Hydraulic conductivity heterogeneity of a local deltaic aquifer system from the kriged 3D distribution of hydrofacies from borehole logs, Valcartier, Canada

Summary

The deltaic aquifer system of the Valcartier sector in Quebec, Canada, is part of a quaternary valley fill contaminated by dissolved trichloroethene (TCE). The objective of our study is to define the aquifer system heterogeneity that should influence TCE transport. Heterogeneity is defined by the distribution of both hydrofacies and hydraulic conductivity (K). Hydrofacies are defined as lithologic facies with distinctive hydraulic conductivity ranges. Our approach was developed to take advantage of the abundant stratigraphic and lithologic data provided by borehole logs (7000 m logged from 430 locations). Four site-specific deltaic hydrofacies were defined on the basis of lithologic descriptions, supported by data from grain size analyses, slug tests and cone penetration tests. Each hydrofacies includes a group of geologic facies found in borehole log descriptors to which an initial mean horizontal conductivity K_H is associated based on slug tests. Borehole logs were converted to hydrofacies proportions over 5-m intervals to provide 1350 data points. The spatial distribution of hydrofacies was interpolated by three successive interconnected 3D kriging steps using the new technique of “imbricated kriging”. Global dual kriging is directly carried out on the 3D grid of a numerical model. Finally, the proportions of hydrofacies were used to estimate horizontal (K_H) and vertical (K_V) hydraulic conductivity fields using generalized means for layered media. Final K_H values assigned to the hydrofacies are calibrated by comparison with 2D trends in K_H shown by slug tests. This approach also provides an estimated vertical K_V field with a spatially varying proportion to K_H, rather than a fixed anisotropy ratio. Imbricated kriging does not preserve the statistical variability of fine scale hydrofacies distribution representative of geological variability. However, the approach provides K_H and K_V estimates over a 3D numerical grid that are coherent with hydrofacies distribution, which in this case control K_H and K_V.

Introduction

Aquifer heterogeneity is important as it controls flow and contaminant transport which are key processes for contamination control and remediation (de Marsily et al., 2005) or for the delineation of representative well head protection areas (Frind et al., 2006). Although present-day computers and numerical models could handle detailed data on aquifer heterogeneity, defining the heterogeneity of an aquifer system is elusive as conventional hydrogeological data (hydraulic tests such as pumping tests of slug tests) are generally insufficient to characterize the distribution of hydraulic conductivity K (Rubin and Hubbard, 2005). It is now generally agreed that “indirect” approaches must be used (geological or geophysical) to complement direct hydrogeological methods in order to define heterogeneity (Crumbling et al., 2003, Rubin and Hubbard, 2005). Our objective is to develop a practical approach making use of the most common available data provided by hydrogeological characterizations, borehole logs, in order to identify hydrofacies, krige their proportions, correlate these proportions with horizontal and vertical conductivity, and thus directly obtain horizontal K_H and vertical K_V hydraulic conductivity estimates over the 3D grid of a numerical groundwater flow or transport model. Such an approach does not aim to represent detailed geological facies variations, but rather to obtain a realistic representation of the hydrogeologic heterogeneity. The Valcartier aquifer system near Quebec City, Canada, the study site chosen to illustrate the approach, contains a major contaminant plume and offers abundant stratigraphic data from borehole logs.

Kolterman and Gorelick (1996) identified three main groups of techniques to depict the heterogeneity of sedimentary deposits: descriptive, structure-imitating and process-imitating techniques. The descriptive approach, which corresponds to the traditional layer cake approach (or averaging), has been widely employed in hydrogeology. Inverse modeling, based on the production of a K distribution allowing the matching of heads and/or solute observations, and genetic models, which attempts to reconstruct a basin’s sedimentation history, are members of the process-imitating techniques. Finally, sedimentation patterns and statistical techniques are part of the structure-imitating group. The sedimentation pattern technique attempts to mimic the lithologic geometry and nature of sedimentary deposits while statistic methods (or geostatistics) use probabilities and statistics to define the aquifer heterogeneity structure. Considering the tools readily available and the applications sought for the output, structure-imitating geostatistics were selected for our study. Moreover, we chose to define the heterogeneity structure with “geostatistical estimation” rather than with “geostatistical simulations”. This approach does not go as far as the geostatistical simulations in the complete description of variability in properties related to aquifer heterogeneity. However, geostatistical estimation produces a representative K field and has the practical advantage to reduce the amount of data that has to be managed in subsequent groundwater flow simulations. Frind et al. (2006) have recently argued that geological variability of an aquifer was more practically approached by the use of “best estimates” of geological features and properties rather than with the multiple realizations involved in geostatistical simulations, since each realization produced by this approach requires its own aquifer parameters calibration of the numerical flow or transport model (inverse problem).

