Retrograde Behavior Research Articles

Phase equilibria, thermodynamic properties, and solubility of quartz in saline-aqueous-carbonic fluids: Application to orogenic and intrusion-related gold deposits

Hydrothermal fluids in orogenic and intrusion-related (mesothermal) gold deposits are dominated by saline-aqueous-carbonic fluids, commonly represented by the ternary system H2O-NaCl-CO2. The phase equilibria, thermodynamic properties (PVTx, density, compositions of fluid phases) and quartz dissolution-precipitation behavior in the H2O-NaCl-CO2 system, which are still poorly constrained, are of great importance to understanding the process of hydrothermal gold mineralization. Here, we conducted thermodynamic modeling to constrain the fluid properties under single- and two-phase conditions in the H2O-NaCl-CO2 system at temperatures of 300 to 500 °C and pressures of 0.001 to 3.5 kbar. Our results illustrate thermodynamic controls rooted in the equilibria of the H2O-NaCl-CO2 system. Increasing CO2 and/or NaCl contents shift the solvus to higher pressures and temperatures, expanding the pressure–temperature region of L + V immiscibility. Calculated isopleths of CO2 content in coexisting, immiscible vapor and liquid describe the maximum amount of CO2 that may be present in fluid inclusions through the studied P-T-x ranges. Quartz solubility in the H2O-NaCl-CO2 fluids shows strong dependence on temperature, pressure, and CO2 content, with several potential triggers for vein mineral deposition. Specifically, solubility of quartz generally decreases with decreasing temperature, pressure, and increasing CO2 content both in the single- and two-phase fluids, but exhibits retrograde behavior in the L + V field or at the phase-transition boundary. In detail, the dependence of quartz solubility on pressure is weak at low temperatures (300 °C), and becomes progressively stronger at high temperatures (400 °C and 500 °C), vice versa for temperature dependency at different pressures.The present study reviews two mechanisms of fluid immiscibility and constrain the conditions at which distinct fluid inclusion types, bedding-parallel shear veins and fault-related extension veins are formed in mesothermal gold deposits. Thermodynamic modeling of the solvus of the H2O-NaCl-CO2 system is consistent with the hypothesis that decompression is an efficient mechanism driving fluid immiscibility at specific ranges of temperature and composition, producing coexisting liquid- and vapor-phase fluids, both with low density and relatively low content of CO2. For fluids with high CO2 contents (>10 mol. %), cooling at relatively high pressure may also lead to fluid immiscibility, producing a liquid with low CO2 content in equilibrium with a vapor of medium to high CO2 content. Very CO2-rich, or “pure CO2” fluid inclusions (>90 mol. % CO2, type I) cannot be produced by immiscibility under these conditions, but may rather be the result of decrepitation of primary H2O-NaCl-CO2 fluid inclusions. Within the P-T-x ranges studied here, cooling-dominated phase separation accounts for the formation of fluid inclusions with moderate to high CO2 contents (50–80 mol. % CO2, type IIa). Fluid inclusions with low to moderate CO2 contents (5–30 mol. % CO2, type IIb) can represent the original ore-forming fluids, or can be produced by decompression-dominated phase separation. And H2O-NaCl fluid inclusions (type III) generally represent the latest-stage ore-forming fluids, or can be produced by decompression-induced immiscibility at high temperature. In orogenic (mesothermal) gold deposits, decompression-induced quartz precipitation during pressure fluctuation is dominant in bedding-parallel shear veins. Fault-related extension veins are associated with initial decompression-induced quartz precipitation and subsequent cooling-dominated deposition.

What is the Diagnosis?

One image and tracings were obtained during the para-Hisian stimulation maneuver in an electrophysiological study. The question is: is there any retrograde nodal or extranodal conduction behavior?

