Solid Liquid Vapor Research Articles

A simple theoretical model for condensed-phase equilibria based on a hard-sphere equation-of-state and its applications

Detailed knowledge of solid–liquid phase transitions is not only of academic interest but is also important for industrial-process applications, such as the use of high-pressure crystallization as a separation method. In previous reports, we have studied solid–liquid phase equilibria of several binary-systems containing aromatic compounds, using our unified solid–liquid–vapor equation-of-state (EOS), and demonstrated that our EOS method can be successfully applied to such systems. However, the procedure of analyses is rather complicated and not necessarily straightforward. In this report, we develop a much simpler model for condensed-phase behaviors. The model is based on our previously reported hard-sphere EOS. Successful applications to real compound systems are demonstrated.

Phase equilibria of benzene–cyclohexane binary mixtures using a solid–liquid–vapor equation-of-state

Based on our previously developed solid–liquid–vapor equation of state (EOS), we have calculated phase equilibria of benzene, cyclohexane, and their mixtures. The model predictions for phase behaviors of pure compounds and vapor–liquid phase equilibria of the binary system have been straightforward and agreed well with the reported data. However, solid–liquid phase equilibria of the binary system are not well correlated to the experimental data with the present unified EOS model. Then, from this fact, we have found that the coexisting solid phases in the present binary system exist in two different solid structures (or two different Gibbs free-energy curves). We have developed a model to overcome such a problem within the present unified EOS model and successfully correlated the experimental data for wide ranges of temperatures and pressures.

Solid–liquid–vapor phases of water and water–carbon dioxide mixtures using a simple analytical equation of state

Recently we have proposed a unified analytical equation of state (EOS) for solid–liquid–vapor phases, and successfully applied the EOS for the solid–liquid–vapor states of pure substances, as well as binary mixtures. The present study is an extension of the earlier EOS work to water and its binary mixtures with carbon dioxide. It is found that the proposed EOS can describe reasonably well the thermodynamic properties of water (having unordinary melting/freezing behaviors) around the triple point, although to set up the EOS parameters requires a special procedure different from the ordinary compounds like CO 2. A simplified version of EOS for water has also been developed by sacrificing accuracy in some of the water properties, in order to model water-containing mixtures. Using such a simplified EOS of water, we examine the feasibility of phase behavior prediction including the solid (clathrate hydrate) state for binary mixtures of water and CO 2. All important three-phase (triple-point) equilibrium lines (vapor–liquid–liquid, solid–liquid–liquid, solid–liquid–vapor equilibria) are fairly well predicted, using only the information of vapor–liquid equilibrium data and the quadruple points. Results are still tentative but are encouraging for further improvement. This is a completely new way to model the clathrate-forming system.

Extended UNIQUAC model for correlation and prediction of vapor–liquid–liquid–solid equilibria in aqueous salt systems containing non-electrolytes. Part B. Alcohol (ethanol, propanols, butanols)–water–salt systems

The Extended UNIQUAC model for electrolyte solutions is an excess Gibbs energy function consisting of a Debye–Hückel term and a term corresponding to the UNIQUAC equation. For vapor–liquid equilibrium calculations, the fugacities of gas-phase components are calculated with the Soave–Redlich–Kwong equation of state. The model only requires binary, temperature-dependent interaction parameters. It has previously been used to describe the excess Gibbs energy for aqueous electrolyte mixtures and aqueous electrolyte systems containing methanol. It has been found to be an adequate model for representing solid–liquid–vapor equilibrium and thermal property data for strongly non-ideal systems. In this work, the model is extended to aqueous salt systems containing higher alcohols. The calculations are based on an extensive database consisting of salt solubility data, vapor liquid equilibrium data, and liquid–liquid equilibrium data for solvent mixtures and for mixed solvent–electrolyte systems. The application of this model to represent the vapor–liquid–liquid–solid equilibria in aqueous systems containing various non-electrolytes (ethanol, 1-propanol, 2-propanol, 1-butanol, 2- butanol, 2-methyl 1-propanol, 2-methyl 2-propanol) and various ions (Na +, K +, NH 4 +, Cl −, NO 3 −, SO 4 2−, SO 3 2−, HSO 3 −, CO 3 2−, and HCO 3 −) shows the capability of the model to accurately represent the phase behavior of these kinds of systems.

