Electrolyte systems, activity coefficient models

Homogeneous mixtures, excess properties, VLB, SLE, LLE in non-electrolyte systems, activity coefficient models. 

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. 

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

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. 

First, 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. 

The chemical potential gradient may be expressed in terms of mole fraction and activity coefficient gradients as shown in Section 2.2. Activity coefficient models for electrolyte systems are discussed by, for example, Newman (1991) and Zemaitis et al. (1986). 

The property packages available in HYSYS allow you to predict properties of mixtures ranging from well defined light hydrocarbon systems to complex oil mixtures and highly nonideal (non-electrolyte) chemical systems. HYSYS provides enhanced equations of state (PR and PRSV) for rigorous treatment of hydrocarbon systems semiempirical and vapor pressure models for the heavier hydrocarbon systems steam correlations for accmate steam property predictions and activity coefficient models for chemical systems. All of these equations have their own inherent limitations and you are encouraged to become more familiar with the application of each equation. 

For the development of activity coefficient models for electrolyte solutions, the theory of Debye and Huckel is usually the starting point. It can be regarded as an exact equation to describe the behavior of an electrolyte system at infinite dilution. 

C2. Chen. C-C, H.I. Britt, J.F. Boston and L.B. Evans, "Two New Activity Coefficient Models for the Vapor-Liquid Equilibrium of Electrolyte Systems", Thermodynamics of Aqueous Systems with Industrial Applications. ACS Symposium Series 133, 61 (1980)... 

The binary sodium chloride-water system has been the object of many studies. As a result there is a wealth of published data for a wide range of temperatures. This data includes solubility, density, vapor pressure lowering and heat of solution measurements. Because of this availability of data and the straightforward strong electrolyte behavior of the system, sodium chloride has almost always been included as an example when illustrating activity coefficient modeling techniques. For this application, Meissner s method of activity coefficient calculation will be used. 

Chemical equilibrium in a closed system at constant temperature and pressure is achieved at the minimum of the total Gibbs energy, min(G) constrained by material-balance and electro-neutrality conditions. For aqueous electrolyte solutions, we require activity coefficients for all species in the mixture. Well-established models, e.g. Debye-Htickel, extended Debye-Hiickel, Pitzer, and the Harvie-Weare modification of Pitzer s activity coefficient model, are used to take into account ionic interactions in natural systems [15-20]. 

More Difficult Systems. The above discussions pertain to easy systems (1) small, nonpolar or slightly polar molecules for equations of state and (2) nonelectrolyte, nonpolymeric substances considerably below their critical tenperatures for liquid-state activity-coefficient models. Most simulators have some models for electrolytes and for polymers, but these are likely to be even more uncertain than for the easy systems. Again, the key is to find some data, even plant operating data, to verify and to calibrate the models. If the overall recovery from a multistage separation is known, for exanple, one can simulate the column, using the best-known thermodynamic model, and the deviation between the plant datum and the simulator result is a crude (optimistic) estimate of the uncertainty. 

Section 3.2.1 describes fiilly dissociated electrolytes. For electrolytes that do not completely dissociate into the respective ions, a chemical-reaction mechanism is implemented in the ePC-SAFT framework (Sec. 3.2.2). Modelling of systems that can form multiple ion pairs is described in Sec. 3.2.3. Finally, we will discuss the experimental behaviour of strong and weak acids and present a respective model strategy (Sec. 3.2.4). Whereas so far activity coefficients of 19 electrolyte systems have been modelled by the MSA-NRTL, the properties of more than 120 systems have been studied with ePC-SAFT. The latter contains not only activity coefficients but also solution densities, which are important quantities for both process design and validation of model parameters. 

