GERG-2008 Equation Research Articles

Особенности решения уравнения состояния GERG-2008

Особенности решения уравнения состояния GERG-2008

Comparative Study of Equations of State for the Dew Curves Calculation in High Pressure Natural Gas Mixtures

The success during the operation of natural gas processing plants depends on the correct estimation of thermodynamic properties of the system. This paper calculates the equilibrium curves of real and synthetic natural gas mixtures means of three Equations of State (EOS). These equilibrium curves were constructed and compared with experimental data found in the literature covered. The results showed that, above 4 MPa the Peng-Robinson equation presented a considerable deviation with respect to the experimental data, reaching an absolute error of 4.36%; therefore, the GERG2008 equation is recommended for systems that operate at high pressures when the components present in the mixture apply.

Accurate experimental (p, ρ, T) data of natural gas mixtures for the assessment of reference equations of state when dealing with hydrogen-enriched natural gas

The GERG-2008 equation of state is the approved ISO standard (ISO 20765-2) for the calculation of thermophysical properties of natural gas mixtures. The composition of natural gas can vary considerably due to the diversity of origin. Further diversification was generated by adding hydrogen, biogas, or other non-conventional energy gases. In this work, high-precision experimental (p, ρ, T) data for two gravimetrically prepared synthetic natural gas mixtures are reported. One mixture resembled a conventional natural gas of 11 components (11 M) with a nominal mixture composition (amount-of-substance fraction) of 0.8845 for methane as the matrix compound with the other compounds being 0.005 for oxygen, 0.04 for nitrogen, 0.015 for carbon dioxide, 0.04 for ethane, 0.01 for propane, 0.002 each for n- and isobutane, and ultimately 0.0005 each for isopentane, n-pentane, and n-hexane. The other mixture was a 13-component hydrogen-enriched natural gas with a low calorific value featuring a nominal composition of 0.7885 for methane, 0.03 for hydrogen, 0.005 for helium, 0.12 for nitrogen, 0.04 for carbon dioxide, 0.0075 for ethane, 0.003 for propane, 0.002 each for n- and isobutane, and 0.0005 each for neopentane, isopentane, n-pentane, and n-hexane. Density measurements were performed in an isothermal operational mode at temperatures between 260 and 350 K and at pressures up to 20 MPa by using a single-sinker densimeter with magnetic suspension coupling. The data were compared with the corresponding densities calculated from both GERG-2008 and AGA8-DC92 equations of state to test their performance on real mixtures. The average absolute deviation from GERG-2008 (AGA8-DC92) is 0.027% (0.078%) for 11 M and 0.095% (0.062%) for the 13-component H2-enriched mixture, respectively. The corresponding maximum relative deviation from GERG-2008 (AGA8-DC92) amounts to 0.095% (0.127%) for 11 M and 0.291% (0.193%) for the H2-enriched mixture.

A new model for predicting the decompression behavior of CO2 mixtures in various phases

Abstract The pipeline transportation has been considered as the best way to transport pressurized CO2 and plays an important role in Carbon Capture and Storage (CCS) technology. The risk of ductile fracture propagation increases when a CO2 pipeline is ruptured or punctured, and CO2 decompression behavior must be determined accurately in order to avoid the catastrophic failure of the pipeline and to estimate the proper pipe toughness. Thus in this work, a new decompression model based on GERG-2008 equation of state was developed for modeling the CO2 decompression behavior. And for the first time, a relaxation model was implemented to calculate the sound speed in two-phase region. The model predictions were in excellent agreement with experimental ‘shock tube’ test data in the literature. Furthermore, via modeling, it has been demonstrated how impurities in the CO2 and initial temperatures would affect the CO2 decompression wave speed in various phases. The results obtained show that the effects of these factors on supercritical and gaseous CO2 mixtures are absolutely different while liquid CO2 mixtures behave very similarly when compared to supercritical CO2 mixtures, which indicate that the toughness required to arrest fracture propagation is highly based on the initial phase states of CO2 fluid.

