Geostatistical modeling of unstructured grids for flow simulation

• Author / Creator

  Manchuk, Johnathan Gregory

• A challenge in petroleum geostatistics is the application of modeling algorithms such as Gaussian simulation to unstructured grids that are being used for flow simulation. Geostatistical modeling is typically applied on a fine scale regular grid and then upscaled to the unstructured grid. This work proposes a fine scale unstructured grid. The grid is designed so that its elements align with the flow simulation grid elements, eliminating the occurrence of intersections between the two grids. Triangular and tetrahedral grids are used for the fine scale grid; however, they introduce a variety of element scales. The approach developed in this work populates the fine scale grid based on the scale of conditioning data. The resulting error due to scale discrepancy is quantified and mitigated though the upscaling process. A methodology to assess the error in upscaled properties is developed and used to control the design of the fine scale grid. Populating the fine scale grid with reservoir properties requires modification of existing geostatistical algorithms. The set of spatial locations for modeling is irregular and three differences that result from this are addressed: random path generation; spatial search; and the covariance lookup table. Results are compiled into an algorithm for sequential indicator and sequential Gaussian simulation on irregular point sets. Checking variogram reproduction on large irregular point sets is a challenge. An algorithm that efficiently computes the experimental variogram for these cases is developed. A flow based upscaling method based on the multipoint flux approximation is developed to upscale permeability models from the fine scale unstructured grid to the flow simulation grid. Triangular grids are assumed for the fine scale. Flow simulation results using the upscaled transmissibilities are very similar to results obtained using traditional flow simulation on high resolution regular grids.

• Subjects / Keywords

  • Geostatistics
  • Uncertainty
  • Unstructured
  • Flow

• Graduation date

  Fall 2010

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3563M

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.