Phase Equilibrium Calculations Research Articles

Investigation on Stabilization of Ladle Furnace Slag with Different Additives

Ladle furnace slag disintegrates into fine powder during cooling due to phase transformations of di-calcium silicate. This creates an adverse impact on working conditions and the environment by dust generation. In this paper, a short overview on different studies to overcome the disintegration problem is provided. An attempt was also made to study the effects of several different additives and their mixtures on disintegration of slag. Phase equilibria calculations were carried out for some additives using FactSage® to understand the phase changes in the slag. Based on the phase equilibria calculations and literature data, initial laboratory experiments were conducted at 1650 °C with different additives such as boric acid, aluminium, and fly ash. Slag samples were analyzed with X-ray fluorescence and X-ray powder diffraction for chemical and phase analysis before and after treatment. The disintegration of slag can be prevented either by addition of 0.5 wt% or more of boric acid or 9 wt% of aluminium or 6 wt% of fly ash or 4–8 wt% fly ash along with 0.125–0.25 wt% of boric acid in slag. Based on the optimized conditions, industrial trials were conducted.

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.

Phase equilibrium modelling for multi-component mixtures using highly accurate Helmholtz energy equation of state

Phase stability of a mixture at given conditions is studied. The modelling of equilibrium phase compositions is considered when the original phase of the mixture is unstable. The tangent plane distance criterion is used for stability analysis and the Gibbs energy minimisation is employed for phase equilibrium calculation when the successive substitution does not work well. With the Helmholtz free energy equation of state, thermodynamic properties in single phase and two-phase equilibrium were calculated for methane-ethane mixtures. Phase envelopes were also calculated.

An evaluation on phase behaviors of gas condensate reservoir in cyclic gas injection

Maintaining the reservoir pressure by gas injection is frequently adopted in the development of gas condensate reservoir. The aim of this work is to investigate the phase behavior of condensate oil and remaining condensate gas in the formation under gas injection. The DZT gas condensate reservoir in East China is taken as an example. The multiple contact calculation based on cell-to-cell method and phase equilibrium calculations based on PR Equation of State (EOS) were utilized to evaluate the displacement mechanism and phase behavior change. The research results show that different pure gas has different miscible mechanism in the displacement of condensate oil: vaporizing gas drive for N2 and CH4; condensing gas drive for CO2 and C2H6. Meanwhile, there is a vaporing gas drive rather than a condensing gas drive for injecting produced gas. When the condensate oil is mixed with 0.44 mole fraction of produced gas, the phase behavior of the petroleum mixture reverses, and the condensate oil is converted to condensate gas. About the reinjection of produced gas, the enrichment ability of hydrocarbons is better than that of no-hydrocarbons. After injecting produced gas, retrograde condensation is more difficult to occur, and the remaining condensate gas develops toward dry gas.

A Gibbs free energy minimization based model for liquid–liquid equilibrium calculation of a system containing oil, brine, and surfactant

Accurate and reliable phase equilibrium calculations of microemulsion systems are of great importance. This study deals with the thermodynamic modeling of Liquid–Liquid Equilibrium (LLE) of a system including oil (n-decane), brine (containing CaCl2 salt), and ionic surfactant (sodium dodecyl sulfonate). Two models of UNIQUAC and UNIQUAC + Debye–Hückel were used for thermodynamic calculations. The LLE experimental data were utilized to estimate the binary interaction parameters of UNIQUAC model and the adjustable parameter, b, of the Debye–Hückel model. The thermodynamic model calculates the microemulsion phase’s compositions by minimizing the Gibbs free energy of the LLE system using a combination of genetic algorithm and fmincon function in order to prevent local minima. The thermodynamic modeling results show an appropriate agreement with the experimental data. Accordingly, the presented model of this study can be used as a suitable method to investigate the liquid–liquid equilibrium of systems containing oil, water, and surfactant.

