Summary
Training images are numerical representations of geological conceptual models that provide prior information on reservoir architecture. A new emerging geostatistical approach named multiple-point statistics (MPS) simulation allows extracting multiple-point structures from such training images and anchoring these structures to the data actually observed in the reservoir. By reproducing multiple-point statistics inferred from training images, MPS enables the modeling of complex curvilinear structures (e.g., sinuous channels) in a much more geologically realistic way than traditional two-point statistics (variogram-based) techniques. However, in the original MPS implementation, all multiple-point statistics moments computed from the training image are exported to the reservoir model without processing, which allows simulating only categorical or discretized variables. This implementation is appropriate with clastic reservoirs for which, typically, depositional facies are simulated first using MPS, then porosity and permeability are distributed within each simulated facies using traditional variogram-based techniques. But for reservoirs, in particular in carbonate environments, where porosity and permeability trends/cycles are not closely tied to any facies distribution, simulating porosity/permeability directly using corresponding continuous training images appears to be a more suitable approach.
In this paper, a new filter-based implementation of MPS, named filtersim, is proposed to reproduce features from continuous variable training images. First, a set of general filters is applied to the training image to transform (summarize) each training pattern into a set of scores accounting for different aspects of the pattern, such as north-south and east-west gradients and curvatures. The training patterns are classified in the score space and grouped into a small number of similarity classes. The simulation consists then of visiting each grid node along a random path, identifying the similarity class that best fits to the local conditioning data, and patching a pattern drawn from that selected similarity class. In our study, this new approach was applied to model the 3D porosity distribution of a carbonate reservoir in Kazakhstan. First, the original "categorical" MPS program snesim was used to model the two main reservoir regions, platform and slope, where the spatial porosity distribution is characterized by significantly different features. Interpreted well markers and seismic data were used to condition the modeling of these two regions. Then porosity was distributed in the platform region using the "continuous" filter-based MPS program filtersim, as described previously. The 3D training images used in that second step displayed porosity trends/cycles controlled by the type of geological sedimentation process believed to have occurred in the reservoir.
Quantile Sampling: a robust and simplified pixel-based multiple-point simulation approach