Experimental study and thermodynamic modeling of clathrate hydrate stability conditions in carbon dioxide + cyclopentane + water system: Retrograde region

In this study, hydrate dissociation conditions for the carbon dioxide + cyclopentane + water system were measured. The pressure-search method at constant volume was employed to measure equilibrium conditions in the temperature range from 287.4–293.1 K and pressure range from 0.99–4.78 MPa. The results exhibit a retrograde behavior at pressures above 4 MPa for this system. Also, the experiments show that cyclopentane would significantly promote carbon dioxide hydrate stability conditions. In addition, based on the minimization of Gibbs free energy, a multiphase flash calculation was performed using the van der Waals and Platteeuw (vdW-P) solid solution theory along with the cubic plus association (CPA) equation of state to predict gas hydrate stability conditions. Modeling results are found in good agreement with the experimental data even in the retrograde region.

Supercritical carbon dioxide extraction of pomegranate (Punica granatum L.) seed oil: Kinetic modelling and solubility evaluation

Experimental and modelling investigations of supercritical fluid CO2 extraction (SC-CO2) of pomegranate seed oil (PSO) were performed at 240, 280 and 320 bar, and 40, 50 and 60 °C with CO2 flow rate of 8 kg/h. A retrograde solubility behaviour was found at 50 °C and 280 bar. The model of broken and intact cells developed by Sovová adequately described SC-CO2 processes (AARD% 0.2497-1.1691). It was demonstrated that the extraction of type A was the most suited to apply. The solubility of PSO in SC-CO2 was estimated and modelled by Chrastil model (AARD% 0.1910-1.1821). The highest value of the oil solubility was obtained at 320 bar and 60 °C. PSO extracted by SC-CO2 was found high-quality, evaluated in terms of antioxidant activity, and richer of punicic acid as compared to Soxhlet extracted oil.

Solubility of cefuroxime axetil in supercritical CO2: Measurement and modeling

In this study, an analytical dynamic method was optimized for small amounts of drugs and used to measure the solubility of cefuroxime axetil in supercritical CO2. After validating the experimental procedure with nimesulide, an active ingredient already studied in the literature, the solubility of cefuroxime axetil in supercritical CO2 was measured at temperatures varying from 308 to 328 K and pressures ranging between 8 and 25 MPa. Experimental values varied between 2.2 × 10−7 and 11.24 × 10-6 (in mole fraction) and a retrograde solubility behavior was observed.The solubility was correlated with semi-empirical density-based models: Kumar and Johnston, Mendez-Santiago and Teja, and Chrastil models. All three models successfully correlated the solubilities of cefuroxime axetil with an average deviation lower than 15%.

Comparative Analysis of Pressure Regions of Gaseous Benzene Using Ground Activated Carbon Sorbents Under Ambient Conditions

The effective removal of atmospheric hazardous pollutants using activated carbon for the real-world application is a crucial and reliable process. Therefore, the performance comparison of ground activated carbon BPL 4×6 (ACb212) based on varied outlet pressure of benzene vapour were analyzed in ambient condition (room temperature and pressure). The maximum adsorption capacity was found ~110 mg. g-1) for all pressure regions. However, the competition showed maximum capacity for higher pressure region i.e., 50.5 mg. g-1, minimum capacity at lower pressure region 7.96 mg. g-1, and moderate for moderate outlet pressure 20.6 mg. g-1. On the other hand, the partition coefficient (PC) behaved inversely to the sorption capacity i.e., high PC (397 mol.kg-1. Pa-1) at the low outlet and low PC (1.47 mol.kg-1. Pa-1) at high outlet benzene partial pressure regions. The adsorption capacity on ACb212 followed the classical Langmuir isotherm of Type-1 at low and high-pressure outlet pressure regions, while a retrograde behaviour isotherm (Type-1) was observed for lowest benzene outlet partial pressure region. Furthermore, the linearized Langmuir isotherm analysis also confirmed the existence of two or more sorption sites for gaseous benzene.

