On matrix diffusion: formulations, solution methods and qualitative effects

 Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φ _m ² R _m D _m  / L _m ², whereas late-time behavior (long tracer tests) depends only on φ _m R _m , and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. Received, October 1997 · Revised, November 1997 · Accepted, December 1997     

Migration of recharge waters downgradient from the Santa Catalina Mountains into the Tucson basin aquifer, Arizona, USA

 Aquifers in the arid alluvial basins of the southwestern U.S. are recharged predominantly by infiltration from streams and playas within the basins and by water entering along the margins of the basins. The Tucson basin of southeastern Arizona is such a basin. The Santa Catalina Mountains form the northern boundary of this basin and receive more than twice as much precipitation (ca. 700 mm/year) as does the basin itself (ca. 300 mm/year). In this study environmental isotopes were employed to investigate the migration of precipitation basinward through shallow joints and fractures. Water samples were obtained from springs and runoff in the Santa Catalina Mountains and from wells in the foothills of the Santa Catalina Mountains. Stable isotopes (δD and δ¹⁸O) and thermonuclear-bomb-produced tritium enabled qualitative characterization of flow paths and flow velocities. Stable-isotope measurements show no direct altitude effect. Tritium values indicate that although a few springs and wells discharge pre-bomb water, most springs discharge waters from the 1960s or later. Received, February 1997 · Revised, September 1997 · Accepted, September 1997     

Natural arsenic in Triassic rocks: A source of drinking-water contamination in Bavaria, Germany

 The aquifer system of the Upper Triassic Keuper Sandstone, an important source of drinking water in northern Bavaria, is affected by elevated arsenic concentrations. Within the study area of 8000 km², no evidence exists for any artificial source of arsenic. Data from about 500 deep water wells show that in approximately 160 wells arsenic concentrations are 10–150 μg/L. The regional distribution of arsenic in the groundwater shows that elevated arsenic concentrations are probably related to specific lithofacies of the aquifers that contain more sediments of terrestrial origin. Geochemical measurements on samples from four selected well cores show that arsenic has accumulated in the rocks. This indigenous arsenic is the source of arsenic in the groundwater of certain facies of the middle unit of the Keuper Sandstone. Received, June 1998 / Revised, January 1999, May 1999 / Accepted, June 1999     

Determining concentration fields of tracer plumes for layered porous media in flow-tank experiments

 In the laboratory, computer-assisted image analysis provides an accurate and efficient way to monitor tracer experiments. This paper describes the determination of detailed temporal concentration distributions of tracers in a flow-tank experiment by analyzing photographs of plumes of Rhodamine dye through the glass wall of the tank. The methodology developed for this purpose consists of four steps: (1) digitally scanning black and white negatives obtained from photographs of the flow–tank experiment; (2) calibrating and normalizing each digitized image to a standard optical-density scale by determining the relation between the optical density and pixel value for each image; (3) constructing standard curves relating the concentration in an optical density from five experimental runs with predetermined concentrations (2–97 mg/L); and (4) converting the optical density to concentration. The spatial distribution of concentration for two photographs was determined by applying these calibration and conversion procedures to all pixels of the digitized images. This approach provides an efficient way to study patterns of plume evolution and transport mechanisms. Received, March 1998 Revised, September 1998 Accepted, October 1998     

Regional characterisation of hydraulic properties of rock using air-lift data

 Hydrogeologic studies are commonly data-intense. In particular, estimations of hydraulic properties of hard rock often require large amounts of data. In many countries, large quantities of hydrogeologic data have been collected and archived over the years. Therefore, the use of existing data may provide a cost-efficient alternative to collecting new data in early stages of hydrogeologic studies, although the available data may be considered imprecise. Initially, however, the potential usefulness, i.e., the expected accuracy, of the available data in each specific case must be carefully examined. This study investigates the possibilities of obtaining estimates of transmissivity from hard-rock air-lift data in Sweden within an order of magnitude of results obtained from high-quality injection-test data. The expected accuracy of the results was examined analytically and by means of statistical methods. The results were also evaluated by comparison with injection-test data. The results indicate that air-lift data produce estimates of transmissivity within an order of magnitude compared to injection-test data in the studied examples. The study also shows that partial penetration and hydrofracturing may only affect the estimations approximately half an order of magnitude. Thus, existing data may provide a cost-efficient alternative to collection of new data in early stages of hydrogeologic studies. Received, January 1998 Revised, November 1998, December 1998 Accepted, December 1998     

