Phase Behavior Of Such Systems Research Articles

Modeling systems relevant to the biodiesel production using the CPA equation of state. Part 2. Systems with supercritical CO2

The CPA EoS is applied to binary mixtures of CO2 with fatty acids and their methyl- or ethyl-esters. The model, using one temperature independent binary interaction parameter, satisfactorily describes the phase behavior of such systems. Correlations of the binary interaction parameters with the number of esters' or acids’ carbon atoms, or with the number of double bonds for compounds with the same number of carbon atoms, were developed in order to make predictions feasible in cases of lack of experimental data. Subsequently, the model was applied for predicting the phase behavior of ternary and multicomponent mixtures. The model rather satisfactorily predicts the vapor-liquid equilibrium of such systems. In accordance with the first part of this series of articles [Tsivintzelis et al. 430 (2016) 75–92], since the binary parameters were optimized solely using experimental data for binary mixtures, CPA results for the ternary and multicomponent mixtures are pure predictions.

Element balance formulation in reactive compositional flow and transport with parameterization technique

We present a novel nonlinear formulation for modeling reactive-compositional flow and transport in the presence of complex phase behavior due to a combination of thermodynamic and chemical equilibria in multi-phase systems. We apply this formulation to model precipitation/dissolution of minerals in reactive multiphase flow in subsurface reservoirs. The proposed formulation is based on the consistent element balance reduction of the molar (overall composition) formulation. To predict the complex phase behavior in such systems, we include the chemical equilibrium constraints to the multiphase multicomponent negative flash calculations and solve the thermodynamic phase and chemical phase equilibria simultaneously. In this solution, the phase equilibrium is represented by the partition coefficients, whereas the chemical equilibrium reaction is represented by the activity coefficients model. This provides a generic treatment of chemical and thermodynamic equilibrium within the successive substitution loop of mulmultiphase flash to accommodate chemical equilibrium reactions (precipitation and dissolution reactions). Equilibrium Rate Annihilation matrix allows us to reduce the governing component conservation equations to element conservation equations, while the coupling between chemical and thermodynamic equilibrium is captured by a simultaneous solution of modified multiphase flash equations. The element balance equation written in terms of overall component mole fractions is modified and defined in terms of element mole fractions. Therefore, the primary set of governing equations are the element balance equations and the kinetic equations. This element composition of the mixture serves as an input to the modified multiphase flash computations, whereas the output is fractions of components in each phase, including solids. The nonlinear element–based governing equations are solved with the modified version of the operator-based linearization (OBL) approach where the governing equations are formulated in terms of space- and state-dependent parameters constrained by the solution of the extended multiphase flash. The element balance molar formulation along with the modified multiphase flash has been tested in a simple transport model with dissolution and precipitation reactions. The simulation of multidimensional problems of practical interest has been performed using the adaptive OBL technique. This is the first time when a robust multiphase multicomponent flash based on element fractions is coupled with an element balance–based compositional formulation and tested for multidimensional problems of practical interest. The proposed technique improves both robustness and performance of complex chemical models.

Thermodynamic properties of gas-condensate system with abnormally high content of heavy hydrocarbons

Gas-condensate systems (GCS) with an abnormally high content of heavy hydrocarbons are characterized by a sharp change in both phase and component compositions with an insignificant decrease in pressure below the start pressure of the phase transitions (the beginning of condensation). Calculation methods for describing the phase behavior of such systems are very sensitive to the quality of the initial information. The uncertainty of the input data leads not only to significant errors in the forecast of phase compositions, but also to an incorrect phase state estimation of the whole system. The research presents the experimental thermodynamic parameters of the GCS of the BT reservoirs on the Beregovoye field, obtained at the phase equilibrium facility. The data contribute to the adaptation of the calculated models of the phase behavior of the GCS with a change in pressure.

