Phase Equilibrium Calculations Research Articles

Tectono-metamorphic interaction of upper mantle peridotites and lower crustal units during continental rifting in the western Betic Cordillera

Recent geological mapping conducted in the Ronda Peridotites (Betic Cordillera, S Spain) has revealed a systematic field correlation between lower crustal metamorphic units and different tectono-metamorphic domains of the ultramafic massif. Mylonitic and highly tectonized Spl ± Grt peridotites (i.e., Grt-Spl mylonite and Spl tectonite domains), which are considered to be derived from a thick continental lithosphere, are in contact with garnet-bearing gneisses (i.e., kinzigites) of the Jubrique unit along a narrow but continuous mylonitic shear zone. Phase equilibrium calculations indicate that the metamorphic rocks of the Jubrique unit are consistent with an initial continental setting characterized by normal crustal thicknesses, which underwent two melting events. The first melting occurred at 0.9–1.0 GPa / 770–800 °C and resulted in 13 %melt, while the second one took place at shallower crustal conditions (0.4–0.5 GPa and 710–765 °C) and led to more restricted melt production (2–3 %melt). In contrast, the Spl ± Pl peridotites (Pl-tectonite domain), which are stable only at shallowest mantle levels within a highly extended continental lithosphere, are consistently found exposed in contact with heterogeneous granites and migmatites of the Guadaiza unit. According to new thermodynamic modeling, the Guadaiza metamorphic rocks record a single melting event characterized by a theoretical melt production of 6 to 11 % at the base of a very thin continental crust (ca. 0.3 GPa and 675–710 °C). This process was likely facilitated by influx of external water, necessary to generate high melt fractions observed in the diatexites. The systematic correlation observed between crustal metamorphic units, consistently overlaying the mantle rocks, and specific ultramafic domains of the Ronda massif, suggests that their juxtaposition primarily resulted from the severe extension of the continental lithosphere.U-Pb radiometric dating of zircons from gneisses, migmatites, and heterogeneous granites in the middle crustal rocks of the Guadaiza unit indicates that extensional processes, crustal anatexis, and melt stagnation occurred at around 280 Ma. Comparison of these new radiometric ages with previous results from the Jubrique unit suggests that a Permian high-temperature / low- to medium-pressure event uniformly affected the crustal units over the Ronda Peridotites. This event coincided with the formation of characteristic ultramafic mineral assemblages within the Ronda massif and provides evidence for the interaction between upper mantle rocks and lower- to mid-crustal metamorphic rocks during this period.

Revealing microstructural degradation mechanism induced by interdiffusion between Amdry365 coating and IN792 superalloy

Metallic coatings are widely employed to improve the oxidation resistance of superalloys. However, the interdiffusion between the metallic coatings and the superalloys leads to microstructural degradation in both. Some of the underlying degradation mechanisms are still elusive, e.g., the γ′ (Ni3Al) phase depletion in superalloys, where a large amount of γ′ precipitates are dissolved in the γ matrix even though the incoming Al from coatings indeed increases the Al content. Here, we investigated the interdiffusion behavior between the Amdry365 coating and the IN792 superalloy at 1100 °C, using multiple microscopic techniques and thermodynamics calculations. Our results showed an excellent agreement between experiments and thermodynamics simulations, indicating the dominant role of Al on the initial diffusion-induced phase transitions. We proposed the Al-Cr interference effect to account for the pile-up behavior of Cr and the reduced Al content near the coating/superalloy interface. The local phase equilibrium calculations revealed that the γ′ depletion in the superalloy is primarily attributed to the loss of γ′-forming elements, such as Ta and Ti. Our findings opened up an avenue for studies on the superalloy/coating interdiffusion, contributing to reducing this damaging impact

Study on the Phase Behavior Simulation Method of High-Salinity Reservoirs.