A robust strategy for SVL equilibrium calculations at high pressures

This work is focused on the analysis of some relevant aspects involved in the solid–vapor–liquid (SVL) equilibrium modeling at high pressure: the parameter estimation of cubic equations of state commonly used in the literature and the application of a stability test to accomplish the calculations. Conversely to the current literature, it is shown in this work that the proposed scheme for phase equilibrium calculations coupled with a stability test enable computation of all SVL systems using a unified and efficient strategy. For this purpose, three systems presented in the literature were used as problem examples to demonstrate the success of the approach developed. The results indicate that the proposed methodology allows fast computations and provide reliable results for SVL equilibrium systems at high pressures.

Compositional effects of fluids on spreading, adhesion and wettability in porous media

The interfacial phenomena of spreading and adhesion of fluids on rock surfaces have serious implications because of their impact on production strategy and oil recovery. The present study reports new experimental data on the effect of brine dilution and surfactant addition on spreading and adhesion behavior of Yates crude oil on dolomite surfaces. Spreading and adhesion have been characterized through measurements of oil–water interfacial tension (IFT) and dynamic (water-advancing and receding) contact angles. The interfacial tension was measured using computerized axisymmetric drop shape analysis (CADSA) technique, which was calibrated against the well-known du Nuoy Ring technique. The dual-drop dual-crystal (DDDC) technique and the Wilhelmy plate technique have been used to measure dynamic contact angles. In order to study the effect of brine dilution, Yates reservoir brine was mixed with deionized water (DIW) in various proportions. The oil–water IFT initially decreased as the volume percent of brine in the mixture decreased but IFT increased with further dilution of reservoir brine with DIW. A decreasing trend was observed in the behavior of water-advancing contact angle with brine dilution. However, a strange behavior of spreading of crude oil drop against brine on the dolomite surface (with large water-receding contact angles) was observed at certain brine dilutions. This spreading of crude oil appears to be related to interfacial tension in a manner similar to Zisman’s observations in solid–liquid–vapor systems. The use of surfactants to enhance oil recovery through reduction in IFT is well known in the industry. However, this study examines the capability of certain surfactants to alter wettability in addition to reducing IFT. For the Yates reservoir rock-fluids system, an ethoxy alcohol surfactant altered the strongly oil-wet nature (advancing angle of 158°) to water-wet (advancing angle of 39°) at a concentration of 3500 ppm. While the DDDC technique yielded significant changes in wettability due to surfactant addition, the Wilhelmy Plate technique remained insensitive throughout the range of surfactant concentrations. The practical significance of this study is that it identifies two simple modes through surfactant addition and brine dilution to alter wettability to minimize capillary trapping of oil.

Phase Behaviors of Binary Hard-Sphere Mixtures Using Simple Analytical Equations of State

Recently, we have proposed a unified analytical equation of state (EOS) for solid–liquid–vapor states of matter, and have examined the thermodynamic properties of argon, carbon dioxide, and methane, as well as binary mixtures of methane and carbon dioxide. Also it has been demonstrated that the EOS can be applied for the solid–fluid transition of hard spheres, by eliminating the attractive part of the EOS. The present work is an extension of the earlier calculations for identical hard spheres, and here we examine the phase behavior of binary hard-sphere mixtures. The hard-sphere EOS employed in this study is $$P = \frac{{RT}}{{V - b}}\left( {\frac{{V - d}}{{V - c}}} \right)^k ,$$ where k = 1 or 2, and k = 0 [or c = d = 0] as a special case. b, c, and d are proportional to a hard-sphere volume, and their mixing rule is a quadratic form in mole fraction x, with a mixing parameter l ij (l ij = l ji and l ii = 0). The b parameter is given by $$b = \sum\limits_{i,j = 1}^2 {\frac{{\left( {b_i + b_j } \right)}}{2}} \left( {1 - 1_{ij} } \right)x_i x_j .$$ Similar mixing rules are applied to c and d. It is shown that various fundamental phase-transition behaviors can be described: ideal or near ideal, azeotropic (maximum and minimum), eutectic, eutectoid, monotectic, peritectic types, and stable fluid–fluid de-mixings without becoming metastable due to the interference of solid–liquid phase transitions. Rather complicated phase diagrams with a combination of various types are also predicted. The present study is a starting point and is useful for understanding the global topology of solid–liquid–vapor phase transitions of binary mixtures.

