Simulation of permeability field conditioned to well test data

Well testing provides critical information about the effective permeability value around the well being tested. That information must be integrated with higher resolution, smaller scale, well log data. The difference of scale is handled by kriging with `block' averages, while the non-linear averaging of permeability values is addressed by working on specific non-linear power transform of the original permeability data. A case study shows the simulated permeability fields to honor, in expected value, the well test-derived effective permeability values in addition to honoring the smaller scale well log data and statistics. Ignoring the well test information would result in permeability fields that are imprecise around the well being tested and which display too large uncertainty. The necessity of data integration, even when data are of widely different scales, is demonstrated. The paper also discusses cases when the well test-derived effective permeability appears inconsistent with the well-log derived Smaller scale permeability data. The paper points out the limitation of the linear power-averaging formulation for capturing the dynamics of fluid flow.