Journal of Materials Research and Technology Journal of Materials Research and Technology
J Mater Res Technol 2017;6:57-64 DOI: 10.1016/j.jmrt.2016.05.006
Original Article
Thermodynamic modeling of phases equilibrium in aqueous systems to recover potassium chloride from natural brines
Ruberlan Gomes da Silvaa,, , Marcelo Secklerb, Sonia Denise Ferreira Rochac, Daniel Saturninod, Éder Domingos de Oliveirad
a Mineral Development Centre of Vale, Santa Luzia, MG, Brazil
b Department of Chemical Engineering, Universidade de São Paulo (USP), São Paulo, SP, Brazil
c Department of Mining Engineering, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG, Brazil
d Department of Chemical Engineering, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG, Brazil
Received 09 November 2015, Accepted 17 May 2016
Abstract

Chemical fertilizers, such as potassium chloride, ammonium nitrate and other chemical products like sodium hydroxide and soda ash are produced from electrolyte solutions or brines with a high content of soluble salts. Some of these products are manufactured by fractional crystallization, when several salts are separated as solid phases with high purity (>90%). Due to the large global demand for potassium fertilizers, a good knowledge about the compositions of salts and brines is helpful to design an effective process. A thermodynamic model based on Pitzer and Harvie's model was used to predict the composition of crystallized salts after water removal by forced evaporation and cooling from multicomponent solutions or brines. Initially, the salts’ solubilities in binary systems (NaCl–H2O, KCl–H2O and MgCl2–H2O) and ternary system (KCl–MgCl2–H2O) were calculated at 20°C and compared with literature data. Next, the model was compared to our experimental data on the quinary system NaCl–KCl–MgCl2–CaCl2–H2O system at 20°C. The Pitzer and Harvie's model represented well both the binary and ternary systems. Besides, for the quinary system the fit was good for brine densities up to 1350kg/m3. The models were used to estimate the chemical composition of the solutions and salts produced by fractional crystallization and in association with material balance to respond to issues related to the production rates in a solar pond containing several salts dissolved, for instance, NaCl, KCl, MgCl2 and CaCl2.

Keywords
Quinary system, Natural brine, Potassium chloride, Pitzer and Harvie's model, Fractional crystallization
1Introduction

The solubility prediction of electrolytes in aqueous solutions is essential for a variety of processes such as brines and seawater desalination, drowning-out crystallization as well as liquid–liquid extraction in chemical, mineral and hydrometallurgical industries [1]. For example, solar evaporation is applied to brine ponds in northern regions of Argentina and Chile to produce saleable salts like potassium chloride, potassium sulphate and lithium salts [2]. The process is based on fractional crystallization [3], which provides separation of inorganic salts with purities compatible with market requirements. Thermodynamic models are useful tools to estimate the solution composition during crystallization, which is needed for reliable industrial process design. In this context, Pitzer's ion-interaction model and its extended Harvie and Weare's model [4–6] are suitable tools because they are reliable for predicting salt's solubility in multicomponent aqueous systems with high ionic strength over a wide range of temperatures (0–300°C) [7–9]. Considering this, it is the objective of this study to analyze the technical feasibility of recovering potassium chloride from a natural complex brine, here represented as the quinary system NaCl–KCl–MgCl2–CaCl2–H2O. Given the lack of information for such quinary system, experimental data on solubilities have been determined and compared to Pitzer's ion-interaction model predictions. The validated model has been used to develop a technically feasible fractional crystallization process.

2Material and methods

Batch crystallization experiments with a natural brine from a dry salt lake located at the north of Argentina were performed in a 2l jacketed glass crystallizer. Temperature was controlled by an electric heating system at 85±3°C. A mechanic stirrer at 250 RPM provided mixing, using a 45° pitched blade impeller. Table 1 shows the chemical composition of the natural brine under investigation.

Table 1.

Density and chemical composition of the natural brine.

