Combination of Gibbs and Helmholtz Energy Equations of State in a Multiparameter Mixture Model Using the IAPWS Seawater Model as an Example

For carbon capture and storage (CCS) applications different sets of equations of state are used to describe the whole CCS-chain. While for the transport and pipeline sections highly accurate equations of state (EOS) explicit in the Helmholtz energy are used, properties under typical geological storage conditions are described by more simple, mostly cubic EOS, and brines are described by Gibbs energy models. Combining the transport and storage sections leads to inconsistent calculations. Since the used models are formulated in different independent variables (temperature and density versus temperature and pressure), mass and energy balances are challenging and equilibria in the injection region are difficult to model. To overcome these limitations, a predictive combination of the Gibbs energy-based IAPWS seawater model (IAPWS R13-08, 2008) with Helmholtz energy-based multi-parameter EOS is presented within this work. The Helmholtz energy model used in this work is based on the EOS-CG-2016 of Gernert and Span (J Chem Thermodyn 93:274–293, 10.1016/j.jct.2015.05.015, 2016). The results prove that a consistent combination of the two different models is possible. Furthermore, it is shown, that a more complex brine model needs to be combined with Helmholtz energy EOS for calculations at storage conditions.

Thermodynamic Properties of Methyl Diethanolamine

The homogeneous density of the liquid phase is experimentally investigated for methyl diethanolamine. Data are obtained along five isotherms in a temperature range between 300 K and 360 K for pressures up to 95 MPa. Two different apparatuses are used to measure the speed of sound for the temperatures between 322 K and 450 K with a maximum pressure of 95 MPa. These measurements and literature data are used to develop a fundamental equation of state for methyl diethanolamine. The model is formulated in terms of the Helmholtz energy and allows for the calculation of all thermodynamic properties in gaseous, liquid, supercritical, and saturation states. The experimental data are represented within their uncertainties. The physical and extrapolation behavior is validated qualitatively to ensure reasonable calculations outside of the range of validity. Based on the experimental datasets, the equation of state is valid for temperatures from 250 K to 750 K and pressures up to 100 MPa.

Vapour-liquid phase equilibria and thermodynamic properties of solutions of the ethylbenzene and n-alkylbenzenes binary systems

The methods of theoretical description of the patterns of changes in thermodynamic properties depending on the composition and structure of solution components are a priority direction in the development of the theory of solutions. This article is devoted to the establishment of relationships between the thermodynamic properties, composition of solutions, and the structure of their components. The study of the thermodynamic properties of binary solutions formed by a common solvent (ethylbenzene) and substances of the homologous series of n-alkylbenzenes contributes to the establishment of the aforementioned relationships. In the production of ethylbenzene and its homologues, solutions based on n-alkylbenzenes are quite common. Alkylbenzenes are widely used in various fields of science and chemical technology as solvents, extractants, and plasticisers. Using the ebuliometric method, we measured the boiling points of solutions of four binary systems formed by ethylbenzene and n-alkylbenzenes under various pressure values. Compositions of equilibrium vapour phases of the binary systems were calculated using the obtained isotherms of saturated vapour pressure of the solutions. Using the Runge-Kutta method, the composition of the vapour phases of the solutions of the systems was calculated by the numerical integration of the Duhem–Margules equation on a computer. The obtained data on the vapour-liquid equilibrium became the basis for calculating the thermodynamic functions of the systems’ solutions. The Gibbs and Helmholtz energy values, the enthalpies of vaporisation and mixing, the internal energy, and entropy of solutions were calculated. The thermodynamic properties of the solutions were calculated using a comparison of the values baed on two standards: an ideal solution and an ideal gas. It was found that the values of the Helmholtz energy linearly depend on the molar mass of the substance (the number of –CH2– groups in a molecule) in the homologous series of n-alkylbenzenes. An increase in the Helmholtz energy values for n-alkylbenzenes in the homologous series is associated with a linear increase in the molar volume of liquid substances and an exponential decrease in the saturated vapour pressure of substances. For binary solutions of constant molar concentrations formed by ethylbenzene and n-alkylbenzenes, the Helmholtz energy linearly depends on the molar mass (number of –CH2– groups in the molecule) of n-alkylbenzene in the homologous series. We obtained an equation that makes it possible to predict the thermodynamic properties of solutions of binary systems with high accuracy. The equation accelerates the process of studying vapour-liquid phase equilibria and thermodynamic properties of solutions of binary systems by 300 times. The determined patterns confirm the hypothesis of the additive contribution of functional groups to the thermodynamic properties of solutions. This hypothesis underlies the statistical theory of group models of solutions. The thermodynamic patterns determined by this study can also be used to solve a wide range of technological issues in the chemical industry.

Experimental and Numerical Study of Supersonic Non-ideal Flows for Organic Rankine Cycle Applications

The organic Rankine cycle (ORC) is low-grade heat recovery technology, for sources as diverse as geothermal, industrial, and vehicle waste heat. The working fluids used within these systems often display significant real-gas effects, especially in proximity of the thermodynamic critical point. Three-dimensional (3D) computational fluid dynamics (CFD) is commonly used for performance prediction and flow field analysis within expanders, but experimental validation with real gases is scarce within the literature. This paper therefore presents a dense-gas blowdown facility constructed at Imperial College London, for experimentally validating numerical simulations of these fluids. The system-level design process for the blowdown rig is described, including the sizing and specification of major components. Tests with refrigerant R1233zd(E) are run for multiple inlet pressures, against a nitrogen baseline case. CFD simulations are performed, with the refrigerant modeled by ideal gas, Peng–Robinson, and Helmholtz energy equations of state. It is shown that increases in fluid model fidelity lead to reduced deviation between simulation and experiment. Maximum and mean discrepancies of 9.59% and 8.12% in nozzle pressure ratio with the Helmholtz energy EoS are reported. This work demonstrates an over-prediction of pressure ratio and power output within commercial CFD packages, for turbomachines operating in non-ideal fluid environments. This suggests a need for further development and experimental validation of CFD simulations for highly non-ideal flows. The data contained within this paper are therefore of vital importance for the future validation and development of CFD methods for dense-gas turbomachinery.

Local-Basis-Function Equation of State for Ice VII–X to 450 GPa at 300 K

Helmholtz energy of ice VII–X is determined in a pressure regime extending to 450 GPa at 300 K using local-basis-functions in the form of b-splines. The new representation for the equation of state is embedded in a physics-based inverse theory framework of parameter estimation. Selected pressures as a function of volume from 14 prior experimental studies and two theoretical studies constrain the behavior of Helmholtz energy. Separately measured bulk moduli, not used to construct the representation, are accurately replicated below about 20 GPa and above 60 GPa. In the intermediate range of pressure, the experimentally determined moduli are larger and have greater scatter than values predicted using the Helmholtz representation. Although systematic error in the determination of elastic moduli is possible and likely, the alternative hypothesis is a slow relaxation time associated with changes in proton mobility or the ice VII to X transition. A correlation is observed between anomalies in the pressure derivative of the predicted bulk modulus and previously suggested higher-order phase transitions. Improved determinations of elastic properties at high pressure would allow refinement of the current equation of state. More generally, the current method of data assimilation is broadly applicable to other materials in high-pressure studies and for investigations of planetary interiors.