Redlich-Kwong Equation Research Articles

Compressibility factor measurement and simulation of five high-temperature ultra-high-pressure dry and wet gases

Five groups of high-temperature ultra-high-pressure natural gas samples (two dry gases and three wet gases) are collected from oilfields in northwestern China. The compressibility factors (Z-factors with a maximum uncertainty of 0.005) of these samples at their reservoir temperatures and different pressures are determined using a (high-pressure) pressure–volume–temperature apparatus. The experimental results indicate that the Z-factors of these natural gases under reservoir conditions are considerably higher than those of conventional natural gases. Moreover, the Z-factors decrease as the pressure decreases within the high pressure ranges considered in this investigation. A simple thermodynamic model based on the Soave–Redlich–Kwong equation of state and newly established binary interaction correlations is proposed to simulate the Z-factors of the gas samples investigated herein. Meanwhile, the performances of four Z-factor prediction empirical correlations and the Groupe Européen de Recherches Gazières (GERE) model reported in literature are compared. It is found that the thermodynamic model proposed in this work exhibits the best prediction accuracy; results show that the average absolute deviations in the calculations of the Z-factors of five natural gas samples are only 0.7%, 2.1%, 1.81%, 0.44%, and 0.92%. Furthermore, the high prediction accuracy of this thermodynamic model is verified by comparing the 428 Z-factor experimental data points of high-temperature ultra-high-pressure natural gases reported in literature.

Population balance modeling: application in nanoparticle formation through rapid expansion of supercritical solution

The rapid expansion of supercritical solution (RESS) process is a novel method to produce free-solvent particles with narrow particle size distribution (PSD), and it is offered to replace conventional particle formation methods. The present study is aimed to investigate the numerical simulation of the RESS process comprising hydrodynamic and particle formation and solving population balance equation to compute PSD of solute-supercritical CO2 (SC-CO2) systems. Mass, momentum and energy balances in addition to an accurate equation of state are used to calculate hydrodynamic behavior of SC-CO2 at various conditions through a nozzle and supersonic free jet with considering heat exchange in the nozzle. The solubility of TBTPP (5, 10, 15, 20-tetrakis (3, 5-bis (trifluoromethyl) phenyl) porphyrin) in SC-CO2 is calculated using the Soave–Redlich–Kwong equation of state with van der Waals mixing rule. After that, supersaturation and nucleation of TBTPP and three other drugs, i.e., aspirin, salicylic acid and ibuprofen, are investigated. Eventually, the method of moments is used to solve the population balance equations to determine PSD of the solutes. The results are presented with and without coagulation. Furthermore, the effect of nozzle length and pre-expansion temperature on PSD is studied. Furthermore, to improve the results of coagulation model on PSD, collision frequency and lognormal function are modified. The modifications improve the coagulation results. The average absolute percent deviation of TBTPP solubility is 1.86. The CO2 hydrodynamic behavior shows the same trend as reported in the literature. Moreover, results of PSD calculation with coagulation indicated there is a good agreement with the experimental ones.

The effect of thermal expansion coefficient on unsteady non-Newtonian supercritical Casson fluid flow past a vertical cylinder

A new thermodynamic computational model has been proposed for the current study, which deals with the free convective supercritical Casson fluid flow past a vertical cylinder. In this model, pressure, temperature and compressibility factor are the critical parameters to govern the thermal expansion coefficient. The present model is based on the Redlich–Kwong equation of state. Comparisons with experimental results and determined values of thermal expansion coefficient for the choice of chemical compound (isobutene) from the present study show great similarity. The chemical compound isobutane has many industrial applications. For instance, in geothermal power plant, supercritical isobutane is employed as a working fluid, it is used in the deactivated (USY alkylation) catalyst regeneration, it is used in heat pumps and many other industrial processes. Furthermore, isobutane finds extensive application as a propellant in foam products and aerosol cans, as a refrigerate gas in freezers and refrigerators, as a feedstock in industries of petrochemical importance, for standardisation of gas mixtures and emission monitoring, etc. In addition, the Casson fluid flow model can be used to study the blood flow rheology, slurry flows, etc. The numerical scheme such as Crank–Nicolson type is demonstrated to simplify the governing nonlinear coupled partial differential equations. The transient results of flow-field variables, coefficients of heat and momentum transport for a Casson fluid under supercritical condition for various values of reduced pressure and reduced temperature are computed and discussed through graphs.

