A new equation-of-state model is presented that accounts for the non-random distribution of free volume in multicomponent fluid mixtures. The classical quasi-chemical approach is used in connection with the Lattice Fluid (LF) model. The model is extended via continuous thermodynamics to polydisperse polymer systems. The algorithm for the application of the model to phase equilibrium calculations is also presented. The model is applied to both solvent-polydisperse polymer and to polydisperse polymer-polydisperse polymer systems. Besides phase equilibrium calculations, the distributions of the polymeric species in principal and conjugate phases are obtained. The comparison with available experimental data is satisfactory.