Electrolyte thermodynamic model and the State of the art 

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A very brief history of thermodynamics

As already said, chemical engineers utilize thermodynamics for process calculations and particularly balances of material and energy streams. However, it would be incorrect to say that before the advent of the industrial age, thermodynamics was an “unknown science”. The invention of the thermometer and the manometer to measure physically quantified relative values of temperature and pressure marked the beginning of the thermodynamic science in mid-1600’s. Two centuries later, Avogadro proposed that « equal volumes of all gases, at same temperature and pressure, have the same number of molecules », which later on led to the development of ideal gas law (the first thermodynamic Equation of state (EoS)). In those times, interest in measuring and correlating Pressure-Volume-Temperature relationships grew. In 1873 J.D. van der Waals proposed a pressure-volume and temperature EoS for real gases, which marked the beginning of modern day thermodynamics and the birth of new EoS, that took into account intermolecular interactions. In the figure 1.3 we present some major events that took place in history and led to the development of present-day thermodynamics. In fig 1.4 we present the major models/ theories/ EoS that has been developed in the last century and will continue to dominate the future of thermodynamics.

Roles of Electrolytes in Various Industries: Scope of this work

The electrolyte along with other solvents are present in the following industry and there are several problems associated with them as mentioned in the following sections. The following discussion will put forth the problems whose solution demands an accurate thermodynamic framework for the mixed-solvent electrolyte.

Biorefining industry

Biorefining industry involves the conversion of biomass or organic material into fuel grade bio-diesel or bio-gasoline. The pre-treated biomass (feed for bio-refinery) units is a complex mixture of oxygenated hydrocarbons and water, a strongly polar solvent which forms a non-ideal mixture with the oxygenated chemicals. Water is also responsible for degradation of processing equipment and worsening of product quality so it needs to be separated.
Aqueous solutions of salts have shown promising trends to aid in separation of these complex molecules encountered during the biofuel generation. The electrolyte causes a significant change in the equilibrium composition (especially liquid-liquid equilibrium), by altering the hydrogen bonding structure and other intermolecular forces. Hence, due to the addition of salt, the mutual solubilities of the solvents change in either phase (water-rich phase and hydrocarbon-rich phase). These phenomena may be used in various industries (Biorefining, Pharmaceuticals, and water treatment) for separation of hydrocarbons. To this end, an accurate representation of mutual solubilities of oxygenated compounds and water in organic and aqueous solvents including salts is of utmost importance. Often, the lack of experimental thermodynamic data for such complex mixtures results in a need for procuring such knowledge from predictive thermodynamic approaches that must be both accurate and efficient at the same time.

Carbon capture and sequestration (CCS)

Carbon capture and sequestration (capture-transport-storage) is a technology aimed at reducing the release of carbon dioxide into the atmosphere from power plants and other industries. Sequestration or storage of trapped CO2 is often done in unminable coalbed methane reservoirs or deep saline aquifers [25]. For designing CCS process, it is very important to possess an accurate knowledge of various primary and derivative thermodynamic properties of various compounds that are encountered [26].

Acid gas injection

Acid gas comprises of CO2 and H2S which is a by-product of natural gas treatment process. The acid gases separated from the natural gas is at low pressure and must be compressed in order to achieve injection pressures. The use of an aqueous solvent in gas sweetening process results in the acid gas mixtures saturated in water which is a major concern in the injection process. A high concentration of water can lead to formation of a separated liquid phase or hydrate formation. Acid gases often contain dissolved hydrocarbons up to 5 mole percent.
The efficient design of acid gas injection process relies on the availability of reliable thermodynamic models that can calculate phase boundaries of systems containing a large amount of water, CO2, and H2S. For instance, efficient design of compression and cooling system is dependent on the ability of the thermodynamic model to accurately calculate dew temperatures and dew pressures [27].


Pharmaceutical industry

Drug solubility in water and organic solvent has a key role in drug discovery and formulation in pharmaceutical processes that comprise of several stages such as design, synthesis, extraction, purification, formulation, absorption, and distribution in body fluids [28]. Electrolytes are quite commonly found in pharmaceutical industry processes at various stages. The pharmaceutical industry thus demands calculative models to predict or provide knowledge of the solubility in mixture of solvents in presence of salts.

