Equilibrium Phase Behavior Research Articles

Unified Theory of Ultimate Hydrocarbon Recovery for Primary and Cyclic Injection Processes in Ultratight Reservoirs

This paper presents a simple method to estimate ultimate recovery factors (URF) of ultratight reservoirs based on equilibrium by diffusion in which URF is only a function of changes in hydrocarbon density between initial and final states. URF is defined at infinite time and therefore does not depend on the transient behavior. Although URF may not be achievable during the life-cycle of the field development and production, it provides valuable insights on the role of phase behavior. We show that equilibrium phase behavior defines the absolute upper-bound for URF during primary production and explains the poor recovery from shale oil reservoirs compared to the high recovery factor in shale gas reservoirs in a unifying way. Further, we quantify how injected solvent compositions (CH4, CO2, N2, and C2H6) during huff’n’puff enhanced oil recovery (EOR) improve recovery based on density reduction and compositional dilution, and show that the largest percentage increase in recovery occurs for heavier oils. Our calculations provide a practical means to define the URF from primary production as a function of reservoir fluid composition, temperature, and pressure drawdown. In addition, our calculations articulate incremental URF (IURF) of solvent huff‘n’puff based on net solvent transfer into ultratight rock, which is a key design consideration. The results illustrate that solvent transfer dilutes the hydrocarbons in place, thus maximizing long-term hydrocarbon recovery. Net mass transfer can be improved by enhancing the diffusion of solvent into the matrix based on the huff‘n’puff design parameters including solvent composition, drawdown pressure, and the net amount of solvent injected based on optimal frequency and cycle duration.

Classical nucleation theory for the crystallization kinetics in sheared liquids.

While statistical mechanics provides a comprehensive framework for the understanding of equilibrium phase behavior, predicting the kinetics of phase transformations remains a challenge. Classical nucleation theory (CNT) provides a thermodynamic framework to relate the nucleation rate to thermodynamic quantities such as pressure difference and interfacial tension through the nucleation work necessary to spawn critical nuclei. However, it remains unclear whether such an approach can be extended to the crystallization of driven melts that are subjected to mechanical stresses and flows. Here, we demonstrate numerically for hard spheres that the impact of simple shear on the crystallization rate can be rationalized within the CNT framework by an additional elastic work proportional to the droplet volume. We extract the local stress and strain inside solid droplets, which yield size-dependent values for the shear modulus that are about half of the bulk value. Finally, we show that for a complete description one also has to take into account the change of interfacial work between the strained droplet and the sheared liquid. From scaling reasons, we expect this extra contribution to dominate the work formation of small nuclei but become negligible compared to the elastic work for droplets composed of a few hundreds of particles.

Solid–Liquid Phase Equilibrium and Phase Behaviors for Binary Mixtures Composed of Tripalmitoylglycerol (PPP), 1,3-Dipalmitoyl-2-oleoyl-glycerol (POP), and 1,2-Dioleoyl-3-palmitoyl-glycerol (POO)

The crystallization and melting behaviors of binary tripalmitoylglycerol (PPP)/1,2-dioleoyl-3-palmitoyl glycerol (POO), tripalmitoylglycerol (PPP)/1,3-dipalmitoyl-2-oleoyl glycerol (POP), and 1,3-d...

