Phase Equilibria Of Mixtures Research Articles

ОЦЕНКА ФАЗОВОГО РАВНОВЕСИЯ НА ОСНОВЕ ТЕРМОДИНАМИЧЕСКИХ МОДЕЛЕЙ UNIQUAC И UNIFAC

The main thermodynamic models for calculating the phase equilibrium of non-ideal liquid mixtures are considered. The basic thermodynamic equations of the UNIQUAC model are considered

High-pressure phase equilibrium and volumetric properties of pseudo-binary mixtures of stock tank oil + nitrogen/carbon dioxide up to 463K

High-pressure phase equilibrium and volumetric properties of pseudo-binary mixtures of stock tank oil + nitrogen/carbon dioxide up to 463K

Screening of Equation-of-State Models for Pure Carbon Dioxide Properties and Binary Mixture (Carbon Dioxide/Water and Carbon Dioxide/Ethanol) Phase Equilibrium

Screening of Equation-of-State Models for Pure Carbon Dioxide Properties and Binary Mixture (Carbon Dioxide/Water and Carbon Dioxide/Ethanol) Phase Equilibrium

Modeling on gas hydrate phase equilibrium at high concentration of alcohols

As the major interest in flow assurance of oil and natural gas production, the concentrations of injected alcohols are commonly high exceeding mass fraction of 30 %. In this work, the non-ideality of aqueous phase is represented by the activity coefficient model, in which the water and inhibitor molecules are regarded as associating compounds, and the differences in size and shape between them are properly considered. Coupled with the Chen-Guo hydrate model, the proposed model has been extended to represent the hydrate phase equilibrium of pure gas and gas mixtures in aqueous alcohol solutions with concentrations up to 50 wt%. Moreover, the hydrate lattice parameter was reoptimized to extend the Chen-Guo hydrate model to systems below 273.15 K, when high-concentration of alcohols is present. The predictions of the proposed model have been compared with the experimental data, with the average relative deviations in pressure and temperature of 3.991 % and 0.108 %, respectively, verifying the reliability of this model. Compared with other thermodynamic models or correlations, the proposed model in this work is equivalent to or outperformed those in predicting hydrate formation conditions, especially at high alcohol concentrations.

Modeling phase equilibria in mixtures of mono- and di-carboxylic acids with hydrocarbons

Modeling phase equilibria in mixtures of mono- and di-carboxylic acids with hydrocarbons

Holding water in a sieve—stable droplets without surface tension

Our understanding of supercritical fluids has seen exciting advances over the last decades, often in direct contradiction to established textbook knowledge. Rather than being structureless, we now know that distinct supercritical liquid and gaseous states can be distinguished and that a higher order phase transition - pseudo boiling - occurs between supercritical liquid and gaseous states across the Widom line. Observed droplets and sharp interfaces at supercritical pressures are interpreted as evidence of surface tension due to phase equilibria in mixtures, given the lack of a supercritical liquid-vapor phase equilibrium in pure fluids. However, here we introduce an alternative physical mechanism that unexpectedly causes a sharpening of interfacial density gradients in absence of surface tension: thermal gradient induced interfaces (TGIIF). We show from first principles and simulations that, unlike in gases or liquids, stable droplets, bubbles, and planar interfaces can exist without surface tension. These results challenge and generalize our understanding of what droplets and phase interfaces are, and uncover yet another unexpected behavior of supercritical fluids. TGIIF provide a new physical mechanism that could be used to tailor and optimize fuel injection or heat transfer processes in high-pressure power systems.

Uncertain characterization of reservoir fluids due to brittleness of equation of state regression

Equations of state (EoS) play a central role in modeling the phase equilibrium of fluid mixtures. Their parameterization involves fitting a model to experimental data, i.e., solving a nonlinear, non-convex, multivariate optimization problem. The latter requires one to select design variables, domains of definition for each variable, and weights assigned to individual measurements. We demonstrate that subjective choices of an optimization algorithm and an initial guess also impact the regression process. Consequently, EoS predictions are fundamentally uncertain even after the EoS tuning to a limited set of experimental data points. We demonstrate this observation for two hydrocarbon reservoir fluids, in which five properties of the heaviest carbon fraction are treated as design variables. While all the optimization algorithms and initial guesses match experimental data for the gas and liquid properties, the resulting EoS parameterizations lead to dramatically different predictions of the fluid’s thermophysical behavior in the unsampled pressure and temperature regions. We propose the probabilistic treatment of design variables to quantify the predictive uncertainty of the resulting fluid models.