Electrolyte terms

In the current section, we will discuss predominantly two aspects of ionic interaction, ion-ion interaction and ion-solvent interactions. These two aspects are crucial in com-prehending electrolyte thermodynamics: how ions interact with the solvent (most often water), move within the solvent; how they associate with the solvent and sometimes form dimers. A pictorial representation is shown in figure 2.3 presents a brief idea about the dissolution of a salt crystal in water, its dissociation into ions and how those ions interact with water molecules.
Since ions are charged species, long range coulombic interaction govern several properties and phenomena of salt systems. According to Debye-Hückel theory,

Table of contents :

List of figures
List of tables
1 Setting up stage 
1.1 Introduction
1.2 A very brief history of thermodynamics
1.3 Motivation for this work
1.4 Roles of Electrolytes in Various Industries: Scope of this work
1.4.1 Biorefining industry
1.4.2 Oil and Gas industry
1.4.3 Carbon capture and sequestration (CCS)
1.4.4 Acid gas injection
1.4.5 Pharmaceutical industry
1.4.6 Other uses of electrolytes
1.5 Aqueous two-phase systems
1.6 Objectives of this research
2 Electrolyte thermodynamic model and the State of the art 
2.1 Introduction
2.2 Activity coefficient models vs EoS
2.3 Interactions in electrolyte systems and theories
2.3.1 Discharge
2.3.2 Repulsion and dispersion
2.3.3 The Structure-forming step
2.3.4 Electrolyte terms
2.4 Review of the existing electrolyte and mixed-solvent electrolyte EoS
2.4.1 State of the art
2.4.2 Choice of thermodynamic model
2.5 Statistical associating fluid theory (SAFT)
2.5.1 Perturbation theory
2.5.2 History of Statistical Associating Fluid Theory (SAFT)
2.5.3 Mathematical description of PC-SAFT
2.5.4 Various terms of ePPC-SAFT
2.5.5 Group contribution approach
2.5.6 Cross association parameters
3 Modified model of PC-SAFT for water 
3.1 Abstract
3.2 Introduction
3.3 Model
3.3.1 Previous Descriptions of Water with the PC-SAFT EoS
3.3.2 A new Temperature Dependence of Water Diameter
3.4 Results for binary mixtures
3.4.1 Mutual solubilities
3.4.2 Octanol/Water Partition coefficient
3.4.3 Gibbs energy of Hydrogen Bonding
3.4.4 Conclusion
4 Modeling of strong electrolytes 
4.1 Abstract
4.2 Introduction
4.3 Some thoughts and arguments related to the choices made in this work .
4.3.1 What is solvation?
4.3.2 Specificities related to the GC-ePPC-SAFT model
4.3.3 Parameters from previous work
4.4 Ion parameterization procedure
4.5 Regression Results
4.5.1 Correlation results for Alkali halide brines
4.5.2 Solvation Gibbs energies for Alkali halide brines
4.6 Alkanes and acid gases with brines: salting out effect in presence of organic compounds
4.7 Mixed solvent electrolytes
4.8 Conclusion
5 Modeling LLE of mixed-solvent electrolytes 
5.1 Introduction
5.2 Algorithmic issue: Electroneutrality
5.2.1 Generalities
5.2.2 Current state: without electroneutrality
5.2.3 A new method for electroneutrality: Modifying the fugacity coefficient
5.3 The machinery
5.3.1 Prediction of the LLE by the non-parameterized model
5.3.2 Partition coefficient of salts
5.4 Parameterizing mixed solvent salt systems using available data
5.4.1 Dielectric constant of mixed-solvents
5.4.2 MIAC of mixed solvent electrolyte systems: Analysis
5.4.3 Approach for parameterization of mixed-solvent salt systems
5.4.4 Result of MIAC for mixed solvent electrolytes
5.4.5 Parameter for 1-Butanol-water-salt systems from LLE data
5.5 Final results
5.6 Conclusion
6 Conclusions and recommendations for future work 
6.1 Conclusion
6.2 Recommendations for future work


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