A coarse grained simulation study on the morphology of ABA triblock copolymers

The Dissipative Particle Dynamics (DPD) simulation technique was used to elucidate the composition-dependent equilibrium morphological behavior of three different symmetric ABA triblock copolymers, which were; poly(ε-caprolactone)-poly(dimethylsiloxane)-poly(ε-caprolactone) (PCL-PDMS-PCL), poly(ε-caprolactone)-poly(ethylene oxide)-poly(ε-caprolactone) (PCL-PEO-PCL) and poly(L-lactide)-poly(dimethylsiloxane)-poly(L-lactide) (PLLA-PDMS-PLLA). These polymers were chosen due to their biomedical and biotechnological importance. Polymeric A and B blocks were modeled as connected chain of beads with varying incompatibility. The impact of the block incompatibilities on the microphase separation as well as on the equilibrium phase behaviors were investigated at the mesoscopic scale. A detailed visual analysis of the DPD images and constructed phase diagram showed that quite different equilibrium morphologies were attainable by controlling the molecular weights of the blocks and the strength of the intermolecular interaction between them. More compatible A and B blocks underwent lamellar to cylindrical and cylindrical to spherical phase transitions at lower B block concentrations. Our results clearly showed that, Flory–Huggins interaction parameter (χ) and degree of polymerization (N) were the only control parameters, which determined the shape and size of the phase domains, as well as the extent of equilibrium nanophase separation. Our DPD simulated morphologies were compared with experimental images obtained by Atomic Force Microscopy (AFM).

Rational design of double salt ionic liquids as extraction solvents: Separation of thiophene/n‐octane as example

AbstractAlthough double salt ionic liquids (DSILs) offer significant advantages over classical two‐ion ionic liquids as separation solvents, relevant studies are still scarce and a systematic DSIL selection method is thus highly desirable. In this contribution, a rational method for designing DSILs as extraction solvents is proposed and exemplified by the thiophene/n‐octane separation. The effects of additional degrees of freedom for DSIL design (i.e., double cations and/or anions and the ion ratio) on the thermodynamic properties are first analyzed by COSMO‐RS. Then, a multilevel DSIL design method combining the prediction of infinite dilution thermodynamic properties, the estimation of physical properties, the evaluation of phase equilibrium behavior, and the experimental validation is proposed. By applying this method, [C2MIm][OAc] x[NO3]1‐x (x = [0, 1]) and [C2MIm][OAc] x[SCN]1‐x (x = [0.70, 1]) are identified as promising DSIL solvents for the thiophene/n‐octane separation. Correspondingly, the liquid–liquid equilibria of {DSILs + thiophene + n‐octane} with the designed DSILs are experimentally studied.

Xenon Hydrate as an Analog of Methane Hydrate in Geologic Systems Out of Thermodynamic Equilibrium

AbstractMethane hydrate occurs naturally under pressure and temperature conditions that are not straightforward to replicate experimentally. Xenon has emerged as an attractive laboratory alternative to methane for studying hydrate formation and dissociation in multiphase systems, given that it forms hydrates under milder conditions. However, building reliable analogies between the two hydrates requires systematic comparisons, which are currently lacking. We address this gap by developing a theoretical and computational model of gas hydrates under equilibrium and nonequilibrium conditions. We first compare equilibrium phase behaviors of the Xe·H2O and CH4·H2O systems by calculating their isobaric phase diagram, and then study the nonequilibrium kinetics of interfacial hydrate growth using a phase field model. Our results show that Xe·H2O is a good experimental analog to CH4·H2O, but there are key differences to consider. In particular, the aqueous solubility of xenon is altered by the presence of hydrate, similar to what is observed for methane; but xenon is consistently less soluble than methane. Xenon hydrate has a wider nonstoichiometry region, which could lead to a thicker hydrate layer at the gas‐liquid interface when grown under similar kinetic forcing conditions. For both systems, our numerical calculations reveal that hydrate nonstoichiometry coupled with hydrate formation dynamics leads to a compositional gradient across the hydrate layer, where the stoichiometric ratio increases from the gas‐facing side to the liquid‐facing side. Our analysis suggests that accurate composition measurements could be used to infer the kinetic history of hydrate formation in natural settings where gas is abundant.