Data evaluations and quantitative predictive models for vapor pressures of polycyclic aromatic hydrocarbons at different temperatures

Polycyclic aromatic hydrocarbons (PAHs) are typical and ubiquitous organic pollutants. Vapor pressures, which can be classified as solid vapor pressure (P S) and (subcooled) liquid vapor pressure (P L), are key physicochemical properties governing the environmental fate of organic pollutants. It is of great importance to develop predictive models of vapor pressures. In the present study, partial least squares (PLS) regression together with 15 theoretical molecular structural descriptors was used to develop quantitative predictive models for vapor pressures of PAHs at different temperatures. Two procedures were adopted to develop the optimal predictive models by eliminating redundant molecular structural descriptors. The cross-validated values for the obtained models have been found higher than 0.975, indicating good predictive ability and robustness of the models. It has been shown that the intermolecular dispersive interactions played a leading role in governing the values of log P L. In addition to dispersive interactions, dipole–dipole interactions also played a secondary role in determining the magnitude of log P S. In view of the scarceness of chemical standards for some PAHs, the difficulty in experimental determinations, and the high cost involved in experimental determinations, the obtained models should serve as a fast and simple first approximation of the vapor pressure values for PAHs at different environmental temperatures.

Effect of pressure on the complete phase behavior of binary mixtures

AbstractUsing Gibbs‐Duhem integration and semigrand canonical Monte Carlo simulations, temperature vs. composition phase diagrams for a binary Lennard‐Jones mixture, σ11/σ22 = 0.85 and ϵ11/ϵ22 = 1.6, are calculated at several reduced pressures in order to examine the effects of pressure on complete phase behavior (that is, equilibrium between vapor, liquid, and solid phases). Interference is observed between the vapor–liquid and solid–liquid coexistence regions at the lowest pressure. As the pressure increases, the vapor–liquid coexistence region shifts to higher temperatures, while the solid–liquid coexistence region remains essentially unaffected. Eventually, the vapor–liquid coexistence region lifts off the solid–liquid coexistence region, ending the interference. Pressure vs. temperature projections for binary Lennard‐Jones mixtures at σ11/σ22 = 0.85, 0.9, and 0.95, and ϵ11/ϵ22 = 0.45 and 1.6 are also presented to explore how the three‐phase loci (solid–liquid–vapor and solid–solid–liquid) change with variations in diameter ratio and well‐depth ratio. It is found that as the diameter ratio decreases, the maximum pressure in the solid–liquid–vapor locus decreases and the characteristic shape of the solid–liquid coexistence region changes from peritectic to eutectic. As the well‐depth ratio decreases, the maximum pressure in the solid–liquid–vapor locus increases. For one mixture, σ11/σ22 = 0.9 and ϵ11/ϵ22 = 1.6, a quadruple point of solid–solid–liquid–vapor coexistence is located. © 2004 American Institute of Chemical Engineers AIChE J, 50: 215–225, 2004

The effect of interface deformation due to gravity on line tension measurement by the capillary rise in a conical tube

Abstract Much research has been done on line tension measurement and interpretation, and attempts have also been made to measure line tension with simple, cheap and reliable methods that do not require excessive sophistication. Of particular interest is the method of determining line tensions of solid–liquid–vapor systems from the capillary rise in a conical tube. This simple and relatively inexpensive method gives line tension values comparable to those reported in the literature obtained via highly sophisticated instruments or techniques such as the well known axisymmetric drop shape analysis technique. The absolute value of line tension obtained using the conical tube method and assuming a spherical liquid–vapor interface is larger but of the same order of magnitude (1 μJ m−1) as that reported in the literature. A theoretical analysis presented herein shows that by including the deformation of the liquid–vapor interface due to gravity in the conical capillary analysis, the line tension value inferred from the experimental data is reduced by approximately 50% and compares better with values in the literature obtained using other sophisticated methods. Thus a relatively simple, cheap, accurate and reliable method of line tension measurement has been advanced.