Sensitivity of natural gas flow measurement to AGA8 or GERG2008 equation of state utilization

The accurate measurement of natural gas flow at metering point is essential for custody transfer. The most used technologies for natural gas measurements are including turbine flow meters, ultrasonic flow meters and orifice flow meters. These flow meters are basically volume flow meter which measure natural gas volume at flow condition. Then the natural gas volume at flow condition should be converted to volume at base (standard) condition by appreciated procedure. Historically, the AGA8 equation of state (EOS) is widely used for such conversion. Recently, a new equation of state (GERG 2008) was presented by European Gas companies for natural gas thermodynamic properties calculation. The main objective of the current study is to present a comparison between AGA8 and GERG2008 EOS in computing conversion factor. Firstly, the Z-factor is calculated based on ISO20765-1 standard which is most recent version of AGA8 EOS. Then, ISO20765-2 standard has been employed to calculate Z-factor based on GERG2008 EOS. Comparing the calculated Z-factor and measured value of previous studies show that the accuracy of GERG2008 EOS is higher than AGA8 for all studied range of pressure and temperature and for various composition ranges. Results also show that GERG2008 equation of state predicts Z-factor higher than AGA8 standard in practical region of measurement. The results also reveal very important findings. Surprisingly, the relative difference is negative for the practical region of measurement. It means that by replacing AGA8 EOS by GERG2008 standard, the less flow is registered by the measurement system. In other words, simply by utilizing the GERG2008 EOS (instead of AGA8 EOS), the buyer benefits.

Vapour-phase (p, ρ, T, x) behaviour and virial coefficients for the (ethane + carbon dioxide) system

Accurate density measurements on three binary (ethane + carbon dioxide) mixtures with ethane mole fractions of 0.05023, 0.20031, and 0.49954 were carried out at temperatures from T = (273.15 to 323.15) K with pressures up to the dew-point pressure or 6.0 MPa, whichever was lower. The gas mixtures were prepared gravimetrically and a well-proven two-sinker magnetic suspension densimeter was utilized for the measurements. It was observed that sorption effects have an impact on the reproducibility of the density measurements of up to 0.04%. Considering all measurement uncertainties in temperature, pressure, density, and composition, the relative combined expanded uncertainty (k = 2) in density was estimated to be less than or equal to 3.8 × 10−4. Relative deviations of the experimental densities from the GERG-2008 equation of state were less than 0.5%, which is clearly within the uncertainty of this equation. Values and uncertainties of the second and third virial coefficients were calculated by correlating the isothermal experimental data to a third-order virial equation. Second interaction virial coefficients were determined as well, and excellent agreement with literature was obtained. The new experimental data presented in this work can be especially used to further improve the performance of multi-parameter equations of state for mixtures, particularly in the vicinity of the dew line.

Density of carbon dioxide with impurities by Coriolis flow meter, oscillation-type densitometer and equations of state

Transporting CO2 from the capture plant to the storage site may encounter challenges in the flow metering due to the unusual physical properties of CO2 – especially when containing impurities. Building on the authors’ previous work on the effect of impurities in CO2 mixtures on the performance of Coriolis flow meters, in this work, the accuracy of the density measurements of CO2 mixtures was investigated using a Coriolis meter and a high-pressure Anton Paar densitometer. The measured density data were then compared to the Peng-Robinson cubic equation of state with CO2 volume correction (PR-CO2) as well as to the multi-parameter GERG-2008 equation of state. The Average Absolute Relative Deviations (AARD) of the density predictions with PR-CO2 and GERG EOSs from the measured densities with the Anton Paar densitometer are 1.2% and 1.0%, respectively. While the Coriolis meter density values were consistently lower than the actual value in the gas phase. A correlation was obtained to correct the measured densities in the gas phase by fitting the measured densities to the prediction values using PR-CO2 and GERG EoSs at elevated pressures and temperatures. The AARD was reduced from 26.1% to 2.3% using PR-CO2 and from 25.4% to 3.6% using GERG EoSs.

