Groundwater Modeling of a Complex Hydrologic System in South ...

GROUNDWATER MODELING OF A COMPLEX HYDROLOGIC SYSTEM IN SOUTH CAROLINA THROUGH THE USE OF ANALYTIC ELEMENTS M. Tolika1 and E. K. Paleologos2,∗ 1

Department of Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece; 2 Department of Geological Sciences, University of South Carolina, Columbia,U.S.A. (*author for correspondence: e-mail: epal@geol.sc.edu; Phone: 803-777-8125; Fax: 803-777-6610)

Abstract. The objective of this study is to evaluate the use of the Analytical Element Method (AEM) toward multiobjective, multiscale, ongoing modeling needs at complex hydrologic sites such as those managed by the US Department of Energy. This method presents several advantages over the traditional numerical methods that include absence of grid, natural incorporation of hydrologic features, and generation of an exact solution at every point in a flow field. The AEM with its semi-analytical formulation is particularly efficient in addressing what-if scenarios, the resolution of boundary conditions, and the incorporation of new data all of which are important aspects of remediation efforts in complex sites. Our model accounted for important hydrologic features in an area of the Savannah River Site, South Carolina that included river branches, artificial surface basins, monitoring wells, and the existence of heterogeneities. Our simulated heads were found to be in excellent agreement with the measured heads, with over 90% of the wells exhibiting a maximum discrepancy of less than 10 ft. The AEM was found to be a very efficient and fast method for the analysis of a flow field even when a limited number of elements was considered. The AEM was seen to lead to better physical understanding and resolution of the critical components of a groundwater system and it can offer significant advantages in using models to guide site characterization and remediation efforts. Keywords: analytic element method, groundwater flow, regional model

1. Introduction This paper presents a regional model of the groundwater flow field at the General Separations Area(GSA), South Carolina that is based on the Analytic Element Method (AEM). The AEM (Strack, 1989; Haitjema, 1995) is an object-oriented, semi-analytical method that resembles the classical boundary element methods with solutions not necessarily being Cauchy integrals but closed-form analytical expressions (Strack, 1999). The method does not make use of a mesh to obtain the hydraulic head or flux at specific points of the grid but rather utilises the superposition of analytical elements, which approximate the influence of various hydrologic features of a region on a background, uniform field, to obtain the overall solution at any point in the hydraulic system. Thus, point analytical elements may represent wells, line elements can approximate creeks, rivers, or geologic contacts, and lakes or aquifer properties (hydraulic conductivity, recharge, and leakage) are represented by area elements (Jankovic and Barnes, 1999a,b; Strack and Jankovic, Water, Air, and Soil Pollution: Focus 4: 215–226, 2004. C 2004 Kluwer Academic Publishers. Printed in the Netherlands.

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1999). Problems of discontinuity induced by heterogeneities in the hydraulic conductivity field or by aquifer variable thickness are addressed with the use of line doublet elements (Strack and Haitjema, 1981b). Traditionally, superposition of analytical solutions was considered to be limited to homogeneous aquifers of constant transmissivity. However, by formulating the groundwater flow problem in terms of potentials rather than piezometric heads the AEM becomes applicable to both confined and unconfined aquifers as well as to heterogeneous aquifers (Strack, 1981, 1984; Strack and Haitjema, 1981a). In particular for sites where development of disposal facilities, data collection, or remediation efforts may be proceeding incrementally (Bakker et al., 1999; Olsthoorn, 1999) AEM may be of interest because it facilitates stepwise modeling and refinement of an initial model. AEM also allows different scales to be treated within the same model by locally refining input data (Haitjema, 1995), and it is efficient in addressing what-if scenarios (Moorman, 1999) as well as incorporating new data, both of which are important aspects of remediation efforts at various sites. In addition, the AEM allows the modeler to concentrate on the hydraulics of the flow situation and to study the effect of each individual element on the groundwater flow, features that cannot be easily observed when modeling with numerical codes. Hunt et al. (1998) and Olsthoorn (1999) recognized the importance of the analytic element models as screening tools for the identification of test parameters and boundary conditions. If used in combination with finite-difference or finite-element models the AEM improved those models’ calibration. Hunt et al. (1998) compared a two-dimensional, analytic element model of the Trout lake basin in northern Wisconsin to a steady state, three-dimensional finite-difference model of the same area. The insight that was obtained from the AEM model led these authors to modify the boundary conditions of the finite-difference model resulting in significant improvement in flux calibration. Hunt et al. (1998) emphasized the proper determination of the boundary conditions in finite-difference modeling and attributed the success of their analytic element model to the more realistic specification of the boundaries. Olsthoorn (1999) used analytic element and finite difference models to analyse the groundwater flow at a dune area, 20 km west of Amsterdam. The AEM provided, with relatively few elements, a detailed picture of the flow field around the 400 ditches that existed in the area, and it was used for the estimation of boundary conditions for the finite difference model. The GSA is situated at the central Savannah River Site (SRS), South Carolina and was developed as a controlled area for nuclear production for national defence purposes. The area has been used for the disposal of several types of hazardous wastes resulting in contamination plumes. The movement of groundwater and the transport of contaminants have been studied at SRS through the use of finite element codes (Flach and Harris, 1999). The objective of this work is to study the application of the AEM to flow fields containing multiple, complex hydrologic features, such as those found at the GSA.