Density at 20°C (g/cm3NaCl (g/L)  KCl (g/L)  MgCl2 (g/L)  CaCl2 (g/L)  CaSO4 (g/L)  Total salts (g/L) 
1.198  244.17  17.20  28.20  58.50  0.19  348.26 

The natural brine sample was distributed in four recipients and concentrated by forced evaporation at 85°C at ambient pressure (∼1 atmosphere). Thereafter, the pulps were cooled to 20°C to increase yield and kept under stirring for 24h at 250 RPM in order to achieve equilibrium. The initial brine (1.198g/cm3 at 20°C) was concentrated up to 1.250g/cm3 at 20°C, which is now called the Step 1 in this methodology. The solid and liquid phases in equilibrium were then separated by vacuum filtration. The liquid phase with 1.250g/cm3 was subjected to another cycle of evaporation at 85°C followed by a cooling process to 20°C in order to increase its density to 1.304g/cm3 at 20°C and this is the Step 2. The crystallization and solids separation procedures were repeated two more times to produce brines with densities of 1.354g/cm3 at 20°C in Step 3 and 1.427g/cm3 at 20°C in Step 4. The evaporation at 85°C is required to concentrate the brine samples to desired densities in a timely manner and then cooling to 20°C. The temperature of 20°C was chosen because it is the average brine temperature processed in dry salt lakes, like Salar de Atacama in Chile [2]. The less soluble and more abundant salts, for example NaCl, crystallized at the beginning of the process, whereas the more soluble and less abundant ones (CaCl2·MgCl2·12H2O) crystallized at the end of the experiment. Sodium, potassium, magnesium, calcium and chloride contents in solution were analyzed as well as in the wet salts obtained in each step.

The solutions were diluted and the respective wet salts dissolved in doubly deionized water to determine the sodium, potassium, magnesium and calcium contents by PerkinElmer NexION 200D ICP-MS. The chloride concentrations in the liquid and solid phases were determined by titration with a standard solution of AgNO3 in the presence of drops of 0.1% (w/v) K2CrO4 as an indicator.

Samples for X-ray diffraction were ground below 200 # TYLER MESH (0.074mm) and analyzed on PANalytical Model X’PERT PRO MPD (PW 3419) with PW3050/60 (θ/θ) goniometer, X-ray ceramics tubes, anode of Cu (Kα1=1.540598Å) and PW3373/00 model (2000 W-60kV). Diffraction patterns were acquired from 5° to 75°2θ at 0.02 steps. The identification of all minerals was done with X’Pert HighScore version 2.1b software from PANalytical.

3Results and discussion

The solubility equilibrium constant, KSP, at a fixed temperature and pressure for the dissolution reaction of hydrated salt (MνMXνX·ν0H2O), having νM positive ions (M), of charge zM, and νX negative ions (X) of charge zX, as well ν0 molecules of water (Eq. (1)) [8] is expressed by Eq. (2)[8]:

Example:

where μ° is the standard chemical potential of solids (µ°S), water (µ°H2O) and for the ions solution (µ°M and µ°X) at a given temperature (T) and R is the gas universal constant. The standard state for the aqueous ions and electrolytes was taken to be a hypothetical one molal solution referenced to infinite dilution at any pressure and temperature. The solid and solvent standard states were taken to be the respective pure phases at the pressure and temperature of interest.

The saturation index (SI) for KCl is expressed by the ratio between the ionic product (IP) and the solubility product according Eq. (3)[10]. In terms of the activities, the ionic product is given by Eq. (4)[10].

where aK+=mK+⋅γK+ for the potassium chloride case, but for a generic cation the equation becomes aM+zM=mM+zM⋅γM+zM. For the anion, the KCl case becomes aCl−=mCl−⋅γCl− and for a generic anion aX−zX=mX−zX⋅γX−zX. Furthermore, ai, is the ionic activity, mi, the molal concentration and γi, the activity coefficient, for single ions, where i=K+, Cl, M+zMor X−zX.

The activity coefficients (γi) are calculated by the Pabalan and Harvie's model according to the literature [5,8]. With these values, it is possible to calculate the IP for a specific salt at a specific temperature. The SI is calculated since the Ksp is known from the literature. If SI=1 the solution is saturated, if SI<1 the solution is unsaturated and if SI>1 the solution is supersaturated. The activity of water (aH2O) is related to the osmotic coefficient, ϕ, by Eq. (5)[8].

where ∑mi is the sum of molalities of species in solution. The osmotic coefficient, Φ, is calculated from ion-interactions [8].

In order to check the results obtained by Pabalan and Harvie's model [5,8], the solubilities in selected binary systems were calculated and compared with data from Pabalan and Pitzer [8]. Fig. 1a and b shows that the molalities calculated by the Pitzer and Harvie's model [5,8] fit well with experimental measurements obtained by Pabalan and Pitzer [5] for the binary systems NaCl–H2O, KCl–H2O and MgCl2–H2O at different temperatures and for the ternary system NaCl–KCl–H2O at 20°C.

