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Relevant bibliographies by topics / Phase rule and equilibrium

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Academic literature on the topic 'Phase rule and equilibrium'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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Journal articles on the topic "Phase rule and equilibrium"

1

Seybold, Paul G., Matthew J. O'Malley, Lemont B. Kier, and Chao-Kun Cheng. "Cellular Automata Simulations of Vapor–Liquid Equilibria." Australian Journal of Chemistry 59, no. 12 (2006): 865. http://dx.doi.org/10.1071/ch06230.

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Phase transitions and phase equilibria are among the most fundamental phenomena in the physical and environmental sciences. In the present work an asynchronous stochastic cellular automata model for the equilibrium between a liquid and its vapor is presented. The model is visual, dynamic, and employs just two rules—an attraction probability and a gravitational preference. Application of the attraction rule alone yields a ‘mist’ within the vapor, whereas application of the gravitational rule by itself yields an isothermal atmospheric profile. Application of both rules together causes the vapor to evolve to a liquid phase with a vapor phase above it. Introduction of a third rule for short-range attraction/repulsion more clearly resolves the liquid/vapor interface.

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Shyu, Guor-Shiarn, Nishawn S. M. Hanif, Kenneth R. Hall, and Philip T. Eubank. "Maximum Partial Area Rule for Phase Equilibrium Calculations." Industrial & Engineering Chemistry Research 35, no. 11 (January 1996): 4348–53. http://dx.doi.org/10.1021/ie960203p.

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3

Chiang, C. S., and William C. Johnson. "Coherent phase equilibria in systems possessing a consolute critical point." Journal of Materials Research 4, no. 3 (June 1989): 678–87. http://dx.doi.org/10.1557/jmr.1989.0678.

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The influence of coherency strains on phase equilibria in a two-phase microstructure is examined for a binary or pseudobinary alloy system possessing a consolute critical point (chemical miscibility gap). The qualitative features of phase equilibria, including the limits of metastability (chemical spinodal), are shown to depend critically on the mechanical loading conditions and the geometric arrangement of the phases in the microstructure. If the elastic state of a phase in a two-phase coherent system is independent of the presence of the other phase, then the equilibrium characteristics usually associated with fluid systems should be observed, even though the system is nonhydrostatically stressed. If the elastic state of a phase depends upon the presence of the other phase, then the equilibrium characteristics that have come to be associated with coherent systems should be observed; tie lines and field lines do not coincide, the common tangent construction is invalid, and Gibbs phase rule is not applicable.

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4

Fujita, Hiroshi. "Non-equilibrium phase formation." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 4 (August 1990): 506–7. http://dx.doi.org/10.1017/s0424820100175661.

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The most important advantage of EM’s is in situ experiments on detailed processes of the same phenomena that occur in bulk materials. In recent years, in situ experiments with HVEM’s, in particular with a 3MV ultra-HVEM , has made it possible to create non-equilibrium phases, which do not exist in nature, or to control and design materials on an atomic scale. Namely, HVEM’s have developed to “Micro-Laboratory”, in which various material-treatments can be done, for natural science from powerful tools for characterization and/or identification of materials.l.The General Rule for Solid Amorphization The author and his cowerkers have succeeded in making amorphous solids of intermetallic compounds by high energy electron irradiation. Using the electron irradiation effect, necessary conditions for the formation of both non-equilibrium phases and extremly supersaturated solid structures[3,4] can be easily and precisely controlled.

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5

Liu, Chengjun, Jiyu Qiu, and Zhengyue Liu. "Phase Equilibria in the System CaO-SiO2-La2O3-Nb2O5 at 1400 °C." Metals 11, no. 12 (November 24, 2021): 1892. http://dx.doi.org/10.3390/met11121892.

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CaO-SiO2-La2O3-Nb2O5 system is of great significance for the pyrometallurgical utilization of Bayan Obo tailing resources. In the present work, the phase equilibrium of this quaternary system at 1400 °C was determined by a thermodynamic equilibrium experiment. On the basis of the recently determined CaO-La2O3-Nb2O5 phase diagram, some boundary surfaces of primary phase fields of CaO-SiO2-La2O3-Nb2O5 phase diagram were modified; then, the 1400 °C isothermal surface in the primary phase fields of SiO2, CaNb2O6, Ca2Nb2O7, and LaNbO4 was constructed, respectively. On this basis, CaO-SiO2-Nb2O5 pseudo-ternary phase diagrams with w(La2O3) = 5%, 10%, 15%, and 20% were determined, respectively. Considering the importance of equilibrium crystallization reaction type, we proposed a new rule named Tangent Line Rule to judge the univariant reaction type in the quaternary phase diagram. By applying Tangent Line Rule and Tangent Plane Rule previously proposed, some univariant and bivariant crystallization reaction types in the CaO-SiO2-La2O3- Nb2O5 phase diagram were determined, respectively. The current work can provide original data for the establishment of a thermodynamic database of Nb-bearing and REE-bearing slag system; the proposed Tangent Line Rule will promote the application of a spatial quaternary phase diagram.

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Karim, Abdul M. A., and Arkan J. Hadi. "Thermodynamic Model for High Pressure Phase Behavior of Carbon Dioxide in Several Physical Solvents at Different Temperatures." Tikrit Journal of Engineering Sciences 15, no. 2 (June 30, 2008): 32–50. http://dx.doi.org/10.25130/tjes.15.2.03.