State of the art of modelling two-phase flow in fractured rock

 Two-phase flow in fractured rock is an important phenomenon for a range of practical problems, not the least of which is non-aqueous phase liquid (NAPL) contamination of groundwater. Although multiphase systems have long been studied in the petroleum field, in the hydrogeological field progress has only just reaches the point where models are being developed. Scale effect is one of the main issues of concern. Although models presented in this paper have the potential to provide useful predictions, they can only be used to investigate a variety of possible scenarios with parameters being specified in the form of distribution of values. The calibration and validation of all but the simplest of these models poses a formidable task, with great demands on hydrogeologists and geophysicists to provide adequate data. Received: 20 May 1996 · Accepted: 19 August 1996     

Simulation of groundwater drainage into a tunnel in fractured rock and numerical analysis of leakage remediation, Romeriksporten tunnel, Norway

Standard geostatistical methods for simulation of heterogeneity were applied to the Romeriksporten tunnel in Norway, where water was leaking through high-permeable fracture zones into the tunnel while it was under construction, causing drainage problems on the surface. After the tunnel was completed, artificial infiltration of water into wells drilled from the tunnel was implemented to control the leakage. Synthetic heterogeneity was generated at a scale sufficiently small to simulate the effects of remedial actions that were proposed to control the leakage. The flow field depends on the variance of permeabilities and the covariance model used to generate the heterogeneity. Flow channeling is the most important flow mechanism if the variance of the permeability field is large compared to the expected value. This condition makes the tunnel leakage difficult to control. The main effects of permeability changes due to sealing injection are simulated by a simple perturbation of the log-normal probability density function of the permeability. If flow channeling is the major transport mechanism of water into the tunnel, implementation of artificial infiltration of water to control the leakage requires previous chemical-sealing injection to be successful. Electronic Publication     

Electrical resistivity imaging of conductive plume dilution in fractured rock

Electrical resistance tomography (ERT) was used to monitor a conductive plume dilution experiment that was conducted in fractured basalt in order to assess its applications in this type of fractured-rock environment. Tap water was injected into an injection well for 34 days to dilute a pre-existing potassium chloride (KCl) plume at a site in Idaho, USA. No further fluids were introduced artificially during a 62-day monitoring period. Both surface ERT and cross-borehole ERT were used to monitor dilution and displacement of the plume. A square grid of land-surface electrodes was used with the surface ERT. Three-dimensional images of surface ERT delineated areas of increased and decreased resistivities. Increasing resistivities are attributed to dilution/displacement of the KCl solution by tap-water invasion or the influx of seasonal recharge. Decreasing resistivities resulted from redistribution of residual KCl solution. Cross-borehole ERT was conducted between the injection well and each of seven surrounding monitoring wells. Polar plots of the injection-well resistivity data in the direction of each monitoring well delineate specific locations where tap water seeped from the injection well via preferential flow paths determined by time-dependent resistivity increases. Monitoring-well data indicate locations of clustered and isolated regions of resistivity changes.     

Effects of quarry mining and of other environmental impacts in the mountainous Chicam-Toctina drainage basin (Córdoba, Argentina)

 The environmental conditions prevailing in the Chicam-Toctina drainage system (approx. 138 km² in Córdoba, Argentina) are considered representative of a number of catchments in Argentina's Sierras Pampeanas Range. Two groups of ions reflect the sources of dissolved species in the catchment: a) a group (Cl^–, SO^2– ₄, and Na⁺) which recognizes natural and anthropogenic sources, and which exhibits significant correlations with N^– ₃ and NO^– ₂, and b) another group of components (Ca²⁺, Mg²⁺, and HCO^– ₃) which is clearly controlled by carbonate rocks and their waste rock products. In the headwaters, stockpiled marble quarry mining wastes provide a more open system to CO₂ gaseous exchange than the outcropping rocks, thus promoting the increase of carbonate dissolution (up to 4.88 g km^–2 s^–1 during the rainy season). This specific yield was 20% higher than the amount estimated for an area with fewer extended mining activities. The dissolved load delivered by the upper reaches is subjected in the lower drainage area to various processes, mainly controlled by the presence of the city of Alta Gracia (approx. 40,000 inhabitants). In the dry season, due to nutrient inputs supplied by the city, photosynthetic activity plays a major role controlling stream pH. Hence, the high values of calcite saturation indexes and the increase of CaCO₃ concentration in bed sediments can be explained by calcite precipitation. Such a process could be accompanied by the coprecipitation on calcium carbonate of low solubility heavy metal carbonates. Received : 17 January 1997 · Accepted : 31 March 1997     

