Stochastic Reservoir Simulation Using Neural Networks Trained on Outcrop Data

Extensive outcrop data or photographs of present day depositions or even simple drawings from expert geologists contain precious structural information about spatial continuity that is beyond the present tools of geostatistics essentially limited to two-point statistics (histograms and covariances). A neural net can be learned to collect multiple point statistics from various training images, these statistics are then used to generate stochastic models conditioned to actual data. In petroleum applications, the methodology developed can be a substitute for objects based-algorithms when facies geometry and reservoir continuity are too complex to be modelled by simple object such as channels. The performance of the neural net approach is illustrated using training images of increasing complexity, and attempts at explaining that performance is provided in each case. The neural net builds local probability distributions for the facies types (categorical case) or for petrophysical properties (continuous case). These local probabilities include multiple point statistics learned from training images and are sampled with a Metropolis-Hastings sampler which also ensures reproduction of statistics coming from the actual subsurface data such as locally varying facies proportions. Introduction Stochastic simulation is a tool that has been driven by the need for more “representative” i~~zage,sthan the smoothed n?aps produced by regression techniques such as kriging. Although locally accurate in a minimum error ~ariance sense, kriging maps are poor representations of reality with various artefacts, Kriging produces conditional bias in the sense that through smoothing small values arc overestimated and large values are underestimated. Moreover, this smoothing is not uniform since it is minimal near the data locations and increases as estimation is performed further from the data locations. Smoothed maps should not be used where spatial patterns of values is important such as in the assessment of travel times or production rates in flow simulations. Reproduction of [he spatial connectivity of extremes is critical in any study involving the determination of risk of a rare event happening. Most current methods of simulation rely on the modeling of two-point statistics such as covariances and variograms and the subsequent reproduction of these second moments. Yet, many phenomena are more complex in the sense that their spatial patterns cannot be captured by two-point statistics only. In particular, identification of two-point statistics only is not sufficient to reproduce patterns of connectivity of extreme values over long ranges. Strings of extreme values, curvilinear or wedgeshaped clusters of similar values are common occurrences in earth sciences, and their importance in water or oil flow simulations cannot be overstated. The most common way of performing stochastic simulation is through some form of Gaussian simulation (Deutsch and Journel, 1997, p. 139). This class of simulation algorithms is based on the congenial properties of multi-Gaussian models, which import some severe restrictions not always fully appreciated: