Modeling Electrolyte Systems

We have seen many successful industrial applications of applied electrolyte thermodynamics models. In particular, the electrolyte NRTL activity coefficient model of Chen and Evans has proved to be the model of choice for various electrolyte systems, aqueous and mixed-solvent. However, there are unmet needs that require further development. 

we need a predictive activity coefficient model for electrolyte systems. The electrolyte NRTL model is correlative, and it requires extensive experimental data sets from which NRTL binary interaction parameters can be identified. The OLI electrolyte model, with its extensive parameter database, has been serving as a pseudo-predictive model. However, use of the OLI electrolyte model is limited to dilute aqueous electrolytes, its parameter database is not open to the public, and its electrolyte speciation is not supported by experiments. 

Second, we need an equation-of-state for electrolyte solutions. Equations-of-state are needed for modeling high-pressure applications with electrolyte solutions. Significant advances are being made in this area. Given that the electrolyte NRTL model has been widely applied for low-pressure applications, we are hopeful that, some day, there will be an equation-of-state for electrolytes that is compatible with the electrolyte NRTL activity coefficient model. 

---

The need to include the carbamate equilibria points up the fact that in order to model electrolyte systems one must identify all relevant species. Ignoring the possibility of solids formation (e.g. ammonium bicarbonate, ammonium carbamate, ammonium carbonate, ammonium sesquicarbonate), these eight equilibria define the water-ammonia-oarbon dioxide system in terms of the twelve species concentrations ... 

Very little work has been done in this area. Even electrolyte transport has not been well characterized for multicomponent electrolyte systems. Multicomponent electrochemical transport theory [36] has not been applied to transport in lithium-ion electrolytes, even though these electrolytes consist of a blend of solvents. It is easy to imagine that ions are preferentially solvated and ion transport causes changes in solvent composition near the electrodes. Still, even the most sophisticated mathematical models [37] model transport as a binary salt. 

Doyle et al. [40] used a mathematical model to examine the effect of separator thickness for the PVDF.HFP gel electrolyte system and found that decreasing separator thickness below 52 pm caused only a minor decrease in ohmic drop across the cell. The voltage drops in the electrodes were much more significant. They state that their model predictions were confirmed experimentally. 

Two New Activity Coefficient Models for the Vapor-Liquid Equilibrium of Electrolyte Systems... 

Recently, there have been a number of significant developments in the modeling of electrolyte systems. Bromley (1), Meissner and Tester (2), Meissner and Kusik (2), Pitzer and co-workers (4, ,j5), and" Cruz and Renon (7j, presented models for calculating the mean ionic activity coefficients of many types of aqueous electrolytes. In addition, Edwards, et al. (8) proposed a thermodynamic framework to calculate equilibrium vapor-liquid compositions for aqueous solutions of one or more volatile weak electrolytes which involved activity coefficients of ionic species. Most recently, Beutier and Renon (9) and Edwards, et al.(10) used simplified forms of the Pitzer equation to represent ionic activity coefficients. 

In this paper, two new models for the activity coefficients of ionic and molecular species in electrolyte systems are presented. The first is an extension of the Pitzer equation and is covered in more detail in Chen, et al. (11). 

However, in most aqueous electrolyte systems of industrial interest, not only strong electrolytes but also weak electrolytes and molecular nonelectrolytes are present. While the modified Pitzer equation appears to be a useful tool for the representation of aqueous strong electrolytes including mixed electrolytes, it cannot be used in the form just presented to represent the important case of systems containing molecular solutes. A unified thermodynamic model for both ionic solutes and molecular solutes is required to model these kinds of systems. 

Recently, the Pitzer equation has been applied to model weak electrolyte systems by Beutier and Renon ( ) and Edwards, et al. (10). Beutier and Renon used a simplified Pitzer equation for the ion-ion interaction contribution, applied Debye-McAulay s electrostatic theory (Harned and Owen, (14)) for the ion-molecule interaction contribution, and adoptee) Margules type terms for molecule-molecule interactions between the same molecular solutes. Edwards, et al. applied the Pitzer equation directly, without defining any new terms, for all interactions (ion-ion, ion-molecule, and molecule-molecule) while neglecting all ternary parameters. Bromley s (1) ideas on additivity of interaction parameters of individual ions and correlation between individual ion and partial molar entropy of ions at infinite dilution were adopted in both studies. In addition, they both neglected contributions from interactions among ions of the same sign. 

