Boom Clay: Integrating Data and Upscaling Using Geostatistical Techniques

Belgian agency for radioactive waste and enriched fissile materials

BOOM CLAY: INTEGRATING DATA AND UPSCALING USING GEOSTATISTICAL TECHNIQUES. TRANSFERABILITY OF REGIONALIZED VARIABLES

N. Jeannée (Geovariances) With a contribution of A. Berckmans

NIROND-TR 2012-01 January 2012

ii NIROND–TR 2012-01, January 2012

ONDRAF/NIRAS NIROND-TR report 2012-01 CATEGORY B&C

Boom Clay: Integrating data and upscaling using geostatistical techniques. Transferability of regionalized variables

N. Jeannée (Geovariances) With a contribution of A. Berckmans

January 2012

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The data, results, conclusions and recommendations contained in this report are the property of ONDRAF/NIRAS. The present report may be quoted provided acknowledgement of the source. It is made available on the basis that it will not be used for commercial purposes. All commercial uses, including copying and re-publication, require prior written authorisation of ONDRAF/NIRAS.

This report is a joint report of GEOVARANCES and ONDRAF/NIRAS ADDRESS of GEOVARANCES: 49bis avenue Franklin Roosevelt, BP 91 77212 AVON Cedex, FRANCE Contact person at GEOVARIANCES: [email protected] Contact person at ONDRAF/NIRAS: [email protected]

ONDRAF/NIRAS Kunstlaan 14 BE-1210 BRUSSELS www.nirond.be

Registration of copyright

iv NIROND–TR 2012-01, January 2012

Document Datasheet Title Boom Clay: Integrating data and upscaling using geostatistical techniques. Transferability of regionalized variables Subtitle Project Safety and Feasability Case -I Author(s) of the document Reviewer(s) of the document

Nicolas Jeannée (Geovariances) Arne Berckmans (ONDRAF/NIRAS)

Laurent Wouters (ONDRAF/NIRAS)

Jean-Paul Chilès (MinesParisTech)

Jacques Deraisme (Geovariances)

Series CATEGORY B&C Publication date 2012-02 Document type NIROND-TR Review status Version 1 Status Open Revision number 1 ONDRAF/NIRAS NIROND-TR 2012-01 Subcontractor NOCA-2006-2427 number of report reference number 251-A41 ISBN NA Total number of 119 pages Approver(s) of the document

Maarten Van Geet (ONDRAF/NIRAS)

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Integration Module

The Boom Clay Formation is situated in the North-East of Belgium (Province of Antwerp and Limburg) gently dipping at 2 degrees from the outcrop up to a depth of 400m at the Dutch border. It is considered by the Belgian Agency of Radioactive Waste and Fissile Materials (NIRAS/ONDRAF) as a reference host formation for the construction of a disposal system of high and medium-level and/or long-lived waste (B&C waste according to the Belgian Classification). This waste is characterized by a high initial radionuclide concentration and by decay heat emission.

In order to evaluate this reference formation a Safety and Feasability Case study is under development. This study verifies the validity of a set of safety statements that, if demonstrated, assure the safety of man and the environment on the long-term. One of these statements requires that the disposal system provides passive long-term safety if implemented according to design specifications. This can be translated into the requirement that the disposal system delays and attenuates radionuclides and other contaminants to the environment as long as required. The latter implies that one should prove that diffusive transport is by far and mainly the only vector by which radionuclides and other contaminants migrate in the host formation. Diffusive transport implies furthermore that the formation has a fine and homogeneous pore structure which results in a low hydraulic conductivity and a hydraulic gradient that is very low.

This diffusive transport condition was demonstrated, in a large section of the Boom Clay package at the data gathering locations, by a large set of data collected over the years through destructive and non-destructive methods (data from boreholes, underground and surface lab- tests as well as geophysical logs).

Still some uncertainty exists on whether the diffusive transport conditions are valid in the entire region where the Boom Clay occurs. This leads to the question on whether the values of variables of interest related to the characteristics of the Boom Clay Formation itself measured in detail in the Mol area and at other borehole locations are extendable (transferable) to the wider zone of the Boom Clay basin.

The transferability of the knowledge obtained at the borehole data throughout the entire basin or a large zone is an exercise that can be conducted through geostatistical methods.

The overall objectives of this geostatistical study are fourfold:

. Firstly, give an indication of the transferability of data (with error_uncertainty maps) from the Mol area and other (borehole) locations to the whole extension of the Boom Clay zone

. Secondly to apply geostatistical techniques to achieve upscaling of designated variables (additive such as granulometry or non-additive such as permeability)

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. Conduct simulations (1 and 3D) and do a faciesmodelling exercise on the entire Basin.

. Advise NIRAS on the optimization of future drilling and sampling campaigns

The objectives were realised by applying the following methodology:

. Data collection & extensive data analysis including a recalibration of all data to a relative depth level as well as comparing data of different campaigns

. Spatial analysis & change of support modelling for additive and non-additive variables - upscaling.

. Estimation of designated regionalised variables (K heterogeneity, diffusion parameters) using the appropriate geostatistical techniques.

. Conditional simulations using the Turning Bands algorithm with Gaussian anamorphosis on 1D level

The 3D conditional simulations and faciesmodelling could not be performed due to a lack of data (only 5 boreholes available for the whole basin).

The study resulted in the following conclusions:

. The ability of geostatistics to provide a suitable framework for analyzing the transferability of these regionalized variables.

. The database presents an important heterogeneity level and covers only scarcely the large area of interest. Classical statistics are obtained for hydraulic conductivity and diffusion parameters. Correlation and variogram analysis helped in better understanding the relationship between variables and the vertical variability of target parameters.

. The use of geostatistical techniques highlighted the areas that show the largest errors on the estimation and thus are target zones for further sampling campaigns.

. Meaningful vertical estimation of target parameters have been obtained on sampled boreholes by applying classical geostatistical algorithms (kriging/cokriging), together with an estimate of the associated uncertainty. The quality of the estimates is largely improved by the use of auxiliary variables: geophysical logs (Gamma Ray and Resistivity) and grain size data. However, very different spatial variability is present if we address either the entire Boom Clay or just focus on central units (Putte and Terhagen).

. 3D modeling has been performed to capture regional vertical and lateral trends over the area of interest. Due to the global dipping and thickness increase of the Boom Clay towards the North-East, this 3D modeling required a preliminary horizontalization, in order to laterally correlate consistent data. The Double Band has

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been chosen as a reference as it can be easily identified, even on boreholes that have not been cored. An uncertainty envelope has been derived for K modeling, providing a confidence interval for possible Kv/Kh values throughout the Boom Clay. This 3D modeling has not been performed for migration parameters due to the insufficient number of borehole samples.

The study resulted in the following recommendations:

. In order to decrease the uncertainty on Kv/Kh, there is a need for an additional cored/sampled borehole in the under-sampled central part of the Boom Clay, around Sint-Lenaarts (not cored); the location of this additional borehole can be supported by using the kriging standard deviation results, which show higher uncertainty values in this area. Also, a cored borehole more towards Mol would allow validating a regional K trend, with decreasing K values when moving towards Mol and increasing variability in Putte and Terhagen when moving towards Weelde; this borehole could be ideally placed at the gravity center of a triangle joining Weelde, Zoersel and Mol. This recommendation is consistent with Yu et al. (2011), where it is stated that “the impacts of compaction (burial depth) and lithology on the lateral variation of hydraulic conductivity need further investigations at the region scale”.

. The importance of good quality geophysical logs (Gamma Ray and Resistivity) has been reminded: quantitative consistency and repeatability between logging campaigns, similarity of tools.

. Grain size gives a good indication on K at the location of the core only and does not allow a sound prediction of K values at neighboring locations. There is thus a limited added value of using grain size data in terms of K spatial prediction (extrapolation) throughout the Boom Clay because of the small-scale variability of both K and grain size due to the silty/clayey beds. But because the statistical correlation between specific grain size with K values is so good, precise Kv/Kv estimates can be done using the grain size measurements on other locations where Kv/Kh was not measured.

. Finally, multiplying the analysis of K samples vertically throughout the Boom Clay is of limited interest to obtain a 1D model for K. Again, due to the small-scale variability of this parameter, having good quality geophysical logs is preferable.

Exploratory data analysis results (correlations, spatial continuity) together with the 3D models for hydraulic conductivity and related uncertainty produced during the project allow providing precise recommendations: sampling locations, number of cores, number of K and grain size measurements. However, these recommendations will depend on the short/long term objectives defined by ONDRAF/NIRAS: validate regional K trends, refine the understanding of K small-scale variability, etc.

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The main conclusions and recommendations are consistent with recent work done at SCK•CEN (Yu at al., 2011) but extend them by integrating the key notion of spatial continuity.

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TABLE OF CONTENTS

1 Introduction 1 1.1 Context 1 1.2 Requirement within the framework of the Safety & Feasibility Case 1 1 1.3 Objectives 2

2 Data collection 4 2.1 Boom Clay overview 4 2.2 Previous work 5 2.2.1 General R&D programme 5 2.2.2 Probabilistic approach 6 2.3 Target parameters and other laboratory measurements 6 2.3.1 Hydraulic conductivity 6 2.3.2 Migration parameters 10 2.3.3 Grain size parameters 11 2.4 Boom geometry and geo-reference system 12 2.5 Geophysical logs 14 2.5.1 ONDRAF/NIRAS and Deep Logs 15 2.5.2 Geological Survey of Belgium (GSB) logs 22

3 Modeling of hydraulic conductivity 25 3.1 Methodology 25 3.2 Statistical Analysis 25 3.2.1 Data analysis 25 3.2.2 Correlation with grain size data 32 3.2.3 Correlation with geophysical logs 35 3.2.4 Conclusion of the statistical analysis 36

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3.3 1D vertical modeling 37 3.3.1 Regional consistency between 1D K 38 spatial structures 3.3.2 Variogram modeling 40 3.3.3 1D Kriging results 44 3.3.4 Cross-validation 47 3.3.5 Uncertainty envelope for K prediction 49 Conclusion 52 3.4 3D modeling 53 3.4.1 Methodology 53 3.4.2 Results 55 3.4.3 Uncertainty envelope for Kv-Kh 59 3.4.4 Results in original geo-reference system 62

4 Modeling of migration parameters 67 4.1 Methodology 67 4.2 Statistical analysis 67 4.3 Dp Modeling 69 4.4 R Modeling 72

5 Sampling recommendations fur future campaigns 74 5.1 Methodology 74 5.2 Geophysical logging 74 5.2.1 For 1D vertical modeling 74 5.2.2 For 3D basin modeling 75 5.3 Target parameters 75 5.3.1 Issues and general sampling recommendations 75 5.3.2 Validation for 1D modeling 77

6 General conclusions 83 7 Bibliography 84

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Appendix A: Final Database 86 A.1 Organization of the file system 86 A.2 Boom Geometry 87 A.3 Reminder on resistivity logging (electrical methods) 89

Appendix B: Correlation analysis on Kv and Kh 92 B.1 Correlation with grain size data 92 B.2 Correlaton with geophysical logs 94

Appendix C: Assessment of local uncertainties with Simulations 100 C.1 Methodology 101 C.2 1D Simulations 101

Appendix D: Illustration of factorial kriging on Mol-1 104 D.1 Data description 104 D.2 Variable AH30 106 D.3 Gamma Ray (GR) 109 D.4 Variable MSFL 114 D.5 Conclusions 117

Appendix E: ISATIS project and journal files 118 E.1 ISATIS project organization 118 E.2 Journal File Master.ijnl 118 E.3 Other Journal Files 119

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LIST OF FIGURES

Figure 1 – Outcrop and subcrop of the Boom Clay also showing depth to base relative to sea level and thickness (from NIRAS/ONDRAF, 2001). Location of the 17 boreholes analyzed for the interlayering analysis (from Mertens, 2005)...... 4 Figure 2 – Log(Kv) data measured by migration (abscissa) or permeameter cells (ordinate) on same cores of the Mol-1 borehole, within the Boom Clay formation. Indication of core number and display of the first bisector (black line) ...... 8 Figure 3 - Identification of double band (DB) depth on Mol-1 geophysical logs: standardized gamma ray and resistivity logs (abscissa) versus depth in meters (ordinate): Entire Boom Clay interval (left) and zoom around the DB interval (right). Location of the local resistivity minimum between the two bands constituting the DB. ……… ...... 12 Figure 4 - Kriging of the Double Band (DB) depth over the area of interest. Contour of the northern Belgian border and measured DB values on boreholes are indicated...... 13 Figure 5 - Kriging of the Boom Clay top, excluding the eroded part at the West. Contour of the northern Belgian border and measured top values on boreholes are indicated...... 14 Figure 6 - Examples of GR curves on NIRAS boreholes (gAPI)...... 16 Figure 7 - GR curves obtained on Mol and Dessel boreholes (gAPI). Depth is in mBDT...... 17 Figure 8 - Average GR values on Putte member for several NIRAS boreholes: basemap (left) and histogram (right)...... 18 Figure 9 - GR curve from Zoersel borehole. Raw GR values (left), smoothed GR values at 10cm (middle) and 1m (right)...... 18 Figure 10 - Smoothed SN curves on NIRAS boreholes (m). Left: Essen (green), Weelde and Zoersel (light and dark blue). Right: zoom on Weelde and Zoersel...... 20 Figure 11 - LLD and LLS curves on NIRAS boreholes: Dessel in orange, Mol in blue (m)...... 21 Figure 12 - MSFL curves on NIRAS boreholes: Dessel in orange, Mol in blue (m)...... 22 Figure 13 - Geological Survey of Belgium boreholes - Gamma-Ray tools. .... 22 Figure 14 - Averaged GR values on Putte member for several GSB boreholes: basemap (left) and histogram (right)...... 23 Figure 15 - Resistivity tools used in well 15-E-298(IIIa)...... 24 Figure 16 - Log(Kv) (left) and Log(Kh) (right) profiles on the sampled boreholes, in the DB-Mol geo-reference system...... 26 Figure 17 - Scatter diagram between Log(Kv) and Log(Kh) measurements for the whole Boom Clay. Indication of correlation coefficient (rho), first bisector (x=y, thin line), linear regression line (bold line). Squares represent data ignored for the correlation computation: cores 6 from Zoersel and 133 from Essen...... 31

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Figure 18 - Scatter diagram between vertical hydraulic conductivity (in logarithm, abscissa) and grain size data d40 (m, in ordinate) for the 6 available boreholes...... 34 Figure 19 – Scatter diagrams between Log(Kv) and the regression with GR and Res data, for Mol, Zoersel and Weelde boreholes. Linear correlation coefficient indicated...... 38 Figure 20 - Vertical (left) or horizontal (right) hydraulic conductivity (in logarithm) experimental variograms for Weelde, Zoersel and Mol (Log(Kh) not displayed). Dotted lines correspond to statistical variances...... 38 Figure 21 - Vertical (left) or horizontal (right) hydraulic conductivity (in logarithm) experimental variograms for Weelde (red), and Zoersel (green), for Putte and Terhagen units (top) and Transition Zone and Belsele-Waas (bottom). Dotted lines correspond to statistical variances. 39 Figure 22 - Mol-1: Mol-1: Cross-variogram modeling of Log(Kv), d40 and reg (GR, Res)...... 41 Figure 23 – Zoersel: Cross-variogram modeling of Log(Kv), Log(Kh), d40 and reg(GR, Res) ...... 42 Figure 24 - Weelde: Cross-variogram model of log(Kh), Log (Kv), d40 and reg(GR, Res)...... 43 Figure 25 – Mol-1: Log(Kv) modeling results (left) and associated standard deviations (right)...... 45 Figure 26 – Mol-1: Log(Kh) modeling results (left) and associated standard deviations (right)...... 45 Figure 27 – Zoersel: Log(Kv) modeling results (left) and associated standard deviations (right)...... 46 Figure 28 – Zoersel: Log(Kh) modeling results (left) and associated standard deviations (right)...... 47 Figure 29 – Mol-1: Cross-validation results for Kv (left) and Kh (right) modeling using kriging (+) and cokriging with d40, GR and Res (x): estimates (abscissa) versus true values (ordinate). Indication of the 1st bisector (x=y)...... 47 Figure 30 – Zoersel: Cross-validation results for Kv (left) and Kh (right) modeling using kriging (+) and cokriging with d40, GR and Res (x): estimates (abscissa) versus true values (ordinate). Indication of the 1st bisecor (x=y)...... 48 Figure 31 – Weelde: Cross-validation results for Kv (left) and Kh (right) modeling using kriging (+) and cokriging with d40, GR and Res (x): estimates (abscissa) versus true values (ordinate). Indication of the 1st bisector (x=y)...... 48 Figure 32 – Mol-1: Log(Kv) cokriging results: local variability coefficient A(x) (left) and related cokriging standard deviation curves (right)...... 50 Figure 33 – Mol-1: Log(Kv) cokriging result and confidence interval at 95%...... 51 Figure 34 – Scatter-diagrams of Log(Kv) (top, ordinate) and Log(Kh) (bottom, ordinate) versus raw GR (left, abscissa) and GR corrected to MOL (right, abscissa). Indication of correlation coefficient (rho)...... 54

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Figure 35 - Hydraulic conductivity (in logarithm) vertical variogram model for 3D modeling...... 55 Figure 36 – Log(Kv) 3D model in the Double-Band geo-reference system: cross-section between Doel-2b, Zoersel and Mol. Location of boreholes with actual Kv data (o)...... 56 Figure 37 – Log(Kv) and Log(Kh) 3D model: horizontal section at DB level; display of integrated boreholes and Belgian border...... 57 Figure 38 – Log(Kv) and Log(Kh) 3D models: standard deviations for horizontal section at DB level; display of integrated boreholes and Belgian border...... 58 Figure 39 – Log(Kv) and Log(Kh) 3D model: horizontal section 20m above DB level; display of integrated boreholes and Belgian border...... 59 Figure 40 – Local variability coefficient curves resulting from the 3D modeling, for Log(Kv) (left) and Log(Kh) (right)...... 60 Figure 41 – 3D standard deviation models obtained for Log(Kv): before (top) and after (bottom) applying the local variability coefficient. Location of main boreholes...... 61 Figure 42 – 3D Log(Kv) model in original geo-reference system...... 62 Figure 43 – 3D Log(Kv) standard deviation model in original geo-reference system...... 63 Figure 44 – 3D Log(Kh) model in original geo-reference system...... 64 Figure 45 – 3D Log(Kh) standard deviation model in original geo-reference system...... 65 Figure 46 – 3D Log(Kv) model in original geo-reference system – complete view...... 66 Figure 47 – Scatter diagrams between log (Dp HTO) (abscissa) and log (Kv) (ordinate) for the three sampled boreholes...... 68 Figure 48 – Scatter diagrams between log (Dp HTO) (abscissa) and R HTO (ordinate) for the three sampled boreholes (same colors than Figure 47)...... 69 Figure 49 – Mol-1: Log(Dp) bivariate variogram model with Log(Kv)...... 70 Figure 50 – Mol-1: Log(Dp) modeling results (left) and associated standard deviations (right)...... 71 Figure 51 – Mol-1: Cross-validation results for Dp modeling using kriging (+) and collocated cokriging with interpolated Log(Kv) (x): estimates (abscissa) versus true values (ordinate). Indication of the 1st bisector (x=y)...... 71 Figure 52 – Mol-1: R variogram model...... 73 Figure 53 – Mol-1: R data and kriging result...... 73 Figure 54 – Mol-1: Cross-validation results for R modeling using kriging: estimates (abscissa) versus true values (ordinate). Indication of the 1st bisector (x=y)...... 73 Figure 55 – Recommended locations for additional cored boreholes with K sampling. Contour of the northern Belgian border and southern limit of the Boom Clay...... 76 Figure 56 – Zoersel: Log(Kv) estimates using varying auxiliary variables (ordinate), by reference to the actual Log(Kv) data at 17 validation locations. First bisector and linear correlation coefficient indicated...... 79