The atomic detail of a wetting/de-wetting flow

Atomistic simulation is used to study flow in the vicinity of the advancing (wetting) and receding (de-wetting) solid–liquid–vapor contact lines of a two-dimensional (in the mean) liquid drop in thermodynamic equilibrium with its own vapor and moving steadily on an atomically smooth solid surface under the influence of an applied body force. Wetting and de-wetting are found to be asymmetric, counter to some predictions based on linear theory. There is a rolling flow of the liquid in the drop and a dividing streamline extends from the wetting common line into the displaced vapor as observed macroscopically. At the de-wetting common line there is substantial evaporation, which alters the flow field behind the drop. Evaporation is also observed above the advancing contact line, but there is a net mass flux into the drop right at the contact line. There is evidence of slip flow just in advance of the wetting contact line, but not at the de-wetting line. Results are discussed in the context of phase-field models.

A Systematic Method to Predict Cloud Point Temperature and Solid Precipitation

Solid precipitations (or depositions) in crude oil operations are undesirable because they may eventually plug the process equipment and/or pipelines; as such, accurate prediction of cloud point temperature is essential in the design and operation of many oil production facilities. Determining the cloud point temperature of a mixture requires a robust solution of a multiphase, multicomponent phase equilibrium problem. Solution of the phase equilibrium problem rests on the relations set by the Gibbs criterion for stable equilibrium and the principle of mass conservation. Mathematically, two solution methods are used to characterize the equilibrium properties of a mixture at given temperature and pressure: the equal-fugacity (iteration-function formulation) and the Gibbs free energy minimization approach. In addition, an accurate solution model capable of predicting multiphase formation is required. In this study, we implement the iteration function method enhanced with a solid–liquid–vapor phase-check procedure to calculate cloud point temperatures and the amount of solid precipitations. The Peng-Robinson equation of state with a modified α function, as suggested by Gasem et al. ([2001]), was utilized to model vapor–liquid equilibria while regular solution theory was used to describe solid-liquid equilibria. We also present a systematic method to characterize the heavy components of oil. The results of this study are in excellent agreement with experimental cloud point temperature and solid precipitation data for four North Sea oils reported by Pedersen et al. ([1991]).

Vapour spreading and the boiling crisis

The boiling crisis (BC) is well known in the world of heat and mass transfer. It isa transition from nucleate boiling (i.e. boiling in its usual sense) to film boiling,where the heater is covered by a continuous vapour film. The BC is observedwhen the heat flux from the heater exceeds a critical value. Heat exchange thenfalls down and endangers the exchanger whose temperature rises abruptly. Thephysical mechanism of the BC is still under debate. We propose the recoil force(the thrust of vapour production) at the solid–liquid–vapour contact line to lie atthe origin of the BC. At large heat flux, the recoil force tends to spread thevapour bubble that otherwise would not wet the solid. We give both analyticaland numerical analysis in support of this idea. We also report experiments undermicrogravity conditions performed with near-critical fluids (SF6 and CO2). Theabsence of gravity effects and the vicinity of the critical point where theliquid–vapour surface tension vanishes emphasize the influence of therecoil force: during heating, the vapour drop is indeed seen to spread.

Extending Wertheim’s perturbation theory to the solid phase of Lennard-Jones chains: Determination of the global phase diagram

Wertheim’s first order thermodynamic perturbation theory (TPT1) [M. S. Wertheim, J. Chem. Phys. 87, 7323 (1987)] is extended to model the solid phase of chains whose monomers interact via a Lennard-Jones potential. Such an extension requires the free energy and contact values of the radial distribution function for the Lennard-Jones reference system in the solid phase. Computer simulations have been performed to determine the structural properties of the monomer Lennard-Jones system in the solid phase for a broad range of temperatures and densities. Computer simulations of dimer Lennard-Jones molecules in the solid phase have also been carried out. The theoretical results for the equation of state, the internal energy, and the sublimation curve of the dimer model in the solid phase are in excellent agreement with the simulation data. The extended theory is used to determine the global (solid–liquid–vapor) phase diagram of the LJ dimer model; the theoretical estimate of the triple point temperature for the LJ dimer is T*=0.653. Similarly, Wertheim’s TPT1 is used to determine the global phase diagram of chains formed by up to 8 monomer units. It is found that the calculated triple point temperature is hardly affected by the chain length, and that for large chain lengths the fluid–solid equilibrium coexistence densities are virtually independent of the number of monomers in the chain when the densities are expressed in monomer units. This is in agreement with experimental indications observed in polyethylene, where both the critical and the triple point temperatures tend to finite values for large molecular weights.