Comparative Analysis of Pressure Regions of Gaseous Benzene Using Ground Activated Carbon Sorbents Under Ambient Conditions

The effective removal of atmospheric hazardous pollutants using activated carbon for the real-world application is a crucial and reliable process. Therefore, the performance comparison of ground activated carbon BPL 4×6 (ACb212) based on varied outlet pressure of benzene vapour were analyzed in ambient condition (room temperature and pressure). The maximum adsorption capacity was found ~110 mg. g-1) for all pressure regions. However, the competition showed maximum capacity for higher pressure region i.e., 50.5 mg. g-1, minimum capacity at lower pressure region 7.96 mg. g-1, and moderate for moderate outlet pressure 20.6 mg. g-1. On the other hand, the partition coefficient (PC) behaved inversely to the sorption capacity i.e., high PC (397 mol.kg-1. Pa-1) at the low outlet and low PC (1.47 mol.kg-1. Pa-1) at high outlet benzene partial pressure regions. The adsorption capacity on ACb212 followed the classical Langmuir isotherm of Type-1 at low and high-pressure outlet pressure regions, while a retrograde behaviour isotherm (Type-1) was observed for lowest benzene outlet partial pressure region. Furthermore, the linearized Langmuir isotherm analysis also confirmed the existence of two or more sorption sites for gaseous benzene.

Density-based phase envelope construction

A new density-based phase envelope construction procedure is proposed. The equations for two-phase saturation molar density and temperature computations are established by equating to zero the tangent plane distance (TPD) function in terms of component molar densities and temperature to find a non-trivial set of component molar densities at various specifications: mixture molar density, temperature and the modified equilibrium constants. The latter are defined as the ratios of feed to incipient phase component molar density. The nonlinear system of equations is solved by the full Newton method. The sequence of calculations is started at some conditions where convergence is easily obtained and an extrapolation procedure provides high quality initial guesses for subsequent calculations. The phase envelope is traced in the molar density-temperature plane, where a unique saturation temperature exists at specified mixture molar density; the representation in the pressure-temperature plane is obtained by calculating explicitly the pressure from the equation of state at given temperature and component molar densities on the saturation curve. The equation of state (EoS) must not be solved for volume and the elements of the Jacobian matrix have simpler expressions than their conventional (pressure-based) counterparts. The proposed method is successfully tested for a variety of mixtures, ranging from binary and ternary mixtures to reservoir fluids, exhibiting usual (closed) and unusual phase envelopes, such as open-shaped envelopes characterized by a bubble point branch extending to infinity, branches with negative pressures constructed in a single run (unlike in the conventional case), several branches, double retrograde behavior and swallowtail pattern corresponding to liquid demixing at low temperatures. The proposed method is not dependent of the thermodynamic model and any pressure-explicit equation of state can be used, provided the required partial derivatives of fugacity and pressure with respect to mole numbers, temperature and volume are available.

Global phase behaviour in carbon dioxide plus n-alkanes binary mixtures

The family of carbon dioxide (CO2) plus linear alkanes is one of the most common type of mixtures found in supercritical CO2 separation and extraction. Consequently, an accurate thermodynamic representation is a key element for a proper process design. In this contribution, the PPC-SAFT equation of state is applied to the construction of the serial-prediction-domain global phase diagram (spd-GPD) of the CO2 plus n-alkanes series to carefully analyse the presence of different thermodynamic phenomena. The goal is to address the capability of the equation to predict the global behaviour of these mixtures, with emphasis in accurately reproducing their mechanisms and topology. The results obtained reveal quantitative agreement with the available experimental data, including a complete description of the emergence of different phenomena as a function of the hydrocarbon chain length, such as azeotropy, double retrograde behaviour, critical transitions, mass and molar density inversions and critical pressure step points.