Phase equilibrium modelling for multi-component mixtures using highly accurate Helmholtz energy equation of state

Phase stability of a mixture at given conditions is studied. The modelling of equilibrium phase compositions is considered when the original phase of the mixture is unstable. The tangent plane distance criterion is used for stability analysis and the Gibbs energy minimisation is employed for phase equilibrium calculation when the successive substitution does not work well. With the Helmholtz free energy equation of state, thermodynamic properties in single phase and two-phase equilibrium were calculated for methane-ethane mixtures. Phase envelopes were also calculated.

C and CO Reduction Proportional Fraction with Copper Slag by a Phase Equilibrium Calculation Model (PECM)

The C and CO reduction proportional fraction was studied in this work to evaluate consumption of the reducer accurately. Based on two-step reaction mechanism (TSRM) theory, a phase equilibrium calc...

A new Zr-rich intermetallic phase in an Al-14Si-3Cu-4.5Ni casting alloy with trace additions of Zr

A trace addition of Zr to a multicomponent Al-14Si-3Cu-4.5Ni casting alloy has often been found to form a coarse plate-like Zr-rich intermetallic compound with a size of a few tens of μm at the beginning of solidification. Evaluation of the phase composition has confirmed that the Zr-rich intermetallic phase consists of multicomponent constituent elements, mainly Al, Si, Ni and Fe, and is present in a form of (Al,Si)3(Zr,Ni,Fe). The existence of such a complex (Al,Si)3(Zr,Ni,Fe) phase has not yet been predicted by phase equilibria calculation of the multicomponent Al-14Si-CuNiMg systems. In this paper, transmission electron microscopy studies combined with electron backscattered diffraction pattern analysis reveals the crystallography information of the (Al,Si)3(Zr,Ni,Fe) phase for the first time and identifies it as a modified Al3Zr-D023 crystal (tetragonal, I4/mmm(139)) with slightly changed lattice parameters of a = b = 3.275 Å and c = 15.475 Å. The primary (Al,Si)3(Zr,Ni,Fe) phase is found to nucleate directly onto AlP particles. The mechanical properties of the Zr-rich intermetallics were also investigated using nanoindentation at both room and elevated temperatures and were compared to those of the Si phase.

Simple solvatochromic spectroscopic quantification of long-chain fatty acids for biological toxicity assay in biogas plants.

Oily organic waste is a promising feedstock for anaerobic co-digestion. Free long-chain fatty acids (LCFAs) produced from lipids can inhibit methanogenic consortia, so optimal control of LCFA concentration is the key to successful operation of co-digestion. Most LCFAs are present in the solid phase, making them difficult to be detected and monitored. This study proposes a simple and easy method for detecting LCFAs in both the liquid and solid phases of anaerobic digestate by combining liquid-liquid extraction followed by solid-phase extraction (SPE) and spectrophotometric analysis. The extraction procedure successfully removed impurities that interfere with the absorbance spectrum and ensured high recovery rates of LCFAs. The utility of the pretreatment used for the extraction was discussed using thermodynamic analysis and calculations of phase equilibrium for the solvent extraction system. The absorbance spectrum shift of pyridinium N-phenolate betaine (PNPB) dye-stained solution showed a good correlation with LCFA concentration and enabled highly sensitive measurements. Good quantification was demonstrated in experiments using various digestate samples obtained from the laboratory, pilot, and full-scale reactors.

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.

Mineral Filling Pattern in Complex Fracture System of Carbonate Reservoirs: Implications from Geochemical Modeling of Water-Rock Interaction

