History matching of petroleum reservoirs using a level set technique

Abstract

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.

Level Set Methods for Structural Inversion and Image Reconstruction

“…The data are the injection and production rates of water and oil, respectively, and sometimes pressure values measured at injection and production wells over production time. For more details, see [35]. Figure 3 shows an image of a disconnected crack embedded in a homogeneous material.…”

Well-posed Bayesian geometric inverse problems arising in subsurface flow

“…The resulting posterior distribution is µ(resp. µ ) µ 0 with Radon-Nikodym derivative given by (13), for each y(resp. y ) ∈ Y .…”

Identification of subsurface structures using electromagnetic data and shape priors

“…For more details about alternative level set representations and the level set method [27] in general, we refer to the review papers [28][29][30]. Note also that a level set representation where dependency of c on r is accounted for, has been proposed in [6,31].…”

“…The main aim with the research presented in this paper is to develop a computationally efficient inversion methodology for CSEM data that is able to preserve prior information about geological strata, and we will therefore apply a model-based representation (see, e.g., [2][3][4][5][6][7][8][9]) of the unknown electric conductivity field. Alternatively, a pixel-based representation (see, e.g., [10][11][12][13]) could have been used, although the tendency for smoothing out the resulting conductivity field makes it less attractive.…”