Transition probability geostatistics in a Quaternary aquifer complex Lars Troldborg ltr@geus.dk Geological Survey of Denmark and Greenland Ministry of Climate and Energy Department of hydrology, Geological Survey of Denmark and Greenland (GEUS)
Outline Introduction to Eggeslevmagle field site Construction of a 3D Markov chain model Stationarity Data quality Horizontal spatial correlations Vertical spatial correlations Hydrogeological models based on stochastic realizations Conditioned and calibrated models Model discrimination Conclusion
Eggeslevmagle
Measurements related Scale related ¹ Non-stationarity Aggregated Observation Elevation Heterogeneity Interpolation Seasonal ² Other³ Group 1 0.1 0.1 1.25 1.25 1.0 0.1 2.0 Group 2 0.1 0.1 1.25 1.25 1.0 3.5 4.0
Cross-section Eggeslevmagle
Geostatistics - considerations Stationarity Geomorphic delineation assuming surface features reflected in the subsurface facies architecture facies proportions
Geostatistics - considerations Stationarity Geomorphic delineation assuming surface features reflected in the subsurface facies architecture facies proportions Soil name Volumetric fraction Hydrofacies Volumetric fraction All area Focus Area All area Focus Area Meltwater sand 15.6% 12.0% Meltwater gravel 3.7% 2.4% Freshwater sand 0.1% 0.1% Sand/gravel 25.5% 17.7% Sand 3.6% 2.4% Gravel 2.6% 0.9% Meltwater clay 3.1% 3.6% Clay 3.5% 4.0% Freshwater clay 0.4% 0.4% Sandy till 1.6% 1.6% Clayey till 53.2% 63.0% Glacial Till 71.0% 78.3% Clay 16.2% 13.7%
Geostatistics - considerations Data Quality Frequency of core samples well construction date samples sent to geological survey lab Conditioning high and low quality data focus area data
Geostatistics - spatial correlation Horizontal spatial correlation Lateral spacing to coarse to estimate directly from logs estimate from soilmaps cross-sectional analysis no apparent directional differences Direction Lithology Measured Mean Data type Horizontal ds,dg,s,g 1000-8000 2000 x-sections Horizontal dl,fl 130-1300 420 Soilmap
Geostatistics - spatial correlation Horizontal spatial correlation Vertical spatial correlation abundant well log data estimated directly from slope approximation Direction Hydrofacies Vertical Horizontal Mean length [m] Focus area All area Sand 5.8 7.8 Clay 4.9 4.1 Till 21.4 18.3 Sand 1000 1000 Clay 420 250 Till 3280 2100
3D (2D) Markov chain - results
Geostatistics - results Conditioned realizations Conditioned to well log data Weak correlated to data outside the focus area Consistency with initial conceptualization
Flow simulations Three of the calibrated models yield a lower optimized objective function than the homogeneous case 1000 950 Least Square Objective Function 900 850 800 LSQ-obj-func from model with uniform aquifer 750 700 Vaar1-10 Vaar1-8 Vaar1-5 Vaar1-4 Vaar1-3 Vaar1-6 Vaar1-7 Vaar1-2 Vaar1-1 Vaar1-9 Realization no. (sorted by ObjFunc)
Flow simulations Calibrated parameter values the sand/gravel facies have a higher hydraulic conductivity than the two other facies clay is expected to have a lower hydraulic conductivity than glacial till 1.0e-01 Estimated hydraulic conductivity [m/s] 1.0e-02 1.0e-03 1.0e-04 1.0e-05 1.0e-06 1.0e-07 1.0e-08 1.0e-09 Sand/gravel Meltwater clay Glacial till 1.0e-10 Vaar1-10 Vaar1-8 Vaar1-5 Vaar1-4 Vaar1-3 Vaar1-6 Vaar1-7 Vaar1-2 Vaar1-1 Vaar1-9
Transport simulations Testing calibrated flow models based on stochastic geological realizations against transport times Stochastic model (vaar1-6) Deterministic model (A)
Transport simulations Comparison of simulated and observed Tritium and CFC- 12 concentrations not impressive model performance variations between models in the same range as deviation between simulations and observations performance of rejected models in the same order as the rest no apparent residual trend
Conclusion The transition probability approach appears suitable also for a complex multi-aquifer system dominated by glacial till the geostatistical simulations, conditioned to well log data, reproduces the apparent layering of the aquifer system the model expresses the complexity of the system and conforms to the well information from geomorphological information, rather than traditional structural sequence stratigraphic analysis, we have identified groups of data with different facies proportions and mean lengths
Conclusion Geostatistics and Tprogs enable ability to characterize subsurface heterogeneity at areas of sparse hard data multiple realizations of geological heterogeneity Lots of assumptions and subjective elements that need to be addressed Flow and transport simulations Difference in calibrated parameter sets Not impressive performance on head and discharge compared with simple deterministic model obvious effect on transport spares and noisy observations
General considerations Model discrimination Qualitative evaluation agreement between certain conceptualization aspects and final models unrealistic parameters or parameter combinations Quantitative evaluation Comparison with initial statistics Calibrated and un-calibrated model performance Ranking between accepted conceptualizations Calibrated model performance; AIK, BIC Model performance outside calibration base Subjectivity Integral part of conceptualization, even when geostatistical methods are applied Freedom in translation of geological data to model-scale Affects the objectivity of model discrimination and ranking