This work aims at modelling bubble column reactors for wet air oxidation (WAO) acid operated under steady flow conditions. Aqueous wastes containing organic pollutants can be treated by WAO, i.e. oxidation by bubbling oxygen through a liquid aqueous phase, under high temperature (200-325 degrees C) and pressure (up to 150 bar). Only an handful of industrial plants are in operation and they were designed by extrapolating results from pilot plants. This paper discusses what needs to be known for a scientific design. The bubble column is divided into a number of cells. Each one is perfectly mixed and connected with the previous (backflow) and next cell. Data are available for the hydrodynamics (axial dispersion, gas hold-up), mass transfer and kinetics of reactions. The thermodynamics of the gas phase are determined by Peng and Robinson's equation of state and Henry's law describes the equilibrium conditions. These data have been used to implement a computer program intended to determine the performance of a WAO reactor. Typical profiles within the reactor are presented, as are dependencies on operating parameters. An ignition phenomenon, leading to an unstable operating regime, is also evidenced.