Towards predictive association theories

Association equations of state like SAFT, CPA and NRHB have been previously applied to many complex mixtures. In this work we focus on two of these models, the CPA and the NRHB equations of state and the emphasis is on the analysis of their predictive capabilities for a wide range of applications. We use the term predictive in two situations: (i) with no use of binary interaction parameters, and (ii) multicomponent calculations using binary interaction parameters based solely on binary data. It is shown that the CPA equation of state can satisfactorily predict CO₂-water-glycols-alkanes VLE and water-MEG-aliphatic hydrocarbons LLE using interaction parameters obtained from the binary data alone. Moreover, it is demonstrated that the NRHB equation of state is a versatile tool which can be employed equally well to mixtures with pharmaceuticals and solvents, including mixed solvents, as well as phase equilibria in mixtures containing glycols. The importance of considering the solvation of CO₂-water (in CPA) when the model is applied to multicomponent mixtures as well as of the multiple associations in heavy glycol-water mixtures (in NRHB) is investigated.     

Modeling of phase equilibria with CPA using the homomorph approach

For association models, like CPA and SAFT, a classical approach is often used for estimating pure-compound and mixture parameters. According to this approach, the pure-compound parameters are estimated from vapor pressure and liquid density data. Then, the binary interaction parameters, k_ij, are estimated from binary systems; one binary interaction parameter per system. No additional mixing rules are needed for cross-associating systems, but combining rules are required, e.g. the Elliott rule or the so-called CR-1 rule. There is a very large class of mixtures, e.g. water or glycols with aromatic hydrocarbons, chloroform-acetone, esters-water, CO₂-water, etc., which are classified as “solvating” or “induced associating”. The classical approach cannot be used and the cross-association interactions are difficult to be estimated a priori since usually no appropriate experimental data exist, while the aforementioned combining rules cannot capture the physical meaning of such interactions (as at least one of the compounds is non-self-associating). Consequently, very often one or more of the interaction parameters are optimized to experimental mixture data. For example, in the case of the CPA EoS, two interaction parameters are often used for solvating systems; one for the physical part (k_ij) and one for the association part (β^cross). This limits the predictive capabilities and possibilities of generalization of the model. In this work we present an approach to reduce the number of adjustable parameters in CPA for solvating systems. The so-called homomorph approach will be used, according to which the k_ij parameter can be obtained from a corresponding system (homomorph) which has similar physical interactions as the solvating system studied. This leaves only one adjustable parameter for solvating mixtures, the cross-association volume (β^cross). It is shown that the homomorph approach can be used with success for mixtures of water and glycols with aromatic hydrocarbons as well as for mixtures of acid gases (CO₂, H₂S) with alcohols and water. The homomorph approach is less satisfactory for mixtures with fluorocarbons as well as for aqueous mixtures with ethers and esters. In these cases, CPA can correlate liquid-liquid equilibria for solvating systems using two adjustable parameters. The capabilities and limitations of the homomorph approach are discussed.     

A cross-association model for CO2-methanol and CO2-ethanol mixtures

A cross-association model was proposed for CO₂-alcohol mixtures based on the statistical associating fluid theory (SAFT). CO₂ was treated as a pseudo-associating molecule and both the self-association between alcohol hydroxyls and the cross-association between CO₂ and alcohol hydroxyls were considered. The equilibrium properties from low temperature-pressure to high temperature-pressure were investigated using this model. The calculated p-x and p-ρ diagrams of CO₂-methanol and CO₂-ethanol mixtures agreed with the experimental data. The results showed that when the cross-association was taken into account for Helmholtz free energy, the calculated equilibrium properties could be significantly improved, and the error prediction of the three phase equilibria and triple points in low temperature regions could be avoided.     

Modelling of phase equilibria for associating mixtures using an equation of state

In the present work, the group contribution with association equation of state (GCA-EoS) is extended to represent phase equilibria in mixtures containing acids, esters, and ketones, with water, alcohols, and any number of inert components. Association effects are represented by a group-contribution approach. Self- and cross-association between the associating groups present in these mixtures are considered. The GCA-EoS model is compared to the group-contribution method MHV2, which does not take into account explicitly association effects. The results obtained with the GCA-EoS model are, in general, more accurate when compared to the ones achieved by the MHV2 equation with less number of parameters. Model predictions are presented for binary self- and cross-associating mixtures.     