Modelling the thermodynamics of air-component mixtures (N2, O2 and Ar): Comparison and performance analysis of available models

With a view to finding which of the available equations of state is the most suitable for the representation of the thermodynamics of mixtures containing nitrogen, oxygen and argon, this paper mainly intends to address the comparison of the performance of the - already optimized - GERG-2008, Bender and Peng-Robinson (PR) Equations of State (EoS) in the calculation of Vapour-Liquid Equilibrium (VLE) and volumetric properties of N2-O2-Ar mixtures. The comparison between experimental measurements collected in the literature and model calculations has led to conclude about the overall superiority of GERG-2008. It is also shown that the Peng-Robinson EoS leads to comparable results in VLE calculations and that the use of Bender EoS should be avoided as it leads, despite its complex multiparameter formulation, to very inaccurate results in the calculation of VLE properties of the binary Ar-O2 and of volumetric properties. For completeness, the paper also shows the poor accuracy of the PR EoS in calculating VLE properties when zero-kij are selected. Moreover, the paper evaluates the impact of deviations on densities, calculated with the different equations of state, on the computation of transport properties (thermal conductivity, viscosity), in turns determined by means of correlations which are typically applied. Liquid thermal conductivity is highly affected by errors on liquid density calculations while the liquid viscosity is independent of density. Differently, errors on vapour thermal conductivity and dynamic viscosity are lower than those observed on vapour density.

Gibbs ensemble Monte Carlo simulations of multicomponent natural gas mixtures

Vapour–liquid equilibrium (VLE) and volumetric data of multicomponent mixtures are extremely important for natural gas production and processing, but it is time consuming and challenging to experimentally obtain these properties. An alternative tool is provided by means of molecular simulation. Here, Monte Carlo (MC) simulations in the Gibbs ensemble are used to compute the VLE of multicomponent natural gas mixtures. Two multicomponent systems, one containing a mixture of six components (, , , S, and ), and the other containing a mixture of nine components (, , , S, , , , and ) are simulated. The computed VLE from the MC simulations is in good agreement with available experimental data and the GERG-2008 equation of state modelling. The results show that molecular simulation can be used to predict properties of multicomponent systems relevant for the natural gas industry. Guidelines are provided to setup Gibbs ensemble simulations for multicomponent systems, which is a challenging task due to the increased number of degrees of freedom.

A new tool for modelling the decompression behaviour of CO2 with impurities using the Peng-Robinson equation of state

Carbon capture and storage is considered as promising technique by the scientific community to reduce CO2 emissions and is composed by three different stages: CO2 capture, transportation and storage. The capturing plant has to be installed where processes involving large CO2 emissions, as power generation from fossil fuel, concrete and iron plants are present. The captured CO2 in real applications will be likely a CO2 dominated mixture with a content of several impurities, depending on the capture process which presence affects the thermo-physical properties of the pure CO2, especially increasing the vapour pressure curve. Such behaviour plays an important role in the control of the ductile fracture, whenever the CO2 is transported using pipelines. In the unfortunate event of a pipeline failure, the study of the pipeline decompression can be useful to estimate whether the fracture will remain confined or will propagate. The residual pressure acting on the crack tip of the pipeline represents the energy source governing the fracture’s propagation. The pressure profile is given by the expansion wave, which propagates along the pipeline during the fracture. In the literature, it is common practice to model the expansion wave by assuming one-dimensional isentropic decompression. In this study, a new code developed by the authors for modelling the decompression behaviour in the fluid is presented. The code is based on the Peng-Robinson equation of state with the Peneloux correction correlation matching the density of pure components to experimental data. The sound velocity in the two-phase region has been modelled with the method proposed by Nichita et al., which increase the accuracy of prediction with respect to the most popular Wood’s method. The code was validated against experimental and numerical data relating to hydrocarbon gas mixtures and CO2-rich mixtures. In particular, the results obtained for the hydrocarbon gas mixture decompression have been compared with experimental data and the predictions calculated by the software GASDECOM, in order to assess the accuracy of the code, that was then utilized to calculate the expansion wave curves for CO2-rich mixtures. The results obtained have been compared with experimental data and with predictions generated by the GERG2008 equation of state, found in literature. The simulated expansion wave curves show a good agreement with the experimental data for the tested compositions, especially for the plateau characterising the two-phase transition of rich gas compositions. The plateau corresponds to the saturation pressure, which is a key parameter for the fracture propagation control in CO2 pipelines, since the material toughness required to prevent a propagating ductile fracture is determined by applying the condition that the fracture propagation curve does not cross this value.