Phase transitions in filtration of Redlich–Kwong gases

In this paper we study a 3-dimensional filtration of real gases described by Redlich–Kwong equations of state. Thermodynamical states are considered as Legendrian (Lagrangian) submanifolds in contact (symplectic) space. Connection between singularities of their projection on the space of intensive variables and phase transitions is shown. Explicit formulae for the Dirichlet boundary problem are given and the distribution of phases in space is shown.

(Vapor + liquid) phase equilibria of an aqueous solution of bromide-based ionic liquids – measurements, correlations and application to absorption cycles

In this work, thermodynamic and physicochemical properties including (vapor + liquid) equilibria (VLE), density and dynamic viscosity of binary mixtures composed of bromide-based ionic liquid (IL) and water were measured as a function of IL mole fraction in a wide range of temperature. The aqueous solution of the following ILs: 1-ethyl-1-methylpiperidinium bromide, ethylpyridinium bromide, 1-(2-hydroxyethyl)pyridinium bromide, 1-ethyl-1-methyl-morpholinium bromide, 1-hydroxyethyl-1-methylmorpholinium bromide, and N-ethyl-N,N-dimethyl-N-hydroxyethylammonium bromide have been tested for potential applications as working fluids in absorption refrigeration technology. The isothermal VLE has been measured by an ebulliometric method within a temperature range from T = (338.15–368.15) K and pressure up to 85 kPa and correlated using Redlich-Kwong equation of state. This work is a continuation of our systematic investigation of an aqueous solution of ionic liquids as a potential working fluid in absorption refrigeration technology. The summary of this research is the modeling of the theoretical cycles using working fluids proposed in this paper. The calculated values of the coefficient of performance (COP) were compared to other ILs from available literature and {LiBr + water} system, conventionally used on the industrial scale in absorption refrigeration technology.

Multicomponent system of trichromatic disperse dye solubility in supercritical carbon dioxide

Using a mixture of dyes to produce a variety of shades is necessary for the industrialization of supercritical fluid dyeing. The solubility of the mixture in supercritical fluid is indispensable for combination dyeing but has been less well-studied. In this study, the solubility of trichromatic disperse dyes (C.I. Disperse Orange 30, C.I. Disperse Red 167 and C.I. Disperse Blue 79) and their blends in supercritical carbon dioxide were measured at temperatures of 333.15, 363.15, and 393.15 K and pressures of 12, 16, 20, and 24 MPa. Considering both the solubility enhancement value and the statistical significance, the solubility of a quaternary system was less than that of a binary system, particularly at higher pressure. To research the relationship between solubility and experimental conditions or properties of the solute, the experimental data were correlated with two semiempirical models (the Kumar–Johnston (K-J) and Sung–Shim (S-S) models) and a phase equilibrium thermodynamic model (a modified Redlich–Kwong equation of state (m-RK-EOS)). The results showed that the calculated solubility by the semiempirical and thermodynamic models had high consistency with the experimental values. In addition, the m-RK-EOS model had better accuracy than the K-J and S-S models for correlating solubility. Therefore, a calculated solubility can be used to offer basic information for the proper design of supercritical fluid dyeing in industry.

