Accounting for non-exclusivity in sequential indicator simulation of categorical variables

Facies models are used to better capture heterogeneity in mineral deposits and petroleum reservoirs. Facies are often considered as mutually exclusive and exhaustive at the scale of the geological model. These two assumptions are needed for sequential indicator simulation and most other facies modeling techniques; however, the assumption that an entire grid block consists of one facies type becomes unreasonable as the scale increases. Most geological models are built at a scale that is larger than the scale of variation of facies. Mixing of multiple facies types within a grid cell is common, especially in zones of transition between different facies. This paper develops a new technique to address the issue of non-exclusivity of facies within grid cells. The approach quantifies the uncertainty resulting from majority-vote upscaling of facies from core or well log scale to the grid cell scale and utilizes this uncertainty to build better models of continuous reservoir properties such as bitumen grade. Uncertainty is quantified using a measure of entropy that is capable of handling situations where there may be similarity between different facies types. A methodology to implement entropy in geo-modeling is introduced and demonstrated with several small examples. An example involving real data from the McMurray formation of Totalʹs Joslyn lease is used to demonstrate the improvement in accuracy compared with traditional modeling workflows.