Spreading of Cu–Si alloys on oxidized SiC in vacuum: experimental results and modelling

The wetting behaviour of a Cu–40 at.% Si alloy, non-reactive with SiC, on oxidized (0001) faces of α-SiC single crystals is studied at temperatures close to the melting point of copper by the “dispensed drop” technique under high vacuum. The experiments focused on wetting kinetics to determine the mechanisms controlling the rate of spreading under conditions allowing for “in situ” deoxidation of silicon carbide. It is shown that spreading occurs in three stages: (i) an initial stage consisting of a rapid spreading of the alloy on the oxidized SiC up to a contact angle which is close to that on vitreous silica, (ii) a second stage with a zero spreading rate during which the alloy goes through the oxide layer by dissolution near the triple line allowing an intimate contact between the alloy and the SiC surface to be established, and (iii) a final stage during which the alloy spreads with a constant rate up to a contact angle equal to that of clean SiC. These results are interpreted on the basis of a dissolution–diffusion–evaporation process occurring in the vicinity of the solid–liquid–vapour triple line.

P-T-X Phase Equilibrium in the Zn-Te System

P-T-X data are the thermodynamic basis for modeling the crystal growth of materials with controlled stoichiometry. In this paper results of the first direct experimental measurement of the total vapor pressure are reported for three-phase equilibria SLV (solid-liquid-vapor) and VLS (vapor-liquid-solid) in Zn-Te, and the P-T projection of the P-T-X phase diagram is constructed. Geometrical analysis of the phase equilibrium showed that three congruent processes are observed in the Zn-Te system: congruent melting (S = L), sublimation (S = V), and vaporization (L = V). All three congruent curves are tangent to SLV. Consequently, all three congruent points are on the Te-side of the maximum melting point of ZnTe. The vapor pressure scanning method was applied to determine the maximum non-stoichiometry as a function of the temperature. The solidus volume of ZnTe was shown to be on the Te-side of the stoichiometric plane.

Monte Carlo simulations of complete phase diagrams for binary Lennard–Jones mixtures

Vapor–liquid, vapor–solid, liquid–liquid, and liquid–solid coexistence lines are calculated for binary mixtures of Lennard–Jones spheres with diameter ratio σ 11/ σ 22=0.85, well-depth ratio ϵ 11/ ϵ 22=0.45, and binary interaction parameters δ 12=1.0, 0.9, and 0.75, using Monte Carlo simulation and the Gibbs–Duhem integration technique. These calculations allow us to construct complete phase diagrams, i.e. showing equilibrium between vapor, liquid, and solid phases. For the mixture with δ 12=1, we find a completely miscible vapor–liquid coexistence region with a eutectic solid–liquid coexistence region. These two regions are separated by a completely miscible liquid phase. For the mixtures with δ 12<1, we find that the vapor–liquid and solid–liquid coexistence regions interfere. This interference results in a vapor–solid coexistence region bounded above and below by solid–liquid–vapor coexistence lines. We also find that the mixtures with δ 12<1 have a region of liquid–liquid immiscibility that is metastable with respect to the solid–fluid phase equilibria.

Determination of the quench velocity and rewetting temperature of hot surfaces. Part II: an integrated approach of hydrodynamic–thermodynamic micro- and macro-scale models