Much research has been conducted on physical and numerical modeling that focus on stress state and structural controls on subsurface geofluid flow, yet very few attempts have been made to discover and quantify the mineral precipitation/dissolution kinetics in complex fracture system such as Tarim Basin of China. We conducted a geochemical simulation study using the outcrop fracture networks in Ordovician carbonate rocks in Tabei Outcrop Area of Tarim Basin. Structural analysis, filling analysis within the fracture networks and surrounding rocks were used to constrain the generation and geochemical evolution of the geofluids. Using an advanced reactive transport simulation platform TOUGHREACT, a pertinent thermodynamic system was applied to establish the geological model of the fracture-surrounding rock, where the corresponding calcium carbonate (CaCO3) solution was configured to replace the deep saturated hydrothermal fluids. Different types of mineral parameters were considered with material balance and phase equilibrium calculation to perform numerical simulation of multi-field, e.g., pressure field, temperature field, seepage field and chemical field under formation conditions. The simulation results were consistent with field observations. The major findings of this simulation study include: (1) Along with fluid injection, local dissolution occurred within the fractures and matrix, but with the gradual saturation of calcium ions and the increasing pH value, considerable calcite precipitation occurred. (2) The dissolution/precipitation in different fractures was mainly affected by their structure and physical properties, resulting in changes in fluid flow rate, temperature, pressure and ion concentration over time. (3) In the same group, the degree of mineral filling of small-aperture fractures, low-angle fractures and shallow fractures was significantly higher than other types of fractures. (4) The better the connectivity between reticular fractures and the higher the linear density of fractures, the lower the mineral filling degree. (5) Dissolution phenomenon strengthened within large-aperture conjugated fractures gradually along the flow direction. The proposed methodologies in this study can be applied to model effective fracture filling of other deep reservoirs.

Thermodynamic modelling of the Ni–Zr system

In this work, we report the thermodynamic modelling of the Ni–Zr system using the Calphad method combined with ab initio calculations. Density functional theory (DFT) is employed to calculate the enthalpy of formation of the intermediate phases. The calculated enthalpies of formation are in close agreement with the experimental data. An approach based on special quasirandom structures (SQS) was used for calculating the enthalpy of mixing of the fcc solid solution. The vibrational contribution to the heat capacities of NiZr, NiZr2, Ni3Zr and Ni7Zr2 phases were calculated using the quasiharmonic approximation (QHA) and the corresponding electronic contribution was obtained using an approach based on Mermin statistics. The total heat capacities for these phases were fitted to appropriate expressions and integrated to obtain the Gibbs energy functions valid down to 0 K. The calculated thermochemical properties along with critically selected experimental constitutional and thermochemical data served as input for the thermodynamic optimisation of the system. The calculated phase equilibria and the thermodynamic properties using the optimised Gibbs energy functions are in good agreement with the input data. The calculated congruent melting points of NiZr and NiZr2 phases are close to the recent experimental data. The Ni10Z7 phase forms by a peritectic reaction, which is also in agreement with the experimental data.

Influence of confinement effect on recovery mechanisms of CO2-enhanced tight-oil recovery process considering critical properties shift, capillarity and adsorption

The primary focus of this study is to develop an understanding of the role of confinement effect during CO2 injection by proposing a new phase equilibrium calculation model, which also accounts for critical properties shift, capillarity and adsorption behavior. An iterative algorithm based on updating of the compositions of components in the bulk phases has been developed to calculate phase equilibrium properties. This new and improved model has been validated by experiment results. Results show that the adsorption behavior would increase the interfacial tension and capillary pressure, and the state of phase equilibrium is greatly affected by pore size. Using findings from our model, relationships between the confinement effect and important recovery mechanisms in CO2 injection, such as, extraction of light hydrocarbons, minimum miscible pressure with oil, diffusivity and mass transfer, oil solubility and viscosity reduction have been investigated. We note that the confinement effect contributes to a decrease in CO2 extraction capability of lighter hydrocarbons, and, to a lower minimum miscible pressure with the oil. On the other hand, the confinement effect could cause an increase in the CO2 diffusion coefficient in the liquid phase with a reduction in the pore size. The mass transfer seems to be enhanced with confinement effect. The CO2 solubility in tigth oil increases and the viscosity of dissolved oil phase could be higher. In general, the confinement effect appears to have a positive impact on the recovery mechanisms of CO2 injection in tight reservoirs.

