U.Bethers¹,J.Sennikovs¹, N.Jekabsons²
 

Abstract

The analysis of groundwater flow patterns requires expertise in geology, hydrogeology, mechanical engineering and mathematical modeling. An attempt to provide toolkit for the above categories of specialists is performed.

An object-oriented engineering software tool is developed for the applications in the investigations of the groundwater flows. It consists of following functional blocks:

1. a geometrical preprocessor including general one to three dimensional CAD functionality,
2. a programmable command interpreter for the geometrical preprocessor,
3. a data assimilator for the interactive export of the geological structure from the field data (multiple survey wells and geological cross sections),
4. an utility package for the construction of the surfaces and volumes characteristic for geological layers,
5. a two and three dimensional finite element mesh generator,
6. a solver for the Darcy flows in complex anisotropic geological structures with internal boundary conditions,
7. "menu" and "command line" driven graphical environment for the performing of pp. 1 to 6 and the visualization of the geological structures and the computational data.

The example is illustrative also from the hydrogeological point of view. The investigation area contains several ancient valleys filled with the glacial deposits. These valleys penetrate sandwich-type structure of aquifers and aquitards of Devonian age. Deluvial and proluvial materials with high filtration capacity on the declivities of these hidden valleys are essentially three-dimensional, thus being a real challenge for a modeling engineer. The project decisions to situate the main building of the plant on the soft moraine and to perform multiple injections of non-permeable material in upper Devonian aquifers would be interesting from the engineering point of view. The long-term (30 years) observation series at more than 300 wells serve as an extensive basis for model tuning and verification.
 

1. Introduction

The calculation of the groundwater flows in local scale models nowadays is rather engineering than research problem. The emphasis then solving filtration problems is shifted from the physics and hydrological sciences towards (1) adequate representation of geological structures, (2) yielding reasonable boundary conditions by means of employing the regional scale models or interpreting rare observations, (3) establishing the user friendly interfaces for data pre- and post-processing, (4) management of huge, heterogeneous survey and observation data sets which as a rule are scattered in time and space to satisfy any arbitrary needs ? but not thus of modeler.

We faced a problem to investigate the paths of groundwater filtration in the vicinity of Plavinas Hydropower plant (HPP) that is a largest one in the chain of HPPs on the major Latvian stream, the River Daugava (see Fig. 1 for geographical location).

Figure 1. The geographical location of the Plavinas HPP.

The very general description would include:

• annual average run-off of the River Daugava is 32 km³,
• the maximum river flow during the spring flooding due the snow melting can reach 15000 m³/s,
• the level difference between the reservoir and lower stream is 40 m, the volume of the reservoir is 0.5 km³,
• the HPP under normal conditions operates to cover peak power consumption, i.e. few hours a day; it causes daily fluctuation of the downstream water level of 4 m order.

An attempt to develop the original system of software tools that would cover the full cycle of modeling requirements for hydrogeological engineer was performed. As a result almost no innovative solutions can be found in particular stages; we would like to emphasize the overall performance of the system and its ability to handle the management of information flows.

The success of application of mathematical model for solving a complex engineering problem as investigation of the groundwater flow beneath [for instance] a dam of hydropower plant and leakage from the respective reservoir cannot be measured by a success in a single phase of modeling process. We tried to split the description of our approach into the following blocks:

• the conceptual approach to the modeling;
• the structure of employed software tools;
• the selection of the model area and the representation of hydrogeological structure;
• the mathematical model of filtration;
• the results of calibration;
• the results of modeling;
• the compatibility of the model with furthers modeling requirements.

• chapter 2 explains the proposed approach;
• chapter 3 describes the structure and the functionality of the toolset for processing of hydrogeological information (HiFiGeo);
• chapter 4 outlines basic concepts and information used for building a geometrical model of 3D geological structure, as well as hydrostratigraphic assumptions;
• chapter 5 is devoted for the description of mathematical model of groundwater flow;
• >chapter 6 presents the results of calibration of model (i.e. solving inverse problem of groundwater flow) describing also the calibration procedure;
• chapter 7 summarizes results yielded by the employment of model for calculation series with various applied forcing, i.e. reservoir?s water levels, drainage and relief regimes.

