Volume 21 (2015): Issue 3 (September 2015)

An overview is presented of scale problems in groundwater flow, with emphasis on upscaling of hydraulic conductivity, being a brief summary of the conventional upscaling approach with some attention paid to recently emerged approaches. The focus is on essential aspects which may be an advantage in comparison to the occasionally extremely extensive summaries presented in the literature. In the present paper the concept of scale is introduced as an indispensable part of system analysis applied to hydrogeology. The concept is illustrated with a simple hydrogeological system for which definitions of four major ingredients of scale are presented: (i) spatial extent and geometry of hydrogeological system, (ii) spatial continuity and granularity of both natural and man-made objects within the system, (iii) duration of the system and (iv) continuity/granularity of natural and man-related variables of groundwater flow system. Scales used in hydrogeology are categorised into five classes: micro-scale – scale of pores, meso-scale – scale of laboratory sample, macro-scale – scale of typical blocks in numerical models of groundwater flow, local-scale – scale of an aquifer/aquitard and regional-scale – scale of series of aquifers and aquitards. Variables, parameters and groundwater flow equations for the three lowest scales, i.e., pore-scale, sample-scale and (numerical) block-scale, are discussed in detail, with the aim to justify physically deterministic procedures of upscaling from finer to coarser scales (stochastic issues of upscaling are not discussed here). Since the procedure of transition from sample-scale to block-scale is physically well based, it is a good candidate for upscaling block-scale models to local-scale models and likewise for upscaling local-scale models to regional-scale models. Also the latest results in downscaling from block-scale to sample scale are briefly referred to.

The Chociwel region is part of the Szczecin Trough and constitutes the northeastern segment of the extended Szczecin-Gorzów Synclinorium. Lower Jurassic reservoirs of high permeability of up to 1145 mD can discharge geothermal waters with a rate exceeding 250 m³/h and temperatures reach over 90°C in the lowermost part of the reservoirs. These conditions provide an opportunity to generate electricity from heat accumulated in geothermal waters using binary ORC (Organic Rankine Cycle) systems. A numerical model of the natural state and exploitation conditions was created for the Chociwel area with the use of TOUGH2 geothermal simulator (i.e., integral finite-difference method). An analysis of geological and hydrogeothermal data indicates that the best conditions are found to the southeast of the town of Chociwel, where the bottom part of the reservoir reaches 3 km below ground. This would require drilling two new wells, namely one production and one injection. Simulated production with a flow rate of 275 m³/h, a temperature of 89°C at the wellhead, 30°C injection temperature and wells being 1.2 km separated from each other leads to a small temperature drop and moderate requirements for pumping power over a 50 years’ time span. The ORC binary system can produce at maximum 592.5 kW gross power with the R227ea found as the most suitable working fluid. Geothermal brine leaving the ORC system with a temperature c. 53°C can be used for other purposes, namely mushroom growing, balneology, swimming pools, soil warming, de-icing, fish farming and for heat pumps.

The study area, situated near the city of Wrocław in southwest Poland, is part of the hydrogeological system of the Quaternary/Neogene MGB 319, inclusive of a buried valley of high water potential, named the Bogdaszowice structure. This structure is an alternative source of water supply for the Wrocław city area. Numerical modelling is the most effective tool in establishing a groundwater protection strategy for Major Groundwater Basins (MGBs) in complex aquifer systems. In the present study, the first step was to assess the hydrodynamic conditions of the Radakowice groundwater intake by analyses of head contours, pathlines, average flow times and capture zones of particular wells. Subsequently, these results were used in combination with other data and compiled as GIS layers. The spatial distribution of hydraulic conductivity was based on the lithology of surface sediments. Other data sets such as the thickness of the unsaturated zone, average soil moisture and infiltration rate were taken either directly from the model or were calculated. Based on the input data obtained, vertical flow time calculations for every model cell were made. The final outcome is a map of the protection zone for the aquifer system of the MGB 319.

Flow in unsaturated porous media is commonly described by the Richards equation. This equation is strongly nonlinear due to interrelationships between water pressure head (negative in unsaturated conditions), water content and hydraulic conductivity. The accuracy of numerical solution of the Richards equation often depends on the method used to estimate average hydraulic conductivity between neighbouring nodes or cells of the numerical grid. The present paper discusses application of the computer simulation code VS2DI to three test problems concerning infiltration into an initially dry medium, using various methods for inter-cell conductivity calculation (arithmetic mean, geometric mean and upstream weighting). It is shown that the influence of the averaging method can be very large for coarse grid, but that it diminishes as cell size decreases. Overall, the arithmetic average produced the most reliable results for coarse grids. Moreover, the difference between results obtained with various methods is a convenient indicator of the adequacy of grid refinement.