A new integrated approach, comprising hydrodynamic–thermodynamic micro- and macro-scale models, for analysis of rewetting systems is presented. This new approach facilitates concurrent prediction of rewetting temperature, T rew *, and quench velocity, U rew *, for a wide range of system properties. To this end, the previously developed, micro-scale hydrodynamic model is combined with a thermodynamic model and the resulting algorithm is used to derive relations between the quench velocity and rewetting temperature. This combined micro-scale thermodynamic–hydrodynamic model is then interfaced with a known macro-scale model. The former predicts a physically feasible relation between rewetting temperature and quench velocity, as dictated by the physical properties and geometry of the phases involved in the micro-scale, three-phase contact zone. This model uses iterative algorithm that seeks the conditions where the contact angle predicted by the hydrodynamic and thermodynamic models match. Results of application of the combined model to several groups of liquids, with diverse thermo-physical properties, are presented. The calculated rewetting temperature is a monotonic increasing function of the quench velocity, for all liquids investigated, and the contact angle decreases with an increase of temperature. Higher rewetting temperatures and smaller contact angles are produced by increasing the intermolecular force as expressed by the parameter ε ω / kT c. The versatility of the model and its sensitivity to small increments in the iteration procedure used in the combined model is demonstrated for the unique case of helium. The mean slope (MS) of the rewetting temperature–quench velocity curve for liquids that pertain to the same group is shown to be nearly invariable. This is a new characteristic property of rewetting systems. The macro-scale model involves operational constraints that are imposed on the system and consequently a macro-scale relation between the rewetting temperature and quench velocity is set. The intersection between the microscopic, physically feasible, and the macroscopically imposed relations of rewetting temperature and quench velocity yields ( T rew *, U rew *) that is expected to prevail, for the given conditions of the system. This intersection is required for rewetting to exist. Otherwise, no rewetting is possible, as either complete wetting or non-wetting characterizes the behavior of the system. The new integrated approach is free of the need for assumptions regarding the value of either T rew or U rew, as both are obtained as its output. This work, which completes the series on determination of quench velocity and rewetting temperature on hot surfaces, relies completely on thermo-physical properties of the solid–liquid–vapor system and its operating conditions, without the need for additional assumed inputs. In this sense, the rewetting system can be fully described, once its own micro- and macro-scale properties and constraints are known.

Drop size dependence of contact angles of oil drops on a solid surface in water

Contact angle is a fundamental quantity in colloid and surface science. Of all the methods employed to measure the contact angles, direct measurement from sessile drops is probably the most popular approach. However, it has long been found that the measured contact angle is not unique for a given solid–liquid–fluid system. There are two types of contact angle multiple-value phenomena — the drop size dependence of contact angles and the contact angle hysteresis. In the literature, the contact angle dependence on the liquid drop size for the solid–liquid–vapour systems has been studied extensively. In this paper, the contact angle dependence on the oil drop size for a solid–oil–water system is measured by applying the axisymmetric drop shape analysis (ADSA) technique. More specifically, a natural sedimentation method is employed to deposit drops of a silicone oil with a density slightly higher than that of water onto the hydrophobic FC725 coated glass slide in the deionized ultra filtered (DIUF) water. It has been observed that the measured equilibrium contact angle decreases by approximately 7.3° as the equilibrium base radius of the silicone oil drop increases from 0.0205 to 0.4684 cm. According to the modified Young equation, the measured contact angle changes are then interpreted in terms of the so-called line tension effect. The line tension of the solid–oil–water system is found to be 0.82 μJ m −1, which is very close to those for similar solid–oil–air systems. Unlike other conventional drop formation methods, the natural sedimentation method used in this study can eliminate all the appreciable mechanical disturbance and vibrations. Furthermore, this deposition can generate liquid drops in a much larger range of drop size such that the line tension effect becomes much more pronounced.

High Pressure Phase Equilibria in the Systems Ammonia+Potassium Iodide, +Sodium Iodide, +Sodium Bromide, and +Sodium Thiocyanate: Solid–Liquid–Vapor and Liquid–Liquid–Vapor Equilibria

Solid salt liquid vapor equilibria and liquid liquid vapor equilibria were determined experimentally for the binary system NH 3 + KI in the temperature range 333 to 673 K and at pressures up to 80 MPa. It is found that the system NH 3 + KI belongs to Type V of fluid phase behavior according to the classification of van Konynenburg and Scott. The pressure of the three-phase curve solid salt liquid vapor is monotonically increasing in the temperature range investigated and reaches a value of 76 MPa at 670 K. The three-phase liquid liquid vapor curve starts in a lower critical end point at 407.3 K and 11.59 MPa and ends in an upper critical end point at 408.8 K and 11.92 MPa. For the systems NH 3 + NaI, NH 3 + NaBr, and NH 3 + NaSCN, Type V fluid phase behavior is also found, In the system NH 3 + NaI, the lower critical end point is found at 406.8 K and 11.52 MPa and the upper critical end point at 408.5 K and 11.86 MPa. For the system NH 3 + NaBr, these coordinates are 404.6 K. 11.03 MPa and 408.8 K, 11.90 MPa, respectively, and, for the system NH 3 + NaSCN, 409.2 K, 11.99 MPa and 409.6 K, 12.06 MPa.