A model for the simulation of continuous-contact separation processes, based on heat and energy balances, multicomponent mass transfer, and chemical engineering correlations for mass and heat transfer coefficients and liquid holdup is developed and solved with the moment transformation method. Polynomials are used to approximate the concentration and flow rate profiles within the packing. The moment transformation method is used to transform the partial differential equations into a system of differential-algebraic equations that is solved with Newton's method. The model can be used for both steady-state and dynamic simulation, and it can also be used for systems with axial dispersion. The features of the model are demonstrated with an example of ternary distillation.