Fig. 1.
(0.19MB).

Comparison between solubilities obtained by Pitzer and Harvie's model [5,8] and experimental data from Pabalan and Pitzer [5] for (a) the binaries systems NaCl–H2O, KCl–H2O and MgCl2–H2O at various temperatures and (b) the ternary system NaCl–KCl–H2O at 20°C.

Experimentally determined equilibrium compositions of brines at 20°C with the respective solids are shown in Tables 2 and 3. It is observed that the pH decreases from 7.4 to 2.1 from Step 1 to Step 4, corresponding to a brine with 528g/L of salts, mainly calcium chloride (29.77% w/w).

Table 2.

Experimental solubility data NaCl–KCl–MgCl2–CaCl2–H2O system at 20°C with natural brine.

Step of forced evaporation  Density at 20°C (g/cm3% w/w evaporated water  Liquid phase composition (%w/w)pH  Total solids dissolved (g/L) 
      NaCl  KCl  MgCl2  CaCl2  CaSO4  H2   
Feed (a1.198  20.38  1.44  2.35  4.88  0.02  70.93  7.4  348 
Step 1  1.250  59  10.07  3.19  5.55  11.69  0.01  69.49  6.5  381 
Step 2  1.304  74  2.76  4.47  9.58  19.47  0.00  63.72  5.5  473 
Step 3  1.354  85  0.85  2.44  7.73  22.49  0.15  66.49  4.3  454 
Step 4  1.427  98  0.24  0.49  6.51  29.77  0.00  62.99  2.1  528 
a

Saturated in NaCl and CaSO4.

Table 3.

Salt composition of NaCl–KCl–MgCl2–CaCl2–H2O system at 20°C with natural brine.

Step of forced evaporation  Composition of solid phases (%w/w)Solid phase identified by XRD in equilibrium with respective brine 
  NaCl  KCl  MgCl2  CaCl2  CaSO4   
Feed  Clear Solution 
Step 1  99.9  0.10  NaCl and CaSO4 
Step 2  62.8  37.2  NaCl and KCl 
Step 3  10.3  7.8  79.3  2.6  NaCl, KCl, Carnallite
(KCl·MgCl2·6H2O), Bischofite (MgCl2·6H2O), Tacahydrate (CaCl2·MgCl2·12H2O) and/or Antractite (CaCl2·2H2O) 
Step 4  3.8  1.8  7.9  86.5  NaCl, KCl, KCl·MgCl2·6H2O, MgCl2·6H2O, CaCl2·MgCl2·12H2O and/or Antractite 

The calculated compositions by the Pitzer and Harvie's model [5,8] of the equilibrium brines at 20°C are given in Table 4. Fig. 2a and b shows a comparison between the compositions of equilibrium brines at 20°C predicted by the model and the experimental values obtained in the present work.

Table 4.

Brine composition for the system NaCl–KCl–MgCl2–CaCl2–H2O system at 20°C calculated by Pitzer and Harvie's model [5,8] with natural brine.

Feed and after forced evaporation Step  Density at 20°C (g/cm3Composition of liquid phase (%w/w)Activity of water (aw
    NaCl  KCl  MgCl2  CaCl2  CaSO4  H2 
Feed  1.198  15.25  1.53  2.51  5.21  0.02  75.38  0.726 
Step 1  1.250  5.30  2.909  5.95  12.33  0.01  73.51  0.643 
Step 2  1.304  1.33  1.14  8.96  18.58  0.00  69.99  0.509 
Step 3  1.354  0.26  0.404  11.253  22.49  0.00  65.60  0.347 
Step 4  1.427  0.16  0.95  0.78  39.53  0.00  58.56  0.324 
Fig. 2.
(0.22MB).

Comparison between predicted Pitzer and Harvie's model [5,8] and experimental values for the NaCl–KCl–MgCl2–CaCl2–H2O system at 20°C: (a) NaCl and KCl, (b) MgCl2 and CaCl2.

Tables 2 and 3 show that in Step 1, after the reduction of about 59% of total initial free water, only NaCl and CaSO4 crystallize in the solid phase, with a composition of 99.9% w/w of NaCl and 0.10% w/w of CaSO4. The content of water reduced in the brine due to the amount of water evaporated and the amount of water of crystallization in the salts. The concentration of all salts, excluding NaCl and CaSO4, increased as the brine density is raised from 1.198g/cm3 to 1.250g/cm3 both measured at 20°C. The brine pH decreased from 7.4 to 6.5. The overflow brine from Step 1 became saturated in KCl and the total soluble salts increased from 348 to 381g/L.