Integrated Characterization and a Tuning Strategy for the PVT Analysis of Representative Fluids in a Gas Condensate Reservoir

Gas condensate reservoirs are characterized by a distinctive retrograde behavior and potential for condensate drop out during production and sampling. Efficient modeling of gas condensate reservoir requires careful phase behavior studies of samples collected prior to and during the production life of reservoir. In this work, an integrated characterization and tuning algorithm is proposed to analyze the pressure-volume-temperature (PVT) behavior of gas condensate samples. Each characterization and tuning scenario is described by a “path” which specifies the class of fluid, splitting and lumping (if any), the type of correlation, and grouping strategy (static or dynamic). Different characterization approaches were tested for the effective description of heavy end. Meanwhile, dynamic and static strategies were implemented to tune the equation of state (EOS) through non-linear regression. The optimum combination of characterization and tuning approach was explored for each sample by a rigorous analysis of the results. It was found out that the exponential distribution function gives the best performance for heavy end characterization in a dynamic tuning strategy. Also, analyses indicate that using higher single carbon number may not necessarily make EOS tuning more accurate. In addition, the optimum step is reached in either the third or fourth step for most cases in a dynamic tuning approach, and is sensitive neither to the characterization path nor to the selected end carbon number.

Wave propagation reversal for wavy vortices in wide-gap counter-rotating cylindrical Couette flow.

We present a numerical study of wavy supercritical cylindrical Couette flow between counter-rotating cylinders in which the wavy pattern propagates either prograde with the inner cylinder or retrograde opposite the rotation of the inner cylinder. The wave propagation reversals from prograde to retrograde and vice versa occur at distinct values of the inner cylinder Reynolds number when the associated frequency of the wavy instability vanishes. The reversal occurs for both twofold and threefold symmetric wavy vortices. Moreover, the wave propagation reversal only occurs for sufficiently strong counter-rotation. The flow pattern reversal appears to be intrinsic in the system as either periodic boundary conditions or fixed end wall boundary conditions for different system sizes always result in the wave propagation reversal. We present a detailed bifurcation sequence and parameter space diagram with respect to retrograde behavior of wavy flows. The retrograde propagation of the instability occurs when the inner Reynolds number is about two times the outer Reynolds number. The mechanism for the retrograde propagation is associated with the inviscidly unstable region near the inner cylinder and the direction of the global average azimuthal velocity. Flow dynamics, spatio-temporal behavior, global mean angular velocity, and torque of the flow with the wavy pattern are explored.

Preparation of solid-state micro- and nanocellular acrylonitrile-butadiene-styrene (ABS) foams using sub- and supercritical CO2 as blowing agents

In this work, micro- and nanocellular acrylonitrile-butadiene-styrene (ABS) foams were prepared by using sub- and supercritical CO2 as blowing agents. The sorption kinetics at 10MPa was first measured. The sorption amount depended on the saturation temperature Arrheniusly. The diffusivities did not follow the Arrhenius relation. This relation was interpreted by a retrograde behavior of ABS/CO2 system. From the kinetics, ABS discs were saturated at 10MPa at the temperatures from −20°C to 40°C, and foamed at the foaming temperature of 20°C–80°C. A network of closed cells with a diameter of 600–700nm and nanopores with a diameter of 100nm were observed in the foam obtained at low saturation temperatures and high foaming temperatures. The closed cell densities were in a range from 1.12×1012−9.87×1012 cells/cm3 and an experimental correlation based on the CNT model was used to fit the data.

Retrograde behavior revisited: implications for confined fluid phase equilibria in nanopores.

Many fluid mixtures exhibit retrograde behavior, including those that define natural gases. While the behavior is well understood for mixtures in bulk, it is not so in nanosize porous space that dominates shale formations in unconventional reservoirs. The lack of experimental data creates the need for modeling works to make estimates as good as possible due to immediate needs in gas recovery. However, such efforts have been straying without firm guidance from systematic studies over what we have known so far. This article is intended to present the results of such a study that would incite further investigations in this area of research. Revisiting the retrograde behavior in the bulk is appropriate to start with, followed by a short review of what we know about fluids confined in nanosize pores. Based on this information, implications for the behavior of confined mixtures in the retrograde region can be inferred. The implied features that have been supported by experimental evidence are the locations of the confined dew point and bubble point at low temperatures, which are both at pressures lower than their bulk counterparts. Another feature found in this study is completely new, and therefore still open for further investigation. We reveal that the dew-point and bubble-point curves of confined mixtures end at moderate pressures on a multiphase curve, beyond which equilibrium occurs among the bulk and confined phases. The well-known points in the bulk retrograde region, i.e. the critical point and cricondenbar, are consequently absent in confined mixtures.

