A generalized treatment of cubic equations of state

1989 ◽  
Vol 54 (11) ◽  
pp. 2879-2895
Author(s):  
Vladimír Míka
Keyword(s):  
Equations Of State ◽  
Compressibility Factor ◽  
Fugacity Coefficient

From the formula proposed for the van Waals type equations of state, general expressions for the compressibility factor, the departure functions and the fugacity coefficient are derived. Easy construction of the formula needed is possible for any of the equations listed in the paper. The method is applicable to other equations of this type.

Technique and results of experimental determination of the compressibility factor of the natural gas

2021 ◽  
pp. 35-40
Author(s):  
Denis Y. Kutovoy ◽  
Igor A. Yatsenko ◽  
Vladimir B. Yavkin ◽  
Aydar N. Mukhametov ◽  
Petr V. Lovtsov ◽  
...  
Keyword(s):  
Natural Gas ◽  
Equations Of State ◽  
Compressibility Factor ◽  
High Accuracy ◽  
State Equations ◽  
Actual Problem ◽  
Temperature Range ◽  
Relative Value ◽  
Compressibility Coefficient

The actual problem of the possibility of using the equations of state for the gas phase of natural gas at temperatures below 250 K is considered. To solve it, the compressibility coefficients of natural gas obtained experimentally with high accuracy are required. The technique was developed and experimental study was carried out of compressibility factor aiming expanding temperature range of the state equations GERG-2004 and AGA8-DC92. The proposed technique is based on the fact that to assess the applicability of the equation of state, it is sufficient to obtain the relative value of the compressibility coefficient and not to determine its absolute value. The technique does not require complex equipment and provides high accuracy. The technique was tested on nitrogen, argon, air and methane. Uncertainty of determination of the compressibility factor is not greater than 0.1 %. For two different compositions of natural gas, obtained experimental data were demonstrated that the equations of state GERG-2004 and AGA8-92DC provide uncertainty of the calculation of the compressibility coefficient within 0.1 % in the temperature range from 220 K to 250 K and pressure below 5 MPa.

Gaseous Solutions

1993 ◽  
Author(s):  
Greg M. Anderson ◽  
David A. Crerar
Keyword(s):  
Equations Of State ◽  
Intermolecular Forces ◽  
Point Of View ◽  
Alternative Methods ◽  
Gaseous Species ◽  
Fugacity Coefficient ◽  
Ideal Gases ◽  
Component Systems ◽  
Liquid Solutions ◽  
History Of

The procedures described in Chapter 15 are well suited to solid and liquid solutions and could also be applied to gases, but in fact, other approaches are generally used. The main reason for this is partly historical; much work was done early in the history of physical chemistry on the behavior of gases, and these methods have continued to evolve to the present day. We have also just seen that the Margules equations become very unwieldy with multi-component systems. Because true gases are completely miscible, natural gases often contain many different components, so the Margules approach is not very suitable. Unfortunately, the most successful alternative methods described in this section are also quite unwieldy; however, they do not become much more complicated for multi-component gases than they are for the pure gases themselves, and this is a definite advantage. We have seen that with real, non-ideal gases, all the thermodynamic properties are described if we know the T, P, and the fugacity coefficient. For gaseous solutions, the fugacity coefficient for each component generally depends on the concentrations and types of other gaseous species in the same mixture. All gases, whether pure or multi-component, should approach ideality at higher T and lower P; conversely, non-ideality is most pronounced in dense, low-temperature gases where intermolecular forces are strongest. The challenge here is to find an equation of state that can adequately cover this range of conditions for gases of many different constituents. In the following discussion we first briefly outline some of the equations of state used to describe pure gases. We will introduce these from the molecular point of view since this helps understand the physical basis (and limitations) of each model. Each of these equations of state can then be applied to mixtures of gases using a set of rules which we describe at the end of this section.

Fluids of Hard Nonspherical Molecules. II. Monte Carlo Data and Equation of State

2008 ◽  
Vol 73 (4) ◽  
pp. 459-480 ◽  
Author(s):  
Pavel Morávek ◽  
Jiří Kolafa ◽  
Magda Francová
Keyword(s):  
Monte Carlo ◽  
Equations Of State ◽  
Full Range ◽  
Finite Size ◽  
Virial Coefficients ◽  
Compressibility Factor ◽  
Width Ratio ◽  
Monte Carlo Data ◽  
Finite Size Corrections ◽  
Reduced Pressures

New accurate data on the compressibility factor of the hard homonuclear diatomics with a full range of elongations and the hard prolate spherocylinders with length-to-width ratio as high as 9 are presented. The data were obtained by Monte Carlo NpT simulations with finite-size corrections in the range of reduced pressures βp* = 0.5-7.0. New equations of state based on simultaneous correlation of the data with the virial coefficients up to the ninth are presented.

scholarly journals Modeling Natural Gas Compressibility Factor Using a Hybrid Group Method of Data Handling

2019 ◽  
Author(s):  
Abdolhossein Hemmati-Sarapardeh ◽  
Sassan Hajirezaie ◽  
Mohamad Reza Soltanian ◽  
Amir Mosavi ◽  
Shahab Shamshirband
Keyword(s):  
Natural Gas ◽  
Equations Of State ◽  
Compressibility Factor ◽  
Absolute Error ◽  
Group Method ◽  
Data Handling ◽  
Hydrocarbon Reservoir ◽  
Compression And Expansion ◽  
Natural Gas Transport ◽  
Gas Compressibility