The brine produced after Step 2, followed by a reduction of about 74% of total initial free water, showed the formation of NaCl and KCl crystals. The salt had a composition of 62.8% w/w of NaCl and 37.2% w/w of KCl. The concentration of all salts, discounting NaCl, increased as the brine density grew up from 1.250g/cm3 to 1.304g/cm3 measured at 20°C. The brine pH decreased from 6.5 to 5.5. The brine became saturated for carnallite salt. The total soluble salts solids increased from 381 to 473g/L.

In Step 3 after evaporation of 85% of total initial free water, NaCl, KCl, KCl·MgCl2·6H2O and a small amount of CaCl2·MgCl2·12H2O/CaCl2·2H2O crystallized. The solid phase showed a composition of 10.3% w/w of NaCl, 7.8% w/w of KCl, 79.3% w/w of MgCl2 and 2.6% w/w of CaCl2. The presence of CaCl2 and MgCl2 is due to a small quantity of brine impregnating the salts. The brine density is raised up from 1.304g/cm3 to 1.354g/cm3 measured at 20°C. The brine pH decreased from 5.5 to 4.3 and the brine reached saturation for calcium salts. The observed decrease of the total soluble salts solid from 473 to 454g/L is not physically consistent and is probably an experimental error.

The last step of forced evaporation, Step 4, led to an evaporation of about 98% of total initial free water and NaCl, KCl, KCl·MgCl2·6H2O, CaCl2·MgCl2·12H2O and CaCl2·2H2O crystallized. The solid phase salts were formed by 3.8% w/w of NaCl, 1.8% w/w of KCl, 7.9% w/w of MgCl2 and 86.5% w/w of CaCl2. The brine density went up from 1.354g/cm3 to 1.427g/cm3 measured at 20°C and the pH reached a low acidic value of 2.1. The final brine was saturated for all salts with a content of soluble salts of 528g/L.

The simulated and experimental results for natural brine (Table 4 and Fig. 2a) with reference to 1–1 electrolytes, sodium chloride (NaCl) and potassium chloride (KCl) are in a good agreement. The systems also showed that sodium chloride crystallized in all steps and reached saturation in potassium chloride after Step 1 (39.88g/L=3.19% w/w, brine density of 1.250g/cm3).

Table 4 and Fig. 2b display the experimental concentrations of 2–2 electrolytes, magnesium chloride (MgCl2) and calcium chloride (CaCl2), in the equilibrium brines as well as those found by the Pitzer's and Harvie's model [5,8]. In experiments with brines of densities up to 1.350g/cm3, it is observed a small difference between the experimental and calculated data. However, for densities above 1.350g/cm3, the Pitzer and Harvie's model [5,8] overpredicted the solubility values of magnesium chloride and calcium chloride.

Fig. 3 shows the X-ray diffractograms for the solids produced after each crystallization step in contact with mother liquor of densities 1.250, 1.304, 1.354 and 1.427g/cm3 at 20°C. It is possible to verify the formation of salts compatible with the mineral structure of halite, sodium chloride (NaCl), for solutions of density of 1.250g/cm3, while potassium chloride (KCl, sylvite) crystallizes from solutions of density of 1.304g/cm3 at 20°C. Potassium magnesium chloride (KCl·MgCl2·6H2O) with a structure similar to carnallite was identified at a density of 1.354g/cm3 at 20°C, while magnesium calcium chloride (MgCl2·CaCl2·12H2O, tacahydrate), calcium chloride dihydrate (CaCl2·2H2O, anthracite), crystallized only at a density of 1.427g/cm3 at 20°C. These experimentally determined crystallographic phases agreed with the Pitzer and Harvie's model [5,8] predictions.

Fig. 3.
(0.14MB).

X ray diffractograms for the crystallized salts produced after the respective equilibrium brines reach densities of 1.250, 1.304, 1.354 and 1.427g/cm3 at 20°C.

