobble empirical correlation.36 Comparing these extrapolated data at 343 K (20.49 kJ/mol) with the experimental ones at the same temperature obtained in this study (20.13 ± 0.50), a small difference was obtained, which gives idea that this work may be useful providing experimental properties for this system at high temperatures, which would be interesting for industrial applications. 10 ACS Paragon Plus Environment

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a)

b)

c)

Figure 4. Reaction heat flow rate ( ) and mass of the reacting mixture ($ ) at different temperatures a) 333 K b) 343 K c) 353 K, for 0.7 mol/L Li2SO4 and 0.92 mol/L Na2CO3.



4.3. Kinetic Parameters. As mentioned before, for a complete reaction without secondary and intermediary reactions (as the reaction involved in this work), the heat flow rate ( ) represents an indirect measure of the reaction rate that relates , ∆ + and 01)2 34 (eq 6). In Figure 5 can be observed (solid line) and 01)2 34 (dotted line) versus time at 343 K with 31% excess reagent, i.e.: 0.7 mol/L Li2SO4 and 0.92 mol/L Na2CO3. The slope of conversion curve is greater at the beginning, due to the reaction is initially faster. Then it decreases while the reaction progresses, reaching a final conversion close to 100%, indicating that chemical reaction finished.

Figure 5. Heat flow rate absorbed by reaction and conversion vs. time for 0.7 mol/L Li2SO4 and 0.92 mol/L Na2CO3 at 343 K.

Conversion curves versus time with 31% excess of Na2CO3 at different temperatures (333 343 and 353 K) and different excesses of Na2CO3 at 343 K (0, 31, 50%) were obtained (Figure 6). At higher temperatures and excess of reagent, the conversion curve is displaced to left and their slopes are greater, since the reaction is favored. A similar behavior was observed with different excess levels of Li2SO4, which are not shown in the figure.


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a)

b)

Figure 6. Conversions versus time under different a) temperatures (333, 343 and 353 K) at 0.7 mol/L Li2SO4 and 0.92 mol/L Na2CO3 and b) excess of Na2CO3 (0, 31, 50 %) at 343 K.

Subsequently, the reagent concentrations in function of time were calculated from the conversion data acquired experimentally using the eqs. 8-12. The Figure 7 shows the concentration of both reagents over time into the reactor, for three different scenarios in which the reaction was carried out at 343 K: a) stoichiometric condition, b) 31% excess Na2CO3 and c) 31% excess Li2SO4. In the all cases the Li2SO4 concentration decreased until the reaction is completed and a sudden slope changing was observed in the curve at five minutes, which is attributed to the transition between the reactor regimes, i.e. from semibatch to batch system. On the other hand, the Na2CO3 concentration increased until reaching a maximum value at the five minutes, time in which the feed of this reagent finished. After this time its concentration starts to decrease.



a)

b)

c) Figure 7. Reagents concentration vs. time to 343 K under different conditions: a) Stoichiometry b) 31% Excess Na2CO3 c) 31% Excess Li2SO4.

According to the mass balance equation for a batch reactor, which was applied once semibatch regime became to a batch system (after first five minutes), the reaction rates from the variation of Li2SO4 concentration with respect to time were calculated for all the experiments (eq. 13). Figure 8 shows the effect of the temperature and excess of Na2CO3 on the reaction rate, which is maximal at the beginning of the batch regime. As temperature increases, the rLi2SO4 is greater, and the reaction finished at briefer times. In this sense, the best temperature for the crystallization of Li2CO3 by this system is 343 K, since greater temperatures induce a fast supersaturation affecting the quality of the product, particularly forming crystals with small sizes. On the other hand, the excess of Na2CO3 produces an increment of the magnitude of rLi2SO4, passing from 0 to 31%. However, no differences were obtained when the addition of the reactant was even greater (50%). The information obtained at this level could be interesting for industrial applications in order to obtain optimized curves with the less involved resources.


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a)

b)

Figure 8. Reaction rate versus time under different a) temperatures (333, 343 and 353 K) at 0.7 mol/L Li2SO4 and 0.92 mol/L Na2CO3 and b) excess of Na2CO3 (0, 31, 50 %) at 343 K, t >5min.

