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Upscaling permeability

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Example upscaling of permeability using effective medium theory, sand-shale system

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Upscaling permeability

  1. 1. Upscaling - effective medium theory • Assume all heterogeneities to be rotational ellipsoids (pancakes), with a certain ratio between horizontal and vertical axes • => Two components of effective/upscaled permeability, horizontal (isotropic) and vertical • Example: Two-component system, sand (1000 md) and shale (0.01 md) • Vertical and horizontal permeability approach harmonic and arithmetic averages, respectivly, as ratio of horizontal to vertical axis approaches infinity Steinar Ekrann, Jan 2016
  2. 2. Ratio of horizontal-to-vertical length scales: 1 Steinar Ekrann, Jan 2016 Steinar Ekrann, Jan 2016
  3. 3. Ratio of horizontal-to-vertical length scales: 10 Steinar Ekrann, Jan 2016 Steinar Ekrann, Jan 2016
  4. 4. Ratio of horizontal-to-vertical length scales: 100 Steinar Ekrann, Jan 2016 Steinar Ekrann, Jan 2016
  5. 5. Ratio of horizontal-to-vertical length scales: 1000 Steinar Ekrann, Jan 2016 Steinar Ekrann, Jan 2016
  6. 6. Ratio of horizontal-to-vertical length scales: 10000 Steinar Ekrann, Jan 2016 Steinar Ekrann, Jan 2016

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