Modeling and Research of Gas Transportation Unit Operation Modes

The main objective of this paper is to describe the methodic and the software developed by authors, which has aimed to simulate operation modes of a centrifugal gas compressor and associated equipment. In this paper, the computer-based design and the analysis of control systems for centrifugal gas compressors are presented. The structure of the mathematical models and the solution methods are discussed. A Visual Basic-based application has been built to solve the system dynamics and to generate the model in installation executable format. The application allows simulating the behavior of a gas compression network through an individual simulation of each component in the network like gas compressor, valve, heat-exchanger, gas-liquid separator, pipe line. Flow through the system elements is modeled as a multi-component compressible gas flow and the Redlich-Kwong Equation of State is used to solve the mass conservation equation. Based on the centrifugal gas compressor theory an anti-surge control strategy has been applied to the model in order to predict and control surge cases. The one-stage gas compression model has been used to verify how the software responds to changes in the suction and discharge conditions.

A numerical study of natural convection properties of supercritical water (H2O) using Redlich–Kwong equation of state

In this article, the Crank-Nicolson implicit finite difference method is utilized to obtain the numerical solutions of highly nonlinear coupled partial differential equations (PDEs) for the flow of supercritical fluid (SCF) over a vertical flat plate. Based on the equation of state (EOS) approach, suitable equations are derived to calculate the thermal expansion coefficient (\( \beta \)) values. Redlich–Kwong equation of state (RK-EOS), Peng-Robinson equation of state (PR-EOS), Van der Waals equation of state (VW-EOS) and Virial equation of state (Virial-EOS) are used in this study to evaluate \( \beta \) values. The calculated values of \( \beta \) based on RK-EOS is closer to the experimental values, which shows the greater accuracy of the RK-EOS over PR-EOS, VW-EOS and Virial-EOS models. Numerical simulations are performed for \( {\text{H}}_{2} {\text{O}} \) in three regions namely subcritical, supercritical and near critical regions. The unsteady velocity, temperature, average heat and momentum transport coefficients for different values of reduced pressure and reduced temperature are discussed based on the numerical results and are shown graphically across the boundary layer.

Development and implementation of mathematical models of working mediums for gas part of combined cycle gas turbine system in Python programming environment

The working mediums in the gas turbine systems are: atmospheric air, natural gas and exhaust gases. For the detailed analysis of thermodynamic performance and values at characteristic points of the cycle it is necessary to know the relations defining: specific volume, specific isobaric and isochoric heat capacity, isentropic exponent, specific enthalpy and specific entropy. Mathematical models of thermodynamic parameters for the mentioned mediums were developed based on dependencies for mixtures of ideal and semi-ideal gases. The functions obtained for semi-ideal gas mixtures were extended by pressure correction factors derived from the Redlich-Kwong and Peng-Robinson equations of state. The thermodynamic parameters of the working mediums were dependent on the mass fractions of the components, temperature and pressure. Developed models approximated the behaviour and parameters of real gas mixtures. All calculation algorithms were implemented and optimized using appropriate numerical methods in the Python programming environment. As a result, mathematical models of working mediums for the gas part of the combined cycle gas turbine system were obtained.

Updated versions of the generalized Soave α-function suitable for the Redlich-Kwong and Peng-Robinson equations of state

More than 40 years after their publication, updated versions of the generalized Soave α-function (α(Tr,ω)=[1+m(ω)(1−Tr0.5)]2) suitable for the Redlich-Kwong (RK) and Peng-Robinson (PR) equations of state (EoS) are proposed in this work. The new mathematical expressions of mRK(ω) and mPR(ω) have been determined by correlating the optimal m values, fitted on vapor pressures (Psat) and/or enthalpies of vaporization (ΔvapH) and/or saturated-liquid heat capacities (cP,liqsat) against the acentric factor ω. The correlations determined in this study can be considered as broad-based and sound since they were established for 1721 pure compounds belonging to many different chemical families (hydrocarbons, halogenated, oxygenated, sulfur, nitrogen compounds …) for which experimental data were available. Significant improvements on the reproduction of vapor pressures were obtained for the PR EoS with respect to the original version. The updated SRK EoS achieved similar average deviations for the three properties of interest (Psat,ΔvapH and cP,liqsat), in comparison with the original SRK equation. A substantial improvement is however noticeable for heavy molecules with an acentric factor larger than 0.9.

