3-D numerical evaluation of density effects on tracer tests
Introduction
A common approach to characterize aquifers is the use of tracer tests. A non-reactive fluid is injected into the ground through a well at a known rate and concentration. The developing plume is then assessed by direct or indirect methods. Direct methods are concentration measurements from water samples taken from down-gradient wells and multilevel piezometers. Indirect methods involve the measurement of changes in electrical conductivity using electrical methods (e.g. White (1988), Bevc and Morrison (1991), Morris (1996), Slater et al. (2000), Kemna et al. (2002), Hoffmann and Dietrich (2004)).
The anions (Br−, Cl−, and F−) are commonly used as tracers in both cases because of their low material and analytical costs. Tracer concentrations used reach from 0.05 to 20 g/l when using direct methods (Istok and Humphrey (1995)). In the case of electrical methods, a high contrast in electrical conductivity between the tracer plume and the ambient groundwater is required. Concentrations used are much higher and range from 10 to 60 g/l (see Table 1). Clearly the density of the tracer-solution is bigger than the one in ambient groundwater. A key question is how significantly density variation may impact groundwater flow and therefore tracer plume development. In this paper, we present numerical simulations for assessing the importance of density-dependent flow on tracer plume development.
Considerable research on variable-density flow in porous media has been done during the last 30 years. A comprehensive review of the subject and the related issue of benchmarking is given in Diersch and Kolditz (2002) and in the textbooks of Nield and Bejan (1999) or Holzbecher (1998). Oswald and Kinzelbach (2004) designed the most recent three-dimensional physical benchmark experiment to test numerical variable-density flow models and Weatherill et al. (2004) suggest several further test cases. Other examples used as benchmarks to test numerical models are given in Diersch (2002) and Park (2004). The subject of variable-density flow in heterogeneous porous media is addressed in Simmons et al. (2001).
Experimental investigations performed to assess the importance of density contrasts on plume development were conducted by different authors: Paschke and Hoopes (1984), Schincariol and Schwartz (1990), Oostrom et al. (1992), Istok and Humphrey (1995), Jalbert et al. (2000) and Wood et al. (2004). The experiments prove density effects even at small density differences. For example the flow container experiments of Schincariol and Schwartz (1990) have shown that tracer concentration of 1 g/l NaCl can produce gravitational instability at realistic groundwater velocities.
Real-world scenarios where density effects are thought to have an influence on mass migration include contaminant plumes under landfill sites (Kimmel and Braids (1980), MacFarlane et al. (1983)) and a large scale tracer test conducted at Cape Cod (LeBlanc et al. (1991)). Both scenarios have been investigated with numerical methods: the study by Zhang et al. (1998) is related to that particular tracer test at Cape Cod and Dorgarten and Tsang (1990) could demonstrate a strong influence of density effects on movement of liquid waste in a deep sloping aquifer. Koch and Zang (1992) provided a numerical study of the effects of variable density on contaminant plume migration in general. The plumes considered in their study are generated from impoundments. Time scales considered range from 3 to 15 years.
In contrast to scenarios examined by Koch and Zang (1992) and the experimental investigations mentioned above, tracer tests considered here are characterized by a short-term input phase. As concentrations decrease rapidly in that case, buoyancy-induced flow due to density differences is expected to take place only near the source term. The objective of this study is to numerically evaluate density effects on tracer plume development during a typical tracer test scenario.
Section snippets
Mathematical model
Following Hassanizadeh and Leijnse (1988), the simplified form of the mass balance equation of the fluid phase is given bywith the specific storativity of the porous medium S0p, the Dary velocity vector q and a source term Qρ. The simplification consists of introducing the Boussinesq approximation, i.e. density variations within the mass balance equation of the fluid phase are neglected but are included by the buoyancy term of the Darcy equation (see Diersch and Kolditz (2002)
Numerical model
The numerical model used for the simulations is the FE Simulater GeoSys/RockFlow (Kolditz et al. (2003)) which is programmed in C and C++ according to object-oriented software concepts (Beinhorn and Kolditz (2004), Kolditz and Bauer (2004)). The numerical approach is based on the Galerkin finite element method using the governing equations given above. Time derivatives are evaluated by a finite difference scheme. The iterative coupling between the discretized flow and transport equations is
Summary and conclusions
Numerical simulations were carried out to assess the importance of density-dependent flow on tracer plume development. The model scenario is characterized by a short-term tracer injection phase into a fully penetrating well and a natural hydraulic gradient. The scenario is thought to be typical for tracer tests conducted in the field. Modelling results were interpreted using concentration contours and a first moment analysis. The results of the study are summarized below:
- (1)
In the scenario
Acknowledgements
This work is funded by the German Ministry of Education and Science (BMBF) under grant 02WT0161-TÜ and 02WT0040 in the framework of the ‘GIJP’ project and by the European Union in the framework of the ‘AquaTerra’- project (project no. 505428). Funding and project management by Prof. Heinz Hötzl (GIJP) and Prof. Peter Grathwohl (AquaTerra) is gratefully acknowledged. Thanks go to Christoph Beyer and Sebastian Bauer for their help concerning heterogeneous aquifers and Chan-Hee Park for prove
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