Theoretical Critical Conditions Of Equations Of State For Geological Fluids And Their Influence On Thermodynamic Calculation

Thermodynamic properties of fluids near critical points exhibit singularity, which is called critical phenomenon or effect. Accurate modeling of thermodynamic properties of fluids in the critical regions is not only helpful for understanding or simulating many geological processes in the Earth and planetary interiors, but also very important for the development of relevant industrial processes and the study of environmental engineering and high-pressure and high-temperature physics. Equations of state(EOS) are the most common means for the representation of the relationship among the pressure–volume–temperature(PVT) properties of fluids. Most of the existing EOS were based on the mean field theory, and thus cannot accurately represent the critical phenomena of fluids.In the past decades, many EOS have been developed(or are applicable) for geological fluids. The applicable ranges of many EOS declared by the original authors cover the critical regions of pure fluids, but there is usually no report of the precisions of the EOS in critical regions. Given this situation, this work is designated to the detailed calculation and analysis of some representative and commonly used EOS for geological fluids in the critical regions, which include:(1) Calculate the theoretical critical conditions of pure fluids with EOS, and design a convenient and stable general algorithm;(2) Calculate and analyze the volume deviations of each EOS on the isotherms at the theoretical and experimental critical temperatures, as well as temperatures near them;(3) Divide the critical region in question into three and four intervals using the theoretical critical temperatures and their mean value as boundaries, then calculate the volume deviations of each EOS in each interval, and analyze the relations between the deviations and temperature and pressure.The above work leads to the following conclusions:(1) All theoretical critical temperature and pressure are higher than experimental values. As a result, the EOS gives a two-phase region, which does not accord with fact.(2) The volume deviations of EOS are all large near the theoretical and experimental critical points; The deviations decrease dramatically when pressure is far away from the critical point; In the experimental subcritical region or theoretical supercritical region, the deviations also decrease rapidly as temperature is far away from the critical temperature.(3) Whether or not an EO can accurately reproduce the experimental critical conditions of fluids has decisive influence on the precision of the EOS in the critical regions. If an EOS cannot exactly reproduce the experimental critical conditions, it cannotbe accurate in the entire critical region.The above results allow one to get accurate knowledge of the precisions of EOS for geological fluids in critical regions, and can also serve as useful reference for choosing suitable EOS for the thermodynamic calculation in the critical regions, or improving the representation of critical phenomena with EOS.