Application of GC-PPC-SAFT EoS to amine mixtures with a predictive approach

The GC-PPC-SAFT equation of state (EoS) is a combination of a group contribution method [S. Tamouza et al., Fluid Phase Equilib. 222-223 (2004) 67-76; S. Tamouza et al., Fluid Phase Equilib. 228-229 (2005) 409-419] and the PC-SAFT EoS [J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 40 (2001) 1244-1260] which was adapted to the polar molecules [D. Nguyen-Huynh et al., Fluid Phase Equilib. 264 (2008) 62-75]. It is here applied to the vapour pressure and liquid molar volume of primary, secondary and tertiary amines and their mixtures with n-alkanes, primary and secondary alcohols, using previously published group parameters. The mixing enthalpy is also evaluated for the binary systems. Binary interaction parameters k_ij are computed using a group-contribution pseudo-ionization energy, as proposed by Nguyen-Huynh [D. Nguyen-Huynh et al., Ind. Eng. Chem. Res. 47 (2008) 8847-8858]. A unique corrective parameter for the cross-association energy between amines and alcohols is used.The agreement with experimental data in correlation and prediction were found rather encouraging. The mean absolute average deviation (AAD) on bubble pressure is about 3.5% for pure amines. The mean AAD on the vapour-liquid equilibria (VLE) are respectively 2.2% and 5.5% for the amine mixtures with n-alkanes and alcohols. The AADs on saturated liquid volume are about 0.7% for the pure compounds and 0.9% for the mixtures. Prediction results are qualitatively and quantitatively accurate and they are comparable to those obtained with GC-PPC-SAFT on previously investigated systems.     

Extension of polar GC-SAFT to systems containing some oxygenated compounds: Application to ethers, aldehydes and ketones

The GC-SAFT equation of state proposed by Tamouza et al. (2004) [51], extended to polar molecular fluids NguyenHuynh et al. (2008) [32], is here applied to model vapor-liquid phase equilibria of various binary mixtures containing at least one oxygenated compound belonging to ethers, ketones or aldehydes chemical families.These systems are modeled using a polar version of the three different versions of SAFT-EOS (original, VR-SAFT and PC-SAFT) in a predictive manner: binary interaction parameters k_ij and l_ij are all set to zero.In the case of alcohol + ether, +ketone, +aldehyde systems, a cross-association interaction between an oxygenated compound (non self-associating compound) and an alcohol is necessary to model/predict accurately the mixture VLE. The corresponding association parameters are assumed to be equal to the self-association parameters of pure 1-alkanols.The above-cited systems have been treated in a comprehensive manner. The general agreement between polar GC-SAFT and experimental data is good (within 4-5% deviation on pressure), similar to the one obtained on previously investigated systems using GC-SAFT.     

Structural features of binary mixtures of supercritical CO2 with polar entrainers by molecular dynamics simulation

Computer simulations of supercritical carbon dioxide and its mixtures with polar cosolvents: water, methanol, and ethanol (concentration, 0.125 mole fractions) at T = 318 K and ρ = 0.7 g/cm³ are performed. Atom-atom radial distribution functions are calculated by classical molecular dynamics, while the probability distributions of relative orientation of CO₂ molecules in the first and second coordination spheres describing the geometry of the nearest environment of CO₂ molecules and the trajectories of cosolvent molecules are found using Car-Parrinello molecular dynamics. Based on the latter, the conclusions regarding structure and interactions of polar entrainers in their mixtures with supercritical CO₂ are made. It is shown that the microstructure of carbon dioxide varies only slightly upon the introduction of cosolvents.     

Liquid structures of 1-butyl-3-methylimidazolium tetrafluoroborate and carbon dioxide mixtures by X-ray diffraction measurements

X-ray diffraction measurements for the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate, [BMIM][BF₄], mixed with CO₂ were carried out at high pressures using our developed polymer cell. The intermolecular distribution functions obtained for [BMIM][BF₄]–CO₂ mixtures showed that CO₂ molecules are preferentially solvated to the [BF₄]⁻ anion. The similar preferential solvation was previously observed in analogous 1-btuyl-3-methylimidazolium hexafluorophosphate, [BMIM][PF₆], with a different anion, which is in harmony with the present results in [BMIM][BF₄]–CO₂.     

Ternary excess molar enthalpies for the mixtures of methanol and ethanol with tetrahydropyran or 1,4-dioxane at 298.15 K

Ternary excess molar enthalpies, H_m^E, at 298.15 K and atmospheric pressure measured by using a flow microcalorimeter are reported for the (methanol+ethanol+tetrahydropyran) and (methanol+ethanol+1,4-dioxane) mixtures. The pseudobinary excess molar enthalpies for all the systems are found to be positive over the entire range of compositions. The experimental results are correlated with a polynomial equation to estimate the coefficients and standard errors. The results have been compared with those calculated from a UNIQUAC associated solution model in terms of the self-association of alcohols as well as solvation between unlike alcohols and alcohols with tetrahydropyran or 1,4-dioxane. The association constants, solvation constants and optimally fitted binary parameters obtained solely from the pertinent binary correlation predict the ternary excess molar enthalpies with an excellent accuracy.     