2. Conceptual approach to modeling

The mathematical equations describing one-phase flow in saturated layered structures are simple to handle from the mathematical and numerical point of view. The emphasis in determination the modeling success shifts from the selection of appropriate equations towards a discretization method and adequate representation of geological structures. A variety of modeling packages is available either on the market or in R&D groups.

The chain of discretization methods ranked by increasing capability of the 3D description of computational domain (and also increasing sophistication in employed mathematics and price) stands as follows:

1. Quasi-3D models formed by sandwich-type set of 2D aquifer models with account for aquitards by way of sink/source terms in 2D equations.
2. 3D finite difference models using

   uniform grids in horizontal direction;

   non-uniform grids;

   curvilinear grids.

3. 3D finite element models.
4. Finite volume models.

3. HiFiGeo: a toolset for processing hydrogeological information

The original software package HiFiGeo was developed for XWindow environment. The software is thus hardware independent, it is capable to run on any UNIX OS that supports XWindows. The particular modeling examples described in this paper were performed on IBM compatible PCs (LINUX) and on HP RISC workstation (HP-UX).

The toolset includes:

• Data assimilation module. Data assimilation assumes the migration of the stratigraphic information represented by survey wells and/or geological cross- sections, construction of the upper surfaces of hydrostratigraphic layers by different interpolation procedures.
• Preprocessing module generates the 2D finite element meshes for surfaces, produces 3D finite element grids based on triangle prisms or tetraedrs, checks the consistency of the topology of created 3D geometric structures. The built-in interpreter of extended command-line language allows multiple CAD-type actions. These functions can be realized interactively or in batch mode.
• The computational core defines and solves the groundwater filtration problem using 3D finite element approach. The solver engine is based on iterative method of conjugated gradients for solving LAES. This allows reaching a high efficiency solving problems in structures with strongly varying properties.
• Data post-processing and visualization module calculates the filtration velocities, fluxes, discharges, etc. It allows a visualization of wells, hydrostratigraphic structure, piezometric and pressure heads, groundwater flows in arbitrary vertical cross sections and on nearly horizontal sections, including surfaces of geological layers.

4. The geological structure and model area

The selected model area is a rectangular 4 km to 4 km region that in z direction extends from the topographic surface (elevations in range 30 to 90 m, see Fig. 2) to -100 m level.

Figure 2. The surface elevations and 2D finite element mesh.

The project solution for construction of HPP was the situating of the main building on the right floodbank of the River Daugava. It is built on the intersection of the pre-quarternary river valley (not seen in landscape) with contemporary one. The buried valley is filled with loam and sandy-loam, thus preventing intensive filtration directly beneath HPP. However, the building of heavy construction on soft sediments determines its reasonable mechanical displacements during exploitation period since 1970. The aquifers of upper Devonian (mainly dolomites and sandstone separated by clay aquitards) age form the bedrock hills on both embankment. Due their rather high permeability the multiple injections of concrete suspension are performed in dolomites beneath the right and left wing earth dams. The major problems of the exploitation of HPP due groundwater flows are:

1. The high-permeable deposits of deluvial and proluvial origin on the slopes of hidden valley causes increased filtration beneath the right wing of HPP, increasing piezometric heads downstream the power plant. The washout of that heterogeneous material cannot be excluded.
2. The drainage system of the main building and relief wells of right embankment are partially discharging downstream in the river. Thus drainage and relief suffers from the continuous reasonable elevation changes.

Figure 3. The cross section of geological layers of the right embankment downstream HPP.

