ON THE STABILITY ANALYSIS OF MULTICOMPONENT SYSTEMS
Advancing the chemical engineering fundamentals
Thermodynamics (T2-1P)
Keywords: thermodynamic stability, phases, multicomponent systems
The thermodynamic stability conditions can be directly used for the analysis and testing of equilibrium data. The significance of stability conditions is well known but the practical usage was limited by the capacities of computation methods. Due to the development of the computer technique the new possibilities of the use of stability conditions have been appeared; accordingly a number of papers on this topics were presented in scientific journals in recent years. The brief review and comparison of thermodynamic methods based on stability conditions and some new methods of the analysis of phase diagrams are considered in the present lecture.
Stability conditions give few ways for the analysis of phase equilibrium diagrams, mainly: i. the problem of phase splitting; ii. the test of intrinsic agreement of thermodynamics data; iii. the limitation on the values of thermodynamics parameters.
i. Michelsen (1982) formulated one of the most known approaches to the first item (phase splitting or a number of equilibrium phases) as a solving of a flash problem. Michelsen's tests are based on Gibbs tangent plane criterion: e.g. condition of convexity for the surface of Gibbs energy. Some forms of equations of states are used for the calculations.
ii. For the test of the intrinsic agreement of experimental data the stability conditions can be used directly. The test consists of the substitution of the data for any pairs of states in stability condition equations (inequalities). In spite of the seeming simplicity of the test procedure some optimization procedure is needed (due to the great variety of the states to be compared). The examples of such calculation are presented in the lecture.
iii. For the estimation of the limitation on the values of thermodynamics parameters one should choose the states to be a base for calculation (reference state). For example, one can calculate the limitation on the parameters of multicomponent system using binary data. The variety of such kinds of computation is rather wide: e.g. a concentration limitation on the ternary azeotrope composition, etc. In a general case of n-component vapor–liquid systems the limitations on the composition or other properties could be determined on the base of the data on k-component sub-systems (k = n - 1, n - 2,…) or another reference states. Limitations for other types of systems (including non-reactive and reactive) are determined in the similar way.
One of significant advantages of stability analysis is the possibility to compare the properties of the system under different conditions. The most known relationship is the one for the heat capacity at constant pressure or volume. The general case is analogous to this one. The results could be presented as chains of inequalities for second derivatives of thermodynamic potentials under different conditions. Of practical interest is the following limiting case: the initial state is a single-phase state but the second phase can arise. It follows from stability conditions that the transition from a homogeneous region of the phase diagram to the heterogeneous one is accompanied by the jump in the value of these second derivatives. This conclusion can be compared with some known results for configuration effects and heat capacities. The analogous thermodynamic inequalities for the systems with chemical reactions also follow from the stability criteria.
In conclusion new examples of calculations based on the application of stability conditions are presented.
Acknowledgement. This research was supported by Russian Foundation for Basic Research (grant 06-03-32493).
Presented Monday 17, 13:30 to 15:00, in session Thermodynamics (T2-1P).
