Article pubs.acs.org/jced
Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Prediction of Solubilities in the System Li++Na++K++Cl−+H2O at 25 °C and Industrial Process of Refining Muriate of Potash J. Lovera,*,† R Tíjaro-Rojas,‡ G. Meruane,§ F. Hernań dez-Luis,∥ and H.R. Galleguillos† †
Department of Chemical Engineering and Mineral Processing, University of Antofagasta, Av. Angamos 601, Antofagasta, Chile Faculty of Engineering and Architecture, Arturo Prat University, Av. Arturo Prat, 2120 Iquique, Chile § Nitratos y Potasio, SQM Industrial S.A., Las Condes, Chile ∥ Departamento de Química Física, Universidad de La Laguna, Tenerife 38207, Spain J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV OF NEW ENGLAND on 02/16/19. For personal use only.
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S Supporting Information *
ABSTRACT: A modified Pitzer model at very high ionic strengths is developed in this work for quaternary systems consisting of three uniunivalent salts with a common ion and water. The proposed model is a combination of the extended Debye−Hückel model and the Pitzer model. This model satisfactorily describes the solubilities for the ternary LiCl+NaCl+H2O, LiCl+KCl+H2O, and NaCl+KCl+H2O systems at 25 °C, and it predicts reasonably acceptably the solubilities of the quaternary system LiCl+NaCl+KCl+H2O at 25 °C, when comparing with the experimental results of the literature and those obtained by the original Pitzer model with modified parameters high concentrations. In addition, the proposed model was applied to the process of refining muriate of potash on an industrial plant of a Chilean mining and chemical company.
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INTRODUCTION The evaluation of the performance of a chemical plant for the production of inorganic salts from a brine requires knowledge of the solubilities of these salts in the brine water. As is it known, the physical properties of the pure water dissolved salts are not the same as those of groundwater or seawater, where other dissolved salts are present.1 For instance, in a kilogram of pure liquid water, 350 g of sodium chloride (NaCl) can be dissolved at a constant temperature of 25 °C. In contrast, in a brine formed by 340 g of lithium chloride (LiCl) and 1 kg of water, only 134 g of NaCl is dissolved at the same temperature (62% less than in pure water). This difference can severely affect the evaluation of a salt recovery process if the correct solubility is not considered.2,3 The solubility of a salt in a brine can be experimentally determined in the laboratory, or it can be predicted from a mathematical model. Currently, there are several commercial software available, with an excellent offer for calculations of electrolytes thermodynamic properties, such as HSC,4 PHREEQC,5 and gPROMS,6 among others. It is known that the thermodynamic models of Pitzer,7 UNIQUAC,8 and their modified versions have been widely used in the prediction of salt solubilities in multicomponent systems and incorporated into software such as those mentioned above. There are many references about both experimental and theoretical studies of electrolyte solutions that have used the Pitzer ionic interaction model to predicting ternary and quaternary systems solubilities,7 with excellent results. A classic example is the calculation of solubilities of the NaCl © XXXX American Chemical Society
+KCl+H2O system at various temperatures. This result constitutes useful information for the design and operation of industrial separation processes of muriate of potash. However, the number of published thermodynamic analyses based on mineral solubility to high concentrations is moderate, especially for systems containing lithium salts with a high solubility. Monin et al.9 have questioned the validity of the original Pitzer model to predict activity and osmotic coefficients for the LiCl+H2O system. They have concluded that, unless the Pitzer model is modified, it could able to predict with a reasonable precision the thermodynamic properties of the system, only up to 10 mol·kg−1. Above this value, they suggested as a more suitable model the average spherical approach (MSA). However, in general, using the original Pitzer model, reasonably acceptable results can be achieved, but with modified binary and mixing parameters at high concentrations, at the risk of losing precision at low concentrations. Christov10 used the original Pitzer model considering the unsymmetrical mixing terms, dependent on the ionic strength, to predict the solubility for the LiX+MgX2+H2O systems (X = Cl, Br). In the case of the system containing LiCl, the binary parameters used were those that are valid up to saturation (19.219 mol·kg−1) instead of the usual binary parameters (valid up to 6 mol·kg−1). Special Issue: Latin America Received: November 1, 2018 Accepted: February 1, 2019
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DOI: 10.1021/acs.jced.8b01018 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
was presented as an alternative procedure and not as the search for a superior method over others. Experimental data of solubilities of the ternary system LiCl +KCl+H2O13,14 at several temperatures have been reported in the literature, and its correlation with two approaches of the Pitzer model was recently addressed by Lassin et al.,15 the best approach being the one including the parametrization of the Pitzer model a neutral aqueous species, LiCl0(aq). Currently, there is a moderate analysis of the experimental solubility of the quaternary system LiCl+NaCl+ KCl+H2O at 25 °C, using a thermodynamic model. Song and Yao16 investigated the salt lake brine system solubility prediction at 25 °C, using the original Pitzer model with the binary and mixing parameters obtained at high concentrations. The reliability of their results is explicitly illustrated for the quinary system Li+, K+, Mg2/Cl−, SO42−+H2O. The motivations of this work are, in the first place, the development of the Pitzer model based on our previous work for a quaternary system based on the binary properties and mixing terms, because such equations are not explicitly given in the scientific literature. In the second place, the application of this model to predict solubilities of the systems LiCl+KCl+H2O and LiCl+NaCl+KCl+H2O at 25 °C. Because of the flexibility of the proposed model, the results obtained by this work are compared with those from the original Pitzer model, by using the parameters from Song and Yao.16 The proposed Pitzer model is also used in this contribution to construct the phase diagram of the NaCl+KCl+H2O system at 25 °C; on such a diagram experimental pseudoequilibrium data of solutions containing both sodium chloride and potassium chloride are presented, which were collected from an industrial refining plant muriate of potash of a Chilean mining and chemical company. A schematic of this process is presented in a block diagram; the global process is represented in the solid−liquid phase diagram, and a simulation of this process is done by using this contribution proposed model.