The deposits of post-Devonian age

1. Quaternary gravel and sand aquifer;
2. upper [silty] moraine;
3. lower [sandy] moraine;
4. proluvial and deluvial pre-quaternary formations (² train² ) on the slopes of hidden valleys;
5. The deposits of upper and middle Devonian age:
6. Daugava aquifer;
7. Salaspils aquitard;
8. Plavinas aquifer and aquitard;
9.-10. upper Amata aquifer and aquitard;
11.-12. lower Amata aquifer and aquitard;
13. Gauja aquifer.
Besides those natural formation we incorporated the technogenic structures
14. concrete HPP building with upper and lower aprons and retaining concrete walls; 15.-17. left, right and river earth dams;
18.-20. concrete injections in Daugava dolomites on both embankments, and in Plavinas dolomites beneath the right earth dam.

• Two river valleys are found in the topography of model area: Daugava valley and Laucese valley (downstream HPP). These sand, gravel, and partially moraine-covered valleys lay on Plavinas dolomites of Devonian age.
• Two main buried valleys intersect the model area. The deeper valley crosses the contemporary Daugava valley beneath the HPP. It penetrates all upper Devonian deposits reaching Gauja sand/sandstone aquifer. Another hidden valley is found along the right bank of Daugava crossing right-wing earth dam. It cuts the Daugava and Salaspils Devonian deposits. Above features are shown on Fig. 4.

  Figure 4. The areas of the presence of the upper (Daugava, Salaspils and Plavinas suites) deposits of Devonian age.

• Both pre-quaternary valleys are filled with moraine; the proluvial / deluvial deposits (² train² ) can be found on the slopes of these valleys beneath the moraine.
• Moraine covers also the bedrock surface of hills on both sides of Daugava and Laucese rivers. It is absent in large areas of Daugava valley on the bottom of reservoir and downstream the HPP. Moraine is not found also on the islet of Daugava dolomites on the right embankment near HPP. See Fig. 5 for moraine and train covered areas.

  Figure 5. The areas of the presence of technogenic materials, moraine and buried proluvial materials.

• The thin sand lenses in moraine as well as clay/marl lenses in the Amata-Gauja complex are distinct features of these layers. They cannot be represented in details from the geological surveys. Therefore the moraine is subdivided in the silty and sandy parts with different permeability. The structure of the Amata - Gauja formation is subdivided into upper, lower Amata, and Gauja aquifers separated by rather thin (from tens of cm to few m) aquitards.

5. Mathematical model

The mathematical model is formulated for the non-steady groundwater flow in anisotropic medium, assuming saturated and non-elastic flow conditions. However, the calibration and all calculations are performed for steady-state conditions in isotropic materials.

The non-flow boundary conditions on the topographic surface allows in first approximation simulate also the unsaturated conditions in the upper layers, i.e. to find the free surface of groundwater. Thus, the model delivers 3D distribution of the piezometric heads; the filtration?s velocities, pressure heads and the locations of the saturation boundary are calculated by post - processor.

We applied the following boundary conditions that to some extent reveals also regional effects influenced by the artificial reservoir:

• the constant piezometric heads on the bottom of reservoir (nearly 72 m), and downstream the HPP on Daugava and Laucese riverbeds (32 to 36 m);
• the non-flow boundary conditions on the rest of topographic surface allowing to perform the 1st estimate of saturation boundary and avoiding non-physical leakage from the bedrock hills;
• the non-flow boundary conditions on the model bottom (-100 m) boundary and side boundaries of upper (quaternary, moraine, Devonian Daugava, Salaspils, Plavinas and upper Amata) layers;
• the constant piezometric heads on the side boundaries of lower Amata and Gauja layers; these two values are determined during calibration stage;
• the respective constant heads on the drainage blankets (surface boundary conditions) below the HPP, lower and upper aprons;
• the respective constant heads along the filter length of relief (line boundary conditions) wells.

6. The calibration of model

Nevertheless the wide possibilities of calibration we limited ourselves in optimizing 22 parameters: 20 permeability of different materials (assumptions of isotropy, and non-varying permeability of each material) and 2 side boundary values for piezometric heads on Gauja and lower Amata.

The aim of optimizations was to reduce the difference of the model results from the measured range of piezometric heads at 240 monitoring wells below 10%. It was reached for 218 wells, while in 152 wells the predictions were within observations' limits.

