1. THERMODYNAMIC MODELING
1.1 Cubic Equations of State (EoS)
1.1.1 The Translated and Modified Peng-Robinson EoS
The modified and translated Peng-Robinson (t-mPR) EoS of Magoulas and Tassios, which was developed using vapor pressure and saturated liquid volume data for n-alkanes up to C20, has been applied in the prediction of Ps and Vs of larger alkanes as well as for a variety of nonpolar and polar compounds. Very satisfactory results for Ps are obtained for nonpolar compounds including large n-alkanes, for which we use the Tc, Pc and ω values from the correlations of Gao et al; and for polar ones in the absence, of course of hydrogen bonding. Equally satisfactory results are obtained for Vs using an extended version of the original expression for the translation. This version thus renders the PR EoS applicable to all type of systems: from small to large hydrocarbons to weakly polar ones.

1.1.2 The Peng-Robinson EoS with Fitted Parameters

Two types of Equations of State (EoS), which are characterized here as "simple" and "complex" EoS, are evaluated in this study. The "simple" type involves two versions of the Peng-Robinson (PR) EoS: the traditional one that utilizes the experimental critical properties and the acentric factor and the other, referred to as PR-fitted (PR-f), where these parameters are determined by fitting pure compound vapor pressure and saturated liquid volume data. As "complex" EoS in this study are characterized the EoS derived from statistical mechanics considerations and involve the Sanchez-Lacombe (SL) EoS and two versions of the SAFT EoS, the original and the PC-SAFT. The evaluation of these two types of EoS is carried out with respect to their performance in the prediction and correlation of vapor-liquid equilibria in binary and multicomponent mixtures of methane or ethane with alkanes of various degree of asymmetry. It is concluded that for this kind of systems complexity offers no significant advantages over simplicity. Furthermore, the results obtained with the PR-f EoS, especially those for multicomponent systems that are encountered in practice, even with the use of zero binary interaction parameters, indicate that this EoS may become a powerful tool for reservoir fluid phase equilibria modeling.

More information and detailed results can be found in:

- E. Voutsas, G. Pappa, K. Magoulas, D. Tassios, "Vapor Liquid Equilibrium Modelling of Alkane Systems with Equations of State: Simplicity versus Complexity", Fluid Phase Equil., 240/2 (2006) 127.

1.2 Predictive EoS/GE Models
1.2.1 The LCVM Model
This model has been very successful in the prediction of Vapor-Liquid Equilibria of a variety of symmetric and asymmetric systems, including those involved in Reservoir fluids modeling.

Details can be found in several publications such as:

- Boukouvalas, C., Spiliotis, N., Coutsikos, Ph., Tzouvaras, N. and Tassios, D., "Prediction of Vapor-Liquid Equilibrium with the LCVM model: a Linear Combination of the Vidal and Michelsen Mixing Rules coupled with the original UNIFAC and the t-mPR equation of state", Fluid Phase Equilibria, 92 (1994) 75-106.
- Boukouvalas, Ch. J., Magoulas, K.G., Stamataki, S.K. and Tassios, D.P., "Prediction of Vapor-Liquid equilibria with the LCVM model: Systems Containing Light Gases", Ind. Eng. Chem. Res., 36(12) (1997) 5454-5460.
- Stamataki, S.K., Magoulas, K.G., Boukouvalas, Ch.J. and Tassios, D.P., "Correlation and Prediction of Phase Equilibria and Volumetric Behaviour of Hyperbaric Binary Fluid", Revue de l' Institute Francais du Petrol, 53(1) (1998) 59-70.
- Boukouvalas, Ch., Magoulas, K., Tassios, D., Kikic, I., "Comparison of the performance of the LCVM model (an EoS/GE model) and the PHCT EoS (the Perturbed Hard Chain Theory Equation of State) in the prediction of the Vapor-Liquid Equilibria of binary systems containing light gases", Journal of Supercritical Fluids, 19(2) (2001) 123-132.

