A dispersion model for three-phase reactors with a chemical reaction of any given order is proposed in this paper. The new more practical boundary conditions are also set up for the countercurrent flow. The numerical approach to design and analysis of multiphase reactors according to the reactor conservation equations is investigated. The concentration profiles in the three phases are calculated using two numerical methods: the Ronge-Kutta method by means of the superposition theorem and the implicit difference method.