Introduction
Quantitative knowledge of the subsurface is a prerequisite for assessing and understanding its storage and energy resource potential, resource producibility and environmental impact. Fine-grained sedimentary rocks such as the Rupel Clay Member may be barriers for fluid flow, where fluids include water, oil or gas. Porosity and permeability are of key importance in this respect. The focus of this paper is on porosity and, especially, permeability of the Rupel Clay Member. The Oligocene Rupel Clay Member (also known as Boom Clay) is part of the Rupel Formation. The current burial depth of the Rupel Clay Member varies from close to the surface to about 1500m (Fig. 1; Vis et al., Reference Vis, Verweij and Koenen2016). The marine sediments of the Rupel Formation were deposited in the southern part of the North Sea Basin. The formation includes three members, from bottom to top: the sandy Vessem Member, Rupel Clay Member and sandy Steensel Member. The Rupel Clay Member consists of clays that become more silty towards the base and top of the Member. Vis et al. (Reference Vis, Verweij and Koenen2016) provide a detailed description of the Rupel Clay Member based on new grain-size analysis data, and interpretation thereof in relation to the geological setting of the Rupel. Texturally, the Rupel Clay Member includes muds, sandy muds and to a lesser extent muddy sands. Vis et al. demonstrate that the Rupel Clay Member shows a spatial variation in lithological composition related to the depositional environment of the sediments: sediments are generally finer-grained and show less vertical variation in the northern Dutch onshore corresponding to a more distal part of the palaeo basin and are coarser-grained and show more vertical heterogeneity in the southern and eastern onshore corresponding to the palaeo basin margin. They subdivide the member into three subunits based on grain-size characteristics: the lower subunit shows a fining upward trend, the middle subunit is finest-grained and the upper subunit shows a coarsening upward trend.
Fig. 1. North–south cross-section showing the variation in burial depth of the Rupel Clay Member (from Vis et al., Reference Vis, Verweij and Koenen2016).
Porosity and permeability or hydraulic conductivity measurements of the Rupel Clay Member in the subsurface of the onshore Netherlands are limited and these measurements are restricted to shallow depths in the order of tens of metres below surface (Rijkers et al., Reference Rijkers, Huisman, De Lange, Weijers and Witmans-Parker1998; Wildenborg et al., Reference Wildenborg, Orlic, De Lange, De Leeuw, Zijl, Van Weert, Veling, De Cock, Thimus, Lehnen-de Rooij and Den Haan2000; Vis & Verweij, Reference Vis and Verweij2014). In the northwestern part of Belgium, however, the Boom Clay has been studied extensively for more than 30 years, especially at the Mol investigation site (the High-Activity Disposal Experiment (HADES) underground research facility), which has been constructed in the middle part of the Boom Clay at 223m depth (Yu et al., Reference Yu, Rogiers, Gedeon, Marivoet, De Craen and Mallants2013). Clay samples from boreholes at Mol and other locations in NW Belgium were used for hydraulic conductivity measurement through laboratory experiments, and in situ tests were performed to determine the hydraulic conductivity under undisturbed conditions (Wemaere et al., Reference Wemaere, Marivoet and Labat2008; Yu et al., Reference Yu, Gedeon, Wemaere, Marivoet and De Craen2011).
The grain sizes measured in samples of the Rupel Clay Member taken from boreholes spread across the Netherlands (Fig. 2; Vis et al., Reference Vis, Verweij and Koenen2016) were used to generate new porosity and permeability data for the Rupel Clay Member located at greater burial depth. The published measured hydraulic conductivity data from the Belgium Boom Clay could be used to test and select appropriate input parameters for the grain-size based calculation methods.
Fig. 2. Location of sampled boreholes for grain-size analysis in the Netherlands. The following sampled boreholes were used to calculate porosity and permeability: northern area (BUR-01, LWO-02, GRD-01, ESG-01, EMO-01, NNE-07); southwest and western area (B48G0159, B49G0191, B49G0959, B50H0373); and eastern and southeastern area (B41G0024, B46C0478, B52E0114).
