Thermodynamic properties of dilute hydrogen in supercritical water
Introduction
The ever-increasing interest in hydrogen energy requires knowledge of thermodynamic properties of hydrogen in its pure state and in mixtures, including a very important H2O-H2 binary system. Technological needs cover a wide temperature range at relatively low pressures, while the studies of processes in deep Earth ask for thermodynamic data at extreme pressures, extending to GPa ranges.
It must be noted that both experimental studies and correlation methods, when applied to hydrogen-containing systems, meet specific difficulties, not characteristic for most other compounds. First, experimental investigations of hydrogen and its mixtures face severe technical problems. A review [1] emphasizes that “hydrogen at high temperatures and/or pressures can have a disastrous effect on the structural soundness of metal alloys” due to “hydrogen permeation and loss”, “hydrogen embrittlement” of materials, “hydrogen attacks” on steel, etc. On the other hand, correlating equations of state (EoS), usually successful in predicting/describing data for most gases, often perform significantly worse for H2-bearing fluids. The likely reason is the very low critical temperature for hydrogen, located in the region where quantum effects are important, therefore, the ordinary scaling methods to estimate EoS′ parameters may not be applicable for H2.
As an illustration, Fig. 1 shows the values of logarithms of fugacity coefficients of H2, (here and below the index 2 refers to H2 (a solute), the index 1 – to H2O (a solvent), the superscript * denotes the property of a pure compound, and the superscript ∞ denotes the property at infinite dilution), predicted by various EoS's at 1000 K and pressures up to 2000 MPa: by SUPERFLUID of Belonoshko et al. [2], based on an experimental and MD-generated [3] data set; by LONER10 of Bakker [4], who coded and offered for download at http://fluids.unileoben.ac.at/Computer.html EoS by Duan et al. [5], [6], [7], also based on a combination of experimental and MD-generated PVT values; and the four-parameter EoS by Churakov and Gottschalk [8], [9], available at http://fluid-eos.web.psi.ch/, which is based on the thermodynamic perturbation theory. At the highest pressure of 2000 MPa, the difference between of various EoS reaches 0.45 units. For comparison, for H2O the difference amounts to only 0.07 units. The line in Fig. 1 shows the values calculated online at http://webbook.nist.gov/chemistry/fluid/using the fundamental EoS for pure H2 [10]. As this EoS was published later, it serves as a stringent test of the quality of other model equations of state. As seen, only SUPERFLUID EoS [2] is in close agreement with reference values. Recently, the SAFT EOS was published for the H2O-H2 system [11]. Judging by comparison of predicted [11] and the NIST [10] recommended PVT properties of pure H2, see Fig. 2 in that paper, the SAFT model systematically overpredicts molar volumes of pure hydrogen, likely overpredicting the fugacity coefficients as well.
Our primary interest lies not in the thermodynamic properties of pure hydrogen, but in another limit – of hydrogen at infinite dilution in water. The goal of the current study is to propose a model specifically for hydrogen at infinite dilution in water at temperatures above the critical temperature of water (647.096 K [12]) valid over wide density/pressure ranges.
Section snippets
The general outline
As practice shows, the success of any correlating model depends very strongly on the theoretical validity of relations in its basis. Over the years, Prof. J.P. O'Connell [13], [14], [15], [16], [17], [18], [19], [20], [21], [22] has advocated the use of relations following from the Fluctuation Solution Theory (FST) [23] to build simple and robust models for correlating and predicting thermodynamic properties. FST provides rigorous relations connecting the thermodynamic properties of a system,
Evaluation of the density dependence of on isotherms
With all parameters in place, the evaluation of for hydrogen in water at supercritical temperatures is straightforward. As before [27], [24], we calculate and plot the values of the functionat various water densities, see Fig. 3.
According to Eq. (2), at = 0 the function is equal to , the initial departure of this function is linear in density, and the example of water shows that the linear part may extend up to 300 kg m−3. The value of has to be
Conclusion
As shown by J.P. O'Connell and his coworkers [14], [15], [19], [20], [21], [22], DCFI-based models (DCFI stands for direct correlation function integrals) offer a simple and robust way for correlating thermodynamic properties of dilute solutions over extremely wide ranges temperatures and solvent's densities. An important feature of DCFI-based models is the simple shape of DCFI everywhere, including the near-critical region. In practice, it may be easier to work with the function , which is
Acknowledgements
AVP is privileged to personally know Prof. J.P. O'Connell, which definitely had an impact on the development of the DCFI-based models for aqueous solutes over wide T and P ranges. The picture of the thermodynamics of mixtures in terms of DCFIs is simpler than those in terms of the partial molar properties themselves, promising advances in the development of robust predictive models for many industrially and scientifically important systems. This research was partially supported by Russian
References (60)
- et al.