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In the present study a thermodynamic model for prediction of gas-liquid equilibrium at high pressures and different temperatures prepared for the binary systems of carbon dioxide (1) with each of the one of the liquid physical solvents (2) (sulfolane, n-methyl-2-pyrrolidone and propylene carbonate) using Peng-Robenson equation of state (PR-EOS) with different mixing rules to show the effect of the type of mixing rule used. Comparison of the experimental phase equilibrium data in the literature with the results of the model showed very good representation for some mixing rules and good for the others.

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IONIŢĂ, Mihaela, Sergiu SIMA, Martin CISMONDI, and Catinca SECUIANU. "Phase equilibria for the carbon dioxide + cyclopentane + cyclohexane system at high pressures." Revue Roumaine de Chimie 66, no. 3 (2021): 303–8. http://dx.doi.org/10.33224/rrch.2021.66.3.11.

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Isothermal vapor–liquid equilibrium measurements for the ternary mixture carbon dioxide + cyclopentane + cyclohexane at 353.15 K are reported. Phase equilibrium measurements were made in a high-pressure visual cell with variable volume using a static-analytical method with phases sampling by rapid online sample injectors (ROLSI) coupled to a gas chromatograph (GC) for analysis. The new measured data were modelled with the RK–PR equation of state (EoS) coupled with classical van der Waals (two-parameter conventional mixing rule, 2PCMR).

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Colin, Samuel, and Antony Valentini. "Instability of quantum equilibrium in Bohm's dynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2171 (November 8, 2014): 20140288. http://dx.doi.org/10.1098/rspa.2014.0288.

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We consider Bohm's second-order dynamics for arbitrary initial conditions in phase space. In principle, Bohm's dynamics allows for ‘extended’ non-equilibrium, with initial momenta not equal to the gradient of phase of the wave function (as well as initial positions whose distribution departs from the Born rule). We show that extended non-equilibrium does not relax in general and is in fact unstable. This is in sharp contrast with de Broglie's first-order dynamics, for which non-standard momenta are not allowed and which shows an efficient relaxation to the Born rule for positions. On this basis, we argue that, while de Broglie's dynamics is a tenable physical theory, Bohm's dynamics is not. In a world governed by Bohm's dynamics, there would be no reason to expect to see an effective quantum theory today (even approximately), in contradiction with observation.

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DU, P. C., and G. A. MANSOORI. "PHASE EQUILIBRIUM OF MULTICOMPONENT MIXTURES: CONTINUOUS MIXTURE GIBBS FREE ENERGY MINIMIZATION AND PHASE RULE." Chemical Engineering Communications 54, no. 1-6 (May 1987): 139–48. http://dx.doi.org/10.1080/00986448708911903.

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Toikka, Alexander, and Maria Toikka. "Solubility and critical phenomena in reactive liquid–liquid systems." Pure and Applied Chemistry 81, no. 9 (August 19, 2009): 1591–602. http://dx.doi.org/10.1351/pac-con-08-11-04.

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The goal of this work is to consider solubility phenomena in reactive fluid mixtures with liquid-phase splitting. One of the main tasks is to analyze peculiarities of liquid–liquid (LL) systems with equilibrium and nonequilibrium chemical reaction. The special aim is to consider the critical states in these systems. The reactive liquid–liquid equilibrium (LLE) is treated on the base of phase rule. The topology of diagrams of reactive LLE is discussed for some types of binary and ternary systems. Examples are presented of a possible transformation of phase diagrams caused by the shifting of chemical equilibrium and by changes in the shape of the binodal. The transformations resulting in the reactive critical phase formation are considered. Quaternary mixtures are also discussed with the use of experimental data on the solubility in the system with n-propyl acetate synthesis reaction. The mutual crossing of the chemical equilibrium surface and binodal in the composition tetrahedron leads to the origin of the area of simultaneous chemical and LLE with two critical points (reactive critical phases). The shape of the curve of simultaneous chemical and phase equilibrium is also presented in the square of transformed composition variables.

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Dissertations / Theses on the topic "Phase rule and equilibrium"

1

Chu, Jennifer Hsing-chung. "Phase behavior and binary interaction energies of copolymer blends /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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Sankarasubramanian, R. "Symmetry-Breaking Transitions In Equilibrium Shapes Of Coherent Precipitates." Thesis, Indian Institute of Science, 2000. https://etd.iisc.ac.in/handle/2005/191.