A COMPLEX HYDROLOGIC SYSTEM IN SOUTH CAROLINA

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2. Site Description The GSA is situated at the central Savannah River Site (SRS), an area of 300 m2 in South Carolina. The SRS (SRS, 1996) was developed in 1950 as a controlled area for nuclear material production (primarily tritium and plutonium-239) for national defence purposes. Parts of the SRS area have been contaminated by radioactive waste, generally low-level, that leaked during weapon production. The GSA is an area of 15 m2 , within the SRS complex, with the main operations taking place there being chemical separation, tritium processing, and receipt of offsite fuel for processing. The main sources of substantial groundwater pollution are two seepage basins that contain a large number of underground storage tanks with high-level liquid radioactive waste that have leaked into the aquifers below the tank farms. Plumes have discharged radionuclides, metals, and nitrates into a nearby creek, the Fourmile creek (Figure 1). Figure 1 shows that the GSA area is partly bounded by three river branches: the Upper Three Runs (UTR) to the north, the Fourmile Branch to the south, and the McQueen Branch to the northeast. The aquifers that are present in the GSA area are the upper zone of the Upper Three Runs Aquifer (UTRA), the lower zone of

Figure 1. Plan view of the GSA with the wells in the Gordon and the UTRA.

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Figure 2. Schematic of a typical cross-section of the GSA aquifer system (modified after Flach and Harris, 1999).

the UTRA, and the Gordon aquifer (Figure 2). Underlying the Gordon aquifer is the Meyers Branch confining unit, which provides the aquifer with a small upward flow. Monitoring wells provide information about the hydraulic head at several locations. The upper zone of the UTRA is monitored by a network of 415 wells, the lower zone of the UTRA is monitored by 173 wells, and information on the Gordon Aquifer is provided through a network of 79 wells. 3. Past Modeling Efforts The need to examine water flow and contaminant transport at a variety of waste sites in SRS, as well as, the requirement to investigate different remedial action scenarios led to the development of a 3D finite element groundwater flow and contaminant transport code (FACT: subsurface Flow And Contaminant Transport code (Hamm et al., 1997)). The data that were utilized for a model of the GSA were collected during 1996. Data collection included well coordinates and elevations, geophysical logs, and drillcore descriptions (Smits et al., 1997). The GSA model consisted of 166 320 elements with areal resolution of 200 × 200 ft, except in peripheral areas. The vertical resolution varied according to hydrogeologic unit and was relatively fine in order to support subsequent contaminant transport analyses (Flach and Harris, 1999).


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To model the GSA aquifer system the following assumptions were made regarding boundary conditions. For the UTRA it was assumed that the water that infiltrated as a result of rainfall and/or man-made surface facilities discharged equally to the Fourmile, the UTR, and the McQueen branches, respectively. Since the discharge was assumed to be symmetrical at both sides of the river branches, no-flow boundary conditions were imposed at the UTRA beneath the river branches. Along the west border of the model where natural boundaries do not exist a prescribed head boundary was specified from a contour map of measured water elevations. The Gordon aquifer was assumed to discharge equally to both sides of the UTR river branch, which resulted into a no-flow assumption along this boundary. Since no other physical boundaries exist to the west, east, and south of the Gordon aquifer prescribed head boundary conditions were imposed along the remaining boundaries. The results of the simulations with the FACT code showed that for the upper zone of the UTRA measured and simulated heads were in stronger agreement at the center than at the eastern or western boundaries of the GSA (Flach and Harris, 1999). 4. AEM Model Development Two different regional groundwater models of the GSA were created. The main hydrologic features that were considered in both models were the UTR, the McQueen, and the Fourmile branches, surface recharge facilities, rainfall, leakage, and smaller river branches (Tolika, 2001). In addition, the first model incorporated more detail in river branches and far-field features and took into account the difference in base elevation at different parts of the UTRA, which ranges between 140 ft and 240 ft. The second model assumed a uniform base height for this aquifer and included a smaller number of hydrologic elements within the GSA (the near-field) or to establish the groundwater flow of the surrounding area (the far-field). Contrary to the previous numerical study that utilized the FACT code (Flach and Harris, 1999), the two AEM models did not rely on artificial boundary conditions but utilized natural elements of known hydraulic head to serve as physical boundaries. Figure 3 illustrates this feature of the analytic element method where a number of additional river branches that extend beyond the vicinity of the GSA have been added in order to establish the background flow field within which the GSA is situated. 4.1. M ODEL

