A rigorous method for predicting the critical properties of multicomponent systems from an equation of state

Abstract

This paper shows how the rigorous critical state criterion enunciated by Willard Gibbs can be used with a recently formulated two-parameter equation of state to obtain an analytical solution to the problem of predicting the critical properties of defined multicomponent mixtures. Comparisons SCOPEThe critical state of multicomponent mixtures is important from both a theoretical and practical point of view, and an ability to predict this condition is highly desirable. Even though the rigorous thermodynamic criterion for the critical state was enunciated by J. Willard Gibbs (1928) one hundred years ago, no satisfactory analytical method for predicting the critical condition in multicomponent systems based on this criterion has ever been formulated. The object of the work undertaken in this study was to develop a solution to the problem of predicting the critical properties of defined multicomponent mixtures from the rigorous thermodynamic method together with a recently developed two-parameter equation of state.The significance of the work is that it has the potential of replacing the more cumbersome, often unreliable, and sometimes inapplicable methods based on semiempirical or empirical procedures or on conformal solution theory with a method that is thermodynamically rigorous, generally applicable, and simple to use. Furthermore, the proposed method for handling critical property calculations is internally consistent with calculations of all other thermodynamic properties using the same equation of state.Although the majority of the comparisons reported in this work are limited to systems containing three or more components, the method works equally well for binary systems. Only one detailed comparison for a binary system is included, because several previous workers have used the thermodynamic criteria for binary cases (Joffe and Zudlievitch, 1967; Spear et al., 1969; Hissong and Kay, 1970). CONCLUSIONS AND SIGNIFICANCEAlthough previous workers (Spencer et al., 1973) have stated recently that it is not practical to extend the methods for predicting the critical state using the minimum Gibbs free energy criterion to multicomponent systems, it has been concluded from the work undertaken in this study that this is not the case. Use of the thermodynamic criterion together with a simple two-parameter equation of state has yielded results which are remarkably reliable and relatively easy to obtain. One of the key factors in the success of the method has been the use of an equation of state (Peng and Robinson, 1976) that predicts the critical density of pure materials better than any earlier models.Extensive testing of the program on ternary and all available multicomponent mixtures has shown that the method predicts critical temperatures with an absolute error of about 1,3170 and an arithmetic average error of +1.1470. It predicts critical pressures with an absolute error of 2.33% and an arithmetic average error of +0.1370,. The thirty-two systems studied included those containing from three to twelve components co...

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

“…The critical point can be determined by computational techniques for solving these two equations simultaneously, as discussed previously for binary and ternary systems [31][32][33][34][35][36][37], and for multi component mixtures [38][39]. These techniques, however, have to evaluate a large number of determinants and are computationally expensive, especially for mixtures with many components.…”

Prospects of Mixtures as Working Fluids in Real-Gas Brayton Cycles

“…Nevertheless, it grasps the basic thermodynamic key features, and, as it is simple and easily extended to many different fluids and mixtures, it is adequate for our aims. For example, in [20], the average errors connected with the equation are stated to be 1.14% and 0.13% for predicting the critical temperatures and pressures of 32 different mixtures, respectively. In [21], the overall average error, for 22 compounds, in the prediction of the specific volumes was declared to be about 5% in the supercritical region.…”

“…Because, in a mixture, there exists a temperature "glide" between the bubble and the dew lines, the critical point (subjected to well-defined equilibrium conditions [20]) is generally not the coexistence point of the two phases at the maximum temperature and pressure ( [27], Section 8-5). This apparent anomaly is responsible for the "retrograde condensation" [26,27] (Section 8-5), and, from our point of view, the outcome is the difficulty in selecting the minimum pressure P 1 and temperature T 1 of the supercritical Brayton cycle.…”

PPR78, a thermodynamic model for the prediction of petroleum fluid-phase behaviour

“…Peng and Robinson [20] used their EoS to calculate the critical coordinates of 32 fluids for which the critical temperature and the critical pressure were known experimentally.…”