There has been considerable interest shown in the use of dynamic gridding techniques for isothermal and thermal compositional simulation. These techniques allow simulation grids to adapt to the physics of complex EOR processes, while retaining a high degree of computational efficiency through the use of relatively coarse grids in areas where there is little activity. Since areas of interest in reservoir models change with time, simulators that use dynamic gridding techniques must be able to deal with changing internal pointer systems as a regular occurrence in their calculations.

There also has been interest in the use of shared memory parallel computers that achieve computational efficiency through the use of various techniques for overall simulator parallelization, as well as for the use of suitable reservoir splittings and associated multi-coloured orderings for ILU linear solvers. These splittings are usually based on some kind of regular cell-based splitting of the reservoir. Unfortunately, such splittings do not immediately apply to the unusual grids generated by dynamic gridding schemes, which exhibit multi- level refinements that are constantly changing.

The goal of this paper is to examine alternate solver orderings based on novel applications of reservoir splittings and also to examine orderings that are applicable to more general systems, such as orderings arising from graph- theoretic notions. The paper will give an overview of different ordering strategies for the parallel linear solver, and will examine how they fare when faced with complex compositional field examples. Results will be shown that indicate that the benefits of dynamic gridding and of the use of a parallel ILU solver can be simultaneously realized in simulations of complex EOR processes. The combination allows for more detailed simulation work and the possibility of working with more reservoir realizations, greatly enhancing the understanding of complex reservoir processes.

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