A cryogenic visual apparatus for solid-liquid equilibrium and the measurement of CH4 + C2H6

In this work, an apparatus was designed to measure the phase equilibrium for cryogenic pure fluids and mixtures. The apparatus features view windows and an internal stirrer, and the solid-liquid equilibrium (SLE) is determined through a combination of visual observation and thermal analysis. The apparatus is capable of operating over a range of temperatures (40–300 K) and pressures (0–5 MPa), and has been validated through the measurement of triple points of various fluids. The standard combined uncertainties of temperature, pressure and mole fraction for the SLE measurements are no greater than ±0.70 K, ±0.012 kPa, and 0.010, respectively. The performance of the apparatus is further demonstrated through the presentation of experimental SLE data for methane-ethane binary mixtures.

Equation of State Associated with Activity Coefficient Model Based on Elements and Chemical Bonds

A new element- and chemical bond-dependent GE-EoS model(SRK-UNICAC) is proposed to consider the deviation of the vapor and liquid phases from the ideal state. The SRK-UNICAC model combines the UNICAC model and the SRK cubic equation of state. It uses the original interaction parameters of the UNICAC model and uses this model to calculate the GE. The SRK-UNICAC model predicted vapor-liquid equilibria for 87 binary systems under low- and medium-pressure conditions, 12 binary systems under high-pressure conditions, and 14 ternary systems; a comparison of the predictions with five other activity coefficient models were also made. The new model predicted the vapor-phase fraction and bubble-point pressure, and temperature for the binary system at high pressure, with a mean relative error of 3.75% and 6.58%, respectively. The mean relative errors of vapor-phase fraction and bubble-point temperature or bubble-point pressure for ternary vapor–liquid phase equilibrium were 6.50%, 4.76%, and 2.25%. The SRK-UNICAC model is more accurate in predicting the vapor–liquid phase equilibrium of high-pressure, non-polar, and polar mixtures and has a simpler and wider range of prediction processes. It can therefore be applied to the prediction of vapor–liquid equilibrium.

Phase diagram to demarcate supercritical, transcritical, and continuous phase regimes for binary fluid equilibrium mixing relevant to combustion applications

A robust methodology to develop phase diagrams of binary fluid mixtures at fixed thermodynamic conditions (pressure, temperature, and mole fraction) as well as of two initially separated fluids undergoing mixing near critical conditions are presented for fluids and conditions relevant to rockets, gas turbines, and diesel engine applications. Phase equilibria of mixtures are first examined to provide insight into the continuous-phase mixing behavior (including but not limited to supercritical behavior), and to develop a broadly applicable phase-diagram for binary fluid mixtures at fixed conditions. Next, adiabatic mixing theory and reduced Helmholtz equations of state are used to predict the thermodynamic conditions required to attain continuous-phase binary fluid mixing near critical conditions. Then, a 3D surface diagram (P, Tfuel, Tamb) separating single and two-phase regions is constructed by varying the ambient pressure and the initial temperatures of the two fluids. Polynomial fits of the 3D surfaces for 10 different binary mixtures are tabulated for nitrogen–alkane and methane–oxygen blends relevant to air-breathing and propellant based engines, respectively.

