GERG-2008 Equation Of State Research Articles

Vapor-Phase (p, ρ, T, x) Behavior and Virial Coefficients for the Binary Mixture (0.05 Argon + 0.95 Carbon Dioxide) over the Temperature Range from (273.15 to 323.15) K with Pressures up to 9 MPa

Accurate density measurements on a binary (argon + carbon dioxide) mixture were carried out at temperatures T = (273.15, 283.15, 293.15, 308.15, and 323.15) K with pressures up to the dew-point pressure or 9.0 MPa, whichever was lower. A two-sinker magnetic suspension densimeter was utilized for the measurements. The composition of the gravimetrically prepared mixture was 0.94951 mole fraction carbon dioxide. Taking the measurement uncertainties in temperature, pressure, density, and composition into account, the relative combined expanded uncertainty (k = 2) in density was estimated to be less or equal 0.043% of the measured density value. Relative deviations of the new experimental data from the GERG-2008 equation of state (EOS) and from the EOS-CG (a recently developed multiparameter EOS optimized for combustion gases) were within 0.95% and 0.18%, respectively. Third-order virial equations were fitted to the new experimental data. The correlated molar masses at different isotherms agreed with the gravi...

High-fidelity reservoir simulations of enhanced gas recovery with supercritical CO2

EGR (Enhanced natural gas recovery) with CO2 sequestration offers the prospect of significant environmental and economic benefits by increasing gas recovery while simultaneously sequestering the greenhouse gas. Field-scale deployment is currently limited as the risks of contamination of the produced gas by injected CO2 are poorly understood. Reservoir simulations offer a method to quantify the risk but only if sufficiently accurate. For the first time, finite element simulations are presented for several EGR scenarios that incorporate the most accurate models available for fluid mixture and rock properties. Specifically, the GERG-2008 EOS (equation of state) is utilised to describe the supercritical fluid mixture's density, as are reference correlations linked to the most accurate experimental data available for diffusivity and viscosity. Realistic values for rock dispersivity and tortuosity determined from high-accuracy core-flooding and NMR (nuclear magnetic resonance) experiments were also integrated. The relative impacts of these properties were investigated for a benchmark layered reservoir with a quarter 5-spot well pattern. Recovery efficiency at different CO2 injection rates was also investigated and was determined to be the dominant consideration: a 100-fold rate increase improved recovery from 53% to 69% while CO2 breakthrough time decreased by less than expected. Collectively, these results emphasise the importance of accurate reservoir simulations for EGR.

Heat capacities and acoustic virial coefficients for a synthetic coal mine methane mixture by speed of sound measurements at T = (273.16 and 250.00) K

Measurements of speed of sound for a synthetic coal mine methane mixture of ten components are reported. Data were obtained using a spherical resonator for two isotherms T=(273.16 and 250.00)K and pressures up to 8MPa. The uncertainty study is detailed and the total uncertainty of the speed of sound is no worse than 0.01%. Heat capacities and acoustic virial coefficients were obtained through said measurements. Results are compared with the GERG-2008 equation of state.

Accurate Density Measurements on Ternary Mixtures (Carbon Dioxide + Nitrogen + Argon) at Temperatures from (323.15 to 423.15) K with Pressures from (3 to 31) MPa using a Single-Sinker Densimeter

The densities of two ternary mixtures (0.900 carbon dioxide + 0.050 nitrogen + 0.050 argon and 0.950 carbon dioxide + 0.040 nitrogen + 0.010 argon in mole fraction) were measured at temperatures from (323.15 to 423.15) K with pressures from (3 to 31) MPa using a single-sinker magnetic suspension densimeter. The expanded measurement uncertainties (k = 2) were 35 mK for temperature, 3.4 kPa for pressure, and 0.033 % for density. Mixture samples were prepared gravimetrically with the expanded uncertainty (k = 2) in composition 0.001 mole fraction. With all of the measurement and composition effects considered, the expanded combined uncertainty (k = 2) in the density determination was generally within 0.2 % except at thermal states at the vicinity of the critical point near the Widom line. Relative deviations of the experimental data from the GERG-2008 equation of state (EOS), a Helmholtz energy model for natural gas mixtures, and from the EOS-CG, another new Helmholtz energy model for humid gases and fluid m...