The presence of salinity affects the accuracy of existing correlations used in the equation of state. Moreover, the variation of salinity is often ignored in the systematic analysis of the phase diagram, resulting in a large error in the final calculation result. It is obvious that the conventional phase equilibrium calculation is not applicable in a high-salinity reservoir. By introducing the hydrocarbon-brine binary interaction coefficient and α-function, combined with the definition of salinity, and considering the variation of salinity under different pressure and temperature conditions, a more perfect phase equilibrium calculation model was established. The complete phase diagram was drawn, and the calculation results of salinity distribution are obtained. The effect of the mole percentage of water and salt content on the phase behavior was simulated. Finally, the phase distribution simulation is carried out based on the measured data. The phase state and salinity variation law of a high-salinity reservoir are obtained. According to the fluid composition of different periods, the real phase state of the high-salinity reservoir can be monitored in real time. It can provide a theoretical basis for the gas reservoir development and the dynamic evaluation of gas storage injection and production with a hydrocarbon-brine two-phase system.

Prediction of Phase Equilibrium Conditions and Thermodynamic Stability of CO2-CH4 Gas Hydrate

With the large-scale promotion and application of CO2 flooding, more and more engineering problems have emerged. Due to the high CO2 mole fraction, the associated gas of CO2 flooding very easily forms solid hydrates, compared to conventional natural gas. This has resulted in production decline or shutdown. Understanding the phase equilibrium conditions for hydrate formation in production fluids is crucial for hydrate prevention and control. In this study, accurate predictions of CO2-CH4 mixed gas hydrate formation conditions were performed using theoretical models. The temperature and pressure ranges for hydrate formation were calculated for different CO2 mole fraction, ranging from −11.5 °C to 20.85 °C and from 0.81 MPa to −28.1 MPa, respectively. Based on the calculated phase equilibrium data, a multi-parameter empirical model was developed using polynomial fitting. The calculation errors for the multi-parameter empirical model were 3.09%. The multi-parameter empirical model established in this study can avoid complex thermodynamic equilibrium calculations and has the advantages of simplicity, high accuracy, and wide coverage of downhole conditions. Based on the calculated phase equilibrium data, the dissociation enthalpy of CO2-CH4 hydrate below and above the freezing point of water was calculated. The results showed that an increase in CO2 mole fraction led to an increase in hydrate dissociation enthalpy and enhanced thermodynamic stability, making hydrate prevention more challenging. Our work can contribute to the optimization of CO2 production fluid treatment processes and the development of hydrate prevention and control technologies.

Modification of the van der Waals and Platteeuw model for gas hydrates considering multiple cage occupancy.

This study reviews available van der Waals- and Platteeuw-based hydrate models considering multiple occupancy of cavities. Small guest molecules, such as hydrogen and nitrogen, are known to occupy lattice cavities multiple times. This phenomenon has a significant impact on hydrate stability and thermodynamic properties of the hydrate phase. The objective of this work is to provide a comprehensive overview and required correlations for the implementation of a computationally sufficient cluster model that considers up to five guest molecules per cavity. Two methodologies for cluster size estimation are evaluated by existing nitrogen hydrate models showing accurate results for phase equilibria calculations. Furthermore, a preliminary hydrogen hydrate model is introduced and compared with the results of other theoretical studies, indicating that double occupancy of small sII cavities is improbable and four-molecule clusters are predominant in large sII cavities for pressures above 300 MPa. This work lays the foundation for further exploration and optimization of hydrate-based technologies for small guest molecules, e.g., storage and transportation, emphasizing their role in the future landscape of sustainable energy solutions.

Pressure-volume-temperature analysis of Caspian oil to improve the analytical delumping procedure