Kinetic parameters ($, B, 9 B' D ) for the synthesis of lithium carbonate from Li2SO4 and Na2CO3 solutions were calculated correlating the experimental reaction rates and the reactants concentrations determined above at different temperatures (333, 343, 353 K) and excess percentages of reactants according to eq. 16 (Table 4). The overall order of reaction is 1.48 ($ + B) and the activation energy is 56.8 kJ/mol, which indicates that the process between 333 at 353 K would be dominated by the chemical reaction and no by diffussion22. Table 4. Reaction Kinetic Parameters fitted for the rate law expression of Lithium Carbonate syntesis from Li2SO4 and Na2CO3 solutions. Kinetic Parameters

Value

Frequency Factor, 9 (L /min mol ) Activation Energy, D (kJ/mol) Reaction order with respect to Li2SO4, $ Reaction order with respect to Na2CO3, B 0.48

1.35∙10 56.8 0.89 0.59

0.48

8

Based on data reported in the literature for other reactive systems, the activation energy obtained in this work is coherent; in the precipitation of Vaterite (one of the CaCO3 crystalline forms) from aqueous solution between 283 and 318 K the D is 57.1 kJ/mol, 20 while for the homogeneous nucleation of CaCO3 is between 57-58 kJ/mol. 23 As observed in Figure 9, the level of agreement between the experimental and calculated reaction rates for the Li+, Na+//CO32-, SO42--H2O reactive system is good, with a X = 0.01231. Despite of the small X , several deviations are obtained at lower temperatures. According to Ojeda, 25 this behavior is probably due to the presence of some phase nonidealities related to the crystallization process at low temperatures. 15 ACS Paragon Plus Environment


a)

b) Figure 9. Comparison between experimental and calculated reaction rate under different a) temperatures (333, 343 and 353 K) at 0.7 mol/L Li2SO4 and 0.92 mol/L Na2CO3 and b) excess of Na2CO3 (31, 50 %) at 343 K, t >5min.

5. CONCLUSIONS In this work, the scarcely reported reactive crystallization of Li2CO3 from Na2CO3 and Li2SO4 solutions was studied, which is a system that has gained attention around the world since it is an important stage in different processes, especially in the processing of brines with high content of Mg/Li, being is a challenge that requires technical information. Physical properties of Li2SO4 and Na2CO3 solutions, like density and specific heat, were measured at different temperatures and concentrations, which are necessary to perform the heat balance in the system and determine the reaction enthalpy. The evolution of the reaction heat was followed in detail through an energy balance of the system every 2 s, which considers the heat flow losses, stored heat in the system and the dosing heat. The reaction between sulfate lithium and carbonate sodium solutions is an endothermic reaction, and the increasing of temperature has a positive influence on the reaction time. Kinetic parameters ($, B, 9 B' D ) were successfully determined (σ2 = 0.01231) through a calorimetric technique. These values are consistent with the magnitude reported for kinetic parameters in other reactive crystallization systems. The results of this work could be used by further studies on crystallization kinetics as the determination of nucleation and growth rates and the modeling and control of the reactive crystallization of Li2CO3 for its production from lithium sulfate sources. NOMENCLATURE

' '(

reaction heat flow (J/s) change of the reactor temperature with respect to time (K/s) 16 ACS Paragon Plus Environment

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Page 17 of 22 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


$

$" %& %&

%&!" 8)

∆

mass of the reacting mixture (sum of all additions) (g) mass of solution inside reactor (g) specific heat of reaction mixture (J/g K) specific heat of solution (J/g K) specific heat of added solution (J/g K) heat capacity of sensors (J/ K) temperature inside the reactor (K) temperature of jacket fluid (K) increase of reactor temperature by heating via the jacket (K)

U

overall heat transfer coefficient (Watts/m2K)

A

heat transfer surface (m2)

'$ '(

!"" ()

(

!"" "" ,

∆ +

∆ +R 0. $ B

dosing rate (g/s)

temperature of dosed solution (K) reaction start time (s) end time of the reaction (s) heat flow through jacket (J/s) accumulated heat (J/s) heat flow through dosing (J/s) lost heat flow (J/s) global heat released by the reaction (J) reaction enthalpy (J) Molar enthalpy of reaction (J/mol) reaction conversion reaction order with respect to Li2SO4 reaction order with respect to Na2CO3

D

activation energy (kJ/mol)

k

Coeficient of reaction rate

9 Q

frequency factor gas constant (kJ/mol K) 17 ACS Paragon Plus Environment


E3 E.

EI ,

° B1) 2 34

° B@ 2 A3F

B@ 2 A3F !! %1)3

%@ A3

volume of Li2SO4 inicial solution (L) total solution Volume at determined time before 5 min (L) total solution Volume in the reactor after 5 min (L) feed flow of Na2CO3 solution (L/min) inicial moles of Li2SO4 (mol)

initial moles of Na2CO3 (mol) added moles of Na2CO3 (mol) molar concentration of Li2SO4 initial solution (mol/L) molar concentration of Na2CO3 initial solution (mol/L)

0. , 01)2 34

analytical conversion of reaction

:; .)

Determination of the Reaction Kinetic Parameters for Li2CO3

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