f Some geostatistical models for filling heterogeneous reservoir with petrophysical properties

One of the main challenges of Geostatistics in reservoir characterization is to populate a portion of 3D earth model with rock properties. Their spatial characteristics are analyzed along the stratigraphic reference system where the variogram is modeled. A base case estimation (kriging) may be sufficient, or complemented by stochastic simulations for a sensitivity analysis. Sometimes properties present multimodal distribution reflecting the heterogeneity within the studied stratigraphic domain. Therefore it makes sense to look for explanatory co-variables, such as the lithotype. Then we simulate the spatial organization of different lithotypes first (using categorical simulation) and afterwards populate each lithotype with the rock property following the rock- dependent spatial characteristics. The previous workflow, which relies on the independence between lithotype and rock property, may not be relevant if the samples show a border effect when crossing the lithotype border. Some statistical tools are introduced to check the relevance of this assumption, such as the transition probabilities and the contact analysis. The border behavior is also checked after the initial simulation outcome has been upscaled. Some stochastic joint models of lithotype and rock property are conceived to reproduce the presence or absence of borders, conditioned to sample data.