Calculation of complex phase equilibria in the critical region of fluid mixture based on multi-fluid lattice equation of state

2000 ◽  
Vol 17 (4) ◽  
pp. 420-423 ◽  
Author(s):  
Hun Yong Shin ◽  
Ki-Pung Yoo ◽  
Chul Soo Lee
Keyword(s):  
Equation Of State ◽  
Phase Equilibria ◽  
Critical Region ◽  
Lattice Equation ◽  
Fluid Mixture ◽  
Complex Phase

An Iterative Sequence for Phase-Equilibria Calculations Incorporating the Redlich-Kwong Equation of State

1978 ◽  
Vol 18 (03) ◽  
pp. 173-182 ◽  
Author(s):  
D.D. Fussell ◽  
J.L. Yanosik
Keyword(s):  
Equation Of State ◽  
Phase Equilibria ◽  
Oil Recovery ◽  
Critical Region ◽  
Single Stage ◽  
Dew Point ◽  
Two Phase ◽  
Fluid Mixture ◽  
Separation Unit ◽  
Stage Separation

Abstract Phase equilibria equations that incorporate the Redlich-Kwong equation of state are nonlinear and, therefore, must be solved by an iterative method. The method of successive substitutions commonly is used. This method, however, almost always diverges near the critical region for bubble point, dew point, and two-phase calculations. Iterative methods that converge for these calculations are presented. These iterative methods are called presented. These iterative methods are called "minimum variable Newton-Raphson" (MVNR) methods because they try to minimize the number of variable for which simultaneous iteration is required and use the Newton-Raphson method for the correction step. Procedures are given for obtaining starting values for the first iteration and several example problems are discussed. Introduction Reservoir performance predictions for gas condensate and volatile oil reservoirs require a knowledge of the vapor-liquid phase equilbria of the reservoir fluids. A similar knowledge also is required when studying multiple-contact, miscible oil recovery methods that involve injection of hydrocarbons and/or carbon dioxide. Such knowledge is obtained experimentally or calculated from physical properties of the components of the physical properties of the components of the reservoir fluid system. Calculation is desirable because experimental determination is both laborious and expensive. A common basis for calculation of vapor-liquid phase equilibria is the single-stage separation unit. phase equilibria is the single-stage separation unit. This unit represents a PVT cell in which a fluid mixture of known over-all composition is equilibrated at the temperature and pressure of interest. Liquid and vapor compositions and moles of liquid and vapor per mole of fluid mixture are determined. Reliable estimates of other fluid properties (such as phase densities and viscosities) are obtained readily with these properties. The Redlich-Kwong equation of state is used widely in the petroleum industry for phase equilibria calculations. The phase equilibria equations that incorporate this equation of state are nonlinear. As a result, they must be solved by an iterative method. The method of successive substitutions commonly is used. This method, however, almost always diverges for bubble point, dew point, and two-phase calculations near the critical region. This region is extremely important when studying multiple-contact, miscible oil recovery methods involving CO2 or rich-gas injection because the path of the over-all fluid mixture passes through path of the over-all fluid mixture passes through this region. The method of successive substitutions also will diverge for some fluid mixtures near their saturation (bubble point or dew point) pressure at conditions removed from the critical region. This paper presents a reliable iterative sequence that can be used to predict phase equilibria of multiple-contact, miscible oil recovery methods. The method includes sequences for calculation of the saturation pressure and phase equilibria in the two phase region. These MVNR methods rely on minimization of the number of unknowns for which simultaneous iteration is required and use the Newton-Raphson method for the correction step. Minimization is subject to the constraint that all additional unknowns can be calculated by using simple linear equations or, at most, an iteration method applied to one equation in one unknown. MVNR is compared with the method of successive substitutions for a two-phase fluid mixture at various pressures for a fixed temperature. MVNR also is compared with the method of successive substitutions for saturation-envelope calculations near the critical region. DESCRIPTION OF PHYSICAL SYSTEM The single-stage separation unit is the basis for the phase equilibria calculations discussed in this study. This unit represents a PVT cell in which a fluid mixture of known over-all composition is equilibrated at the temperature and pressure of interest. SPEJ P. 173

Calculation of complex phase equilibria of DMF/alkane systems using the PCP-SAFT equation of state

2014 ◽  
Vol 115 ◽  
pp. 49-57 ◽  
Author(s):  
Elisabeth Schäfer ◽  
Gabriele Sadowski ◽  
Sabine Enders
Keyword(s):  
Equation Of State ◽  
Phase Equilibria ◽  
Complex Phase

Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

2010 ◽  
Vol 75 (3) ◽  
pp. 359-369 ◽  
Author(s):  
Mariano López De Haro ◽  
Anatol Malijevský ◽  
Stanislav Labík
Keyword(s):  
Equation Of State ◽  
Binary Mixtures ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Fluid Mixture ◽  
Binary Fluid ◽  
Virial Series ◽  
Consolute Point ◽  
Critical Constants

Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

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.

Solid-Fluid Phase Equilibria Measurement for Mixtures of Methane, Carbon-Dioxide and N-Hexadecane

2021 ◽  
Author(s):  
Oluwakemi Victoria Eniolorunda ◽  
Antonin Chapoy ◽  
Rod Burgass
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Equation Of State ◽  
Phase Equilibria ◽  
Activity Coefficients ◽  
Fluid Phase ◽  
Ternary Mixtures ◽  
Binary Interaction ◽  
Thermodynamic Models ◽  
Methane Carbon

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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