Supercritical fluid chromatography of imidazole derivatives

Summary The aim of this work was to use SFC to separate simple, slightly basic, imidazole derivatives which are used for the synthesis of more complex molecules with therapeutic properties. Control of their purity utilizes separation techniques and this paper shows what SFC can do in comparison with LC which requires derivatization before detection and with GC where peak tailing can be a problem. Our results concern the use of sub-critical mixtures of CO₂ and polar modifiers because imidazole derivatives react with neat CO₂, thus failing to elute from packed columns, and are only partially resolved on capillary columns with neat N₂O. Therefore, separations with CO₂-alcohol-amine-water mixtures on aminopropyl-bonded silica with UV detection are discussed. The resolution and sensitivity limits allow real sample analysis within a very short time.     

Application of the CPA equation of state to reservoir fluids in presence of water and polar chemicals

The complex phase equilibrium between reservoir fluids and associating compounds like water, methanol and glycols has become more and more important as the increasing global energy demand pushes the oil industry to target reservoirs with extreme or complicated conditions, such as deep or offshore reservoirs. Conventional equation of state (EoS) with classical mixing rules cannot satisfactorily predict or even correlate the phase equilibrium of those systems. A promising model for such systems is the Cubic-Plus-Association (CPA) EoS, which has been successfully applied to well-defined systems containing associating compounds. In this work, a set of correlations was proposed to calculate the CPA model parameters for the narrow cuts in ill-defined C₇₊ fractions. The correlations were then combined with either the characterization method of Pedersen et al. or that of Whitson et al. to extend CPA to reservoir fluids in presence of water and polar chemical such as methanol and monoethylene glycol. With a minimum number of adjustable parameters from binary pairs, satisfactory results have been obtained for different types of phase equilibria in reservoir fluid systems and several relevant model multicomponent systems. In addition, modeling of mutual solubility between light hydrocarbons and water is also addressed.     

Representation for binary mixtures of n-alcohols + sub and supercritical CO2 by a group-contribution method

In order to represent vapour–liquid equilibria of binary n-alcohol–carbon dioxide mixtures the excess function-equation of state method is used in which carbon dioxide is described by the IUPAC equation of state and alcohols by a Peng–Robinson type equation where the attractive parameter is estimated by a group-contribution method. The excess function is of the Van Laar type in which the interaction parameters are calculated by a group-contribution method. This approach allows to correlate and predict with quite good accuracy VLE of binary systems of alcohols and CO₂, even for heavier alcohols.     

Phase equilibria modeling of biodiesel related mixtures using the GCA-EoS model

In this work, a group-contribution equation of state that takes into account association effects (GCA-EoS) is extended to model the phase behavior of fatty esters (biodiesel) in binary mixtures with glycerol, alcohols and water and ternary mixtures with glycerol and methanol. A new associating group (glycerol hydroxyl group: OH^Gly) was defined to take into consideration the association effects in the glycerol molecule. Self-association of methanol, water and glycerol and cross-association between methanol–glycerol, alcohol–ester, water–ester and glycerol–ester groups were considered. New pure-group, binary interaction and association parameters have been determined. The correlations and predictions of the model are found in acceptable agreement with selected experimental data reported in the literature.     

On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols

Nagata, I., 1985. On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols. Fluid Phase Equilibria, 19: 153–174.Binary vapor—liquid and liquid—liquid equilibrium data for alcohol solutions includin one or two alcohols are correlated with the UNIQUAC associated solution theory (Nagata and Kawamura). The theory uses pure liquid association constants determined by the method of Brandani and a single value of the enthalpy of the hydrogen bond equal to ?23.2 kJ mol ^?1 for pure alcohols. For alcohol-active nonassociating component mixtures and alcohol—alcohol mixtures the theory involves additional solvation constants. The theory is extended to contain ternary mixtures with any number of alcohols. Ternary predictions of vapor—liquid and liquid—liquid equilibria are performed using only binary parameters. Good agreement is obtained between calculated and experimental results for many representative mixtures.     

Solubility of phenobarbital in aqueous cosolvent mixtures revisited: IKBI preferential solvation analysis

The preferential solvation parameters of phenobarbital in aqueous binary mixtures of 1,4-dioxane, t-butanol, n-propanol, ethanol, propylene glycol and glycerol were derived from solution thermodynamic properties by using the IKBI method. This drug is sensitive to preferential solvation effects in all these mixtures. The preferential solvation parameter by the cosolvent (δx_1,3) is negative in almost all the water-rich mixtures but positive in mixtures with similar proportions of solvents and cosolvent-rich mixtures, except in 1-propanol + water mixtures, where negative values are also found in mixtures with x₁ ≥ 0.70. Hydrophobic hydration around the non-polar ethyl and phenyl groups of this drug in water-rich mixtures could play a relevant role in drug solvation. Otherwise, in mixtures of similar solvent compositions and in cosolvent-rich mixtures the preferential solvation by cosolvent could be due to the acidic behaviour of the drug.     

