Equation Of State For Methane Research Articles

A Combined Equation of State for Methane, Based on Bender’s Regular Equation with a Scaling Part in Explicit Form up to 50 MPa

A Combined Equation of State for Methane, Based on Bender’s Regular Equation with a Scaling Part in Explicit Form up to 50 MPa

Eighth-Order Virial Equation of State for Methane from Accurate Two-Body and Nonadditive Three-Body Intermolecular Potentials.

The second to eighth virial coefficients of methane were determined for temperatures up to 1200 K using an existing ab initio-based and empirically fine-tuned two-body potential combined with a new empirical nonadditive three-body potential. Nuclear quantum effects were accounted for by the semiclassical Feynman-Hibbs approach. The numerical evaluation of the high-dimensional integrals through which the virial coefficients are expressed was performed employing the Mayer-sampling Monte Carlo technique. By fitting suitable mathematical functions to the calculated virial coefficients, an analytical eighth-order virial equation of state (VEOS8) was obtained. Pressures p computed as a function of temperature T and density ρ using VEOS8 agree highly satisfactorily with p(ρ, T) values obtained with the experimentally based reference equation of state for methane of Setzmann and Wagner (SWEOS) at state points at which VEOS8 is sufficiently converged. It is shown that it is essential to account for nonadditive three-body interactions in the calculations in order to achieve good agreement with the SWEOS.

Equation of liquid, gas, and fluid state for methane

Using methods and approaches, previously developed by the authors, a new fundamental low-parametric equation of state for methane (in the form of the reduced Helmholtz function) has obtained to describe the thermodynamic properties. It allows describing the thermal properties of gas, liquid, and fluid at pressures of up to 20 MPa with sufficiently high accuracy close to the experimental one (with the exception of the critical region). The sound speed and caloric properties of methane have been calculated without involving any caloric data, with the exception of ideal gas enthalpy. The values of speed of sound, isochoric heat capacity, and other thermodynamic properties obtained by calculations are in good agreement with the experimental data.

A new application of NMR in characterization of multiphase methane and adsorption capacity of shale

Adsorbed and free methane are the primary contributor for gas production from shale. To accurately quantify the multiphase methane in shale is of great significance for shale gas exploration and exploitation. The conventional calculation methods to quantify the multiphase methane in shale are typically mathematical extrapolation from reservoir information, which tend to generate large error and is hard to be applied for shale reservoir because of its heterogeneity characteristics. Meanwhile, the most commonly used volumetric or manometric experimental methods are tedious, time-consuming and indirect measurement that requires assuming adsorbed phase density. Any volumetric effect or impurities can distort the shape of the isotherm measured with volumetric or manometric method. Therefore, it is necessary to explore a new quantitative method that can directly detect the multiphase methane in shale. In this study, several special experimental setups and methods were designed to evaluate the multiphase methane in shale. By introducing the low-field nuclear magnetic resonance (NMR) into the isothermal methane adsorption experiments of shale samples, this study developed a methodology for quantitative identification of multiphase methane gases in shale. Results show that the transverse relaxation time (T2) spectra of methane in shale contain four distinctive peaks, among which the peak (P1) with shortest T2 (<~1 ms) represents adsorbed methane and the one (P2) with longer T2 (~ 1–50 ms) symbolizes free methane in shale. The P2 increased linearly with methane pressure, whereas the P1 increased with increasing pressure to a very limited extent and reached a limiting value, similar to Langmuir equation. The provided method can directly measure the absolute and relative amounts of free and adsorbed methane gases in shale at a certain pressure, which is applicable to measure the in-situ gas content of the pressure coring shale samples, or alternatively, to theoretically estimate maximum adsorbed and free gas content when only the conventional core sample is available for analysis. This study also reports a newly developed technique that directly measures methane adsorption capacity and adsorption isotherm of shale, without the application of the equation of state for methane or volumetric corrections of any kind. The results show that the proposed method that is based on analysis of NMR relaxation time of methane in shale with respect to increasing pressure, is in excellent agreement with the conventional gravimetric method performed paralleled with the NMR method using the same experimental conditions. The developed theory and analytical technique to determine the multiphase methane and methane adsorption isotherm of shale provide an alternative method for in-situ gas content test and monitoring gas transport processes in shale such as desorption, diffusion and seepage.

