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Data-Driven Model Reduction, Scientific Frontiers, and Applications

Michael King, Harold Vance Department of Petroleum Engineering
Improved Localization in Upscaling of Fluid Flow in Porous Media


  • Michael J. King
  • Krishna Nunna


An example of model reduction that arises in computational petroleum reservoir engineering is the reduction of extremely large detailed 3D geologic models into merely large 3D flow simulation models. Typical computational cell volumes are 50m × 50m × 10cm for geologic models (offshore reservoirs). This is usually adequate to resolve reservoir heterogeneity between wells, while having sufficient vertical resolution to capture the variability in reservoir properties as measured by well logs. Such models can easily have up to 108 cells in a computational grid. In contrast, flow simulation models need to have significantly fewer cells in order to perform performance analysis, prediction and design in reasonable amounts of time. Typical degrees of model reduction are 1×1 or 2×2 areally, but in excess of ×30 vertically. Areal resolution is chosen to resolve fluid flow between wells, while the vertical resolution is largely driven by the requirements of reduced computational cost. Consequently, the reservoir properties in the flow simulator will be significantly averaged, especially vertically.

Static properties (porosity, net-to-gross, bulk rock volumes) are simple to average. However, dynamic properties (permeability, transmissibility) are flow based and will naturally couple local flow patterns to global flow fields through their boundary conditions, which (unfortunately) are unknown. This leads to a lack of localization in the calculation of upscaled flow properties. We report on recent progress in developing transient diffuse source and pseudo steady state based upscaling algorithms, which are completely local in their formulation. We demonstrate excellent upscaling performance with significant improvements in localization compared to other algorithms currently in use within the industry.