Viscosity and Dew Point Measurements of {xCH4 + (1 – x)C4H10} for x = 0.9484 with a Vibrating-Wire Viscometer

The viscosity of {xCH4 + (1 – x)C4H10} with x = 0.9484 has been measured at temperatures and pressures in the range (200 to 423) K and (2 to 30) MPa, respectively, corresponding to densities between (20 and 371) kg·m–3. The measurements were made using a vibrating-wire-viscometer with the wire clamped at both ends and operated in steady-state mode with a combined relative uncertainty of 1 %. The viscometer was also used to investigate the ability of a vibrating-wire instrument to determine the upper and lower dew pressures of the mixture in the retrograde region at (263 and 273) K. The dew pressures were determined by identifying the point along an isothermal pathway at which the slope of the wire’s resonance half-width with pressure exhibited a discontinuity. At the upper dew pressures near 10 MPa the results were consistent to within 0.2 MPa of predictions made using the GERG-2008 equation of state (EOS), while at the lower dew pressures near 3 MPa the agreement was within 0.3 MPa. To facilitate future ...

Reference Quality Vapor–Liquid Equilibrium Data for the Binary Systems Methane + Ethane, + Propane, + Butane, and + 2-Methylpropane, at Temperatures from (203 to 273) K and Pressures to 9 MPa

A specialized cell designed for vapor liquid equilibrium (VLE) measurements at cryogenic temperatures and high pressures was used to measure new (p,T,x,y) data for binary mixtures of methane + ethane, + propane, + 2-methylpropane (isobutane), and + butane from (203 to 273) K at pressures up to 9 MPa. A literature review of VLE data for these binary mixtures indicates that a significant number have large uncertainties; however, because estimates of uncertainties in measured phase compositions are often not quantified sufficiently, it can be difficult for equation of state (EOS) developers to identify which data sets are of poor quality. Robust quantitative uncertainties were estimated for the VLE data acquired in this work, which allowed the identification of literature data sets that should not be included in future EOS development. The new data were compared with the predictions of the Peng–Robinson (PR) EOS and the Groupe European de Recherche Gaziere (GERG-2008) multiparameter EOS. The former describes the new data measured at low pressures within experimental uncertainty but deviates systematically from the data as the bubble point pressure is increased; for the binary mixtures containing either of the butanes, the maximum relative deviation of the data from the PR EOS amounted to nearly 10 % of the methane liquid mole fraction. The GERG-2008 EOS was better able to describe the new high-pressure data for the CH4 + C3H8 system than the PR EOS. However, for both the CH4 + C4H10 mixtures, the GERG EOS deviated from these data by an amount twice as large as the PR EOS because of ambiguity about which VLE literature data sets should be used in model development. The new data resolve these ambiguities and should facilitate the development of improved EOS as needed, for example, in simulations of low temperature natural gas separation processes.

Interfacial tensions of the (CO2 + N2 + H2O) system at temperatures of (298 to 448) K and pressures up to 40 MPa

Interfacial tension measurements of the (CO2+N2+H2O) and (N2+H2O) systems are reported at pressures of (2 to 40)MPa, and temperatures of (298.15 to 448.15)K. The pendant drop method was used in which it is necessary to know the density difference between the two phases. To permit calculation of this difference, the compositions of the coexisting phases were first computed from a combination of the Peng–Robinson equation of state (applied to the non-aqueous phase) and the NRTL model (applied to the aqueous phase). Densities of the non-aqueous phase were computed from the GERG-2008 equation of state, while those of the aqueous phase were calculated knowing the partial molar volumes of the solutes. The expanded uncertainties at 95% confidence are 0.05K for temperature, 0.07MPa for pressure, 0.019γ for interfacial tension in the binary (N2+H2O) system; and 0.032γ for interfacial tension in the ternary (CO2+N2+H2O) system. The interfacial tensions in both systems were found to decrease with both increasing pressure and increasing temperature. An empirical correlation has been developed for the interfacial tension of the (N2+H2O) system in the full range of conditions investigated, with an average absolute deviation of 0.20mN·m−1, and this is used to facilitate a comparison with literature values. Estimates of the interfacial tension for the (CO2+N2+H2O) ternary system, by means of empirical combining rules based on the coexisting phase compositions and the interfacial tensions of the binary sub-systems, (N2+H2O) and (CO2+H2O), were found to be somewhat inadequate at low temperatures, with an average absolute deviation of 1.9mN·m−1 for all the conditions investigated. To enable this analysis, selected literature data for the interfacial tensions of the (CO2+H2O) binary system have been re-analysed, allowing for improved estimates of the density difference between the two phases. The revised result on eleven isotherms were fitted with empirical models that generally represent the data to within 1mN·m−1.