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Figure 57 – Zoersel: Log(Kv) 1D models using varying auxiliary variables. .. 80 Figure 58 – Zoersel: Log(Kv) 1D models using varying auxiliary variables (ordinate), by reference to the cokriging model using all available data (abscissa). First bisector and linear correlation coefficient indicated...... Figure 59 - Overview of database organization …………………………… 86 Figure 60 - Principles of measuring resistivity in Ohm-meter; resistivity equal to 10 Ohm-meter in the example...... 89 Figure 61 - System used to make induction logs...... 91 Figure 62 - Scatter diagram between vertical hydraulic conductivity (in logarithm, abscissa) and grain size data d40 (m, in ordinate) for each litho-stratigraphic unit of Mol-1 borehole...... 92 Figure 63 - Scatter diagrams between vertical hydraulic conductivities (ordinate, in logarithm) and grain size data d40 (m, in abscissa) for Mol (left) and Essen (right) boreholes. Samples of interest represented in blue, using triangles for the Belsele-Waas member...... 93 Figure 64 - Scatter diagrams between vertical (left) and horizontal (right) hydraulic conductivities (in logarithm) and grain size data d40 (m, in abscissa) for Weelde (top) and Zoersel (bottom) boreholes. Samples of interest represented in blue, respectively using circles if they are located in the Transition Zone and triangles for the Belsele-Waas member...... 93 Figure 65 – Mol-1: Scatter diagrams between vertical (left) or horizontal (right) hydraulic conductivity (in logarithm) and gamma ray measures obtained from tools ait4 and elan. Linear correlation coefficient indicated (rho)...... 94 Figure 66 - Doel 2b - Scatter diagrams between vertical (hydraulic conductivity (in logarithm) and geophysical logs: HSGR (left) and FF (right). Linear regression line and correlation coefficient indicated (rho)...... 95 Figure 67 - Weelde - Scatter diagram between hydraulic conductivities (left: :Log(Kv), right: Log(Kh)) and GR, raw (top) or smoothed (bottom). Linear regression line and correlation coefficient indicated (rho)...... 96 Figure 68 - Weelde - Scatter diagram between hydraulic conductivities (left: :Log(Kv), right: Log(Kh)) and resistivity LN. Linear regression line and correlation coefficient indicated (rho)...... 97 Figure 69 - Zoersel - Scatter diagram between hydraulic conductivities (top: :Log(Kv), bottem: Log(Kh)) and GR (left) and resistivity ILD (right). Linear regression line and correlation coefficient indicated (rho)...... 98 Figure 70 - Zoersel - Scatter diagram between hydraulic conductivities (left: :Log(Kv), right: Log(Kh)) and GR smoothed with a radius of 0.5m (top) and 1m (bottom). Linear regression line and correlation coefficient indicated (rho)...... 99 Figure 71 - Essen - Scatter diagram between hydraulic conductivities (top: :Log(Kv), bottom: Log(Kh)) and GR (left) and resistivity LN (right). .. 100 Figure 72 –Co-simulation results for Log(Kv) at Mol (left) and Log(Kh) at Zoersel (right): cokriging, simulation example (grey) and confidence interval at 90%. Data locations (black circles)...... 102

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Figure 73 –Co-simulation results with gaussian anamorphosis for Log(Kv) at Mol (left) and Log(Kh) at Zoersel (right): cokriging, simulation example (grey) and confidence interval at 90%. Data locations (black circles)...... 103 Figure 74 – Organization of ISATIS project...... 118

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List of Tables

Table 1 – Number of hydraulic conductivity data available on each borehole, depending on the analysis type (migration experiment or permeameter cells). Indication of the SCK•CEN report detailing the core sampling and analysis...... 7 Table 2 – Number of migration data available on each borehole 10 Table 3 – Number of grain size data available on each borehole...... 11 Table 4 – List of ONDRAF/NIRAS and Deep boreholes considered...... 15 Table 5 – List of GSB boreholes with relevant resistivity tools...... 24 Table 6 – Basic Kv statistics within the Boom Clay (in logarithm)...... 26 Table 7 – Basic Kv statistics within the Boom Clay (in logarithm), per litho- stratigraphic unit...... 28 Table 8 – Basic Kh statistics within the Boom Clay (in logarithm)...... 29 Table 9 – Basic Kh statistics within the Boom Clay (in logarithm), per litho- stratigraphic unit...... 30 Table 10 – Basic Kh/Kv statistics within the Boom Clay (in logarithm), per litho-stratigraphic unit...... 32 Table 11 – Basic d40 statistics (in µm) within the Boom Clay, per litho- stratigraphic unit...... 33 Table 12 – Linear correlation coefficients () between hydraulic conductivity (in logarithm) and grain size data d40 (m). Number of samples (Nb) available to calculate the correlation coefficient ()...... 35 Table 13 – Linear correlation coefficients for sampled boreholes between hydraulic conductivities (in logarithm) and geophysical tools: gamma ray (GR) and Resistivity (Res). Tool name indicated between brackets. . 36 Table 14 – Cross-validation results for Kv/Kh modeling in Mol, Zoersel and Weelde using kriging and cokriging (with d40, GR and Res): correlation coefficient (rho), average error (bias) and variance of standardized error (Var std err)...... 49 Table 15 – Mol-1: Log(Kv) average value and confidence interval bounds per litho-stratigraphic unit derived from the cokriging model...... 52 Table 16 – Probable values and confidence interval bounds at 95% or more for Log(Kv) and Log(Kv) in each Boom Clay unit...... 61 Table 17 – Average values for migration parameters on sampled boreholes: apparent diffusion coefficient Dp [m2.s-1] and ηR [-]...... 67 Table 18 – Correlation analysis between apparent diffusion coefficient Dp [m2.s-1] and ηR [-] for HTO and auxiliary variables, for Mol-1 (left) and Doel-2b boreholes (right)...... 68 Table 19 – Mol-1: Cross-validation results for Dp modeling using kriging and collocated cokriging with interpolated Log(Kv): correlation coefficient (rho), average error (bias) and variance of standardized error (Var std err)...... 72 Table 20 – Statistical analysis of prediction errors at the 17 Log(Kv) validation samples, using various auxiliary variables: correlation coefficient, min/mean/max errors and quadratic errors...... 78 Table 21 – Statistical analysis of prediction errors on the Log(Kv) vertical model using various auxiliary variables, by comparison with the model

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obtained with all available data: correlation coefficient, min/mean/max errors and quadratic errors...... 81 Table 22 – Location of boreholes and depth (in mBDT) of the main geological top/base horizons and DB...... 87 Table 23 – Linear correlation coefficients for Mol-1 borehole between hydraulic conductivities (in logarithm) and geophysical tools: gamma ray (GR) and Resistivity (Res). Tool name indicated between brackets. . 94 Table 24 – Linear correlation coefficients for Doel-2b borehole between vertical hydraulic conductivity (in logarithm) and geophysical tools: gamma ray (HSGR) and resistivity (FF). Indication of the tool from which the log is derived...... 95 Table 25 – Weelde - Linear correlation coefficients between hydraulic conductivities (in logarithm) and geophysical tools: gamma ray (GR) and Resistivity (LN, SN)...... 95 Table 26 – Zoersel - Linear correlation coefficients between hydraulic conductivities (in logarithm) and geophysical tools: gamma ray (GR) and Resistivity (LN, SN)...... 98 Table 27 – Linear correlation coefficients for Essen borehole between hydraulic conductivities (in logarithm) and geophysical tools: gamma ray (GR) and Resistivity (LN, SN)...... 99

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xxii NIROND–TR 2012-01, January 2012

1 Introduction

1.1 Context

The Boom Clay Formation is situated in the North-East of Belgium (Province of Antwerp and Limburg). It dips gently at 2 degrees from the outcrop up to a depth of 400m at the Dutch border. (see Figure 1) At the town of Mol where the Boom Clay is situated between 190 and 290m below surface an underground laboratory was constructed. This laboratory is used by the Belgian Agency of Radioactive Waste and Fissile Materials (NIRAS/ONDRAF) for research objectives as the Agency consideres the Boom Clay as a potential host formation for the construction of a disposal facility of medium and high level waste (B&C waste). The R&D research program collected over the years and during different campaigns, a large set of data using destructive and non destructive methods in the Boom Clay. These data have been partially analyzed and modeled mainly at the local level of the Mol site and locally at boreholes dispersed in the basin.

1.2 Requirement within the framework of the Safety & Feasibility Case 1

If one wants to consider the Boom Clay formation as a potential host for a disposal facility it is imperative that the general safety objective of disposal as the final step of radioactive waste management protects Man and environment, now and in the future. The safety objective and the strategy for disposal are implemented through different safety functions, i.e. functions that the disposal system should fulfill to achieve its general safety objective of providing long- term safety through concentration and confinement strategy. One of the safety functions considered by ONDRAF/NIRAS is “delay and attenuate of the releases”, itself subdivided into limitation of contaminant releases from the waste forms, limitation of the water flow through the disposal system and retardation of contaminant migration. The geological host formation is the most important barrier to fulfill the two latter sub-functions. A number of engineered and natural barriers, fulfilling different safety functions, are placed between the contaminants and the accessible environment. The set of components and barriers constitute the “disposal system”. This system thus relies on the multiple barrier principle: the “supercontainer” containing the vitrified waste, the repository itself and the host formation in which the disposal could be constructed. Based on SAFIR 2, the latter is the most important as it is the one that has to slow the migration of radionuclides towards the biosphere for a sufficiently long time when the man-made barriers are no longer effective. For the SFC-I to be applicable on a regional scale one needs to ascertain, apart from the transferability of the technical-engineering concept and solution, whether the values of

NIROND- TR 2008-41 E, December 2008 1

variables of interest related to the characteristics of the Boom Clay Formation itself measured in detail in the Mol area are extendable (transferable) to a wider zone. The formation is expected to play a role of natural barrier, to slow the migration of radionuclides towards the biosphere for a sufficiently long time when the man-made barriers are no longer effective. Therefore, the Boom Clay aquitard requires to be precisely characterized in terms of hydrogeological parameters, to confirm its role of geological barrier between its surrounding aquifers.

1.3 Objectives

The overall main objectives addressed in this document are threefold: . Qualitatively and quantitatively analyze a large set of available data from different sampling campaigns and compile a subset for future use;

. Give an indication of the transferability of data (with error / uncertainty maps) from the Mol area and other (borehole) locations to the whole extension of the Boom Clay zone within the framework of a 3D model;

. Apply geostatistical techniques to achieve upscaling of designated variables (additive such as grain size data or non-additive such as permeability).

To realize these objectives several tasks have to be executed: . Extensive data analysis all available data on accuracy and quality (compare data from different campaigns) and develop a reliable subset that can be used in this and future work;

. Statistical analysis of this dataset;

. Use the reliable dataset and develop a consistent geo-reference system (through recalibration if necessary) allowing to laterally correlating thin observations derived from boreholes separated by several tens of kilometers;

. Describe the spatial variability of hydraulic conductivity, grain size, migration parameters, gamma ray, resistivity;

. Provide a reliable 3D model by integrating the correlation between the scarcely sampled target parameters (core measurements) and numerous geophysical logs (gamma ray, resistivity);

. Integrate correlated variables though the use of geostatistical techniques to quantify the uncertainty attached to the hydraulic conductivity estimates;

. Provide a complete set of journal files assuring traceability and reproducibility of results as well as for auditing purposes and use in future analysis;

2 NIROND-TR 2008-41 E, December 2008

. Formulate recommendations on future sampling campaigns of the different type of data as a function of the objectives posed.

Several scientific papers about this work have been presented at international conferences [Jeannee et al., 2008, 2009].

NIROND- TR 2008-41 E, December 2008 3

2 Data collection

This chapter presents data integrated to the study, consistency between datasets and the choice of an appropriate geo-reference system.

2.1 Boom Clay overview

The Boom Clay is a marine Oligocene clay of approximately 100m thick. It is the unit stratotype of the Lower-Oligocene Rupelian stage. The clay was deposited in the North Sea basin. It is known in Germany, The Netherlands and Belgium as a continuous gently dipping (~1-2°) layer. Early diagenesis transformed some of the originally marly horizons into septaria beds (limestone concretions), which borrowed its name to the clay in Germany, known as “Septarienton”. The location of the Boom Clay in Belgium is illustrated on Figure 1. The Boom Clay dips towards the north-north-east and gains thickness in this direction. The reason for the latter is dual: firstly the sedimentation rate was larger more towards the center of the basin situated more northerly and secondly the southern part experienced significant erosion at the end of the Oligocene.

4 NIROND-TR 2008-41 E, December 2008

2.2 Previous work

2.2.1 General R&D programme

The SCK•CEN and the Geological Survey of Belgium took an interest in the Boom Clay beneath the nuclear zone at Mol-Dessel at a very early stage of the R&D programme, i.e. in the mid seventies. The initial results obtained were very encouraging in terms of what was found regarding the lithology of the clay, its containment capability and its accessibility. These reasons prompted SCK•CEN to intensify their research efforts on this formation. Consequently, the Boom Clay has been intensively studied over the last 30 years. The work achieved during the nineties has been synthesized in the SAFIR 2 report [NIRAS/ONDRAF, 2001]. Regarding the assessment of host formations, the R&D programme had in particular the following objectives: . to identify and characterize the structural discontinuities (faults, etc.) and lithological heterogeneities of the Boom Clay and to study their impact on the migration of radionuclides;

. to study the thermo-hydro-mechanical behaviour of the Boom Clay;

. to refine the understanding and modeling of the regional and local hydrogeology around the Mol–Dessel nuclear zone;

. to provide a preliminary characterisation of the Ypresian Clays beneath the Doel nuclear zone.

Given the results of the previous SAFIR programmes and in the absence of any significant technical problem found by the studies to date, ONDRAF/NIRAS currently views: . The Boom Clay as a reference host formation for research purposes and for the assessment (safety, feasibility) of the deep disposal of high-level and/or long-lived radioactive waste in Belgium;

. The Mol-Dessel zone as the reference site for research, development and demonstration studies on the Boom Clay.

For clarity purpose, the report numbers of the SCK•CEN and ONDRAF/NIRAS reports will be used as references in the following, for instance R-3590 for the report “Mol-1 borehole (April-May 1997) – Core manipulations and determination of hydraulic conductivities in the laboratory, by Wemaere I., Marivoet J., Labat S., Beaufays R. and Maes T., October 2002 (R- 3590).

NIROND–TR 2012-01, January 2012 5

2.2.2 Probabilistic approach

The SAFIR 2 Evaluation Commission pointed out the need of a better characterization at a regional scale of the parameters governing the diffusion inside the Boom Clay. This justifies the present work, which aims at: . Evaluating, on the basis of all available information, the transferability of hydrogeological parameters of the Boom Clay (not the aquifers) from the investigated areas (mainly the Mol-Dessel) to the entire Boom Clay;

. Applying geostatistics to model the hydrogeological parameters and quantify the associated uncertainties.

The probabilistic approach is justified by the importance to characterize local heterogeneities when modeling the hydrogeological parameters governing the diffusion inside the Boom Clay: hydraulic conductivity, diffusion coefficient and porosity accessible to diffusion. These heterogeneities should be extrapolated inside the Boom Clay, from the available data to the regional level. Such a geostatistical approach has been recently applied by Huysmans (2006), based mainly on the Mol-1 borehole. This work demonstrated the importance of integrating the local heterogeneity of hydrogeological parameters for transport modeling in low-permeability media. The present work now aims at transferring this modeling approach to a regional scale.

2.3 Target parameters and other laboratory measurements

2.3.1 Hydraulic conductivity

Focusing exclusively on the Boom Clay formation, hydraulic conductivity (K) has been determined on samples coming from 6 boreholes: Mol-1, Weelde, Doel-2b, Zoersel, Essen-1 and Herenthout. These data are described in the next paragraphs, together with the measurements obtained from boreholes drilled around the HADES-URF (Underground Research Facility). In this report, the “-1” extension following most boreholes’ names will sometimes be omitted, without lack of information.

6 NIROND–TR 2012-01, January 2012

2.3.1.1 Geological boreholes

Regarding the migration experiments, it is noted in Mol-1 that the influence of the tracer is not significant, differences between measurements varying from 1 to 7%, which is consistent with the estimated relative measurement error [R-3590]; therefore, results obtained with HTO tracer are retained for further analysis

Table 1 summarizes the number of available hydraulic conductivity data for the Boom Clay. Depending on boreholes, horizontal and vertical hydraulic conductivities have been potentially measured using two different approaches: . permeameter cells (both Kv and Kh),

. migration experiments using both HTO and 131I tracers (Kv only).

K K /K Borehole v v h Reference Report (migration exp) (permeameter cells) Mol-1 41 11 R-3590 Weelde 28 R-4187 Zoersel 34/33 R-3892 Doel-2b 10 R-3503 Essen-1 10 0/10 ER-68 Herenthout 1 ER-59 Total 61 74/83 In order to evaluate the consistency between the hydraulic conductivities measured with permeameter cells or migration experiments, the hydraulic conductivity has been measured using both techniques on seven cores of Mol-1 borehole. These measurements are performed on different plugs, as it is not possible to use the same sample (plug) for both experiments. The average difference in depth between the plugs is 15 cm, which is significant compared to possible variations of hydraulic conductivities between the clayey and silty beds. Note that it is however difficult to guarantee an accurate correlation between the K samples and the sequence of clayey/silty beds visible on geophysical logs [R-3590]. The differences between the logarithms of the two measurement techniques on Kv are much below one, ie. one order of magnitude of K, as illustrated on Figure 2; indeed, the

NIROND–TR 2012-01, January 2012 7 largest difference between the Kv logarithms, observed for core 49 within the Transition Zone, is equal to 0.19. This is consistent with observations from report R-3590 on Mol-1.

Figure 2 – Log(Kv) data measured by migration (abscissa) or permeameter cells (ordinate) on same cores of the Mol-1 borehole, within the Boom Clay formation. Indication of core number and display of the first bisector (black line).

Consequently, the final vertical hydraulic conductivity database is obtained by merging the two types of measurements. This leads to 135 Kv and 83 Kh measurements for the Boom Clay formation. One also has to keep in mind that Kv and Kh measurements are neither performed on the same plug but with a vertical depth difference of about 15 cm. The Herenthout borehole focused on the lower geological horizons deeper of the Boom Clay, one couple of Kv/Kh data has been measured on the Belsele-Waas member; this couple is therefore considered in the study.

2.3.1.2 Hades - URF

Following report R-3162 about hydraulic data within the perturbated area around the HADES laboratory in Mol, it seems that there are limited differences in hydraulic conductivities between the perturbated and the non-perturbated clay at micro scale. It could therefore be useful to consider the K measurements performed on piezometers around the laboratory in order to quantify the short-scale variability of hydraulic conductivity within the Clay, particularly in the horizontal direction. Only the measurements derived from the “single point” method will be potentially integrated. The two Kv and Kh measurements derived from interference tests are therefore ignored, to

8 NIROND–TR 2012-01, January 2012

avoid mixing short-scale variability of the conductivity and potential variability due to the comparison of different measurement methods. We also exclude vertical and oblique piezometers, to avoid mixing different clayey/silty beds. Among the 35 “single point” measurements, this selection leads to retain 27 hydraulic conductivities. Being acquired at different depth values around HADES, not all these values will be of interest, as we aim at finding couples of K values coming from similar depths. In particular: . the value obtained on the F.H. piezometer is excluded, the latter being drilled 20m shallower than the others (around 246m depth instead of 222-223m depth); therefore, this value does not contribute to any pair of points and does not bring any information about K spatial variability.

. the samples from the R32-2 multi-piezometers are excluded, as we have a 1 meter uncertainty between the different piezometers,

. the MEGAS E5-A-17 sample, which has a significantly different conductivity value, measured at 15m from the extrados of HADES while the other samples are located between 2 and 10m. This anomalous conductivity value might result from a measurement issue.

We will actually focus on K values coming from piezometers drilled at approximately 223m depth: . the two samples from 14d and 13e-H, both drilled at 222.9m depth,

. the 9 samples from the CP1 piezometers, drilled at 223.2m depth,

. the 4 samples from the R34-1 piezometers (depth 222.8m),

. the 7 samples from the R32-3 piezometers (depth 222.8m)

Some of these 22 remaining samples are coming from up to 10m around the HADES laboratory. Having in mind the 2% global dip of the Boom Clay, it is not impossible that we still compare samples coming from different clayey/silty beds. This will be analyzed later on.

