Mathematical models for simulating the VERTECH deep well reactor under steady-state and non-steady-state conditions are presented. The basic assumptions of the model involve parallel chemical reactions and multiphase heat and mass-transfer problems over the whole reactor length on the basis of a non-equilibrium thermodynamic state. After selecting the required model parameters from the literature, a steady-state reactor model has been constructed and the resulting differential equations solved by means of a special numerical iteration scheme. The simulation runs carried out demonstrate the feasibility of the process. Under steady-state conditions, COD can be reduced up to ca. 65%-90% at a bottom temperature of nearly 280 degrees C. The dynamic model has been developed in two steps of increasing accuracy. To investigate safety aspects, a failure of the jacket cooling system has been simulated successfully by means of a dynamic reaction zone model. As an extension, a more sophisticated dynamic model for the whole deep well reactor has been developed, based on the model assumptions of the steady-state reactor but for non-steady-state conditions. As an example of the reaction engineering power of this computer code, a reactor start-up phase realized in several consecutive steps has been simulated.