Multicomponent Phase Equilibria Research Articles

Dominance analysis to assess solute contributions to multicomponent phase equilibria

Phase separation in aqueous solutions of macromolecules underlies the generation of biomolecular condensates in cells. Condensates are membraneless bodies, representing dense, macromolecule-rich phases that coexist with the dilute, macromolecule-deficient phases. In cells, condensates comprise hundreds of different macromolecular and small molecule solutes. How do different solutes contribute to the driving forces for phase separation? To answer this question, we introduce a formalism we term energy dominance analysis. This approach rests on analysis of shapes of the dilute phase boundaries, slopes of tie lines, and changes to dilute phase concentrations in response to perturbations of concentrations of different solutes. The framework is based solely on conditions for phase equilibria in systems with arbitrary numbers of macromolecules and solution components. Its practical application relies on being able to measure dilute phase concentrations of the components of interest. The dominance framework is both theoretically facile and experimentally applicable. We present the formalism that underlies dominance analysis and establish its accuracy and flexibility by deploying it to analyze phase diagrams probed in simulations and in experiments.

Energy landscape analysis for two-phase multi-component NVT flash systems by using ETD type high-index saddle dynamics

With the increasingly accurate modeling and simulation demands and techniques, obtaining the knowledge of the multi-component phase equilibrium states holds the bottleneck challenge in the study of multi-phase fluid flow. In order to resolve the shortages in computational efficiency and stability in the conventional iterative flash calculation, a new phase equilibrium prediction method is proposed by solving the saddle point of the multi-phase system. In this paper, the HiSD (High-index saddle point dynamics) algorithm is used for the first time to calculate the saddle points on the energy landscape of the two-phase two-component NVT flash model based on the Peng-Robinson equation of state, and the up-down search algorithm of HiSD is applied to generate the solution landscape of the flash system. The Rosenbrock-Euler ETD (exponential time differencing) format is involved to reduce the interference of system rigidity to the calculation. It can be referred from the numerical analysis that there are at most the 1st-order saddle points in the energy landscape of the two-component two-phase NVT flash system, and all these saddle points are located on one straight line of the hyperplane, where the energy is equal everywhere. All these 1st-order saddle points can converge to the same or equivalent local minima, which indicates that the two-component two-phase flash system is a system with only one single solution with physical meanings. In addition, the saddle points also obey a linear relationship and the energy remains the same at different temperatures. Therefore, using the method proposed in this paper, the conventional two-step efforts of phase stability test and phase separation calculation can be simplified. The 1st-order saddle points of the system can be directly calculated, reducing the need for an initial guess. The local minima can be directly searched through the downward direction of the saddle point, which greatly reduces the calculation amount of phase equilibrium calculations. Furthermore, the minimum states at different temperatures can be calculated in batch by using one certain initial value, which significantly improves the adaptability and reliability for complex engineering problems with drastic temperature changes.

Capturing molecular interactions in graph neural networks: a case study in multi-component phase equilibrium

We propose a graph neural network architecture that captures molecular interactions in an explicit manner by combining atomic-level (local) graph convolution and molecular-level (global) message passing through a molecular interaction network.

Study on Hydrate Phase Equilibrium Diagram of Methane Containing System Based on Thermodynamic Model