Experimental study and thermodynamic modeling of solid-liquid equilibrium of binary systems: Dodecane-tetradedcane and tridecane-pentadecane for cryogenic thermal energy storage

In the present work, the equilibrium phase behaviors and thermal characteristics (phase diagrams, enthalpies, melting/freezing temperatures) of the binary systems dodecane-tetradedcane (C12H26-C14H30) and tridecane-pentadecane (C13H28-C15H32) were experimentally investigated to employ the potential PCMs for cryogenic applications. In addition, the phase diagrams were theoretically obtained by using both the ideal and non-ideal thermodynamic models. Results show that the compositions of eutectic points appear at 18 wt% C14 for the C12-C14 system and 10 wt% C15 for the C13-C15 system. The specific eutectic compositions of these two systems have satisfied enthalpies (158.0 J/g for C12-C14 and 143.1 J/g for C13-C15 in the melting process), slight supercooling (0.3 °C for C12-C14 and 0.4 °C for C13-C15), minor hysteresis (3.9 °C for C12-C14 and 2.2 °C for C13-C15) and superior thermal stability. Therefore, they are very attractive as the candidate PCMs in cryogenic energy storage systems. Moreover, the melting temperatures calculated by the theoretical models agree well with the experimental data. Especially for the non-ideal solubility model, the mean relative deviations are only 4% for the C12-C14 system and 8% for the C13-C15 system, respectively.

Thermodynamic assessment of the hollandite high‐level radioactive waste form

AbstractHollandite has been studied as a candidate ceramic waste form for the disposal of high‐level radioactive waste due to its inherent leach resistance and ability to immobilize alkaline‐earth metals such as Cs and Ba at defined lattice sites in the crystallographic structure. The chemical and structural complexity of hollandite‐type phases developed for high‐level waste immobilization limits the systematic experimental research that is required to understand phase development due to the large number of potential additives and compositional ranges that must be evaluated. Modeling the equilibrium behavior of the complex hollandite‐forming oxide waste system would aid in the design and processing of hollandite waste forms by predicting their thermodynamic stability. Thus, a BaO–Cs2O–TiO2–Cr2O3–Al2O3–Fe2O3–FeO–Ga2O3 thermodynamic database was developed in this work according to the CALPHAD methodology. The compound energy formalism was used to model solid solution phases such as hollandite while the two‐sublattice partially ionic liquid model characterized the oxide melt. Results of model optimizations are presented and discussed including a 1473 K isothermal BaO–Cs2O–TiO2 pseudo‐ternary diagram that extrapolates phase equilibrium behavior to regions not experimentally explored.

CO₂ in Lyotropic Liquid Crystals: Phase Equilibria Behavior and Rheology.

The CO2 absorption of liquid crystalline phases of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (Pluronic L92, (EO)8(PO)47(EO)8), monoethanolamine (MEA), and water, with a composition of 60% L92/10% MEA/30% water has been investigated to assess potential use in carbon capture and storage applications. Vapor–liquid equilibrium data of the liquid crystalline system with CO2 was recorded up to a CO2 partial pressure of 6 bar, where a loading of 38.6 g CO2/kg sample was obtained. Moreover, the phase transitions occurring during the loading process were investigated by small angle X-ray scattering (SAXS), presenting a transition from lamellar + hexagonal phase to hexagonal (at 25 °C). In addition, the rheology of samples with varying loadings was also studied, showing that the viscosity increases with increasing CO2-loading until the phase transition to hexagonal phase is completed. Finally, thermal stability experiments were performed, and revealed that L92 does not contribute to MEA degradation.

Ethanol and methanol Unifac subgroup parameter estimation in the prediction of the liquid-liquid equilibrium of biodiesel systems