Waste cold energy recovery from liquefied natural gas (LNG) regasification including pressure and thermal energy

The world has been concentrating on waste heat recovery for several decades. The attention has recently been turned to waste energy in cold streams. This work focuses on the recovery of waste cold energy released from the Liquefied Natural Gas (LNG) regasification process, including pressure energy and thermal energy. A direct expansion configuration involving different steps of expansion and mass flow rate extraction at intermediate pressure levels is adopted in the mathematical models for pressure energy recovery. A direct-configuration organic Rankine cycle (ORC) is employed subsequently to recover residual cold energy. An equation of state for methane (the main component of LNG) is used to estimate the thermodynamic properties of LNG in a long-range phase transition of the regasification process. The modified Peng-Robinson (PR) and the Soave-Redlich-Kwong (SRK) equations of state are used to calculate thermodynamic properties of the ORC working fluids. All the models are developed and solved using MATLAB. By adopting propane as the ORC working fluid, the multistage expansion and thermal energy extraction can recover 215 kJ per kilogram of flowing LNG, which can generate 1.7 GWh annually for 1 kg/s LNG, with a payback period less than seven years.

Waste energy recovery including pressure and thermal energy from lng regasification

The world has been concentrating on waste heat recovery for several decades, with the vast majority of achievements making a significant contribution to the development of industry and economy. The attention has recently been paid to waste energy from cold streams. This work focuses on the recovery of waste cold energy released from Liquefied Natural Gas (LNG) regasification process, including pressure and thermal energy. A direct expansion configuration involving different steps of expansion and mass flow rate extraction at intermediate pressure levels is adopted in the mathematical models for pressure and cold energy recovery. An equation of state for methane (the main component of LNG) is employed to calculate LNG thermodynamic properties in a long-range phase transition of the regasification process. A direct configuration of the organic Rankine cycle (ORC) is employed to recover waste cold energy. The modified Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state (EOS) play important roles in calculation of thermodynamic properties of the organic working fluids used in the ORC. Several fluids are examined to select the most suitable one as the ORC working fluid. All the models are developed and solved by using MATLAB. By adopting propane as the working fluid in the ORC, the multi-stage expansion along with thermal energy extraction is shown to be the most thermodynamically efficient configuration with the recovery of up to 170 kJ pressure energy for each kg of the flowing LNG, and up to 74 kJ from thermal energy recovery.

Simulation of real gas effects in supersonic methane jets using a tabulated equation of state with a discontinuous Galerkin spectral element method

Abstract Modern direct gas injectors for natural-gas-powered internal combustion engines operate at ever-increasing pressures to maximize efficiency. At the operating point of current devices, real gas effects already become relevant, for example in the determination of mass flow rates. These effects have to be considered in the design process of such components. Motivated by this fact, we investigate the real gas effects of high-pressure supersonic methane jets. A discontinuous Galerkin spectral element method for computational fluid dynamics is used in combination with a tabulated equation of state for methane. We first evaluate self-similar profiles for subsonic jets to validate our simulation approach. Then we discuss our simulations of a supersonic jet, where we observe well-resolved shocks and transient structures. Additionally, real and ideal gas modeling are compared and we discuss the significant differences in general flow structure as well as density, pressure and mass flow that occur and make an ideal-gas description inappropriate for our simulation. The influence of pressure level and temperature on the behavior of the jet is discussed. We analyze the influence of the thermodynamic and viscous properties of the gas for the shock location and mass flow. The use of a tabulated equation of state makes jet simulations with occurring phase changes possible.

Methane storage in nanoporous material at supercritical temperature over a wide range of pressures.

The methane storage behavior in nanoporous material is significantly different from that of a bulk phase, and has a fundamental role in methane extraction from shale and its storage for vehicular applications. Here we show that the behavior and mechanisms of the methane storage are mainly dominated by the ratio of the interaction between methane molecules and nanopores walls to the methane intermolecular interaction, and a geometric constraint. By linking the macroscopic properties of the methane storage to the microscopic properties of a system of methane molecules-nanopores walls, we develop an equation of state for methane at supercritical temperature over a wide range of pressures. Molecular dynamic simulation data demonstrates that this equation is able to relate very well the methane storage behavior with each of the key physical parameters, including a pore size and shape and wall chemistry and roughness. Moreover, this equation only requires one fitted parameter, and is simple, reliable and powerful in application.

Calculation of Orthobaric Densities from Equations of State

A numerical method for calculation of densities of saturated vapour and liquid phases, and of saturated vapour pressure using an equation of state is proposed. The method proved to be both robust and efficient using the Redlich-Kwong equation of state for methane. The method can be straightforwardly extended for the case of multicomponent systems.

A new flow calorimeter for the measurement of the isobaric enthapy increment and the isenthalpic Joule–Thomson effect. Results for methane and (methane + ethane)

The present paper describes the design of a new adiabatic flow calorimeter which is capable of measuring the integral Joule–Thomson effect an the isobaric enthalpy increment in the gaseous phase. The underlying principles for calorimetric measurements are discussed, and the measuring devices are described. Heat losses were shown to be significantly less then the experimental accuracy. A theoretical maximum error calculation yielded values within the bounds of 0.9 per cent for the isobaric enthalpy increment and 180 mK for the integral Joule–Thomson effect. The direct measurement results are given for pure methane in the temperature range between room temperature and about 580 K at pressures up to 7 MPa, and for {xC2H6+(1−x])CH4} atx=0.11 andx=0.25 forp=7 MPa in the temperature range between 380 K and 480 K. Other properties such as enthalpy residual and molar heat capacity at constant pressure are also derived and correlated. Good agreement was found with available experimental results from the literature and with the prediction made by the accurate Wagner–Setzmann equation of state for methane. Our results confirm the validity of our experimental and evaluation procedures and extend the experimentally investigated temperature range for methane. Further results for binary and ternary mixtures with water will be published in a subsequent paper.

