Numerical problems encountered in the simulation of reactive absorption: DAE index reduction and consistent initialisation

Abstract

A general simulation model able to represent mass transfer in the presence of chemical reactions is presented. The model developed describes the behaviour of an absorption column. This model needs to be able to access certain information such as kinetic constants, equilibrium constants, activity coefficients, etc. Among these auxilary models, is the need to be able to calculate the mass flux and compositions at the boundary of the diffusional film. A set of equations describing the film has therefore been developed, and its resolution has proved to be troublesome. Indeed we have run into two problems that have had to be tackled. The problems encountered are directly due to the nature of the equations to be solved, that is a system of differential algebraic equations (DAE). These problems arise from the approach desired to treat the equations, based on Gear's algorithm. The first problem deals with the solution of high order index systems, and the second involves the necessity of having consistent initial conditions. A suitable procedure has been implemented for index reduction, and several techniques have been tested for the obtention of consistent initial conditions.