Factors influencing mud porosity and permeability
Muds mostly comprise sediments of fraction <63µm, i.e. mostly consisting of a clay fraction (<2µm) and a silt fraction (2µm–<63µm). In general, depositional porosities of muds are high, the more so for the clay-rich muds, reaching magnitudes of 80–90% (e.g. Aplin & Macquaker, Reference Aplin and Macquaker2011). Porosity decreases with increasing burial depth. At shallow depths of <2km (at temperatures <70°C) porosity reduction is mainly due to mechanical compaction driven by the increase of effective stress. Compressibility of mud, and therefore its rate of compaction, is strongly influenced by grain size: finer-grained muds have higher depositional porosities, but their rate of compaction is higher (Yang & Aplin, Reference Yang and Aplin2004; Aplin & Macquaker, Reference Aplin and Macquaker2011). In addition, clay mineralogy influences compressibility and compaction. For example, Mondol et al. (Reference Mondol, Bjørlykke, Jahren and Høeg2007) demonstrated with experimental mechanical compaction of clay mineral aggregates that coarse-grained kaolinite is more compressible than finer-grained smectite. The clay mineralogy of the Rupel Clay Member consists of a suite of different clays, including kaolinite, smectite, illite and interstratified clay minerals (Koenen & Griffioen, Reference Koenen and Griffioen2014). At a certain porosity, clay-rich mudstones have smaller pore sizes than silt-rich mudstones (Schlömer & Krooss, Reference Schlömer and Krooss1997; Dewhurst et al., Reference Dewhurst, Aplin, Sarda and Yang1998, Reference Dewhurst, Aplin and Sarda1999).
Permeability closely relates to pore size and pore-size distribution. Schneider et al. (Reference Schneider, Flemings, Day-Stirrat and Germaine2011) showed that mudstone permeability increases with a decrease in clay fraction due to the development of a dual-porosity system, where large pore throats between silt grains that act as high-permeability pathways are preserved in addition to small pores within the clay matrix. Just like porosity, permeability of mudstones is also strongly controlled by their grain size, grain-size distribution, and mineralogy. At a given porosity, vertical permeabilities vary over orders of magnitude (Neuzil, Reference Neuzil1994; Reece et al., Reference Reece, Flemings, Dugan, Long and Germaine2012; Casey et al., Reference Casey, Germaine, Flemings, Reece, Gao and Betts2013), while clay-rich mudstones have lower permeabilities than clay-poor ones. This porosity–permeability relation as a function of clay content in fine-grained sediments is consistent with findings of Daigle & Screaton (Reference Daigle and Screaton2015).
Database
Grain-size measurements from 107 samples of the Rupel Clay Member from 13 boreholes in the Netherlands were used to calculate porosity and permeability. The boreholes are listed in Tables 1–3 in Appendix 1, and Figure 2 shows the location of the boreholes. The sampling and grain-size measurement procedures are described in Vis et al. (Reference Vis, Verweij and Koenen2016). Grain size was measured by Qmineral bvba in Belgium (www.qmineral.com), using both laser diffraction (low-angle laser light scattering) and SediGraph® (X-ray measurements). The Excel spreadsheet program GRADISTAT8 (Blott & Pye, Reference Blott and Pye2001) was used to analyse the measured grain-size data (Vis et al., Reference Vis, Verweij and Koenen2016). The grain-size measurements of the Rupel Clay Member carried out by two different methods provided the opportunity to compare the clay size measurements of both methods.
Published measured hydraulic conductivity and grain-size data of the Boom Clay at four borehole locations (Mol-01, Zoersel, Weelde-01, Doel-2b) in Belgium (Yu et al., Reference Yu, Gedeon, Wemaere, Marivoet and De Craen2011) were used to test the grain-size based method for calculating porosity and permeability. Figure 3 shows the location of these boreholes.
Fig. 3. Location of sampled boreholes and distribution of the ‘Boom Clay’ in NW Belgium (from Yu et al., Reference Yu, Rogiers, Gedeon, Marivoet, De Craen and Mallants2013, after Wemaere et al., Reference Wemaere, Marivoet and Labat2008).
Methodology
Luijendijk & Gleeson (Reference Luijendijk and Gleeson2015) provided an overview and comparison of grain-size based equations to calculate porosity and permeability developed for sand–clay mixtures using experimental and field datasets. The grain-size based equations discussed are not exclusively for application to muds (grain-size fraction mostly <63µm and sand content <10%). Yang & Aplin (Reference Yang and Aplin2004, Reference Yang and Aplin2010) developed equations specially designed to calculate mud porosity and vertical permeability, respectively. These equations were selected to calculate porosity and vertical permeability using the grain-size analysis data from mud samples derived from the Rupel Clay Member. Yang & Aplin (Reference Yang and Aplin2004) used mudstone samples from the North Sea and Gulf of Mexico to describe the mechanical compaction and associated decrease in porosity of mudstones. The relatively shallow sampling depths of the Rupel Clay Member in the Netherlands (21–672 mTVDss (metres true vertical depth below ground surface)) are well within the realm of mechanical compaction. The porosity–permeability equation of Yang & Aplin (Reference Yang and Aplin2010) was used to calculate permeability. Yang & Aplin derived their permeability equation based mainly on marine mudstones, using more than 300 samples, most of them from the North Sea and Gulf of Mexico. The Yang & Aplin (Reference Yang and Aplin2004, Reference Yang and Aplin2010) equations include clay content and effective stress as important parameters.
