In the characterization of oil fields in the petroleum industry, 3D modeling using geostatistics is often used to assess reservoir heterogeneity and connectivity. Geostatistics often uses kriging to interpolate between data points or conditioning data. Conditioning data includes well log hard data, but can also include soft data, typically seismic data.
Conventional 3D modeling methods are based on variogram or two-point-statistics. Variogram-based algorithms allow integrating well and seismic data using a pixel-based approach. First, well data are blocked to the reservoir stratigraphic grid, i.e. well data values are assigned to the cells that the wells penetrate and sample. Then, all unsampled cells in the reservoir stratigraphic grid are simulated conditional to well and seismic data using some form of kriging. However, the models built using conventional variogram-based methods are most often not consistent with geological interpretation. Variogram-based geostatistics is inadequate in integrating geological concepts: two-point statistics variograms do not allow modeling complex geological heterogeneity. As a result, the variogram-based methods usually generate models that provide poor reservoir performance forecasting.
Over the past 10 years, the traditional variogram-based methods have been replaced by Multiple Point Statistics (MPS) methods. The MPS approach replaces traditional variograms with 3D numerical conceptual models of the subsurface geology, also known as training images.
MPS simulation is a reservoir facies modeling technique that uses conceptual geological models as 3D training images (or training cubes) to generate geologically realistic reservoir models. The training images provide a conceptual description of the subsurface geological geobodies, based on well log interpretation and general experience in reservoir architecture modeling. MPS simulation extracts multiple-point patterns from the training image and anchors the patterns to reservoir well data.
A 3D data template is provided by a user to define the dimensions of the multi-point patterns to be reproduced from the training image. Specifically, a size of the 3D data template corresponds to the maximum number of conditioning data used to infer statistics from the training image during the MPS simulation process. The larger the template (i.e., the larger the number of conditioning data), the better the reproduction of the geological features displayed by the training image. However, because computation time of MPS simulation increases exponentially with the size of the template, a trade-off is made between simulation computation time and training pattern reproduction quality. The trade-off is a function of the number of facies to model and the complexity of the training image.
One conventional approach to optimize the template size, i.e. the number of conditioning data used in MPS simulation, for a given training image is by trial-and-error where multiple MPS simulations are run using various template sizes, and the smallest template size that allows reasonable training image reproduction is retained. However, this conventional approach is extremely computation time-intensive (i.e., CPU time-intensive) and seldom used. Instead, common conventional methods consist of setting, by the experienced modeler, the template size (i.e., the maximum number of conditioning data) to an arbitrary number that is conservative and high enough to ensure reasonable pattern reproduction, even with complex multi-facies training images. For example, in some cases, the default template size is set to 40 cells. In this case, pattern reproduction is, in most cases, satisfactory. However, one drawback is that the simulation can take up to several hours (in some instances tens of hours).
Therefore, there is a need for a method for optimizing conditioning data templates that cures these and other deficiencies in the conventional methods so as to find an optimal template size, or optimal number of conditioning data, that would minimize computation time of an MPS simulation while preserving training pattern reproduction quality.