Parameters of the UNIQUAC model for describing the vapor-liquid phase equilibrium of D<sub>2</sub>-T<sub>2</sub>, D<sub>2</sub>-DT, DT-T<sub>2</sub> hydrogen isotope mixtures

Objectives. Determination of the parameters of the binary energy interaction of the (UNIversal QUAsiChemical) UNIQUAC model on the basis of mathematical processing of experimental literature data on the phase equilibrium of hydrogen isotopic mixtures D2-T2, D2-DT, DT-T2 to calculate the activity coefficients of the components D2, DT, and T2.Methods. The method of successive approximations was used in junction with the “from stage to stage” method, which consists in calculating a single evaporation process on a theoretical plate.Results. Equations were written for calculating the activity coefficients of hydrogen isotopes on the basis of the Sherwood theory as applied to binary D2-T2, D2-DT, DT-T2 and ternary D2-DT-T2 hydrogen isotope mixtures. The graphical dependences of the activity coefficients and separation coefficients of mixtures D2-T2, D2-DT, and DT-T2 are compared in the range of the concentration of a highly volatile component from 0 to 100 mol % at atmospheric pressure for three options: ideal mixtures; non-ideal mixtures using the Sherwood theory; non-ideal mixtures on the basis of the UNIQUAC model. The dependences of the separation coefficients a were found to be similar for all binary isotopic mixtures. However, when considering mixtures as ideal, a increases.According to Sherwood's theory, a remains a practically constant value, which is independent of the composition of the mixture. The UNIQUAC model predicts a decrease in a with an increase in the concentration of a less volatile component in the mixture. The profile of the distribution of hydrogen isotopes D2, DT, and T2 of a three-component mixture D2-DT-T2, along the height of a distillation column operating in a closed mode was calculated for three variants. It was accepted that: pressure along the height of the column is constant and equal to atmospheric 760 mm Hg. Art.; number of theoretical plates 21; concentration of components in the liquid phase on the first plate (stage), in mol %: XD₂ = 65; XDT= 10; XT₂= 25; the accuracy of calculating the composition of the vapor phase is 10-10.Conclusions. The parameters of the binary energy interaction of the UNIQUAC model of hydrogen isotopic mixtures D2-T2, D2-DT, and DT-T2 are determined. The UNIQUAC model is adequate in relation to experimental data on the coefficient of separation. Due to systematic deviations in the theoretical Sherwood and ideal models, they are not suitable for further calculations of phase equilibrium of isotopic mixtures of hydrogen D2-T2, D2-DT, DT-T2, and D2-DT-T2.

Phase equilibrium, dynamics and rheology of phospholipid-ethanol mixtures: a combined molecular dynamics, NMR and viscometry study.

Binary mixtures of ethanol and phospholipids DOPC and DOPE have been investigated in a composition range relevant for topical drug delivery applications. This was done using a combined computer simulation and experimental approach where molecular dynamics simulations of ethanol-lipid mixtures with different compositions were performed. Several key properties including diffusion coefficients, longitudinal relaxation times, and shear viscosity were computed. In addition, diffusion coefficients, viscosities and NMR longitudinal relaxation times were measured experimentally for comparison and in order to validate the results from simulation. Diffusion coefficients and relaxation times obtained from simulations are in good agreement with results from NMR and computed viscosities are in reasonable agreement with viscometry experiments indicating that the simulations provide a realistic description of the ethanol-phospholipid mixtures. Structural changes in the simulated systems were investigated using an analysis based on radial distribution functions. This showed that the structure of ethanol-DOPC mixtures remains essentially unchanged in the investigated concentration range while ethanol-DOPE mixtures undergo structural rearrangements with the tendency for forming small aggregates on the 100 ns time scale consisting of less than 10 lipids. Although our simulations and experiments indicate that no larger aggregates form, they also show that DOPE has stronger aggregation tendency than DOPC. This highlights the importance of the character of the lipid headgroup for lipid aggregation in ethanol and gives new insights into phase equilibrium, dynamics and rheology that could be valuable for the development of advanced topical drug delivery formulations.