In applying this equation to multi-solute systems, the ionic concentrations are of sufficient magnitude that molecule-ion and ion-ion interactions must be considered. Edwards et al. (6) used a method proposed by Bromley (J7) for the estimation of the B parameters. The model was found to be useful for the calculation of multi-solute equilibria in the NH3+H5S+H2O and NH3+CO2+H2O systems. However, because of the assumptions regarding the activity of the water and the use of only two-body interaction parameters, the model is suitable only up to molecular concentrations of about 2 molal. As well the temperature was restricted to the range 0° to 100 oc because of the equations used for the Henry1s constants and the dissociation constants. In a later study, Edwards et al. (8) extended the correlation to higher concentrations (up to 10 - 20 molal) and higher temperatures (0° to 170 °C). In this work the activity coefficients of the electrolytes were calculated from an expression due to Pitzer (9) ... 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

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). 

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. 

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. 

Reactive absorption processes occur mostly in aqueous systems, with both molecular and electrolyte species. These systems demonstrate substantially non-ideal behavior. The electrolyte components represent reaction products of absorbed gases or dissociation products of dissolved salts. There are two basic models applied for the description of electrolyte-containing mixtures, namely the Electrolyte NRTL model and the Pitzer model. The Electrolyte NRTL model [37-39] is able to estimate the activity coefficients for both ionic and molecular species in aqueous and mixed solvent electrolyte systems based on the binary pair parameters. The model reduces to the well-known NRTL model when electrolyte concentrations in the liquid phase approach zero [40]. 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

In this chapter the thermodynamic analysis of the Nd(N03)3-HN03-H20 system is presented. The determination of the activity and the activity coefficient of the free neodymium (III) ion and the development of an accurate model for the activity behavior of aqueous binary electrolyte solutions consisting of the neodymium nitrate and nitric acid are presented. 

The latest models propose to represent electrolyte solutions as a collections of hard spheres of equal size, ions, immersed in a dielectric continuum, the solvent. For such a system, what is called the Mean Spherical Approximation, MSA, has been successful in estimating osmotic and mean activity coefficients for aqueous 1 1 electrolyte solutions, and has provided a reasonable fit to experimental data for dilute solutions of concentrations up to -0.3 mol dm". The advantage in this approach is that only one... 

There are several limitations which lead to the discrepancies in Tables IV-X. First of all, no model will be better than the assumptions upon which it is based. The models compiled in this survey are based on the ion association approach whose general reliability rests on several non-thermodynamic assumptions. For example, the use of activity coefficients to describe the non-ideal behavior of aqueous electrolytes reflects our uncertain knowledge of ionic interactions and as a consequence we must approximate activity coefficients with semi-empirical equations. In addition, the assumption of ion association may be a naive representation of the true interactions of "ions" in aqueous solutions. If a consistent and comprehensive theory of electrolyte solutions were available along with a consistent set of thermodynamic data then our aqueous models should be in excellent agreement for most systems. Until such a theory is provided we should expect the type of results shown in Tables IV-X. No degree of computational or numerical sophistication can improve upon the basic chemical model which is utilized. 

Currently available thermodynamic and kinetic data bases are incomplete to support quantitative modeling of many corrosion systems, particularly those where predictions of behavior under extreme conditions or over extended periods of time are desired. Because the unavailability of data limits the use of models, a critical need exists to upgrade and expand the sources of information on the thermodynamic properties of chemical species, exchange current densities, activity coefficients, rate constants, diffusion coefficients, and transport numbers, particularly where concentrated electrolytes under extreme conditions are involved. Many of these data are obtained in disciplines that traditionally have been on the periphery of corrosion science, so it will be necessary to encourage interdisciplinary collaboration to meet the need. 

To calculate the partial pressures of volatile electrolytes above solutions of known composition, values of the activity coefficients of the dissolved components are needed in addition to the appropriate Henry s law constants. In this work activity coefficients are calculated using the ion-interaction model of Pitzer (4). While originally formulated to describe the behavior of strong electrolytes, it is readily combined with explicit recognition of association equilibria (1,1), and may be extended to include neutral solutes (4, . The model has previously been used to describe vapor-liquid equilibria in systems of chiefly industrial interest (2). 