The biodiesel conventional production method is based on the homogeneous transesterification reaction, in which the quality and quantity of the raw materials used have considerable effect on the separation of phases of the generated products. The presence of glycerol in biodiesel, for example, has a maximum permissible value of only 0.02% (EM 14214). On the other hand, high purity glycerol needs to be marketed separately. In this way, a better understanding of the phase equilibrium becomes fundamental for the proper design, operation and optimization of the process. In the literature, the thermodynamic modeling focuses on the UNIQUAC and NRTL models. Such models can predict phase equilibrium for each system separately, and the interaction parameters are distinct and unique. However, the use of several types of vegetable or residual oils has been reported for biodiesel production. On the other hand, group-contribution thermodynamic models, such as UNIFAC, could be used to predict the phase equilibrium behavior of reactional biodiesel systems formed from these different types of oils. This work contributes to this subject, providing generalized UNIFAC interaction parameters for the already specified subgroup methanol (CH3OH) and a new specific subgroup, ethanol (CH3CH2OH). The UNIFAC-LL database parameters were used, except for methanol and ethanol subgroups proposed here, for calculations with ten vegetable oils, for which experimental data are available. The mean square error (0.92%, methanol; 1.20%, ethanol) was considerably lower when compared to the available UNIFAC-LL data (10.58%, methanol; 8.89%, ethanol) and work of the literature (2.21%, methanol; 3.92%, ethanol) that uses a greater number of adjustable parameters. The results show that the methodology employed is consistent and can be useful in predicting liquid-liquid phase equilibrium for both reactive methyl and ethyl biodiesel systems considered.

Modeling solubility of refrigerants in ionic liquids using Peng Robinson-Two State equation of state

In recent years ionic liquids (ILs) are introduced as new absorbents for refrigerants in the refrigeration processes. In this paper, we investigate the phase equilibrium behavior of refrigerants and ILs binary solutions as novel potential systems in refrigeration industries. A simple association model namely Peng Robinson-Two State equation of state (PR-TS EoS), is used to model the phase equilibrium data (P-T-x) of 37 various imidazolium-based ionic liquids and refrigerants binary systems at different temperatures and pressures with a total of 969 data points. In the first step, the PR-TS EoS is applied on pure components and the parameters of the model are determined. The percent of average absolute relative deviation (AARD%) between the calculated results and the experimental data of vapor pressures and liquid densities of the refrigerants are 0.58% and 1.59%, respectively. The similar AARD% for the liquid density of the ionic liquids is 0.20%. In the following, the present model is applied to calculate the vapor-liquid equilibrium of refrigerant + IL binary systems. The results of the current model show a deviation as AARD = 3.54%. Also, the performance of the PR-TS EoS is compared with the Peng-Robinson (PR) EoS and Peng Robinson-Kwak Mansoori (PR-KM) EoS. In summary, the results of the PR-TS EoS represent a good agreement with the experiments and the present model shows superiority with respect to PR and PR-KM EoSs.

Phase behavior and morphology of multicomponent liquid mixtures.

Multicomponent systems are ubiquitous in nature and industry. While the physics of few-component liquid mixtures (i.e., binary and ternary ones) is well-understood and routinely taught in undergraduate courses, the thermodynamic and kinetic properties of N-component mixtures with N > 3 have remained relatively unexplored. An example of such a mixture is provided by the intracellular fluid, in which protein-rich droplets phase separate into distinct membraneless organelles. In this work, we investigate equilibrium phase behavior and morphology of N-component liquid mixtures within the Flory-Huggins theory of regular solutions. In order to determine the number of coexisting phases and their compositions, we developed a new algorithm for constructing complete phase diagrams, based on numerical convexification of the discretized free energy landscape. Together with a Cahn-Hilliard approach for kinetics, we employ this method to study mixtures with N = 4 and 5 components. We report on both the coarsening behavior of such systems, as well as the resulting morphologies in three spatial dimensions. We discuss how the number of coexisting phases and their compositions can be extracted with Principal Component Analysis (PCA) and K-means clustering algorithms. Finally, we discuss how one can reverse engineer the interaction parameters and volume fractions of components in order to achieve a range of desired packing structures, such as nested "Russian dolls" and encapsulated Janus droplets.