Natural gas hydrate is a potential energy source in the future, which widely occurs in nature and industrial activities, and its formation and decomposition are identified by phase equilibrium. The calculation of multicomponent gas phase equilibrium is more complex than that of single component gas, which depends on the accurate model characterized by enthalpy and free energy. Based on the Kvamme-Tanaka statistical thermodynamic model, theoretical and experimental methods were used to predict and verify the phase equilibrium of pure methane hydrate and carbon dioxide hydrate in the temperature range of 273.17–289.05 K. The phase equilibrium curves of methane-containing gases such as CH4+CO2,CH4+C2H6,CH4+H2S and CH4+CO2+H2S under different mole fractions were drawn and analyzed, and the decomposition or formation enthalpy and free energy of hydrate were calculated. The results show that, the phase equilibrium curves of the methane containing systems is mainly related to the guest molecule type and the composition of gas. The evolution law of phase equilibrium pressure of different gases varies with composition and temperature, and the phase splitting of CO2at the quadruple point affects the phase equilibrium conditions. Due to the consideration of the interaction between the motion of guest molecules and the vibration of crystal lattice, the model exhibits a good performance, which is quantified in terms of mean square error (MSE) with respect to the experimental data. The magnitudes of MSE percent are respectively 1.2, 4.8, 15.12 and 9.20 MPa2for CH4+CO2, CH4+C2H6, CH4+H2S and CH4+CO2+H2S systems, and the values are as low as 3.57 and 1.32 MPa2for pure methane and carbon dioxide, respectively. This study provides engineers and researchers who want to consult the diagrams at any time with some new and accurate experimental data, calculated results and phase equilibrium curves. The research results are of great significance to the development and utilization of gas hydrate and the flow safety prediction of gas gathering and transportation.

An Investigation of Real-Gas and Multiphase Effects on Multicomponent Diesel Sprays

<div class="section abstract"><div class="htmlview paragraph">Lagrangian spray modeling represents a critical boundary condition for multidimensional simulations of in-cylinder flow structure, mixture formation and combustion in internal combustion engines. Segregated models for injection, breakup, collision and vaporization are usually employed to pass appropriate momentum, mass, and energy source terms to the gas-phase solver. Careful calibration of each sub-model generally produces appropriate results. Yet, the predictiveness of this modeling approach has been questioned by recent experimental observations, which showed that at trans- and super-critical conditions relevant to diesel injection, classical atomization and vaporization behavior is replaced by a mixing-controlled phase transition process of a dense fluid. In this work, we assessed the shortcomings of classical spray modeling with respect to real-gas and phase-change behavior, employing a multicomponent phase equilibrium solver and liquid-jet theory. A Peng-Robinson Equation of State (PR-EoS) model was implemented, and EoS-neutral thermodynamics derivatives were introduced in the FRESCO CFD platform turbulent NS solver. A phase equilibrium solver based on Gibbs free energy minimization was implemented to test phase stability and to compute phase equilibrium. Zero-dimensional flash calculations were employed to validate the solver with single- and multi-component fuels, at conditions relevant to diesel injection. The validation showed that 2-phase mixture temperature in the jet core can deviate up to 40K from the single-phase solution. Surface equilibrium with Raoult’s law employed for drop vaporization calculation was observed to deviate up to 100% from the actual multiphase real-gas behavior. Liquid-jet spray structure in high pressure fuel injection CFD calculations was modeled using an equilibrium-phase (EP) Lagrangian injection model, where liquid fuel mass is released to the Eulerian liquid phase, assuming phase-equilibrium in every cell. Comparison to state-of-the-art modeling featuring KH-RT breakup and multicomponent fuel vaporization highlighted the superior predictive capabilities of the EP model in capturing liquid spray structure at several conditions with limited calibration efforts.</div></div>

Real-fluid phase transition in cavitation modeling considering dissolved non-condensable gas

In this article, a fully compressible two-phase flow model combined with a multi-component real-fluid phase equilibrium solver is proposed for cavitation modeling. The model is able to simulate the dissolving process of non-condensable gas through resolving the real-fluid phase change equations. A three-dimensional cavitating nozzle test is considered to validate the suggested model. The achieved numerical results have been compared to the available x-ray experiments. The results have confirmed that the model can tackle the phase transition phenomena including gas dissolving and homogeneous nucleation processes. Thus, the cavitation inception has been modeled dynamically when the fluid crosses the phase boundary from the single-phase state to the two-phase state and vice versa. The effects of non-condensable gas on the cavitation inception, development, and unsteadiness have been particularly analyzed, based on the large eddy simulations and x-ray experiments. Finally, the encountered challenges are mentioned, aiming at providing recommendations for similar research studies.