In order to test the applicability of the calculation method for the Rupel Clay Member, we compared the permeability based on measured hydraulic conductivity of the Belgian Boom Clay at four borehole locations (Yu et al., Reference Yu, Gedeon, Wemaere, Marivoet and De Craen2011) with the calculated permeability using the Yang & Aplin (Reference Yang and Aplin2004, Reference Yang and Aplin2010) equations for published measured clay size data from the Boom Clay (Yu et al., Reference Yu, Gedeon, Wemaere, Marivoet and De Craen2011) (Fig. 4). Figure 4 shows that the difference between calculated and measured permeability decreases with depth. The largest difference is observed for samples from Doel-2b from depths of <100m. At depths exceeding 200m there is a slight overestimation of permeability of less than one order of magnitude.
Fig. 4. Cross plots showing measured and calculated permeability of the ‘Boom Clay’ versus depth at four borehole locations in NW Belgium (see Fig. 3 for location of the boreholes) (modified after Imberechts, Reference Imberechts2014 and Verweij et al., Reference Verweij, Daza Cajigal, De Bruin and Geel2014). Published measured hydraulic conductivity and grain-size data of the Boom Clay (Yu et al., Reference Yu, Gedeon, Wemaere, Marivoet and De Craen2011) were used to derive the measured vertical permeability (‘Yu’) and the calculated vertical permeability (‘Y & A’), respectively.
The clay content is a very important input parameter in the equations. As stated above, the grain sizes of the Rupel Clay Member were measured by two different methods (laser diffraction and Sedigraph). The results with respect to clay percentage were found to vary strongly depending on the measurement and analysis technique used (Vis et al., Reference Vis, Verweij and Koenen2016). According to Konert & Vandenberghe (Reference Konert and Vandenberghe1997), the <8µm grain-size fraction defined by laser techniques corresponds to a grain size of <2µm defined by classical pipette analysis. They proposed to use the measured fraction smaller than 8µm (using laser diffraction) as representing the clay fraction, i.e. representing a grain size smaller than 2µm. Based on grain-size measurements of 146 samples from the Rupel Clay Member at 17 borehole locations, Imberechts (Reference Imberechts2014) investigated which grain size measured with the laser diffraction method corresponds best with the clay fraction of the Rupel Clay Member determined with the Sedigraph. Different grain-size fractions of the laser diffraction measurements, ranging from 2 to 8µm, plotted together with the standard clay grain size of 2µm of the Sedigraph measurements, showed that the best agreement was found for laser diffraction grain-size measurement of 5µm and a Sedigraph measurement of 2µm (Fig. 5). Figure 5 shows that the laser grain-size fraction <8µm overestimates the Sedigraph clay fraction of 2µm. Imberechts also compared porosity and permeability calculations using Sedigraph clay % (<2µm with laser clay % <5µm and laser clay % <8µm. The cross plots of calculated porosity and permeability vs depth for the different boreholes showed that in general the porosity and permeability decreases with depth for the Sedigraph and the two laser clay fractions, and that only for about 50% of the boreholes does the laser clay % <5µm show a better fit with the Sedigraph clay % <2µm.
Fig. 5. (A) Comparison of grain-size fraction of <8µm resulting from laser diffraction measurements with the standard grain size for clay (<2µm) measured with the Sedigraph. (B) Comparison of grain-size fraction of <5µm resulting from laser diffraction measurements with the standard grain size for clay (<2µm) measured with the Sedigraph. (From Imberechts, Reference Imberechts2014.)
The calculation of the porosity and permeability, using the Yang & Aplin (Reference Yang and Aplin2004, Reference Yang and Aplin2010) equations was applied to those samples of the Rupel Clay Member that are texturally characterised as mud.
Given the results of Imberechts (Reference Imberechts2014) and published variations in the measured clay percentages depending on the technique used (Konert & Vandenberghe, Reference Konert and Vandenberghe1997; Buurman et al., Reference Buurman, Pape, Reijneveld, De Jong and Van Gelder2001; Vis et al., Reference Vis, Verweij and Koenen2016), we performed the calculation of porosity and permeability of the mud samples for the following ‘clay fraction’ measured by laser diffraction and analysed by GRADISTAT8 software (Blott & Pye, Reference Blott and Pye2001), i.e. fraction of grain size <8µm (corresponding to laser-measured fraction of clay + very fine silt + fine silt). The laser diffraction measurements were selected because laser diffraction is the most used method for measuring grain sizes in the Netherlands and calculations based on these measurements allow more direct comparison with older and future permeability calculations.