1.2.2 A Universal Mixing Rule for Cubic Equations of State: the UMR Model

A mixing rule for cubic equations of state (CEoS) applicable to all type of system asymmetries –referred to hereafter as Universal Mixing Rule (UMR)– is proposed. For the cohesion parameter of the CEoS the mixing rule involves the Staverman-Guggenheim part of the combinatorial term and the residual term of the original UNIFAC Gibbs free energy expression. For the co-volume parameter of the CEoS the quadratic concentration dependent mixing rule is used with the combining rule for the cross parameter bij = [(bi(1/2)+bj(1/2))/2]2. This UMR is applied to the volume translated and modified version of the Peng-Robinson equation of state of Magoulas and Tassios leading to what is referred to as the UMR-PR model. Very satisfactory results are obtained using the existing interaction parameters of the Original UNIFAC model for vapor-liquid equilibrium predictions at low and high pressures for a wide range of system asymmetries including mixtures containing polymers. Satisfactory liquid-liquid equilibrium predictions are also obtained with the UMR-PR model. 

More information and detailed results can be found in:

- E. Voutsas, K. Magoulas, D. Tassios, "A Universal Mixing Rule for Cubic Equations of State Applicable to Symmetric and Asymmetric Systems: Results with the Peng-Robinson Equation of State", Ind. Eng. Chem. Res., 43 (2004) 6238.

1.2.3 The Universal Mixing Rule for EoS/GE Models: Results with the Peng-Robinson EoS and a UNIFAC Model: the UMR-PRU Model

The Universal Mixing Rule (UMR), which incorporates an activity coefficient model in a cubic equation of state (EoS), and is applicable to all type of system asymmetries up to solvent/ polymer ones, has been recently developed in our Laboratory (Voutsas et al., Ind. Eng. Chem. Res., 43 (2004) 6238). The original UNIFAC model with temperature independent interaction parameters was used in the original publication, which leads, however, to unsatisfactory VLE predictions at high temperatures and poor heats of mixing predictions. In this study the UMR is applied by coupling the translated and modified Peng-Robinson (t-mPR) EoS with an original UNIFAC-type model that utilizes linearly temperature-dependent interaction parameters, eliminating, thus, the aforementioned weaknesses. The performance of the resulting EoS/GE model, referred to as UMR-PRU, utilizing the available UNIFAC interaction parameters, as well as some parameters developed here for gas involving pairs, is evaluated in the prediction and, when necessary, correlation/prediction, of various i.e. VLE, LLE, VLLE, SGE and heats of mixing. The results indicate that the new model represents a unique, simple and reliable tool for thermodynamic property calculations for systems of various degrees of non-ideality and asymmetry, including polymer solutions.

More information and detailed results can be found in:

- E. Voutsas, V. Louli, C. Boukouvalas, K. Magoulas, D. Tassios, "Thermodynamic Property Calculations with the Universal Mixing Rule for EoS/GE Models: Results with the Peng-Robinson EoS and a UNIFAC Model", Fluid Phase Equil., 241 (2006) 216.

1.3 EoS Accounting for Association: The Cubic-plus-Association (CPA) EoS

An equation of state (EoS) suitable for describing associating fluids has been developed. The equation combines the simplicity of a cubic equation of state (Soave-Redlich-Kwong or Peng-Robinson), which is used for the physical part and the theoretical background of the perturbation theory employed for the chemical (or association) part. The resulting EoS (Cubic Plus Association, CPA) is not cubic with respect to volume and contains five pure compound parameters which are determined using vapor pressures and saturated liquid densities. Excellent description are obtained of both vapor pressures and saturated liquid volumes of pure associating compounds such as alcohols, phenols, glycols, acids and water.

CPA has been also successfully applied to the correlation and prediction of phase equilibria (vapour-liquid, liquid-liquid, vapor-liquid-liquid) in a variety of systems where association is present as described in several publications.