The results obtained in this way are consistent with experimental measurements. Later, Li et al.11 addressed the prediction of solubilities for the LiCl+HCl+H2O and LiCl +MgCl2+H2O systems at 0 and 20 °C with the same model and similar approach on binary parameters but considering the mixing parameters independent of the ionic strength and neglecting the effect of asymmetric mixtures such as LiCl +MgCl2+H2O. They also obtained satisfactory results when comparing them with experimental data. Weber,12 in his monograph about the estimation of parameters of the Pitzer model at high ionic strengths, suggested a special statistical methodology to extend Pitzer’s binary parameters with solubility data of ternary systems. Weber does not correlate the solubilities in a particular way for each ternary system but considers a family of ternary systems containing a common electrolyte. For example, to estimate the binary parameters of NaCl in a range of high ionic strength, Weber selected three ternary systems NaCl+HCl+H2O, NaCl +NaOH+H2O, and NaCl+NaNO3+H2O at 25 °C. Weber’s hypothesis is that the values of the binary parameters of the original Pitzer model are generally valid up to 6m and are not suitable for calculations of electrolyte solubilities in ternary systems involving very high ionic strengths (exceeding 20m values). A special and abbreviated form of writing the Pitzer model of the MX electrolyte activity coefficient in a ternary system MX+NX+H2O (MX and NX are uniunivalent salts with a common ion X) is the following:3,12 b b b ln γMX = ln γMX + y(φNX − φMX ) ÄÅ ÉÑ ÅÅ ÑÑ yy i + ymÅÅÅθMN + mjjj1 − zzzψMNX ÑÑÑ ÅÅÇ ÑÑÖ 2 k {
(1)
where γ and ϕ are the binary activity and osmotic coefficients evaluated in the ionic strength I of the mixture, y represents the molar fraction of the NX salt in dry base, m is the total molality (in this case m = I), and θ and ψ are the mixing parameters. A particular characteristic of eq 1 is that, instead of using the Pitzer model for the binary properties, γb and ϕb (see Appendix S1), another model can be used. This advantage was used by Weber in his correlation of solubilities in ternary systems at high ionic strength, where he used the extended Debye− Hückel model in a series of powers of ionic strength for the calculation of binary properties. In a previous work,3 we used the modified Pitzer model mentioned above for the solubility correlation of the ternary system LiCl+NaCl+H2O at 15, 25, 50, and 100 °C. This particular system involves very high ionic strengths in the order of 6 and 30 mol·kg−1, exceeding the application range of the original Pitzer model (I < 6 mol·kg−1). To succeed in this correlation, similar to Weber, the extended Debye−Hückel model and the Pitzer model for ternary systems were combined. Only the mixing parameters and some equilibrium constants were necessary in the estimation of parameters for a successful correlation of solubilities. Unlike Weber’s method, the binary parameters of the salts in our model proposal remained constant. This formalism considerably reduced the number of estimation parameters. The proposed solubility correlation method is essentially the same as that of Cristov and Li et al.; the difference is in the used binary model. The modified Pitzer model,3 in this sense, has the advantage of being more flexible, because it allows the use of a combination of models, as it was previously mentioned. This new approach b
b
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THERMODYNAMIC MODELING Pitzer Model. The Pitzer ionic interaction model7 has been widely used since 1973 in the prediction of solid−liquid equilibrium, mainly in brines and in seawater. Pitzer presented a modification to the electrostatic term of Debye−Hückel by adding a series of the virial, which expresses the Gibbs energy in excess depending on the composition of the solution. From this thermodynamic function, the equations for the activity coefficients and the osmotic coefficient are deduced, these are, respectively:17 ÄÅ ÅÅ Z ij 2νM yz zz ∑ maÅÅÅÅBMa + CMa lnγMX = |Z MZ X|F + jj Å 2 ÅÅÇ k ν { a É ij νX yz ÑÑÑÑ + jjj zzzθXa ÑÑÑ+ j ν z ÑÑ k M { ÑÖ É ÅÄÅ i νM zy ÑÑÑÑ ÅÅ Z ij 2νX yz j j z Å jj zz ∑ mc ÅÅBc X + Cc X + jj zzθMc ÑÑÑ+ j ν z ÑÑ ÅÅ 2 k ν { c k X { ÑÖ ÅÇ 1 ∑ ∑ mcma[2νMZ MCca + νMψMca + νXψXac]+ ν c a i νX yz zzψcc ′ X + kν{
∑ ∑ mcmc′jjj c