2.3.1.3 Upscaling

Classically, assuming a log-normal distribution of hydraulic permeability within each hydrostratigraphic unit, the mean value of log K in a given hydrostratigraphic unit is taken as the mean of data log Ki (i=1,…,n) in that unit; equivalently, the average permeability is approximated by the geometric mean of the sample hydraulic conductivities Ki:

n Kgeom  K1  K 2 K n For modeling/simulation purposes and comparison with for instance pumping tests, it is compulsory to consider larger unit, in our case the entire Boom Clay aquitard unit. Since we are in a sedimentary context, equivalent hydraulic conductivities Kveq and Kheq will then be calculated by taking respectively the harmonic mean and the mean of the representative

NIROND–TR 2012-01, January 2012 9 hydraulic conductivities (Kgeom) of each sub-unit weighted by its thickness (see for instance report R-4187):

 K hi geom  ei e K eq  and K eq  i v h e  ei    i  K vi geom  where:

. Kveq and Kheq are the equivalent vertical and horizontal conductivity of the Boom Clay (m/s), . e is the total thickness of the Boom Clay (m),

. ei is the thickness of the hydrostratigraphic unit (m).

2.3.2 Migration parameters

Migration parameters have been derived from migration experiments performed on three boreholes : Mol-1, Doel-2b and Essen (see Table 2). Table 2 – Number of migration data available on each borehole.

Borehole Migration data Mol-1 41 Doel-2b 10 Essen-1 7 Total 58

We focus on the (apparent) diffusion coefficient Dp or Dapp (depending on ONDRAF and SCK reports) and the diffusion accessible porosity η. These parameters are not directly measured, but derived from the following equations: . V = VDarcy/ ηR with V the apparent velocity and R the retardation factor. The migration experiments being conducted with unretarded tracers (tritiated water and iodide), R=1 and as a consequence we can access the diffusion accessible porosity:

η = VDarcy/V (1)

. the transport equation, where the dispersion coefficient D is expressed as a linear function of the apparent velocity V:

D = a V + Dp (2)

. with a the dispersion length and Dp the apparent diffusion coefficient, equal to the diffusion coefficient as we deal with unretarded tracers.

10 NIROND–TR 2012-01, January 2012

Within the Boom Clay, the apparent diffusion coefficient Dp and the diffusion accessible porosity η have been obtained for HTO and iodide on 41 samples from Mol-1 [R-3590] and 10 samples from Doel-2b [R-3503]. The dispersion length a is determined using a linear regression between the estimated D and V and equal to: . Mol-1: a is equal to 4.0 ± 1.0 10-3 m for HTO and 1.5 ± 1.0 10-3 m for iodide.

. Doel-2b: a is equal to 5.0 10-3 m for HTO and 4.0 10-3 m for iodide.

Assuming a constant a for all samples leads to derive the diffusion coefficient Dp using equation (2). Note that, for Essen-1, Dp values have been directly transmitted, without detail about D or a.

2.3.3 Grain size parameters

Grain size data have been obtained from the main boreholes (see Table 3). On the Weelde and Zoersel borehole the largest number of grain size analysis were conducted, followed by Mol-1 and Doel-2b. Only a few samples are available in Essen and Herenthout.

Table 3 – Number of grain size data available on each borehole. Borehole Grain size data Mol-1 74 Weelde 160 Zoersel 152 Doel-2b 60 Essen-1 10 Herenthout 14 Total 470

All samples of the “Transition“, “ Putte” and “Terhagen” units comprise minimum of 40% of particles smaller than 32 m and 70% of the particles smaller than 62,5 m. The “Transition” zone is characterized by the presence of more sandy samples than in Putte and Terhagen unit. The “Belsele-Waas” unit differs from the other units by its lower content of finer particles. Consistently with Huysmans (2006), the project will mainly consider the variable d40 as potential explanatory variable for hydraulic conductivity modeling. This variable is defined as the size such that 40% of the particles are finer than this diameter (in µm). Indeed, it as been proven that d40 is the grain size derived variable which provides the best possible correlation with hydraulic conductivity data.

NIROND–TR 2012-01, January 2012 11

2.4 Boom geometry and geo-reference system

Mertens (2005) homogeneously analyzed resistivity logs obtained from 17 boreholes distributed throughout the North of Belgium (see Figure 1). Note that his analysis is restricted to the main NIRAS/ONDRAF boreholes with good quality logs, in order to make possible a detailed interpretation; as a consequence, Zoersel has been excluded from his analysis because of the poor precision of the initial logging campaign. Mertens performed a systematic identification of interlayers, illustrating the strong lateral continuity of the Boom Clay. The main goal of the work was to compute and compare cumulative thickness differences, in order to identify trends and evolutions in sedimentation rate. As a consequence, this detection gives precise and consistent knowledge for the top/base of the main Boom Clay units and also for the Double Band. This Double Band corresponds to two silty beds located towards the base of the Putte member. Using gamma ray and resistivity logs, it can be defined by two resistivity peaks located just above a high positive Gamma Ray peak (see Figure 3).

Figure 3 - Identification of double band (DB) depth on Mol-1 geophysical logs: standardized gamma ray and resistivity logs (abscissa) versus depth in meters (ordinate): Entire Boom Clay interval (left) and zoom around the DB interval (right). Location of the local resistivity minimum between the two bands constituting the DB.

Analyzing the lateral variability of hydrogeological parameters within the Boom Clay implies to work in a geo-reference system which is consistent with the formation. Due to the global dipping and the thickness increase of the Boom Formation towards the North-East, an « horizontalization » step (unfolding) is compulsory. Therefore, we used the DB-level as a vertical « zero » reference. This is justified by the clear identification of this level in most

12 NIROND–TR 2012-01, January 2012

boreholes (see Appendix A.2). Working with the DB as vertical reference also avoids having to manage topographic uncertainties and errors in topographic references that sometimes occur on logs and available tables. Consequently, the DB depth value has been identified on most boreholes and interpolated using a non-stationary geostatistical approach (universal kriging with a quadratic trend). The result, displayed on Figure 4, is consistent with the known global dipping. Apart from the vertical reference, it is also compulsory to compensate varying thickness of the Boom formation and rescale to an homogeneous thickness reference. Several approaches have been tested to address this issue. Finally, the Boom Clay thickness at Mol-1 is taken as a reference and all other boreholes are rescaled to this thickness, in order to be globally consistent. The resulting geo-reference system will be referred to as “ref DB-Mol” in the following. Back-transformation to the original geographic reference system will only be required for the 3D visualization of produced models.

Figure 4 - Kriging of the Double Band (DB) depth over the area of interest. Contour of the northern Belgian border and measured DB values on boreholes are indicated.

A more sophisticate approach to ensure lateral consistency of the modeling approach would be to correlate sequentially each bed, using the cyclo-stratigraphic approach developed by Lefranc (2007). The underlying idea of this approach is to put into evidence cyclicities with factorial kriging, in order to simplify the identification of similar beds on various boreholes; appendix F details and illustrates this approach on Mol-1 borehole. However, the large number of beds (more than 120) makes the application of this approach very difficult in the Boom Clay case. The approach could be applied on a restricted interval but still poses the problem of identifying the same bed on various boreholes, which highly relies on the availability of a good quality logging. Figure 5 illustrates the model obtained for the top of the Boom Clay, combining the information from boreholes where the Boom Clay intersection is complete and from the ones where the top of the formation has been eroded. The special behavior in the northern central

NIROND–TR 2012-01, January 2012 13 part of the Boom Clay (around Sint Lenaarts, where the depth of Boom Clay’s top is equal to –210m), has to be noted: the Boom Clay is clearly thinner in this area, which is confirmed by geophysical logs and also by the work of Mertens (2005).

Figure 5 - Kriging of the Boom Clay top, excluding the eroded part at the West. Contour of the northern Belgian border and measured top values on boreholes are indicated.

2.5 Geophysical logs

The project is mainly focusing on gamma ray and resistivity logs because of their expected correlation with permeability data. Sonics and density logs will also be considered later on. Geophysical logs are the main source of information for transferring knowledge about the target parameters outside from the few boreholes that have been cored and analyzed. It will therefore be essential to evaluate the consistency between these logs and the target parameters. A preliminary quality control of the gamma ray and resistivity logs allow to select relevant curves and put aside useless logs. The geophysical database consists mainly of ONDRAF/NIRAS and some deep GSB logs on the one hand and, on the other hand, the Geological Survey of Belgium shallow logs. They will be analyzed separately, as the ONDRAF/NIRAS boreholes globally lead to numerous runs. Two preliminary empirical tests allowed to discard logs with insufficient resolution, by looking at:

. the general shape and the noisy aspect of the log,

. the possibility to identify the double band using the gamma ray / resistivity pair of logs.

14 NIROND–TR 2012-01, January 2012

Indeed, as the double band is the easiest/clearest identifiable geological feature of the Boom Clay, having difficulties to locate it on logs means that the latter are inappropriate to use. This is even more the case for logs without cores, as in this case the geo-referencing of the log is fully based on the DB identification.

2.5.1 ONDRAF/NIRAS and Deep Logs

Table 4 lists the deep boreholes drilled either by ONDRAF/NIRAS- SCK•CEN or by Distrigas and the GSB. Several inconsistencies about boreholes locations have been noticed and corrected between different databases. The validated database is presented in Annex A.

Table 4 – List of ONDRAF/NIRAS and Deep boreholes considered. Operated by ONDRAF/NIRAS – Other operator (Distrigas, GSB, etc.) SCK•CEN MOL-1 WEELDE RIJKEVORSEL MERKSPLAS-1 (KB- DESSEL-1 DOEL-2B (DzH14) 165) ZOERSEL ESSEN-1 ST-LENAARTS MEER-1 (KB-149) Ignored: SCK-15, RIJKEVORSEL (DzH15) HERENTHOUT Two main issues occur regarding the vertical reference of the boreholes and other information: . Usually, depths along the hole are defined below drilling table (BDT), but they can also be defined below ground level, and the reference is not always specified.

. The reference system for the Z levels, which is sometimes the average sea level (ASL) or the SGL (Second General Levelling), which refers to low water spring and is about 2m below the ASL.

As we aim at characterizing thin vertical heterogeneities within the Boom Clay (20-30cm thickness), the Z reference should be clearly defined for all boreholes. Working in the DB- Mol reference system limits the impact of inconsistencies about this Z reference level. Several borehole logs contained the same logging tools ID, and different acronyms commonly refer to the same logging tool. These issues have been as far as possible corrected. The Rijkevorsel borehole operated by the SCK has been discarded from the analysis for several reasons: bad resistivity resolution [see R-3930], gamma ray log measured in cps (see below) and the availability of the Distrigas borehole DzH14 nearby. The latter is therefore preferred. The SCK-15 borehole is also finally ignored, being very old, not deep enough and located near the more recent boreholes Mol-1 and Dessel.

NIROND–TR 2012-01, January 2012 15

2.5.1.1 Gamma-ray tools

Classical Gamma Ray is measured in almost every borehole. All GR logs are measured in API for this dataset. API, or equivalently gAPI, is a standard and every tool must be calibrated according to this standard. API is determined in a unique borehole in Houston. Some countries dispose of a borehole that has been calibrated vis-à-vis the one of Houston in order to be able to calibrate the tools easily in their own country. So some small differences could be caused by the calibration site. The borehole diameter could also affect the response, as well as the salinity of the drilling mud. The quality of Gamma ray logs is individually acceptable in terms of general shape and DB identification. However, the joint analysis of several gamma ray logs directly reveals inconsistencies between absolute gamma ray values. This is first illustrated on Figure 6 for all available GR curves, after rescaling to the DB-Mol geo-reference system.

Figure 6 - Examples of GR curves on NIRAS boreholes (gAPI).

Knowing that the Boom Clay is expected to be a laterally homogeneous geological formation, it is important to analyse whether the observed GR variations could be explained by geological trends or are only due to calibration or technical logging issues, such as for instance the salinity of the drilling mud. Also, the application of environmental corrections to raw measured GR curves is not always clear. This is analyzed in detail within the Mol-Dessel area. Figure 7 presents several GR curves measured on Mol and Dessel boreholes for the Boom Clay depth interval. It is reminded that both boreholes have been logged by the same company, Dessel in 1993 and Mol in 1997. Though the consistency between the two GR curves from Dessel borehole is clear, clear discrepancies are noticeable on Mol-1 GR runs: GR curves derived from ROCKCLASS

16 NIROND–TR 2012-01, January 2012

and ELAN are consistent but differ from the resistivity run (ait4). In this case, differences obviously cannot be due to the borehole geometry. Such discrepancies can therefore be attributed to calibration issues. This analysis can be extended to other boreholes. For instance, Figure 8 presents averaged GR values on boreholes located throughout the area of interest (mainly ONDRAF/NIRAS – SCK•CEN). The GR values are averaged on the Putte member only, expected to present the smoothest GR behaviour within the Boom Clay. The highest values are obtained for Essen and Herenthout, even if one should be cautious about the latter as the focus was on deeper horizons and not on the logging of the Boom Clay horizon. One can notice that there is almost as much variability between Mol and Dessel than between any pair of boreholes from the area. Notice that, the GR average difference for the Putte member on Mol-1 borehole between a certain run (ait4 used in Figure 8) and the GR contained in the ELAN compilation is equal to 8 API-units. To conclude, it is clear that there is an important lateral variability of gamma ray curves throughout the area of interest, and this variability is at least partly attributable to technical issues. Having in mind this calibration issue, putting into evidence regional trends on gamma ray runs is not feasible.

Figure 7 - GR curves obtained on Mol and Dessel boreholes (gAPI). Depth is in mBDT.

NIROND–TR 2012-01, January 2012 17

Figure 8 - Average GR values on Putte member for several NIRAS boreholes: basemap (left) and histogram (right).

Raw GR curves are really noisy on several boreholes, in particular Zoersel and Weelde, as it is illustrated on Figure 9. In such cases, smoothing is compulsory before any interpretation. The noisy aspect of the raw GR curve could be due to a sampling time which is too small to allow for a robust estimate of the number of disintegrations. Vertical smoothing, though decreasing the vertical resolution, improves the quality of the curve and allows for an easier interpretation.

Figure 9 - GR curve from Zoersel borehole. Raw GR values (left), smoothed GR values at 10cm (middle) and 1m (right).

18 NIROND–TR 2012-01, January 2012

Regarding the type of GR logging tool, it is interesting to note that the quality of the gamma ray curves derived from more recent tools such as HSGR(well Mol and Doel 2b) and HCGR (well Mol) have a better resolution, allowing to identify more easily the DB. The SGR tool available on boreholes Dessel and St Lenaarts also allow a clear identification of the DB peak. Regarding deep GSB logs, the Gamma ray logs available on Meer-1 and Merksplas-1 have a consistent global shape and allow a clear identification of the double band.

2.5.1.2 Resistivity tools

Numerous electrical methods have been used for measuring resistivity in boreholes operated by ONDRAF/NIRAS or SCK•CEN, particularly on Mol-1, Dessel-1 and Doel-2b. Among the main tools used, we can cite (see Appendix A.5 for a reminder on resistivity logging): . Normal resistivity logs (SN, LN): they are widely used in groundwater hydrology, even though the long normal log has become rather obsolete in the oil industry. The electrode spacing, from which the normal curves derive their name, is commonly equal to 40 cm (16 in – short normal) or 162 cm (64 in – long normal). The volume of investigation of the normal resistivity devices is considered to be a sphere, with a radius approximately twice the electrode spacing. Long normal response is affected significantly by bed thickness; this problem can make the logs quite difficult to interpret.

. Lateral logs (LLD, LLS): they are designed to measure resistivity beyond the invaded zone, which is achieved by using a long electrode spacing. They have several limitations that have restricted their use in environmental and engineering applications. Best results are obtained when bed thickness is greater than twice the distance between the position of the current electrode and the centre of the tool or more than 12 m for the standard spacing. Lateral logs usually difficult to interpret in the case of thin beds.

. Focused resistivity logs (FEL, MSFL): inversely to lateral logs, these systems were designed to measure the resistivity of thin beds or high-resistivity rocks in wells containing highly conductive fluids (for instance « guard » log, « laterolog »). Microfocused devices include all the focusing and measuring electrodes on a small pad; they have a depth of investigation of only several centimeters.

. Induction logs (ILD, ILM): these devices originally were designed to make resistivity measurements in oil-based drilling mud, where no conductive medium occurred between the tool and the formation. Induction devices provide resistivity

NIROND–TR 2012-01, January 2012 19

measurements regardless of whether the fluid in the well is air, mud, or water, and excellent results are obtained through plastic casing. They therefore provide high- resolution information on lithology .The measurement of conductivity usually is inverted to provide curves of both resistivity and conductivity. The unit of measurement for conductivity is usually milliSiemens per meter (mS/m). Calibration is checked by suspending the probe in air, where the humidity is low, in order to obtain a zero conductivity.

Several factors may affect the quantitative response obtained from the resistivity log: borehole diameter, mud resistivity, bed thickness, etc. It is therefore quite difficult to perform a quantitative comparison between resistivity curves. This is illustrated on Figure 10 for short normal (SN) resistivity curves obtained from Essen, Weelde and Zoersel boreholes; one can clearly see the shift between Essen resistivity values and the two other curves. Similar observations are made for long normal resistivity logs.

Figure 10 - Smoothed SN curves on NIRAS boreholes (m). Left: Essen (green), Weelde and Zoersel (light and dark blue). Right: zoom on Weelde and Zoersel.

Lateral logs (LLS, LLD) available on Mol and Dessel boreholes provide a flat behavior within the main Boom Clay part. This behavior does not allow to identify properly the DB (see Figure 11).

20 NIROND–TR 2012-01, January 2012

Figure 11 - LLD and LLS curves on NIRAS boreholes: Dessel in orange, Mol in blue (m).

Induction curves (ILD, ILM) are either provided in terms of conductivity of resistivity depending on the logs. For instance, the induction results are provided in conductivity for Zoersel borehole. The transformation to resistivity values can provide a qualitatively acceptable curve but without confidence on the quantitative values derived. DB identification is also difficult on these logs. Micro-spherically focused logs present a flat behaviour on Mol and particularly on Dessel.

NIROND–TR 2012-01, January 2012 21

Figure 12 - MSFL curves on NIRAS boreholes: Dessel in orange, Mol in blue (m).

To summarize this preliminary analysis, normal and induction resistivity logs seem to give the most suitable curves in terms of general shape (high resistivity values at the top and bottom of the Boom Clay (Transition zone and Belsele-Waas member). The DB interpretation is however not always easy even when combined with other logs.

2.5.2 Geological Survey of Belgium (GSB) logs

2.5.2.1 Gamma-Ray tools

On GSB logs, gamma ray has been measured in cps (counts per second) except for boreholes name (archive nr. 27-W-137) and name (28-E-725) where the GR is measured in API. It is important to keep in mind that there is no linear relationship between cps and API, as the amount of cps depends of the crystal inside the tool (the larger the crystal, the higher the number of counts/second). Figure 13 presents the available GR curves for the GSB logs.

Figure 13 - Geological Survey of Belgium boreholes - Gamma-Ray tools.

22 NIROND–TR 2012-01, January 2012

The two GR logs available in gAPI unit are useless: irrelevant general shape and no clear peak below the DB. Regarding the logs in cps, only a few of them are of acceptable quality in terms of peak identification near the DB: 47-W-260, 45-W-337, 31-W-237, 60-W-238, 15-E- 267, 31-E-341, 31-E-338, 30-W-372, 17-W-280, 45-W-348, 09-W-147, 15-E-298. Similar lateral variability is observed between gamma ray logs, as illustrated on Figure 14 for the Putte member.

Figure 14 - Averaged GR values on Putte member for several GSB boreholes: basemap (left) and histogram (right).

2.5.2.2 Resistivity tools

Several types of resistivity tools have been used on the GSB boreholes, the normal tools and lateral resistivity tools are the most common. Note that it is not always obvious to identify which type of tool has been used, as various names can be given to the same tool. For instance, the names 16N, LN16, R16N, L160, SN20 or SN40 all correspond to short normal logs, and LN16 should not be misinterpreted as long normal log LN. Different tools are sometimes used within the same borehole, as it is illustrated hereafter for borehole 15-E-298(IIIa) (Wuustwezel, also called SCK-19).

