Elsevier

Fluid Phase Equilibria

Volume 470, 25 August 2018, Pages 140-148
Fluid Phase Equilibria

Thermodynamic properties of dilute hydrogen in supercritical water

https://doi.org/10.1016/j.fluid.2017.11.004Get rights and content

Abstract

A thermodynamic model is developed to calculate the fugacity coefficients and partial molar volumes of hydrogen at infinite dilution in water at 647.1–2000 K and pure water densities between 0 and 1500 kg m−3. The model is based on the predicted values of DCFI (the dimensionless integral of the infinite dilution hydrogen - water direct correlation). Values of DCFI at low water densities are calculated from accurately known second cross virial coefficients; at high water densities predictions are based on the relations from the theory of a mixture of hard spheres; DCFI values at intermediate water densities are interpolated using a variant of corresponding-states correlation. Predicted values of the hydrogen fugacity coefficients at infinite dilution in water are compared with experimental data and results of the literature equations of state. The included Excel spreadsheet allows calculations provided that values of T, P, ρ1, and κT for pure water are entered by a user.

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, log10ϕ2 (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 log10ϕ2 of various EoS reaches 0.45 log10 units. For comparison, for H2O the difference amounts to only 0.07 log10 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 A12 on isotherms

With all parameters in place, the evaluation of A12 for hydrogen in water at supercritical temperatures is straightforward. As before [27], [24], we calculate and plot the values of the functionY=(A121)/ρ1at various water densities, see Fig. 3.

According to Eq. (2), at ρ1 = 0 the function (A121)/ρ1 is equal to 2B12, 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 B12 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 A12, 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

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