Groundwater circulation in the allochthonous limestone units between Lake Girdev and Kazanpınarı Spring, Antalya, southwestern Turkey

 The aim of the study is to investigate the interaction between waters of Lake Girdev and groundwater in the allochthonous limestone units exposed in the area between Lake Girdev and Kazanpınarı Spring, southwestern Turkey. The features analyzed include the flow direction and apparent groundwater velocity, their relationship with Lake Girdev, and the effect of lithological and structural features on the groundwater circulation. The results of a fluorescein tracer test indicate that groundwater flows east-northeast and the apparent flow velocity ranges from 26.2 to 35.6 m h^–1 between the injection site and various observation points. Tritium data suggest that the water of Lake Girdev and groundwater are probably similar in age, and oxygen-18 isotope data indicate that water derived from Lake Girdev is the main source of recharge to the aquifer. The aquifer is fed not only by Lake Girdev but also by rainfall percolating through allochthonous limestones; together, these provide the discharge of springs in Elmalı Polje. The permeability of the allochthonous limestone aquifer has been enhanced as a result of jointing and faulting. Received, June 1997 / Revised, June 1998, March 1999 / Accepted, July 1999     

The use of laboratory experiments for the study of conservative solute transport in heterogeneous porous media

 Laboratory experiments on heterogeneous porous media (otherwise known as intermediate scale experiments, or ISEs) have been increasingly relied upon by hydrogeologists for the study of saturated and unsaturated groundwater systems. Among the many ongoing applications of ISEs is the study of fluid flow and the transport of conservative solutes in correlated permeability fields. Recent advances in ISE design have provided the capability of creating correlated permeability fields in the laboratory. This capability is important in the application of ISEs for the assessment of recent stochastic theories. In addition, pressure-transducer technology and visualization methods have provided the potential for ISEs to be used in characterizing the spatial distributions of both hydraulic head and local water velocity within correlated permeability fields. Finally, various methods are available for characterizing temporal variations in the spatial distribution (and, thereby, the spatial moments) of solute concentrations within ISEs. It is concluded, therefore, that recent developments in experimental techniques have provided an opportunity to use ISEs as important tools in the continuing study of fluid flow and the transport of conservative solutes in heterogeneous, saturated porous media. Received, December 1996 · Revised, July 1997 · Accepted, August 1997     

Environmental impact of uncontrolled waste disposal in mining and industrial areas in Central Germany

The present-day landscape in Central Germany, in particular the region of Leipzig, Halle and Bitterfeld, is characterized by the scars of former industrial activities. Vast districts have been devastated by lignite strip mining. Industrial and domestic waste, residues from ore smelting, and highly toxic waste products from petrochemical plants and pesticide production were deposited in abandoned pits near population centers. The chief effects of waste on the environment are the contamination of groundwater by dissolved pollutants, the acidification of soil and water by the oxidation of pyrite-containing mining waste, and the salinization of shallow aquifers by rising brines from adjacent confined groundwater affected by mining. The consequences for the region are serious: mining lakes used for recreational purposes are contaminated by leachates from adjacent waste dumps. Pyrite-containing refuse from lignite mining under oxidation gives rise to the acidification of surface and groundwater, a basic condition for pollutant mobilization. In former metal mining districts, metalliferous and radioactive residues from smelting jeopardize public health. These effects are described in detail using three case studies. Received: 30 July 1996 · Accepted: 24 February 1997     

The influence of Cenozoic tectonics on the groundwater-production capacity of fractured zones: a case study in Sao Paulo, Brazil

