Precisely describing subsurface structures can lead to the discovery of by-passed oil and gas, to reliable development planning, and hence to maximized proved reserves1). Geostatistics has become popular as a key technique for describing the subsurface structures. Among a variety of geostatistical methods, indicator based approaches including indicator kriging (IK) and sequential indicator simulation (SIS) enable the estimation of distributions of categorical variables (e.g., facies). In addition to these traditional two-point geostatistical methods, a multiple-point statistics (MPS) approach has been proposed for reconstructing complex patterns of a structure such as curvilinear shapes.
In this study, first, we constructed the geostatistical program (Program-1) capable of estimating the distribution of categorical variables by IK, SIS and MPS. The comparison among the facies distributions estimated by these methods revealed that MPS was superior in reproducing complex facies distributions.
Second, we developed the program (Program-2) to modify/tune the facies distribution estimated by Program-1, through the history matching using the genetic algorithm (GA). GA is an adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetics. We verified that the facies distribution estimated by Program-1 was successfully improved so that it could rigorously reproduce the dynamic well performances such as bottomhole pressure and oil/water production rates.
The well performances are simulated with every realization for the selection of superior realizations by GA, which results in the significant amount of CPU-time. Hence, we further improved Program-2 applying a multi-dimensional scaling (MDS) and k-means clustering. MDS can map the distance of the similarity between each realization into a low dimensional space. In accordance with this mapped similarity, each realization of facies distribution can be grouped by k-means clustering. In this modified Program-2, the well performances are simulated only for the representative ones for each group of realizations for the selection of superior realizations, which contributed to the dramatic reduction of CPU-time by Program-2.