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We present a general approach for determining the equilibrium shape of isolated, coherent, misfitting particles by minimizing the sum of elastic and interfacial energies using a synthesis of finite element and optimization techniques. The generality derives from the fact that there is no restriction on the initial or final shape, or on the elastic moduli of the particle and matrix, or on the nature of misfit. The particle shape is parameterized using a set of design variables which are the magnitudes of vectors from a reference point inside the particle to points on the particle/matrix interface. We use a sequential quadratic programming approach to carry out the optimization. Although this approach can be used to find equilibrium shapes of particles in three dimensional systems, we have presented the details of our formulation for two dimensional systems under plane strain conditions. Using our formulation, we have studied the equilibrium shapes in two dimensional systems with cubic anisotropy; the precipitate and matrix phases may have different elastic moduli, and the misfit may be dilatational or non-dilatational. The equilibrium shapes and their size dependence are analysed within the framework of symmetry-breaking shape transitions. These transitions are further characterized in terms their dependence on the cubic elastic anisotropy parameter, defined by A = 2C44/(C11 – C12), and on the modulus mismatch, defined by δ=μp/μm, where /μp and μm are the effective shear moduli of the precipitate and matrix phases, respectively. Depending on the type of misfit, the systems may be classified into the following four cases: Case A: For dilatational misfit, the equilibrium shapes in isotropic systems are circular (with an isotropic or I symmetry) at small sizes and undergo a transition at a critical size to become ellipse-like (with an orthorhombic or O symmetry). This I --O transition is continuous and is obtained only when the precipitate phase is softer than the matrix. These results are in good agreement with the analytical results of Johnson and Cahn. In cubic systems with dilatational misfit, the particles exhibit a transition from square-like shapes (with a tetragonal or T symmetry) at small sizes to rectangle-like shapes (with an O symmetry) at large sizes. This T -- O transition is continuous. It occurs even in systems with stiffer precipitates; however, it is forbidden for systems with δ >δC, where δ C represents a critical modulus mismatch. The critical size decreases with increasing cubic anisotropy (i.e., with increasing values of (A-1)/(A+1). The sides of the square-like and rectangle-like shapes are along the elastically soft directions. Case B: In these systems, the principal misfits e*xx and e*yy differ in magnitude but have the same sign. The precipitates at small sizes become elongated along the direction of lower misfit; this shape has an O symmetry. In systems with A > 1, they continue to become more elongated along the same direction, exhibiting no symmetry-breaking transition. However, in systems with A < 1, particles at large sizes are elongated along an intermediate direction between the direction of lower misfit and one of the elastically soft <11> directions; this shape has only a monoclinic or M symmetry. This O - M transition, in which the mirror symmetries normal to the x and y axes are lost, may be discontinuous or continuous. The critical size increases with δ (in the range 0.8 < δ <1.25), indicating that this transition would also be forbidden for systems with δ > δC. In systems with A < 1, the critical size decreases with increasing values of A-1/ A+1 Case C: In these systems, the principal misfits differ in both magnitude and sign, and the misfit strain tensor allows an invariant line along which the normal strain is zero. The precipitates at small sizes are elongated along the direction of lower absolute misfit, and possess an 0 symmetry. At large sizes, the mirror symmetries normal to the x and y axes are broken to yield shapes which are elongated along a direction between that of lower misfit and the invariant line. This 0 -> M transition is continuous and occurs in all the systems irrespective of the value of A The critical size increases with A and decreases with δ. Case D; The misfit in this case is a special form of that in Case C; the principal misfits have the same magnitude but opposite signs. The precipitates at small sizes have a square-like shape with its sides normal to the < 11 > axes, irrespective of the type of cubic anisotropy. At large sizes, they become rectangle-like with the long axis oriented along one of the <11> directions. Similar to Case C, this T - 0 transition is continuous and occurs in all the systems irrespective of the values of A. The critical size increases with A and decreases with δ. Thus, we have identified all the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two dimensional systems. We have identified their origin and nature, and characterized them in terms of their dependence on the anisotropy parameter and modulus mismatch.

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3

Sankarasubramanian, R. "Symmetry-Breaking Transitions In Equilibrium Shapes Of Coherent Precipitates." Thesis, Indian Institute of Science, 2000. http://hdl.handle.net/2005/191.