Supercritical heat transfer characteristics of couple stress convection flow from a vertical cylinder using an equation of state approach

The present work describes numerical simulations of the supercritical heat transfer characteristics of couple stress fluid flow from a vertical cylinder using the equation of state approach. Redlich-Kwong (RK-EOS) and Van der Waals (VW-EOS) equations of state (EOS) are deployed to derive the equation for the thermal expansion coefficient (β). The β values calculated based on RK-EOS are sufficiently close to the experimental values when compared with those based on VW-EOS. Due to the presence of couple stresses in the fluid, highly nonlinear coupled partial differential equations are generated. These primitive equations are reduced to dimensionless form by using suitable non-dimensional quantities. An unconditionally stable finite difference technique is used to solve the normalized conservation equations under physically viable boundary conditions, in order to describe the natural convection heat transfer characteristics of couple stress fluid external to a vertical cylinder in the supercritical region. For different values of the emerging physical parameters, numerical data for couple stress fluid for the case of Nitrogen is generated and presented in the form of graphs and tables. The present computations indicate that the velocity field is suppressed close to the cylinder whereas it is enhanced away from the cylinder with increasing values of reduced temperature in the supercritical fluid region. The reverse behavior is observed for reduced pressure. The present results are compared with the previous results and found to be in good agreement. Applications of the model include super-critical coating dynamics in the aerospace and medical industries.

Modeling of the Asphaltene Onset Pressure from Few Experimental Data: A Comparative Evaluation of the Hirschberg Method and the Cubic-Plus-Association Equation of State

Asphaltene onset pressure (AOP) is a key parameter to determine the flow assurance of live oils. In this study, the capabilities of the cubic-plus-association (CPA) equation of state (EoS) and the Hirschberg method of calculating the AOP of five oils are compared to a new approach using few experimental data. Two experimental data points of AOP and only one of the bubble pressure (BP) are required for adequate parametrization of both models. The number of non-zero binary interaction parameters needed for the CPA EoS is reduced to only four binary pairs. In the Hirschberg method, the BP calculations were performed with the Soave–Redlich–Kwong EoS. For all oils, the CPA EoS provided lower deviations for both AOP and BP. To achieve a good correlation, the Hirschberg method requires the use of AOP experimental data to calculate the difference between the liquid-phase solubility parameter and the asphaltene solubility parameter. Similarly, CPA EoS requires the calculation of the cross-associating energy parame...

Transient Flow and Heat Transfer Characteristics of non-Newtonian Supercritical Third-Grade Fluid (CO2) past a Vertical Cylinder

Abstract The present study deals with the time-dependent natural convective supercritical third-grade fluid flow past a vertical cylinder. A new thermodynamic model for the supercritical carbon di-oxide (CO2) has been derived. In this model the thermal expansion coefficient is characterized as a function of pressure, temperature and compressibility factor. This model uses the Redlich-Kwong equation of state (RK-EOS). The numerically calculated thermal expansion coefficient values of CO2 are validated with available experimental results. The governing non-linear coupled partial differential equations are solved by using Crank-Nicolson method. The obtained numerical data is described in terms of velocity, temperature, skin-friction and Nusselt number through the graphs and tables for the different set of physical parameters. It is observed that the unsteady velocity is an increasing function of reduced pressure and reduced temperature; whereas it is a decreasing function with respect to third-grade fluid parameter. The temperature field is enhanced near the critical point for the increasing values of third-grade fluid parameter. In supercritical fluid region for the increasing values of reduced pressure and reduced temperature, the skin-friction values are magnified against time. Also, the average heat transfer rate decreases for increasing values of third-grade fluid parameter.