NIROND–TR 2012-01, January 2012 23

Figure 15 - Resistivity tools used in well 15-E-298(IIIa).

The table below summarizes, for the GSB boreholes, the most satisfactory resistivity tools. Both short and long normal resistivity logs are retained, depending on the borehole. Several boreholes do not present any relevant resistivity log: 27-W-137, 42-W-361, 42-W-362, 42-W- 365, 43-W-326. Table 5 – List of GSB boreholes with relevant resistivity tools.

Borehole Resistivity log Borehole Resistivity log

47-W-260 L200 31-E-338 SN20 29-W-378 L200 60-w-238 SN20 45-W-337 L200 30-W-372 SN40 60-W-254 LN 17-W-280 L160 28-E-725 LN16 45-W-348 L160 31- W- 237 RES1 07-E-195 L200 15-E-267 L100 09-W-147 SN20 18-W-265 L100 15-E-298 L200 61-w-171 L160 43-E-210 L200 31-E-341 SN20 43-W-301 SN40

24 NIROND–TR 2012-01, January 2012

3 Modeling of hydraulic conductivity

3.1 Methodology

A preliminary statistical analysis of hydraulic conductivities is first conducted, aiming at describing the main trends and significant figures about hydraulic conductivity over the cored boreholes. Then, the correlation of Kv/Kh with grain size and geophysical data is analyzed, the latter being of potential added value in terms of uncertainty reduction when predicting Kv/Kh values at unsampled locations. Afterwards, a 1D vertical modeling of target parameters for each cored borehole is developed, illustrating the integration of auxiliary information available on the borehole for the hydraulic conductivity prediction. Finally, the feasibility of 3D modeling is assessed. It is reminded that this 3D model is a key point regarding the transferability of target parameters from cored boreholes to the entire area of interest. Regarding auxiliary variables, due to the lateral variability of geophysical logs and the heterogeneity of the geophysical logging database (a few boreholes with numerous tools, others with just a few tools), the 3D modeling approach will only integrate grain size and GR logs, the latter being less subject to lateral variability than resistivity curves. Note that hydraulic conductivities are systematically presented and discussed in log scale throughout the chapter.

3.2 Statistical Analysis

3.2.1 Data analysis

The general shape of both vertical and horizontal hydraulic conductivities is visualised on Figure 16, which presents their profile on the six available cored and sampled boreholes. The Top and Base members of the Boom Clay (Transition Zone and Belsele-Waas) present higher hydraulic conductivities, due to the increased presence of silt to sand layers.Tthe central members (Putte and Terhagen) show a more stable behavior of lower hydraulic conductivities.

The statistical analysis of Kv is done first, subsequently Kh and finally the Kh/Kv ratio. Basic statistics about Kv values are presented in Table 6 for the whole Boom Clay. Kv statistics and correlation analysis on Mol-1 borehole are computed only with migration data, the permeameter cells data allowing just to quantify the small scale variability for variogram modeling (see §3.3).

The sampling of Essen and Doel is sparser than for the other boreholes. The Herenthout Kv value is just presented for information, as this borehole is much more focused on deeper

NIROND–TR 2012-01, January 2012 25 horizons; furthermore, the measured value for this borehole comes from the bottom of the

Belsele-Waas member, which explains the higher Kv value.

Figure 16 - Log(Kv) (left) and Log(Kh) (right) profiles on the sampled boreholes, in the DB-Mol geo-reference system.

Apart from this borehole, minimum Kv values are similar for the different boreholes. There is much more variability for the maximum values, that range from -7.68 for Zoersel to –10.35 for Doel. For the latter, the low maximum value most probably comes from the fact that the top part of the Boom Clay is missing due to erosion. In average, Mol-1 apparently presents the smallest Kv values, with an approximate difference of half an order of magnitude compared to the other boreholes. It is also interesting to note that Zoersel presents the highest variability level, with a standard deviation being almost twice the value on other boreholes.

Table 6 – Basic Kv statistics within the Boom Clay (in logarithm). Borehole N min max mean st. dev. Mol 41 -11.91 -10.01 -11.58 0.40 Weelde 28 -11.84 -9.92 -11.26 0.53 Zoersel 34 -11.51 -7.68 -11.05 0.79 Doel 10 -11.40 -10.35 -10.96 0.30 Essen 10 -11.47 -10.00 -11.06 0.47 Herenthout 1 -8.87 -8.87 -8.87 - TOTAL 124 -11.91 -7.68 -11.25 0.64

26 NIROND–TR 2012-01, January 2012

Analyzing Kv variations for each litho-stratigraphic unit extends this global analysis (see

Table 7). The empirical observation of larger Kv values on Transition Zone and Belsele Waas units is clearly confirmed, associated with an increased variability. The Putte member is definitely the less permeable and variable unit, with an average value of 3.90 10-12 m/s (-11.49 in log scale). The Terhagen unit is slightly more permeable and variable; this could be attributed to a fuzzy delineation between Terhagen and Belsele-Waas members.

It is interesting to note that the lower Kv value globally observed in Mol is reproduced here, particularly for the most homogeneous units: Putte and Terhagen. This is not the case for the Belsele-Waas member, though the confidence associated to statistics for this unit is probably low, due to the limited number of data (maximum of 4 samples per borehole). One could expect that, due to compaction, the hydraulic conductivity is increasing towards the

North-East. This would imply that Weelde presents the lowest Kv values. However, this is only true for the Belsele-Waas member, keeping in addition in mind the less reliability of statistical results for this member. For the other units, Mol surprisingly presents lower Kv values. This important point will be discussed further in the next chapters. Also, a larger variability is observed in the Putte and Terhagen units for the Weelde borehole compared to Mol or Zoersel borehole. Note that it would be possible to compute an equivalent hydraulic conductivity for the whole Boom Clay using the harmonic mean of the hydraulic conductivity of the different sub-units weighted by their thickness (see paragraph 2.3.1.3). This analysis might be found in Wemaere et al. (2008) and is therefore not reproduced here, being beyond the goal of the present analysis.

NIROND–TR 2012-01, January 2012 27

Table 7 – Basic Kv statistics within the Boom Clay (in logarithm), per litho- stratigraphic unit. st. Unit Borehole Nb min max mean dev. Mol 13 -11.86 -10.99 -11.55 0.24 Weelde 9 -11.42 -9.92 -10.76 0.52 Zoersel 6 -11.51 -10.83 -11.26 0.25 Transition Doel 0 Essen 2 -11.21 -11.08 -11.14 0.07 All 30 -11.86 -9.92 -11.23 0.48 Mol 17 -11.87 -11.28 -11.71 0.13 Weelde 11 -11.72 -11.39 -11.61 0.11 Zoersel 15 -11.47 -11.14 -11.34 0.08 Putte Doel 6 -11.40 -10.79 -11.08 0.24 Essen 4 -11.47 -11.30 -11.40 0.07 All 53 -11.87 -10.79 -11.49 0.25 Mol 7 -11.91 -11.64 -11.77 0.10 Weelde 4 -11.66 -11.30 -11.54 0.14 Zoersel 9 -11.42 -11.09 -11.28 0.11 Terhagen Doel 2 -11.14 -10.99 -11.06 0.08 Essen 2 -11.17 -10.00 -10.59 0.59 All 24 -11.91 -10.00 -11.39 0.39 Mol 4 -11.71 -10.01 -10.75 0.70 Weelde 4 -11.84 -10.39 -11.18 0.52 Zoersel 4 -10.06 -7.68 -9. 12 0.93 Belsele- Doel 2 -10.67 -10.35 -10.51 0.16 Waas Essen 1 -11.26 -11.26 -11.26 Herenthout 1 -8.87 -8.87 -8.87 All 16 -11.84 -7.68 -10.43 1.06

This statistical analysis is reproduced hereafter on horizontal hydraulic conductivities Kh (see Table 8 and Table 9), for the whole Boom Clay and per litho-stratigraphic unit. Horizontal conductivities are globally slightly larger than vertical conductivities. Though the main

comments made for Kv also apply here, the small amount of samples for Mol, Essen and even more Doel and Herenthout (0 and 1 sample) make difficult any discussion based on statistical results. Weelde presents lower Kh values than Zoersel, as one could expect, but still with more associated variability.

28 NIROND–TR 2012-01, January 2012

Table 8 – Basic Kh statistics within the Boom Clay (in logarithm).

Borehole N min max mean st. dev.

Mol 11 -11.47 -9.55 -11.15 0.52

Weelde 28 -11.50 -9.68 -10.95 0.52 Zoersel 33 -11.26 -7.32 -10.62 1.00 Doel 0 Essen 10 -11.18 -7.94 -10.29 1.03 Herenthout 1 -9.30 -9.30 -9.30 TOTAL 83 -11.50 -7.32 -10.75 0.86

NIROND–TR 2012-01, January 2012 29

Table 9 – Basic Kh statistics within the Boom Clay (in logarithm), per litho- stratigraphic unit. Unit Borehole Nb min max mean st. dev. Mol 2 -11.34 -11.23 -11.29 0.05 Weelde 9 -11.29 -9.68 -10.55 0.55 Zoersel 6 -11.26 -8.69 -10.45 0.92 Transition Doel 0 Essen 2 -10.88 -10.17 -10.52 0.35 All 19 -11.34 -8.60 -10.59 0.70 Mol 6 -11.41 -11.16 -11.34 0.08 Weelde 11 -11.36 -10.94 -11.24 0.14 Zoersel 14 -11.12 -10.85 -11.03 0.07 Putte Doel 0 Essen 4 -11.18 -10.93 -11.01 0.10 All 35 -11.41 -10.85 -11.15 0.17 Mol 0 Weelde 4 -11.40 -11.13 -11.31 0.11 Zoersel 9 -11.19 -10.94 -11.07 0.08 Terhagen Doel 0 Essen 2 -11.16 -9.45 -10.31 0.85 All 15 -11.40 -9.45 -11.03 0.44 Mol 3 -11.47 -9.55 -10.70 0.83 Weelde 4 -11.50 -10.07 -10.71 0.51 Zoersel 4 -10.27 -7.32 -8.47 1.13 Belsele- Doel 0 Waas Essen 2 -9.21 -7.94 -8.57 0.63 Herenthout 1 -9.30 -9.30 -9.30 All 14 -11.50 -7.32 -9.69 1.38

The correlation between Kv and Kh on available boreholes is illustrated on Figure 17. If we except outliers coming from the Transition Zone or Belsele-Waas unit, the correlation is really high, with a linear correlation coefficient equal to 0.895. Obviously, this correlation is merely driven by the few samples coming from the more permeable units (Transition Zone and Belsele-Waas).

30 NIROND–TR 2012-01, January 2012

Figure 17 - Scatter diagram between Log(Kv) and Log(Kh) measurements for the whole Boom Clay. Indication of correlation coefficient (rho), first bisector (x=y, thin line), linear regression line (bold line). Squares represent data ignored for the correlation computation: cores 6 from Zoersel and 133 from Essen.

Comparison between Kv and Kh can be detailed by computing hydraulic conductivity anisotropies. Statistics about Kh/Kv ratio are computed and summarized per borehole and unit on Table 10. Computing the ratio of averaged hydraulic conductivities seems to lead to more robust estimates. For the Putte member, which is well sampled, the average Kh/Kv ratio is equal to 1.8. This value is slightly lower for the Transition Zone and higher for the Belsele- Waas, but again with a limited confidence in these statistical results due to the limited number of data. Regarding the Terhagen member, if we exclude Essen borehole (only 2 samples) the average Kh/Kv ratio is around 1.5. Though scarcely sampled, Essen seems to systematically present higher Kh/Kv ratios.

NIROND–TR 2012-01, January 2012 31

Table 10 – Basic Kh/Kv statistics within the Boom Clay (in logarithm), per litho- stratigraphic unit. Mean Unit Borehole N Mean(Kh)/Mean(Kv) (Kh/Kv) Mol 2 2.0 2.1 Weelde 9 1.7 1.8 Transition Zoersel 5 4.5 3.4 Zone Essen 2 5.6 6.3

All 18 2.1 2.8

Mol 6 2.0 2.1 Weelde 11 2.4 2.4 Putte Zoersel 14 2.1 2.2 Essen 4 2.4 2.5

All 35 2.2 2.3

Mol 0 Weelde 4 1.7 1.7 Terhagen Zoersel(1) 9 1.6 1.6 Essen 2 3.4 2.3

All 15 2.7 1.7

Mol 3 3.8 2.5 Weelde 4 2.5 3.1 Belsele- Zoersel 4 3.1 8.8 Waas Essen(2) 0 Herenthout 1 0.4 0.4

All 12 2.9 4.6 (1)Without core 6 Zoersel (Kh/Kv = 277.1) (2) Without core 133 Essen (Kh/Kv = 2072.1)

3.2.2 Correlation with grain size data

Grain size data have been acquired for the Boom Clay on six boreholes: Mol, Doel, Weelde, Zoersel, Essen, Herenthout (1 sample on Boom Clay). As explained in §2.3.3, we focus on the grain size variable d40 (m). Basic statistics mainly confirm the finer size of materials within Putte and Terhagen units, together with a much more homogeneous distribution of grain size (see Table 11). Transition

32 NIROND–TR 2012-01, January 2012

Zone and even more Belsele-Waas present larger and more variable d40 values. These results are logically consistent with the observations made on hydraulic conductivities. Essen and Herenthout results should be interpreted cautiously due to the limited number of samples.

Table 11 – Basic d40 statistics (in µm) within the Boom Clay, per litho-stratigraphic unit. st. Unit Borehole Nb min max mean dev. Mol 17 0.9 10.3 3.1 2.6 Doel 0 Transition Weelde 54 0.5 38.8 9.2 10.6 Zone Zoersel 33 0.2 24.7 5.1 6.8 Essen 2 7.6 12.4 10.0 3.4 All 106 0.2 38.8 7.0 8.8 Mol 31 0.4 10.4 2.0 1.9 Doel 39 0.5 18.6 3.2 3.6 Weelde 62 0.5 15.8 3.1 3.7 Putte Zoersel 55 0.2 4.2 1.1 0.9 Essen 4 1.1 5.4 3.5 2.0 All 191 0.2 18.6 2.4 2.9 Mol 12 0.4 5.4 1.8 1.4 Doel 12 0.5 12.4 3.6 3.4 Weelde 21 0.5 7.9 2.3 2.0 Terhagen Zoersel 39 0.5 14.0 2.3 2.4 Essen 2 8.8 27.2 18.0 13.0 All 86 0.4 27.2 2.8 3.6 Mol 11 1.5 35.9 12.0 11.2 Doel 9 2.1 41.1 23.3 12.3 Weelde 23 0.7 39.7 11.6 11.4 Belsele- Zoersel 24 0.9 48.9 23.3 14.0 Waas Essen 2 13.3 32.4 22.9 13.5 Herenthout 1 51.5 51.5 51.5 All 70 0.7 51.5 18.1 14.0

It is interesting to note that Mol presents the lowest d40 average values on each unit, which is

also consistent with the Kv results and gives a better confidence in the latter. The correlation with hydraulic conductivity is evaluated by comparing neighboring samples up to 30 cm. This parameter has an impact on the correlation model and there is a compromise to find between having enough information to derive robust statistics and the risk

NIROND–TR 2012-01, January 2012 33 to correlate inconsistent samples. For instance, depending on the maximum accepted distance to consider K and d40 samples as neighbors, the number of pairs highly varies: Max. distance of 0.1m: 85 sample pairs, rho = 0.86 (only 5 couples for Mol)

Max. distance of 0.3m: 130 sample pairs, rho = 0.82 (30 couples for Mol)

As a consequence, a maximum distance of 0.30m is finally chosen in order to have enough data to build a multivariate model on individual boreholes. The resulting scatter diagram between Kv and d40 is illustrated on Figure 18. The correlation level is high, with a linear correlation coefficient equal to 0.84. An increased variability of d40 data with similar

Log(Kv) values can be observed on Transition Zone and Belsele-Waas data. This variability could come from samples coming from different silt/clay beds. Detailed scatter-diagrams about the correlation between hydraulic conductivities and d40 data are available in Appendix B.1.

Figure 18 - Scatter diagram between vertical hydraulic conductivity (in logarithm, abscissa) and grain size data d40 (m, in ordinate) for the 6 available boreholes.

Table 12 summarizes the correlation level between hydraulic conductivities and d40 for individual boreholes. Note that Log(Kh) data are not available on Doel-2b and Essen.

Zoersel presents the highest correlation level between Log K and d40 (0.97 for Kv and 0.90 for Kh). Essen also presents a very high correlation between Kv and d40. Weelde and Mol present intermediate correlation levels between Kv and d40, and higher levels between Kh and d40 despite the smaller amount of available samples, particularly for Mol. The limited amount of available couples on Doel-2b does not allow reliable results.

34 NIROND–TR 2012-01, January 2012

Table 12 – Linear correlation coefficients () between hydraulic conductivity (in logarithm) and grain size data d40 (m). Number of samples (Nb) available to calculate the correlation coefficient (). Borehole Log(Kv) Log(Kh) Nb  Nb  Mol 30 0.77 3 0.99 Doel-2b 5 -0.36 0 Weelde 28 0.67 6 0.98 Zoersel 34 0.97 13 0.90 Essen 10 0.92 0 All 0.84 0.71

3.2.3 Correlation with geophysical logs

This paragraph aims at analyzing the most appropriate gamma ray and resistivity tools to help the modeling of hydraulic conductivity. This is based on the correlation analysis between hydraulic conductivity samples and nearby geophysical measurements. Apart from the qualitative information brought by a given tool about the geology, it is fundamental to keep in mind that integrating such tools require that the measured values are quantitatively correlated with target parameters, not only qualitatively. A detailed correlation analysis is provided in Appendix B.2, only the main results are presented here. Table 13 summarizes for each borehole the correlation level between the best (in terms of correlation level) GR and Resistivity logs and hydraulic conductivities. A preliminary smoothing with a radius of 1m is applied on boreholes Weelde and Zoersel. Subsequent improvement of the correlation level as compared to raw curves is illustrated in the Appendix. Gamma Ray globally presents an intermediate correlation level (between 0.6 and 0.7) with both Kv and Kh, this correlation being even stronger (approx. 0.80) for Kh on Zoersel and

Essen, also for Kv on Doel-2b. The correlation is much weaker on Weelde (-0.51 for Kv, -0.42 for Kh) due to the poor quality of the logging on this borehole. Resistivity generally presents slightly higher correlation levels with hydraulic conductivity, though this correlation fluctuates much more on some boreholes. The correlation is intermediate (0.7) with Kv on Mol, Zoersel and Weelde, and is even higher on Mol and

Zoersel. However, for Weelde, the correlation with Kh is weak and, for this borehole, though the smoothing improved the correlation with gamma ray, it has no impact on correlation with resistivity. Finally, the correlation is negligible between resistivity and K on Doel and null on Essen (with or without smoothing).

NIROND–TR 2012-01, January 2012 35

Table 13 – Linear correlation coefficients for sampled boreholes between hydraulic conductivities (in logarithm) and geophysical tools: gamma ray (GR) and Resistivity (Res). Tool name indicated between brackets. Log(Kv) Log(Kh) Borehole GR Res GR Res Mol -0.66 0.70 (1) -0.66 0.86 (1) Zoersel -0.68 (s) 0.71 (2,s) -0.80 (s) 0.74 (2,s) Weelde -0.49 (s) 0.70 (3) -0.40 (s) 0.63 (3) Doel-2b -0.82 0.54 (4) - - Essen -0.60 -0.18 (3) -0.79 -0.09 (3) (1)AH30 from ait4. (2)ILD. (3)LN. (4)FF. (s)Smoothed with a radius of 1m.

It has to be stressed that these correlation levels are not systematically robust, as a few K samples coming from the Transition Zone or the Belsele-Waas member can sometimes significantly modify the relationship between the variables. Regarding the tool choice for Mol, due to better correlation with hydraulic conductivities the run ait4 is preferred to elan, though the later is expected to be more accurate and provides more consistent curves (see Figure 7).