Liquid-liquid equilibrium of poly (ethylene glycol) 4000 + sodium sulfate + urea/guanidine hydrochloride aqueous two-phase systems at different pH: Experimental results and thermodynamic modeling

Aqueous two-phase systems in the presence of denaturants (urea or guanidine hydrochloride) have been used for the initial recovery steps during protein refolding process. To investigate phase behavior of such systems, liquid-liquid equilibrium data for a poly (ethylene glycol) (PEG) 4000 + sodium sulfate + urea/guanidine hydrochloride (5% and 10% mass) aqueous two phase system was investigated at 25 °C and pH values of 5.3 and 9.2. The calibration plots for refractive index and conductivity were prepared to obtain the compositions of the top and bottom phase. It was observed that the heterogeneous region decreases with the increase in the denaturants concentration. The effect of pH, denaturants concentration, tie line length, and slope of tie line on the partition behavior of denaturants was examined. In this study, the modified UNIQUAC-FV and extended UNIQUAC models are used to calculate the phase equilibria of mention aqueous two phase systems. The values of average AAD% (partition coefficients) for modified UNIQUAC-FV and extended UNIQUAC are 3.48 and 13.80, respectively.

Polymorphs, Hydrates, Cocrystals, and Cocrystal Hydrates: Thermodynamic Modeling of Theophylline Systems

Polymorphic transitions and hydrate formation often occur in systems of cocrystal-forming components. To increase the efficiency of cocrystal formation and purification processes, the complex phase behavior of such systems was modeled using perturbed-chain statistical associating fluid theory (PC-SAFT). This is demonstrated for theophylline, a well-studied pharmaceutical, exhibiting polymorphs, as well as formation of a hydrate, cocrystals, and even cocrystal hydrates. The solubility of theophylline in water was modeled including hydrate formation (1:1) as well as polymorphic transitions of theophylline between the anhydrate forms IV, II, and I. The solubilities of theophylline(IV), the thermodynamically stable form at ambient conditions, and the theophylline/glutaric acid (1:1) cocrystal could be predicted without performing additional measurements. Moreover, the complex phase behavior of the theophylline/citric acid/water system could be correlated accounting for the formation of the theophylline hydrat...

Liquid–liquid equilibria, electrical conductivity, and refractive indices of Poly(ethylene glycol) + sodium sulfate + guanidine hydrochloride aqueous two-phase systems: Correlation and thermodynamic modeling

The initial recovery steps for recombinant protein were carried out using aqueous two-phase systems in the presence of guanidine hydrochloride. To investigate the phase behavior of such systems, equilibrium data was obtained for molecular weight fractions of PEG (3000 and 6000) + sodium sulfate (pH 7) + guanidine hydrochloride (5% and 10% mass) + water at 25 °C. Displacement of the binodal toward higher concentrations through an increase in guanidine hydrochloride concentration was clearly observed. A slightly larger two-phase was obtained as the PEG molecular weight increased from PEG 3000 to 6000. The experimental binodal data of the system was successfully correlated with Bleasdale equations (high R2 and low SE). The effects of molecular weight, guanidine hydrochloride concentration, tie-line length, and slope of tie-line on the partition behaviors of guanidine hydrochloride were examined at constant pH. The compositions of each aqueous phase were calculated using two thermodynamic models for the activity coefficient. The calculated results showed that the extended Pitzer and extended UNIQUAC models can predict the data in the quaternary system well. The fitted binary interaction parameters of the models were reported.

Phase behavior of glycol ether surfactant systems in the presence of brine and hydrocarbon: Experiment and modeling

In this study, liquid–liquid equilibrium measurements were performed for the ternary (water/non-ionic surfactant/decane) systems at T = 298.15 K and atmospheric pressure. Propylene glycol mono propyl ether and ethylene glycol monobutyl ether were selected as surfactant; the first one is propylene glycol ether, while the second one is ethylene glycol ether. New experimental liquid–liquid equilibrium data were presented for the corresponding systems. Effect of salinity and surfactant structure (EO or PO functional group) on the phase behavior of such systems has been studied by both experimental measurements and thermodynamic modeling. The experimental phase behavior data were predicted by the perturbed hard sphere chain (PHSC) equation of state. In the presence of electrolyte, mean spherical approximation (MSA) term has been coupled with the PHSC EoS to account the contribution of long-range interactions. The calculated results indicate acceptable qualitative agreement of PHSC results with the experimental data.