Phase Equilibria in Mixtures of Differently Polar Fluids: Molecular Simulation and Perturbation Theory

Phase Equilibria in Mixtures of Differently Polar Fluids: Molecular Simulation and Perturbation Theory

Phase Equilibrium of Cross-Associating Mixtures Using Association Theory-Based Equation of State

Phase Equilibrium of Cross-Associating Mixtures Using Association Theory-Based Equation of State

A temperature-independent prediction model predicts the vapor-liquid equilibrium of CO2-based binary mixtures

CO2-based binary mixtures are considered good alternative working fluids in the refrigeration and power cycle due to their excellent performance and environmental friendliness. The vapor-liquid phase equilibrium of CO2-based binary mixtures is the basis for calculating mixing enthalpy and heat capacity, which is essential for thermodynamic analysis. In this work, based on the vdW mixing rules, we proposed a kij model (kij=θjki-θikj). In the proposed model, ki and kj are defined as pure interaction factors of the pure components, θj is the influence factor of component j to component i, and θi is the influence factor of component i to component j. After continuous fitting and trial calculation, we developed a semi-empirical formula, which is called a temperature-independent prediction model. The model does not have any adjustable parameters, which are only related to the physical properties (critical pressure (kPa), critical temperature (K), and acentric factor) and molecular structure (carbon-carbon double bonds, carbon-fluorine, chlorine, iodine, and oxygen atoms) of the components. The temperature-independent prediction model can predict the bubble-point pressures, vapor phase molar fractions, and relative volatilities very well, which is better than the prediction model based on the vdW mixing rules by others and the group contribution model based on the excess free energy (GE) mixing rules (PR+MHV1+UNIFAC). The total average absolute relative deviation of pressures, the total average absolute deviation of vapor phase molar fractions, and the total average absolute relative deviation of relative volatilities by the temperature-independent prediction model are 2.23%, 0.0095, and 5.21%, respectively.

An internally consistent procedure to characterize single carbon number fractions for phase equilibrium of petroleum mixtures: Application to Brazilian pre-salt reservoir fluids

Each natural accumulation of hydrocarbons has unique chemical and molecular characteristics. A complete experimental assessment of every substance involved is impossible and, in most cases, gaps left by laboratory tests must be filled by empirical correlations to provide the minimum set of parameters necessary for the proper functioning of a thermodynamic model. In the present work, a new procedure is developed for calculating the critical properties and acentric factor of single carbon number (SCN) fractions, valid for the C7-C22 interval (Mw≤300g/mol) and successfully tested for mixtures containing heavy fractions with average molecular weights up to 520g/mol. The proposed method is based on a refit of existing correlations that fully respects the internal consistency of the equations. These, in turn, were selected by observing the trends described by the critical compressibility factor in the Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR) cubic equations of state, resulting from the introduction of a volume translation parameter. After applying the new procedure to characterize ten oil samples collected from High-Pressure High-Temperature (HPHT) reservoirs in the Brazilian pre-salt cluster, thermodynamic parameters derived from flash and differential liberation tests were successfully predicted. With average absolute deviations of 8.38% and 8.32% for the SRK and PR equations of state, respectively, the proposed method is superior (or at least equivalent) to other characterization schemes considered in the study, with the advantage of being thermodynamically consistent.

Thermodynamics of carbon dioxide mixtures at cryogenic conditions

Carbon capture and sequestration / utilization using cryogenic conditions have found attention due to lower energy penalty compared to other separation methods. In cryogenic processes, carbon dioxide is likely to desublimate from a vapor phase or freezes out from a liquid phase. This study deals with phase equilibrium calculations where solid carbon dioxide forms in the presence of vapor phase (SLV), liquid phase (SLE), or both (SLVE). Two of the successful solid fugacity models are used with predictive cubic equations of state (EOSs) in calculating the phase equilibrium of carbon dioxide mixtures. The advantages and limitations of the models are discussed. In addition, a new fugacity model which describes solid carbon dioxide along solid–liquid coexistence curve is developed. This model remedies the previous models and is used from low to very high pressure. This model reduces to an analytical expression for describing carbon dioxide melting curve. When coupled with the predictive cubic EOSs, this model satisfactorily describes the SVE, SLE, and SVLE of carbon dioxide mixtures.