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We present a general approach for determining the equilibrium shape of isolated, coherent, misfitting particles by minimizing the sum of elastic and interfacial energies using a synthesis of finite element and optimization techniques. The generality derives from the fact that there is no restriction on the initial or final shape, or on the elastic moduli of the particle and matrix, or on the nature of misfit. The particle shape is parameterized using a set of design variables which are the magnitudes of vectors from a reference point inside the particle to points on the particle/matrix interface. We use a sequential quadratic programming approach to carry out the optimization. Although this approach can be used to find equilibrium shapes of particles in three dimensional systems, we have presented the details of our formulation for two dimensional systems under plane strain conditions. Using our formulation, we have studied the equilibrium shapes in two dimensional systems with cubic anisotropy; the precipitate and matrix phases may have different elastic moduli, and the misfit may be dilatational or non-dilatational. The equilibrium shapes and their size dependence are analysed within the framework of symmetry-breaking shape transitions. These transitions are further characterized in terms their dependence on the cubic elastic anisotropy parameter, defined by A = 2C44/(C11 – C12), and on the modulus mismatch, defined by δ=μp/μm, where /μp and μm are the effective shear moduli of the precipitate and matrix phases, respectively. Depending on the type of misfit, the systems may be classified into the following four cases: Case A: For dilatational misfit, the equilibrium shapes in isotropic systems are circular (with an isotropic or I symmetry) at small sizes and undergo a transition at a critical size to become ellipse-like (with an orthorhombic or O symmetry). This I --O transition is continuous and is obtained only when the precipitate phase is softer than the matrix. These results are in good agreement with the analytical results of Johnson and Cahn. In cubic systems with dilatational misfit, the particles exhibit a transition from square-like shapes (with a tetragonal or T symmetry) at small sizes to rectangle-like shapes (with an O symmetry) at large sizes. This T -- O transition is continuous. It occurs even in systems with stiffer precipitates; however, it is forbidden for systems with δ >δC, where δ C represents a critical modulus mismatch. The critical size decreases with increasing cubic anisotropy (i.e., with increasing values of (A-1)/(A+1). The sides of the square-like and rectangle-like shapes are along the elastically soft directions. Case B: In these systems, the principal misfits e*xx and e*yy differ in magnitude but have the same sign. The precipitates at small sizes become elongated along the direction of lower misfit; this shape has an O symmetry. In systems with A > 1, they continue to become more elongated along the same direction, exhibiting no symmetry-breaking transition. However, in systems with A < 1, particles at large sizes are elongated along an intermediate direction between the direction of lower misfit and one of the elastically soft <11> directions; this shape has only a monoclinic or M symmetry. This O - M transition, in which the mirror symmetries normal to the x and y axes are lost, may be discontinuous or continuous. The critical size increases with δ (in the range 0.8 < δ <1.25), indicating that this transition would also be forbidden for systems with δ > δC. In systems with A < 1, the critical size decreases with increasing values of A-1/ A+1 Case C: In these systems, the principal misfits differ in both magnitude and sign, and the misfit strain tensor allows an invariant line along which the normal strain is zero. The precipitates at small sizes are elongated along the direction of lower absolute misfit, and possess an 0 symmetry. At large sizes, the mirror symmetries normal to the x and y axes are broken to yield shapes which are elongated along a direction between that of lower misfit and the invariant line. This 0 -> M transition is continuous and occurs in all the systems irrespective of the value of A The critical size increases with A and decreases with δ. Case D; The misfit in this case is a special form of that in Case C; the principal misfits have the same magnitude but opposite signs. The precipitates at small sizes have a square-like shape with its sides normal to the < 11 > axes, irrespective of the type of cubic anisotropy. At large sizes, they become rectangle-like with the long axis oriented along one of the <11> directions. Similar to Case C, this T - 0 transition is continuous and occurs in all the systems irrespective of the values of A. The critical size increases with A and decreases with δ. Thus, we have identified all the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two dimensional systems. We have identified their origin and nature, and characterized them in terms of their dependence on the anisotropy parameter and modulus mismatch.

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4

Billman, John Frederick. "Structure and phase behavior in microemulsions /." Thesis, Connect to this title online; UW restricted, 1990. http://hdl.handle.net/1773/9825.

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Maeda, Nobuo. "Phase transitions of long-chain n-alkanes at interfaces." View thesis entry in Australian Digital Theses Program, 2001. http://thesis.anu.edu.au/public/adt-ANU20011203.151921/index.html.

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6

Hong, Seung-pyo. "Role of hydrocarbon structures in gas solvent + hydrocarbon multiphase equilibria /." Access abstract and link to full text, 1992. http://0-wwwlib.umi.com.library.utulsa.edu/dissertations/fullcit/9303400.

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Variankaval, Narayan. "Structure and thermodynamics of associating solutions : prediction of phase equilibria." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/8304.

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Bhansali, Anil P. "Heat transfer resulting from a turbulent, submerged jet impinging on a phase change material." Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/19568.

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Bush, David Martin. "Phase equilibria of solid-supercritical carbon dioxide solutions." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/12075.

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Smith, Richard Lee Jr. "Measurement and correlation of critical states." Diss., Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/10099.

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Books on the topic "Phase rule and equilibrium"

1

S, Roth Robert, Vanderah Terrell A, American Ceramic Society, and National Institute of Standards and Technology., eds. Phase equilibria diagrams. Westerville, Ohio: American Ceramic Society, 2005.

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S, Roth Robert, American Ceramic Society, and National Institute of Standards and Technology, eds. Phase equilibria diagrams. Westerville, Ohio: American Ceramic Society, 2001.

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3

Chu-kun, Kuo. High temperature phase equilibria and phase diagrams. Oxford [England): Pergamon Press, 1990.

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4

Ahmed, Tarek H. Hydrocarbon phase behavior. Houston: Gulf Pub. Co., 1989.

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5

Engels, Hans. Phase equilibria and phase diagrams of electrolytes. Frankfurt/Main: DECHEMA, 1990.

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6

Kociński, Jerzy. Commensurate and incommensurate phase transitions. Amsterdam: Elsevier, 1990.

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Ehlers, Timothy P. Polymer phase behavior. Hauppauge, N.Y: Nova Science Publishers, 2011.

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Ghose, S. Structural and Magnetic Phase Transitions in Minerals. New York, NY: Springer New York, 1988.

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9

N, Romanenko V., ed. Raschet fazovykh ravnovesiĭ v mnogokomponentnykh sistemakh. Moskva: "Metallurgii͡a︡", 1987.

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Petrov, D. A. Dvoĭnye i troĭnye sistemy. 2nd ed. Moskva: "Metallurgii͡a︡", 1986.

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Book chapters on the topic "Phase rule and equilibrium"

1

Zaidi, Sheza. "Phase Equilibria: The Phase Rule." In Phase Rule and its applications, 1–12. London: CRC Press, 2022. http://dx.doi.org/10.1201/9781003297949-1.

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McHale, Anna E. "The Phase Rule and Heterogeneous Equilibria." In Phase Diagrams and Ceramic Processes, 63–69. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-010-9605-8_5.