To test the validity of the extended Pitzer equation, correlations of vapor-liquid equilibrium data were carried out for three systems. Since the extended Pitzer equation reduces to the Pitzer equation for aqueous strong electrolyte systems, and is consistent with the Setschenow equation for molecular non-electrolytes in aqueous electrolyte systems, the main interest here is aqueous systems with weak electrolytes or partially dissociated electrolytes. The three systems considered are the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution at 293.15°K and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process. In each case, the chemical equilibrium between all species has been taken into account directly as liquid phase constraints. Significant parameters in the model for each system were identified by a preliminary order of magnitude analysis and adjusted in the vapor-liquid equilibrium data correlation. Detailed discusions and values of physical constants, such as Henry s constants and chemical equilibrium constants, are given in Chen et al. (11). 

A fundamental difference between electrolyte systems and nonelectrolyte systems is the presence of long range ion-ion electrostatic forces in electrolyte systems. No attempt was made to develop a long-range contribution model based on the... 

Among the various models incorporating the local composition concept for short-range interactions, the NRTL equation is adopted in this study. Electrolyte systems are characterized by extraordinarily large heats of mixing. 

It should be noted that the local composition model is not consistent with the commonly accepted solvation theory. According to the solvation theory, ionic species are completely solvated by solvent molecules. In other words, the local mole fraction of solvent molecules around a central ion is unity. This becomes unrealistic when applied to high concentration electrolyte systems since the number of solvent molecules will be insufficient to completely solvate ions. With the local composition model, all ions are, effectively, completely surrounded by solvent molecules in dilute electrolyte systems and only partially surrounded by solvent molecules in high concentration electrolyte systems. Therefore, the local composition model is believed to be closer to the physical reality than the solvation theory. 

A wide variety of data for mean ionic activity coefficients, osmotic coefficients, vapor pressure depression, and vapor-liquid equilibrium of binary and ternary electrolyte systems have been correlated successfully by the local composition model. Some results are shown in Table 1 to Table 10 and Figure 3 to Figure 7. In each case, the chemical equilibrium between the species has been ignored. That is, complete dissociation of strong electrolytes has been assumed. This assumption is not required by the local composition model but has been made here in order to simplify the systems treated. 

In general, data are fit quite well with the model. For example, with only two binary parameters, the average standard deviation of calculated lny versus measured InY of the 50 uni-univalent aqueous single electrolyte systems listed in Table 1 is only 0.009. Although the fit is not as good as the Pitzer equation, which applies only to aqueous electrolyte systems, with two binary parameters and one ternary parameter (Pitzer, (5)), it is quite satisfactory and better than that of Bromley s equation (J). 

Another type of ternary electrolyte system consists of two solvents and one salt, such as methanol-water-NaBr. Vapor-liquid equilibrium of such mixed solvent electrolyte systems has never been studied with a thermodynamic model that takes into account the presence of salts explicitly. However, it should be recognized that the interaction parameters of solvent-salt binary systems are functions of the mixed solvent dielectric constant since the ion-molecular electrostatic interaction energies, gma and gmc, depend on the reciprocal of the dielectric constant of the solvent (Robinson and Stokes, (13)). Pure component parameters, such as gmm and gca, are not functions of dielectric constant. Results of data correlation on vapor-liquid equilibrium of methanol-water-NaBr and methanol-water-LiCl at 298.15°K are shown in Tables 9 and 10. 

Two activity coefficient models have been developed for vapor-liquid equilibrium of electrolyte systems. The first model is an extension of the Pitzer equation and is applicable to aqueous electrolyte systems containing any number of molecular and ionic solutes. The validity of the model has been shown by data correlation studies on three aqueous electrolyte systems of industrial interest. The second model is based on the local composition concept and is designed to be applicable to all kinds of electrolyte systems. Preliminary data correlation results on many binary and ternary electrolyte systems suggest the validity of the local composition model. 