A new procedure is developed to correlate structural lineaments recognised through air-photo interpretation with subsurface fracture features that are associated with zones of high groundwater production in fractured-rock environments. The analysis approach is referred to as the homogeneous tectonic domain (HTD) method and involves correlating the lineament features of a given area with the orientation of the primary stress fields and fracture structures associated with the recent tectonic history that affected the region of study. The main premise of the method is that the most recent tectonic events in a given area have had the most significant influence on the nature of the existing fracture network and subsequently on the regional groundwater flow characteristics. A study site was selected within the state of S?o Paulo, Brazil, where a complex tectonic history dating back to Precambrian time has generated significant fracture porosity in the bedrock environment. The bedrock is heavily used in this area as a domestic and industrial aquifer. The most recent tectonic activity is associated with five distinct Cenozoic events that generated fracture features through both shear and extension stress fields. Due to the mode of formation, fracture zones generated by extension tend to have the largest effective apertures and are the most conductive to groundwater. By applying the HTD method in a series of test areas where specific Cenozoic events were dominant, fracture trends generated by shear and extension mechanisms could be identified. Water-well production capacity was correlated with proximity to extension-type structures in most cases. Other factors, such as the type of rock the well was completed in, had a much weaker influence on well capacity. Through this application, the HTD approach is shown to provide a methodology for delineating fractured areas within rock environments that have high potential for groundwater-resource development by combining classical lineament analysis with a clear understanding of the tectonic history of a given area. Electronic Publication     

Delineation of groundwater protection zones based on tracer tests and transport modeling in alluvial sediments

 Regulations aiming to protect exploitable groundwater resources were edicted in Belgium a few years ago. Therefore, prevention and protection zones are defined by law and must be determined practically around each pumping well or spring, based on local hydrogeological conditions. The determination of hydrodynamic and hydrodispersive parameters, characterizing the local flow and transport properties of the aquifer, requires pumping and tracing tests. The interpretation of these field experiments, considering the heterogeneity of the geological layers, is performed through the use of numerical FEM simulations of the groundwater flow and pollutant transport conditions in a deterministic framework. After calibration of the model on experimental measurements, multiple simulations with contaminant injections at various points of the modeled domain allow the determination of the transfer time of the pollutant in the studied aquifer whilst taking the updated heterogeneity into account. On the basis of the computed transfer times in the saturated zone, the various prevention and protection areas can be assessed based on provisions of the law. Received: 27 June 1997 · Accepted: 29 July 1997     

DNA tracers with information capacity and high detection sensitivity tested in groundwater studies

 In order to investigate the usefulness of unique synthetic DNA tracers in groundwater, a field experiment was conducted in Norway. DNA tracers and a sodium-chloride tracer were injected into an aquifer. The transport of DNA molecules was interpreted by comparing with the plume of chloride ions under forced-gradient steady-state flow conditions. Spatial concentration moments described the migration of conservative tracers. Mobility and migration of DNA in groundwater demonstrate that DNA tracers can be detected by using the polymerase chain reaction (PCR) and DNA sequence analysis. The results indicate that DNA tracers can be valuable tools as tracers in groundwater investigations. Received, June 1997 / Revised, July 1998, December 1998 / Accepted, January 1999     

In situ estimation of the effective chemical diffusion coefficient of a rock matrix in a fractured aquifer

An in situ method of estimating the effective diffusion coefficient for a chemical constituent that diffuses into the primary porosity of a rock is developed by abruptly changing the concentration of the dissolved constituent in a borehole in contact with the rock matrix and monitoring the time-varying concentration. The experiment was conducted in a borehole completed in mudstone on the campus of the University of the Free State in Bloemfontein, South Africa. Numerous tracer tests were conducted at this site, which left a residual concentration of sodium chloride in boreholes that diffused into the rock matrix over a period of years. Fresh water was introduced into a borehole in contact with the mudstone, and the time-varying increase of chloride was observed by monitoring the electrical conductivity (EC) at various depths in the borehole. Estimates of the effective diffusion coefficient were obtained by interpreting measurements of EC over 34 d. The effective diffusion coefficient at a depth of 36 m was approximately 7.8×10^?6 m²/d, but was sensitive to the assumed matrix porosity. The formation factor and mass flux for the mudstone were also estimated from the experiment.     