SUPERFLUID: a FORTRAN-77 program for calculation of Gibbs free energy and volume of C-H-O-N-S-Ar mixtures
Comp. Geosci.
(1992) - et al.
A unified equation of state for fluids of C-H-O-N-S-Ar composition and their mixtures up to very high temperatures and pressures
Geochim. Cosmochim. Acta
(1992) Package FLUIDS 1. Computer programs for analysis of fluid inclusion data and for modelling bulk fluid properties
Chem. Geol.
(2003)- et al.
Molecular dynamics simulation of PVT properties of geological fluids and a general equation of state of nonpolar and weakly polar gases up to 2000 K and 20,000 bar
Geochim. Cosmochim. Acta
(1992) - et al.
Molecular dynamics equation of state for nonpolar geochemical fluids
Geochim. Cosmochim. Acta
(1995) - et al.
A general equation of state for supercritical fluid mixtures and molecular dynamics simulation of mixture PVTX properties
Geochim. Cosmochim. Acta
(1996) - et al.
Perturbation theory based equation of state for polar molecular fluids: I. Pure fluids
Geochim. Cosmochim. Acta
(2003) - et al.
Perturbation theory based equation of state for polar molecular fluids: II. Fluid mixtures
Geochim. Cosmochim. Acta
(2003) - et al.
Calculations of vapor–liquid equilibria of the H2O-N2 and H2O-H2 systems with improved SAFT-LJ EOS
Fluid Phase Equil
(2015) Application of fluctuation solution theory to thermodynamic properties of solutions
Fluid Phase Equil
(1995)
Thermodynamic modelling of near-critical solutions
Fluid Phase Equil
Infinite dilution partial molar properties of aqueous solutions of nonelectrolytes. I. Equations for partial molar volumes at infinite dilution and standard thermodynamic functions of hydration of volatile nonelectrolytes over wide ranges of conditions
Geochim. Cosmochim. Acta
A new equation of state for correlation and prediction of standard molal thermodynamic properties of aqueous species at high temperatures and pressures
Chem. Geol.
Correlation and prediction of thermodynamic properties of nonelectrolytes at infinite dilution in water over very wide temperature and pressure ranges (2000 K and 10 GPa)
Geochim. Cosmochim. Acta
Equation of state of the H2O, CO2, and H2O–CO2 systems up to 10 GPa and 2573.15 K: Molecular dynamics simulations with ab initio potential surface
Geochim. Cosmochim. Acta
Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: standard partial molal properties of inorganic neutral species
Geochim. Cosmochim. Acta
Theory-based constraints on variations of infinite dilution partial molar volumes of aqueous solutes at various temperatures and water densities
Fluid Phase Equil
Corresponding-states correlations for estimating partial molar volumes of nonelectrolytes at infinite dilution in water over extended temperature and pressure ranges
Fluid Phase Equil
Solubility near the solvent's critical point
J. Supercrit. Fluids
Empirical evaluation of the Krichevskii parameter for aqueous solutes
J. Mol. Liq.
Infinite dilution partial molar properties of aqueous solutions of nonelectrolytes. II. Equations for the standard thermodynamic functions of hydration of volatile nonelectrolytes over wide ranges of conditions including subcritical temperatures
Geochim. Cosmochim. Acta
Estimation of the Krichevskii parameter for aqueous nonelectrolytes
J. Supercrit. Fluids
Fugacity-concentration relationship of dilute hydrogen in water at elevated temperature and pressure
Earth Planet. Sci. Lett.
The measurement of Henry's constant for hydrogen in high subcritical and supercritical aqueous systems
J. Electroanal. Chem.
Water in the deep Earth: the dielectric constant and the solubilities of quartz and corundum to 60 kb and 1200°C
Geochim. Cosmochim. Acta
Problems in working with hydrogen under hydrothermal conditions
Fundamental equations of state for parahydrogen, normal hydrogen, and orthohydrogen
J. Phys. Chem. Ref. Data
The IAPWS formulation for the thermodynamic properties of ordinary water substances for general and scientific use
J. Phys. Chem. Ref. Data
Thermodynamic properties of solutions based on correlation functions
Mol. Phys.
Corresponding states correlations for liquid compressibility and partial molal volumes of gases at infinite dilution in liquids
AIChE J.
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