History matching of petroleum reservoirs using a level set technique

We describe a novel technique for the characterization of structured reservoirs from production data. A level set technique is used in order to be able to incorporate interfaces between different lithofacies in the reservoir. The new algorithm is able to reconstruct, in addition to the shapes and topologies of the individual lithofacies, their internal permeability profiles simultaneously from the given production data. Here either a pixel-by-pixel or a parameterized model can be used for describing each of the internal profiles, and any hybrid combination of them. If n lithofacies are present in the reservoir, n - 1 level set functions are employed during the characterization. Overlapping regions of these n - 1 level set functions are treated by a special technique tailored to the reservoir characterization application. Here our approach differs significantly from standard techniques for describing more than two values by a level set representation. We also describe techniques for testing the existence and characteristic features of certain geometrical structures ( such as channels or barriers) inside the reservoir by suitable topological perturbations of the describing level set function. Numerical results in 2D are presented which demonstrate the performance of our novel scheme for a variety of simulated but realistic situations which are of importance in reservoir engineering applications.