ZJ at 293.15°K and the K2CO3-CO2 aqueous solution of tTTe Hot Carbonate Process with temperatures from 343.15°K to 413.15°K and concentrations up to 40 weight percent equivalent potassium carbonate. The success of the correlations suggests the validity of the model for aqueous electrolyte systems of industrial interest. 

For the industrially important class of mixed solvent, electrolyte systems, the Pitzer equation is not useful because its parameters are unknown functions of solvent composition. A local composition model is developed for these systems which assumes that the excess Gibbs free energy is the sum of two contributions, one resulting from long-range forces between ions and the other from short-range forces between all species. 

The long-range term has been satisfactorily described by the Debye-Huckel formula and is retained. The short-range contribution is modeled by utilizing the concept of local compositions in a manner similar to Renon and Prausnitz (20) but with additional assumptions appropriate for electrolyte systems. Preliminary results suggest the validity of the model since good fits to experimental data have been obtained for a wide range of binary and ternary systems with only binary parameters. 

VAN AKEN et al. 0) and EDWARDS et al. (2) made clear that two sets of fundamental parameters are useful in describing vapor-liquid equilibria of volatile weak electrolytes, (1) the dissociation constant(s) K of acids, bases and water, and (2) the Henry s constants H of undissociated volatile molecules. A thermodynamic model can be built incorporating the definitions of these parameters and appropriate equations for mass balance and electric neutrality. It is complete if deviations to ideality are taken into account. The basic framework developped by EDWARDS, NEWMAN and PRAUSNITZ (2) (table 1) was used by authors who worked on volatile electrolyte systems the difference among their models are in the choice of parameters and in the representation of deviations to ideality. 

The correlation presented in this paper can be very simply applied to phase-equilibrium calculations for concentrated electrolyte systems, however, care must be taken to remember that it is basically a correlational approach and not a molecular model for aqueous electrolyte solutions. 

The electrolyte concentration is very important when it comes to discussing mechanisms of ion transport. Molar conductivity-concentration data show conductivity behaviour characteristic of ion association, even at very low salt concentrations (0.01 mol dm ). Vibrational spectra show that by increasing the salt concentration, there is a change in the environment of the ions due to coulomb interactions. In fact, many polymer electrolyte systems are studied at concentrations greatly in excess of 1.0 mol dm (corresponding to ether oxygen to cation ratios of less than 20 1) and charge transport in such systems may have more in common with that of molten salt hydrates or coulomb fluids. However, it is unlikely that any of the models discussed here will offer a unique description of ion transport in a dynamic polymer electrolyte host. Models which have been used or developed to describe ion transport in polymer electrolytes are outlined below. 

Table 2.3 Molecular model used in the molecular theory for gold/MPS/PAH-Os/electrolyte system.

In addition, a model is needed that can describe the nonideality of a system containing molecular and ionic species. Freguia and Rochelle adopted the model developed by Chen et al. [AIChE J., 25, 820 (1979)] and later modified by Mock et al. [AIChE J., 32, 1655 (1986)] for mixed-electrolyte systems. The combination of the speciation set of reactions [Eqs. (14-74a) to (14-74e) and the nonideality model is capable of representing the solubility data, such as presented in Figs. 14-1 and 14-2, to good accuracy. In addition, the model accurately and correctly represents the actual species present in the aqueous phase, which is important for faithful description of the chemical kinetics and species mass transfer across the interface. Finally, the thermodynamic model facilitates accurate modeling of the heat effects, such as those discussed in Example 6. 

Chen CC, Evans LB. A local composition model for the excess Gibbs energy of aqueous electrolyte systems. AIChE J 1986 32 444-459. 

The local composition model (LCM) is an excess Gibbs energy model for electrolyte systems from which activity coefficients can be derived. Chen and co-workers (17-19) presented the original LCM activity coefficient equations for binary and multicomponent systems. The LCM equations were subsequently modified (1, 2) and used in the ASPEN process simulator (Aspen Technology Inc.) as a means of handling chemical processes with electrolytes. The LCM activity coefficient equations are explicit functions, and require computational methods. Due to length and complexity, only the salient features of the LCM equations will be reviewed in this paper. The Aspen Plus Electrolyte Manual (1) and Taylor (21) present the final form of the LCM binary and multicomponent equations used in this work. 

---