Bubble-Point Measurements of n-Butane + n-Octane and n-Butane + n-Nonane Binary Mixtures

Mixtures of small gaseous hydrocarbons with longer chain hydrocarbons are of interest to the natural gas industry as well as other industries in which separations are critical. In particular, binary mixtures of n-nonane are of interest, because n-nonane was recently incorporated into the GERG-2008 equation of state, but there is little experimental vapor–liquid equilibrium (VLE) data available to support the equation. The bubble-point pressures of four compositions of each of the binary mixtures n-butane + n-octane and n-butane + n-nonane were measured over the temperature range of 270 to 370 K. The data and the expanded uncertainty (at a 95 % confidence level, k = 2) of each point are reported. Additionally, the data are compared to existing literature data for the n-butane + n-octane and the GERG-2008 equation for both systems. This is the first report of vapor–liquid equilibrium measurements on n-butane + n-nonane binary mixtures.

Study of the consequences of CO2 released from high-pressure pipelines

The development of the Carbon Capture and Storage (CCS) technique requires an understanding of the hazards posed by the operation of high-pressure CO2 pipelines. To allow the appropriate safety precautions to be taken, a comprehensive understanding of the consequences of unplanned CO2 releases is essential before the deployment of CO2 pipelines. In this paper, we present models for the predictions of discharge rate, atmospheric expansion and dispersion due to accidental CO2 releases from high-pressure pipelines. The GERG-2008 Equation of State (EOS) was used in the discharge and expansion models. This enabled more precise ‘source strength’ predictions. The performance of the discharge and dispersion models was validated against experimental data. Full-bore ruptures of pipelines carrying CO2 mixtures were simulated using the proposed discharge model. The propagation of the decompression wave in the pipeline and its influence on the release rate are discussed. The effects of major impurities in the CO2 mixture on the discharge rate were also investigated. Considering typical CO2 mixtures in the CCS applications, consequence distances for CO2 pipelines of various sizes at different stagnation pressures were obtained using the dispersion model. In addition, the impact of H2S in a CO2 mixture was studied and the threshold value of the fraction of H2S at the source for which the hazardous effects of H2S become significant was obtained.

Viscosity of {xCO2 + (1 − x)CH4} with x = 0.5174 for temperatures between (229 and 348) K and pressures between (1 and 32) MPa

A vibrating wire instrument, in which the wire was clamped at both ends, was used to measure the viscosity of {xCO2+(1−x)CH4} with x=0.5174 with a combined uncertainty of 0.24μPa·s (a relative uncertainty of about 0.8%) at temperatures T between (229 and 348)K and pressures p from (1 to 32)MPa. The corresponding mass density ρ, estimated with the GERG-2008 equation of state, varied from (20 to 600)kg·m−3. The measured viscosities were consistent within combined uncertainties with data obtained previously for this system using entirely different experimental techniques. The new data were compared with three corresponding states-type models frequently used for predicting mixture viscosities: the Extended Corresponding States (ECS) model implemented in REFPROP 9.1; the SUPERTRAPP model implemented in MultiFlash 4.4; and a corresponding states model derived from molecular dynamics simulations of Lennard Jones fluids. The measured viscosities deviated systematically from the predictions of both the ECS and SUPERTRAPP models with a maximum relative deviations of 11% at (229K, 600kg·m−3) and −16% at (258K, 470kg·m−3), respectively. In contrast, the molecular dynamics based corresponding states model, which is predictive for mixtures in that it does not contain any binary interaction parameters, reproduced the density and temperature dependence of the measured viscosities well, with relative deviations of less than 4.2%.