More information and detailed results can be found in:

- Kontogeorgis, G.M., Voutsas, E.C., Yakoumis, I. and Tassios, D.P., "An Equation of State for Associating Fluids", Ind. Eng. Chem. Res., 35 (1996) 4310-4318.
- Yakoumis, I.V., Kontogeorgis, G.M., Voutsas E.C., Tassios, D.P., "Vapor-Liquid Equilibria for Alcohol/Hydrocarbon Mixtures Using the CPA Equation of State", Fluid Phase Equil., 130 (1997) 31.
- Voutsas, E.C., Kontogeorgis, G.M, Yakoumis I.V., Tassios, D.P., "Correlation of Liquid-Liquid Equilibria for Alcohol/Hydrocarbon Mixtures Using the CPA Equation of State", Fluid Phase Equil., 132 (1997) 61.
- Yakoumis, I.V., Kontogeorgis, G.M., Voutsas, E.C., Hendriks, E.M., Tassios, D.P., "Prediction of Phase Equilibria in Binary Aqueous Systems Containing Alkanes, Cycloalkanes and Alkenes with the CPA EoS", Ind. Eng. Chem. Res., 37 (1998) 4175.
- Voutsas, E.C., Yakoumis I.V., Tassios, D.P., "Prediction of Phase Equilibria in Water/Alcohol/Alkane Systems", Fluid Phase Equil., 158(1) (1999) 151.
- E.C. Voutsas, G.C. Boulougouris, I.G. Economou and D.P. Tassios, "Water/hydrocarbon Phase Equilibria Using the Thermodynamic Perturbation Theory", Ind. Eng. Chem. Res., 39 (2000) 797.
- Ch. Perakis, E. Voutsas, K. Magoulas, D. Tassios "Thermodynamic Modeling of the Vapor-Liquid-Equilibrium of the water/ethanol/CO2 System", Fluid Phase Equil., 243 (2006) 142.

1.4 The mS-UNIFAC: A Group-Contribution Model for Sugars and Sugar Derivatives
The S-UNIFAC model of Spiliotis and Tassios (Fluid Phase Equilib., 173, 2000, 39), developed for systems containing sugars, is modified here by replacing the LLE-UNIFAC model with the modified UNIFAC model of Larsen et al. (Ind. Eng. Chem. Res., 26, 1987, 2274). This modification was motivated after an extensive evaluationsespecially in systems containing molecules that differ significantly in size (asymmetric systems) such as those considered heresof the commonly used UNIFAC models. The applicability of the new model, called modified S-UNIFAC (mS-UNIFAC), is extended, as compared to S-UNIFAC, to mixtures of sugars with acids and esters and to mixtures containing sugar derivatives, such as sugar esters. Through the use of a better combinatorial term and new data, the model becomes more reliable than S-UNIFAC, providing satisfactory predictions for multicomponent systems involved in the enzymatic esterification reactions for the production of fatty acid sugar esters, for which S-UNIFAC fails.

More information and detailed results can be found in:

- P. Tsavas, E. Voutsas, K. Magoulas, D. Tassios, "Phase Equilibrium Calculations in Aqueous and Nonaqueous Mixtures of Sugars and Sugar Derivatives with a Group-Contribution Model", Ind. Eng. Chem. Res., 43 (2004) 8391.

1.5 Ionic Liquids
Sugars and antioxidants are compounds of high interest for the food industry, while antioxidants are also very important compounds for the drug industry. On the other hand, ionic liquids are compounds with a growing interest for the scientific and industrial community because of their unique physical properties such as negligible saturation vapor-pressure and therefore non-flammability, thermal stability, wide liquid temperature range, good dissolution capabilities for polar, non-polar, organic and inorganic compounds.

A systematic research in the field of ionic liquids has taken place only the last few years, where ionic liquids are examined more and more instead of the conventional organic solvents not only in chemical reactions but also in separation methods.

With a view of a better understanding of the usage of ionic liquids for chemical reactions or separation processes, the knowledge of thermodynamic properties and, especially, phase equilibrium data is needed. Such data in the case of mixtures containing sugars and antioxidants are almost inexistent.

1.6 Thermophysical Properties of Pure Compounds
1.6.1 Prediction of Vapor Pressures and Enthalpies of Vaporization of Organic Compounds from the Normal Boiling Point Temperature
Our Laboratory has proposed a model for the prediction of vapor pressures of organic compounds that requires only the knowledge of the normal boiling point of the compound involved, and a compound specific Kf for which generalized expressions for several classes of organic compounds as functions of the normal boiling point and the molecular weight have developed. This model provides very satisfactory results in the temperature range from the melting up to the normal boiling point and up to the critical, where no hydrogen-bonding is involved. Also, the accuracy of our model is much better than that proposed by Lyman, especially for the high molecular weight compounds.

