ISSN:
1572-9567
Keywords:
perturbation method
;
mixtures
;
thermodynamic properties
;
vapor-liquid equilibrium
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract In phase equilibrium problems, the thermodynamic model used often contains a small parameter. For example, for cubic equations of state the interaction coefficients occurring in van der Waals-type mixing rules are often numerically small. The small parameter (ɛ) enters the model then via the formula $$a = \sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {x_i x_j \sqrt {a_i a_j } (1 - \varepsilon \theta _{ij} )} }$$ Other examples include mixtures with compounds whose characteristic parameters cover a narrow range, diluted solutions, small amounts of polydisperse material in a solvent, and so on. In this paper we develop a general scheme to obtain the solution of thermodynamic problems such as the prediction of phase equilibria, using an expansion in the small parameter ε. We also give a method to obtain a suitable zero-order (ɛ = 0) system. The perturbation scheme may be helpful in the solution of difficult problems or as a tool in a sensitivity analysis. As an example we apply it to multicomponent mixtures, described through a two-parameter equation of state with small interaction coefficients. We show that for that case, if the number of components is large, it leads to computational savings.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00500708
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