Theoretical prediction of phase behaviour at high temperatures and pressures for non-polar mixtures. Part 1.—Computer solution techniques and stability tests

Abstract

The classical mathematical description of critical points of binary mixtures and the computer technique used to solve the relevant equations are described. The techniques used here are applicable to any closed equation of state and one fluid model prescription.The critical points, in a given range of temperature and volume are located as the solution of two simultaneous equations :( ~P / ~u ) T , x (a2G/a&,p = 0 ( Z P / ~U ) T , X (a3G/ax9h,p = 0 with reduced volume 8 and reduced temperature f as independent variables. The search procedure

Critical temperatures and pressures for hydrocarbon mixtures from an equation of state with renormalization-group theory corrections

“…Michelsen [44] used an alternate efficient technique that does not use any determinants but depends on an eigenvalue method. Another efficient algorithm was proposed by Hicks and Young [45] and extended by Sadus [46][47]; first, eq. (1.a) is solved separately and then D2 is evaluated using the solution of eq.…”

Stability criteria for a polydisperse system

“…Young [20] for obtaining the roots of Eqs (6) and (8). Although this method requires many evaluations of objective functions Eqs.…”

On the calculation of critical liquid-vapor lines of binary mixtures

“…In fact equation (6) was solved for a given fixed ratio of th e critical volume of the pure compo nents, and the ratio of the critical temperatures then varied until the minimum value of this temperature ratio was found which wou ld satisfy equation (7) or (8) . Table 1 lists the results, i.e., the appropriate value of Tg2/T~1 for fixed values of vg 2 / V~l between 0_7 and 4 .5 .…”

“…In particular, some variations of the critical line over a range of pressure, P, temperature, T, and mole fraction, x, for various types of mixtures are described in section 4. Brief comparisons with the more restricted approach from simple equations of state [7,8] are given.…”