Integration of biogas in the natural gas grid: Thermodynamic characterization of a biogas-like mixture

The composition of biogas may vary significantly due to the diversity of production sources, making it essential to have a detailed knowledge of their thermophysical properties in order to develop and validate methods for the estimation of density, heat capacity and calorific value of biogas and biomethane. In this work the thermodynamic behavior of a synthetic biogas-like mixture, composed of methane (50%), carbon dioxide (35%), nitrogen (10%) and carbon monoxide (5%), is studied through accurate (p,ρ,T) experimental data obtained by using a single sinker densimeter with magnetic suspension coupling. The mixture was prepared by the gravimetric method at the Spanish National Metrology Institute (Centro Español de Metrología, CEM) and the accurate density measurements have been performed in the temperature range from (275 to 400)K and pressures up to 20MPa. This work is part of the research project ‘Metrology for Biogas’ supported by the European Metrology Research Program. Experimental data are compared with the densities calculated with the GERG-2008 equation of state. The deviation between experimental and estimated densities is within a ±0.2% band at all temperatures, except at the lower temperature, 275K, and pressures from (6 to 15)MPa, which shows a higher deviation.

Decompression wave speed in CO2 mixtures: CFD modelling with the GERG-2008 equation of state

The development of CO2 pipelines for Carbon Capture and Storage (CCS) raises new questions regarding the control of ductile fracture propagation and fracture arrest toughness criteria. The decompression behaviour in the fluid must be determined accurately in order to estimate the proper pipe toughness. However, anthropogenic CO2 may contain impurities that can modify the fluid decompression characteristics quite significantly. To determine the decompression wave speed in CO2 mixtures, the thermodynamic properties of these mixtures must be determined by using an accurate equation of state. In this paper we present a new decompression model developed using the Computational Fluid Dynamics (CFD) package ANSYS Fluent. The GERG-2008 Equation of State (EOS) was implemented into this model through User Defined Functions (UDF) to predict the thermodynamic properties of CO2 mixtures. The model predictions were in good agreement with the experimental data of two ‘shock tube’ tests. A range of representative CO2 mixtures was examined in terms of the changes in fluid properties from the initial conditions, with time and distance, immediately after a sudden pipeline opening at one end. Phase changes that may occur within the fluid due to condensation of ‘impurities’ in the fluid were also investigated. Simulations were also conducted to examine how the initial temperature and impurities would affect the decompression wave speed.

Viscosity of {xCH4 + (1 – x)C3H8} with x = 0.949 for Temperatures between (200 and 423) K and Pressures between (10 and 31) MPa

The viscosity of {xCH4 + (1 – x)C3H8} with x = 0.949 was measured at temperatures between (200 and 423) K and pressures in the range (10 to 31) MPa using a vibrating-wire-viscometer with the wire clamped at both ends and operating in steady-state mode. Over these conditions the fluid mass density, which was calculated from the measured temperature and pressure using the GERG-2008 equation of state, ranged from (120 to 360) kg·m–3. A three-parameter polynomial in density was able to represent the measured viscosities, which ranged between (19 and 53) μPa·s, with an r.m.s. deviation of 0.47 μPa·s. This was comparable to the average combined uncertainty of the measurements (0.43 μPa·s), and no temperature dependence of the viscosity was resolvable within the experimental uncertainty beyond that incorporated within the density obtained from the equation of state. The viscosity of CH4 + C3H8 reported herein along with measurements previously reported in the archival literature at densities up to 500 kg·m–3 hav...

Speeds of sound in (0.95 N2 + 0.05 CO and 0.9 N2 + 0.1 CO) gas mixtures at T = (273 and 325) K and pressure up to 10 MPa

The measurements of speed of sound for two mixtures of (N2+CO) are reported. The data have been obtained using a spherical resonator for two isotherms T=(273.15 and 325.15)K and pressures up to 10MPa. The uncertainty study is detailed and the total uncertainty of the speed of sound is not worse than 0.016%. The results have been compared with the GERG-2008 equation of state.