Finite difference analysis of unsteady natural convection properties of carbon dioxide in the supercritical region using the Redlich-Kwong equation of state

In this research article, the transient boundary layer flow of laminar viscous incompressible supercritical fluid produced by an isothermal vertical flat plate is solved by using the finite difference method. Unlike other numerical methods, the Crank-Nicolson implicit finite difference approach gives precise numerical approximations that are uniformly valid for all non-dimensional time. Moreover, simple and precise numerical formulae for the average skin-friction and heat-transport coefficients are given, which agree well with analytic results and hence are advantageous in the related industries. To predict the natural convection properties of carbon dioxide, a new equation for thermal expansion coefficient is obtained based on the Redlich-Kwong equation of state (RK-EOS) in the supercritical region. The calculated values of thermal expansion coefficient based RK-EOS is closer to the experimental values, which confirms the accuracy of the proposed model. The numerical simulations are performed for carbon dioxide in the supercritical region adjacent to the vertical plate. The solution of velocity, temperature, average momentum and heat transport coefficients has been obtained and is discussed in detail through the graphical results for various flow parameters in the supercritical region. Numerical results showed that the time required to attain the steady-state rises for the amplifying values of reduced pressure and reduced temperature in the supercritical region. It is also observed that the thermodynamic properties of supercritical carbon dioxide are more sensible to temperature changes than pressure changes.

CFD predictions for hazardous area classification

Abstract This study aimed to describe a Computational Fluid Dynamics (CFD) procedure using the ANSYS CFX software 16.1 and Design of Experiments for the determination of volume and extension of explosive atmospheres due to fugitive emissions of flammable gases. The multidimensional statistical sampling technique Latin Hypercube was used, which defined 100 simulations of random methane gas leak conditions. The CFD model proved to be robust in predicting the extension and volume of the explosive atmosphere for orifice diameters from 0.1 to 2.5 mm, pressure from 0.1 MPa to 12 MPa and temperatures from 0 °C to 400 °C. It was found that the calculation domain must be parameterized 8 m in length for each millimeter of the diameter of the source of release to ensure the predictions. In order not to lose precision for very small diameters, the mesh was parameterized with 50 elements along the orifice diameter. It was proved that gravity does not influence the extension and volume of the explosive atmosphere at sonic emissions. The deviation from the ideal gas behavior in the reservoir, achieved by applying the Soave–Redlich–Kwong equation of state, also has not significantly influenced the extension and volume of the explosive atmosphere. The results showed that the size of the explosive atmosphere varies directly with the diameter of the source emission and reservoir pressure, and inversely with the temperature of the reservoir. The diameter of the source is the parameter that has the major effect on the extension of the explosive atmosphere, followed by the pressure and lastly the temperature of the reservoir.

Transient Natural Convection Heat Transfer to CO2 in the Supercritical Region

Present research paper investigates the transient laminar free convective supercritical carbon dioxide flow past a semi-infinite vertical cylinder using numerical methods. Two new thermodynamic models for the supercritical fluid (SCF) flow are considered. Based on these models, for supercritical carbon dioxide, two new equations for thermal expansion coefficient are obtained on the basis of Redlich–Kwong equation of state (RK-EOS) and Van der Waals equation of state (VW-EOS). Based on the calculated values of thermal expansion coefficient, it is shown that not only RK-EOS is closer to experimental values but also gives greater accuracy when compared to VW-EOS validating RK-EOS as suitable model for predicting natural convective properties of carbon dioxide under supercritical condition. The governing equations of SCF flow are solved numerically using Crank–Nicolson implicit finite difference scheme. Numerical simulations are performed for carbon dioxide in the region of its critical point. Results in subcritical, supercritical, and near-critical regions are shown graphically and discussed for different physical parameters. From the obtained numerical results, it is clear that the steady-state time increases for the increasing values of reduced temperature and reduced pressure for carbon dioxide in supercritical region.