The emphasis was put on reaching the best agreement in the wells far from HPP, because the situation in the vicinity of power station is almost defined by drainage/relief.
 
 

Table 1. Values of permeability.

No. (m/d) HiFiGeo  Project evaluation  1. Quaternary aquifer 1.5 0.5-20  2. Upper moraine 0.005 0.002-5  3. Lower moraine 0.1 0.025-5  4. Train 20 4-55  5. Daugava aquifer 30 50-100  6. Salaspils aquitard 0.0001 0.000015  7. Plavinas aquifer 1.5 1-500  8. Plavinas aquitard 0.02 0.000003-0.003  9. Upper Amata aquifer 1.5 0.4-50  10. Upper Amata aquitard 0.01 0.0000002-0.003  11. Lower Amata aquifer 3 0.2-4  12. Lower Amata aquitard 0.01 0.01-0.2  13. Gauja aquifer 25 25-40  14. Concrete buildings 0.00001 -  15. Left earth dam 1 -  16. Right earth dam 2 -  17. River earth dam 0.025 - 18.-20. Concrete injections 0.05 -

The side boundary conditions found by model calibration are piezometric heads of 45 m and 48 m for lower Amata and Gauja aquifers, respectively.
 

7. The results of calculation series

The calculation series by the calibrated model have been performed to investigate groundwater flow patterns at different reservoir and downstream water levels, assuming varying drainage/relief regimes.

These series included hypothetical changes in relief regime of right embankment, as well as change in drainage conditions below HPP. Besides that, the consequences of the closure of several high debit relief wells were investigated. Example of piezometric heads in the vertical structure of right embankment (geological structure in Fig. 3) 60 m downstream HPP see on Fig. 6.

Figure 6. The distribution of piezometric heads in the geological cross-section of Fig. 3.

We can summarize the four major paths of groundwater flows that have to be investigated closer to evaluate safety measures for the operation of HPP (see also Fig. 7 for the distribution of piezometric heads on the top of Plavinas aquifer):

1. The flow perpendicular to the HPP mainly through the ²train² on the right-bank slope of buried valley. This flow pattern originates from reasonable hydrological link of reservoir with train through the right embankment. This would be the most important feature from the safety considerations due to possible washout of heterogeneous material just below the right wing of HPP.
2. The flow from the reservoir through the upper Devonian deposits of right riverbank, partially around the concrete injection in Daugava and Plavinas dolomites. This filtration pattern together with p.1 is responsible for enlarged piezometric pressures on the right bank quite far downstream the HPP.
3. The flow beneath the central earth dam through mainly Plavinas aquifer is due to high connectivity of reservoir and Plavinas dolomites in the natural riverbed of Daugava.
4. The filtration from the reservoir to the Laucese valley through the left bank Devonian hill that has been a local groundwater divide in pre-dam period. This flow pattern is partially isolated by concrete injections beneath the left earth dam; however serious leakage can be expected to this aquifer also from the upstream reservoir?s part.

Figure 7. The distribution of piezometric heads on the upper surface of Plavinas aquifer.

8. Conclusions

The proposed approach to the groundwater modeling allowed forming a toolset for engineer-hydrogeologist. The full cycle of modeling from geological data assimilation through calibration, numerical simulation until post-processing and visualization of calculation results are included in software package.

The example of the groundwater flow modeling by developed package was performed illustrating the application of toolset.

The principal output of the groundwater flow modeling is the boundary conditions and/or stress tensor distribution delivered for the implementation of mechanical (stress-deformation) models. The finite element mesh from HiFiGeo has been successfully exported to the commercial package for solving mechanical problems ANSYS at the Institute for Polymer Mechanics, Riga. However, no attempt is performed to migrate also the results of groundwater filtration calculations to this package yet.

1. Scientist, Laboratory for mathematical modeling of environmental and technological processes, University of Latvia, 8 Zellu, Riga LV1002, Latvia
2. PhD student, Department of Materials and Manufacturing Engineering, Lulea University of Technology, Lulea, Sweden