Fast iterative method for processing Hamilton-Jacobi equations

摘要

Fast iterative method for processing Hamilton-Jacobi equations Abstract 5 Disclosed herein is a method for analyzing the connected quality of a hydrocarbon reservoir. The method comprises obtaining a model of a portion of the reservoir and dividing it into cells, each cell having a volume and attributes. A speed function is to a portion of the cells. A reference cell is chosen. A connectivity between cells in the reservoir is determined using a solution to an Eikonal equation, describing a 10 propagating front in a heterogeneous medium, said front progressing outward from a reference cell until an ending condition is met. The Eikonal equation is solved by a fast iteration method with propagation velocity as a function of spatial position being provided by the speed function. Regions of the reservoir are characterised by their connective quality to the reference cell using the connectivity. WO 2009/059045 PCT/US2008/081855 100a/ 104b 106b 1O00b 104c 106c 1l00O 106a 104a (a) Initial stage (b) After first update (c) After second update