Field observations of hydrogeological scale effects in crystalline rocks

 

PATRIK VIDSTRAND

 

M.Sc., Civ. Eng.

Department of Geology

Chalmers University of Technology

s-412 96 Göteborg, Sweden

phone + 46 31 772 2046

fax + 46 31 772 2070

Patrik.Vidstrand@geo.chalmers.se

 

 

Abstract

In order to test and establish how the effective hydraulic conductivity varies with increasing scale at a crystalline rock site in south-east Sweden a test programme named La Scale was performed during the spring of 1998. The field test was performed with systematically scaled sections from the 2-metre scale up to the entire borehole scale, of approximately 300 metres. From this field data set it was possible to test an earlier proposed scale trend and also to test the ability of different upscaling methods to predict the larger scale conductivity. This paper presents some of the results of the field test La Scala and also the results from some previous conducted investigations at the same site. All presented data clearly indicate a scale effect in the effective hydraulic conductivity when calculated as the geometric mean of each scale.

 

Keywords: crystalline rocks, field tests, hydraulic conductivity, scale effects

 

Introduction

In hydrogeological measurements it is frequently observed that effective hydraulic conductivity values varies with the scale of measurement. This effect is most common in fractured, fissured and karstic media and hence an important problem in the field of modelling groundwater fluxes around and towards underground facilities, such as nuclear waste repositories.

 

In the south-east part of Sweden a hard rock laboratory, Äspö HRL (Figure 1), has been constructed by Swedish Nuclear Fuel and Waste Management Company (SKB) in order to investigate the ability to predict, construct and maintain the safety and performance of a nuclear waste repository. The Äspö HRL project began in the mid-eighties and at present the whole underground construction is finished. Many repository-associated investigations have been and are presently conducted, among others hydraulic tests in order to establish scale relations of the effective hydraulic conductivity at the Äspö HRL. During the spring of 1998 a test programme named La Scala was performed in order to test and establish the scale relation of effective conductivity values, which had previously been proposed based on sub-vertical surface borehole data (e.g. Rhén et al., 1997).

 

 

Figure 1. Location of the Äspö HRL (from Rhén et al., 1997) The thick block line illustrate the location of the tunnel chainage.

 

The La Scala test programme

The hydraulic tests were performed in a sub-horizontal borehole at a depth of approximately 340 metres below sea. The length of the borehole is approximately 300 metres and it is dominated by one single rock type, i.e. granite (e.g. Rhén et al., 1997). The ambient formation pressure is approximately 250 metres of groundwater giving that the borehole is highly pressurised and traditionally tests are difficult to conduct. In order to be able to perform underground hydraulic tests without loosing too much of the ambient formation pressure before the actual test, SKB has developed an equipment, named UHT1, which is thoroughly described by Hansson (1997, in Swedish). With this equipment it is possible to perform tests and also to move the packer-ensemble without any significant losses of formation pressure.

 

The borehole was divided into sub-sections, which could be added up to the larger scales, where scale just relates to the interesting rock volume. The scales were 2, 10, 30, 90 metres and the entire borehole. It is herein assumed that the distance between the packers can be used as an indicator of the tested rock volume (scale). By the use of these sub-sections it was possible to test the borehole systematically and hence compare the results directly.

 

The observations

Hydraulic conductivity is in many cases found to be log-normally distributed (e.g. Jetel,1964; Carlsson & Carlstedt, 1976; Rhén et al, 1997). The geometric mean is used as a characteristic value for the hydraulic conductivity at each scale. Matheron (1967) showed mathematically that for a statistically homogeneous medium, the effective hydraulic conductivity equals the geometric mean of the individual block values in a 2D environment, e.g. cylindrical flow towards a borehole. However, if hydraulic measurements are averaged by the geometric mean at each scale it has frequently been observed that the effective conductivity increases with increasing scale of observation (e.g. Beauheim, 1988; Guimerà et al., 1995).

 

During the pre-investigation phase at the Äspö HRL project a number of sub-vertical surface boreholes were drilled and tested with numerous hydraulic test methods (e.g. Rhén et al., 1997). Eight of these boreholes were tested with packer tests at the three-metre scale. These three-metre packer tests were more or less systematic (i.e. complete series from top to bottom) and comprehensive through the whole borehole length. Three of the surface boreholes were partly tested with thirty-metre packer tests. However, the untested sections were few and compensations could be implied. From four of the boreholes it was possible to produce transmissivity estimates for the 100-metre scale. Finally, all eight boreholes were also tested with traditional pumping tests, giving transmissivity values for the entire borehole scale.