The Pitzer's and Harvie's model [5,8] were used to simulate the process to recover saleable salts from natural brine. A solar evaporation process has been designed for the extraction of potassium chloride from brine deposits of dry salt lakes, like Salar de Atacama in northern Chile. The basic stream for the material balance around a single solar pond is shown in Fig. 4 where: (i) Leakage is the brine lost from the pond through porous dikes and floors. The quantity of leakage is usually described in kg per day and it is a function of the pond area [4]. It was assumed a leakage of 0.011kg/day/m2; (ii) the water evaporated is usually expressed in mm/day or kg/day/m2. For steps 1, 2 and 3, it was assumed 3.5, 2.8 and 2.0kg per day per m2 of water evaporated. (iii) Entrainment is related to the brine that is lost attached to the salts deposit.

Fig. 4.
(0.1MB).

Basic streams of a solar pond for Step 1, 2 and 3.

As the salt crystals grow or accumulate on the pond floor, voids are created and some brine is trapped therein. The quantity of entrainment is a function of the quantity and type of salt deposited. The entrainment is generally expressed as a weight percent of the combined salts in the deposit and correspondent entrained brine. It was assumed an entrainment loss of 15% in steps 1, 2 and 3. Salts combined to entrainment are here denominated impregnated salts.

Generally, the brine concentration throughout the solar pond is uniform and equal to the concentration in the brine that exists at each step. This observation is a key assumption for the pond material balance. It was assumed that the leakages and the exit brines have the same concentration, so these streams can be created as a single stream to simplify the material balance.

For fixed concentrations at the entrance and exit points of the pond, the material balance is represented by a system of five variables: flowrate of feeding brine, flowrate of exit brine, evaporation rate, amount and composition of salts formed and pond area. The brines and salts compositions were calculated by the Pitzer and Harvie's model [5,8]. Of these five variables, only two are independent. By establishing the value of any two of these variables, the system may be solved and the material balance is obtained.

The overflow brine from Step 1 feeds the Step 2 and the overflow brine from Step 2 feeds the Step 3. The overflow brine from Step 3 is called bittern brine, rich in the most soluble salts, like, MgCl2 and CaCl2. Table 5 shows the results of the material balance for Step 1, Step 2 and Step 3 using solar evaporation process to crystallize the desired salt. Table 6 shows the composition of feed and overflow brines.

Table 5.

Material mass balance results in solar ponds.

  Step 1  Step 2  Step 3 
Pond area (m23050  937  980 
Feed brine (kg/h)  1000.00  378.69  231.48 
Water evaporation (kg/h)  444.77  109.31  81.68 
Leakage (kg/h)  1.40  0.43  0.45 
Impregnated salts (kg/h)  175.14  37.47  38.20 
Entrainment (kg/h)  26.27  5.62  5.73 
Non impregnated salts (kg/h)  148.87  31.85  32.47 
Overflow brine (kg/h)  378.69  231.48  111.15 
% Accumulated evaporated water  59%  74%  85% 
Composition of impregnated salts (%w/w)
NaCl  76.14  45.37  7.32 
KCl  2.44  22.30  5.75 
MgCl2  1.43  4.67  21.42 
CaCl2  2.96  9.69  46.86 
CaSO4  0.02  0.01  0.01 
Total water  17.02  17.96  18.65 
Composition of non impregnated salts (%w/w)
NaCl  87.65  49.63  5.99 
KCl  2.33  24.31  0.00 
KCl·MgCl2·6H20.00  0.00  17.46 
MgCl2·6H21.33  7.81  21.89 
CaCl2·6H21.71  10.05  47.41 
CaSO4·2H20.12  0.04  0.02 
Free water (% w/w)  6.88  8.16  7.23 
% w/w of feed KCl crystallized (accumulated)  28  82  97 
% w/w of feed KCl crystallized (in the respective Step)  28  54  15 
Table 6.

Composition of initial and overflow brines (% w/w).

Component  Feed  Overflow Step 1  Overflow Step 2  Overflow Step 3 
NaCl (%w/w)  15.35  5.30  1.33  0.26 
KCl (%w/w)  1.53  2.90  1.14  0.40 
MgCl2 (%w/w)  2.51  5.95  8.96  11.25 
CaCl2 (% w/w)  5.21  12.34  18.58  22.49 
CaSO4(% w/w)  0.02  0.01  0.00  0.00 
Total water (% w/w)  75.39  73.50  69.99  65.61 
Density at 20°C (g/cm31.198  1.250  1.304  1.354 
KCl (g/L)  18.34  36.31  14.88  5.39 
MgCl2 (g/L)  30.07  74.33  116.78  152.27 
Total soluble solids (g/L)  295  331  391  466 

According to the solubility calculated by the Pitzer and Harvie's model [5,8] and the material balance, a sequence of three stages could lead to the crystallization of halite (87.65%w/w of NaCl) in Step 1, sylvinite (49.63% w/w of NaCl+24.31% w/w of KCl) in Step 2 and a mixture of halite (5.99% w/w of NaCl), carnallite (17.46% w/w of KCl·MgCl2·6H2O), bischofite (21.89% w/w of MgCl2·6H2O) and calcium chloride (47.41% w/w CaCl2·6H2O) in Step 3.

