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The narrative progress report

The 3 years project sponsored by PRF has been concluded by complete fulfillment of all the tasks listed in the original proposal, although not all the initial ideas have demonstrated their values in practice. In particular, the originally proposed van der Waals-type form of the model has been finally found less successful that the scheme based of the Perturbed Hard Chain Theory. These facts outline the importance of the more realistic description of the intermolecular potential provided by another family of thermodynamic models, namely the equations of state based on the Statistical Association Fluid Theory (SAFT). Indeed, it has been concluded that SAFT models might describe the liquid phase compressibility and the related thermodynamic properties more accurately that cubic equations.

However, often there is a price to pay for the increased model's complexity. In particular, most versions of SAFT are not free of the undesirable numerical pitfalls responsible for inaccurate and sometimes even non-physical predictions. One of these numerical pitfalls generated by the excessively complex dispersion terms is the multiple phase equilibria for pure compounds. It has been demonstrated that this problem affects several popular versions of SAFT, such as the Chen-Kreglewski's SAFT of Huang and Radosz (CK-SAFT), the Perturbed Chain (PC-SAFT) and the Soft-SAFT. At the same time, other dispersion terms, such as those implemented by the SAFT of Chapman et al., result in prediction of the classical van der Waal's shapes of isotherms. Thus, the problem of fictive phase splits can be avoided by the appropriate selection of SAFT's dispersion term. The additional numerical pitfalls, namely the negative heat capacities at the extremely high pressures and the intersections of isotherms generated by the temperature dependencies attached to the reduced densities have been addressed by this research.

However there is another serious drawback characteristic for SAFT models, namely the wrong estimation of the pure compounds critical pressures and temperatures. It comes into view that SAFT models typically have a limited capability of simultaneous description of the critical and sub-critical PVT, comparing even with simple cubic EOSs. Paradoxically, it comes therefore into view that in spite of their weak theoretical basis, van der Waals–type equations might in fact provide practically important advantages. This observation leads to the idea of gathering the strong sides of both SAFT and cubic EOSs by hybridizing both approaches and the novel theoretically based equation, namely SAFT + Cubic has been proposed. This model is given as follows:

(1)

Adjusting SAFT + Cubic to the data of most alkanes requires fitting of only one adjustable parameter m to the liquid densities. The remaining four parameters (c, a, s, and ) are not adjustable but obtained by solving a system of four equations:

(2)

(3)

(4)

In the cases of other compounds fitting of both m and c should be performed, while the non-adjustable a, s, and are obtained by solving a system of eqs 3-4. The mixing rules for the novel equation of state have been developed as well.

In a series of the already published and the submitted for publication works it has been demonstrated that the proposed model has doubtless advantage in predicting large variety of thermodynamic properties in the entire thermodynamic phase space over the most successful theoretically based and empirical models, such as different variations of SAFT and Benedict-Webb-Rubin equations of state. Thus it should be concluded that the aims formulated in the research proposal have been successfully achieved.

The present research had a very important impact on the principal investigator's career. The support of the Petroleum Research Fund has allowed to the principal investigator publication in the leading chemical engineering research journals. It is hard to overestimate the impact of the scholarships from the Petroleum Research Fund on careers of the undergraduate students that had participated in the research. This support allowed them to dedicate full time to the research work, to earn many important skills, such as the ability to use the professional Data Bases and the software and, finally, to be better engineers. Some of the students have become co-authors of published papers, which had contributed a lot for their chances to be accepted to the post-graduated programs in other institutions in Israel or abroad. Three students (Maxim Katz, Naor Cohen and Avi Itzhak have continued the research in the recently opened M Sc program under the supervision of the principle investigator. Ilya Bourgin has obtained a prestigious engineering position in Intel Israel.