Table 2 Results for 3603 Darcy blocks.

From: Upscaling the porosity–permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning

Size [voxels3]

Volume 1

Volume 2

Volume 3

Volume 4

Volume 5

Volume 6

Volume 7

Volume 8

Volume 9

Volume 10

RMSE

Total run time [min]*

Porosity

0.36

0.43

0.35

0.40

0.38

0.34

0.40

0.36

0.34

0.34

–

–

360

Darcy Stokes Brinkman (ground truth) permeability [m2]

6.59 × 10–14

9.47 × 10–15

7.67 × 10–14

3.10 × 10–14

3.69 × 10–14

6.50 × 10–15

8.19 × 10–14

9.05 × 10–15

2.45 × 10–14

4.11 × 10–13

–

1500

60

Numerical DBS upscaled permeability [m2]

5.85 × 10–14

1.01 × 10–14

1.50 × 10–14

1.70 × 10–14

3.40 × 10–14

5.76 × 10–15

7.93 × 10–14

9.63 × 10–14

3.71 × 10–14

4.00 × 10–13

0.11

240

Machine learning upscaled permeability [m2]

7.36 × 10–14

1.07 × 10–14

1.48 × 10–14

1.68 × 10–14

2.61 × 10–14

5.91 × 10–15

5.91 × 10–14

1.01 × 10–14

2.74 × 10–14

2.26 × 10–13

0.14

3

KC upscaled permeability [m2]

3.40 × 10–14

4.60 × 10–14

2.26 × 10–14

4.22 × 10–14

3.30 × 10–14

1.20 × 10–14

3.97 × 10–14

2.27 × 10–14

1.74 × 10–14

4.30 × 10–14

0.44

3

120

Numerical DBS upscaled permeability [m2]

7.46 × 10–14

8.79 × 10–15

1.39 × 10–14

2.08 × 10–14

3.90 × 10–14

6.83 × 10–15

9.89 × 10–14

8.39 × 10–15

3.74 × 10–14

5.89 × 10–13

0.10

240

Machine learning upscaled permeability [m2]

6.98 × 10–14

1.02 × 10–14

1.76 × 10–14

1.76 × 10–14

2.43 × 10–14

7.50 × 10–15

3.99 × 10–14

9.65 × 10–15

2.80 × 10–14

2.64 × 10–13

0.16

3

Kozeny–Carman upscaled permeability [m2]

1.49 × 10–14

3.43 × 10–14

1.83 × 10–14

3.20 × 10–14

2.37 × 10–14

1.03 × 10–14

3.84 × 10–14

1.61 × 10–14

1.12 × 10–14

1.24 × 10–14

0.58

3

  1. *All model run times are for a 24 CPU workstation and summed across all volumes.
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