Multibody Interactions, Phase Behavior, and Clustering in Nanoparticle-Polyelectrolyte Mixtures.

We present the results of a computational study of the interactions, phase-behavior and aggregation characteristics of charged nanoparticles (CNPs) suspended in solution of oppositely charged polyelectrolytes (PEs). We used an extension of the mean-field polymer self-consistent field theory (SCFT) model presented in our earlier work ( Macromolecules , 2014 , 47 , 6095 - 6112 ) to explicitly characterize the multibody interactions in such systems. For dilute-moderate particle volume fractions, the magnitudes of three and higher multibody interactions were seen to be weak relative to the contributions from pair interactions. On the basis of such results, we embeded the pair-interaction potentials within a thermodynamic perturbation theory approach to identify the phase behavior of such systems. The results of such a framework suggested that the gas and FCC crystal phases were thermodynamically stable, whereas the fluidlike phase was metastable in such systems. To complement the parameters studied using SCFT, we used a recently developed multibody simulation approach to study the aggregation and cluster morphologies in CNP-PE mixtures. For low particle charges, such systems mainly exhibited clusters arising from direct contact aggregation between CNPs. However, for higher particle and PE charges and low PE concentrations, large regions of PE-bridged clusters were seen to form. We present a morphological phase diagram summarizing such results.

The phase behaviour of mixed saturated and unsaturated monoglycerides in hydrophobic system

Lyotropic liquid crystals are formed on the dissolution of most surfactants in water as represented by regions on the phase diagram, and are more common than micellar solutions. Monoglycerides with saturated or unsaturated fatty acids are one of the most commonly used food surfactants. While there is considerable interest in the behaviour of monoglycerides mixed with oils (particularly triglycerides), limited information is available regarding the phase behaviour of such systems. We have examined the phase behaviour of mixed saturated and unsaturated monoglycerides1:1 (by weight) together with different oils systems. The main technique employed was X-ray diffraction, supplemented by optical microscopy, proton nuclear magnetic resonance (NMR) and differential scanning calorimetry (DSC). Our results suggest that six phases (L2, α-gel phase, sub α- phase, β1 and oil crystallisation phase (β` for palm oil or β2 for miglyol oil or olive oil) were observed for G50/oil mixture. Furthermore, this paper proves that miglyol and palm oil incorporate into α-gel phase of G50. In contrast, olive oil dose not incorporate into α-gel phase of G50.

Thermodynamic properties of binary aqueous solutions of orthophosphate salts, sodium, potassium and ammonium at T = 298.15 K

In this investigation, the thermodynamic properties of the aqueous solutions of orthophosphate salts M3−nHnPO4 H2O with n=0, 1, or 2 and M=Na+, K+ or NH4+ at 298.15K are determined. The water activity measurements for NaH2PO4(aq), Na2HPO4(aq), Na3PO4(aq); KH2PO4(aq), K2HPO4(aq), K3PO4(aq), (NH4)H2PO4(aq), (NH4)2HPO4(aq) and (NH4)3PO4(aq) are effectuated from dilution to saturated solution using the hygrometric method. The activity coefficients are evaluated using ionic-interaction model. The mineral solubility of these phosphate salts is investigated at T=298.15K. The prediction of solubility is made for minerals and other solid phases in aqueous solutions of phosphates. Correlating and predicting the phase behavior in such systems is a difficult task, partially caused by chemical reactions in the liquid phase but also due to the possible formation of one or more solid phases. Solid phases, molality of saturated binary solutions ms(exp) and logarithm of solubility product K°sp are also determined at 298.15K. The standard molar Gibbs energies of dissolution ΔG°diss, formation ΔGf Calc° and the literature ΔGf Ref°, of solid phases crystallizing from saturated phosphate salts solutions are evaluated.This investigation allows understanding physicochemical nature and structure of phosphate solutions, in particular, questions of anion or cation hydration, especially at higher concentrations, ion-pairing formation, and the possibility of phosphate complex formation.