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McHale, Anna E. "The Phase Rule and Heterogeneous Equilibria." In Phase Diagrams and Ceramic Processes, 63–69. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-6173-3_5.

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Richet, Pascal. "Phase Rule and Simple Univariant Equilibria." In The Physical Basis of Thermodynamics, 197–214. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1237-0_9.

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Blankschtein, Daniel. "Criteria of Phase Equilibria, and the Gibbs Phase Rule." In Lectures in Classical Thermodynamics with an Introduction to Statistical Mechanics, 281–89. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-49198-7_27.

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Liu, Zi-Kui, and John Ågren. "Thermodynamics of Constrained and Unconstrained Equilibrium Systems and Their Phase Rules." In Zentropy, 349–62. New York: Jenny Stanford Publishing, 2024. http://dx.doi.org/10.1201/9781032692401-6.

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Raal, J. David, and Andreas L. Mühlbauer. "The Modern Direct Method and Novel Eos Mixing Rules for Hpvle Computation." In Phase Equilibria, 409–36. Boca Raton: Routledge, 2023. http://dx.doi.org/10.1201/9780203743621-21.

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Carreón-Calderón, Bernardo, Verónica Uribe-Vargas, and Juan Pablo Aguayo. "Phase Equilibrium." In Thermophysical Properties of Heavy Petroleum Fluids, 177–271. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58831-1_6.

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Romano, Antonio, and Addolorata Marasco. "Phase Equilibrium." In Continuum Mechanics, 113–32. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4870-1_4.

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Gooch, Jan W. "Phase Equilibrium." In Encyclopedic Dictionary of Polymers, 529. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_8625.

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Conference papers on the topic "Phase rule and equilibrium"

1

Tavakolifaradonbe, Javad, Sumudu Karunarathne, and Knut Vågsæther. "Evaluating the acceptability and accuracy of Phasepy as a Phyton framework to calculate the interfacial properties and phase equilibrium." In 63rd International Conference of Scandinavian Simulation Society, SIMS 2022, Trondheim, Norway, September 20-21, 2022. Linköping University Electronic Press, 2022. http://dx.doi.org/10.3384/ecp192028.

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Phasepy is a scientifically defined open-source package in python for computational thermodynamics. Phasepy indeed calculates the interfacial properties and fluid phases equilibrium using an equation of state. In addition, Phasepy enables the scientists to optimize the relevant parameters to the equilibrium of multicomponent vapor-liquid, liquid-liquid, or vapor-liquid-liquid mixtures. The Phasepy can model the equilibrium in the continuous approach (combining a cubic equation of state and a mixing rule) or the discontinuous approach (using a virial equation and an activity coefficient model). So, this study is to develop a code in a continuous approach using a combination of Soave-Redlich-Kwong (SRK) or Peng Robinson (PR) as the equation of state and quadratic mixing rule (QMR) and modified-Huron-Vidal mixing rule (MHV) as the mixing Rule. Although the algorithm of the developed model is new, it is tried to utilize the predefined function of Phasepy to calculate fluid phase equilibrium and interfacial properties. In fact, the five well-performed previous experimental studies are modeled using Phasepy, and in the following, the outputs of the developed models are compared with the relevant experimental results. The bubble point features, dew point features, liquid and gas composition, and density of multicomponent mixtures are considered parameters in this extended study to evaluate the accuracy of the Phasepy function based on experimental results.

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Sun, Ziting, and Huazhou Li. "Phase Behavior Modeling for Carbon Dioxide/Brine Mixtures Using PR EOS and Huron-Vidal Mixing Rule." In ASME 2022 41st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/omae2022-80010.

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Abstract Accurately predicting CO2 solubility in saline aquifers is very important for CO2 capture and storage. A reliable and accurate thermodynamic model is needed to predict the phase equilibrium of the CO2+brine systems over a wide range of temperature, pressure, and molality. In this study, a cubic-EOS-based thermodynamic model is presented to predict the phase equilibrium of CO2+brine mixtures. Peng-Robinson equation of state and Huron-Vidal mixing rule are applied to predict the phase behavior of CO2+brine systems containing salt species including NaCl, KCl, CaCl2, and MgCl2. Binary interaction parameters for specific CO2+single-salt+H2O systems are established as functions of temperature and salt molality. To investigate the impact of multiple salts mixtures on CO2 solubility in brine solutions, the model is extended to CO2+mixed-salt+H2O systems under the practical geological conditions (273–550K, 0–800 bar, 0–6 mol/kg). PR EOS with a modified BIP model in the HV mixing rule is implemented to capture the phase compositions in vapor-liquid equilibria (VLE). The collected experimental data are used to determine the optimal BIP model. Comparison of the experimental data and the computed data indicates that the average absolute deviation (AAD) in reproducing the CO2 concentration in the mixed-salt brine is 0.0015. Compared to other state-of-the-art models in the literature, the new model can more accurately predict the VLE of CO2+brine systems over a large temperature, pressure, and molality range.

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Eniolorunda, Oluwakemi Victoria, Antonin Chapoy, and Rod Burgass. "Solid-Fluid Phase Equilibria Measurement for Mixtures of Methane, Carbon-Dioxide and N-Hexadecane." In SPE Nigeria Annual International Conference and Exhibition. SPE, 2021. http://dx.doi.org/10.2118/208245-ms.

