Transport in Porous Media

, Volume 98, Issue 2, pp 377–400 | Cite as

A Comparison Study Between an Adaptive Quadtree Grid and Uniform Grid Upscaling for Reservoir Simulation

  • Masoud BabaeiEmail author
  • Ahmed H. Elsheikh
  • Peter R. King


An adaptive quadtree grid generation algorithm is developed and applied for tracer and multiphase flow in channelized heterogeneous porous media. Adaptivity was guided using two different approaches. In the first approach, wavelet transformation was used to generate a refinement field based on permeability variations. The second approach uses flow information based on the solution of an initial-time fine-scale problem. The resulting grids were compared with uniform grid upscaling. For uniform upscaling, two commonly applied methods were used: renormalization upscaling and local-global upscaling. The velocities obtained by adaptive grid and uniformly upscaled grids, were downscaled. This procedure allows us to separate the upscaling errors, on adaptive and uniform grids, from the numerical dispersion errors resulting from solving the saturation equation on a coarse grid. The simulation results obtained by solving on flow-based adaptive quadtree grids for the case of a single phase flow show reasonable agreement with more computationally demanding fine-scale models and local-global upscaled models. For the multiphase case, the agreement is less evident, especially in piston-like displacement cases with sharp frontal movement. In such cases a non-iterative transmissibility upscaling procedure for adaptive grid is shown to significantly reduce the errors and make the adaptive grid comparable to iterative local-global upscaling. Furthermore, existence of barriers in a porous medium complicates both upscaling and grid adaptivity. This issue is addressed by adapting the grid using a combination of flow information and a permeability based heuristic criterion.


Adaptive quadtree grid Permeability- and flow-based gridding  Renormalization upscaling Local-global upscaling  Downscaling 



The authors are grateful to one of the anonymous reviewers for suggesting to implement transmissibility-based upscaling. This suggestion has made the numerical comparison more consistent. We also, would like to thank the editor and the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Masoud Babaei
    • 1
    Email author
  • Ahmed H. Elsheikh
    • 1
  • Peter R. King
    • 1
  1. 1.Department of Earth Science & EngineeringImperial College LondonLondonUK

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