Theoretical aspects of quantitative mass spectrometry of gas mixtures

The problem of calibration of mass spectrometers with standard gas mixtures is studied theoretically. The results obtained can be used in deciding the number and optimum composition of standard mixtures. An analogy is drawn between this calibration problem and the mathematical theory of experimental design when mixtures are considered. It is shown that calibration based on a number of standard mixtures is more accurate than calibration with pure gases. A procedure for correction of calibration coefficients is described; it can be applied during measurements on the composition of gas mixtures or gas flows. Application to gas mixtures containing CO, N₂ and CO₂ is discussed.     

One‐Pot Alkoxylation of Phenols with Urea and 1,2‐Glycols

A one‐pot epoxide‐free alkoxylation process has been developed for phenolic compounds. The process involves heating phenols and urea in 1,2‐glycols at 170‐190 °C using Na₂CO₃/ZnO as co‐catalysts under atmospheric conditions. During the course of this new alkoxylation reaction, a five‐membered ring cyclic carbonate intermediate, ethylene carbonate (EC) or propylene carbonate (PPC), was produced in‐transit as the key intermediate and was subsequently consumed by phenols to form alkoxylated ether alcohols as final products in excellent yields. For instance, phenol, bisphenol A (BPA), hydroquinone and resorcinol were converted into their respective mono‐alkoxylated ether alcohols on each of their phenolic groups in 80‐95% isolated yields. In propoxylation of phenols, this approach shows great product selectivity favoring production of high secondary alcohols over primary alcohols in isomeric ratios of nearing 95/5. Since ammonia (NH₃) and carbon dioxide (CO₂) evolving from the reaction can be re‐combined in theory into urea for re‐use, the overall net‐alkoxylation by this approach can be regarded as a simple condensation reaction of phenols with 1,2‐glycols giving off water as its by‐product. This one‐pot process is simple, safe and environmentally friendlier than the conventional alkoxylated processes based on ethylene oxide (EO) or propylene oxide (PO). Moreover, this process is particularly well‐suited for making short chain‐length alkoxyether alcohols of phenols.     

Preferential solvation of some n-alkyl p-substituted benzoates in propylene glycol + water cosolvent mixtures

The preferential solvation parameters by propylene glycol (PG) of the homologous series of the n-alkyl esters of p-hydroxybenzoic and p-aminobenzoic acids, namely, methyl, ethyl, propyl and butyl derivatives, were derived from their thermodynamic properties of solution by means of the inverse Kirkwood–Buff integrals (IKBI) method. The preferential solvation parameters by the cosolvent, δx_1,3, are negative in water-rich mixtures, but positive in PG-rich mixtures, and the relative magnitudes of δx_1,3 are proportional to the alkyl chain length despite of the solvent involved in the preferential solvation, i.e. PG or water. It is possible that the hydrophobic hydration around aromatic ring and/or methylene groups plays a relevant role in the drugs solvation in water-rich mixtures. The more solvation by PG in PG-rich mixtures could be due mainly to polarity effects and acidic behaviour of the hydroxyl or amine groups of the compounds in front to the more basic solvent present in the mixtures, i.e. PG.     

Excess molar enthalpy for methanol,ethanol, 1-propanol, 1-butanol + <Emphasis Type="Italic">n</Emphasis>-butylamine mixtures at 288.15 and 308.15 K at atmospheric pressure

Experimental data of excess molar enthalpy (H _m^E) of binary liquid mixtures containing (methanol or ethanol or 1-propanol, or 1-butanol) + n-butylamine mixtures have been determined as a function of composition at temperatures 288.15 and 308.15 K, at atmospheric pressure, using a modified 1455 PARR mixture calorimeter. The H _m^E values are negative for both systems over the whole composition range. The applicability of the ERAS Model to correlate H _m^E of mixtures studied is tested, and the agreement between experimental and theoretical results is satisfactory. The model results are discussed in terms of the cross-association interactions with temperature variation as well as in terms of the variation of the carbon chain in the alcohols presents in the mixtures.     

Carbon monoxide production in silent discharge plasmas of air and air-methane mixtures

CO production in high-voltage alternating current (HVAC) silent discharge plasmas of air and air-methane mixtures at atmospheric pressure has been investigated by matrix isolation FTIR spectroscopy. In pure air, CO is produced by decomposition of CO₂. A steady-state CO/CO₂ ratio was determined by varying the flow rate. CO production was considerably enhanced when methane was added to the plasmas. CO production was observed even at very low oxygen concentrations, and did not noticeably decrease due to secondary oxidation reactions, even when methane was discharged in a pure oxygen carrier. CO production in air-methane mixtures is shown to depend on input power. CO production from CO₂ and hydrocarbons in air appears to be a significant obstacle for development of a plasma-based air purification device.