Various studies have been directed toward the use of qualitative lithologic information to describe aquifer heterogeneity with geostatistical techniques. In all cases, to perform numerical flow or transport simulation, stratigraphic information must first be converted to hydrogeologic parameters (hydraulic conductivity, storativity, etc.) that can then be used in the simulator. Fogg et al. (1998) described the correlation between K measurements from pump tests and a combination of the sediment textures and the depositional facies of the corresponding screens. They could then distinguish four hydrogeologic facies and analyze aquifer heterogeneity with the Markov chains technique. Johnson and Dreiss, 1989, Ritzi et al., 1996 coded lithologic information using a binary system, indicating either the presence of aquitard or aquifer facies. The dataset was then used with indicator kriging (Journel, 1983) to evaluate the aquitard distribution within the aquifer. Flach et al. (1998) developed a relationship between mud fraction and K values measured in the laboratory. Used as a proxy to K, mud fraction data derived from numerous geophysical logs were interpolated.

In this study, we develop a new approach, called “imbricated kriging”, to estimate the proportions of various hydrofacies in volumes corresponding to the flow simulator finite element grid. Our new approach has the advantage, over raw kriging of proportions, to automatically ensure the sum of the kriged proportions equals 1.

In 1997, TCE was discovered in drinking water of the Valcartier Garrison from wells tapping groundwater from the area (Fig. 1). Then, in 2000, TCE was detected in private wells of the neighboring municipality of Shannon. Initial studies and a detailed characterization program allowed a better understanding of the local groundwater flow system, delineated the extent of the dissolved plume and identified potential source zones (Lefebvre et al., 2004). A crescent-shaped buried valley, with bedrock as deep as 50 m, extends east–west in the study area (Fig. 1). Two north–south rivers bound the site to the east and west.

Fig. 2 shows a 3D geological model whose aerial extent corresponds to the interpolation area shown in Fig. 1. Stratigraphic units overlying bedrock from bottom to top are: diamictons (till and proglacial sediments), glaciomarine silt and the deltaic system sediments (Lefebvre et al., 2004). The deltaic sands and the diamictons are considered as aquifer units, whereas prodeltaic and glaciomarine silts are aquitards. Bedrock and till are relatively impermeable (Boutin, 2004). The deltaic sand unit is the main aquifer in the Valcartier sector and most of the TCE contamination occurs in that unit. The study of heterogeneity presented in the paper thus focuses on the sediments of the deltaic system.

The deltaic system consists of two units: the deltaic sands and the prodeltaic silty unit. The deltaic sands are comprised of medium to coarse sands and are locally gravelly, while the prodeltaic silty unit includes a layering of generally fine sediments (silts, clayey silts and sandy silts). The deltaic system thickness reaches up to 45 m. The eastern part of the deltaic aquifer system is split in two by a wedge of prodeltaic silty sediments. In this sector, deltaic sands occur below and above the prodeltaic silty unit. Where the prodeltaic silty unit is absent, the deltaic sands are unconfined. However, on the eastern part of the sector, the deltaic sands are semi-confined underneath the prodeltaic silty unit, while the overlying sands are unconfined. As seen in Fig. 2, there is lateral continuity in the upper and lower deltaic sands with the deltaic sands found to the west where the prodeltaic silty unit is absent. This silty unit has a horseshoe shape and is itself continuous in the east of the study area.