Isothermal vapor–liquid equilibrium in CH4/H2/N2 system at a cryogenic temperature range from 100.0 K to 125.0 K

Isothermal vapor–liquid equilibrium data for CH4/H2/N2 system are determined by an experimental apparatus based on the static analytic method at a temperature range from 100.0K to 125.0K, corresponding to pressure above atmospheric pressure up to 4.5MPa. Meanwhile, GERG-2008 equation of state is used to calculate the vapor–liquid equilibrium data for CH4/H2/N2 ternary system with a good consistence. The maximum absolute liquid composition deviations are 0.0033 and 0.0011 for hydrogen and nitrogen, respectively. And the maximum absolute vapor composition deviations are 0.0869 and 0.0203 for hydrogen and nitrogen, respectively. In addition, Peng–Robinson (PR) equation of state is used to correlate the experimentally measured pressure–temperature–liquid phase compositions (p–T–xi) for CH4/H2 binary system to propose a temperature-dependent interaction coefficient kij for CH4/H2 system which improves the calculation accuracy in vapor–liquid equilibrium for mixtures containing hydrogen and methane.

Accurate thermodynamic characterization of a synthetic coal mine methane mixture

In the last few years, coal mine methane (CMM) has gained significance as a potential non-conventional gas fuel. The progressive depletion of common fossil fuels reserves and, on the other hand, the positive estimates of CMM resources as a by-product of mining promote this fuel gas as a promising alternative fuel. The increasing importance of its exploitation makes it necessary to check the capability of the present-day models and equations of state for natural gas to predict the thermophysical properties of gases with a considerably different composition, like CMM. In this work, accurate density measurements of a synthetic CMM mixture are reported in the temperature range from (250 to 400)K and pressures up to 15MPa, as part of the research project EMRP ENG01 of the European Metrology Research Program for the characterization of non-conventional energy gases. Experimental data were compared with the densities calculated with the GERG-2008 equation of state. Relative deviations between experimental and estimated densities were within a 0.2% band at temperatures above 275K, while data at 250K as well as at 275K and pressures above 10MPa showed higher deviations.

The GERG-2008 Wide-Range Equation of State for Natural Gases and Other Mixtures: An Expansion of GERG-2004

A new equation of state for the thermodynamic properties of natural gases, similar gases, and other mixtures, the GERG-2008 equation of state, is presented in this work. This equation is an expanded version of the GERG-2004 equation. GERG-2008 is explicit in the Helmholtz free energy as a function of density, temperature, and composition. The equation is based on 21 natural gas components: methane, nitrogen, carbon dioxide, ethane, propane, n-butane, isobutane, n-pentane, isopentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, hydrogen, oxygen, carbon monoxide, water, hydrogen sulfide, helium, and argon. Over the entire composition range, GERG-2008 covers the gas phase, liquid phase, supercritical region, and vapor–liquid equilibrium states for mixtures of these components. The normal range of validity of GERG-2008 includes temperatures from (90 to 450) K and pressures up to 35 MPa where the most accurate experimental data of the thermal and caloric properties are represented to within their accura...

Accurate (p, ρ, T) data for two new (carbon dioxide + nitrogen) mixtures from (250 to 400) K at pressures up to 20 MPa

Recently our group published a set of (p,ρ,T) data for two (carbon dioxide+nitrogen) mixtures with a low carbon dioxide content (xCO2=0.10,0.15). These data showed larger relative deviations from the GERG-2008 equation of state than expected, specially at low temperatures, high pressures, and for the mixture with higher carbon dioxide content (xCO2=0.15). In order to analyze whether the mentioned deviations from the equation of state increase with the carbon dioxide content, it was decided to measure the (p,ρ,T) behavior of two additional mixtures with higher carbon dioxide molar fractions (xCO2=0.20,0.50). The new experimental data show again an appreciable disagreement with the GERG-2008 equation of state at low temperatures and high pressures. Relative deviations, which depend on temperature, arise to 0.4% at 250K and 20MPa and to 0.24% at 275K and 20MPa for the xCO2=0.20 and xCO2=0.50 mixture, respectively. Second virial coefficients are calculated for the two new mixtures presented in this work and also for those presented in our previous paper.