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 km 2 ) upper 500 m ArcGIS raster layers resolution 100 x 100 m (hydro) geological units with: top, base, thickness uncertainties hydraulic parameters 10 januari 2011 M Bouman TNO Nieuwe huisstijl 1

Voxel models nation-wide (~41,000 km 2 ) upper 30 m resolution 100 x 100 x 0.5 m each voxel contains: stratigraphic unit + uncertainty lithology (sand, clay, peat) + uncertainty 15 km 10 januari 2011 M Bouman TNO Nieuwe huisstijl 2 Anthropogenic Clay Peat Fine sand Medium sand Coarse sand Clayey sand

Parameterization of Voxel models 10 januari 2011 M Bouman TNO Nieuwe huisstijl 3 Stratigraphy Lithology and sand grain-size Hydraulic conductivity Groundwater flow models +

Measuring hydraulic conductivity 10 januari 2011 M Bouman TNO Nieuwe huisstijl 4 How? Measure from samples Pumping tests Slug tests Empirical relationships linking lithology and grain-size to conductivity

Measuring hydraulic conductivity 10 januari 2011 M Bouman TNO Nieuwe huisstijl 5 Systematic sampling of stratigraphic units and lithologies in the Netherlands

Application: hydraulic resistance map 10 januari 2011 M Bouman TNO Nieuwe huisstijl 6 days Calculated directly from measured values 70 km

Scale difference between measurement and model 10 januari 2011 M Bouman TNO Nieuwe huisstijl m 0.1 m

Small-scale heterogeneity 10 januari 2011 M Bouman TNO Nieuwe huisstijl m Alternating sand and clay layers in a tidal environment lowhigh Hydraulic conductivity (m/day) 100 m 1 m 100 m

10 januari 2011 M Bouman TNO Nieuwe huisstijl 9 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 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 2011 M 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 100 m 1 m 100 m 40% 60% Step 1: Model the spatial distribution of sand and clay within a single voxel

10 januari 2011 M Bouman TNO Nieuwe huisstijl 11 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 2011 M Bouman TNO Nieuwe huisstijl 12 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 10 januari 2011 M Bouman TNO Nieuwe huisstijl 13 Clay Sand N=50 70% 30% Effective vertical hydraulic conductivity of a heterogeneous sand-clay voxel 40% 60%

Application: hydraulic resistance map 10 januari 2011 M Bouman TNO Nieuwe huisstijl km days Calculated from upscaled hydraulic resistance

Application: hydraulic resistance map 10 januari 2011 M Bouman TNO Nieuwe huisstijl 15 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 10 januari 2011 M Bouman TNO Nieuwe huisstijl 16

Thank you for your attention 10 januari 2011 M Bouman TNO Nieuwe huisstijl 17 Stratigraphy Lithology and sand grain-size Hydraulic conductivity Groundwater flow models +

10 januari 2011 M Bouman TNO Nieuwe huisstijl 18 Grafiekobject (cijfers bewerken) Resultaat kopieren en plakken als plaatje

10 januari 2011 M Bouman TNO Nieuwe huisstijl 19 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