Hydraulic parameterization of 3D subsurface models: from measurement-scale to model-scale

Jan L. Gunnink, Jan Stafleu, Denise Maljers and Jan Hummelman

TNO – Geological Survey of the Netherlands

Layer-based models

nation-wide (~41,000 km2)

upper 500 m

ArcGIS raster layers

resolution 100 x 100 m

(hydro) geological units with:

top, base, thickness

uncertainties

hydraulic parameters

10 januari 2011M Bouman

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Voxel models

nation-wide (~41,000 km2)

upper 30 m

resolution 100 x 100 x 0.5 m

each voxel contains:

stratigraphic unit + uncertainty

lithology (sand, clay, peat) + uncertainty

15 km

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Anthropogenic

Clay

Peat

Fine sand

Medium sand

Coarse sand

Clayey sand

Parameterization of Voxel models

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Stratigraphy

Lithology and sand grain-size

Hydraulic conductivity

Groundwaterflow models

+

Measuring hydraulic conductivity

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How?

Measure from samples

Pumping tests

Slug tests

Empirical relationships linking

lithology and grain-size to

conductivity

Measuring hydraulic conductivity

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Systematic sampling of

stratigraphic units and

lithologies in the Netherlands

Application: hydraulic resistance map

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days

Calculated directly from

measured values

70 km

Scale difference between measurement and model

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100 m

0.1 m

Small-scale heterogeneity

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0.1 m

Alternating sand and clay

layers in a tidal environment

low high

Hydraulic conductivity (m/day)

100 m

1 m

100

m

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Sand

Clay 50 realizations of

sand-clay

distribution

Block composed

of small voxels of

0.5 x 0.5 x 0.05 m

1 m

100 m100 m

Step 1: Model the spatial distribution of sand and clay within a single voxel

Sand-clay

proportion

80%

20%

5 different

sand-clay

proportions

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Sand

Clay 50 realizations of

sand-clay

distribution

Block composed

of small voxels of

0.5 x 0.5 x 0.05 m

100 m

1 m

100 m

40%

60%

Step 1: Model the spatial distribution of sand and clay within a single voxel

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Block composed

of small voxels of

0.5 x 0.5 x 0.05 m

5 * 50 realizations

of vertical

hydraulic

conductivity

5 * 50

different

sand-clay

distributions

Step 2: Model the spatial distribution of vertical hydraulic conductivity

100 m

1 m

100 m

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5 * 50

different

distributions

of vertical

hydraulic

conductivity

Block composed

of small voxels of

0.5 x 0.5 x 0.05 m

Effective vertical

hydraulic

conductivity of

the entire block

(m/day)

Step 3: Apply Modflow-model

Vertical flow

Results

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Clay

Sand

N=50

Effective vertical hydraulic conductivity

of a heterogeneous sand-clay voxel

40%

60%

Application: hydraulic resistance map

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70 km

days

Calculated from upscaled

hydraulic resistance

Application: hydraulic resistance map

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days

Calculated from measured

hydraulic resistance,

without upscaling

70 km

Conclusions

Systematically measure hydraulic conductivity from samples

New procedure to assign effective hydraulic conductivity values to

each voxel in our models

Procedure accounts for:

difference in scale between laboratory measurements and voxels

small-scale heterogeneity within voxels

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Thank you for your attention

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Stratigraphy

Lithology and sand grain-size

Hydraulic conductivity

Groundwaterflow models

+

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Keff = Kg * (1 + variance(ln(k)/6)) for 3D effective conductivity

This applies for the sandy facies, with almost no heterogeneity

Kg=exp(E[ln(K)])

Gutjahr, 1978; Desbartes, 1992