Direct detection of double retrograde behavior in binary systems for equation of state models

In this work, a straightforward methodology is proposed to establish at a glance, for binary systems, whether a model of the equation of state type predicts the occurrence of double retrograde behavior (DRB), and to also establish what the ranges of conditions of DRB existence are. This is accomplished by computing three hyper-lines, which usually are highly non linear. One of them is the vapor–liquid critical line. The other two are loci of cricondenbar points and of cricondentherm points. Each line is efficiently calculated in a single computer run by resorting to a robust numerical continuation method.

Phase diagrams for hydrates beyond incipient condition — Complex behavior in methane/propane and carbon dioxide/iso-butane hydrates

We have recently developed an algorithm for multiphase equilibrium calculations and stability analysis involving hydrates. This algorithm allows phase equilibrium calculations in scenarios presenting different number of phases that may also be in distinct physical states.Here, we present P×T phase diagrams calculated using our algorithm that involve mixed hydrates of natural gas beyond incipient condition and show complex behavior. Our phase diagrams show a global overview of the behavior of phase equilibrium involving hydrates in a mixture of water, methane and propane and in a mixture of water, carbon dioxide and iso-butane. We accomplish that using a global phase diagram in a wide range of pressure and temperature to show diverse phase equilibrium regions.We present an approach to tune the Peng–Robinson equation of state to improve the calculations of the chemical potential of water in liquid state at high pressure and therefore, improve the prediction of the phase equilibrium between this phase and ice or hydrates, up to pressure conditions as high as 100 MPa.Our calculations predict 3-phase equilibrium regions and 4-phase equilibrium univariant lines in binary hydrates of methane and propane and in binary hydrates of carbon dioxide and iso-butane. We use local phase diagrams highlighting details in regions with complex behavior of phase equilibrium to show how the phase boundary isopleths and univariant lines relate in a phase diagram for water, methane and propane.Our calculations for a mixture of water, carbon dioxide and iso-butane predicts structural transitions occurring below the dew point line of the guest components, in a mixture with excess of guest components, and 5- phase equilibrium invariant point. We show equilibrium lines that present retrograde behavior in the phase diagram for this mixture.

Global phase behaviour in methane plus n-alkanes binary mixtures

The methane plus linear alkanes series is one of the simpler and most common type of mixtures presented in the industry and its accurate representation is paramount because of the diversity of its applications. From a theoretical perspective, its structural simplicity due to the low degree of synergy and the absence of short-range dispersive forces suggests that a good model should represent these systems with acceptable accuracy. Based on these ideas and the relatively regular behaviour of n-alkanes, these systems have become particularly suitable for trial calculation in convoluted models, in order to verify their capabilities in both quantitative and qualitative predictions. In this contribution, the soft-SAFT equation of state is used for the construction of the serial prediction domain global phase diagram (spd-GPD) of the methane plus linear alkanes series. The main goal is to address the capability of the equation of state to predict the global behaviour of the binary mixtures until methane plus n-decane, with special emphasis in accurately reproducing the mechanism and topology of mixtures. All systems shown here are predicted with quantitative accuracy, including a complete description of their taxonomy. The information obtained from the equation of state allows the validation of some predictions of the spd-GPD in the absence of experimental data. Following this analysis, the double retrograde behaviour lies between the methane plus propane and methane plus n-butane systems, while the tricritical transition of the series is found between the methane plus n-pentane and methane plus n-hexane mixtures. Also, the presence of the molar density inversion phenomenon is predicted to begin between the methane plus n-hexane and methane plus n-heptane systems, while no signals of mass density inversions are found on these mixtures.

Heterovalent Dopant Incorporation for Bandgap and Type Engineering of Perovskite Crystals.

