Numerical Simulation of Deep‐Well Wet Oxidation Reactor using Steam

Abstract

A finite element model is developed for the numerical simulation of the start‐up of a deep‐well wet oxidation reactor using steam. The model is capable of handling different cases of start‐up, using saturated steam of arbitrary quality including hot water. The transient temperature field in the well‐earth system is studied. The governing equation for the earth is the conductive heat equation. For the reactor, the analysis involves solving the energy balance equations describing the convective and intertube heat transfer, mass balance equations, and thermodynamic relations for the fluid in the tubes. The equations for the reactor and the earth are coupled by the continuity of the temperature and heat flux at the interface between them. A Galerkin finite element formulation is used for the spatial discretization of the heat equation in the earth; a Petrov‐Galerkin finite element formulation is employed for the energy balance equations in the reactor tubes. The resulting set of ordinary differential equations is discretized in time and solved by a predictor‐multicorrector algorithm. The model is tested on a typical deep‐well reactor to study its start‐up dynamics. The results can be used to estimate the start‐up time and the amount of steam or water required to obtain the necessary initiation temperature for the process.