Adaptive multigrid solution strategy for the dynamic simulation of petroleum mixture processes

Abstract

The paper presents the extension of our work on the adaptive steady-state simulation of refinery processes to dynamic problems. The results show that the adaptive algorithm is capable of following the changes in the composition by adapting the composition representation during the course of simulation. The method is based on a continuous model formulation. In principle, each model given in a discrete (or pseudocomponent) formulation can be rewritten by means of continuous distribution functions. This continuous formulation does not yet reduce the model size but comprises the full detailed model. A model reduction is accomplished by applying a discretization scheme to the continuous formulation. Thus, the continuous reformulation allows the usage of modern discretization techniques including grid adaptation (adaptive wavelet-Galerkin discretization) and multigrid methods. In the iterative algorithm suggested, the approximate solution of the dynamic process model is obtained on the full composition grid. In each iteration loop the current iterate is corrected by a correction term, which is determined on a coarse grid for the composition representation. According to the multigrid framework the obtained intermediate solution is prolongated to the full composition detail by means of a linearization of the model equations. Within these iterations, the discretization grid is adapted by exploitation of the particular properties of the employed wavelet basis functions.