Accurate characterization of subsurface oil reservoirs is an essential prerequisite to the design and implementation of enhanced oil recovery (EOR) scenarios. Specifically, in reservoir characterization, integrating static and dynamic data into reservoir models to construct accurate and realistic models has received considerable attention. Unlike most of the conventional geostatistical approaches of integrating data into reservoir models that are based on semi-variograms (two point statistics) as a measure of spatial connectivity, a complete multiple point statistic framework is presented in this paper. In contrast to two point statistic methods, multiple point statistics based methods are capable of reproducing curvilinear geological structures. The algorithm starts with extracting multiple point statistics from training images using an optimal spatial template. After collecting different patterns and building the mp histogram, the pattern reproduction process commences. It begins from data locations and then grows to fill the whole reservoir domain. The algorithm accounts for three main practical issues: uncertainty in geological scenarios, scanning template and non-stationarity. Growthsim is capable of integrating data from multiple data sources. One of these data types is dynamic data or flow history.
The conventional approach to integrate production information into reservoir models is by iterative perturbation of the reservoir model until the production history of the reservoir is matched. Iterative methods have been applied till date to random fields that are completely characterized by a two-point covariance function. In contrast, this paper presents a forward modeling approach that investigates history matching within a multiple point modeling framework. A novel technique is implemented in this research is based on the merging of mps inferred from history matched and geological models. Pattern growth is performed subsequently by sampling from the merged mp histograms. History matched models using the presented approach show an excellent agreement with underlying geological descriptions and match production history.
Simulation was introduced by Matheron (1973) and Journel (1974) to correct for the smoothing effects and other artifacts of kriging, allowing the reproduction of spatial variance predicted by the variogram model. Different algorithms were developed including sequential simulation (Journel, 1983, Isaaks, 1990; Srivastava, 1992; Goovaerts, 1997; Chiles and Delfiner, 1999), which have become the workhorse for many current geostatistical applications. Stochastic simulation provides the capability to generate multiple equiprobable realizations, thereby permitting assessment of spatial uncertainty (Journel and Huijbregts, 1978). To reproduce the curvilinear structures and pattern continuity, anisotropy directions could be modified locally (Deutsch and Lewis, 1992). One could also correct for additional connectivity of the geological patterns through modification of the variogram ranges (Deutsch and Gringarten, 2000).
Initially Srivastava (1992), and later Caers (1998) and Strebelle (2000), proposed the idea of borrowing conditional probabilities directly from a training image, allowing the use of higher order or multiple point statistics to reproduce geological structures and patterns. Advantages of this approach over the Boolean object-based methods (Stoyan, Kendal and Mecke, 1987); Haldorsen and Damsleth, 1990) include the pixel-based non-iterative process and ease of integration of data of multiple types.