Compositional modeling of the reservoir isn’t complete without calculations of phase equilibrium and is a complex process involving many calculations. In nature, hydrocarbons don’t occur as separate components, they’re mainly mixtures. When modeling the reservoir composition for phase equilibrium calculations, in order to reduce computational costs, in practice, hydrocarbon mixtures are grouped into pseudo-components. The number of grouped pseudo-components varies from 4 to 10. This grouping process is called lumping. However, when crude oil comes to the surface, it’s important to know its detailed composition, since mixtures grouped into pseudo-components don’t allow you to know this. In this regard, modeling of the detailed composition of hydrocarbons is the main tool for understanding the detailed phase separation and design of surface facilities. In practice, this process is called delumping. In the case of this process, the detailed composition of the fluid is presented and the amount reaches up to 36 components, sometimes more. The delumping process, due to the precise separation of heavy plus fractions into carbons with single ordinal numbers (C7, C8, etc.), makes it possible to clearly recognize non-zero BIP’s in the equation of state. The new analytical approach has not previously been applied to the oils of the Caspian region, so this approach has an important role for the oil industry in the Caspian region. Analytical delumping in this paper was done to improve the PVT modeling. This paper presents the results of PVT research of Caspian oil and presents a comparison of analytical and numerical methods of delumping. As a result of the study, it was found that the analytical approach is in excellent agreement with experimental data and data from software such as PVTsim

Phase equilibria calculations of a hydrocarbon system consisting water and asphaltene using association equation of state: A generalized auto-tune procedure

A generalized algorithm is proposed for four-phase flash calculations in hydrocarbon-water systems in which asphaltene has tendency to be precipitated. The systems which are going to be studied in this paper can be either single phase, two-phase, three-phase or four-phase of gas, oil-rich, asphaltene-rich and aqueous phases. The properties of vapor and oil-rich (liquid) phases can be predicted using any EOS while Henry's law is performed for calculating the properties of water-rich (aqueous) phase. In addition, an association equation of state (AEOS) has been used to predict the amount of the precipitated asphaltenes at different conditions. Using the proposed algorithm, one can predict the number and types of phases and also the properties of each phase, as accurate as possible. As tuning of EOS models is tedious and time consuming, a generalized and auto-tune method based on sensitivity and optimization algorithms is also applied in this study so that the best model could be found easily, quickly and automatically. The proposed approach proved to be efficient, and very good agreement between the results of the presented method and experimental data was found for different test problems. This new procedure can be very useful in compositional reservoir simulation of certain enhanced oil recovery methods and in surface facility process simulation.

An initial value insensitive method for phase equilibrium calculation: Constrained backtracking search optimization algorithm

Phase equilibrium calculations are frequently encountered in various industrial processes and many methods, including direct solution methods based on Newton's method and indirect solution methods based on thermodynamic principles sprang out. They all can calculate the satisfactory solutions of phase equilibria problem under given volume, temperature, and moles (NVT-flash), but there still exist problems of initial value sensitivity and solving complex derivatives. Thus, a constrained backtracking search optimization algorithm (CBSA), which added constraints handling of the NVT-flash problem to the original operation of BSA, is presented in this paper. The proposed algorithm takes the total Helmholtz free energy as the objective function, and the moles vector and volume of a certain phase as the decision variables. The direct search method and exterior point method were used to handle the constraints of NVT-flash problem. The numerical test results are 100% consistent with the published data, which verify the effectiveness and energy decay property of the proposed algorithm. The proposed scheme is the first successful attempt to apply meta-heuristic algorithm to the field of phase equilibrium calculation. This hints the wide application prospect of meta-heuristic algorithms in this field as well as broadens the application range of meta-heuristic optimization algorithms.

Method for determining estimates of random variable models for describing phase equilibrium in rectification processes

The phase equilibrium modeling for multi-component systems is essential in process systems engineering. In particular, phase stability analysis, Gibbs free energy minimization and estimation of parameters in thermodynamic models are challenging global optimization problems involved in phase equilibrium calculations and modeling for both reactive and non-reactive systems. To date, many significant works have been performed in the area of global optimization, and several algorithms and computational contributions of global optimization have been used for solving these problems; global optimization methods used include both deterministic and stochastic algorithms. To the best of our knowledge, there is no review in the literature that focuses on the global optimization methods and their applications to phase equilibrium modeling and calculations. In this paper, we briefly describe the deterministic and stochastic optimization algorithms selected for our rectification process, and then consider their use for phase stability analysis, Gibbs free energy minimization, and parameter estimation in phase equilibrium models. In short, we present an overview of global optimization for modeling and computing the phase behavior of systems with and without chemical reactions, including the prediction of azeotropes and critical points.