Characterization of a biomethane-like synthetic gas mixture through accurate density measurements from (240 to 350) K and pressures up to 14 MPa

In this work the thermodynamic behavior of a synthetic four-component biomethane-like mixture, composed mainly of methane (96.48%), with small amounts of carbon dioxide (2.00%), nitrogen (1.50%), and traces of oxygen (0.02%), is studied using accurate (p,ρ,T) experimental data. Two mixtures of identical nominal compositions were prepared by the gravimetric method at the Spanish National Metrology Institute (Centro Español de Metrología, CEM) and at the Slovak National Metrology Institute (Slovenský Metrologický Ústav, SMÚ). The composition was double checked by Gas Chromatography, at both NMI and at the beginning and end of the measurements. An additional test of the consistency of the given compositions was performed by measuring the density of both mixtures at selected points, with two different techniques, in two different laboratories. Accurate density measurements have been taken over a wide temperature range, from (240 to 350) K, and pressures up to 14MPa, using a single-sinker densimeter with magnetic suspension coupling. Experimental data are compared with the densities calculated with the GERG-2008 and AGA8-DC92 equations of state. Deviations between experimental and GERG-2008-estimated densities are within a ±0.03% band at all temperatures, which shows the outstanding performance of the current reference equation for natural gases when describing a biomethane-like mixture. Deviations between experimental and AGA-8-estimated densities are higher than 0.04% at 250K for pressures greater than 10MPa and also at 240K for pressures higher than 9MPa. This work is part of the research project ‘Metrology for Biogas’ supported by the European Metrology Research Program.

Effective Critical Constants for Helium for Use in Equations of State for Natural Gas Mixtures

Most of the world’s helium supply is obtained by the cryogenic distillation of natural gas. Modeling the distillation conditions requires equations of state capable of predicting vapor–liquid equilibria over wide ranges of conditions. Equations of state, including cubic equations and multiparameter Helmholtz models, depend on the critical properties of pure substances for predicting various properties of multicomponent fluid mixtures. Predictions for helium are problematic as its critical point (5.195 K, 0.2275 MPa) is influenced strongly by quantum effects; large, empirical interaction parameters tend to be used in equations of state to compensate for these effects. Prausnitz and co-workers proposed an alternative approach using effective critical constants for quantum gases but demonstrated it for only three helium-containing binary mixtures. Here, we demonstrate that the use of an effective critical point at (11.73 K, 0.568 MPa) for helium substantially improves the prediction of VLE by the Peng–Robinson equation of state for 15 binary and 2 ternary mixtures, including the major components of natural gas. This effective critical point for helium was selected from a critical analysis of pTxy data for the (methane + helium) binary. The effective critical constants for helium are compatible with an acentric factor near zero, as expected for a small spherical molecule and similar to the acentric factors of heavy noble gases. The possibility of applying this approach to address recognized limitations of the GERG-2008 equation of state is discussed.

Density measurements of liquefied natural gas (LNG) over the temperature range from (105 to 135) K at pressures up to 8.9 MPa

The (p, ρ, T, x) behaviour of five different synthetic liquefied natural gas (LNG) mixtures was investigated over the temperature range from (105 to 135)K at pressures up to 8.9MPa utilizing a single-sinker magnetic suspension densimeter for cryogenic liquid mixtures. Due to the supercritical liquefaction procedure and the integration of a special VLE-cell, it was possible to measure densities in the homogeneous liquid phase of LNG without changing the composition. The mixtures were prepared gravimetrically and then analysed by gas chromatography according to highest metrological standards. The relative combined expanded uncertainty (k=2) in density considering all effects, including the uncertainty in composition, was approximately 0.044% for all measurements. Comparisons of the new experimental data to the GERG-2008 equation of state for natural gas mixtures revealed clear and systematic deviations up to 0.22%. The reported uncertainty for the GERG-2008 equation is (0.1 to 0.5)% for the conditions considered, thus, all measured densities are represented well within this uncertainty range. Comparisons to density calculation methods often used in LNG industry, such as the revised Klosek and McKinley method as well as the COSTALD correlation, revealed that the quality of the calculations clearly depends on the pressure range and on the composition of the LNG mixture.