Second and third acoustic virial coefficients of methane at temperatures between 125 K and 375 K

The speed of sound in methane has been measured with an estimated uncertainty of 0.003 per cent in the temperature range 125 K to 250 K at pressures up to 1.4 MPa. The results are compared with the most recent equation of state for methane and the agreement is generally within 0.03 per cent except near to the vapour pressure where deviations of up to 0.1 per cent are found. Isobaric perfect-gas heat capacities and second and third acoustic virial coefficients have been determined from the results. These same quantities have also been obtained at temperatures in the range 275 K to 375 K from a re-analysis of earlier measurements of the speed of sound.

A theoretical equation of state for methane

A theoretical equation of state for methane is derived and compared with experimental data. The EOS for the solid phase was constructed from the Debye model. The EOS for the fluid phase was constructed from thermodynamic perturbation theory. Tables of the calculated thermodynamic properties are available for temperatures from 20 to 104 K and for densities up to 2.5 g/cm3. Agreement with experiment is good.

An equation of state for methane in the form of Bender's equation for temperatures between 91 K and 625 K and pressures up to 500 bar

Abstract Sievers, U. and Schulz, S., 1980. An equation of state for methane in the form of Bender's equation for temperatures between 91 K and 625 K and pressures up to 500 bar. Fluid Phase Equilibria , 5: 35–54. The coefficients of Bender's equation of state for pure fluid methane are refitted using recent, precise experimental data. This equation of state represents the thermodynamic properties of methane in the fluid region for temperatures between 90.68 K and 625 K, densities up to 28.6 mole dm -3 and pressures up to 500 bar with high accuracy. Only in the critical region is there a slightly lower accuracy. Compared with the results obtained with Bender's original coefficients, improvements are achieved in wide regions, especially for the calculation of vapour-liquid phase equilibria and liquid properties.

Adsorption of methane on dry coal at elevated pressure

Methane equilibrium adsorption isotherms were determined on Illinois No.6 (Herrin seam), Oklahoma Hartshorne, Pennsylvania Pittsburgh, and Virginia Pocahontas No.3 United States coal seams, using a volumetric method and an equation of state for methane: the amount of methane adsorbed on crushed and dried coal was measured as a function of pressure. Isotherms were measured at 30 °C for the Illinois coal and at 0, 30 and 50 °C for the others. Most measurements were made to 150 atm pressure, but a few to 240 atm. The data were correlated by the Langmuir and the Polanyi adsorption models. The methane—coal system, uncorrected for adsorbate density, adhered well to the Langmuir model up to 150 atm pressure, but Polanyi behaviour could not be demonstrated satisfactorily, with or without a correction for adsorbate density. Monolayer volumes at 30 °C from the Langmuir equation were 28, 24, 19 and 20cm 3 (STP)/g coal respectively for the four coals studied (the range for several investigators was 13 to 39 cm 3/g and for the Langmuir constant b 0.03 to 0.23 atm −1). Isosteric heats of adsorption at zero coverage and 30 °C were 4.2, 2.4 and 5.3 kcal/mol for the Hartshorne, Pittsburgh and Pocahontas coals, which indicate that the adsorption is physical. No effect of particle size on equilibrium adsorption was observed in the U.S. mesh range 6–325.

An equation of state for methane in the gas and liquid phases

AbstractAn equation of state was developed which represented experimental methane P‐V‐T data over the temperature range of 130 to 625° K. for pressures to 10,000 lb./sq. in. obs. with densities to 0.36 g./cc. For 598 experimental points the mean square percent deviation in the predicted pressures was 0.07% with only 10 points having deviations above 0.2%. The low density limit of the equation predicted second virial coefficients within 1 cc./mole of the accepted values for temperatures above 200° K.The equation was developed by first analyzing isochoric data from the saturation point to the high temperature or pressure limit. An expression was then obtained, reflecting qualitative behavior of the isochores, that reproduced experimental data along each isochore with an average pressure error of 0.02% and a maximum error of 0.08%. This expression had the form P = A + BT + C exp [E (T — T0)] + D exp (k—F/T) where k and T0 were normalizing constants and A through F were functions of density. From the density dependence of these parameters a single expression was obtained which fit the entire range of experimental data.