Phase Behaviors of Gas Condensate at Pore Scale: Direct Visualization via Microfluidics and In-Situ CT Scanning

Summary Gas condensate is stored in multiscale pores, fractures, and vugs within geological formations. Confinement within these structures significantly influences the phase behavior of gas condensate, rendering it challenging to characterize through conventional bulk pressure/volume/temperature (PVT) measurements. In this study, we used microfluidics and in-situ computed tomography (CT) scanning to directly measure the upper dewpoint of gas condensate and the gas/oil ratio in porous media during depressurization. We used two microfluidic chips with different pore sizes to investigate the confinement effects on gas condensate phase behavior at various scales, including pores as small as 50 nm. Our results revealed a significant increase in the upper dewpoint within the pores compared to bulk PVT measurements, with a more pronounced deviation at smaller pore sizes. Additionally, the proportion of condensate oil in porous media exceeded that observed in bulk PVT measurements at the same pressure. To validate our microfluidic findings, we conducted in-situ CT scanning experiments using a porous media model created by packing quartz particles. CT scans revealed pores ranging from a few micrometers to over 100 micrometers. Consistently, we observed an increase in the upper dewpoint and liquid ratio within these pores. Our study provides crucial experimental evidence indicating that the phase behavior of gas condensate in porous media deviates from bulk PVT measurements. The observed increase in the upper dewpoint, even within micrometer-sized pores, has important implications for phase equilibrium calculations.

Force Field for Calculation of the Vapor-Liquid Phase Equilibrium of trans-Decalin

Based on the TraPPE force field, previously unknown values of the parameters of the intermolecular interaction potential of trans-decalin were determined. Parametrization was carried out using experimental data on saturated vapor pressure and density at atmospheric pressure. The found parameters make it possible to adequately describe the boiling and condensation lines of trans-decalin and also predict the critical values of pressure, density, and temperature with satisfactory accuracy. Calculations of vapor-liquid phase equilibrium conditions for a binary CO2—trans-decalin mixture in supercritical conditions for CO2 were carried out. When quantitatively comparing the calculated values with experimental data, an underestimation of pressure at a temperature of 345.4 K by 30% is observed, which decreases to 5% for temperatures up to 525 K.

Calculation of Phase Equilibria of Pure Light Hydrocarbons Using the PC-SAFT Equation of State and the Direct Energy Minimization Algorithm

In the oil and gas industry, there is growing interest in using the PC-SAFT equation of state for predicting the phase behaviour and physical properties of hydrocarbons. This article demonstrates how this equation of state can be used in combination with the direct energy minimization algorithm of an isochoric-isothermal system for calculating vapour-liquid equilibrium parameters of hydrocarbons. The proposed approach is tested on four substances: methane, ethane, propane, and n-butane.

Mid-Neoproterozoic (ca. 845 Ma) metamorphism of the southwestern Yangtze Block and its tectonic implications

The evolutionary history of the Yangtze Block plays an increasingly important part in reconstructing Proterozoic paleogeography and associated supercontinent cycles. We document mid-Neoproterozoic amphibolite facies metamorphism related to crustal thickening and possible terrane accretion within an accretionary orogen along the southwestern margin of the Yangtze Block. Kyanite-staurolite bearing schists in the Dahongshan Group record a main deformation stage and a peak metamorphic assemblage Grt rim + Ky + St + Bt + Ms + Rt + Pl ± Ilm. Petrography and phase equilibrium calculations suggest a clockwise P-T path under medium-pressure facies condition. Monazite U-Th-Pb ages from the Dahongshan Group constrain the timing of peak metamorphism to 845 ± 6 Ma (n = 33, MSWD = 1.01), which overlaps the metamorphic climax in the northern segment of the southwestern Yangtze Block. Based on the comprehensive analysis of geochemical, metamorphic and sedimentary data from the Yangtze Block, we consider that the outboard domain occupied by the Dahongshan Group along with the Hekou, Huili, Julin (Yuanmou) groups constitutes a terrane(s) that was separated from the rest of the Yangtze Block by a marginal sea formed at the end of the Mesoproterozoic. Mid-Neoproterozoic re-accretion to the inner Yangtze Block during ongoing convergent plate margin activity resulted in the deformation and metamorphism of these rock units. Similarities in the Neoproterozoic evolution of the Yangtze Block, the Seychelles, and the western margin of Greater India suggest a protracted history of oceanic plate subduction periodically interrupted by coupling across the plate margin driving deformation and metamorphism.