Our model is also used for the prediction of enthalpies of vaporization at the normal boiling point. Excellent results are obtained that are comparable or better than those obtained with two recommended models in “The Properties of Gases and Liquids” book, where the latter, however, require as input information except form the normal boiling point the critical properties of the compound involved as well.

More information and detailed results can be found in:

- E. Voutsas, M. Lampadariou, K. Magoulas and D. Tassios, "Prediction of Vapor Pressures of Pure Compounds from Knowledge of the Normal Boiling Point ", Fluid Phase Equil., 198/1 (2002) 81.
- E. Panteli, E. Voutsas, K. Magoulas and D. Tassios, "Prediction of Vapor Pressures and Enthalpies of Vaporization of Organic Compounds from the Normal Boiling Point Temperature", Fluid Phase Equil., 248 (2006) 70.

1.6.2 Prediction of Vapor Pressures of Solid Organic Compounds with a Group Contribution Method
Our Laboratory has developed a group-contribution model for the prediction of vapor pressures of organic solids based on the concept of the hypothetical liquid. The group-contribution parameters can be applied in the prediction of vapor pressures for a variety of solids involving aliphatic and aromatic hydrocarbons, halogenated hydrocarbons, oxygenated hydrocarbons (alkanols, phenols, acids and ketones), and some multifunctional ones. Satisfactory results are obtained with errors below one order of magnitude down to very low pressures well below the Pa level. The required entropy of fusion is also predicted with a simple group-contribution method also developed. The obtained predictions are – as expected from a simple method – not very accurate, but sufficient for the purpose of this study. Extrapolation, finally, of the method in the liquid range up to 1 atm gives satisfactory predictions provided that the temperature range of the vapor pressure data is not far beyond that involved in the parameter estimation.

More information and detailed results can be found in:

-
P. Coutsikos, E. Voutsas, K. Magoulas, D. Tassios, "Prediction of Vapor Pressures of Solid Organic Compounds with a Group-Contribution Method", Fluid Phase Equil., 207 (2003) 263.

1.6.3 Differential Molar Heat Capacities of Organic Compounds at Their Melting Point
Methods for the estimation of the differential molar heat capacity, the difference between the heat capacity of the solid and the liquid form of organic compounds at their melting point ΔCp(Tm), have been investigated. Three schemes are considered: the first involves use of group contribution methods for the prediction of solid heat capacity (CpS) and liquid heat capacity (CpL); the other two, empirical correlations through the entropy of fusion at the melting point ΔSf(Tm). Recommendations for the different categories of organic compounds are made that provide substantial improvement over the commonly used assumption of ΔCp=0, in the prediction of ideal solid solubility and solid vapor pressure.

More information and detailed results can be found in:

- G. Pappa, E. Voutsas, K. Magoulas, D. Tassios, "Estimation of the Differential Molar Heat Capacities of Organic Compounds at their Melting Point", Ind. Eng. Chem. Res., 44/10 (2005) 3799.

1.7 Development of a Simulator for the Prediction of the Acid Dew Point of Flue Gases in Thermal Power Plants
During combustion of fossil fuels, fuel-bound sulfur is converted into sulfur dioxide (SO2) in much the same way as carbon is oxidized to carbon dioxide (CO2).

Depending on the sulfur content of the fuel, the amount of excess air in combustion, and the flame temperature, approximately 1% to 2% of the sulfur dioxide is further oxidized into sulfur trioxide by the catalytic oxidation of SO2 with molecular oxygen. Boilers utilize air heaters to transfer energy from the combustion gases exiting the economizer to the air flowing into the boiler. As the flue gas passes through the air heater, the gas phase SO3 reacts with superheated H20 vapor to form H2SO4 vapor. The extent of this reaction is temperature dependent and the reaction is essentially complete by the time the flue gas has reached the cold end of the air heater. The dew point is a function of both H2O and H2SO4 concentrations in the flue gas. It is noted that though the H2SO4 vapor is not corrosive, the H2SO4 condensate is a powerful corrosive and can cause serious damage to downstream equipment such as air heaters, baghouses, and electrostatic precipitators.