Estimation of PC-SAFT binary interaction coefficient by artificial neural network for multicomponent phase equilibrium calculations

Perturbed-Chain Statistical Associating Fluid Theory Equation of State (PC-SAFT EoS) requires cross interaction parameter for each binary pair in the mixture. For real mixtures, these parameters should be corrected by binary interaction coefficients (kij's). The values of kij's are tuned by an optimization method in order to minimize the deviation from equilibrium data. The Particle Swarm Optimization (PSO) algorithm is employed for optimization of kij's due to the continuous nature of kij and highly nonlinear nature of PC-SAFT EoS. Although kij can be adjusted using the mentioned algorithm, it is cumbersome and highly time-consuming because the optimization should be performed for each pair that exists in the multicomponent mixture. It has been shown that these optimal values can be obtained based on the basic characteristic properties of the participating molecules in each pair, this is particularly useful to avoid solving any optimization problem. Furthermore, Artificial Neural Networks (ANNs) as powerful function approximators have been used to predict binary interaction coefficients based on basic characteristic properties of molecules that exist in each pair. Two types of characteristic properties have been examined as inputs of the ANN's utilized to predict the optimum kij's. The first one contains PC-SAFT parameters (m, ε/k, σ) and molecular weight of each component; while the second category contains specific gravity, normal boiling point and molecular weight of each component.The best structure of ANN has been obtained by two approaches: 1) Genetic Algorithm (GA) and 2) a constructive approach. GA can find the structure with any possible connections between neurons whereas the constructive approach can only find the best structure for fully connected networks. The results show that the genetically designed ANN that uses the second set of inputs outperforms the others. This ANN is used to estimate kij's of PC−SAFT for a wide range of non-associating materials where the predicted kij's are in close agreement with those obtained by PSO with coefficient of determination R2 = (0.9921, 0.9631) for training and validation data, respectively. In addition to the evaluation of the ANN by validation data, its performance has been examined by using its estimated kij's in flash calculation of a synthesized multi-component mixture and bubble point calculation of a reservoir fluid. Comparing the results of equilibrium calculations with their experimental counterparts shows that they closely follow the measured data. Furthermore, its performance has been compared with other approaches of estimation of kij such as London theory and QSPR method and the results show that the proposed ANN outperforms the others.

Implementation of the UNIQUAC model in the OpenCalphad software

The UNIQUAC model is often used, for example in engineering, to obtain activity coefficients in multicomponent systems, while the CALPHAD method is known for its capability in phase stability assessment and equilibrium calculations. In this work, we combine them by representing the UNIQUAC model according to the CALPHAD method and implementing it in the OpenCalphad software. We explain the harmonization of nomenclature, the handling of the model parameters and the equations and partial derivatives needed for the implementation. The successful implementation is demonstrated with binary and multicomponent phase equilibrium calculations and comparisons with literature data. Additionally we show that the implementation of the UNIQUAC model in the OpenCalphad software allows for the calculation of various thermodynamic properties of the systems considered. The combination provides a convenient way to assess interaction parameters and calculate thermodynamic properties of phase equilibria.

Nanoscale confined multicomponent hydrocarbon thermodynamic phase behavior and multiphase transport ability in nanoporous material