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Abstract In this study, new experimental data using a reliable approach are reported for solid-fluid phase equilibrium of ternary mixtures of Methane-Carbon-dioxide- n-Hexadecane for 30-73 mol% CO2 and pressures up to 24 MPa. The effect of varying CO2 composition on the overall phase transition of the systems were investigated. Three thermodynamic models were used to predict the liquid phase fugacity, this includes the Peng Robison equation of state (PR-EoS), Soave Redlich-Kwong equation of state (SRK-EoS) and the Cubic plus Association (CPA) equation of state with the classical mixing rule and a group contribution approach for calculating binary interaction parameters in all cases. To describe the wax (solid) phase, three activity coefficient models based on the solid solution theory were investigated: the predictive universal quasichemical activity coefficients (UNIQUAC), Universal quasi-chemical Functional Group activity coefficients (UNIFAC) and the predictive Wilson approach. The solid-fluid equilibria experimental data gathered in this experimental work including those from saturated and under-saturated conditions were used to check the reliability of the various phase equilibria thermodynamic models.

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Zhang, Hao, and Yanhua Yang. "A Two-Phase Flow Computation Code Based on Two-Fluid Seven-Equation Model." In 2022 29th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/icone29-92367.

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Abstract The present work is developing a computation code based on two-fluid seven-equation model. This model is fully non-equilibrium. It not only assumes two phases are mechanical and thermal non-equilibrium, but also it assumes the pressure is non-equilibrium. The governing equations include seven partial differential equations, which are two continuity equations, two momentum equations, two energy equations, and one volume fraction evolution equation. The computation framework is based on split scheme, including Godunov split and Strang split, and the problem is split into two independent subproblems. One is a homogenous partial differential equation (PDE) problem, and the other one is an ordinary differential equation (ODE) problem. The homogenous PDE problem is reduced to linear equation by a Roe-type Riemann solver, and the linear equation is solved by upwind and MUSCL-Hancock (MHM) scheme. The ODE problem is solved by an implicit ODE solver, including Euler backward method, trapezium rule method and TR-BDF2. This code is verified by three types of problems. MHM converges faster than upwind for smooth solution problem, however MHM’s convergency rate is not always large than that of upwind for shock problem. The source term problem shows that the calculation result is sensitivity to the numerical schemes.

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Sirignano, William A., and Albert Jorda Juanos. "Analytical / Computational Approach to Liquid Spray Heating and Vaporization at Supercritical Pressures." In ILASS2017 - 28th European Conference on Liquid Atomization and Spray Systems. Valencia: Universitat Politècnica València, 2017. http://dx.doi.org/10.4995/ilass2017.2017.4615.

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Our findings from two areas of background research will define an approach to the study of liquid spray heating andvaporization in gases at supercritical pressure: (i) vaporizing droplets at supercritical pressure and (ii) supercritical combustion in simple configurations, e.g., counterflow. The a priori conclusion that only one phase exists at super- critical pressure is based on false “lore” and not physical law. The question about the phases must be left open until the analysis reaches a conclusion; a proper approach will be defined. Proper equations of state for density and en- thalpy and the determination of phase equilibrium, liquid composition due to dissolved gas, energy of vaporization, surface tension, and transport properties for high pressures will be discussed. The case of an isolated droplet will be reviewed and origin of the transcritical concept will be explained. A counterflow spray configuration at pressures above the liquid critical pressure will be analyzed. The concept of shifting phase equilibrium will be applied as the droplets in the spray heat. Hydrocarbon liquids and oxidizing gaseous environments will be studied. Differences between real fluids and ideal fluids at high pressures will be emphasized. Proper rules for gaseous mixtures andliquid solutions will be discussed.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4615

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Huang, Desheng, Yunlong Li, and Daoyong Yang. "Phase Behaviour and Physical Properties of Dimethyl Ether DME/CO2/Water/Heavy Oil Systems under Reservoir Conditions." In SPE Annual Technical Conference and Exhibition. SPE, 2021. http://dx.doi.org/10.2118/206171-ms.

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Abstract In this paper, techniques have been developed to quantify phase behaviour and physical properties including phase boundaries, swelling factors, and phase volumes for reservoir fluids containing polar components from both experimental and theoretical aspects. Experimentally, a total of five pressure-volume-temperature (PVT) experiments including three sets of DME/CO2/heavy oil systems and two sets of DME/CO2/water/heavy oil systems have been carried out to measure saturation pressures, phase volumes, and swelling factors by using a versatile PVT setup. Theoretically, the modified Peng-Robinson equation of state (PR EOS) incorporated with the Huron-Vidal mixing rule and the Péneloux volume-translation strategy is employed as the thermodynamic model to perform phase equilibrium calculations. It is observed that the experimentally measured saturation pressures of DME/CO2/water/heavy oil mixtures are higher than those of DME/CO2/heavy oil mixtures at the same temperature and same molar ratio of solvents and heavy oil, owing to the fact that more water molecules can be evaporated into vapour phase. The binary interaction parameters (BIPs) between DME/heavy oil and CO2/DME pair, which are obtained by matching the measured saturation pressures of DME/CO2/heavy oil mixtures, work well for DME/CO2/heavy oil mixtures in the presence and absence of water. In addition, a swelling effect of heavy oil can be enhanced by adding the DME and CO2 mixtures compared to only DME or CO2. The new model developed in this work is capable of accurately reproducing the experimentally measured multiphase boundaries, swelling factors, phase volumes with a root-mean-squared relative error (RMSRE) of 4.68%, 0.71%, and 9.35%, respectively, indicating that it can provide fundamental data for simulating, designing, and optimizing the hybrid solvent-thermal recovery processes for heavy oil reservoirs.