High-pressure phase equilibrium and volumetric properties of pseudo-binary mixtures of stock tank oil + methane up to 463K

High-pressure phase equilibrium and volumetric properties of highly asymmetric mixtures related to reservoir fluids are critical to the development of high-pressure and high-temperature (HPHT) reservoirs. However, there is a lack of the relevant data and accurate modeling tools. In this work, we prepared asymmetric pseudo-binary mixtures of methane (CH4) + stock tank oil (STO) and systematically measured their phase equilibrium and densities at temperatures from (298.15 to 463.15) K and pressures up to 140 MPa. The methane mole fraction in these mixtures range from 0.20 to 0.61 for the density measurement, and from 0.20 to 0.81 for the phase equilibrium measurement. From the experimental densities, the isothermal compressibility values, as well as the pseudo-excess volumes, were determined. Moreover, phase envelopes, relative volumes, and liquid volume fractions below the saturation point were also measured. These data are valuable for evaluating and improving thermodynamic models for HPHT reservoir fluids. The experimental results were modeled by the Soave-Redlich-Kwong (SRK) equation of state (EoS), the Peng-Robinson (PR) equation of state, their volume translated versions SRK-VT and PR-VT, and the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT). For density, SRK and PR gave large deviations of ~18% and ~8%, respectively, as compared with ~3% for PC-SAFT. Inclusion of volume translation reduced their deviations to the same level as that for PC-SAFT. For isothermal compressibility, all the models gave deviations of 20-30%, with PC-SAFT, SRK-VT and PR-VT being slightly better. The excess volumes calculated by SRK, PR and PC-SAFT were similar and close to the experimental values. The deviations in the calculated excess volumes resulted in only ~1% deviations in the calculated densities if the experimentally determined STO densities were used. It was illustrated that the small deviations could be utilized in the excess volume method to accurately estimate the high-pressure live oil densities from the high-pressure STO densities. This excess volume method gave ~1% density deviation on average for all the models, with PC-SAFT giving the smallest maximum deviation. The deviations in calculated saturation pressures were ~5% for all the models with the overall deviation for PC-SAFT being slightly smaller.

Modeling of the Interfacial Behavior of Carbon Dioxide + Methyl Myristate, Carbon Dioxide + Palmitate, and Carbon Dioxide + Methyl Myristate + Methyl Palmitate Mixtures Using CPA-EOS and Gradient Theory

This work presents the vapor–liquid equilibrium and the interfacial behavior modeling of binary and ternary CO $$_2$$ + ester mixtures, with the cubic plus association equation of state (CPA-EOS) combined with the density gradient theory. The binary mixtures, CO $$_2$$ + methyl myristate and CO $$_2$$ + methyl palmitate, were studied at temperatures from 313.15 K to 333.15 K, considering the ester molecules as non-associating and the carbon dioxide as non-associating or self-associating (2B scheme) molecule. Phase behavior was predicted with binary interaction parameters adjusted from binary mixture phase equilibrium experimental data. Results show than there are some points better represented by the associating scheme, but the overall trend shows that the CPA-EOS with the non-associating scheme for all the molecules is the best option for describing the phase equilibrium and calculating the interfacial tension for the CO $$_2$$ + ester binary mixtures. For this reason, the CO $$_2$$ + methyl myristate + methyl palmitate mixture at 313.15 K was modeled only with non-associating fluids. The AAD% for the calculated interfacial tensions, considering non-associating molecules in the mixture is 9.7 % for the CO $$_2$$ + methyl myristate mixture, 15.1 % for the CO $$_2$$ + methyl palmitate mixture, and 7.9 % for the CO $$_2$$ + methyl myristate + methyl palmitate mixture.

Phase Equilibrium, Morphology, and Physico-Mechanics in Epoxy-Thermoplastic Mixtures with Upper and Lower Critical Solution Temperatures.

The mutual solubility of epoxy oligomer with polysulfone (PSU) and polyethersulfone (PES) was studied by optical interferometry. Additionally, phase diagrams (PDs) were plotted and their evolution during the curing process was shown. The phase structures of modified hardened systems, as well as their tensile strengths, elastic moduli, and crack resistance, have been studied by scanning electron microscopy and physico-mechanical techniques. The effect of initial components’ mutual solubility on the phase structure and, subsequently, on the physico-mechanical properties of the composite material is shown. Differences in the structure and properties of the cured modified compositions depending on the type of PD (with Upper Critical Solution Temperature (UCST) for PSU and Lower Critical Solution Temperature (LCST) for PES) of the initial components are shown.