Equation of state and critical point of cesium

1990 ◽  
Vol 11 (3) ◽  
pp. 467-476 ◽  
Author(s):  
N. B. Vargaftik ◽  
E. B. Gelman ◽  
V. F. Kozhevnikov ◽  
S. P. Naursakov
Keyword(s):  
Equation Of State ◽  
Critical Point

A Rational Equation of State for Water and Water Vapor in the Critical Region

1964 ◽  
Vol 86 (3) ◽  
pp. 320-326 ◽  
Author(s):  
E. S. Nowak
Keyword(s):  
Water Vapor ◽  
Equation Of State ◽  
Thermodynamic Properties ◽  
Specific Heat ◽  
Critical Point ◽  
Critical Region ◽  
Constant Pressure ◽  
Parametric Equation ◽  
Enthalpy And Entropy ◽  
Specific Volumes

A parametric equation of state was derived for water and water vapor in the critical region from experimental P-V-T data. It is valid in that part of the critical region encompassed by pressures from 3000 to 4000 psia, specific volumes from 0.0400 to 0.1100 ft3/lb, and temperatures from 698 to 752 deg F. The equation of state satisfies all of the known conditions at the critical point. It also satisfies the conditions along certain of the boundaries which probably separate “supercritical liquid” from “supercritical vapor.” The equation of state, though quite simple in form, is probably superior to any equation heretofore derived for water and water vapor in the critical region. Specifically, the deviations between the measured and computed values of pressure in the large majority of the cases were within three parts in one thousand. This coincides approximately with the overall uncertainty in P-V-T measurements. In view of these factors, the author recommends that the equation be used to derive values for such thermodynamic properties as specific heat at constant pressure, enthalpy, and entropy in the critical region.

Feynman-Graph Expansion for the Equation of State near the Critical Point (Ising-like Case)

1972 ◽  
Vol 29 (9) ◽  
pp. 591-594 ◽  
Author(s):  
E. Brézin ◽  
D. J. Wallace ◽  
Kenneth G. Wilson
Keyword(s):  
Equation Of State ◽  
Critical Point ◽  
Feynman Graph ◽  
Graph Expansion

scholarly journals A Quasiparticle Equation of State with a Phenomenological Critical Point

2018 ◽  
Vol 48 (2) ◽  
pp. 160-167 ◽  
Author(s):  
Hong-Hao Ma ◽  
Wei-Liang Qian
Keyword(s):  
Equation Of State ◽  
Critical Point

An Equation of State Compositional Model

1980 ◽  
Vol 20 (05) ◽  
pp. 363-376 ◽  
Author(s):  
Keith H. Coats
Keyword(s):  
Equation Of State ◽  
Critical Point ◽  
Oil And Gas ◽  
Numerical Models ◽  
Volatile Oil ◽  
Gas Condensate ◽  
Numerical Dispersion ◽  
Stable Convergence ◽  
Compositional Model ◽  
Miscible Flooding

Abstract This paper describes an implicit, three-dimensional formulation for simulating compositional-type reservoir problems. The model treats three-phase flow in Cartesian (x-y-z) or cylindrical (r-theta-z) geometries. Applicability ranges from depletion or cycling of volatile oil and gas condensate to miscible flooding operations involving either outright or multicontact-miscibility.The formulation uses an equation of state for phase equilibrium and property calculations. The equation of state provides consistency and smoothness as gas- and oil-phase compositions and properties converge near a critical point. This avoids computational problems near a critical point associated with use of different correlations for K values as opposed to phase densities. Computational testing with example multicontact-miscibility (MCM) problems indicates stable convergence of this formulation as phase properties converge at a critical point. Results for these MCM problems show significant numerical dispersion, primarily affecting the calculated velocity of the miscible-front advance. Our continuing effort is directed toward reduction of this numerical disperson and comparison of model results with laboratory experiments for both MCM and outright-miscibility cases.We feel that the implicit nature of the model enhances efficiency as well as reliability for most compositional-type problems. However, while we report detailed problem results and associated computing times, we lack similar reported times to compare the overall efficiency of an implicit compositional formulation with that of a semi-implicit formulation. Introduction Many papers have treated increasingly sophisticated or efficient methods for numerical modeling of black-oil reservoir performance. That type of reservoir allows an assumption that reservoir gas and oil have different but fixed compositions, with the solubility of gas in oil being dependent on pressure alone.A smaller number of papers have presented numerical models for simulating isothermal "compositional" reservoirs, where oil and gas equilibrium compositions vary considerably with spatial position and time. With some simplification, the reservoir problems requiring compositional treatment can be divided into two types. The first type is depletion and/or cycling of volatile oil and gas condensate reservoirs. The second type is miscible flooding with MCM generated in situ.A distinction between these types is that the first usually involves phase compositions removed from the critical point, while the second type generally requires calculation of phase compositions and properties converging at the critical point. A compositional model should be capable of treating the additional problem of outright miscibility where the original oil and injected fluid are miscible on first contact.A difficulty in modeling the MCM process is achievement of consistent, stable convergence of gas-and oil-phase compositions, densities, and viscosities as the critical point is approached. A number of studies have reported models that use different correlations for equilibrium K-values as opposed to phase densities. Use of an equation of state offers the advantage of a single, consistent source of calculated K-values, phase densities, and their densities near a critical point. SPEJ P. 363＾

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