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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...

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The gasificiation of coal, shale-oil, or other lower grade hydrocarbon base stocks inevitably leads to the production of process streams which contain a very wide range of paraffinie, naphthenic, aromatic and olefinic hydrocarbons in the presence of associated non-hydrocarbons such as hydrogen, nitrogen, carbon dioxide, hydrogen sulfide and ammonia. These streams are often contacted with water at process conditions which normally lead to either gas -water -rich liquid equilibrium or gaswater -rich liquid -hydrocarbon rich liquid equilibrium. The processing conditions and stream compositions which may lead to the formation of these different phases and the distribution of the components between phases are of great importance to the design engineer. For this reason the establishment of reliable procedures for predicting the behavior of these mixtures in the one-, two-, and three-phase regions is a matter of considerable importance.In an earlier paper (1), the authors presented an efficient procedure for predicting the phase behavior of systems exhibiting a water -rich liquid phase, a hydrocarbon -rich liquid phase, and a vapor phase.The Peng-Robinson equation of state (2) was used to represent the behavior of all three phases.It has the following form: v v-b " v(v+bj + b(v-b) where a(T) = a α = KL . a(T) (1) ac = 0.45724 -j ± = 1 + K(1-TR^2)