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Jung, Jin-Young, and Michael M. Chen. "Numerical Simulation of Dendritic Solidification." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1481.

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Abstract It is well known that the dendritic microstructure of alloys is a consequence of morphological instability of the solidification process, which is a result of the coupling of heat and mass transfer with the composition-dependent phase equilibrium condition mediated by the surface energy. There have been many numerical simulations of dendritic solidification. However, many successful simulations of dendritic growth have used non-discrete front tracking method such as artificial source method or phase field method, with demonstrably first order accuracy. Many also found it necessary to continuously inject random noise during simulation. The continuous injection of random noise raises the suspicion that the numerical schemes used may be overly dissipative. The noise is apparently capable of creating nonuniform solidification, but not sufficient to ensure growth with a clear dendritic pattern. In the present study, to rule out the numerical diffusivity as a cause of the damping of dendritic perturbations, artificial perturbations are either not used, or injected only as initial conditions. Under the unstable solidification mode, the initial perturbation triggers the onset of interface instability. Computations were performed for both sub-cooled pure material as well as directional solidification of alloys. The successful simulation of dendritic solidification without the intentional injection of random noise provided evidence that the present method has less numerical diffusion than many existing front tracking methods.

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Pakala, V. K. Chaitanya, and O. A. Plumb. "Heat Transfer at an Evaporating Front in Porous Media." In ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences. ASMEDC, 2009. http://dx.doi.org/10.1115/ht2009-88240.

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Evaporating fronts propagate through porous media during drying processes, underground coal gasification, geothermal energy production from hot dry rock, and around nuclear waste repositories. Present work will focus on the one-dimensional heat transfer at the interface between vapor saturated porous matrix and water saturated porous region and evaluate the conditions for which various approximations yield an accurate representation of front velocity. An implicit finite difference scheme is utilized to simulate the propagation of an evaporating front in a porous medium saturated with water and undergoing the phase change process. The assumption of local thermal equilibrium (LTE) which results in a one-equation model and a simple two-equation model that does not assume LTE are examined by comparison with a quasi-analytic numerical model. We consider the case for low Reynolds number, hence Nusselt number is assumed constant. Results illustrate that the one-equation model does not yield accurate results even if the length scale for diffusion in the solid phase is relatively small. The one-equation model predicts faster front propagation than the two-equation model. It is illustrated that the one-equation model yields satisfactory results only when thermophysical properties characterized by the volume weighted ratio of thermal diffusivities is reduced to an order of magnitude less than those for the applications of interest. In addition, consistent with the established “rule of thumb”, for Biot < 0.1, the traditional two-equation model which makes the lumped capacitance assumption for the solid phase compares well with a two-equation model that more accurately predicts the time dependent diffusion in the solid phase using Duhamel’s theorem.

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Nikbakht, Ali, Alireza Fallahi Arezoodar, Mojtaba Sadighi, and Ali Tale Zadeh Lari. "Indentation of a Functionally Graded Plate by a Rigid Spherical Indenter in the Presence of a Semi-Elliptic Surface Crack." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82714.

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Graded materials, also known as functionally graded materials (FGMs), are multiphase composites mainly composed of a ceramic and a metal; thus, they exploit the heat, oxidation and corrosion resistance typical of ceramics, and the strength, ductility and toughness typical of metals. These materials are mainly used as heat barriers. In addition, many of the present and potential applications of FGMs involve contact problems. On the other hand, the production process of FGMs is somewhat complex and leaves some defects in the produced structure. One of the most important defects in such structures is surface cracks. Here, the combination of the contact and crack problems is investigated in a functionally graded rectangular plate containing a semi–elliptic surface crack indented by a frictionless rigid spherical indenter. The plate is simply supported and the crack is located in the middle of the plate surface in the tension part. The crack surface is parallel to one of the plate edges. The gradient of mechanical properties variation is considered through the thickness of the plate and the volume fraction distribution of the constituting phases is modeled by a polynomial function and the Poisson’s ratio is kept constant. The analyzing of the problem is divided into two steps. At the first step, for an uncracked plate the equations of equilibrium are derived in terms of the displacement field and are solved numerically to find the contact rule. As the second step in studying the problem, the contact problem of a cracked plate is modeled by using ABAQUS finite element package. The aim of this step is to find the effect of the presence of the crack on the contact rule. The optimum mesh for the ABAQUS model is found by using the results of the first step. In order to do so, an ABAQUS model is created for the uncracked plate. The analytical results and the obtained results from ABAQUS for specified plate and indenter dimensions and material properties are compared. After finding the optimum mesh, a crack is added to the ABAQUS model of the plate under contact loading. The effects of gradient changes and indenter dimensions on the contact rule and stress distribution at the crack tip are then investigated by using the obtained ABAQUS model. The acquired results show that the influence of the material nonhomogeneity on the stress distribution around the crack tip and in the plate (uncracked and cracked) and contact rule can be quite significant. In general, increasing the overall volume fraction of the metal phase increases the load carrying capacity in an uncracked plate. In a cracked plate, the changes in material distribution as well as the changes of the indenter diameter does not affect the results that much.