Ternary phase diagram of phenanthrene and carbazole in different solvents and its application in the separation of them

The separation of phenanthrene (PHE) and carbazole (CAR) has been a tough job since the formation of solid solutions. Development of new separation strategy for PHE-CAR mixture highly depends on their phase equilibrium behaviour. In this work, ternary phase diagrams of phenanthrene (PHE) and carbazole (CAR) in dimethylformamide (DMF), acetone, acetonitrile (MeCN) and toluene at T = 308.15 K under normal atmosphere were determined through wet residue method. It was found that PHE-rich solid solution α was formed in the particular composition range of PHE-end. On the contrary, no CAR-rich solid solution was formed in CAR-end. These results were further verified through powder X-ray diffraction (PXRD) and differential scanning calorimetry (DSC). Based on the ternary phase diagrams, a difference coefficient of solubility (Ds) was put forward to assist screening and evaluation of solvents for solution crystallization. Among the four tested solvents, toluene is the most suitable one for separating PHE-CAR mixture.

Phase equilibrium and dynamic behavior of methane hydrates decomposition via depressurization in the presence of a promoter tert‑butanol

Abstract The vapor–liquid equilibrium (VLE) or vapor–liquid–liquid (VLLE) phase boundaries and the liquid–vapor–hydrate three-phase coexistence pressures are measured at temperatures from 276 K to 285 K for the mixtures of water + methane +9 mass% or 20 mass% of tert‑butanol, a methane hydrate promoter. The Peng–Robinson equation of state is utilized to correlate the VLE data and then to estimate the methane solubility in the liquid phase before and after methane hydrate decomposition. In the presence of tert‑butanol, the dynamic behavior of methane hydrate decomposition is also investigated at temperatures from 276 K to 285 K through a depressurization process. During the course of hydrate dissociation, data acquisition system collects the dynamic data, including temperature profile, pressure, and total volume of released methane. A first-order kinetic model represents satisfactorily the hydrate dissociation behavior. It is found that the rate constant of methane-hydrate dissociation significantly increases by using the promoter, tert‑butanol.

Effect of specific interaction of CO2 with poly(ethylene glycol) on phase behavior

The specific interaction (i.e., Lewis acid-base interaction) between CO2 and the ether group in poly(ethylene glycol) (PEG) is expected to significantly affect the mutual solubility in CO2/PEG systems. Therefore, in order to understand the liquid-liquid equilibrium (LLE) phase behavior under supercritical CO2, the specific intermolecular interaction between CO2 and PEG should be involved in the theoretical modeling of LLE phase behavior for the PEG/CO2 system. In this work, this interaction (i.e., CO2-PEG complex due to the Lewis acid-base interaction) is treated by the perturbed-chain SAFT (PC-SAFT) model as a cross-association between CO2 and PEG. The cross-association energy parameter is estimated from the experimental enthalpy by the Fourier transform IR (FT-IR) spectroscopy method for CO2 and the ether group in PEG. The correlated pressure and temperature (P-T) isopleth curve with the cross-association between CO2 and PEG is much closer to the experimental data. The degree of cross-association decreases as the temperature increases. This strong cross-association leads to a lower critical solution temperature (LCST) phase behavior, even at supercritical conditions.

On the phase diagram of Mackay icosahedra.

Using Monte Carlo and molecular dynamics simulations, we investigate the equilibrium phase behavior of a monodisperse system of Mackay icosahedra. We define the icosahedra as polyatomic molecules composed of a set of Lennard-Jones subparticles arranged on the surface of the Mackay icosahedron. The phase diagram contains a fluid phase, a crystalline phase, and a rotator phase. We find that the attractive icosahedral molecules behave similar to hard geometric icosahedra for which the densest lattice packing and the rotator crystal phase have been identified before. We show that both phases form under attractive interactions as well. When heating the system from the dense crystal packing, there is first a transition to the rotator crystal and then another to a fluid phase.