3.2.4 Conclusion of the statistical analysis

As a conclusion for this statistical analysis, the following points can be emphasized, some of them confirming previous work by ONDRAF-NIRAS/SCK•CEN: . The central Putte member is definitely the less permeable and less variable unit, with an average Log(Kv) value of -11.49 (-11.15 for Log(Kh)). The Terhagen unit is slightly more permeable and variable, which could be attributed to a fuzzy delineation between Terhagen and Belsele-Waas members. Transition Zone and Belsele Waas units area clearly more permeable and also more variable in terms of hydraulic conductivity.

. Mol-1 presents the smallest Kv values, with an approximate difference of half an order of magnitude compared to the other boreholes; this is not the case for Kh measurements.

. Grain size data constitute a really promising auxiliary variable for hydraulic conductivity modeling, being globally well correlated and much heavily sampled on cored boreholes (particularly Zoersel and Weelde).

. About the correlation between hydraulic conductivity and geophysical logs, the following points can be stressed:

- Average to good correlation between Kv-Kh and Gamma Ray curves, excepted on Weelde borehole due to the poor quality of the logging;

36 NIROND–TR 2012-01, January 2012

- Good correlation between Kv-Kh and resistivity logs, mainly using normal- resistivity and induction tools. However, the correlation can be non-existent on some boreholes, for instance Essen, due to poor quality logs.

- Therefore, resistivity logs present a less robust relationship with hydraulic conductivities than gamma ray logs.

3.3 1D vertical modeling

This paragraph aims at analyzing and illustrating on cored boreholes the added value of auxiliary variables (geophysical logs, grain size data) for hydraulic conductivity modeling. Also, the important question of assessing the uncertainty around the Kv-Kh estimates is discussed. From a geostatistical point of view, the 1D modeling of Kv/Kh is obtained using a classical cokriging approach between the following variables: Kv, Kh, d40, regression(GR, Res). This model is justified by the following considerations:

- independent processing of Kv and Kh could lead to inconsistencies, for instance if one aims at deriving a Kv/Kh estimated ratio from Kv and Kh estimates;

- d40 is clearly correlated with the target parameters;

- GR and resistivity logs are pre-processed using a multi-linear regression with Kh as the target variable. Despite the possible loss of information due to the fact that we do not consider separately these two auxiliary variables, summarizing their contribution with just one regressed variable limits the size of the spatial structure system to be inferred. It has been verified with cross-validation on Mol-1 borehole that this has no significant impact on the model quality.

As a consequence, for each cored borehole four variables are jointly considered for the modeling. The cokriging result is compared with a univariate kriging approach, based on Kv or Kh data only. Focusing on boreholes Mol, Weelde and Zoersel, which are well sampled in terms of hydraulic conductivity, the correlation between Log(Kv) and the regression derived from GR and Res curves is illustrated on Figure 19. By construction, the correlation level increases compared to the individual correlation between geophysical data and Log(Kv). The weaker correlation observed on Weelde is not surprising and consistent with the ones observed on individual GR and resistivity variables.

NIROND–TR 2012-01, January 2012 37

Figure 19 – Scatter diagrams between Log(Kv) and the regression with GR and Res data, for Mol, Zoersel and Weelde boreholes. Linear correlation coefficient indicated.

3.3.1 Regional consistency between 1D K spatial structures

Focusing on boreholes Mol, Weelde and Zoersel, Figure 20 illustrates the spatial variability of hydraulic conductivity. The higher variability observed on Zoersel comes from the Belsele- Waas member, which contains much larger Kv-Kh data than for the other boreholes (as discussed in paragraph 3.2). An apparent nugget effect is visible, particularly on Weelde and Zoersel boreholes. However, 22 couples with approximately the same depth, taken from HADES (see §2.3.1.2), present hydraulic conductivities between (in logarithm) –11.57 and –11.32, with an average value of –11.46 and a variance equal to 4.3 10-3. Given the fact that these data are not precise duplicates, their variance constitutes an upper limit for the nugget effect value, at least in the Putte member. This would mean that the measurement error is almost negligible; however the measurement technique used around HADES is not the same than for the other data (permeameter cells and migration experiments). Therefore, integrating the information derived from HADES about the hydraulic conductivity small scale variability is not recommended.

Figure 20 - Vertical (left) or horizontal (right) hydraulic conductivity (in logarithm) experimental variograms for Weelde, Zoersel and Mol (Log(Kh) not displayed). Dotted lines correspond to statistical variances.

38 NIROND–TR 2012-01, January 2012

The clear difference between Zoersel, Mol and Weelde experimental variograms poses the question of the robustness of the K spatial variability. Is this variability between boreholes coming from (i) lack of data to ensure a robust computation or (ii) real regional differences in terms of K spatial variability? Comparing Zoersel and Weelde, which present similar K sampling schemes, helps to answer this question. Experimental variograms are computed for each borehole, but distinguishing the homogeneous part from the Boom Clay (Putte and Terhagen) from the most heterogeneous ones (Transition Zone and

Belsele-Waas). Figure 20 illustrates the obtained results, which are similar for Kv and Kh. First, on Weelde (red curves), variability level is consistent between the two types of units, which is definitely not the case on Zoersel. Actually, on the latter the variability observed on Transition Zone and Belsele-Waas members is more than 10 times greater than on the homogeneous units. Also, it has been shown that Zoersel presents larger K differences than Weelde between the central members and the others. These considerations explain why, on Figure 20, the overall spatial continuity on Weelde is weak whereas Zoersel present a clear spatial structure. Putte – Terhagen

Transition Zone – Belsele-Waas Figure 21 - Vertical (left) or horizontal (right) hydraulic conductivity (in logarithm) experimental variograms for Weelde (red), and Zoersel (green), for Putte and Terhagen units (top) and Transition Zone and Belsele-Waas (bottom). Dotted lines correspond to statistical variances.

NIROND–TR 2012-01, January 2012 39

These results also show that the central part of the Boom Clay (Putte-Terhagen) presents a weaker spatial structure in terms of hydraulic conductivity, at least at the current sampling resolution (1m in the most favorable case). The better vertical continuity is not clear on the Top and Bottom units of the Boom Clay due to the lack of data. Actually, despite a clear K trend within these units, K also presents a much higher variability and lesser data than on the central part.

3.3.2 Variogram modeling

Variogram modeling is illustrated below for Mol-1, Zoersel and Weelde boreholes. For Mol- 1, due to the small number of Kh samples, Kh variogram has been derived from the simple and cross-variograms of Kv with auxiliary variables, just rescaled to Kh variability by taking into account the correlation observed at permeameter cells between Kv and Kh. Note that, due to the absence of resistivity curves correlated to hydraulic conductivities on Essen and Doel-2b, 1D specific modeling of these boreholes is not appropriate and they will be directly addressed with the 3D model discussed below. The multivariate variogram fitting is performed in the framework of the linear model of coregionalization, assuming that all simple and cross-variograms are linear combinations of the same basic structures. These basic structures are similar for the three boreholes: a nugget effect and an exponential structure with a range equal to 35m.

40 NIROND–TR 2012-01, January 2012

Figure 22 - Mol-1: Cross-variogram modeling of Log(Kv), d40 and reg(GR, Res).

NIROND–TR 2012-01, January 2012 41

For Zoersel, note that Log(Kh) data have been migrated at Kv locations to allow cross- variogram computation; indeed, the measurements coming from separate plugs, they are not directly considered as duplicates. The Log(Kv) variability level is much higher than on Mol. This will probably lead to larger uncertainty around the estimates (cokriging standard deviations).

Figure 23 – Zoersel: Cross-variogram modeling of Log(Kv), Log(Kh), d40 and reg(GR, Res).1

1 This figure and the similar ones, which are not fully readable due to the number of graphics, are just provided to illustrate the global shape of the multivariable spatial structure model.

42 NIROND–TR 2012-01, January 2012

The multivariate variogram model fitted on Weelde clearly differs from the preceding ones. Actually, consistently with the discussion of last paragraph, Kv and Kh both present a larger variability at small scale. The regression from GR and Resistivity logs is also much smoother. Experimental cross-variograms between this regression and hydraulic conductivities show a weak correlation at small scale.

Figure 24 - Weelde: Cross-variogram model of Log(Kh), Log(Kv), d40 and reg(GR, Res).

NIROND–TR 2012-01, January 2012 43

3.3.3 1D Kriging results

Kriging and cokriging results are displayed for both Kv and Kh on the following figures for Mol-1 and Zoersel boreholes. Note that the vertical resolution is the raw one for Mol (10cm) and is 1m for Zoersel (smoothing of the logs). It can be observed that the kriged profiles are by construction relatively smooth, particularly on scarcely sampled Kh in Mol, this smoothing being reinforced by the presence of a nugget effect in the Kv and Kh variogram models. Cokriging reduces this smoothness due to the weight given to both grain size and geophysical data. One has to keep in mind that the amount of information integrated in the cokriging procedure is much larger than for the kriging, as it includes numerous grain size data and exhaustive knowledge of the geophysical logs at each target location (collocated variable).

The most appealing impact of these auxiliary variables on the estimated profile is for Kv on Mol-1, at the bottom of the Transition Zone (Depth approx. equal to 43m in the DB-Mol system), where a peak is clearly visible on the cokriged profile. This peak is due to the resistivity log. One major advantage of geostatistical estimation techniques is the ability to estimate the uncertainty associated to the Log(K) (co)kriged profile. The (co)kriging standard deviation profiles associated to the preceding estimates are displayed hereafter. The average kriging standard deviation is equal to 0.24. Local increases of this standard deviation can be observed on depth intervals under-sampled in terms of Log(Kv), for instance around 35-40m depth (DB-Mol reference system). Compared to kriging, the cokriging approach leads to an average reduction of the standard deviation equal to 19%. This reduction locally reaches 36% in under-sampled depth intervals that are scarcely sampled with Log(Kv). In such depth intervals, the reduction of uncertainty in the Log(Kv) prediction is explained by the presence of well correlated grain size data.

44 NIROND–TR 2012-01, January 2012

Kriging Cokriging

Kriging

60 60 60

60 60 60 Cokriging Transition Zone Kv data

d40 data

40 40 40

Putte

20 20 20

Z (m - ref DB) ref - (m Z Z (m - ref DB) ref - (m Z

0 0 0

Terhagen

-20 -20 -20

Belsele-Waas

-12.0 -11.5 -11.0 -10.5 -10.0 -9.5 -9.0 0.15 0.20 0.25 0.30 0.35 0.40 Log(Kv) Standard Dev. of Log(Kv) Figure 25 – Mol-1: Log(Kv) modeling results (left) and associated standard deviations (right).

Kriging

Cokriging

60 60

60 Kriging

60 60 60 Transition Zone Cokriging Kh data

d40 data

40 40 40

Putte

20 20 20

Z (m - ref DB) ref - (m Z Z (m - ref DB) ref - (m Z

0 0 0

Terhagen

-20 -20 -20

Belsele-Waas

-12.0 -11.5 -11.0 -10.5 -10.0 -9.5 -9.0 0.1 0.2 0.3 0.4 0.5 0.6 Log(Kh) Standard Dev. of Log(Kh) Figure 26 – Mol-1: Log(Kh) modeling results (left) and associated standard deviations (right).

NIROND–TR 2012-01, January 2012 45

Figure 27 – Zoersel: Log(Kv) modeling results (left) and associated standard deviations (right).

Kriging

Cokriging Kriging

60 60

60 Cokriging

60 60 60 Transition Zone Kv data

d40 data

40 40 40

Putte

20 20 20

Z (m - ref DB) ref - (m Z Z (m - ref DB) ref - (m Z

0 0 0

Terhagen

-20 -20 -20

Belsele-Waas

-12.0 -11.5 -11.0 -10.5 -10.0 -9.5 -9.0 0.1 0.2 0.3 0.4 0.5 0.6

Log(Kv) Standard Dev. of Log(Kv)

46 NIROND–TR 2012-01, January 2012

Kriging Cokriging Kriging

Cokriging

60 60 60

60 60 60 Kh data Transition Zone

d40 data

40 40 40

Putte

20 20 20

Z (m - ref DB) ref - (m Z Z (m - ref DB) ref - (m Z

0 0 0

Terhagen

-20 -20 -20

Belsele-Waas

-12.0 -11.5 -11.0 -10.5 -10.0 -9.5 -9.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Log(Kh) Standard Dev. of Log(Kh) Figure 28 – Zoersel: Log(Kh) modeling results (left) and associated standard deviations (right).

3.3.4 Cross-validation

Complementary to the empirical control of the quality of the results, cross-validation allows quantifying the predicting quality of the models. Scatter-diagram of true vs. predicted Log(Kv) values, displayed hereafter, clearly demonstrate that cokriging outperforms kriging. This confirms what was expected, because of the integration of well correlated auxiliary variables in the cokriging procedure.

Figure 29 – Mol-1: Cross-validation results for Kv (left) and Kh (right) modeling using kriging (+) and cokriging with d40, GR and Res (x): estimates (abscissa) versus true values (ordinate). Indication of the 1st bisector (x=y).

NIROND–TR 2012-01, January 2012 47

Figure 30 – Zoersel: Cross-validation results for Kv (left) and Kh (right) modeling using kriging (+) and cokriging with d40, GR and Res (x): estimates (abscissa) versus true values (ordinate). Indication of the 1st bisecor (x=y).

Figure 31 – Weelde: Cross-validation results for Kv (left) and Kh (right) modeling using kriging (+) and cokriging with d40, GR and Res (x): estimates (abscissa) versus true values (ordinate). Indication of the 1st bisector (x=y).

Statistical results complement these observations (see Table 14), especially if we focus on the correlation coefficient results, which are the most significant in this case. Despite that, one can notice that prediction errors in K can reach one order of magnitude, in particular for more permeable data observed in top and bottom units, which show increased variability.

48 NIROND–TR 2012-01, January 2012

Table 14 – Cross-validation results for Kv/Kh modeling in Mol, Zoersel and Weelde using kriging and cokriging (with d40, GR and Res): correlation coefficient (rho), average error (bias) and variance of standardized error (Var std err). Log(Kv) Log(Kh) Borehole Criterion Kriging Cokriging Kriging Cokriging

Rho. 0.45 0.82 -0.25 0. 30 Bias -2 -2 -2 -2 Mol-1 -1.1 10 0.3 10 -5.6 10 0.9 10 Var. Std. 1.96 1.43 2.42 2.89 Err.

Rho. 0.86 0.98 0.74 0.94 Bias -2.9 10-2 1.5 10-2 -5.1 10-2 -3.3 10-2 Zoersel Var. Std. 0.85 0.78 0.91 0.54 Err.

Rho. 0.26 0.83 0.14 0.81 Bias -2 -4 -2 -2 Weelde -2.2 10 -2.6 10 -2.7 10 -1.6 10 Var. Std. 4.07 1.21 2.28 1.86 Err.

3.3.5 Uncertainty envelope for K prediction

Because of the stationary assumption, the uncertainty described by the preceding standard deviation curves remains similar throughout the Boom Clay. This should be improved, the hydraulic conductivity being more variable in the upper and lower units than in the central part of the Boom Clay2. Following a methodology presented by Chilès (1990), a local variogram fitting is therefore made by taking a proportional model; despite the lack of data in the upper and lower parts of the Boom Clay, this proportional model seems reasonable and compatible with observations (see § 3.3.1). It is assumed that the variogram evolves gradually through the units and that, around a point x, it has the following form:

2  (h; x)  A (x) 0 (h) with  0 (h) the average variogram already fitted and A(x) a local variability coefficient. This local coefficient will only impact the kriging standard deviation map, not the kriging itself; indeed, a global rescale of the variogram model leaves the kriging weights unchanged, so the kriging. can be determined using a standard cross-validation method and is equal to the mean of the absolute standardized errors divided by  / 2 . ______2This stationary assumption also explains the unexpected values obtained, in the cross-validation results, for the variance of standardized errors. These variances should be the close to 1, which is not the case because the local variability observed in practice is not fully consistent with the average variability described by the variogram model.

NIROND–TR 2012-01, January 2012 49

This approach is illustrated on Log(Kv) modeling in Mol-1. Using cross-validation, A(x) is first computed at each Kv data location, being equal to the absolute value of the estimation error (true value – kriging estimate), divided by the kriging standard deviation and by  / 2 . values range from 0 to 0.5 in the central part of the Boom Clay to almost 2 in the upper part and up to 4 in the lower part (see Figure 32). This coefficient is locally quite variable, due to the high variability of the target variable Kv itself. The values of are then smoothed, in order to be available at each target node. Figure 32 illustrates the resulting standard deviation curve, compared to the one based on the average variogram only.

Global Stdev

60 60

A(x) Data 60 60 60 Local Stdev A(x) Smoothed Kv data

d40 data

40 40 40

40 40

20 20 20

20 20

Z (m - ref DB) ref - (m Z

0 0 0

0 0

-20 -20 -20

-20 -20

0 1 2 3 4 5 0.0 0.1 0.2 0.3 0.4

A(x) Standard Dev. of Log(Kv) Figure 32 – Mol-1: Log(Kv) cokriging results: local variability coefficient A(x) (left) and related cokriging standard deviation curves (right).

In the gaussian case, a confidence interval at 95% for the target parameter can be obtained by adding ± 2 standard deviations to the kriging result. This result is useless in our case, as the target parameters do not follow a gaussian statistical distribution. However, a more general and conservative result still applies even outside the gaussian framework. Provided that the target variable follows a unimodal statistical distribution, which is our case, then the interval of ± 3 standard deviations around the kriged value is at least a 95% confidence interval [Chilès and Delfiner, 1999]. This confidence interval is illustrated below for Log(Kv) in Mol-1 borehole. From this confidence interval, confidence limits for Log(Kv) can be derived per litho-stratigraphic unit. These values, summarized in Table 15, constitute extreme admissible scenarii for subsequent

50 NIROND–TR 2012-01, January 2012

safety studies. Confidence interval bounds are similar for Putte and Terhagen members, despite the fact that, graphically, the interval seems to be narrower for Putte; this is due to the increased variability at the bottom of the Putte member, around the Double Band and below, and also at the top of the unit, close to the Transition Zone. If we exclude these depths and compute the confidence interval at 95% or more for the 30 meters above the Double Band, we obtain for Log(Kv) a confidence interval at 95% equal to [-12.04 ; -11.43], around an average value of –11.75.

Figure 33 – Mol-1: Log(Kv) cokriging result and confidence interval at 95%.

NIROND–TR 2012-01, January 2012 51

Table 15 – Mol-1: Log(Kv) average value and confidence interval bounds per litho- stratigraphic unit derived from the cokriging model. Unit Min 95% Probable Max 95% Boom Clay -12.38 -11.55 -8.77 Transition Zone -12.26 -11.50 -9.78 Putte -12.25 -11.75 -11.14 Terhagen -12.38 -11.73 -11.00 Belsele-Waas -12.27 -10.70 -8.77 An alternative approach for quantifying uncertainties, using stochastic simulations, is presented in the Appendix.

Conclusion The following points can be emphasized, as a conclusion for the 1D modeling of hydraulic conductivities: . Confirmation of the increased spatial variability for the upper and lower parts of the Boom Clay;

. Existence of a spatial structure and ability to propose a multivariate model linking hydraulic conductivities to grain size and geophysical logs (gamma ray and resistivity);

. Better precision of the multivariate model, the auxiliary variables allowing to provide more precise estimates for the target parameters;

. Ability to take into account the locally varying variability of target parameters, in order to provide an uncertainty envelope for the latter. In the more stable part of the Putte unit (first 30 meters above the Double Band), the confidence interval at 95% for Log(Kv) is equal to [-12.04 ; -11.43], around an average value of -11.75. This methodology can now be applied for the 3D modeling of hydraulic conductivities.

