Graph theory applications to continuity and ranking in geologic models

Abstract Continuity of permeable and impermeable units strongly affects the flow simulation response in geologic media. Important factors include the size of permeable and impermeable bodies, their internal geometries, and whether they connect to injection and production wells at different stages of reservoir development. Most of the currently available analysis tools for geologic modeling cannot easily handle irregularities such as faults, onlap and truncations, or they are strongly limited in the dimensions of the models that are amenable to analysis. We adopt algorithmic graph theory for computationally efficient, continuity analysis. This method can treat irregularities in the geologic model including unstructured grids of unequal cell sizes. Geologic models are transformed from a cell-based representation to a node- and connection-based representation, where both nodes and arcs (connections) can have associated properties. Quantities such as connected components, maximum flow, shortest paths, minimum-cost paths and many other connectivity measures can be determined. These connectivity measures involve connections whose lengths or values are weighted by reservoir parameters such as porosity and permeability. Because graph algorithms are efficient, connectivity can be rapidly evaluated for different wells that might become important during reservoir development. Graph theory algorithms can be applied to rank the anticipated flow performance of different geologic model realizations, to aid in delineating contiguous regions of similar character for use in up-scaling, as well as to assess how well a scaled-up model preserves the continuity of the original detailed geologic model.