Given the above, it is obvious that determining the acid dew point of the flue gases is of major importance for the operation of boilers in fossil fuel power plants and will assist with on-line control of flue gas temperatures, minimising maintenance costs and improving the total efficiency of the process.

The acid dew point (ADP) temperature depends on the partial pressures (concentrations) of H2SO4 and water. The degree of H2SO4 formation is influenced by the fuel sulfur content, the excess air level during combustion, as well as the ash content and its composition. Ash contains Ca and Mg oxides which physically or chemically absorb SO3 reducing thus the concentration of H2SO4 in the flue gas. On the other hand, minerals contained in the fuel can act as catalysts of the oxidation of SO2 to SO3.

The aim of this study is the development of a simulator that will predict the acid dew point temperature, given the composition of the fuel, the excess air level and the combustion temperature. The procedure followed involves the following steps:
  1. Flue gas composition prediction: Based on the combustion reaction and the fuel composition the flue gas composition is determined. In order to calculate the conversion of the produced SO2 to SO3, an expression for the reaction constant (K) was developed in this study using experimental thermodynamic data (ΔHof, ΔGof, Cp) from the literature.
  2. ADP prediction assuming negligible ash content: In order to develop a thermodynamic tool for the prediction of the ADP, the NRTL model was employed. The necessary interaction parameters of the model were fitted to experimental H2SO4 and water partial pressures over aqueous H2SO4 solutions. 

In Figure 1 partial pressure results for the H2SO4/H2O binary at 140°C using the parameters calculated in this study are compared with corresponding experimental data. As shown, there is very good agreement between them. Figure 2 presents ADP prediction results, also with the NRTL model of this study, at H2SO4 concentrations from 0.1 up to 1000 ppm and water content equal to 10%, which is typical water content for flue gases. As evidenced by Figure 2 the results of this study are in very good agreement with those obtained by two empirical correlations widely used in industry: the Verhoff-Banchero (V-B) and Muller-Okkes (M-O) ones.

Use of a thermodynamic model, such as the one developed in this study, for the ADP calculation has some major advantages over the use of empirical correlations such as those shown in Figure 2: It can be applied to pressures other than atmospheric and, if necessary, it can take account of the effect of the rest of the gases contained in the flue gas on the ADP.

     3.  ADP prediction taking into account the ash content: In the case of lignite combustion, the ash content of the fuel is significant and 
          influences strongly the flue gas ADP. This effect will be introduced in the simulator though correlations that relate the alkali content of
          the ash with the SO3 captured by the ash.


Figure 1: H2SO4 and H2O partial pressure prediction for the H2SO4/H2O binary at T = 140°C with the NRTL model.


Figure 2: Comparison of the ADP prediction results obtained with the NRTL model with those from the Verhoff-Banchero and Muller-Okkes correlation, assuming water content equal to 10%.

1.8 Thermodynamic Measurements and Modelling in Acid Gas-Alkanolamine-Water Systems
1.8.1 VLE Measurements in Binary Aqueous Alkanolamine Solutions
The accurate design of acid gas treatment processes requires the knowledge of vapor-liquid equilibrium of acid gas aqueous alkanolamine systems, and, consequently, that of the binary systems involved. To this purpose we have performed: (a) isobaric vapor-liquid equilibrium (VLE) measurements at 300, 400 and 500 mmHg of aqueous N-methyldiethanolamine (MDEA) solutions, (b) vapor pressure measurements of pure 2-amino-2-methyl-1-propanol (AMP), and, (c) isobaric vapor-liquid equilibrium (VLE) measurements at 500, 600 and 760 mmHg of aqueous AMP solutions. The data measured in this work along with some other data, which were taken from the literature, were used for the thermodynamic modeling of the water/MDEA and water/AMP binary system with the UNIQUAC and NRTL activity coefficients models.

More information and detailed results can be found in:

- E. Voutsas, A. Vrachnos, K. Magoulas, "Measurement and Thermodynamic Modeling of the Phase Equilibrium of Aqueous N-Methyldiethanolamine Solutions", Fluid Phase Equil., 224 (2004) 191.