WITH I NHOMOGENEITIES

The superposition principle employed by the analytic element method requires specification of the hydraulic head at an arbitrary point in the flow field (called the reference point) for the determination of a constant of integration entering the near-field solution. Given enough hydrologic elements for the definition of the nearand far-flow field characteristics one would expect that an AEM solution should be relatively insensitive to selection of a reference point. However, choosing the

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Figure 3. River elements in near- and far-fields.

location and head value of the reference point is not trivial but appears to influence an AEM solution disproportionately. In general, “the reference point should be placed far away, outside the far-field features and given a neutral head: approximately the average head in the model domain” (Haitjema, 1995). Hence, several tests were conducted in order to determine reference locations and values of head that provided for a robust near-field solution, and the reference point was placed south of the Fourmile river branch in an area surrounded by a large number of river branches. In order to account for the boundaries of the upper zone of the UTRA rainfall and extraction polygons were added (Figures 2 and 4). The rainfall polygon simulated the infiltration that took place on the top of the upper part of the UTRA. The extraction polygon simulated the leakage that took place from the upper to the lower part of the UTRA. Additionally, on the surface of the GSA there are several artificial surface sources (infrastructures) that contribute to the infiltration rate and these were also represented with polygons approximating their areal distribution. In Figure 4 artificial surface sources of constant infiltration rate are represented by polygons with a star within. The extraction rate did not remain constant along the base of the aquifer because the hydraulic head, as well as, the resistance of the confining unit changed spatially. Extraction rates were calculated through Equation (1) N=

φ−H , c

(1)

where N represents the infiltration rate, φ the value of hydraulic head in an upper unconfined aquifer, H the value of hydraulic head at a lower confined aquifer and c the resistance of the confining, between the aquifers, layer. The resistance to flow was defined as c ≡ L/KV , where L is the average value of the vertical


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Figure 4. Model with inhomogeneity areas: Heads (in ft) in the upper zone of the UTRA.

distance traveled by water (the thickness of the confining layer) and Kv is the vertical hydraulic conductivity of the confining layer. The above manipulation was performed because of the availability to us at that time of the Single Layer version of the AEM code (SLAEM) only, necessitating generation of the leakage from the upper to the lower part of the UTRA outside of the SLAEM code. Instead of calculating point extraction rates by choosing wells at points where the hydraulic head was known for both the lower and the upper zone of the UTR aquifer and then calculating the extraction rates at these points, mean areal values of hydraulic head were calculated and mean areal extraction rates were used. This was deemed necessary for our study since all terms in Equation (1) change spatially and thus erroneous estimation of the value of one of these terms might have affected the solution more than mean areal values would. For our study the extraction rate from the bottom of the upper zone of the UTRA was calculated at 10 locations and measurements of wells within a radius of 1060 ft around each location were utilized. The mean confining tan clay layer thickness was estimated from altitude maps of the top and bottom surfaces for this layer and values of the vertical hydraulic conductivity, Kv , were obtained from Flach and Harris (1999). The final AEM model is shown in Figure 4. In this figure the uppermost line segment represents the UTR river branch modeled by AEM as curvilinear elements of constant head. The next line segments from the top represent the north boundaries

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of the extraction and rainfall polygons, respectively. The triangles on these line segments indicate positions of specified head value. Head data points were applied at certain positions within the modeled domain where the hydraulic head was known from measuring wells and served as control points. Artificial surface sources (infrastructures) contributing to the infiltration rate are represented in this figure by polygons containing a star within. The polygons’ shape approximated the actual shape of the basins and the star indicates constant infiltration rate. Figure 4 also included two areas with inhomogeneities in aquifer base elevation representing domains of piecewise constant base height. To avoid a jump in the value of hydraulic head at the intersection of an inhomogeneity and the aquifer “a doublet element” (Strack, 1989) was used for the northeastern inhomogeneity depicted with a tetragon of bold outline. Calibration of the model was done with regards to infiltration and extraction rates primarily at the northeastern part of the modeling area, where the number of wells to the UTRA zones is low. Comparison between measured and simulated heads was made for all 415 well locations of the upper part of the UTRA. The discrepancy between simulated and measured hydraulic heads is depicted in Figure 5. Table I summarizes the outcome of this comparison. Figure 5 and Table I show satisfactory agreement between modeled and measured heads with 78% of the wells having an absolute head difference of less than 10 ft. There is however an area near the middle part of the Fourmile river branch (star symbols) where systematic discrepancies (larger than 10 ft) were

Figure 5. Model with inhomogeneity areas: Difference between measured and simulated heads.