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Sha, W., A. E. Paul, S. Patkar, and Arthur L. Smirl. "Excitation-Induced Phase Shifts of Heavy and Light Hole Quantum Beats in Multiple Quantum Wells." In International Conference on Ultrafast Phenomena. Washington, D.C.: Optica Publishing Group, 1994. http://dx.doi.org/10.1364/up.1994.tud.24.

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In recent years, transient four-wave mixing (FWM) techniques have been used to investigate the dephasing times of non-equilibrium carriers in semiconductor heterostructures by monitoring the decay of the macroscopic polarization. Initially, this decay was measured by temporally-integrating the scattered FWM signal as a function of time delay between two (or more) pump pulses. More recently, the macroscopic polarization decay has been measured by time-resolving the FWM signal by cross correlating it with an ultrashort laser pulse via frequency up-conversion in a nonlinear crystal. When excitons with slightly different energies are excited, oscillations (or beats) have been observed both in the time-integrated FWM signal and in the time-resolved FWM signal. Such beats have been observed, for example, between light- and heavy-hole excitons and between excitons in wells of different widths. Both the spectral behavior1 of the time-integrated FWM signal and the temporal behavior2 of the time-resolved signal have been shown to allow the distinction between the polarization interference associated with two independent oscillators and the quantum beats associated with two coupled oscillators which share a common level. In addition, it has been demonstrated3 that the quantum beats produced by incident pulses with parallel polarizations are exactly out of phase (by π) with the beats produced by orthogonally polarized pulses. In each case1-3, the period and phase of the beats and the polarization of FWM signal were explained by using a six-level model, which excluded many-body effects, to describe the J=1/2 conduction and J=3/2 valence states. Within the last few months, however, it has been shown that a complete description of the polarization selection rules for the FWM signal requires excitation-induced dephasing4 or disorder-induced coupling of the σ + and σ – excitonic transitions5.

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Reports on the topic "Phase rule and equilibrium"

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Mottola, E., F. M. Cooper, A. R. Bishop, S. Habib, Y. Kluger, and N. G. Jensen. Non-equilibrium phase transitions. Office of Scientific and Technical Information (OSTI), December 1998. http://dx.doi.org/10.2172/307958.

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Froese, E. An outline of phase equilibrium. Natural Resources Canada/ESS/Scientific and Technical Publishing Services, 2013. http://dx.doi.org/10.4095/292552.

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Evans, R. A., A. D. Saunders, and G. G. Worley. Toxics Release Inventory Expansion Rule Phase 3 (TRI-P3). Office of Scientific and Technical Information (OSTI), September 1998. http://dx.doi.org/10.2172/1839.

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Deymier, P. A. Grain boundary phase equilibrium in metallic systems. Office of Scientific and Technical Information (OSTI), April 1991. http://dx.doi.org/10.2172/5836281.

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Karwat, H., and Y. Q. Ruan. Entropy analysis on non-equilibrium two-phase flow models. Office of Scientific and Technical Information (OSTI), September 1995. http://dx.doi.org/10.2172/106993.

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Kincaid, J. Theoretical studies of multicomponent mixtures: Phase equilibrium and transport. Office of Scientific and Technical Information (OSTI), May 1990. http://dx.doi.org/10.2172/6883357.

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Glandt, E. Thermodynamics of systems with very many components phase equilibrium. Office of Scientific and Technical Information (OSTI), October 1989. http://dx.doi.org/10.2172/7167377.

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Liu, Jing, Channing Arndt, and Thomas Hertel. Parameter Estimation and Measures of Fit in A Global, General Equilibrium Model. GTAP Working Paper, March 2003. http://dx.doi.org/10.21642/gtap.wp24.

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Computable General Equilibrium (CGE) models have been widely used for quantitative analysis of global economic issues. However, CGE models are frequently criticized for resting on weak empirical foundations. This paper builds on recent work in macro-econometric estimation, developing an approach to parameter estimation for a widely employed global CGE model, the Global Trade Analysis Project (GTAP) model. An approximate likelihood function is developed and the set of optimum elasticity values is obtained by maximizing this approximate likelihood function in the context of a back casting exercise. In addition, two statistical tests are performed. The first of these tests compares the standard GTAP elasticity vector with the estimated trade elasticity vector. It rejects the null hypothesis of equality between the two sets of trade elasticities. The second test examines the widely maintained hypothesis known as the “rule of two”, by which the elasticity of substitution across imports by sources is set equal to twice the elasticity of substitution between domestic goods and imports. We fail to reject this common rule of thumb. We conclude that there is much to be gained by nesting CGE models within an estimation framework as this opens the way for formal evaluation of model performance and parameterization.

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Robinson, R. L. Jr, K. A. M. Gasem, N. A. Darwish, and A. M. Raff. Phase equilibrium data for development of correlations for coal fluids. Office of Scientific and Technical Information (OSTI), February 1991. http://dx.doi.org/10.2172/6089730.

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Robinson, R. L. Jr. Phase equilibrium data for development of correlations for coal fluids. Office of Scientific and Technical Information (OSTI), January 1990. http://dx.doi.org/10.2172/6506233.

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