An aggregation model reduction method for one-dimensional distributed systems

Abstract

This thesis discusses a model reduction method for one-dimensional distributed systems. These systems can be spatially discretely distributed, like staged distillation columns, or spatially continuously distributed, like packed distillation columns, tubular reactors etc. The method takes its starting point in the aggregated modeling method of L´evine and Rouchon (1991) for simple staged distillation column models. The derivation of the method is substantially simplified, making it possible to apply the method to more complex models that include mass and energy balances. The basic principle of the method is to divide the system into intervals of steadystate systems, which are connected by dynamic aggregation elements. In discrete systems, the aggregation elements are some selected units, and the remaining units form the steady-state systems. In continuous systems, the aggregation elements are dynamic equations connecting the steady-state systems described by boundary value problems.

In order to obtain models of lower complexity than the original models, the steady-state systems have to be eliminated from the reduced models. This can be achieved by solving them either numerically or analytically as functions of the independent variables of the aggregation elements. The resulting functions can be substituted into the dynamic equations, yielding reduced models that retain the original structure of the original model, but have a much lower number of states.

As a case study, a complex distillation column including mass and energy balances and complex hydraulic and thermodynamic relationships is investigated. The steady-state equations in the reduced model are replaced by  tabulated functions that are implemented using linear multi-dimensional interpolation. The reduced model is compared with a fast implementation of the original model, and is shown to be several times faster at comparable accuracy.

For spatially continuous systems, the method is a new approach to derive discretized equations from the original partial differential equations. It requires more implementation effort, but yields more accurate models than alternative discretization methods such as finite difference and finite element approximations. The method is demonstrated on a fixed bed reactor model and a heat exchanger model.