52 NIROND–TR 2012-01, January 2012

3.4 3D modeling

3.4.1 Methodology

Regarding the vertical resolution of the 3D model, there is an important vertical variability of K and GR values and it is difficult to have a vertical precision on data location less than 10- 15cm, which is huge compared to the thickness of the clayey/silty beds (sometimes 20cm). So, the vertical resolution of the 3D model, initially expected to be equal to 10cm, is decreased to approximately 1m, which is satisfying for subsequent use of this 3D hydraulic conductivity model. The size of the horizontal model mesh is set to 0.5km. Because of the scarcity of cored and sampled boreholes, an efficient 3D modeling approach definitely requires the integration of geophysical logs. As a consequence, the horizontal consistency between these logs is a key point. Due to the presence of various types of resistivity runs, it is not possible to build a global correlation model between hydraulic conductivities and this variable. Despite calibration issues, gamma ray logs are less subject to such inconsistencies. However, a preliminary additive correction has been applied on each borehole in order to have similar average GR values for the central part of the Boom Clay (Putte and Terhagen members). This correction may be interpreted as an indirect way to reduce the impact of GR calibration issues on K modeling. The only underlying assumption is that regional differences between GR log are only attributable to calibration issues. Under this assumption, the approach is fully justified. Of course, correcting these logs to a common average value makes impossible to identify regional trends from such corrected logs; this solution is however preferred to the one that would consist in working with raw GR curves. Indeed, working with raw GR curves leads to: . poor correlation level with hydraulic conductivities, as illustrated below,

. a 3D model with regional trends highly impacted by logging technical issues and variability between logs.

As illustrated on Figure 34, the resulting correlation between hydraulic conductivities and GR are much improved by the GR correction, the correlation coefficient increasing from 0.25 to 0.56 for Log(Kv) and from 0.39 to 0.62 for Log(Kh). Note that the outlier data from the top right diagram of Figure 34 comes from the Top of the Transition Zone, subject to increased variability of both GR and Log(Kv). Similarly, the group of brown points with large GR values on the top left diagram all come from Essen. An attempt has been made to consider a unique GR log of good quality for the entire area, avoiding to deal with potential inconsistencies between different GR curves. However, using the Zoersel GR log, which presents the best correlation levels with hydraulic conductivities, it has been observed that the resulting correlation level is slightly weaker (0.52 for Log(Kv) and 0.55 for Log(Kh)) than with the previous model (individual GR logs corrected to MOL).

NIROND–TR 2012-01, January 2012 53

Figure 34 – Scatter-diagrams of Log(Kv) (top, ordinate) and Log(Kh) (bottom, ordinate) versus raw GR (left, abscissa) and GR corrected to MOL (right, abscissa). Indication of correlation coefficient (rho).

54 NIROND–TR 2012-01, January 2012

Consequently, a multivariate model between Log(Kv), Log(Kh), d40 and GR corrected to Mol-1 is considered for the 3D modeling of hydraulic conductivities. The vertical part of the variogram model fitted is illustrated on Figure 35. A linear behavior is assumed for the horizontal variograms, due to the lack of available data to allow a reliable fit.

Figure 35 - Hydraulic conductivity (in logarithm) vertical variogram model for 3D modeling.

3.4.2 Results

A cross-section derived from the resulting 3D cokriging is illustrated on Figure 36. This section is globally orientated West-East (slightly dipping towards the South) and passes through 3 key boreholes: Doel at the West, Zoersel in the center part and Mol at the East. Note that, because of erosion, the top of the Boom Clay formation disappears when going towards the West. The cross-section illustrates important trends of vertical hydraulic conductivities. First, vertically one can notice the expected more permeable behavior of the Boom Clay Bottom unit (Belsele-Waas member) and, though less pronounced, of the Top one. Also, the slightly more permeable DB-level (Depth ~0m in the DB system) is visible. Laterally, a global decrease of Log(Kv) is remarkable from West to East. This can be

NIROND–TR 2012-01, January 2012 55 explained by the compaction increase as the Boom Clay goes deeper (in the original structural system) towards the East.

Figure 36 – Log(Kv) 3D model in the Double-Band geo-reference system: cross- section between Doel-2b, Zoersel and Mol. Location of boreholes with actual Kv data (o).

The following figures present Log(Kv) and Log(Kh) resulting model at the DB level. It is interesting to note that, the increasing trend towards the North in the central part of the area of interest is only due to boreholes without K samples (Meer-1, Sint-Lenaarts, Rijkevorsel and Merksplas). We therefore give all the predicting weight to GR curves in this area.

56 NIROND–TR 2012-01, January 2012

Figure 37 – Log(Kv) and Log(Kh) 3D model: horizontal section at DB level; display of integrated boreholes and Belgian border.

NIROND–TR 2012-01, January 2012 57

Figure 38 – Log(Kv) and Log(Kh) 3D models: standard deviations for horizontal section at DB level; display of integrated boreholes and Belgian border.

58 NIROND–TR 2012-01, January 2012

Figure 39 – Log(Kv) and Log(Kh) 3D model: horizontal section 20m above DB level; display of integrated boreholes and Belgian border.

3.4.3 Uncertainty envelope for Kv-Kh

(Co-)kriging results presented in the preceding paragraphs provided, for each target parameter, a most probable estimate together with an associated uncertainty. However, such techniques do not allow to quantify the local uncertainty attached to the estimated parameter nor to reproduce its real variability, as (co-)kriging are by construction smoothing this variability. An attempt has therefore been made to provide probabilistic realizations for the target parameters. Each realization will honor the initial data (up to the nugget effect), their statistical distribution and spatial variability model.

NIROND–TR 2012-01, January 2012 59

1D stochastic simulations have been performed. Several issues appeared from the analysis of results: vertical non stationarity, need of a Gaussian transformation which is difficult to parametrize in the present case. These simulation results are available in the Appendix. As a consequence, it has been decided not to perform 3D simulations to derive an uncertainty envelope for hydraulic conductivities over the area of interest. The uncertainty envelope has therefore been derived from the cokriging estimate and its attached standard deviation, as explained in §3.3.5. Due to the scarce sampling of some boreholes, for instance Essen-1 and Doel-2b, deriving a robust model for the local variability coefficient A(x) is difficult. As illustrated on Figure 40, a vertical smoothing of A(x) results (derived from 3D cross-validation) leads to slightly different coefficients depending on the borehole: the well sampled Zoersel gives the lower A(x) values for Log(Kv), while Essen-1 gives higher values. The interpolation of A(x) in the upper and lower units of the Boom Clay only relies on 2-3 points and is consequently not robust. Interpolating laterally these curves is performed using a linear kriging. The resulting A(x) 3D models are then applied on the cokriging standard deviation models. Figure 41 illustrates on a vertical cross-section the effect of A(x) model on standard deviation, for Log(Kv)

Figure 40 – Local variability coefficient curves resulting from the 3D modeling, for Log(Kv) (left) and Log(Kh) (right).

Using these models, a confidence interval is derived for Log(Kv) and Log(Kh) in each litho- stratigraphic unit. The results, summarized in Table 16, are computed only from areas where the K modeling is precise (selection based on cokriging standard deviation values). The confidence interval bounds obtained for the upper and lower units are not realistic, especially for Log(Kh) modeling. This is most probably due to the local fitting of the variability coefficient A(x) in these units. One also has to note that confidence interval of at least 95% (and possibly 99%) is really conservative and also includes highly non probable values. Maximum values at a 95% (or more) confidence level are equal for the Putte member, which is the less permeable unit, to –9.71 for Log(Kv) and –8.53 for Log(Kv).

60 NIROND–TR 2012-01, January 2012

Table 16 – Probable values and confidence interval bounds at 95% or more for Log(Kv) and Log(Kv) in each Boom Clay unit.

Log(Kv) Log(Kh) Unit IC min Probable IC max IC min Probable IC max Transition Zone -13.38 -11.17 -6.86 -14.98 -10.77 -2.44 Putte -12.75 -11.37 -9.71 -13.65 -11.23 -8.53 Terhagen -13.23 -11.34 -8.87 -14.72 -11.23 -8.00 Belsele- Waas -13.24 -10.70 -7.75 -15.38 -10.06 -4.28

Figure 41 – 3D standard deviation models obtained for Log(Kv): before (top) and after (bottom) applying the local variability coefficient. Location of main boreholes.

NIROND–TR 2012-01, January 2012 61

3.4.4 Results in original geo-reference system The obtained results are finally projected back in the real geo-reference system, using the interpolated models for the Double Band surface, the Boom thickness and the Top Boom surface (eroded). The resulting models are displayed hereafter.

Figure 42 – 3D Log(Kv) model in original geo-reference system.

62 NIROND–TR 2012-01, January 2012

Figure 43 – 3D Log(Kv) standard deviation model in original geo-reference system.

NIROND–TR 2012-01, January 2012 63

Figure 44 – 3D Log(Kh) model in original geo-reference system.

64 NIROND–TR 2012-01, January 2012

Figure 45 – 3D Log(Kh) standard deviation model in original geo-reference system.

NIROND–TR 2012-01, January 2012 65

Figure 46 – 3D Log(Kv) model in original geo-reference system – complete view.

66 NIROND–TR 2012-01, January 2012

4 Modeling of migration parameters

4.1 Methodology

Migration parameters are available on boreholes Mol-1, Doel-2b and Essen-1. However, it is important to keep in mind that the sampling effort completely differs from Mol-1 (41 migration data) to Doel-2b (10 samples) and Essen (7 samples).

4.2 Statistical analysis

Average values of diffusion coefficient Dp and diffusion accessible porosity R per unit and borehole are displayed in Table 17 for the two tracers I and HTO. Discussing these statistics is difficult due to the limited amount of samples. Actually, only Mol deserves a more precise analysis. Diffusion coefficients are rather homogeneous for the entire Boom Clay, around 2.3 10-10 m².s-1, excepted for Belsele-Waas for which it is clearly higher (4.1 10-10 m².s-1). R values range between 0.34 for B-W and Terhagen to 0.37 for the Transition Zone and 0.39 for the Putte member.

Table 17 – Average values for migration parameters on sampled boreholes: apparent diffusion coefficient Dp [m2.s-1] and ηR [-]. HTO Iodide Unit Borehole Nb Dp R Dp R Mol 13 2.4 E-10 0.37 1.6 E-10 0.16 Transition Doel 0 Zone Essen 2 2.4 E-10 0.39 2.9 E-10 0.24 Mol 17 2.2 E-10 0.39 1.3 E-10 0.17 Putte Doel 6 2.7 E-10 0.38 1.6 E-10 0.23 Essen 4 1.9 E-10 0.46 1.7 E-10 0.26 Mol 7 2.3 E-10 0.34 1.3 E-10 0.15 Terhagen Doel 2 3.2 E-10 0.40 2.0 E-10 0.26 Essen 1 2.7 E-10 0.35 2.8 E-10 0.24 Mol 4 4.1 E-10 0.34 3.6 E-10 0.17 Belsele-Waas Doel 2 2.9 E-10 0.41 1.6 E-10 0.27 Essen 0

In the following, only the results derived from HTO tracer are illustrated for sake of simplicity, results for Iodide being similar.

NIROND–TR 2012-01, January 2012 67

Table 18 summarizes correlation levels of migration parameters (tracer HTO) with hydraulic conductivities and other auxiliary variables. Focusing on Mol, for which the number of migration data leads to an increased confidence in statistical results, we see that the only variable strongly correlated to one of the migration parameters if Log(Kv), with Dp. All the other correlation levels are negligible or intermediate, except on Essen but with a poor confidence due to the limited number of data (7 samples). Consequently, the relationship between Kv and Dp is more precisely assessed. The scatter- diagram between the two variables, though promising, shows that individual boreholes present differing relations between Kv and Dp. Also, the correlation between Dp and ηR is illustrated on Figure 48, showing that a joint modeling of these parameters seems to be useless.

Table 18 – Correlation analysis between apparent diffusion coefficient Dp [m2.s-1] and ηR [-] for HTO and auxiliary variables, for Mol-1 (left) and Doel-2b boreholes (right).

Dp R Log(Kv) d40 GR Res Mol Dp 1 -0.43 0.89 0.64 -0.61 0.59 R -0.43 1 -0.25 -0.34 0.21 -0.22 Doel-2b Dp 1 -0.31 0.23 -0.28 0.04 0.26 R -0.31 1 0.00 0.11 -0.34 -0.17 Essen Dp 1 -0.90 0.94 0.57 -0.41 0.18 R -0.90 1 -0.89 -0.81 0.48 -0.46

Figure 47 – Scatter diagrams between log (Dp HTO) (abscissa) and log (Kv) (ordinate) for the three sampled boreholes

68 NIROND–TR 2012-01, January 2012

Figure 48 – Scatter diagrams between log (Dp HTO) (abscissa) and R HTO (ordinate) for the three sampled boreholes (same colors than Figure 47).

4.3 Dp Modeling

Given the high correlation level between Dp and Log(Kv), it is suggested to use the interpolated vertical hydraulic conductivity as a collocated variable for the modeling of Dp. It has been checked that, considering interpolated Log(Kv) instead of actual Log(Kv) data for the auxiliary variable still leads to a correlation level larger than 0.8 with Log(Dp HTO). Collocated cokriging takes into account the entire Log(Kv) interpolated profile to help the modeling of Dp. The bivariate variogram model is illustrated on Figure 49. Consistently with Log(Kv), the variogram model is still fitted using a nugget effect and an exponential component with range 35m.

NIROND–TR 2012-01, January 2012 69

Figure 49 – Mol-1: Log(Dp) bivariate variogram model with Log(Kv).

1D interpolated results clearly illustrate the impact of the Log(Kv) profile, particularly on Top and Base parts of the Boom Clay. Due to the high correlation between the variables, the reduction of uncertainty when switching from kriging to cokriging is substantial. As illustrated by Figure 51 and Table 19, cross-validation confirms the added value of collocated cokriging compared to kriging.

70 NIROND–TR 2012-01, January 2012

Kriging

Cokriging Kriging

60 60 60

60 60 60 Cokriging

Transition Zone Dp data

40 40 40

20 20

Putte 20

20 20 20

Z (m - ref DB) ref - (m Z

0 0

DB 0

0 0 0

Terhagen

-20 -20 -20

Belsele-Waas

-9.8 -9.6 -9.4 -9.2 -9.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Log(Dp) Standard Dev. of Log(Dp) Figure 50 – Mol-1: Log(Dp) modeling results (left) and associated standard deviations (right).

Figure 51 – Mol-1: Cross-validation results for Dp modeling using kriging (+) and collocated cokriging with interpolated Log(Kv) (x): estimates (abscissa) versus true values (ordinate). Indication of the 1st bisector (x=y).

NIROND–TR 2012-01, January 2012 71

Table 19 – Mol-1: Cross-validation results for Dp modeling using kriging and collocated cokriging with interpolated Log(Kv): correlation coefficient (rho), average error (bias) and variance of standardized error (Var std err).

Log(Dp HTO) Criterion Kriging Cokriging

Rho. 0.39 0.75 Bias 1.3 10-3 1.0 10-3 Var. Std. Err. 2.17 2.57 Despite the limited number of boreholes with migration data, a 3D model could be considered because of the high correlation level with hydraulic conductivities. However, this correlation is varying a lot between boreholes. Consequently, a plausible 3D model for Dp cannot be computed for the time being.

4.4 R Modeling

Due to the lack of significantly correlated auxiliary variables, only an ordinary kriging of R is applied and displayed on Figure 53, using the variogram model of Figure 52. Cross- validation shows the importance of the kriging smoothing effect, reinforced because of the high nugget effect (see Figure 51).

72 NIROND–TR 2012-01, January 2012

60 60

40 40

20 20

Z (m - ref DB) ref - (m Z

0 0

-20 -20

0.30 0.35 0.40 0.45 R Figure 52 – Mol-1: R variogram model. Figure 53 – Mol-1: R data and kriging result.

Figure 54 – Mol-1: Cross-validation results for R modeling using kriging: estimates (abscissa) versus true values (ordinate). Indication of the 1st bisector (x=y).

NIROND–TR 2012-01, January 2012 73

5 Sampling recommendations for future campaigns

5.1 Methodology This project allowed an in-depth analysis of both target parameters and auxiliary variables measured in the Boom Clay: grain size data and geophysical logs. The results obtained after the geostatistical analysis and interpolations, though meaningful, put to the fore several uncertainties attributable to the following reasons:

. a lack of data in certain areas, leading to potentially non robust correlation and spatial variability models,

. an important heterogeneity of the database itself.

This chapter aims to summarize the main uncertainties that still exist regarding collection of geophysical logs and the data collection relative to the target parameters. Sampling recommendations for future campaigns are given relative to the desired objective;

. for 1D and 3D basin modeling using target parameters and geophysical logs,

. for 3D modeling using geophysical logs.

Applying these recommendations would progressively lead to the reduction of remaining uncertainties about hydrogeological parameters within the Boom Clay in Belgium. Finally some general conclusions are drawn.

5.2 Geophysical logging

Geophysical logs are the main source of information for transferring observations from scarce cored boreholes to the entire area of interest. Issues and recommendations are closely linked, the second ones aiming at reducing the observed issues. They are therefore presented together and as a function of the desired objective. Sampling recommendations for geophysical logging depend on their expected goal: help in the 1D modeling of target parameters within a cored borehole, or provide basin modeling and mapping of local trends in areas without cored/sampled boreholes.

5.2.1 For 1D vertical modeling

As far as we focus on 1D modeling, the availability of samples with measurements of target parameters allows rescaling the logs and therefore reduce the risk of uncertainties coming from calibration or technical issues. Regarding Gamma Ray, the only recommendation would

74 NIROND–TR 2012-01, January 2012

be to have a sufficiently large measuring time to reduce the uncertainty attached to the estimated number of disintegrations; indeed, several available logs were useless because of very high variability due to a short measuring time. Regarding Resistivity logs, classical normal resistivity logs and induction logs appeared well acceptable on several boreholes. Obviously, a precise reporting of the sampling conditions is highly recommended, to trace the potential influence of external factors on the logs.

5.2.2 For 3D basin modeling

Things could be much more improved if we now focus on performing 3D modeling, in order to transfer target parameters from scarcely distributed cored/sampled boreholes to the entire area of interest. To achieve this, the fundamental point is to ensure the quantitative consistency and repeatability between logging campaigns: systematic proper calibration of tools, systematic use of the same tools. Indeed, different tools are more or less influenced by numerous external factors, which is particularly true for resistivity logs. As a consequence, taking into account gamma ray or resistivity logs derived from different tools is almost impossible without associated cored data to rescale the resulting logs. The latter being impossible, the similarity of logging campaigns on each new borehole is the most important recommendation. In the present project, the lack of similarity between logs led to the withdrawal of numerous available logs.

5.3 Target parameters

5.3.1 Issues and general sampling recommendations

Following the previous chapters, it is possible to emphasize several issues and draw sampling recommendations about the target parameters: Kv/Kh measurements

. The first issue is obviously related to the small number of cored boreholes which makes difficult to confirm regional trends. There is a need for an additional cored/sampled borehole in the clearly under-sampled central part of the Boom Clay, around Sint-Lenaarts (not cored); the location of this additional borehole is supported by the kriging standard deviation results, which show higher uncertainty values in this area. Also, a cored borehole more towards Mol would allow validating a regional trend, with decreasing K values when moving towards Mol and increasing variability in Putte and Terhagen when moving towards Weelde; this borehole could

NIROND–TR 2012-01, January 2012 75

be ideally placed at the gravity center of a triangle joining Weelde, Zoersel and Mol. This recommendation is consistent with Yu et al. (2011), where it is stated that “the impacts of compaction (burial depth) and lithology on the lateral variation of hydraulic conductivity need further investigations at the region scale”.The priority which has to be given to each of these boreholes should also depend on the potential importance of a particular regional area in terms of future set-up of the deep disposal facility.

Figure 55 – Recommended locations for additional cored boreholes with K sampling. Contour of the northern Belgian border and southern limit of the Boom Clay.

. There is no need for acquiring numerous samples in the Putte - Terhagen members in future boreholes, as sampled on Zoersel or Weelde, because of the low variability of target parameters inside these units.

. As far as possible, it is recommended to analyze at least a few similar layers on future cored boreholes: similarity of sampled levels is important for analyzing regional trends. For instance, systematic sampling and analysis of key layers, such as the Double Band, should be performed.

. More samples should be analyzed in transitions areas, to provide a better understanding of the behavior of target parameters at these depths (Transition Zone and Belsele-Waas). Indeed, these areas, an increased variability of the target parameters has been observed.

. A better understanding at small scale (a few centimeters) of the relationship between hydraulic conductivities, grain size and geophysical logs would be valuable and precious, in order to address more easily positioning errors and related uncertainties on the available dataset.

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Migration parameters: similar recommendations than for hydraulic conductivities are not necessarily requested, though one aims at reaching similar goals. Indeed, the use of correlation between Dp and vertical hydraulic conductivity, if confirmed on forthcoming boreholes using a few samples from each litho-stratigraphic unit, could interestingly limit the need for numerous analysis of this parameter. This is however not the case for R.