Influence of Cyclic Dimer Formation on the Phase Behavior of Carboxylic Acids. II. Cross-Associating Systems

The doubly bonded dimer association scheme (DBD) proposed by Sear and Jackson is extended to mixtures exhibiting both self- and cross-associations. The PC-SAFT equation of state is combined with the new DBD association contribution to describe the vapor-liquid equilibria of binary mixtures of carboxylic acids + associating compounds (water, alcohols, and carboxylic acids). The effect of doubly bonded dimers on the phase behavior in such systems is less important than in mixtures of carboxylic acids with nonassociating compounds, due to the cross-associations that compete with the formation of DBDs. Nevertheless, a clear improvement in the description of vapor-liquid coexistence curves is achieved over the classical 2B association model, particularly for the dew point curves.

Phase equilibria in hydrogen-containing binary systems modeled with the Peng–Robinson equation of state and temperature-dependent binary interaction parameters calculated through a group-contribution method

The study of phase equilibria in hydrogen-containing mixtures is essential for petroleum and chemical engineering, electricity production, transportation and for many other energy needs. Fluid-phase diagrams are however atypical because of the size-asymmetric nature of these mixtures and the quantum behavior of hydrogen. Therefore, the development of a thermodynamic model able to accurately predict the phase behavior of such systems over wide ranges of pressure and temperature is a difficult and challenging task. In this work, the H2 group is added to the well-established PPR78 model in order to predict mutual solubility and critical loci of hydrogen-containing systems. Such a model combines the widely used Peng–Robinson equation of state (EoS) with a group-contribution method aimed at estimating the temperature-dependent binary interaction parameters [kij(T)]. In our previous papers, 15 groups were defined: CH3, CH2, CH, C, CH4 (methane), C2H6 (ethane), CHaro, Caro, Cfusedaromaticrings, CH2,cyclic, CHcyclic⇔Ccyclic, CO2, N2, H2S, and SH. It was thus possible to estimate the kij for any mixture containing alkanes, aromatics, naphthenes, CO2, N2, H2S and mercaptans regardless of the temperature. In this study, the addition of the H2 group makes it possible to extend the PPR78 model to hydrogen-containing systems.

Measurement and prediction of phase behaviour for 1-alkyl-3-methylimidazolium tetrafluoroborate and carbon dioxide: Effect of alkyl chain length in imidazolium cation

The high-pressure phase behaviour of the binary system {1-ethyl-methylimidazolium tetrafluoroborate ([EMIM][BF 4]) + CO 2} was determined over the temperature range of (293.2 to 323.2) K at intervals of 5.0 K with the CO 2 mole fraction ranging from 0.153 to 0.578 by using a high-pressure variable-volume view cell. Further, the (vapour + liquid) equilibrium of the binary system {1-hexyl-methylimidazolium tetrafluoroborate ([HMIM][BF 4]) + CO 2} was measured over the temperature range of (303.2 to 328.2) K with the CO 2 mole fraction ranging from 0.314 to 0.593. The Peng–Robinson equation of state along with two-parameter mixing rules has been employed to correlate the experimental results. In case of the ([EMIM][BF 4] + CO 2) system, the (vapour + liquid + liquid) equilibrium and (vapour + liquid) equilibrium have been observed at a high CO 2 mole fraction. The experimental values obtained in this study were compared with the available phase behaviour data of the binary system (1-alkyl-3-methylimidazolium tetrafluoroborate + CO 2) in order to investigate the effect of the alkyl chain length in the imidazolium cation on the phase behaviour of such systems.