COMPREHENSIVE FLUID DESCRIPTION THROUGH LUMPING PROCEDURES: FOR KAZAKHSTANI OIL

Reservoir modeling requires a multitude of phase equilibrium calculations, particularly in the context of compositional reservoir simulations. To accelerate these calculations, the many components of the heptane plus fraction should be grouped into pseudocomponents. Moreover, accurate fluid compositions demand extensive laboratory analysis, a process both costly and time-consuming. The exercise of grouping and splitting are important for reservoir modeling. In our research, we introduce a lumping methodology for fluid characterization, focusing on the unique context of Kazakhstani oil. More specifically, we delve into the Whitson lumping and splitting techniques. For this study, a sample was taken from the X field, and detailed fluid composition data was acquired through laboratory analysis. We employed both numerical and analytical approaches to study the lumping process. Additionally, we compared our calculations with simulation results. As we navigate the intricacies of fluid characterization, we highlighted the advantages and limitations of lumping procedures and emphasized the effectiveness of Whitson method. Detailed fluid compositions obtained through laboratory PVT analysis were then compared with the results of simulation using PVTsim software and numerical delumping procedures The results of this work demonstrated the effectiveness of Whitson methods for lumping and splitting procedures for describing Kazakhstani fluids.

Fluid phase behavior in multi-scale shale reservoirs with nano-confinement effect

Shale reservoirs are featured by widely distributed micro-scale fractures and nano-scale pores. The phase behavior of reservoir fluids in these complex environments remains uncertain. Hence, an efficient model is developed to investigate the fluid phase behavior in multi-scale shale reservoirs based on a pore-size-dependent equation of state. The porous space is discretized into specific sizes of nanopores and fractures regions. Phase equilibrium calculations for pure components, binary mixtures and multi-component shale oils show that adsorption and critical properties shifts display opposite effects on a fluid distribution, and the shifts in the critical properties are the main reason for more lighter components present in nanopores. The nano-confinement effect enhances the ability of CO2 to enter nanopores. An innovative multi-scale model of partial equilibrium is developed to explore changes in fluid properties during pressure depletion. The results reveal that gas appears in the fracture region, while the confined fluids within nanopores are always kept in the oil phase. Lighter components within nanopores are rapidly released as pressure drops. However, the content of heavier components within nanopores gradually decreases if the pressure stabilizes for a while, meaning that a slow pressure drop is more conducive to the recovery of shale oil from nanopores.

Phase Separation, Reaction Equilibrium, and Self-Assembly in Binary Telechelic Homopolymer Blends.

We study a binary blend of telechelic homopolymers that can form reversible AB-type bonds at the chain ends. Reversibly bonding polymers display novel material properties, including thermal tunability and self-healing, that are not found in conventional covalently bonded polymers. Previous studies of reversibly bonding polymer systems have been limited by the computational demand of accounting for an infinite number of possible reaction products in a spatially inhomogeneous, self-assembled structure. We demonstrate that newly developed theoretical models and numerical methods enable the simultaneous computation of phase equilibrium, reaction equilibrium, and self-assembly via self-consistent field theory. Phase diagrams are computed at a variety of physically relevant conditions and are compared with nonreactive analogues as well as previous experimental studies of telechelic polymer blends.