The Origin of Garnets in Anatectic Rocks from the Eastern Himalayan Syntaxis, Southeastern Tibet: Constraints from Major and Trace Element Zoning and Phase Equilibrium Relationships

AbstractAmphibolite- and granulite-facies metamorphic rocks are common in the eastern Himalayan syntaxis of southeastern Tibet. These rocks are composed mainly of gneiss, amphibolite and schist that underwent various degrees of migmatization to produce leucogranites, pegmatites and felsic veins. Zircon U–Pb dating of biotite gneiss, leucocratic vein and vein granite from the syntaxis yields consistent ages of ∼49 Ma, indicating crustal anatexis during continental collision between India and Asia. Garnets in these rocks are categorized into peritecitc and anatectic varieties based on their mode of occurrence, mineral inclusions and major- and trace-element zoning. The peritectic garnets mainly occur in the biotite gneiss (mesosome layer) and leucocratic veins. They are anhedral and contain abundant mineral inclusions such as high-Ti biotites and quartz, and show almost homogeneous major-element compositions (except Ca) and decreasing HREE contents from core to rim, indicating growth during the P- and T-increasing anatexis. Peak anatectic conditions at 760–800°C and 9–10·5 kbar are well constrained by phase equilibrium calculations, mineral assemblages, and garnet isopleths. In contrast, anatectic garnets only occur in the vein granite. They are round or subhedral, contain quartz inclusions, and exhibit increasing spessartine and trace-element contents from core to rim. The garnet–biotite geothermometry and the garnet–biotite–plagioclase–quartz geobarometry suggest that the anatectic garnets crystallized at ∼620–650°C and 4–5 kbar. Some garnet grains show two-stage zoning in major and trace elements, with the core similar to the peritectic garnet but the rim similar to the anatectic garnet. Mineralogy, whole-rock major- and trace-element compositions and zircon O isotopes indicate that the two types of leucosomes were produced by hydration (water-present) melting and dehydration (water-absent) melting, respectively. The leucocratic veins contain peritectic garnet but no K-feldspar, have lower whole-rock K2O contents and Rb/Sr ratios, higher whole-rock CaO contents and Sr/Ba ratios, and show homogeneous δ18O values that are lower than those of relict zircons, indicating that such veins were produced by the hydration melting. In contrast, the vein granite contains peritectic garnet and K-feldspar, has higher whole-rock K2O contents and Rb/Sr ratios, lower whole-rock CaO contents and Sr/Ba ratios, and shows comparable δ18O values with those of relict zircons, suggesting that this granite were generated by the dehydration melting. Accordingly, both hydration and dehydration melting mechanisms have occurred in the eastern Himalayan syntaxis.

Tidal Response of Mars Constrained From Laboratory‐Based Viscoelastic Dissipation Models and Geophysical Data

AbstractWe employ laboratory‐based grain size‐ and temperature‐sensitive rheological models to describe the viscoelastic behavior and tidal response of terrestrial bodies with focus on Mars. We consider five rheological models: Maxwell, extended Burgers, Andrade, Sundberg‐Cooper, and a power law approximation. The question of which model provides the most appropriate description of dissipation in planetary bodies, remains an open issue. To examine this, we build crust and mantle models of Mars (density and elasticity) that are computed self‐consistently through phase equilibrium calculations as a function of pressure, temperature, and bulk composition, whereas core properties are based on an Fe‐S parameterization. We assess the compatibility of the viscoelastic models by inverting tidal response, mean density, and moment of inertia of Mars for its thermal, elastic, and attenuation structure. Our results show that although all viscoelastic models fit the data, (1) their predictions of the tidal response at other periods and harmonic degrees are distinct, implying that our approach can be used to distinguish between the various models from seismic and/or tidal observations (e.g., with InSight), and (2) Maxwell is only capable of fitting data for unrealistically low viscosities. All viscoelastic models converge upon similar interior structure models: large liquid cores (1,750–1,890 km in radius) that contain 17–20.5 wt% S and, consequently, no silicate perovskite‐dominated lower mantle. Finally, the methodology proposed here is generally formulated and applicable to other solar and extrasolar system bodies where the study of tidal dissipation presents an important means for determining interior structure.