1.8.2 Thermodynamic Modelling of Acid Gas-Alkanolamine-Water Systems
A thermodynamic framework for representing chemical and vapor-liquid equilibria in acid gas-alkanolamine-water systems has been developed in our Laboratory. The vapor-liquid equilibrium is calculated through a new EoS/GE model called the electrolyte-LCVM model. Very satisfactory predictions of acid gas (CO2, H2S) vapor-liquid equilibrium over MDEA, MEA and their blends at various concentrations, acid gas loadings and temperatures are obtained.

More information and detailed results can be found in:

- A. Vrachnos, E. Voutsas, K. Magoulas, A. Lygeros, "Thermodynamics of Acid Gas-MDEA-Water Systems", Ind. Eng. Chem. Res., 43 (2004) 2798.
- A. Vrachnos, G. Kontogeorgis, E. Voutsas, "Thermodynamic Modeling of Acid Gas Solubility in Aqueous Solutions of MEA, MDEA and MEA-MDEA blends", Ind. Eng. Chem. Res., 45 (2006) 5148.

1.9 Melting Point Depression of Organic Compounds with Supercritical CO2
(In collaboration with Dr. Ralf Dohrn, Bayer Technology Services GmbH, Thermophysical Properties, Leverkusen, Germany)
The melting point of solid substances can be depressed considerably by using supercritical fluids. This characteristic property can be used in processes for fine particles generation such as: the Particle from Gas Saturated Solutions (PGSS), the Gas Antisolvent Solutions (GAS) and the Rapid Expansion of Supercritical Solutions (RESS). For the design and optimization of these processes the knowledge of the solid – liquid – gas (SLG) equilibrium of the systems involved is of great importance. In the present study the SLG line of binary systems of naphthalene, phenanthrene, benzoic acid, palmitic acid and stearic acid with CO2 has been determined, with the "first melting point method", which is based on the observation of the initial appearance of the liquidphase of the material under investigation. Also, a thermodynamic model for describing the phase equilibria of such binary systems was developed implementing the Peng – Robinson equation of state and two different approaches concerning the fugacity of the solid phase.

1.10 Experimental Measurements and Modelling of Solid Solubilities of Compounds of Interest in the Pharmaceutical and Food Industry
1.10.1 Solubility of Antibiotics in Different Solvents
(In collaboration with: (a) Prof. I. Marrucho, University of Aveiro, Portugal; (b) Dr. Ralf Dohrn, Bayer Technology Services GmbH, Thermophysical Properties, Leverkusen, Germany)
The production of pharmaceutical and medium-sized biochemicals customarily involves liquid solvents for reaction, separation, and formulation. The procedure of solvent selection is a thermodynamic problem that is solved based on the phase equilibrium theory, experience and empirical descriptions of experimental results. In this study, the solubilities of tetracycline hydrochloride, moxifloxacin hydrochloride and ciprofloxacin hydrochloride were measured in several solvents such as water, ethanol, 2-propanol and acetone. Also, the thermodynamic modeling of the experimental SLE data, using NRTL and UNIQUAC, proves that these models can correlate satisfactorily the solubility of studied antibiotics in the temperature range for which experimental data are available, with UNIQUAC being, in general, slightly superior to NRTL.

More information and detailed results can be found in:

- F. Varanda, M. J. de Melo, A. Caço, R. Dohrn, F. Makrydaki, E. Voutsas, D. Tassios, I. Marrucho, "Solubility of Antibiotics in Different Solvents. Part I: Hydrochloride Forms of Tetracycline, Moxifloxacin and Ciprofloxacin", Ind. Eng. Chem. Res., 45(18) (2006), 6368–6374.

1.10.2 Solubility of Antioxidants in Organic Solvents
Antioxidants are compounds of major importance for the food and pharmaceutical industry. Solvent selection for reaction and separation purposes requires the knowledge of their solubility in them. In this study, which is currently under way, the solubility of several antioxidants (catechin, ferulic acid, caffeic acid, methyl ferulate, methyl caffeate etc.) in various solvents is measured. In the next step, the experimental SLE data will be modeled using appropriate activity coefficient models.