Reservoir Modeling Using Multiple-Point Statistics

Abstract

Two approaches are traditionally used to build numerical models for facies distributions within a reservoir. Pixel-based techniques aim at generating simulated realizations that honor the well data values, and reproduce a given variogram which models two-point spatial correlation. However, because the variogram cannot look at spatial continuity between more than two locations at a time, pixel-based algorithms give poor representations of the actual facies geometries. In contrast, object-based techniques allow reproducing crisp geometries, but the conditioning on well data requires iterative ``trial-anderror'' corrections, which can be time-consuming, particularly when the data are dense with regard to the average object size. This paper presents a new approach that combines the easy conditioning of pixel-based algorithms with the ability to reproduce ``shapes'' of object-based techniques, without being too time and memory demanding. In this new approach, the complex geological structures expected to be present in the reservoir are characterized by multiple-point statistics, which express joint variability at many more than two locations at a time. Such multiple-point statistics cannot be inferred from typically sparse well data but could be read from training images depicting the expected subsurface heterogeneities. A training image need not carry any locally accurate information on the reservoir; it need only reflect a prior stationary geological/structural concept. Thus training images can be generated by object-based algorithms freed of the constraint of data conditioning. The multiple-point statistics inferred from the training image(s) are then exported to the reservoir model, where they are anchored to the well data using a pixel-based sequential simulation algorithm. * Now with Chevron Petroleum Technology Co. This algorithm is tested for the simulation of a turbidite system where flow is controlled by meandering channels with cross-bedding. The training image reflecting the channel patterns is an unconditional realization generated by an objectbased algorithm. The final simulated numerical models reproduce these channel patterns, and honor exactly all well data values at their locations. The methodology proposed appears to be practical, general, and fast.

Application of Multiple-Point Geostatistics on Modelling Groundwater Flow and Transport in a Cross-Bedded Aquifer

“…Their inference requires a training image depicting the expected patterns of geological heterogeneities. Training images can be obtained from observations of outcrops, geological reconstructions and geophysical data (Strebelle and Journel, 2001). In this study, training images are constructed based on observations of outcrops.…”

“…Multiple-point geostatistics (Strebelle 2000;Strebelle 2002;Strebelle et al 2002;Caers and Zhang 2003;Feyen and Caers , 2006) aims to overcome the limitations of the variogram. The premise of multiple-point geostatistics is to move beyond two-point correlations between variables and to obtain (cross) correlation moments at multiple locations at a time (Strebelle and Journel, 2001). Because of the limited direct information from the subsurface, such statistical information cannot directly be obtained from samples.…”

Stratigraphic and structural connectivity

“…A numerical representation of a synthetic reservoir, composed of channelized sand deposits is used as a benchmark to assess the relative performance of two geostatistical simulation algorithms in predicting compartmentalization under various well densities (dynamic data which could define reservoir compartments is not considered in this example). The two algorithms examined here are: Sequential Indicator Simulation (Journel & Isaaks 1984) and Multiple-Point Statistics simulation (Strebelle & Journel 2001). Since the synthetic reservoir that is being inverted is perfectly known, no uncertainty is implied in the input parameters of the simulation algorithms.…”

“…The nonstationary issue is addressed by using probability cubes describing local probabilities of net-to-gross ratio, at any location in the reservoir, as soft conditioning to a Multiple-Point Statistics algorithm. The third issue, regarding specific stratigraphic sequences can be addressed using advanced modelling algorithms, such as Multiple-Point statistics simulation (Strebelle & Journel 2001), object modelling or an Event Based approach (Pyrcz & Strebelle 2008). Figure 9a represents three stochastic reservoirs in three deepwater environments: a slope valley channel complex, a weakly confined channel complex, and an unconfined channel and sheet complex.…”

Discrete Fracture-Vug Network Modeling in Naturally Fractured Vuggy Reservoirs Using Multiple-Point Geostatistics: A Micro-Scale Case

“…In other words, they borrow the patterns to be reproduced from training images. A training image is defined as the numerical representation of expected subsurface heterogeneities believed to exist in the area being modeled and does not necessarily carry any locally accurate information (Strebelle 2000;Strebelle and Journel 2001). However, a training image should reflect a spatial continuity style similar to the actual phenomenon (Arpat and Caers 2007).…”