WDA Consultants Inc. - Mathematical modelling of groundwater flow

Mathematical modelling of groundwater flow directions for designing groundwater monitoring systems

Weyer (1995a, 1995b, 1966) simulated groundwater flow directions in geological cross-sections at two prominent and widely known German contaminated sites, Bielefeld-Brake and Münchehagen. The results of the models are shown in diagrams 1 and 2. The flow directions in these figures were drawn automatically by the program FLONET (Guiguer et al., 1991) used for the simulation.

Figure 1

Figure 2

The cross-sections in Brake (Fig. 1) and Münchehagen (Fig. 2) were derived from publicly available information only, namely geological maps and profiles in the scale 1:25,000. In both Figure 1 and 2 the depth of active groundwater flow systems, surprisingly, reaches down to depth between 800 and 1000 m below surface. Parts of both models were verified by field data collected by other consultants.

At both sites the simulation focused on the determination of groundwater flow directions only, ignoring the amount and velocities of groundwater flow. In such cases only an estimate of relative permeabilities is needed and modeling under these conditions is very tolerant to inaccurate estimations. The directions of flow do usually not change significantly in response to considerable changes in the contrast of relative permeabilities. The results obtained are important in their own right as it is the direction of groundwater flow that determines the migration direction of plumes of contaminants dissolved in groundwater. Thus the result of the relative simple and inexpensive model calculations in 2D-vertical cross-sections allow the installation of piezometers to be thoroughly optimized.

Figure 3

Investigators at the Brake site had previously adopted the concept of flow parallel to the groundwater table (Fig. 3). Therefore, a great number of piezometers had been installed in areas assumed to be upstream and downstream in term of the assumed flow directions. On numerous occasions these piezometers were sampled without detecting any of the contaminants abundant at the nearby industrial waste disposal site.

Nevertheless, it was concluded by regulatory agencies that there was a risk for the contaminants to migrate laterally away from the site. Hence remedial action was based on this assumption. It cost approximately DM 30 million to install a cover, a circular cut-off wall, and a series of groundwater remediation wells outside of the cut-off wall. Had the downward directed groundwater flow pattern at the site been understood (Fig. 1) the installation of the circular cutoff wall and of the remediation wells could have been avoided reducing the costs by probably two thirds.

In the Münchehagen case variable density flow occurs with densities up to 1.03 gr/cm3, the density of seawater. Calculation of flow directions for variable density flow was achieved by assuming a constant density of 1 gr/cm3, the density of fresh water (Fig. 2). The validity of this approach was corroborated by the fact that the depth of the freshwater/saltwater interface was practically the same in the model as at a borehole at the waste disposal site. In both cases it was approximately 50m below surface.

Figure 4

Also it was shown (Fig. 4) why, at a density of 1.03 gr/cm3, the direction of resultant force vectors for flow of salt water diverts only marginally from the direction of resultant force vectors for freshwater (density 1.0 gr/cm3).

More detailed explanations of the two case histories are contained in Weyer 1995a, Weyer, 1995b, and Weyer, 1996. The first two papers can be downloaded from this web site.

It needs to be pointed out that both models did not undergo any calibration phase. The results are those of the first runs with the groundwater tables (or their approximations) as boundary conditions. The geologic structures were taken from the 1:25,000 geologic maps. These structures determined the distribution of the relative permeabilities. The value of the relative permeabilities were based on rough estimates.

Flow directions in the cross-sections were calculated with the code FLONET v.1.02 of Waterloo Hydrogeologic Inc. (Guiguer et al., 1991). A word of caution if you decide to use FLONET/TRANS v.3.1 (Waterloo Hydrogeologic Inc. and Waterloo Centre for Groundwater Research, 1997): we found this version to contain a major bug in its interface. In geologically complicated cases the plotted result of the flow line calculations can be significantly erroneous. Waterloo Hydrogeologic Inc. stopped selling this program in 2000.