The porosity and permeability for samples characterised as sandy mud or muddy sand were calculated by conventional lithology-dependent porosity–depth and porosity–permeability relations. The porosity equation is a porosity–depth relation for mechanical compaction based on the conventional Athy's law, and the applied porosity–permeability relation is the multi-point model (Hantschel & Kauerauf, Reference Hantschel and Kauerauf2009).
Results
The results of the porosity and permeability calculations are presented in Appendix 1 and Figure 6. The vertical permeability values of the mud part of the Rupel Clay Member at depths of >400m are all in the range of 10−19m2 (corresponding to a vertical hydraulic conductivity of 10−12ms−1).
Fig. 6. Cross plot of calculated vertical permeability versus depth for samples of mud, sandy mud and muddy sand of the Rupel Clay Member (see Appendix 1 for the calculated values).
The spatial variation in lithological composition of the Rupel Clay Member is reflected in variation in its permeability. Samples of the boreholes in the northern part of the Netherlands (LWO-02, GRD-01, EMO-01; and seven out of eight samples of ESG-01) are all muds and show the least vertical variation in permeability (Fig. 6). For example, the vertical permeability of the Rupel Clay Member in GRD-01 varies between 5.0E-19 and 6.9E-19m2 over a depth interval of 448–569m. The four low permeability outliers for their depth of measurement (Fig. 6) are associated with a high clay content of about 55–70%. In both the east-southeastern and the southwest-southern areas the ‘mud’ part of the Rupel Clay Member is overlain and/or underlain by coarser-grained sediments: the vertical variation in permeability over the Rupel Clay Member reflects this heterogeneity (Fig. 6). For example, the vertical permeability of the Rupel Clay Member in B52E0114 (east-southeastern area) varies between 4.6E-14m2 and 1.6E-19m2 over a depth interval 381–524m, and that in B50H0373 (southern area) varies between 6.0E-17m2 and 7.4E-19m2 over a depth interval of 325–470m. The highest permeability for the depth of measurement is related to very high sand contents: for example, the two samples with highest permeability have sand contents of 76.3 and 82.2%. It should be realised by comparing permeability of muds and coarser-grained textures, that different calculation methods were used to estimate the permeability of the mud and the coarser-grained muddy-sand and sandy-mud parts of the Rupel Clay Member.
Spatial variation in the calculated vertical permeability of the Rupel Clay Member also reflects differences in its burial depth in addition to differences in lithology (Fig. 6). The calculated permeability for the samples in the southwest and southern area also clearly shows this influence. The calculated vertical permeability for mud samples decreases from 7.7E-17m2 at a very shallow depth of 21m (B48G0159), 1.2E-17m2 (B49G0191; 82m), 5.8E-18m2 (B49G0959; 129m), to 9.2E-19m2 at 442m (B50H0373).
Discussion
There are a number of uncertainties involved in the application of the Yang & Aplin (Reference Yang and Aplin2004, Reference Yang and Aplin2010) equations for calculating porosity and permeability of the mud part of the Rupel Clay Member:
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• An important uncertainty concerns the clay content to be used. The two methods, laser diffraction and Sedigraph, that were used to measure grain sizes of the samples produce different results for the clay content. Several authors have shown that clay content is underestimated by the laser-diffraction method (Konert & Vandenberghe, Reference Konert and Vandenberghe1997; Buurman et al., Reference Buurman, Pape, Reijneveld, De Jong and Van Gelder2001). This is confirmed by the present study. There is, however, uncertainty about the magnitude of the underestimation. Here we followed Konert & Vandenberghe (Reference Konert and Vandenberghe1997) and used clay <8µm measured by laser diffraction.
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• The permeability model of Yang & Aplin (Reference Yang and Aplin2010) is based on the assumption of homogeneity of the mud sample. The spatial lithological heterogeneity in muds at cm to m scale is not taken into account in the model. Heterogeneity at this scale also affects the pore size distribution and as a consequence its permeability to a greater or lesser extent (Hildenbrand, Reference Hildenbrand2003; Drews, Reference Drews2012; Hemes et al., Reference Hemes, Desbois, Urai, De Craen and Honty2013). Heterogeneity at this scale occurs in the Rupel Clay Member, especially in the southern and eastern parts of the country. In this study the vertical permeability was calculated for sample scale only. On a larger scale, the grain-size data and associated permeability showed that the Rupel Clay Member exhibits layering on a member scale. The Rupel Clay Member is probably also anisotropic to a greater or lesser extent. This was also demonstrated by vertical and horizontal hydraulic conductivity measurements performed on the Belgian Boom Clay. The measurements showed that the horizontal conductivity, at formation scale, can be 5–60 times higher than the vertical ones (Wemaere et al., Reference Wemaere, Marivoet and Labat2008).