Grain size data: despite being the most robust covariate in terms of point-to-point correlation, it has been observed that it is difficult to calibrate logging tools in boreholes without real K data.

5.3.2 Validation for 1D modeling

As previously discussed, 3D modeling will mainly benefit from well calibrated gamma ray logs and additional cored boreholes. Consequently, the validation of practical recommendations, in terms of what could be a reasonable K sampling on future boreholes, is performed only in 1D. The analysis is based on Zoersel borehole, which is particularly well sampled. The methodology aims at decreasing the number of Kv (34 available) and grain size (152 available) measurements. The spatial variability of target parameters is assumed to be known, to avoid introducing additional sources of uncertainty. This assumption is reasonable, given the lateral continuity of the Boom Clay. The sensitivity of Kv modeling to sampling reduction is evaluated in two ways:

. first, by assuming that only 50% of Kv samples is available (17 samples); the modeling is tested on the remaining 17 samples (see Figure 57).

. then, by testing the impact of sampling reduction on the entire 1D model, by reference to the Kv model obtained by cokriging with all available measurements.

In each case, several criteria allow to evaluate the impact of sampling reduction in terms of Kv model’s precision (for the entire 1D model, the “true” value corresponds to the Kv model obtained using all available data):

. correlation coefficient between true values and estimates,

. min, average and max errors (true value – estimate),

. min, average and max quadratic errors.

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5.3.2.1 Validation on 17 Log(Kv) actual samples

Four Log(Kv) models are compared, all of them assuming that only 17 Kv samples are available:

. using all available auxiliary variables: d40, Gamma Ray and Resistivity curves,

. using all available auxiliary variables, but with d40 sub-sampled in order to keep only one grain size measurement every 2meters (42 samples instead of 152),

. using only geophysical logs (GR and Res), combined using linear regression,

. using only Gamma Ray log.

All these prediction models rely on the same spatial variability model, derived from all available data. By doing this, we do not take into account the robustness lost due to the decrease of the sampling conditions. Table 20 and Figure 56 describe the results, in terms of prediction errors at 17 validation samples and by displaying scatter-diagrams between actual Log(Kv) values and estimates. Table 20 – Statistical analysis of prediction errors at the 17 Log(Kv) validation samples, using various auxiliary variables: correlation coefficient, min/mean/max errors and quadratic errors.

Correlation Error Quadratic Error Auxiliary variables coefficient Min Mean Max Min Mean Max d40 - GR - Res 0.955 -0.212 0.060 0.227 0.000 0.017 0.052 d40 (2m sampling) 0.832 -0.505 0.017 0.408 0.000 0.046 0.255 GR - Res 0.723 -0.523 0.017 0.609 0.000 0.076 0.371 GR 0.713 -0.718 0.043 0.621 0.000 0.072 0.516

As expected, the Log(Kv) model using only the Gamma Ray log gives the worst results, whatever the criterion used (excepted in terms of mean error). It is however interesting to note that the highest errors with this model are still below one order of K magnitude. Integrating the Resistivity curve slightly improves the result, but it is the integration of grain size data that has a significant impact in terms of prediction quality improvement. It is however interesting to note that, if grain size are not available at Log(Kv) locations, the quality of results decreases. Due to the presence of thin silty-clayey beds, knowing d40 at a 2m vertical resolution only is not enough to provide meaningful grain size values. This drawback of grain size data will have to be investigated further, as it is obviously not possible to analyze grain size throughout the entire log. Scatter-diagrams between true and actual values confirm these comments. The sensitivity of the estimates for the high Log(Kv) value located in Belsele-Waas member is clear. Also, it can be noted that d40 data allow more precise estimates even with a 2m resolution only.

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Figure 56 – Zoersel: Log(Kv) estimates using varying auxiliary variables (ordinate), by reference to the actual Log(Kv) data at 17 validation locations. First bisector and linear correlation coefficient indicated.

5.3.2.2 Validation on vertical 1D Log(Kv) model

The same validation approach has been reproduced but now on the entire Zoersel Boom Clay thickness, by comparison with the Log(Kv) model obtained with all available data. The following models are compared:

. using all available auxiliary variables, but with d40 sub-sampled in order to keep only one grain size measurement every 2 meters,

. using only 17 Log(Kv) samples and all available auxiliary variables, but with d40 sub-sampled in order to keep only one grain size measurement every 2 meters,

. using only geophysical logs (GR and Res), combined using linear regression,

. using only Gamma Ray log.

The resulting 1D models are illustrated on Figure 57. Compared to the reference model (black), the other curves show more or less similar trends. The smoother behavior of the

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model using only Gamma Ray log is noticeable; it can be explained by the high nugget effect

affecting the Gamma Ray at this 1m vertical resolution. 60

Transition Zone 40 CK d40-GR-Res CK d40(sub2m)-GR-Res CK 17samples d40(sub2m)-GR-Res CK GR-Res CK GR

Log(Kv) sel 17 samples 20 Log(Kv) 17 complementary

Putte Z (m - ref DB) ref - (m Z

DB 0

Terhagen -20

Belsele-Waas

-11 -10 -9 -8

Log(Kv) - Zoersel

Figure 57 – Zoersel: Log(Kv) 1D models using varying auxiliary variables.

Statistical results on prediction errors are summarized in Table 21. It is important to note that only 50% of Zoersel Kv samples (17 instead of 34) allow to obtain low prediction errors, confirming the importance of auxiliary variable for K modeling. Having decreased the resolution of d40 data leads to errors that can reach 0.4 in Log(K). These errors are quite comparable to those obtained without grain size data. This confirms the huge importance of good quality geophysical logs. Furthermore, without Resistivity logs, quadratic errors show that the prediction quality is poorer; Figure 58, shows that this is particularly the case for the central units, with low K values.

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Table 21 – Statistical analysis of prediction errors on the Log(Kv) vertical model using various auxiliary variables, by comparison with the model obtained with all available data: correlation coefficient, min/mean/max errors and quadratic errors. Auxiliary variables Correlation Error Quadratic Error coefficient Min Mean Max Min Mean Max 17samples Kv - d40 (2m) - GR - Res 0.989 -0.255 0.013 0.368 0.000 0.012 0.135 All samples Kv - d40 (2m) - GR - Res 0.993 -0.205 0.006 0.401 0.000 0.008 0.161 All samples Kv - GR - Res 0.991 -0.203 0.031 0.457 0.000 0.018 0.209 All samples Kv - GR 0.978 -0.620 0.021 0.560 0.000 0.030 0.384

Figure 58 – Zoersel: Log(Kv) 1D models using varying auxiliary variables (ordinate), by reference to the cokriging model using all available data (abscissa). First bisector and linear correlation coefficient indicated.

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5.3.2.3 Conclusions about sampling recommendations for 1D sampling

Testing various modifications of sampling availability for the modeling of Log(Kv) on Zoersel allowed to confirm several key recommendations:

. The importance of good quality geophysical logs (Gamma Ray and Resistivity),

. The limited added value of grain size data in terms of K spatial prediction throughout the Boom Clay, because of the small-scale variability of both K and grain size due to the silty/clayey beds. Indeed, grain size gives a good indication on K at the location of the core only and does not allow a sound prediction of K values at neighboring locations. However, in terms of statistical analysis, grain size measurements interestingly allow to precise K estimates, using a correlation model between these variables.

These remarks are based on Zoersel borehole, assuming that the spatial variability model linking together the variables is known. This assumption seems reasonable given the current knowledge we have about target parameters but will be interestingly validated on future cored boreholes. Establishing more precise sampling recommendations (number and location of cores to be analyzed) for future cored boreholes will require further discussions with ONDRAF-NIRAS and SCK•CEN, in order to precise and validate the expected objectives of such a borehole: validate a regional K trend, refine the understanding of K small-scale variability, etc.

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6 General conclusions

Being currently investigated as potential host formation for deep disposal of high-level and/or long-lived radioactive waste in Belgium, the Boom Clay formation needs to be precisely characterized in terms of hydrogeological parameters. Focusing on hydraulic conductivities and migration parameters sampled on a few key boreholes, this project aims at illustrating the ability of geostatistics to provide a suitable framework for analyzing the transferability of these regionalized variables. The methodology consisted of the following points: . In-depth analysis of the database consistency has been a key aspect of this methodology, as the database presents an important heterogeneity level (various types of both core measurements and geophysical logs) and covers only scarcely the large area of interest.

. Meaningful vertical estimates of target parameters have been obtained on sampled boreholes by applying classical geostatistical algorithms (kriging/cokriging), together with an estimate of the associated uncertainty. The quality of the estimates is largely improved by the use of auxiliary variables: geophysical logs (Gamma Ray and Resistivity) and grain size data.

. 3D modeling has been performed to capture regional vertical and lateral trends over the area of interest. Horizontal continuity is largely assumed, due to the small number of cored and sampled boreholes (5 in the most favorable case). Due to the global dipping and thickness increase of the Boom Clay towards the North-East, this 3D modeling required a preliminary horizontalization, in order to laterally correlate consistent data. The Double Band has been chosen as a reference as it can be easily identified, even on boreholes that have not been cored. An uncertainty envelope has been derived for K modeling, providing a confidence interval for possible Kv/Kh values throughout the Boom Clay. This 3D modeling has not been performed for migration parameters due to the insufficient number of borehole samples.

The final part of the project aimed at deriving, from the achieved work, recommendations for future sampling campaigns. Locations for future cored boreholes have been suggested and the added value of each type of data has been discussed, based on Zoersel borehole which is favorable in terms of sampling density. Several scientific papers about this work have been presented at international conferences [Jeannee et al., 2009, 2010].

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7 Bibliography

Labat S., Wemaere I., Marivoet J., Maes T. (2008) Herenthout-1 and Herenthout-2 borehole of the hydro/05neb campaign: technical aspects and hydrogeological investigations, SCK•CEN External Report ER-59, April 2008.

Chilès JP. (1990) The use of External-drift kriging for designing a piezometric observation network, In Geostatistical Methods: Recent Developments and Applications in Surface and Subsurface Hydrology – Proceedings of an International Workshop help at Karlsruhe, Germany, from 17 to 19 July 1990, Ed. Bàrdossy, UNESCO, Paris 1992, IHP-IV, SC/92/WS/29, pp. 11-20.

Chilès JP., P. Delfiner (1999) Geostatistics – Modeling Spatial Uncertainty, Wiley series in Probability and Statistics, New-York, 695p.

Jeannée N., Berckmans A., Wouters L., Deraisme J., Chilès JP (2009) Assessing the spatial continuity of low permeability media for deep waste disposal: the Boom Clay case, In Proceeding of the Global 2009 congress, in press.

Jeannée N., Berckmans A., Wouters L., Deraisme J., Chilès JP (2010) Quantifying the transferability of hydraulic parameters using geostatistics: the Boom Clay case, Accepeted for oral presentation in Proceedings of the conference « Clays in Natural & Engineered Barriers for Radioactive Waste Confinement », Nantes, March 2010.

Labat S., Marivoet J., Wemaere I., Maes T. (2008) Essen-1 borehole of the hydro/05neb campaign: technical aspects and hydrogeological investigations, SCK•CEN External Report ER-68.

Lefranc M. (2007) Variations et variabilité spatio-temporelle des argillites callovo- oxfordiennes de Meuse/Haute-Marne – Valorisation géostatistique de données diagraphiques, Thèse de Doctorat, Ecole des Mines de Paris, 275 p.

Mertens J. (2005) Comparison of interlayers in the Boom Clay throughout the Campine area, Internal note ref. 2005-0059 (rev. 0), ONDRAF/NIRAS.

Vandenberghe N., M. Dusar, P. Laga & J. Bouckaert (1988) The Meer well in North Belgium, Mémoires pour servir à l’Explication des Cartes Géologiques et Minières de la Belgique, Mémoire N°25, Service Géologique de Belgique, 23 p.

Wemaere I., Marivoet J., Labat S., Beaufays R., Maes T. (2002) Mol-1 borehole (April- May 1997) – Core manipulations and determination of hydraulic conductivities in the laboratory, SCK•CEN Restricted Contract Report R-3590.

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Wemaere I., Marivoet J., Labat S., Beaufays R., Maes T. (2004) Rijkevorsel borehole of the hydro/05neb campaign: technical aspects and hydrogeological investigations, SCK•CEN Restricted Contract Report R-3930.

Wemaere I., Marivoet J., and Labat S. (2008) Hydraulic conductivity of the Boom Clay in north-east Belgium based on four core-drilled boreholes. Physics and Chemistry of the Earth, Parts A/B/C, Volume 33, Supplement 1, 2008, Pages S24-S36, doi:10.1016/j.pce.2008.10.051.

Wouters L. (1995) Boring Dessel-1 – Algemene Technische Synthese, Internal note ref. 95- 4608, ONDRAF/NIRAS.

Yu L., Gedeon M., Wemaere I., Marivoet J., De Craen M. (2011) Boom Clay Hydraulic Conductivity – A synthesis of 30 years of research, SCK•CEN External Report ER-122.

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Appendix A: Final Database

A.1 Organization of the file system The final database is transmitted to ONDRAF as a folder, named “Database”, of the main ISATIS project folder (see Appendix E).

Figure 59 – Overview of database organization.

Data Files: . Available target parameters data on the Boom Clay formation

. Available grain size data considered on the Boom Clay formation

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A.2 Boom Geometry Table 22 – Location of boreholes and depth (in mBDT) of the main geological top/base horizons and DB. Borehole Municipality X Y BaseBW TopBW TopTerh TopPutte TopTZ TopBoom Approx.DB DB 18-W-265 ARENDONK 197390 222680 -301.76 -301.76 31-E-338 BALEN 208980 208050 -307.78 -304.60 28-E-725 BORGERHOUT 155600 212100 -84.09 15-E-267 BRASSCHAAT 161725 224550 -206.05 -185.35 -171.45 -145.90 -167.26 -166.30 DESSEL-1 DESSEL 199177 213382 -293.20 -279.10 -263.15 -216.40 -191.10 -191.10 -259.89 -260.10 DOEL2B DOEL 142239 224443 -115.00 -104.75 -91.80 -64.50 -88.29 -88.45 43-W-326 EDEGEM 152900 205475 -48.04 -48.04 ESSEN-1 ESSEN 156663 238672 -281.10 -259.50 -237.62 -200.00 -153.00 -153.00 -232.25 -232.25 30-W-372 HERENTALS 181885 208886 -187.50 -168.20 -151.80 -106.20 -89.00 -148.30 -148.30 45-W-337 HERENTALS 185001 207740 -150.15 60-W-238 HULSHOUT 180709 196786 -92.60 -78.50 -64.40 -27.00 -16.50 -61.40 -60.80 47-W-264 Kerkhoven 213939 206366 -329.56 -329.60 47-W-260 KOERSEL,_Hem. 215223 198267 -214.35 -213.65 43-E-210 KONTICH 156020 200694 -35.25 -34.70 31-E-341 Lommel 209640 215490 -414.77 SCK 12 Lommel 212425 217790 -502.50 -489.10 -474.25 -428.75 -399.75 -399.75 -471.25 -471.25 7-E-205 Meer 177378 237304 -339.60 -322.50 -308.60 -249.40 -230.60 -230.60 -303.78 -303.50 17-W-265 Merksplas 181938 225856 -298.20 -280.40 -265.50 -210.00 -191.00 -191.00 -261.52 -261.40 17-W-280 Merksplas 182012 225742 -260.80 31-W-237 MOL 198395 211710 -235.88 SCK-15 SCK-15 198406 211730 -271.50 -255.50 -239.70 -192.80 -167.30 -167.30 -236.18 MOL-1 MOL 200191 211652 -292.50 -277.70 -262.05 -217.00 -190.30 -190.30 -258.86 -259.45 27-W-137 NIEUWK. 136578 210721 -40.55

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29-W-378 OELEGEM 164455 212040 -113.16 9-W-147 Poppel 200078 235542 -470.00 -451.00 -435.75 -372.60 -352.00 -352.00 -431.01 -430.80 43-W-301 REET 152249 200614 -43.00 -36.90 -28.20 -21.75 -26.35 -26.40 DZH#14 RIJKESVORSEL 175610 227356 -280.20 -259.60 -244.20 -197.00 -239.70 -239.55 42-W-365 ST.NIKLAAS 134739 205061 -20.81 42-W-361 ST.NIKLAAS 134750 207150 -28.14 DZH#15 ST-LENAARTS 172063 228544 -265.00 -247.10 -233.10 -209.90 -228.60 -228.50 61-W-171 TESSENDERLO 201715 195593 -56.67 SCK ? Turnhout 190600 221400 -311.30 -292.40 -276.60 -219.30 -198.40 -198.40 -272.60 -272.60 42-W-362 WAASMUNSTER 132653 203015 -11.28 -11.24 WEELDE WEELDE 190649 231963 -389.80 -368.40 -351.30 -291.40 -273.60 -273.60 -346.75 -346.75 45-W-348 WESTERLO 185030 199690 -138.80 -121.60 -106.80 -68.20 -57.00 -103.88 -103.20 60-W-254 WESTMEERBEEK 183990 195730 -64.86 -65.00 15-E-298A WUUSTWEZEL 160165 227770 -175.02 -176.30 ZOERSEL ZOERSEL 173321 214841 -188.10 -179.10 -159.80 -112.50 -90.00 -90.00 -156.00 -156.00 HERENTHOUT HERENTHOUT 175304 202909 -130.50 -112.50 -92.50 -49.20 -88.00 -88.00

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A.3 Reminder on resistivity logging (electrical methods) The information provided below mainly comes from the US Department of Transportation website (http://www.cflhd.gov/AGM/index.htm). Normal resistivity logs are widely used in groundwater hydrology, even though the long normal log has become rather obsolete in the oil industry. The principles of measuring resistivity are illustrated in Figure 60. If 1 amp of current from a 10-V battery is passed through a 1-m3 block of material, and the drop in potential is 10 V, the resistivity of that material is 10 m. The current is passed between electrodes A and B, and the voltage drop is measured between potential electrodes M and N, which, in the example, are located 0.1 m apart-, so that 1 V is measured rather than 10 V. The current is maintained constant, so that the higher the resistivity between M and N, the greater the voltage drop will be.

Figure 60 - Principles of measuring resistivity in Ohm-meter; resistivity equal to 10 Ohm-meter in the example. For normal-resistivity logging, electrodes A and M are located in the well relatively close together, and electrodes B and N are distant from AM and from each other, as shown on the previous figure. Electrode configuration may vary in equipment produced by different manufacturers. The electrode spacing, from which the normal curves derive their name, is the distance between A and M, and the depth reference is at the midpoint of this distance. The most common AM spacings are 40 cm (16 in – short normal) and 162 cm (64 in – long normal); however, some loggers have other spacings available, such as 10, 20, 40 and 81 cm (4, 8, 16, and 32 in). The distance to the B electrode, which is usually on the cable, is approximately 15 m; it is separated from the AM pair by an insulated section of cable. The N electrode usually is located at the surface, but in some equipment, the locations of the B and N electrodes may be reversed. The volume of investigation of the normal resistivity devices is considered to be a sphere, with a radius approximately twice the AM spacing. This volume changes as a function of the resistivity, so that its size and shape are changing as the well is being logged. Long normal response is affected significantly by bed thickness; this problem can make the logs quite difficult to interpret.