Phase behavior of colloidal superballs: Shape interpolation from spheres to cubes

The phase behavior of hard superballs is examined using molecular dynamics within a deformable periodic simulation box. A superball's interior is defined by the inequality |x|(2q)+|y|(2q)+|z|(2q)≤1 , which provides a versatile family of convex particles (q≥0.5) with cubelike and octahedronlike shapes as well as concave particles (q<0.5) with octahedronlike shapes. Here, we consider the convex case with a deformation parameter q between the sphere point (q=1) and the cube (q=∞). We find that the asphericity plays a significant role in the extent of cubatic ordering of both the liquid and crystal phases. Calculation of the first few virial coefficients shows that superballs that are visually similar to cubes can have low-density equations of state closer to spheres than to cubes. Dense liquids of superballs display cubatic orientational order that extends over several particle lengths only for large q. Along the ordered, high-density equation of state, superballs with 1<q<3 exhibit clear evidence of a phase transition from a crystal state to a state with reduced long-ranged orientational order upon the reduction of density. For q≥3 , long-ranged orientational order persists until the melting transition. The width of the apparent coexistence region between the liquid and ordered, high-density phase decreases with q up to q=4.0. The structures of the high-density phases are examined using certain order parameters, distribution functions, and orientational correlation functions. We also find that a fixed simulation cell induces artificial phase transitions that are out of equilibrium. Current fabrication techniques allow for the synthesis of colloidal superballs and thus the phase behavior of such systems can be investigated experimentally.

Dna Lipoplexes: Prediction of Phase Architectures Using Cg Simulations and Experimental Validation

DNA lipoplexes are important mediators of transfection that offer a safer, although less efficient alternative to their viral counterparts. Thus improving the efficacy of DNA lipoplexes is essential for their exploitation in nanomedicine. Experimentally, it has been shown that the architecture of DNA lipoplexes is linked to their biological efficacy. Therefore the ability to predict the architectures of compositions of DNA lipoplexes would be highly desirable. However, prediction of the phase behaviour of such systems is difficult, largely owing to a complex interplay of intermolecular forces. Molecular dynamics simulations provide a potential strategy for predicting phase behaviour, but traditional, atomistic methods are not applicable to large DNA-lipid systems. Here, we present coarse-grained simulations of the lyotropic phase transitions of DNA lipoplexes as a function of lipid composition and water content. Our coarse-grained model of DNA uses a ∼ 4 to 1 mapping of atoms to particles and is compatible with existing coarse-grained models of biomolecules. With the appropriate balance of water content and lipid composition, we are able to capture the transition from the originally lamellar phase to the inverse hexagonal phase. Our simulation results show an inverse hexagonal phase with a calculated d-spacing of 6.2 nm for a DOPE-DNA system. Together with the disorder of the hexagonal phase, this d-spacing increases with increasing cationic lipid (DOTAP) content, in agreement with experimental data obtained by SAXS and polarizing light microscopy. Our simulations have provide insights into the rearrangements that occur to effect the transition to the inverse hexagonal phase; this level of detail is difficult to obtain using experimental methods alone. Furthermore, our simulations have highlighted the increasingly important role of coarse-grained simulation methods for the design of novel DNA lipoplexes and applications in synthetic biology, in general.

One-pot synthesis of amino functionalized mesoporous silica materials: using simulations to understand transitions between different structures

The rich phase behavior of surfactants can be exploited to design materials with a given desired structure and properties. One example includes amino functionalized mesoporous silicas, which can be used in different environmental applications, including removal of heavy metals from water and CO2 separation and purification. These applications may require a high concentration of functional groups, but the increased concentration of hybrid organic–inorganic precursors can lead to the destruction of the liquid crystals or transformation into other phases. In this work, we modeled the phase behavior of such systems using lattice Monte Carlo simulations and analyzed the distribution of hybrid organic–inorganic precursors to explain the observed changes in the liquid crystal structures. In particular, we observed that if the hybrid precursor is sufficiently hydrophobic, it can act as a cosurfactant, swell the core of the surfactant liquid crystal, and lead to structures with smaller interfacial curvature. On the other hand, if the hybrid precursor acts as a cosolvent it will solubilize the surfactant leading to the destruction of the preformed liquid crystal.