Abstracts Multicomponent hydrocarbon transport in nanoporous material is influenced by the nanoscale thermodynamic phase behavior, heterogeneous pore structure and hydrocarbon-molecules-pore wall interaction. Little is known about the multicomponent hydrocarbon transport mechanisms in realistic 3D nanoporous material. We here propose a nanoscale pore network multiphase multicomponent hydrocarbon transport model to study multicomponent hydrocarbon thermodynamic phase behavior and transport ability across a wide range of pressure and temperature. A novel thermodynamic phase equilibrium calculation model is proposed considering the multiphase interface curvature change and phase saturation in irregular pore cross-sections. The multicomponent gas slippage effect and liquid phase boundary slip length variation with pore size are incorporated into the mode. Study results find that for low liquid phase saturations with high capillary pressure, the liquid mainly resides in the pore corners, and for high saturations with low capillary pressure it forms liquid bridges. The formation of liquid bridges, and thus ultimately decrease in gas phase transport ability, depends on the interplay of multicomponent hydrocarbon composition, pressure, temperature, the local pore shape, pore size as well as three-phase contact angle. The multicomponent hydrocarbon gas phase permeability through 3D pore network is influenced by the composition and temperature when the pore pressure is less than 15 MPa, while multicomponent gas phase permeability is unaffected by the pore pressure and temperature change at relatively high pressure (>15 MPa). The liquid phase permeability increases with the increase of dense phase composition and the decrease of temperature at pressure less than 15 MPa. This work provides a new multicomponent hydrocarbon thermodynamic phase equilibrium model and a novel work flow of assessing multicomponent hydrocarbon multiphase transport ability in heterogeneous irregular nanoporous material.

A New Model of Displacement Efficiency of Gas Hydrate Considering the Influence of Temperature

The model of natural gas hydrate displacement failed to accurately analysis the influence degree of temperature, and it is not accurate enough to calculate the volume of gas under high pressure owing to the influence of compressibility factor, which leading to a result that the model has great error in calculating the displacement efficiency. In this paper, a new model of displacement efficiency affected by temperature is derived in the design of displacement experiment based on the law of conservation of mass, Multicomponent gas equation of state, Multicomponent thermodynamic phase equilibrium principle at the first. Next, several methods for calculating the compressibility factor of natural gas at different temperatures and pressures are compared by using Visual Basic software, and the Setzmann equation with the smallest error is selected. Finally, compared with the new model, the traditional model as well as the experimental data, the results show that the new model is closer to the experimental data. At the same time, the displacement efficiency of natural gas hydrate at different temperatures is analyzed. It is suggested that higher displacement efficiency can be obtained by reasonably increasing the temperature of the displacement reaction system.

Адаптация алгоритма расчета фазового равновесия многокомпонентной системы применительно к месторождениям с неопределенностью в исходных данных

Адаптация алгоритма расчета фазового равновесия многокомпонентной системы применительно к месторождениям с неопределенностью в исходных данных

Isobaric Vapor-Liquid Phase Diagrams for Multicomponent Systems with Nanoscale Radii of Curvature.

At any given temperature, pressure, and composition, a compound or a mixture of compounds will exist either in a single phase, whether solid, liquid, or vapor, or in a combination of these phases coexisting in equilibrium. For multiphase systems, it is known that the geometry of the interface impacts the equilibrium state; this effect has been well-studied in single component systems with spherical interfaces. However, multicomponent phase diagrams are usually calculated assuming a planar interface between phases. Recent experimental and theoretical work has started to investigate the effect of curved interfaces on multicomponent phase equilibrium, but these analyses have been limited to isothermal conditions or to a portion of the isobaric phase diagram. Herein, we consider complete vapor-liquid phase diagrams (both bubble and dew lines) under isobaric conditions. We use Gibbsian composite-system thermodynamics to derive the equations governing vapor-liquid equilibrium for systems with a spherical interface separating the phases. We validate our approach by comparing the predicted nitrogen/argon dew points with reported literature data. We then predict complete isobaric phase diagrams as a function of radius of curvature for an ideal methanol/ethanol system and for a nonideal ethanol/water system. We also determine how the azeotropic composition of ethanol/water changes. The effect of curvature on isobaric phase diagrams is similar to that seen on isothermal phase diagrams. This work extends the study of curved-interface multicomponent phase equilibrium to isobaric systems, expanding the conditions under which nanoscale systems, such as nanofluidic systems, shale gas reservoirs, and cloud condensation nuclei, can be understood.