Pitzer electrolytes allows modeling the composition of different water-salt systems in a wide range of temperature with sufficiently high accuracy. In Figure 1.7 calculation results of activities coefficients after Pitzer may be compared with the data of other methods. 

A thermodynamic model developed by Barba, Brandani and di Giacomo (1982) described the solubility of calcium sulphate in saline water. A system of equations based on Debye Hiickel and other models was used to describe isothermal activity coefficients of partially or completely dissociated electrolytes. Using binary parameters, good agreement was claimed between experimental and predicted values of calcium sulphate solubility in sea water and brackish brines including those with a magnesium content. 

The exact calculation equations are given in [25], where it has also been proved that the Gibbs-Duhem equation is fulfilled. As well, NRTL parameters have been fitted up to molalities of 30mol/kg for a number of systems. Together with the ionic diameters, they are listed in [25]. Osmotic and mean ionic activity coefficients could be reproduced in an excellent way for a number of systems. Furthermore, the parameters fitted to binary systems have been successfully applied to ternary systems, that is, one salt in a binary solvent mixture, which always causes problems with the Electrolyte NRTL model [25]. 

It is thus clear that identification of salts which complex and techniques for proper formulation of electrolyte models and activity coefficients is a very important task particularly since many systems of commercial interest exhibit this behavior. The high concentrations found in many industrial applications tend to promote significant formation of complexes. 

Due to the need to model the equilibria of solutions containing multiple weak electrolytes, such as the H2O - NHs CO2 system, it became necessary to go beyond the Setschenow equation for activity coefficient calculations. For such solutions to be modeled well, the ion-molecule interactions must affect not only the molecular activity coefficients, but also the ionic activity coefficients and water activities. An early attempt by Edwards. Newman and Prausnitz (P5) used the Guggenheim equation for activity coefficients and assumed the water activity to be unity. This application was felt to be good for low weak electrolyte concentrations at temperatures no higher than 80° C. 

This 268 page article is concerned with the prediction of the thermodynamic properties of aqueous electrolyte solutions at high temperatures and pressures. There is an extensive discussion of the fundamental thermodynamics of. solutions and a discussion of theoretical concepts and models which have been used to describe electrolyte solutions. There is a very extensive bibliography ( 600 citations) which contains valuable references to specific systems of interest. Some specific tables of interest to this bibliography contain Debye-Hiickel parameters at 25 C, standard state partial molar entropies and heat capacities at 25 °C, and parameters for calculating activity coefficients, osmotic coefficients, relative apparent and partial molar enthalpies, heat capacities, and volumes at 25 °C. 

The necessary model parameters for the activity coefficients of electrolytes in the system at 298.15 K were fit from obtained osmotic coefficients and the sub-ternary subsystems by the multiple and unary linear regression methods. 

A more quantitative prediction of activity coefficients can be done for the simplest cases [18]. However, for most electrolytes, beyond salt concentrations of 0.1 M, predictions are a tedious task and often still impossible, although numerous attempts have been made over the past decades [19-21]. This is true all the more when more than one salt is involved, as it is usually the case for practical applications. Ternary salt systems or even multicomponent systems with several salts, other solutes, and solvents are still out of the scope of present theory, at least, when true predictions without adjusted parameters are required. Only data fittings are possible with plausible models and with a certain number of adjustable parameters that do not always have a real physical sense [1, 5, 22-27]. It is also very difficult to calculate the activity coefficients of an electrolyte in the presence of other electrolytes and solutes. Even the definition is difficult, because electrolyte usually dissociate, so that extrathermodynamical ion activity coefficients must be defined. The problem is even more complex when salts are only partially dissociated or when complex equilibriums of gases, solutes, and salts are involved, for example, in the case of CO2 with acids and bases [28, 29]. 

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