Roland Span

A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple‐Point Temperature to 1100 K at Pressures up to 800 MPa

This work reviews the available data on thermodynamic properties of carbon dioxide and presents a new equation of state in the form of a fundamental equation explicit in the Helmholtz free energy. The function for the residual part of the Helmholtz free energy was fitted to selected data of the following properties: (a) thermal properties of the single‐phase region (pρT) and (b) of the liquid‐vapor saturation curve (p s, ρ′, ρ″) including the Maxwell criterion, (c) speed of soundw and (d) specific isobaric heat capacityc p of the single phase region and of the saturation curve, (e) specific isochoric heat capacityc v , (f) specific enthalpyh, (g) specific internal energyu, and (h) Joule–Thomson coefficient μ. By applying modern strategies for the optimization of the mathematical form of the equation of state and for the simultaneous nonlinear fit to the data of all these properties, the resulting formulation is able to represent even the most accurate data to within their experimental uncertainty. In the technically most important region up to pressures of 30 MPa and up to temperatures of 523 K, the estimated uncertainty of the equation ranges from ±0.03% to ±0.05% in the density, ±0.03% to ±1% in the speed of sound, and ±0.15% to ±1.5% in the isobaric heat capacity. Special interest has been focused on the description of the critical region and the extrapolation behavior of the formulation. Without a complex coupling to a scaled equation of state, the new formulation yields a reasonable description even of the caloric properties in the immediate vicinity of the critical point. At least for the basic properties such as pressure, fugacity, and enthalpy, the equation can be extrapolated up to the limits of the chemical stability of carbon dioxide. Independent equations for the vapor pressure and for the pressure on the sublimation and melting curve, for the saturated liquid and vapor densities, and for the isobaric ideal gas heat capacity are also included. Property tables calculated from the equation of state are given in the appendix.

A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa

A new formulation for the thermodynamic properties of nitrogen has been developed. Many new data sets have become available, including high accuracy data from single and dual-sinker apparatuses which improve the accuracy of the representation of the pρT surface of gaseous, liquid, and supercritical nitrogen, including the saturation states. New measurements of the speed of sound from spherical resonators yield accurate information on caloric properties in gaseous and supercritical nitrogen. Isochoric heat capacity and enthalpy data have also been published. Sophisticated procedures for the optimization of the mathematical structure of equations of state and special functional forms for an improved representation of data in the critical region were used. Constraints regarding the structure of the equation ensure reasonable results up to extreme conditions of temperature and pressure. For calibration applications, the new reference equation is supplemented by a simple but also accurate formulation, valid on...

A New Equation of State for Argon Covering the Fluid Region for Temperatures From the Melting Line to 700 K at Pressures up to 1000 MPa

This work reviews the available data on thermodynamic properties of ethylene and presents a new equation of state in the form of a fundamental equation explicit in the Helmholtz energy. The functional form of the residual part of the Helmholtz energy was developed by using state-of-the-art linear optimization strategies. The new equation of state contains 35 coefficients which were fitted to selected data of the following properties: (a) thermal properties of the single phase (pρT) and (b) of the liquid–vapor saturation curve (ps,ρ′,ρ″) including the Maxwell criterion, (c) speed of sound w of the single-phase region and the saturated vapor and liquid, (d) isochoric heat capacity cv, (e) specific isobaric heat capacity cp of the single-phase region and of the saturated liquid, and (f) second and third thermal virial coefficients B and C. For the density, the estimated uncertainty of the new equation of state is less than ±0.02% for pressures up to 12 MPa and temperatures up to 340 K with the exception of t...

Equations of State for Technical Applications. II. Results for Nonpolar Fluids

New functional forms have been developed for multiparameter equations of state for non- and weakly polar fluids and for polar fluids. The resulting functional forms, which were established with an optimization algorithm which considers data sets for different fluids simultaneously, are suitable as a basis for equations of state for a broad variety of fluids. The functional forms were designed to fulfill typical demands of advanced technical applications with regard to the achieved accuracy. They are numerically very stable and their substance-specific coefficients can easily be fitted to restricted data sets. In this way, a fast extension of the group of fluids for which accurate empirical equations of state are available becomes possible. This article deals with the results found for the non- and weakly polar fluids methane, ethane, propane, isobutane, n-butane, n-pentane, n-hexane, n-heptane, n-octane, argon, oxygen, nitrogen, ethylene, cyclohexane, and sulfur hexafluoride. The substance-specific parameters of the new equations of state are given as well as statistical and graphical comparisons with experimental data. General features of the new class of equations of state such as their extrapolation behavior and their numerical stability have been discussed in a preceding article. Results for typical polar fluids will be discussed in a subsequent article.

Equations of State for Technical Applications. I. Simultaneously Optimized Functional Forms for Nonpolar and Polar Fluids

New functional forms for multiparameter equations of state have been developed for non- and weakly polar fluids and for polar fluids. The resulting functional forms, which were established with an optimization algorithm which considers data sets for different fluids simultaneously, are suitable as a basis for equations of state for a broad variety of fluids. With regard to the achieved accuracy, the functional forms were designed to fulfill typical demands of advanced technical application. They are numerically very stable, and their substance-specific coefficients can easily be fitted to restricted data sets. In this way, a fast extension of the group of fluids for which accurate empirical equations of state are available becomes possible. This article deals with characteristic features of the new class of simultaneously optimized equations of state. Shortcomings of existing multiparameter equations of state widely used in technical applications are briefly discussed, and demands on the new class of equations of state are formulated. Substance specific parameters and detailed comparisons are given in subsequent articles for the non- and weakly polar fluids (methane, ethane, propane, isobutane, n-butane, n-pentane, n-hexane, n-heptane, n-octane, argon, oxygen, nitrogen, ethylene, cyclohexane, and sulfur hexafluoride) and for the polar fluids (trichlorofluoromethane (CFC-11), dichlorodifluoromethane (CFC-12), chlorodifluoromethane (HCFC-22), difluoromethane (HFC-32), 1,1,2-trichlorotrifluoroethane (CFC-113), 2,2-dichloro-1,1,1-trifluoroethane (HCFC-123), pentafluoroethane (HFC-125), 1,1,1,2-tetrafluoroethane (HFC-134a), 1,1,1-trifluoroethane (HFC-143a), 1,1-difluoroethane (HFC-152a), carbon dioxide, and ammonia) considered to date.

