Finite element simulation of deep-well wet-oxidation reactor

A finite element model is developed for the numerical simulation of a deep-well wet-oxidation reactor. The temperature distribution in the well-earth system is investigated. The governing equations involved in the analysis are the conductive heat equation for the earth, and an energy balance equation describing convective heat transfer and reaction in the reactor tubes. The two equation sets are coupled by the continuity of the temperature and heat flux at the interface between the earth and the reactor tubes. Proper scaling is carried out for the di-mensionless forms of these equations. A Galerkin finite element formulation is used for the spatial discretization of the heat equation in the earth. A Petrov-Gal-erkin finite element formulation is employed for the convection-reaction equation in the reactor tubes. The resultant set of ordinary differential equations is solved by a predictor/multi-corrector algorithm. A numerical test is performed for a model deep-well reactor. Compared to our previously published work, this formulation is more accurate and consumes less CPU time. It can be used in the design of a deep-well reactor for oxidation of aqueous sludge. It can also be employed to test control strategies for the operating reactor system.