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