A Natural gas is increasingly being sought after as a vital source of energy, given that its production is very cheap and does not cause the same environmental harms that other resources, such as coal combustion, do. Understanding and characterizing the behavior of natural gas is essential in hydrocarbon reservoir engineering, natural gas transport, and process. Natural gas compressibility factor, as a critical parameter, defines the compression and expansion characteristics of natural gas under different conditions. In this study, a simple second-order polynomial model based on the group method of data handling (GMDH) is presented to determine the compressibility factor of different natural gases at different conditions, using corresponding state principles. The accuracy of the model evaluated through graphical and statistical analyses. The results show that the model is capable of predicting natural gas compressibility with an average absolute error of only 2.88%, a root means square of 0.03, and a regression coefficient of 0.92. The performance of the developed model compared to widely known, previously published equations of state (EOSs) and correlations, and the precision of the results demonstrates its superiority over all other correlations and EOSs.

scholarly journals The role of the critical compressibility factor in the equation of state for the critical fluid

2021 ◽  
pp. 26-36
Author(s):  
A.D. Alekhin ◽  
O.I. Bilous ◽  
Ye.G. Rudnikov
Keyword(s):  
Critical Point ◽  
Linear Model ◽  
Thermodynamic Potential ◽  
Equations Of State ◽  
Compressibility Factor ◽  
Fluctuation Theory ◽  
Thermodynamic Quantities ◽  
Phase Boundaries ◽  
Critical Isochore ◽  
Critical Isotherm

Based on the literature data of PVT measurements, the amplitudes of the equations of the critical isotherm D0(Zk), the critical isochore Г0(Zk), the phase boundaries В0(Zk) are expressed in terms of the critical factor of compressibility of the substance Zk=PkVk/RTk  in the entire fluctuation region near the critical point. By doing so, a phenomenological method has been used for calculating the values of the critical exponents of the fluctuation theory of phase transitions based on the introduction of small parameters into the equations of the fluctuation theory. It has been shown that, within the limits of the PVT measurement errors, these dependences D0(Zk) and В0(Zk) on the compressibility factor are linear, and Г0  practically does not depend  on the compressibility factor Zk. The relationship of these amplitudes with the amplitudes a and k of the linear model of the system of parametric scale equations of state of substance near the critical point has been established. It has been shown that the dependences k(Zk) and а(Zk) are also linear in the entire fluctuation region near the critical point. The obtained dependences k(Zk) and а(Zk) agree with the known relationship between the amplitudes of the critical isotherm D0(Zk), critical isochore Г0(Zk), phase boundaries В0(Zk) Aerospace Institute of the National Academy of Sciences of Ukrainewithin the framework of the system of parametric scaling equations. The relations а(Zk), k(Zk)  make it possible, on the basis of a linear model of the system of parametric scale equations of state of substance, to determine such important characteristics of the critical fluid as the temperature and field dependences of the correlation length Rc(T,m)  and the fluctuation part of the thermodynamic potential Ф(T,m)  in the entire fluctuation region near the critical point. Then, based on the form of the fluctuation part of the thermodynamic potential Ф(T,m)~Rc(T,m)-3, the results obtained allow one to calculate the field and temperature dependences of the thermodynamic quantities for a wide class of molecular liquids in the close vicinity of the critical point (DP<10-3, Dr<10-2, t<10-4), where precision experiments are significantly complicated, and its can also be used when choosing the conditions for the most effective practical application of the unique properties of the critical fluid in the newest technologies.

Effect of Using Different Equations of State in the Analysis of Rotary Displacer Stirling Engine

2018 ◽  
Author(s):  
AmirHossein Bagheri ◽  
Pavlina J. I. Williams ◽  
Phillip R. Foster ◽  
Huseyin Bostanci
Keyword(s):  
Equations Of State ◽  
Compressibility Factor ◽  
Ideal Gas ◽  
Stirling Engine ◽  
Operating Conditions ◽  
Distributed Power Generation ◽  
Realistic Representation ◽  
Isothermal Analysis ◽  
Ideal Gas Model ◽  
The Ideal

The ideal gas equation of state is defined for a theoretical gas composed of molecules that have perfect elastic collisions and no intermolecular interchange forces. However, it has been widely reported that such an ideal model may not be a realistic representation under certain circumstances, in particular when the compressibility factor (Z) is not close to unity, and the consideration of other equations of state (real models) is imperative. This study investigates the effect of using different equations of state, namely, the van der Waals, Redlich-Kwong, and Peng-Robinson equations, in the ideal isothermal analysis of a rotary displacer Stirling engine with the most commonly used gases, helium and air. The results are obtained numerically considering two major SE applications (cryocooling and distributed power generation) and two sets of operating conditions, and plotted in the form of Pressure-Volume diagrams. The amount of work per cycle based on the ideal gas model is taken as reference to compare the results from other models. The data show that at low pressure or high temperature conditions (corresponding to low density), the ideal gas equation is suitable for both gases, and using different models has no significant impact in the overall analysis. Additionally, while the use of ideal gas model is rather practical and fast, implementation of other models necessitate intensive computational processes.

Mathematical round up

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Equations Of State ◽  
Compressibility Factor ◽  
Chain Rule ◽  
New Material ◽  
Mathematical Equations ◽  
Thomson Coefficient ◽  
Thermodynamic Equations

This chapter draws together all the main mathematical equations into a single, structured, sequence, so providing a source of reference, as well as enabling the student to appreciate how superficially different equations are, in fact, component parts of a ‘bigger picture’. The chapter also introduces some new material, such as the Maxwell relations, the chain rule, the thermodynamic equations-of-state, isenthalpic throttling processes, the Joule-Thomson coefficient and the compressibility factor – so setting the scene for the discussion of real systems in the following chapter.

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