IDENTIFICATION OF PARAMETERS IN THE FOGELSON–LIKHACHEV MODEL

Abstract

The Fogelson-Likhachev (FL) model has proven itself in oil production practice. It generalizes the Ishikawa – Chung – Lu, Peng – Robinson, Redlich – Kwong and Soave – Redlich – Kwong equations, but is irrational since it has fractional values ​​of k and m in (V+c)^kT^m. The coefficients c, k, m depend on the calculated values ​​of P_c, T_c, V_c at the critical point K. To study first-order phase transitions P_c, T_c, V_c, c, k, m in FL-models are defined. For helium, hydrogen, neon, acetylene and benzene k=2 on the linear section P(V), therefore the FL-model is reduced to a fractional rational form and is represented by a cubic polynomial. In this form, the model is convenient for studying stability according to the Hurwitz criterion and finding the roots of a third-order equation according to the Cardano formula. The analysis of the equation of state by A. Andronov's method identifies the region admissible values ​ of the eigenvalues ​​λ_n of a polynomial of degree n and the stability region. By integrating the equation of state, the internal energy carried by molecules in a closed volume of the medium is calculated, where the closed volume is an element of volume ΔV with a certain mass and density of the substance, by which the Kamerling – Onnes virial decomposition is determined. Thus, the closed volume V under consideration is an element of the Levi Civita volume ΔV to which the differentiation operation is applicable.