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Lateral logs are made with four electrodes like the normal logs but with a different configuration of the electrodes. The potential electrodes M and N are located 0.8 m apart; the current electrode A is located 5.7 m above the center (O) of the MN spacing in the most common petroleum tool, and 1.8 m in tools used in groundwater. Lateral logs are designed to measure resistivity beyond the invaded zone, which is achieved by using a long electrode spacing. They have several limitations that have restricted their use in environmental and engineering applications. Best results are obtained when bed thickness is greater than twice AO, or more than 12 m for the standard spacing. Lateral logs usually difficult to interpret. Focused resistivity systems were designed to measure the resistivity of thin beds or high-resistivity rocks in wells containing highly conductive fluids. (ex : « guard » log, « laterolog ») Induction logging devices originally were designed to make resistivity measurements in oil-based drilling mud, where no conductive medium occurred between the tool and the formation. The basic induction logging system is shown in Figure 61. A simple version of an induction probe contains two coils: one for transmitting an AC current, typically 20 to 40 kHz, into the surrounding rocks, and a second for receiving the returning signal. The transmitted AC generates a time-varying primary magnetic field, which induces a flow of eddy currents in conductive rocks penetrated by the drill hole. These eddy currents set up secondary magnetic fields, which induce a voltage in the receiving coil. That signal is amplified and converted to DC before being transmitted up the cable. Magnitude of the received current is proportional to the electrical conductivity of the rocks. Induction logs measure conductivity, which is the reciprocal of resistivity. Additional coils usually are included to focus the current in a manner similar to that used in guard systems. Induction devices provide resistivity measurements regardless of whether the fluid in the well is air, mud, or water, and excellent results are obtained through plastic casing. The measurement of conductivity usually is inverted to provide curves of both resistivity and conductivity. The unit of measurement for conductivity is usually milliSiemens per meter (mS/m). Calibration is checked by suspending the sonde in air, where the humidity is low, in order to obtain a zero conductivity. A copper hoop is suspended around the sonde while it is in the air to simulate known resistivity values. The volume of investigation is a function of coil spacing, which varies among the sondes provided by different service companies. For most tools, the diameter of material investigated is 1.0 to 1.5 m; for some tools, the signal produced by material closer to the probe is minimized.

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Figure 61 - System used to make induction logs.

Induction logs provide high-resolution information on lithology through casing and are excellent for this purpose when combined with gamma logs.

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Appendix B: Correlation analysis on Kv and Kh B.1 Correlation with grain size data Correlation diagrams are described hereafter for various ONDRAF- NIRAS/SCK•CEN boreholes.

Figure 62 - Scatter diagram between vertical hydraulic conductivity (in logarithm, abscissa) and grain size data d40 (m, in ordinate) for each litho-stratigraphic unit of Mol-1 borehole.

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Figure 63 - Scatter diagrams between vertical hydraulic conductivities (ordinate, in logarithm) and grain size data d40 (m, in abscissa) for Mol (left) and Essen (right) boreholes. Samples of interest represented in blue, using triangles for the Belsele- Waas member.

Figure 64 - Scatter diagrams between vertical (left) and horizontal (right) hydraulic conductivities (in logarithm) and grain size data d40 (m, in abscissa) for Weelde (top) and Zoersel (bottom) boreholes. Samples of interest represented in blue, respectively using circles if they are located in the Transition Zone and triangles for the Belsele- Waas member.

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B.2 Correlation with geophysical logs Mol borehole Correlation levels are described in table hereafter. Values are not completely robust as it sometimes depend on 1 point. Note that GR from ait4 is better correlated with Log(Kv) even though elan and rockclass curves more consistent (see Figure 7). Table 23 – Linear correlation coefficients for Mol-1 borehole between hydraulic conductivities (in logarithm) and geophysical tools: gamma ray (GR) and Resistivity (Res). Tool name indicated between brackets. Log(Kv) Log(Kh) Run GR Res GR Res 0.65 (MSFL) 0.75 (MSFL) -0.66 -0.66 0.70 (AH30) 0.86 (AH20) ait4 (-0.83) 0.71 (AH20) 0.86 (AH30) 0.62 (LLD) -0.53 0.80 (LLD) -0.57 rockclass 0.59 (LLS) (-0.84) 0.73 (LLS) -0.32 (HCGR) -0.63 (HCGR) -0.57 (HSGR) hngs -0.58 (HSGR) (-0.96) -0.54 -0.55 elan (-0.84) (correlation coefficients without core 133 in the B-W member, with log GR and Kh)

Figure 65 – Mol-1: Scatter diagrams between vertical (left) or horizontal (right) hydraulic conductivity (in logarithm) and gamma ray measures obtained from tools ait4 and elan. Linear correlation coefficient indicated (rho). Correlation between Log(Kh) and all resistivity tools vanishes if we just remove the only sample from the B-W member (core 136). Doel-2b borehole No Kh data on this borehole. Correlation between log (kv merged) and the auxiliary variables is intermediate. Hereafter are the correlation graphics.

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Table 24 – Linear correlation coefficients for Doel-2b borehole between vertical hydraulic conductivity (in logarithm) and geophysical tools: gamma ray (HSGR) and resistivity (FF). Indication of the tool from which the log is derived. Tool Log(Kv) HSGR -0.82 (permeability tool) 0.54 (cmr-perm. tool) FF -0.27 (permeability tool)

Figure 66 - Doel 2b - Scatter diagrams between vertical (hydraulic conductivity (in logarithm) and geophysical logs: HSGR (left) and FF (right). Linear regression line a and correlation coefficient indicated (rho).

Weelde borehole Table 25 – Weelde - Linear correlation coefficients between hydraulic conductivities (in logarithm) and geophysical tools: gamma ray (GR) and Resistivity (LN, SN).

Tool Log(Kv) Log(Kh) GR -0.28 -0.03 correlation GR_smooth1m -0.51 -0.42 indicatted LN 0.70 0.59 SN 0.61 0.54

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The correlation between the GR and log (kv merged) is low. Smoothing improves the correlation with GR but has no impact on correlation with resistivity.

Figure 67 - Weelde - Scatter diagram between hydraulic conductivities (left: :Log(Kv), right: Log(Kh)) and GR, raw (top) or smoothed (bottom). Linear regression line and correlation coefficient indicated (rho).

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Figure 68 - Weelde - Scatter diagram between hydraulic conductivities (left: :Log(Kv), right: Log(Kh)) and resistivity LN. Linear regression line and correlation coefficient indicated (rho).

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Zoersel borehole Table 26 – Zoersel - Linear correlation coefficients between hydraulic conductivities (in logarithm) and geophysical tools: gamma ray (GR) and Resistivity (LN, SN). Tool Log(Kv) Log(Kh) GR -0.43 -0.54 GR_smooth0.5m -0.70 -0.75 GR_smooth1m -0.68 -0.80 LN 0.22 0.48 SN 0.43 0.69 ILD -0.56 -0.63 ILD_smooth1m -0.60 -0.63 ILM -0.55 -0.62 Take care to negative sign of res correlation, which indicate conductivities! After conversion to resistivity, the correlation for smoothed ILD reaches 0.71 (Kv) and 0.74 (Kh). Correlation with the induction resistivity tools is intermediate (-0.57, -0.56).

Figure 69 - Zoersel - Scatter diagram between hydraulic conductivities (top: :Log(Kv), bottem: Log(Kh)) and GR (left) and resistivity ILD (right). Linear regression line and correlation coefficient indicated (rho).

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Figure 70 - Zoersel - Scatter diagram between hydraulic conductivities (left: :Log(Kv), right: Log(Kh)) and GR smoothed with a radius of 0.5m (top) and 1m (bottom). Linear regression line and correlation coefficient indicated (rho). In order to perform the cokriging, the auxilary variables ILD, GR have been chosen. Essen borehole Table 27 – Linear correlation coefficients for Essen borehole between hydraulic conductivities (in logarithm) and geophysical tools: gamma ray (GR) and Resistivity (LN, SN). Tool Log(Kv) Log(Kh) GR -0.60 -0.79 LN -0.18 -0.09 SN -0.07 -0.05 FEL -0.16 -0.08

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The correlation between the resistivity tools and log(Kv merged ) seems to be null. On the contrary the correlation with Gamma Tools is intermediate. Smoothing the resistivity curves has no impact on the correlation level.

Figure 71 - Essen - Scatter diagram between hydraulic conductivities (top: :Log(Kv), bottom: Log(Kh)) and GR (left) and resistivity LN (right).

Appendix C: Assessment of local uncertainties with simulations

C.1 Methodology (Co-)kriging results presented in the chapter 3.3 provided, for each target parameter, a most probable estimate together with an associated uncertainty. However, such techniques do not allow to quantify the local uncertainty attached to the estimated parameter nor to reproduce its real variability, as (co-)kriging is by construction smoothing this variability. This appendix aims at providing such probabilistic realizations for the target parameters, using stochastic simulations. Each realization will honor the initial data (up to the nugget effect), their statistical distribution and spatial variability model.

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Several issues will be observed and discussed, leading to abandon this approach for 3D modeling. An alternative approach has therefore been applied in chapter 3.4.3.

C.2 1D Simulations For each cored borehole, 1D co-simulations are performed using the classical Turning Bands (TB) algorithm, based on the same model than for the cokriging (see § 3.3.2). This simulation algorithm normally requires to be applied within a gaussian framework, eg. on (multi-)gaussian variables. However, in the present case this transformation was first skipped for several reasons: . the lack of data to ensure a robust transformation, particularly for Log(Kh) on Mol-1, . a weaker correlation model observed on gaussian transformed data. The consistency of the results therefore partly relies on the conditioning efficiency. 200 co-simulations have been performed on each borehole with 500 turning bands and reviewed in terms of statistics reproduction. The computation of a confidence interval at 90% was finally performed. Simulation results for Log(Kv) on Mol and Log(Kh) on Zoersel are illustrated on Figure 72. The higher variability of individual realizations compared to cokriged estimates is clear. An important drawback of these simulation results is the constant size of the confidence interval throughout the Boom Clay, particularly visible on Zoersel Log(Kh) profile: this interval seems to be much larger than what could be expected given the homogeneity of Log(Kh) within Putte and Terhagen members. Two explanations contribute to this result: . the stationary assumption: a unique stationary variogram model has been considered throughout the Boom Clay, though the increased variability on the Top and Base units is clearly known; . the absence of gaussian transformation: even though applying a stationary model, performing gaussian realizations and transforming them back in raw scale with an anamorphosis model usually allows, because of data conditioning, to retrieve confidence intervals of varying sizes. Consider sills (variability level) that are locally varying with the unit could solve this issue. However, though practicable when dealing with only one simple variogram, applying such technique in a multivariate framework is definitely not straightforward. Consequently, despite the robustness issues for the anamorphosis, a proper model based on gaussian-transformed Log(Kv) and Log(Kh) has been developed (Fig. 72).

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Cokriging CoSim.

IC 90% 60

Transition Zone 40

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20 Z (m - ref DB) ref - (m Z

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Figure 72 –Co-simulation results for Log(Kv) at Mol (left) and Log(Kh) at Zoersel (right): cokriging, simulation example (grey) and confidence interval at 90%. Data locations (black circles).

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Cokriging CoSim.

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Appendix D: Illustration of factorial kriging on Mol-1 This application of the cyclo-stratigraphic approach developed by Lefranc (2007) has been run using the package RGeoS-3.3.7 developed by the Center of Geostatistics of the Ecole des Mines de Paris. It aims at illustrating how cyclic components visible on logs might be filtered out, putting into evidence other structural components of interest.

D.1 Data description The data set is composed of 8 variables measured for 600 samples. It is provided in an ASCII file where the variables are called: DEPTH, GR, AH90, AH20, AH10, AH60, AH30 and MSFL. The first column shows that data have been measured regularly along the depth, with a starting depth equal to 220.1m and a step of 0.1m. The data provide the following basic statistics:

Minimum Maximum Mean St. deviation AH10 2.607 6.626 4.191 0.564 AH20 2.462 6.787 4.275 0.591 AH30 2.717 6.914 4.284 0.578 AH60 2.717 7.107 4.289 0.585 AH90 2.717 6.914 4.284 0.578 GR 74.237 122.345 89.300 7.042 MSFL 2.726 25.424 7.898 1.280

One can check that the variables AH30 and AH90 are exactly similar: the variable AH90 will be abandoned. Remaining variables are displayed in the next figures, where the depth is represented horizontally.

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One can easily check that the AH* variables are very similar. On the other hand, both GR and MFSL variables show a series of larger values in the depth interval [255m,260m].

D.2 Variable AH30

We now focus on one of the AH* variables, say the AH30. There will be no need to perform the same set of operations on all the AH* variables, due to their resemblance.

Experimental variograms

We can calculate the experimental variogram with a lag equal to the distance between two consecutive data (i.e. 0.1), for a number of lags equal to 300 (recalling that the total number of samples is 600).

The variogram presents an abrupt change at the origin to reach a variability of 0.3 (the dispersion variance is 0.334). Then the variogram shows a quasi- periodic behavior with a slight regular increase.

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Variogram Model

We focus on the origin of the variogram by calculating the first 100 lags. This variogram can be fitted by a model defined as a combination of two standard basic structures: A short range cubic scheme: range (0.4) and sill (0.204) A periodic component (exponential cosine): range (4), period (1.45) and sill (0.078)

Factorial Kriging Analysis

We use the factorial kriging analysis which is an estimation procedure which decomposes the variable in three independent components: . A phenomenon which is related to the short range cubic model . A phenomenon linked to the periodic behavior of the variogram . A phenomenon representing the large scale behavior Obviously, the sum of the three components must be equal to the initial variable. The factorial kriging analysis procedure derives each estimated component at each target point, as a linear combination of the data available (i.e. the AH90 information). The weights of this linear combination are given by the variogram model, taking into account the various distances (data to target, data to data). For practical reasons, this linear combination is limited to the closest data to the target point: this is referred to as a moving neighborhood. Its dimension is fixed to 20 samples on each side of the target point: the total neighborhood corresponds to approximately three periods. The choice of these neighborhood parameters has a secondary impact on the results: for sake of simplicity, the factorial kriging analysis is performed only when a complete neighborhood (centered on the target point) is available. This is the reason why no result is available at both edges of the profile.

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The estimation is provided together with the variance of the estimation error (constant in each target point). This value is given through its square root: the Standard Deviation of Kriging error (STDV) Short range component (STDV = 0.210)

Periodic component (STDV = 0.177)

Large scale component (STDV = 0.121)

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The short range component shows an almost erratic noise, although the corresponding basic structure “cubic” usually refers to a continuous variable. The periodic variable is correctly represented: all the periods are marked with some fluctuations in the amplitudes that should be considered more carefully. The large scale component shows some long range fluctuations that should be correlated with some peculiarities on the other components at the same depth values. They could even be considered as a very long range cycle corresponding to an additional periodic component.

D.3 Gamma Ray (GR) The same operation is reproduced on the GR variable.

Variographic analysis

The results (with 300 lags) are less satisfactory than with the AH90 variable: no periodic component can be clearly depicted. A sudden drop appears at a distance of approximately 18.

This “peak” possibly shows the impact of the area of high values located around depth 262, i.e. 18m before the end of the well.

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The variogram, calculated on 100 lags only, shows a new component: the strong regular increase of the variogram with the distance.

In order to improve the variogram analysis, one can think to disregard the area where the values become “abnormal”, for depths larger than 260. The variogram calculated on the remaining area and for 100 lags shows a periodic behavior (at least in the two first periods). Moreover its global variability has been almost cut by 2.

This variogram is now fitted using three components:

. A short scale cubic structure with range (1.0) and sill (7.2) . A periodic component (exponential cosine) with range (3), period (1.45) and sill(3)

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. A large range spherical structure with range (5.5) and sill (10.0)

Factorial Kriging Analysis

The idea now is to run the Factorial Kriging Analysis on the whole data set to decompose the global variable into 4 components (adding the large scale one), keeping the same moving neighborhood parameters as before. We obtain the following extracted components: Short scale component (STDV = 1.896)

The periodic component (STDV = 1.194)

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The component due to the large range spherical structure (STDV = 2.888)

The large scale component (STDV = 2.657)

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It is interesting to notice that the periodic component is not too much altered by the “abnormal” values, which are reflected mainly in the large scale component, but also, to a lesser extent, in the other two components. This tends to prove that this “event” is not part of the periodic component.

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D.4 Variable MSFL The variable MSFL is expected to be even more difficult to analyze than the GR variable, as it presents several isolated peaks and the rest of the signal seems rather “flat”.

Variographic analysis

The initial variogram is calculated on the whole data set for 100 lags. The variogram rises very quickly to its variance and does not present much structure, other than standard fluctuations.

We discard the area located between 255 and 260, responsible for the largest peak. The variogram calculated on the remaining data, for 100 lags, is presented in the next figure.

The general behavior of the variogram remains flat but a periodic component starts showing up. A more interesting property is demonstrated when calculating the experimental variogram after discarding all the information located below depth 255.

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The variogram shows an obvious periodic component this time. This proves that the large peak is not only an “abnormal” value for the MSFL variable, but it also corresponds to an event which shifts the phase of the periodic variable.

The model is composed of 2 basic structures: . A short range exponential structure with range (0.9) and sill (0.465) . A periodic component (exponential cosine) with range (3.0), period (1.45) and sill (0.14)

Factorial Kriging Analysis

Once more, the challenge is to run the Factorial Kriging Analysis in order to decompose the whole set of data into three components, using the same neighborhood as before:

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The short range component (STDV = 0.354)

The periodic component (STDV = 0.253)

The large scale component (STDV = 0.252)

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Concerning the MSFL variable and as expected, the decomposition is more difficult to perform. As a matter of fact, the periodic structure reflects the peak, which cannot be split among the other two components this time. On the other hand, the Factorial Kriging Analysis has taken rid of all the secondary peaks (above or below the mean value).

D.5 Conclusions The various variables all show a cyclical component with a common period of 1.45m. This cyclicity could be due, like in other situations, to Milankovitch cycles. To corroborate this hypothesis, it is necessary to have a rough idea of the sedimentation rate, or equivalently of the geological time interval corresponding to the studied column, and to know the approximate geological age of this formation, because Milankovitch cycles vary with geological time. If this hypothesis is confirmed, the slight variations in the period which can be seen in the factorial kriging results could be interpreted as changes in the sedimentary rate, provided that they are consistent for the three variables (this is the case at about 258m, but there are some exceptions). Identifying the Milankovitch cycles in the boreholes can help in the task of correlating boreholes. In the present case, the high number of cycles makes that approach hardly feasible.

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Appendix E: ISATIS project and journal files

E.1 ISATIS project organization The ISATIS project is organized in several directories, named in a selft- explanatory way.

Figure 74 – Organization of ISATIS project. E.2 Journal File Master.ijnl The Isatis journal files are contained in the “journal” physical folder of the ISATIS archive containing the Boom Clay project. The file master.ijnl reproduced below allows paths’ definition together with the selection of the step to be performed. ######################################################################### # Geostatistical Modeling of Hydraulic Parameters - Boom Clay # # # # Author: Nicolas Jeannée (Geovariances) # # Version: Isatis V9.0 (August 2009) # # # # To execute a given part, remove the '#' of the corresponding line. # ######################################################################### # Definition of access paths: %VAR path_ijnl = E:\ONDRAF\ONDRAF-BoomClay.i80\journal\ %VAR path_database = E:\ONDRAF\ONDRAF-BoomClay.i80\Database\

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# ######################################################################### # Import of target parameters and grainsize data: #%INCLUDE $path_ijnlimport_target_param.ijnl # # # Import of geophysical logs: #%INCLUDE $path_ijnlimport_logs.ijnl # # # Import of Boom geometry, including DB values at key drillholes: #%INCLUDE $path_ijnlimport_geometry.ijnl # # # Georeferencing to DB level: #%INCLUDE $path_ijnlhorizontalisation.ijnl # ######################################################################### # Migration of K data to geophysical logs for correlation analysis: # (useless except for preliminary correlation analysis) #%INCLUDE $path_ijnlmigrate_kv.ijnl # # Create file "Logs for Modeling 3D / Logs" by merging relevant curves: # NB: before running the merge journal file, delete files in "Logs for # modeling 3D": Logs, Logs header, Logs - NIRAS only, Logs - NIRAS # only header #%INCLUDE $path_ijnlmerge_logging_tools.ijnl #%INCLUDE $path_ijnlclean_merged_logs.ijnl # # Migration of grain size data to geophysical logs and target parameters, # creation of final target param file with all grainsize: #%INCLUDE $path_ijnlmigrate_grainsize.ijnl # ######################################################################### # 1D Kriging (Mol, Zoersel and Weelde): #%INCLUDE $path_ijnlkriging_1D.ijnl # # 3D modeling (stratigraphic grid): #%INCLUDE $path_ijnl3D_modeling.ijnl # # Copy of 3D model to original space #%INCLUDE $path_ijnl3D_model_back_original_space.ijnl

E.3 Other Journal Files The other files are transmitted to ONDRAF at the same location than the Master.ijnl one.

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