MATHEMATICAL PROBLEMS IN THERMODYNAMIC TESTING OF VAPOR-LIQUID-EQUILIBRIUM DATA

A generalized method for thermodynamic consistency to test binary and multicomponent vapour-liquid equilibrium data is reported. The essenti al step of the method is to solve the coexistence equation (deduced fr om the Gibbs-Duhem equation). This coexistence equation is an implicit differential equation - an ordinary one in the binary case and a part ial one in any other multicomponent case. The unknown function in the differential equation is the molar excess Gibbs energy in all cases.Th e boundaries of an n-component system consist of the corresponding (n- 1) component systems, and the properties of the latter serve also as b oundary conditions for the differential equation. Mathematically the f ollowing problems arise: Discretization considering the measured point s; Multivariable interpolation or fitting in the non-binary cases; Err or estimation. Possibilities of the generalization in the n-dimensiona l space are discussed, and results for the binary and ternary systems are shown.