Adiabatic calorimeter for isochoric specific heat capacity measurements and experimental data of compressed liquid R1234yf

In this paper, an adiabatic calorimeter has been developed to measure the isochoric specific heat capacity of compressed liquid. A spherical bomb with platinum resistance thermometer inserted was used to hold the measured liquid and two adiabatic shields were arranged to reduce the heat loss of thermal radiation. The isochoric specific heat capacity of liquid propane was measured over temperatures from (236 to 340) K and pressures up to 14 MPa. Satisfactory agreement with published heat capacity data is found and the reliability of the experimental setup is verified. Moreover, the experimental isochoric specific heat capacity data of liquid R1234yf were obtained in the temperatures from (240 to 341) K and pressures up to 13 MPa. The standard uncertainties were estimated to be 10 mK for temperature, 5 kPa for pressure and 1.0% for isochoric specific heat capacity. The data of R1234yf are represented by two Helmholtz equations of state with average absolute relative deviations of 2.0% and 1.3%, respectively. Comparisons are made between the Helmholtz equations of state and the cubic equations of state for the calculation of the specific heat capacity property. The Helmholtz equations of state give a better description than the cubic equations of state, and the Peng–Robinson equation of state performs slightly better than the Patel–Teja and Soave–Redlich–Kwong equations of state.

Interruption Features in SF6 Circuit Breaker Based on Real Gas Redlich-Kwong Equation

Interruption Features in SF6 Circuit Breaker Based on Real Gas Redlich-Kwong Equation

Heat flow visualization of a chemical compound isobutane (C4H10) past a vertical cylinder in the subcritical, near critical and supercritical regions

Supercritical fluids (SCF's) found to have a large number of applications in science and engineering field particularly in separation and purification, green technologies etc. The present research paper investigates the heatline visualization of unsteady free convection supercritical fluid flow over a vertical cylinder using Bejan's heat function concept by using isobutane as a model compound. A new thermodynamic equation has been obtained to calculate the volumetric thermal expansion coefficient (β) based on the Redlich-Kwong equation of state (RK-EOS), in order to determine the free convection properties of isobutane in supercritical fluid (SCF) region. In this model the thermal expansion coefficient is characterized as a function of compressibility factor, temperature and pressure. Crank-Nicolson type of implicit finite difference method is utilized to obtain the results in terms of the streamlines (ψ), isotherms (θ) and heatlines (Π) for the different values of reduced temperature and reduced pressure in the SCF region. The numerically calculated thermal expansion coefficient values are validated with existing experimental results. Numerical simulations are performed for isobutane in three regions namely, subcritical, near critical and supercritical regions. The unsteady boundary layer flow analysis shows that the streamlines are beginning from the leading edge to the far downstream, whereas the heatlines ends at a finite distance from the surface of cylinder. The non-dimensional values of heat function are closely associated with the overall heat transfer rate. The SCF flow analysis implies that in the vicinity of the hot cylindrical surface the heatlines are observed to be denser. Further, the deviation of streamlines, isotherms and heatlines from the hot cylindrical surface increases as reduced temperature and reduced pressure increases.

A Numerical Comparison of Soave Redlich Kwong and Peng-Robinson Equations of State for Predicting Hydrocarbons’ Thermodynamic Properties

Mixture phase equilibrium and thermodynamic properties have a significant role in industry. Numerical analysis of flash calculation generates an appropriate solution for the problem. In this research, a comparison of Soave Redlich Kwong (SRK) and Peng-Robinson (PR) equations of state predicting the thermodynamic properties of a mixture of hydrocarbon and related compounds in a critical region at phase equilibrium is performed. By applying mathematical modeling of both equations of states, the behavior of binary gases mixtures is monitored. The numerical analysis of isothermal flash calculations is applied to study the pressure behavior with volume and mole fraction. The approach used in this research shows considerable convergence with experimental results available in the literature.