Solid-phase equilibria on Pluto's surface

Pluto's surface is covered by volatile ices that are in equilibrium with the atmosphere. Multicomponent phase equilibria may be calculated using a thermodynamic equation of state and, without additional assumptions, result in methane-rich and nitrogen-rich solid phases. The former is formed at temperature range between the atmospheric pressure-dependent sublimation and condensation points, while the latter is formed at temperatures lower than the sublimation point. The results, calculated for the observed 11 μbar atmospheric pressure and composition, are consistent with recent work derived from observations by New Horizons.

A sharp interface method for coupling multiphase flow, heat transfer and multicomponent mass transfer with interphase diffusion

Mixing of partially miscible fluids plays an important role in many physical and chemical processes. The modeling complexities lie in the tight coupling of the multiphase flow, heat transfer and multicomponent mass transfer, as well as diffusions across the phase interface. We present a sharp interface method for modeling such process. The non-ideal equation of state is used to compute the fluid properties such as density, fugacity and enthalpy, and to predict phase equilibrium composition. The phase interface location is tracked using the phase propagation velocity. A third-order one-sided finite difference scheme using a variable grid size according to the interface location is utilized to discretize the partial derivatives immediately next to the interface, while a second-order central scheme is used for the bulk of fluids. An optimization method, the Nelder–Mead method, is applied to search for (1) the phase compositions on both sides of the interface, and (2) the phase propagation velocity based on the coupling of the multicomponent phase equilibrium and the species' balance across the interface. The temperature at the interface is determined by the energy balance. Numerical results are used to demonstrate the convergence of our method and show its capability to simulate the mixing of multicomponent partially miscible fluids.

A Critical Assessment of Thermodynamic and Phase Diagram Data for the Ge-O System

A critical assessment of the thermodynamic and phase diagram data for the crystalline and liquid phases of the Ge-O system at ambient pressures has been carried out to provide a set of parameters which can be used as a basis for the calculation of ternary and multicomponent phase equilibria. The phase diagram reported by Massalski (Binary Alloy Phase Diagrams, ASM International, Materials Park, 1990) does not correctly reproduce the rather limited experimental information for the system. There is some inconsistency between the rather more extensive experimental thermodynamic data for the three phases of GeO2 stable at ambient pressures.

Negative Flash for Calculating the Intersecting Key Tielines in Multicomponent Gas Injection

Gas injection is a widely used enhanced oil recovery method, and its application is expected to increase in the foreseeable future. In order to build a method of characteristics solution to a two-phase gas injection system, we must construct the composition route from the injection gas to the initial oil where all the intersecting key tielines must be identified. Calculation of these intersecting tielines requires a series of special negative flashes, which allow not only phase fractions outside the physical interval [0,1] but also negative feed compositions. The phase compositions from one negative flash are used to recombine the feed for the next negative flash. Despite the apparent complexity due to multicomponent phase equilibrium and transport, for pure component gas injection, negative flash and elimination of components can be performed in an alternating manner. In particular, if K-values are constant, there exists a simple feature that the vapor fraction roots (β-roots) for the Rachford–Rice equat...

Measurements of the solubility of sulphur dioxide in water for the sulphur family of thermochemical cycles

In recent years, the Hybrid Sulphur (HyS) and Sulphur Iodine (SI) cycles have emerged as promising routes for the massive scale thermochemical production of Hydrogen from water. Common to these two cycles is a high temperature stage involving the decomposition of sulphuric acid to sulphur dioxide, water and oxygen. The work considered here focuses on the oxygen separation stage of the process where, in order for a science based design approach to be taken, thermodynamic data are required for multicomponent phase equilibrium relationships between the decomposition products; H 2O–SO 2–O 2. A method of making flash calculations, useful in the separation equipment design, has been proposed and coded into Mathematica ®. Further, a vapour–liquid equilibrium still has been designed and built to make measurements of the multicomponent solubility of sulphur dioxide and oxygen in water. The experiments presented here concentrate on the binary SO 2–H 2O system, covering a wider range of pressures than that found in the literature. Solubility, expressed in molality, was obtained at 25 and 40 °C and pressures ranging from 0.2 to 3.6 atm. Good agreement is seen between the experimental data and the model at lower pressures, however improvements are needed at higher pressure. Preliminary data for the ternary system at 40 °C is presented, showing good agreement with the multicomponent model. Future work will focus on the three component system.