 

The La Scala test programme was aimed at creating a systematic test sequence. This can be achieved if the borehole is divided into two sub-categories. The first sub-category is the first ninety metres of the borehole. This part of the borehole is the most permeable section and was tested with packer tests in 2 metres, through 10-metre, 30-metre as well as the entire 90-metre section. The second sub-category was the entire borehole, which could be systematically tested with the packer tests from 10 metres, through 30 and 90 up to the entire borehole. The reason for not testing the entire borehole with the 2-metre packer tests was simply the available time.

 

The hydraulic tests described above gave rise to the following scale to estimated hydraulic conductivity relationship (Figure 2). Where the hydraulic conductivity is calculated as the ratio of the evaluated transmissivity and the length of the tested section, the latter is also representing the scale. Data are taken from Rhén et al. (1997) and Vidstrand (1999).

 

In figure 2, it can clearly be observed that the rock volume at Äspö HRL does show the same trend of scale versus hydraulic conductivity relationship as many previous investigations at other crystalline rock sites have shown (e.g. Clauser, 1992; Rhén et al., 1997).

 

 

Figure 2. The relationship between scale and the geometric mean of the hydraulic conductivity. Data are taken from Rhén et al. (1997) and Vidstrand (1999).

 

Discussion

The problems that the scale effects in effective hydraulic conductivity create for numerical simulations have long been well known. Models with a stochastic continuum approach require a hydraulic conductivity distribution to assign to model cells. Since the cell size in general deviates in scale from the scale of measurements the need for good and of course plausible upscaling methods is obvious. Through the years many theoretical and numerical methods have been developed (e.g. Renard & de Marsily, 1997). Within the Äspö HRL project an alternative method have been tested together with more "traditional" upscaling methods. This alternative method is to use the result of a curve-regression performed on data presented by Rhén et al. (1997). This regression was conducted with the values of both the scale (length of test section) and the geometric mean of the hydraulic conductivity plotted in logarithmic space. This kind of upscaling is believed to be site correct and hence give good predictions. The new data from the La Scala test programme do not change the important behaviour of the regression line. However, it can be stated (Vidstrand, 1999) that some theoretical upscaling methods (e.g. based on stochastic thoery by e.g. Gutjahr et al. 1978) shows much better agreement with measured larger scale field values.

Conclusions

The crystalline rock mass at Äspö HRL does show an increasing effective hydraulic conductivity if the geometric mean values are used at each scale with increasing scale of observation. This is the "classical" scale effect in effective hydraulic conductivity and it is frequently reported from many different hard rock sites.

 

The need of good upscaling methodologies is crucial for many numerical models. Results such as these gives good opportunities to create site specific knowledge and/or to test established theoretical upscaling methods.

 

Acknowledgement

Both SKB and the European Commision, DG XII are acknowledged for economic support. Professor Gunnar Gustafson at Chalmers University of Technology and Ingvar Rhén at Sweco AB are acknowledged for discussions and valuable comments.

 

References

Beauheim, R., 1988: Scale effects in well testing in fractured media. In: Proceedings; Canadian/ American conference on Hydrogeology., pp 152-159.

 

Carlsson, L. & Carlstedt, A., 1976: Estimation of Transmissivity and Permeability in Swedish Bedrocks, (Nordic Hydrology) 8, 1977.

 

Clauser, C., 1992: Permeability of crystalline rocks. EOS, Vol. 73, No. 21, pp. 233, 237-238.

 

Guimerà, J., Vives, L. And Carrera, J.; 1995: A discussion of scale effects on hydraulic conductivity at a granitic site (El Berrocal, Spain). Geophysical Research Letters. Vol. 22, No. 11, pp 1449-1452.

 

Gutjahr, A. L., Gelhar, L. W., Bakr, A. A. & MacMillan, J. R., 1978: Stochastic analysis of spatial variability in subsurface flow 2. Evolution and application., Water Resources Research, Vol 14, No 5, pp 953-959.

 

Hansson, K., 1997: Manual for Underground Hydraulic Test system UHT-1, Part 1, Measurement procedures (In Swedish).

 

Jetel, J., 1964: Pouziti hodno specifickévydatnostia novýcg odvozených parametrúv hydrogeologi (geol. Pruzk), 5, 144-145, Praha.

 

Rhén, I. (ed.), Gustafson, G., Stanfors, R., Wikberg, P., 1997: ÄSPÖ HRL - Geoscientific evaluation 1997/5. Models based on site characterization 1986-1995. SKB, Technical Report 97-06, Stockholm, Sweden

 

Vidstrand, P., 1999: Hydrogeological scale effects in crystalline rocks - comparison of field data from Äspö HRL with data from predictive upscaling methods. Chalmers Tekniska Högskola, Geologiska institutionen. Publ. A 88. Göteborg, Sverige.