Sequential simulation with patterns

TL;DR: A pattern-based geostatistical sequential simulation algorithm (SIMPAT) is proposed that redefines reservoir characterization as an image construction problem and works equally well with both continuous and categorical variables while conditioning to a variety of local subsurface data.

Abstract: Flow in a reservoir is mostly controlled by the connectivity of extreme permeabilities (both high and low) which are generally associated with marked, multiple-scale geological patterns such as fluvial channels. Accurate characterization of such patterns requires multiple-point correlations that are much beyond the reach of the two-point correlations provided by a traditional variogram model. In this thesis, a pattern-based geostatistical sequential simulation algorithm (SIMPAT) is proposed that redefines reservoir characterization as an image construction problem. The approach utilizes the training image concept of multiple-point geostatistics (MPS) but is not developed through probability theory. Rather, it considers the training image as a collection of multiple-scale patterns from which patterns are selected and pasted into the reservoir model such that they match any local subsurface data. A training image pattern is defined as a multiple-pixel configuration identifying a meaningful geological structure believed to exist in the reservoir. The framework of sequential simulation is used to achieve the simulation and conditioning of patterns. During sequential simulation, at each visited grid location, the algorithm looks for the training image patterns that is most ‘similar’ to the data event (the neighborhood of the currently visited grid node), i.e. the traditional conditional probability calculations of MPS are replaced with similarity calculations of computer vision and image processing. One way of conceptualizing the proposed algorithm is to envision it as a method for solving jigsaw puzzles: The technique builds images (reservoir models) by assembling puzzle pieces (training image patterns) that interlock with each other in a certain way. The method works equally well with both continuous (such as porosity and permeability) and categorical (such as facies) variables while conditioning to a variety of local subsurface data such as well logs, local angle information and 3D seismic.