Development of a Thermodynamically Consistent Volume Translation Method in Peng-Robinson Equation of State

• Author / Creator

  Shi, Jialin

• Cubic equations of state (CEOS) are frequently used to predict the phase behavior and volumetric properties of pure compounds and mixtures encountered in the field of chemical and petroleum engineering. Volume translation is proposed to further improve the accuracy of density predictions by CEOS. Previous research shows that a temperature-dependent volume-translated EOS could result in crossing of pressure-volume isotherms for a pure compound, which leads to an anomalous behavior that the predicted molar volume for a pure component can be lower at a higher temperature at an isobaric condition. Such crossover phenomenon fails to consistently predict the thermodynamic properties of a pure compound, thus restricting the wide applications of the temperature-dependent volume translated EOS. Aiming at addressing the above thermodynamic inconsistency in some volume-translated EOSs, a criterion is proposed to judge whether a volume-translated EOS will result in crossover issues, and if so, the extent of the temperature and pressure range over which the crossover phenomenon occurs. The criterion is developed based on a fundamental fact that the isobaric expansivity for a pure gas or liquid is positive. The recently proposed volume translations are evaluated on the basis of the developed criterion. For the various types of temperature-dependent volume translations, we obtain the specific temperature/pressure conditions over which there is certainly no crossover phenomenon. It can be concluded that there is thermodynamic inconsistency at a lower pressure for most nonlinear temperature-dependent volume translations, but no any crossover issues exist for the constant volume translations and linear temperature-dependent volume translations with a negative coefficient of temperature. Next, a generalized temperature-dependent volume translation model is developed for the more accurate prediction of the liquid densities of pure components. On the basis of the criterion on thermodynamic consistency we have proposed, a mathematical constraint is introduced into the proposed model. The model parameters are determined based on the regression of the density data collected for16 pure compounds. The new volume-translated PR EOS can improve the liquid density prediction with an overall absolute average percentage deviation of 1.42%. Notably, the new volume translation model does not lead to the crossing of pressure-volume isotherms over a wide range of pressure and temperature (up to 100 MPa and 1000 K).

• Subjects / Keywords

  • Crossing of isotherms
  • Volume translation
  • Thermodynamic consistency
  • PR EOS

• Graduation date

  Fall 2017

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3571823V

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.