Designing high entropy alloy-ceramic eutectic composites of MoNbRe0.5TaW(TiC)x with high compressive strength

Combining the advantages of composites and eutectic high entropy alloys, novel MoNbRe0.5TaW(TiC)x high entropy alloy-ceramic eutectic composites with high strength were successfully designed and investigated based on the computer assisted thermodynamic calculation. The MoNbRe0.5TaW(TiC)x composites are composed of body-centered cubic (BCC) solid solution and multi-component (MC) carbide with face-centered cubic (FCC) structure. With increasing TiC addition, microstructure exhibits an evolution from hypo-eutectic to eutectic and then to hyper-eutectic, which is explained by the solidification process analysis in calculated equilibrium phase diagram. The MoNbRe0.5TaW(TiC)x composites possess high strength. The MoNbRe0.5TaW(TiC)1.0 fully eutectic composite has the highest compressive strength of 1943 ± 13 MPa with high yield strength of 1496 ± 17 MPa. The strengthening mechanism is contributed by the synthetic effect of second-phase and boundary strengthening.

Calculation of thermodynamic equilibria with the predictive electrolyte model COSMO-RS-ES: Improvements for low permittivity systems

The predictive electrolyte model COSMO-RS-ES is refined to improve the description of systems at 25 °C in which strong ion pairing is expected due to a low static permittivity of the liquid phase. Furthermore, the short-range ion energy interaction equations have been modified to better describe the interactions between ions and solvent molecules. In addition, the salt solubility database is extended with additional non-aqueous systems containing solvents that have a low (εs<15) dielectric constant and promote near to full ion association. Throughout this work it is demonstrated that liquid-liquid equilibrium calculations and solid-liquid equilibrium predictions for electrolyte systems can be markedly improved with the inclusion of Bjerrum treatment based phenomenological considerations while introducing only one general additional parameter. Our modified approach reinforces the capabilities of COSMO-RS-ES as a powerful predictive tool for the calculation of phase equilibria in systems with scarce experimental data.

Practical application of machine learning on fast phase equilibrium calculations in compositional reservoir simulations

To accurately describe the fluid phase behaviour in reservoir simulation, Equation-of-State-based compositional models are usually used. However, phase equilibrium calculations, including stability tests and phase splitting calculations, may require huge computational costs. An improved artificial neural network model is developed based on our previous work to achieve the prediction of phase stability with high accuracy and reduce the computational costs in order of magnitude. This model does not directly tell if a hydrocarbon mixture at given compositions, pressure and temperature is stable or unstable, and it is able to predict the saturation pressures. By comparing the given pressure with the predicted saturation pressure, it is natural to tell the stability of a hydrocarbon mixture. For the phase splitting calculations, another artificial neural network model is developed to provide more reliable initial guesses for commonly used equilibrium methods to reduce their nonlinear iterations. Compared with our previous work, multi-layer neural networks are employed in the models. The improved models have more efficient training processes and more accurate prediction results. Additionally, an adaptive data generation process is introduced to optimize the quality and size of training data; the data transformation and normalization are discussed to reduce the skewness of the data and rescale the data; and a model training and selection strategy is also discussed to efficiently train a high-quality model. The efficiency of the ANN models is first validated by standalone phase equilibrium calculations with a three-component hydrocarbon mixture. Then the ANN models are successfully applied in compositional simulation examples, which demonstrates the practical value of these ANN models on speeding up the phase equilibrium calculations during compositional simulations.

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.

Thermodynamics of an austenitic stainless steel (AISI-348) under in situ TEM heavy ion irradiation

The stability of the face-centred cubic austenite (γ-Fe) phase in a commercial stainless steel (AISI-348) was investigated through in situ transmission electron microscopy (TEM) with heavy ion irradiation at 1073 K up to a fluence of 1.3×1017 ions⋅cm−2 (corresponding to a dose of 46 dpa). The γ-Fe phase was observed to decompose at a fluence of around 7.8×1015 ions⋅cm−2 (3 dpa) when a new phase nucleated and grew upon increasing irradiation dose. Scanning transmission electron microscopy (STEM) with energy dispersive X-ray (EDX) spectroscopy and multivariate statistical analysis (MVSA) were used to characterise the irradiated specimens. The combination of such experimental techniques with calculated equilibrium phase diagrams using the CALPHAD method led to the conclusion that the new phase formed upon irradiation is the body-centred cubic Cr-rich α' phase. At the nanoscale, precipitation of M23C6 (τ-carbide) was also observed. The results indicate that ion irradiation can assist the austenitic stainless steel to reach a non-equilibrium state similar to a calculated equilibrium state observed at lower temperatures.