The Development of a Thermodynamic Database for Calculation and Prediction of Phase Equilibria in High-Temperature Refractory Alloys: A Tribute to Ted Massalski

AbstractThere is an increasing demand for materials capable of withstanding ever-higher temperatures. However, because the difficulties associated with carrying out experimental investigations at very high temperatures are significant, the published information relating to the phase stability of potential refractory materials is, in many instances, still lacking. The work described in this paper attempts to rectify this deficit through the on-going development of a thermodynamic database for high-temperature materials based on carbides, nitrides, borides, and silicides. Because of technological requirements of high-temperature stability and strength, combined with lightness, these are the materials that come into question most frequently for high-temperature applications. In developing the present database, and to ensure reliability of its use, emphasis has been placed on the need to maintain the compatibility of data and modeling when assessing experimental data and estimating missing values. The methods used to achieve compatibility of published information are described and calculations of phase equilibria relevant to the industrial application of various refractory materials are presented. The similarity to, and the importance of the scientific background and published work of Ted Massalski for the work of the present author is stressed.

The pH value influence on the waylandite-structured BiAl3(PO4)2(OH)6 compound formation under hydrothermal conditions

The present work has found that the rate of the waylandite-structured BiAl3(PO4)2(OH)6 compound formation under conditions of hydrothermal treatment at 200 °C of a suspension obtained at 25 °C as a result of the nanocrystalline hexagonal BiPO4 and the amorphous phase precipitation, increases in the 5 – 9 pH range specified for this water-salt suspension. The rate of this compound formation decreases under conditions of isothermal exposure of the initial suspension with pH 11. This is due to the increased solubility under these conditions of the amorphous phase, predominantly consisting of aluminum hydroxide. Thermodynamic calculation of phase equilibria at 200 °C in the BiAl3(PO4)2(OH)6-BiPO4-Al(OH)3-H2O(HNO3, NaOH) system showed that the BiAl3(PO4)2(OH)6 compound, resulting from the water-salt suspension treatment, is stable in the 4.2–11.7 pH range specified for this suspension. It was experimentally established that this compound is not formed under conditions of hydrothermal treatment of the suspension with the specified pH 3. This is consistent with the calculation results and is explained by the increased stability of nanocrystalline BiPO4 under these conditions.

A study on the vapor–liquid equilibria of vinyl acrylate-acetic acid and vinyl acetate-acetic acid with GEMC method

Vinyl acetate (VAc) is one of the widely utilized industrial organic raw materials. In the acetoxylation of ethylene to vinyl acetate, there is a by-product vinyl acrylate. However, the vapor–liquid phase equilibrium data of this component with acetic acid and vinyl acetate have not been reported. Here, by Density Functional Theory calculations, we fitted the TraPPE-UA force field parameters of vinyl acrylate. The vapor–liquid phase equilibrium data of the vinyl acrylate-acetate and vinyl acrylate-vinyl acetate binary systems were calculated using the Gibbs Ensemble Monte Carlo (GEMC) method. The calculated phase equilibrium data were utilized to fit the binary interaction parameters of the NRTL equations for the binary systems which were used for the separation process simulation of the vinyl acrylate, acetic acid and vinyl acetate systems. It was verified that the TraPPE-UA force field parameters fitted in this paper have high accuracy. The results clarify the concentration distribution of vinyl acrylate gas–liquid phase components in the distillation column, which builds the foundation for the development of the separation process.

Deep learning–assisted phase equilibrium analysis for producing natural hydrogen

The development of natural hydrogen is an emerging topic in the current energy transition trend. The production process involves compositional multiphase flow via subsurface porous media. This makes studying the compositional phase equilibrium behavior essential for reliable reservoir simulation and prediction. Herein, we develop an iterative flash calculation scheme and a deep learning algorithm using a thermodynamics-informed neural network (TINN) to perform accurate, robust, and fast phase equilibrium calculations for realistic fluid mixtures of natural hydrogen. The application of TINN architecture can accelerate the calculations for nearly 20 times. The effect of capillarity on phase equilibrium states is demonstrated. Based on simulation results, suggestions for the natural hydrogen industry chain are provided to control the possible phase transitions under certain environmental conditions that may be observed in the natural hydrogen reservoirs, storage and transportation facilities. The extremely low critical temperature of hydrogen challenges the robustness of flash calculations but facilitates the separation of impurities by liquefying certain undesired species. Moreover, phase transitions under control can be an effective approach for carbon dioxide capture and sequestration with optimized operating conditions over the phase equilibrium analysis.