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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
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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
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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
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Parameterization of Voxel models
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Stratigraphy
Lithology and sand grain-size
Hydraulic conductivity
Groundwaterflow models
+
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Measuring hydraulic conductivity
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How?
Measure from samples
Pumping tests
Slug tests
Empirical relationships linking
lithology and grain-size to
conductivity
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Measuring hydraulic conductivity
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Systematic sampling of
stratigraphic units and
lithologies in the Netherlands
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Application: hydraulic resistance map
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days
Calculated directly from
measured values
70 km
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Scale difference between measurement and model
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100 m
0.1 m
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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%
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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
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Results
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Clay
Sand
N=50
Effective vertical hydraulic conductivity
of a heterogeneous sand-clay voxel
40%
60%
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Application: hydraulic resistance map
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70 km
days
Calculated from upscaled
hydraulic resistance
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Application: hydraulic resistance map
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days
Calculated from measured
hydraulic resistance,
without upscaling
70 km
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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