An evaluation of the performance of the Cubic-Plus-Association equation of state in mixtures of non-polar, polar and associating compounds: Towards a single model for non-polymeric systems

The aim of this work is to investigate the possibility of identifying a single model that will be able to accurately describe the phase equilibrium in non-polymeric systems, which involve non-polar, polar and hydrogen bonding compounds. To this purpose the Cubic-Plus-Association (CPA) EoS, developed in this laboratory about 10 years ago, is examined in the correlation of phase equilibrium in binary systems and prediction of multicomponent phase equilibrium from binary data. When possible the results of the CPA EoS are compared with those obtained from the PC-SAFT EoS. To account for dipolar or quadrupolar interactions, present when molecules such as acetone or carbon dioxide are involved, these molecules are treated using the concept of “pseudo-association”, i.e. as being able to act as associating compounds. This approach renders CPA applicable to systems that involve polar compounds without the need of extra terms to account for polar and/or quadrupolar interactions. It is concluded that CPA, coupled with the “pseudo-association” approach for polar molecules, represents a model that is able to accurately describe the phase equilibrium in a variety of binary systems involving non-polar, polar and hydrogen bonding compounds and provide satisfactory prediction of multicomponent phase equilibrium from binary data.

Modelamento termodinâmico e cinético por meio do método Calphad do processamento térmico e termoquímico de aços

Na década de 1970 Kaufman e Bernstein realizaram trabalho pioneiro sobre modelamento numérico da termodinâmica de sistemas multicomponentes e fundaram o grupo CALPHAD (Computer Coupling of Phase Diagrams and Thermochemistry), que tem como propósito promover a termodinâmica computacional e desenvolver programas computacionais para: (i) avaliar e validar dados experimentais (e teóricos) para incorporá-los às bases de dados auto-consistentes, (ii) representar as propriedades termodinâmicas de sistemas multicomponentes, (iii) modelar processos tecnológicos. Além de programas para modelamento termodinâmico, vários programas computacionais CALPHAD têm sido desenvolvidos, também, para calcular a cinética de transformações de fase controladas por difusão, os quais têm interfase com programas de calculo termodinâmico e com bases de dados de mobilidades atômicas. No presente trabalho relatam-se diferentes exemplos do uso do método CALPHAD para o modelamento matemático de diferentes processamentos térmicos e termoquímicos de aços, os quais correspondem a estudos de casos realizados no departamento de Engenharia Metalúrgica e de Materiais da Escola Politécnica da Universidade de São Paulo. Por meio de modelamento CALPHAD foi possível otimizar os parâmetros de processamento durante: a nitretação de aços de alta liga, o processamento térmico de aços TRIP, a produção de nitretos CrN e Cr2N a partir de pó de cromo, o tratamento térmico de solubilização de aços inoxidáveis e o tratamento térmico de decomposição de carbonetos em aços ferramenta.

Predictions of Titanium Alloy Properties Using Thermodynamic Modeling Tools

Thermodynamic modeling tools have become essential in understanding the effect of alloy chemistry on the final microstructure of a material. Implementation of such tools to improve titanium processing via parameter optimization has resulted in significant cost savings through the elimination of shop/laboratory trials and tests. In this study, a thermodynamic modeling tool developed at CompuTherm, LLC, is being used to predict β transus, phase proportions, phase chemistries, partitioning coefficients, and phase boundaries of multicomponent titanium alloys. This modeling tool includesPandat, software for multicomponent phase equilibrium calculations, andPanTitanium, a thermodynamic database for titanium alloys. Model predictions are compared with experimental results for one α-β alloy (Ti-64) and two near-β alloys (Ti-17 and Ti-10-2-3). The alloying elements, especially the interstitial elements O, N, H, and C, have been shown to have a significant effect on the β transus temperature, and are discussed in more detail herein.