Effects of thermal pretreatment on anaerobic digestion of Nannochloropsis salina biomass.

The marine microalga Nannochloropsis salina was investigated as feedstock for anaerobic digestion under batch and semi-continuous conditions for the first time. Biodegradability and methane yield were low under both digestion conditions. Thermal pretreatment prior to anaerobic digestion significantly increased the methane yield from 0.2 to 0.57 m(3) kg VS(-1) under batch conditions and from 0.13 to 0.27 m(3) kg VS(-1) in semi-continuous digestion. Still, the methane yield was limited with semi-continuous feeding due to volatile fatty acid (VFA) accumulation in the digester caused by high ammonium and salt concentrations in the feedstock. Despite VFA accumulation adaption of the microorganisms to the changing conditions and high buffer capacity resulted in steady methane production. A first energy balance considering the required heat for thermal pretreatment revealed significant benefit from the pretreatment. Conversely, the high energy demand for dewatering algal cultures is one major bottleneck for industrial-scale processing of microalgae.

An accurate Van der Waals-type equation of state for the Lennard-Jones fluid

A new equation of state (EOS) is proposed for the Helmholtz energyF of the Lennard Jones fluid which represents the thermodynamic properties over a wide range of temperatures and densities. The EOS is written in the form of a generalized van der Waals equation.F =Fu +Fv. WhereFu is a hard body contribution andFA an anttractive dispersion force contribution. The expression forFH is closely related to the hybrid Barker Henderson pertubation theory. The construction ofFA is accomplished with the Setzmann Wagner optimization procedure on the basis of virial coefficients and critically assessed computer simulation data. A comparison with the EOS of Johnson et al. shows improvement in the description of the vapor liquid coexistence properties, thepvT data. and in peculiar, of the calorie properties. A comparison with the EOS of Kolafa and Nezbeda which appeared after the bulk of this work was finished shows still by about 30%.

A Reference Quality Equation of State for Nitrogen

A new formulation describing the thermodynamic properties of nitrogen has been developed. New data sets which have been used to improve the representation of the p–ρ–T surface of gaseous, liquid and supercritical nitrogen, including the saturated states are now available. New measurements on the speed of sound from spherical resonators have been used to improve the accuracy of caloric properties in gaseous and supercritical nitrogen. State-of-the-art algorithms for the optimization of the mathematical structure of the equation and special functional forms for an improved description of the critical region were used to represent even the most accurate data within their experimental uncertainty. The uncertainty in density of the new reference equation of state ranges from ±0.01% between 270 and 350 K at pressures less than 12MPa, within ±0.02% over all other temperatures less than 550 K and pressures less than 12 MPa, and up to a maximum of ±0.6% at the highest pressures. The equation is valid from the triple point to temperatures of 1000 K and pressures up to 2200 MPa. The new formulation yields a reasonable extrapolation up to the limits of chemical stability of nitrogen as indicated by comparison to experimental shock tube data. Constraints regarding the structure of the equation ensure reasonable extrapolated properties up to temperatures and pressures of 5000 K and 25 GPa. For typical calibration applications, the new reference equation is supplemented by a simple but also highly accurate formulation, valid only for supercritical nitrogen between 270 and 350 K at pressures up to 30 MPa.

18 Multiparameter equations of state

Publisher Summary Accurate thermophysical properties of fluids are needed for the development of reliable mathematical models of energy systems. Although significant improvements are being made in predicting thermodynamic properties of pure fluids and mixtures using theory-based methods, there is a need for more accurate equations of state both for applications in engineering system design and analysis and to satisfy scientific data needs. Current practice in the development of computer programs, property tables, and charts involves the correlation of selected experimental data for a particular fluid or mixture using a model, which is accurate for calculating properties over a wide range of pressures and temperatures. A typical thermodynamic property formulation is based on an equation of state, which allows the correlation and computation of all thermodynamic properties of the fluid, including properties such as entropy that cannot be measured directly. The term “fundamental equation” is often used in the literature to refer to empirical descriptions of one of four fundamental relations: internal energy as a function of volume and entropy, enthalpy as a function of pressure and entropy, Gibbs energy as a function of pressure and temperature, and Helmholtz energy as a function of density and temperature. Modern equations of state for pure fluid properties are usually fundamental equations explicit in the Helmholtz energy as a function of density and temperature.

Multiparameter Equations of State - Recent Trends and Future Challenges

The purpose of this article is to update the common knowledge on characteristic features of empirical multiparameter equations of state, to increase the confidence of potential users, and possibly to attract other scientists to theoretical and experimental work that is relevant for the future development of these kinds of thermodynamic property models. To do so, the most important features of current multiparameter equations of state and of the algorithms which are used to develop such formulations are briefly explained. Future challenges are outlined with regard both to the development of multiparameter equations of state and to the underlying experimental basis. Relevant references are given for further studies.