Surface tension and critical point measurements of methane + propane mixtures

Surface tension predictions of hydrocarbon mixtures at vapour-liquid equilibrium are crucially important and used in the design of many unit operations in the production of liquefied natural gas (LNG). Predictive models for surface tension are not well tested for hydrocarbon mixtures at high pressures due to the limited data available at relevant conditions. A differential capillary rise apparatus consisting of a high-pressure sapphire equilibrium cell was constructed and used to measure the surface tension of methane+propane mixtures along three isotherms T=(272.23, 285.51 and 303.34)K at pressures up to 9MPa. The capillary diameters were calibrated using pure saturated propane at 271K, and the technique was validated by measurements of pure ethane. The measured surface tensions were compared with the available data and the predictions of various models, including the Parachor method and Linear Gradient Theory: both were able to describe the data within their uncertainty. However, the default surface tension model for hydrocarbon mixtures implemented in the widely-used software package REFPROP 9.1 gave poor predictions; this was rectified through the implementation of the Parachor method in a beta-version of REFPROP 9.2. Critical points were also measured from observations of critical opalescence and the disappearance of the bulk interface. The measured mixture critical points were consistent with, and extended, literature values for this binary system. The measured critical points differed by between 0.5 and +27K from predictions made with the GERG-2008 equation of state (EOS) and between −5 and +10K for the Peng-Robinson EOS.

Density, speed of sound and derived thermodynamic properties of a synthetic natural gas

Densities (ρ) and speed of sound (SOS) of a synthetic natural gas (∼88 mol% methane) were determined simultaneously at temperatures between 323 and 415 K and pressure up to 58 MPa. Densities and speed of sound were measured using a high pressure and high temperature Vibrating Tube densitometer (VTD) and an in-house acoustic cell, respectively. Moreover, to extend the PρT measurements to a wider range of temperature, isochoric measurements were conducted in a temperature range of 210–270 K.The AGA8-DC92, GERG-2008, SBWR and PR-78 equations of state (EoS) were used to evaluate the experimental data. Finally, the SBWR EoS was tuned on the experimentally measured density to determine other thermodynamic properties such as isobaric heat capacity (Cp), isochoric heat capacity (Cv) and Joule-Thomson coefficients (μJT).

Calculation of critical points for natural gas mixtures with the GERG-2008 equation of state

Critical points of natural gas mixtures containing linear alkane molecules (C1-n-C8), branch alkanes (i-C4-i-C5), nitrogen (N2), and carbon dioxide (CO2) are calculated using a criterion based upon the Helmholtz free energy. We use the GERG equation of state with its mixing rules together with needed derivatives evaluated numerically. A multivariable iterative method is used to solve the system of non-linear equations that appear in this procedure. Results are checked for stability using mechanical, diffusional and global stability tests. Our results are compared with the literature values. Maximum error for the temperature and pressure are 1.301 and 11.087% respectively. The predictive capability of the GERG-2008 equation of state is compared with PR, SRK, PSRK, SPHCT, and PC-SAFT equations of state. For binary mixtures, all equations of state are capable of representing global phase behavior types I to IV. Results show that the GERG-2008 equation of state with binary interaction parameters is adequate for the prediction of critical points.

