چكيده به لاتين
In this study, the equilibrium of vapor-liquid phase was investigated by modifying the mPR-CPA equation of state and predicting the unusual trend of water at low temperatures. Water is one of the most important polymorph liquids with at least two different forms at low temperatures. The concept of the polymorph is defined based on various solid forms that can affect the performance of the material. The anomalous properties of cold and supercooled water such as density reduction and sudden increase in congestion with temperature reduction and when the fluid is subjected to stress, has been considered for long term scientists and significant improvements have been observed over the last 20 years. The mPR-CPA equation of state combines the Peng-Robinson equation of state modified by feyzi et al and an association term of wertheim theory that has been applied in the SAFT equation. Modifying parameters of the mPR-CPA EOS is performed to optimize 10 parameters of this equation of state using MATLAB 2016 software. Of these ten parameters, eight parameters related the Peng-Robinson EOS are modified and two other parameters are association energy and association volume. This optimization is done by minimizing the value of the objective function, which is the total
absolute errors percent of thermodynamic functions (density, isobar expansivity and isothermal compressibility) and saturated vapor density and saturated liquid density and vapor pressure. The results showed performance equation of state by modifying the equation parameters is well improved and the absolute error percent of thermodynamic functions with optimized parameters had a significant reduction compared to the previous. Mean absolute error for saturation liquid density, saturation vapor density and saturated vapor pressure in the range of 0.42 to 0.95 reduced temperature, respectively, 0.56, 3.67, and 3.42 percent, is obtained. The amount of density error, isothermal compressibility, isobar expansivity of liquid water and supercooled water density for the modified mPR-CPA equation of state compared to the pre-correction parameters have been reduced 88, 82, 95 and 58 percent, respectively and shows that by correcting the parameters, we could predict the equilibrium of the liquid-vapor phase and the anomalous behavior of the thermodynamic functions of water at low temperatures.