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TABLE I Comparison between measured and simulated heads for all wells: Model with inhomogeneities Absolute difference in head (ft)

Well count

% of wells

0–5 5–10 >10

241 84 90

58% 20% 22%

observed. This appears to be a local problem of the model indicating that more elements need to be placed at this location or that further calibration is required. The average absolute difference between simulated and measured heads is 7 ft and this may be improved if local refinement at the Fourmile river branch area is performed. 4.2. M ODEL WITHOUT I NHOMOGENEITIES A second model for the upper zone of the UTRA was developed that did not contain areas of different base heights but assumed a uniform base height of 177 ft for the whole aquifer. (The two inhomogeneity polygons depicted in Figure 4 were omitted.) Another difference with the first model was that the second model assumed that the upper zone of the UTRA extends infinitely and is not bounded south of the UTR river branch. The head values calculated with this model are depicted in Figure 6. Dots indicate the physical boundary of the upper zone of the UTR aquifer. The modeled aquifer

Figure 6. Model without inhomogeneity areas: Heads (in ft) in the upper zone of the UTRA.

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Figure 7. Model without inhomogeneity areas: Differences between measured and simulated heads.

extends infinitely but the solution has physical meaning only up to the area south of the dots, where the actual aquifer extends. Figure 7 depicts the discrepancies between simulated and calculated hydraulic heads for the second model. The agreement is good for the whole model with the exception of some individual points (cross and star symbols) situated mainly at the eastern part of the model. The average absolute difference between simulated and measured hydraulic heads is 5.1 ft. This model appears to give better results than the first model both in terms of average difference between simulated and measured heads and percentage of wells that exhibit less than 10 ft absolute head difference. Table II summarizes the results from this model. TABLE II Comparison between measured and simulated heads for all wells: Model without inhomogeneities Absolute difference in heads (ft)

Well count

% of wells

0–5 5–10 >10

230 153 32

55% 37% 8%


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5. Discussion and Conclusions Analytic element methods are useful tools for obtaining general information about the hydrology of a regional domain without including too much detail in the model. The ideal use of analytic element methods may be as screening tools, facilitating or improving the calibration and the choice of boundary conditions of more complicated finite-difference and finite-element models. A combination of both methods that includes the use of the analytic element method at the beginning of the modeling process for understanding the hydrology of the area, and for estimating the boundary conditions would provide the most accurate results by refining detailed numerical models. The analytic element method’s run time for the General Separations Area model was of the order of seconds. In contrast, the GSA/FACT finite element model run on an IBM Intellistation M Pro with a Pentium III with 1GHz CPU and 1 GB of memory and took about 5 1/2 min to converge from a uniform initial condition of 250 ft, using a convergence tolerance of 0.25 ft. The memory requirement for the GSA/FACT model was 269 MB. The simulated field from the AEM model did not differ substantially from that of the finite element model and the relative poorer performance of both models at the edges of the modeling domain (northeast and northwest) is clearly attributed to the lack of data in these areas. A limitation of the analytic element method was the representation of the inhomogeneities. For our study, apart from base elevation inhomogeneities, an attempt was made to include in our model some areas that exhibited inhomogeneities in the horizontal hydraulic conductivity. However, this did not produce satisfactory results and these areas were omitted from our model with a constant horizontal hydraulic conductivity utilized for the whole aquifer. A conclusion reached during this study was that the analytic element method was ideal for modeling cases where inhomogeneities played a limited role. Acknowledgements This work has been partially supported by grant DE-FG02-97EW09999 from the U.S. Department of Energy, Office of Environmental Management. We would like to acknowledge G. Flach of the Savannah River Technology Center, D. Tolikas of the Aristotle University of Thessaloniki, and T. Sarris of the University of South Carolina for their help during development of the model. We would also like to thank the anonymous reviewers for their suggestions that improved our manuscript. References Bakker, M., Anderson, E. I., Olsthoorn, T. N. and Strack, O. D.: 1999, ‘Regional groundwater modeling of the Yucca Mountain site using analytic elements’, J. Hydrol. 226, 167–178.

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