Cryogenic pressure temperature swing adsorption process for natural gas upgrade

Abstract Removal of carbon dioxide from natural gas for LNG production, can be carried out by cryogenic distillation using a multicolumn sequence to obtain a product stream with less than 50 ppm of CO 2 . Cryogenic adsorption-based processes, particularly pressure thermal swing adsorption, arise as a reliable and innovative alternative to replace the distillation columns, in particular the last one. In this work, the implementation of a new methodology to design and simulate an industrial scale pressure and temperature swing adsorption process at low temperature (Cryo-PTSA) is presented, in order to produce an almost pure methane stream, with a maximum of 50 ppm of CO 2 , maximizing the methane recovery. Binderless 13X zeolite was selected as adsorbent and adsorption equilibrium isotherms of methane and carbon dioxide were determined experimentally, in the temperature range 183–473 K, up to 80 bar. The GERG2008 equation of state (EoS) was used during the dynamic simulations to account for deviation from ideal gas law, through the use of REFPROP (REFerence fluid PROPerties) software package. Since this method leads to high simulation time consumption, Surface Equations (SE) were used as alternative calculation method to determine the compressibility factor and the heat capacities at constant pressure and volume. A methane recovery of 90.7% and a product stream with 41.8 ppm of CO 2 in CH 4 is achieved after cyclic steady state is reached. Cryo-PTSA simulation results were then compared with an existing cryogenic distillation process. The results obtained by process simulation showed that it is possible to replace the 3 rd column of the cryogenic distillation process by a Cryo-PTSA achieving higher CH 4 recovery and lower power consumption (2.2 MW).

Experimental and modelling study of the densities of the hydrogen sulphide + methane mixtures at 253, 273 and 293 K and pressures up to 30 MPa

Densities of three binary mixtures of hydrogen sulphide and methane (xH2S + (1 − x) CH4), with mole fractions of 0.1315, 0.1803 and 0.2860 of acid gas, were determined experimentally at three temperatures (253, 273 and 293) K and at pressures up to 30 MPa. Densities were measured continuously using a high temperature and high pressure Vibrating Tube densitometer (VTD), Anton Paar DMA 512. The SAFT-VR Mie, PR and GERG2008 equations of state (EoS) are used to describe the experimental data with different levels of success.

Density Measurements for Ethane, Carbon Dioxide, and Methane + Nitrogen Mixtures from 300 to 470 K up to 137 MPa Using a Vibrating Tube Densimeter

This paper presents experimental p–ρ–T measurements for nitrogen + methane mixtures containing approximately 0.25, 0.50, and 0.75 mole fraction methane at T = 300, 350, 400, and 470 K with p = 10–137 MPa. Methane, nitrogen, and argon are used as calibration fluids, and measurements on carbon dioxide and ethane verify the calibration methodology. An error contribution analysis indicates that the expanded uncertainty (95% confidence limit) is 0.1 kg·m–3 for densities lower than 200 kg·m–3 and 0.0005·ρ for higher densities. The GERG-2008 equation of state describes the measurements for all three mixtures to within ±0.0015·ρ with the largest deviations occurring at the highest pressures.

Characterisation of a microwave re-entrant cavity resonator for phase-equilibrium measurements and new dew-point data for a (0.25 argon + 0.75 carbon dioxide) mixture

An apparatus based on a microwave re-entrant cavity resonator, originally built for accurate measurements of the dielectric permittivity of natural gas mixtures, was refurbished and extensively characterised. This was done to enable the future investigation of phase equilibria and (p, ρ, T, x) behaviour of fluid mixtures utilizing the present experimental technique. Vacuum resonance frequencies and Q-factors of the resonator’s modes were modelled using both analytic and finite element methods, and found to compare well with experimental values. The finite element models helped to identify two whispering gallery-type modes not previously reported for such cavity geometries. The models also predict distributions of the electric and magnetic fields in the re-entrant cavity resonator useful for identifying regions in the cavity more sensitive to the presence of a liquid. Following the resonator’s characterisation, its ability to measure dew points was tested using a gravimetrically prepared (0.2501 argon+0.7499 carbon dioxide) mixture over the temperature range from (252 to 280)K at pressures from (2.8 to 6.9)MPa. The combined expanded uncertainty with a level of confidence of approximately 95% (k=2) in dew-point temperature and pressure ranged between (0.025 and 0.044)K and from (0.009 to 0.015)MPa, respectively. We compared the experimental dew-point pressures with the recently developed multi-parameter equation of state optimised for combustion gases (EOS-CG), showing relative deviations in the range of (0.044 to 0.479)%. In contrast, relative deviations of up to −4% from the GERG-2008 equation of state and two different implementations of the Peng-Robinson equation were observed, although these models are not optimised for dew point calculations of carbon dioxide rich mixtures.