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

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. Ratio of horizontal-to-vertical length scales: 1
Steinar Ekrann, Jan 2016 Steinar Ekrann, Jan 2016

3. Ratio of horizontal-to-vertical length scales: 10
Steinar Ekrann, Jan 2016 Steinar Ekrann, Jan 2016

4. Ratio of horizontal-to-vertical length scales: 100
Steinar Ekrann, Jan 2016 Steinar Ekrann, Jan 2016

5. Ratio of horizontal-to-vertical length scales: 1000
Steinar Ekrann, Jan 2016 Steinar Ekrann, Jan 2016

6. Ratio of horizontal-to-vertical length scales: 10000
Steinar Ekrann, Jan 2016 Steinar Ekrann, Jan 2016