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 modelsnation-wide (~41,000 km2)upper 500 mArcGIS raster layersresolution 100 x 100 m(hydro) geological units with:

top, base, thicknessuncertaintieshydraulic parameters

10 januari 2011M Bouman

TNO Nieuwe huisstijl

2

Voxel models

nation-wide (~41,000 km2)upper 30 mresolution 100 x 100 x 0.5 meach voxel contains:

stratigraphic unit + uncertaintylithology (sand, clay, peat) + uncertainty

15 km

10 januari 2011M Bouman

TNO Nieuwe huisstijl

3

Anthropogenic

Clay

Peat

Fine sand

Medium sand

Coarse sand

Clayey sand

Parameterization of Voxel models

10 januari 2011M Bouman

TNO Nieuwe huisstijl

4

Stratigraphy

Lithology and sand grain-size

Hydraulic conductivity

Groundwaterflow models

+

Measuring hydraulic conductivity

10 januari 2011M Bouman

TNO Nieuwe huisstijl

5

How?Measure from samplesPumping testsSlug testsEmpirical relationships linking lithology and grain-size to conductivity

Measuring hydraulic conductivity

10 januari 2011M Bouman

TNO Nieuwe huisstijl

6

Systematic sampling of stratigraphic units and lithologies in the Netherlands

Application: hydraulic resistance map

10 januari 2011M Bouman

TNO Nieuwe huisstijl

7

days

Calculated directly from measured values

70 km

Scale difference between measurement and model

10 januari 2011M Bouman

TNO Nieuwe huisstijl

8

100 m

0.1 m

Small-scale heterogeneity

10 januari 2011M Bouman

TNO Nieuwe huisstijl

9

0.1 m

Alternating sand and clay layers in a tidal environment

low high

Hydraulic conductivity (m/day)

100 m

1 m

100

m

10 januari 2011M Bouman

TNO Nieuwe huisstijl

10

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

10 januari 2011M Bouman

TNO Nieuwe huisstijl

11

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

10 januari 2011M Bouman

TNO Nieuwe huisstijl

12

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

10 januari 2011M Bouman

TNO Nieuwe huisstijl

13

5 * 50 different distributionsof 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

10 januari 2011M Bouman

TNO Nieuwe huisstijl

14

Clay

Sand

N=50

Effective vertical hydraulic conductivity of a heterogeneous sand-clay voxel

40%

60%

Application: hydraulic resistance map

10 januari 2011M Bouman

TNO Nieuwe huisstijl

15

70 km

days

Calculated from upscaled hydraulic resistance

Application: hydraulic resistance map

10 januari 2011M Bouman

TNO Nieuwe huisstijl

16

days

Calculated from measured hydraulic resistance, without upscaling

70 km

Conclusions

Systematically measure hydraulic conductivity from samplesNew procedure to assign effective hydraulic conductivity values to each voxel in our modelsProcedure accounts for:

difference in scale between laboratory measurements and voxelssmall-scale heterogeneity within voxels

10 januari 2011M Bouman

TNO Nieuwe huisstijl

17

Thank you for your attention

10 januari 2011M Bouman

TNO Nieuwe huisstijl

18

Stratigraphy

Lithology and sand grain-size

Hydraulic conductivity

Groundwaterflow models

+

10 januari 2011M Bouman

TNO Nieuwe huisstijl

20

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