Water quality assessment in Akpabuyo, Cross River basin, South-Eastern Nigeria

 A baseline study involving analyses of surface and subsurface water samples from the Akpabuyo area was carried out in order to assess their suitability for drinking, domestic and agricultural purposes. Study results show that the waters are acidic (3.41≤pH≤6.28), soft (hardness 2.09–10.68 mg/l as CaCO₃), fresh (conductivity <1400 μs/cm) and characterised by low sodium adsorption ratio, SAR (0.08–0.59). In addition, the mean values of the major cations (Ca²⁺, Mg²⁺, Na⁺, K⁺) and anions (SO₄ ^2–, Cl^–, HCO₃ ^–) are all within the World Health Organisation (WHO) standards. Taking all this into consideration (except pH), the waters may be regarded as excellent for drinking, domestic and agricultural purposes. On the basis of regression equations, the major cations (K, Na, Ca, Mg) correlate well with conductivity. Finally, results also show that four chemical facies are delineated. These include Ca-Cl, Na-Cl, Ca-SO₄ and Ca-HCO₃. Received: 19 June 1996 / Accepted: 15 April 1997     

A comparison of estimated and calculated effective porosity

 Effective porosity in solute-transport analyses is usually estimated rather than calculated from tracer tests in the field or laboratory. Calculated values of effective porosity in the laboratory on three different textured samples were compared to estimates derived from particle-size distributions and soil–water characteristic curves. The agreement was poor and it seems that no clear relationships exist between effective porosity calculated from laboratory tracer tests and effective porosity estimated from particle-size distributions and soil–water characteristic curves. A field tracer test in a sand-and-gravel aquifer produced a calculated effective porosity of approximately 0.17. By comparison, estimates of effective porosity from textural data, moisture retention, and published values were approximately 50–90% greater than the field calibrated value. Thus, estimation of effective porosity for chemical transport is highly dependent on the chosen transport model and is best obtained by laboratory or field tracer tests. Received, March 1997 · Revised, August 1997 · Accepted, August 1997     

Phosphate pollution in the groundwater of lower Vamsadhara river basin, India

 The lower Vamsadhara river basin, spreading over an area of 817 sq.km in northern Andhra Pradesh, represents a typical rural setting. The occurrence of phosphorus-bearing minerals reported in literature, and the increasing application of phosphatic fertilizers in the area have prompted these studies. Water samples from 113 wells were analysed for Ca, Mg, Na, K, Cl, SO₄, HCO₃, F, NO₃ and PO₄. The results indicate the presence of phosphate in the groundwater ranged from 0.72 to 7.07 mg/l, which is beyond the limits recommended for domestic and water treatment purposes. Samples of soils and weathered rocks were analyzed for their water-soluble phosphate and other chemical parameters. The water-soluble phosphate in the widely used fertilizers of the area was determined. The spatial variation of phosphate in the aquifer and the soil leachate characteristics supplemented by the chemical equilibrium calculations clearly indicate the dominance of geological sources over the fertilizer sources in contributing PO₄ to the groundwaters. Received: 4 March 1996 / Accepted: 29 July 1996     

Stable-isotopes of groundwaters from the Albuquerque, New Mexico, basin: one decade later

In the spring of 1995, 24 samples were collected from a widely distributed system of municipal water wells in Albuquerque, N.M., and analyzed for hydrogen (δD) and oxygen (δ¹⁸O) isotopic compositions. δD values for 15 of these samples are largely similar to those reported by Yapp in 1985, but have locally become more negative by as much as 5 per mil (ö). δD–δ¹⁸O data define two endmembers that are well aligned along the familiar meteoric water line (MWL): (1) the eastern domain (mountain precipitation runoff), having δD>–86ö (similar to the criteria of Yapp) and δ¹⁸O>–12.1ö (this work); and (2) a central basin domain, which may be in part derived from water seepage from the Rio Grande, having δD<–95ö and δ¹⁸O<–13.2ö. Only a few wells across the basin have δD values near the "baseline" value of the Rio Grande, defined by Yapp as –92ö. The proximity of these wells to the Rio Grande is consistent with recharge by seepage from the river bed under baseline conditions. Extensive pumping in the eastern domain and West Mesa areas may be partly responsible for an apparent expansion of the central-basin regime of water more depleted in δD, much as a plume migrating in response to transient perturbations in original hydraulic gradients. Vertically stacked groundwater occurrences having limited interconnection are inferred from the significant differences in isotopic compositions of samples from two wells screened at multiple depths. The central and western parts of the basin are little influenced by contributions from the eastern domain. Some groundwaters from the western part of the basin plot below the MWL and clearly cannot be mixtures solely of the eastern domain and central basin endmembers. The origins of these western groundwaters and the most depleted central basin groundwaters are as yet unknown, but we speculate they may have received recharge under climatic conditions different from the present.