Controllable doping of semiconductors is a fundamental technological requirement for electronic and optoelectronic devices. As intrinsic semiconductors, hybrid perovskites have so far been a phenomenal success in photovoltaics. The inability to dope these materials heterovalently (or aliovalently) has greatly limited their wider utilizations in electronics. Here we show an efficient in situ chemical route that achieves the controlled incorporation of trivalent cations (Bi(3+), Au(3+), or In(3+)) by exploiting the retrograde solubility behavior of perovskites. We term the new method dopant incorporation in the retrograde regime. We achieve Bi(3+) incorporation that leads to bandgap tuning (∼300 meV), 10(4) fold enhancement in electrical conductivity, and a change in the sign of majority charge carriers from positive to negative. This work demonstrates the successful incorporation of dopants into perovskite crystals while preserving the host lattice structure, opening new avenues to tailor the electronic and optoelectronic properties of this rapidly emerging class of solution-processed semiconductors.

Network modelling and prediction of retrograde gas behaviour in natural gas pipeline systems

As retrograde gases are transported through pipeline systems, retrograde condensation may occur. The presence of this additional liquid phase is responsible for additional pressure losses in natural gas surface production systems. Gases and liquids have markedly different routing behaviour when moving concurrently through a network system and the determination of their distribution within the network is of vital importance for retrograde gas surface transportation operations. This study is aimed at developing and testing an analytical tool that predicts phase behaviour of retrograde gas in natural gas pipeline systems. This tool will allow operators to make better decisions regarding liquid phase removal from the network, pressure loss mitigation, design and location of surface production and separation equipment with an accurate map of the pressure, phase distribution and phase property inside the network. The proposed network model for retrograde gas is able to handle realistic field situations and allows the user to effectively track liquid and gas preferential routing within the network and provide guidance for improving the performance of the entire gas pipeline system.

Pore diameter effects on phase behavior of a gas condensate in graphitic one-and two-dimensional nanopores

Molecular dynamics (MD) simulations were performed on a hydrocarbon mixture representing a typical gas condensate composed mostly of methane and other small molecules with small fractions of heavier hydrocarbons, representative of mixtures found in tight shale reservoirs. The fluid was examined both in bulk and confined to graphitic nano-scale slits and pores. Numerous widths and diameters of slits and pores respectively were examined under variable pressures at 300 K in order to find conditions in which the fluid at the center of the apertures would not be affected by capillary condensation due to the oil-wet walls. For the bulk fluid, retrograde phase behavior was verified by liquid volumes obtained from Voronoi tessellations. In cases of both one and two-dimensional confinement, for the smallest apertures, heavy molecules aggregated inside the pore space and compression of the gas outside the solid structure lead to decreases in density of the confined fluid. Normal density/pressure relationships were observed for slits having gaps of above 3 nm and pores having diameters above 6 nm. At 70 bar, the minimum gap width at which the fluid could pass through the center of slits without condensation effects was predicted to be 6 nm and the corresponding diameter in pores was predicted to be 8 nm. The models suggest that in nanoscale networks involving pores smaller than these limiting dimensions, capillary condensation should significantly impede transmission of natural gases with similar composition.

Dendritic growth velocities in an undercooled melt of pure nickel under static magnetic fields: A test of theory with convection

Dendritic growth velocities in an undercooled melt of pure nickel under static magnetic fields up to 6 T were measured using a high-speed camera. The growth velocities for undercoolings below 120 K are depressed under low magnetic fields, but are recovered progressively under high magnetic fields. This retrograde behavior arises from two competing kinds of magnetohydrodynamics in the melt and becomes indistinguishable for higher undercoolings. The measured data is used for testing of a recent theory of dendritic growth with convection. A reasonable agreement is attained by assuming magnetic field-dependent flow velocities. As is shown, the theory can also account for previous data of dendritic growth kinetics in pure succinonitrile under normal gravity and microgravity conditions. These tests demonstrate the efficiency of the theory which provides a realistic description of dendritic growth kinetics of pure substances with convection.