Stochastic Modeling of Geometric Objects and Reservoir Heterogeneities

Abstract The object based method used for reservoir characterization is a technique for geometric modeling and stochastic simulation of geological units and reservoir heterogeneity. A set of geological objects representing basic reservoir units is conceptually and quantitatively defined, has its parameters quantified and modeled on an interactive computer environment. The objects include channels, lobes, sigmoids, dunes, ellipsoids, plane beds and wedges. The conditional stochastic simulation of these objects produce 3-D models of the depositional or diagenetic reservoir architecture. This methodology has been applied in fluvial (Potiguar basin) and turbidite (Campos basin) reservoirs. Introduction Modeling of reservoir geometry and heterogeneity is a necessary activity of oil exploitation. Mathematical and computer methods are used to integrate efforts in geology, geophysics and reservoir engineering for defining optimal reservoir characterization and oil production. The use of probabilistic mathematical models to represent reservoir heterogeneities is booming. However, the stochastic simulation models based only on variograms is insufficient to represent the geometry and distribution patterns of genetic units as well as the diagenetic and structural reservoir features (Fig. 1). The combination of stochastic and geometric methods in the object based approach has proved an adequate alternative to generate equiprobable realizations of the reservoir architecture. An object based method for reservoir characterization is presented in this work. This technique consists of geometric modeling and stochastic simulation of discrete features such as, genetic units and diagenetic heterogeneities of the reservoirs. Boolean and Object Based Models The Boolean model has been designed to express the intuitive idea of an union of independent objects located at random, and a mathematical morphology method used mainly to 2-D modeling of natural or technical images. The object oriented model, according to the stochastic geometry terminology, is a Point Process, more specifically defined as a Random Closed Set.