Self-consistent field theory for lipid-based liquid crystals: Hydrogen bonding effect

A model to describe the self-assembly properties of aqueous blends of nonionic lipids is developed in the framework of self-consistent field theory (SCFT). Thermally reversible hydrogen bonding between lipid heads and water turns out to be a key factor in describing the lyotropic and thermotropic phase behavior of such systems. Our model includes reversible hydrogen bonding imposed in the context of the grand canonical ensemble and exact conditions of binding equilibrium. The lipid molecules are modeled as a rigid head and a flexible Gaussian tail, and the water molecules are treated explicitly. Here, we focus on systems where the lipid molecule has a relatively small hydrophilic head compared to the hydrophobic tail, such as monoolein in water. Experimentally, this system has both normal phase sequences (inverted hexagonal to inverted double gyroid cubic phase) and reverse phase sequences (lamellar to inverted double gyroid cubic phase) as the water volume fraction increases. From SCFT simulations of the model, two phase diagrams corresponding to temperature independent or dependent interaction parameters chi are constructed, which qualitatively capture the phase behavior of the monoolein-water mixture. The lattice parameters of the simulated mesophases are compared with the experimental values and are found to be in semiquantitative agreement. The role of various structural and solution parameters on the phase diagrams is also discussed.

Solubilities in supercritical fluids

Abstract Solubilities in supercritical fluids are of great importance in a wide variety of applications. These applications include: production of controlled drug delivery systems, powder processing, pollution prevention and remediation, methods for spraying paints and coatings, precipitation/crystallization processes, bioseparations, and food processing. Examples of some of these applications will be given. Supercritical fluid processes make use of the significant variation of solubility with pressure when the solvent is a supercritical fluid. This permits the accomplishment of many processes that would be otherwise very difficult to achieve. To fully understand the benefits of such processes, one must understand the phase behavior of such systems. The types of phase behavior that can be observed will be discussed, along with the ways that this behavior can be used to modify solubilities in such fluids. There have been many methods proposed for the experimental determination of solubilities in supercritical fluids. These will be reviewed in general, and recommendations for preferred methods given. Solubilities in supercritical fluids can be correlated and predicted by making use of thermodynamic calculations involving equations of state, as well as by other methods. The various methods will be reviewed, and recommendations given for various applications.

Effective interactions and phase behaviour for a model clay suspension in anelectrolyte

Since the early observation of nematic phases of disc-like clay colloids byLangmuir in 1938, the phase behaviour of such systems has resisted theoreticalunderstanding. The main reason is that there is no satisfactory generalization forcharged discs of the isotropic DLVO (Derjaguin, Landau, Verwey and Overbeek)potential describing the effective interactions between a pair of spherical colloidsin an electrolyte. In this paper, we show how to construct such a pair potential,incorporating approximately both the non-linear effects of counter-ioncondensation (charge renormalization) and the anisotropy of the chargedplatelets. We discuss the consequences for the phase behaviour of laponitedispersions (thin discs of 30 nm diameter and 1 nm thickness), and we presentan investigation into the mesostructure via Monte Carlo simulations.

Surface tension and nucleation rate of phases of a charged colloidal suspension.

The square gradient approximation is used to calculate the surface tension between two phases of differing density in a charged colloidal suspension, and the results are compared with experimental and theoretical evidence from various colloidal systems. The nucleation rate of a colloidal liquid cluster from a metastable colloidal gas is estimated using a version of classical nucleation theory. We explain in terms of nucleation phenomena the recently described "Swiss cheese effect," which involves the formation of crystals from an initial disordered state, followed by the formation of disordered regions within the crystals and at the interfaces between them. We argue that this sequence of events shows evidence both of homogeneous and of heterogeneous nucleation. The experimental prominence of homogeneous nucleation suggests that metastability is very important in colloidal systems, and therefore that the consideration of nucleation rates is essential to the study of phase behavior in such systems. We also predict that the occurrence or nonoccurrence of phase separation into a dense and a rarefied phase is governed by the ratio of the macroion charge to the macroion radius.