The feed brine in Step 1 is saturated in NaCl and in CaSO4, but it is not saturated in other salts, so these are the first two salts to be crystallized. Considering the amount of evaporated water (444.77kg/h) and an evaporation rate of 3.5mm/day, it will be necessary a pond area of about 3050m2. Halite crystallized in Step 1 will be harvested and fed to a NaCl Industrial Plant. The brine density at 20°C changes from 1.198 to 1.250g/cm3, crystallizing approximately 394kg of halite per 1000kg of evaporated water. Around 28% of entering potassium will be lost by impregnated brine in the salts.

Saturation in KCl is achieved in the overflow brine from Step 1 that feeds Step 2 (36.31g/L of KCl). In the solar ponds of Step 2 and Step 3, KCl-rich salts (sylvinite and carnallite) crystallize. The sylvinite crystallized in Step 2 is collected and fed to an industrial KCl Plant. The brine density at 20°C changes from 1.250 to 1.304g/cm3 in Step 2, resulting in the crystallization of approximately 343kg of salts per 1000kg of evaporated water. About 54% of entering potassium will crystallize. Considering the amount of evaporated water in Step 2 (109.31kg/h) and an evaporation rate of 2.8mm/day, a pond area of about 937m2 will be necessary.

A mixture of halite, carnallite, bischofite and calcium chloride salts crystallizes in Step 3. This mixture is harvested and fed to an industrial KCl Plant as well. The brine density at 20°C changes from 1.304 to 1.354g/cm3, crystallizing approximately 468kg of salts per 1000kg of evaporated water. About 15% of entering potassium will crystallize. Considering the amount of evaporated water in Step 3 (81.68kg/h) and an evaporation rate of 2.0mm/day, a pond area of about 980m2 will be necessary.

The brine leaving Step 3 has small amounts of NaCl and KCl and CaSO4, therefore upon further processing (above a brine density of 1.354g/cm3) mainly magnesium and calcium salts are expected to crystallize, so this option is not pursued.

The total KCl recovery from the solar pond is 69%, consisting of 54% in the step 1 plus 15% in Step 3. The KCl obtained in Step 1 is not recovered due to the low KCl content in relation to the NaCl content. Considering a KCl recovery of 70%, an on-stream factor of 90% to process the salts in an industrial KCl Plant, for a calculation basis of one ton of KCl 60% K2O, the plant will result in about 22.5ton of solid residues, 10.6m3 of bittern brine, 82ton of evaporated water and an area of 73m2 of solar pond.

4Conclusions

Experimental solubility data for various electrolyte systems were obtained and compared to Pitzer and Harvie's model [5,8] predictions at 20°C. The Pitzer and Harvie's model agrees well with literature data on the binary systems (NaCl–H2O, KCl–H2O, MgCl2–H2O) and ternary systems (NaCl–KCl–H2O) at 20°C considered in this study. The experimental data on the quinary system NaCl–KCl–MgCl2–CaCl2–H2O also compared well with the Pitzer and Harvie's model for brine densities up to 1.350kg/m3. The model was used to design a fractional crystallization process with three evaporation steps. We have shown that the model is useful for solubility prediction of complex systems and also supply a theoretical basis for the extraction of salts from naturally complex occurring brines.

Conflicts of interest

The authors declare no conflicts of interest.

Acknowledgments

Authors would like to thank Vale S.A., especially Patrice Mazzoni and Keila Gonçalves for authorizing the publication of this work; Nancy Parada, Consultant of Chemicals from Brines for participating in the study for the project involving production of potassium chloride from natural brine. CNPq and CAPES (Brazilian Council for Scientific and Technological Development) are also acknowledged.

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Copyright © 2016. Brazilian Metallurgical, Materials and Mining Association
J Mater Res Technol 2017;6:57-64 DOI: 10.1016/j.jmrt.2016.05.006