Equilibrium phase behavior of aqueous two-phase system formed by triblock copolymer + sulfate salt + water at different temperatures

Equilibrium data for the ternary liquid-liquid system formed of a triblock copolymer (L64 or F68), sulfate salts (Cu(II) or Fe(III)) and water were investigated in this work. The effects of temperature (278.15, 288.15 and 298.15 K), the nature of the cation and the copolymer molar mass on the phase diagram of the aqueous two-phase system were investigated. An increase in temperature decreased the biphasic region for the entire system. Cu(II) and F68 were better able to induce phase separation compared to Fe(III) and L64. The nature of the cation and the copolymer molar mass effect are discussed as a function of the formation of aqua acids through the reaction between the cation and water (Brønsted acids) and in relation to Flory-Huggins theory for macromolecule solutions, respectively. The consistencies of the tie line and binodal curve experimental compositions were evaluated by applying the Othmer-Tobias and Merchuk correlations, respectively.

Thermodynamic representation of ionic liquids phase equilibrium with the PDH-Wilson-NRF model

Experimental studies on ionic liquids have shown that a systematic review of the behavior of ionic liquids with thermodynamic models is important. Ionic liquid (ILs) can be introduced as a green solvent and used to replace organic solutions in industrial and academic projects. In this paper, the electrolyte and non-electrolyte were compared by PDH-Wilson-NRF and Wilson-NRF models respectively. Liquid–Liquid equilibrium phase behavior of 10-ILs comprising sulfate-based anions, also included Imidazolium and Pyridinium cations. All systems at 298.15 K and 313 K. Calculation of LLE for 56 ternary (495 Tie-Line) systems were carried out using Wilson-NRF and PDH-Wilson-NRF model. The applied model had very good satisfactory results for electrolyte and non-electrolyte models with rmsd values of 5.762 and 0.273 respectively. Comparison of the results is expressed by root mean square deviation (rmsd) between the experimental and calculated compositions. It is demonstrated that the Wilson-NRF model presents very good satisfactory results with rmsd values of about 0.273 so that this model is highly appropriate to calculate thermodynamic properties of ionic liquid solutions.

Refractive Index and Vapor–Liquid Equilibrium Data for the Binary Systems of Anisole with Xylene Isomers at 93.13 kPa

Phase equilibrium behavior of binary systems of anisole with xylene isomers was analyzed experimentally. An apparatus which establishes equilibrium conditions through continuous circulation of equilibrium vapor condensate and equilibrium liquid was used. Experimental data comprising refractive indices of binary mixtures, equilibrium compositions of vapor and liquid, and equilibrium temperature are reported for all binary systems. Thermodynamic consistency of vapor–liquid equilibrium data was established for using the Herington, Van Ness and absolute mean deviation tests. Interaction parameters of activity coefficient models, Wilson, nonrandom two liquid, and universal quasichemical, which are important for accounting nonideal behavior in process modeling, are also estimated through regression of the respective binary VLE data. Although VLE data shows that binary systems are nonazeotropic in nature, a pinch in the T–x,y plot indicates that separation of all binary system using distillation may need a signi...

Phase Equilibrium Behavior in Mixtures Containing Tributyl Citrate, Citric Acid, Butan-1-ol, and Water

This work focused on the development of the phase equilibria models required to describe the behavior of mixtures involved in the synthesis of tributyl citrate (TBC) via esterification of citric acid (CA) and butan-1-ol (BuOH). Vapor–liquid equilibrium (VLE) for the mixture TBC–BuOH, liquid–liquid equilibrium (LLE) for the ternary mixture TBC–H2O–BuOH, and solubility data for the mixture CA–BuOH–TBC were measured at different temperatures. The thermodynamic consistency was verified with the Wisniak test for VLE data, and the LLE data exhibited linear behavior in an Othmer and Tobias plot. Anhydrous citric acid was characterized by differential scanning calorimetry exhibiting a melting point of 424.9 K, an enthalpy of fusion of 59.2 kJ/mol, an average heat capacity of 255.48 J/mol·K in the evaluated temperature range (320–375 K), and a change of heat capacity from solid to liquid of 236 J/mol·K. Together with reported equilibrium data from the open literature, and the evaluated physicochemical properties, the measured equilibrium data were regressed with the UNIQUAC equation to fit the binary interaction parameters of the components in the mixture. The obtained model agrees well with the whole set of experimental data and can be used for further process design.