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• Yang & Aplin (Reference Yang and Aplin2010) reported that for their database (300 samples of marine mudstones, mostly from the North Sea and Gulf of Mexico) an uncertainty of magnitude in permeability at a given porosity is one order of magnitude. The mud samples from the Rupel Clay Member belong to one system, in contrast to the samples from the Yang & Aplin (Reference Yang and Aplin2010) study. It is currently not known if this more homogeneous sample set reduces the uncertainty in calculated permeability for the Dutch mudstones.
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• The porosity and permeability has been calculated using effective stress values related to current burial depth. Burial history has not been taken into account. If previous deeper burial of the Rupel Clay has occurred at a certain location, this may have led to overcompaction of the clay. Such a condition is known/expected to occur in the SW of the Netherlands where the Rupel Clay Member is at very shallow depths (Vis et al., Reference Vis, Verweij and Koenen2016). Hitherto no influence of past glacial loading has been identified for Paleogene mudrocks in the northern part of the Netherlands (Kooi, Reference Kooi2000).
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• The calculation method does not take into account the influence of variation in mineralogy. Koenen & Griffioen (Reference Koenen and Griffioen2014, Reference Koenen and Griffioen2016) analysed samples from the Rupel Clay Member across the Netherlands to characterise geochemistry and mineralogy. They found that the clay mineralogy of the Rupel Clay Member consists of a suite of different clays, including kaolinite, smectite, illite and interstratified clay minerals.
In order to obtain insight into the applicability of the calculation method for the Rupel mud samples, the results of calculations were compared with measured hydraulic conductivity values for the Belgian Boom Clay. This comparison indicated that for a depth of >200m there is a slight overestimation of permeability of less than one order of magnitude. The calculated vertical permeability of the mud part of the Rupel Clay Member in the Netherlands probably also slightly overestimates its real value.
Conclusions
Comparison of the permeability based on measured hydraulic conductivity of the Belgian Boom Clay at four borehole locations (Yu et al., Reference Yu, Gedeon, Wemaere, Marivoet and De Craen2011) with the calculated permeability using the Yang & Aplin (Reference Yang and Aplin2004, Reference Yang and Aplin2010) equations for published measured clay size data from the Boom Clay (Yu et al., Reference Yu, Gedeon, Wemaere, Marivoet and De Craen2011) showed that the calculated permeability slightly overestimates measured permeability by less than one order of magnitude for burial depths exceeding 200m. An important uncertainty in the application of the calculation method concerns the clay content to be used from laser diffraction grain-size measurements.
The calculated porosity and vertical permeability of the Rupel Clay Member provide, for the first time, insight into these key properties at depths beyond a few tenths of a metre.
The spatial variation in lithology, heterogeneity and also burial depth is apparent in the variation of the calculated vertical permeability using the grain-size analyses of the samples of the Rupel Clay Member. The samples from the north of the country consist almost entirely of muds with calculated vertical permeability of less than 8.3E-19m2 (8.3E-12ms−1) (calculated using clay + very fine silt + fine silt % from laser diffraction measurements). The vertical variation in permeability in the more heterogeneous Rupel Clay Member in the southern and east-southeastern part of the country can reach several orders of magnitude due to increased permeability of the coarser-grained sandy-mud and muddy-sand layers.
Acknowledgements
The research leading to these results has received funding from the Dutch research programme on geological disposal OPERA. OPERA is financed by the Dutch Ministry of Economic Affairs and the public limited liability company Elektriciteits-Produktiemaatschappij Zuid-Nederland (EPZ) and coordinated by Centrale Organisatie Voor Radioactief Afval (COVRA). We thank the reviewers for comments and suggestions that improved the paper.
Appendix 1: Calculated porosity and vertical permeability of the Rupel Clay Member
Table 1. Calculated porosity and vertical permeability of the Rupel Clay Member in the northern area. Figure 2 shows the borehole locations.
Table 2. Calculated porosity and vertical permeability of the Rupel Clay Member in the southwest and southern area. Figure 2 shows the borehole locations.
Table 3. Calculated porosity and vertical permeability of the Rupel Clay Member in the east and southeastern area. Figure 2 shows the borehole locations.
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