Theoretical Study On Virial And Cubic Equations Of State For Geological Fluids

In order to promote the improvement and development of the equations of state for fluids and meet the different requests in thermodynamic calculation of geological fluids, the author made a systematic study on the theoretical bases of some cubic equations, as well as modifying some cubic equations, developing some virial equations for geological fluids composed of small molecules. The research mainly included following content:1 Based on the virial equation, some of the cubic equations of state in the literature were derived appoximately and strictly, respectively, and the parameters in some quasi-empirical cubic equations were also analyzed and interpreted. The results can offer a theoretical basis for the mutual transformation of the virial and cubic equations under some specific conditions. Besides, the author also derived some new cubic equations, and some of them may be well perspective in application.2 The theoretical values of the second virial coefficient are precisely fitted into some simple expressions. According to one of them, a new temperature function for the quadratic terms in cubic equations was derived:The function is simple, general, without acentric factor, truly predictive, theoretically sound, and applicable to all the van der Waals-type equations. The precisions and the applicable ranges of the modified RKS, PR and PT equation are very similar to those of the original equations. A special critical parameter method was used to derive the approximate expression of the second upto sixth virial coefficient at critical temperature. Combined with the formerly fitted expressions of the second virial coefficient, some multi-parameter virial equations are proposed. Among them, a quintic virial equation was chosen to predict the vapor-liquid equilibria of some very polar fluids, and the results are notably better than those of the usual cubic equations. Some virial equations for the precise calculation of the supercritical geological fluids were put forward, and two cubic equations were also improved. 1) general quartic and quintic virial equation:They are general for geological fluids composed of small molecules including very polar, weakly polar, non-polar and quantum fluids (F^O-CC^-CI-LrCO-I-k-Ch-N^). In the range from critical temperature upto 4000~5000K, 0 upto 90~200GPa, the average deviation of the calculated volumes (ADV) was within 1.0%~3.5%, 0.7%~3.0%, respectively. The pVT properties of some binary and ternary mixtures of the supercritical fluids were calculated with the two equations above, and the deviations were less than or very close to the experimental ones.2) High-order virial equation. For the above geological fluids in the range from critical temperature upto 4000-5000K, 0 upto 90~600GPa, the AD F was within 0.3%~0.8%.3) Modified Holloway and van der Waals equation. Its applicable/ and Tranges are wider than Holloway equation. TheADFwas within 0.9%~2.1%.5 The fugacity coefficients, residual enthalpies and residual entropies of the pure fluids at low temperatures and high pressures were predicted with the general quintic virial equation.