Testing And Evaluation Of The Equation Of State Of Water At High Temperature And Pressure

Thermodynamic properties of water at high temperatures and pressures are very important for understanding, analyzing or simulating many geological processes in the Earth and planets. Equations of state can be used to get the pressure-volume-temperature(PVT) properties of water, and to indirectly derive many other physical and chemical properties, such as phase equilibrium properties, enthalpy, entropy, free energy, fugacity or fugacity coefficient, as well as expansion and compression of coefficients.In this paper, the highly accurate thermodynamic model IAPWS-95 and high-precision PVT data from molecular dynamics simulations are used as a reference to test, analyze and assess the commonly used equations of state for water as a geological fluid at high temperatures and pressures:(1) Calculate the deviations of volumes, pressures and other related thermodynamic properties from the equations, analyze and assess the distribution of the deviations in P-T space(including the variation of systematic deviations with P-T conditions), particularly the deviations of the equations in the critical region of the water;(2) Examine the magnitudes and signs of the deviations beyond the applicable range of each equation declared the original author(s), as well as their distribution in P-T space, and then determine the most suitable P-T range for each equation;(3) Give qualitative analysis and assessment of the equations of state, including the characteristics, merits and weaknesses of each equation in functional form, difficulty in solving the equation, whether the critical conditions are met, or whether the equation of state of ideal gases is met at low pressures;(4) Analyze the principal factors contributing to the deviations of the equations.These results can provide useful reference for correct option, use or improvement of the equations, or for developing more and better equations.According to the results mentioned above, the following conclusions can be drawn:(1) Some equations of state have their own theoretical critical conditions that are different from experimental results. This difference leads to large deviations in the vicinities of both theoretical and experimental critical points. Of the equations examined,only one can be approximately used in the critical region of water.(2) Some equations of state cannot be used at low pressures, because the equations cannot degenerate into the equation of state of ideal gases when Pâ†'0, or because ofunreasonable parameter expression(s), or improper fitting of parameters.(3) The vast majority of the equations have systematic deviations. Their magnitudes and dependence on P-T conditions vary with from one equation to another.(4) The original authors of a few equations did not state(or did not clearly state) the applicable ranges of their equations, and the applicable ranges of most equations declared by original authors are different from the real results.Based on the above results, some useful suggestions are proposed for establishing new equations, or improving the existing equations.