Introduction to hydromechanical well tests in fractured rock aquifers

This article introduces hydromechanical well tests as a viable field method for characterizing fractured rock aquifers. These tests involve measuring and analyzing small displacements along with pressure transients. Recent developments in equipment and analyses have simplified hydromechanical well tests, and this article describes initial field results and interpretations during slug and constant-rate pumping tests conducted at a site underlain by fractured biotite gneiss in South Carolina. The field data are characterized by displacements of 0.3 μm to more than 10 μm during head changes up to 10 m. Displacements are a hysteretic function of hydraulic head in the wellbore, with displacements late in a well test always exceeding those at similar wellbore pressures early in the test. Displacement measurements show that hydraulic aperture changes during well tests, and both scaling analyses and field data suggest that T changed by a few percent per meter of drawdown during slug and pumping tests at our field site. Preliminary analyses suggest that displacement data can be used to improve estimates of storativity and to reduce nonuniqueness during hydraulic well tests involving single wells.     

Regional flow simulation in fractured aquifers using stress-dependent parameters

A model function relating effective stress to fracture permeability is developed from Hooke's law, implemented in the tensorial form of Darcy's law, and used to evaluate discharge rates and pressure distributions at regional scales. The model takes into account elastic and statistical fracture parameters, and is able to simulate real stress-dependent permeabilities from laboratory to field studies. This modeling approach gains in phenomenology in comparison to the classical ones because the permeability tensors may vary in both strength and principal directions according to effective stresses. Moreover this method allows evaluation of the fracture porosity changes, which are then translated into consolidation of the medium.     

Stochastic delineation of well capture zones

In this work, we describe a stochastic method for delineating well capture zones in randomly heterogeneous porous media. We use a moment equation (ME) approach to derive the time-dependent mean capture zones and their associated uncertainties. The mean capture zones are determined by reversely tracking the non-reactive particles released at a small circle around each pumping well. The uncertainty associated with the mean capture zones is calculated based on the particle displacement covariances for nonstationary flow fields. The flow statistics are obtained either by directly solving the flow moment equations derived with a first-order ME approach or from Monte Carlo simulations (MCS) of flow. The former constitutes a full ME approach, and the latter is a hybrid ME-MCS approach. This hybrid approach is invoked to examine the validity of the transport component of the stochastic method by ensuring that the ME and MC transport approaches have the same underlying flow statistics. We compared both the full ME and the hybrid ME-MCS results with those obtained with a full MCS approach. It has been found that the three approaches are in excellent agreement when the variability of hydrologic conductivity is small (_Y²=0.16). At a moderate variability (_Y²=0.5), the hybrid ME-MCS and the full MCS results are in excellent agreement whereas the results from the full ME approach deviate slightly from the full MCS results. This indicates that the (first-order) ME transport approach renders a good approximation at this level of variability and that the first-order ME flow approximation may not be sufficiently accurate at this variability in the case of divergent/convergent flow. The first-order ME flow approach may need to be corrected with higher-order terms even for moderate _Y² although the literature results reveal that the first-order ME flow approach is robust for uniform mean flow (i.e., giving accurate results even with _Y² as large as four).     

Stochastic modelling of groundwater flow and solute transport in aquifers

This paper presents an introductory overview of recently developed stochastic theories for tackling spatial variability problems in predicting groundwater flow and solute transport. Advantages and limitations of the theories are discussed. Lastly, strategies based on the stochastic approaches to predict solute transport in aquifers are recommended.     

Stochastic analysis of groundwater flow in aquifers with leakage

 Stochastic analysis of one- and two-dimensional flow through a shallow semi-confined aquifer with spatially variable hydraulic conductivity K represented by a stationary (statistically homogeneous) random process is carried out by using the spectral technique. The hydraulic head covariance functions for flows in a semi-confined aquifer bounded by a leaky layer above and an impervious stratum below are derived by assuming that the randomness forcing the head variation to originate from the hydraulic conductivity field of the aquifer. The head covariance functions are studied using two convenient forms of the logarithmic hydraulic conductivity process. The results demonstrate the significant reduction in the head variances and covariances due to the presence of a leaky layer. The hydraulic head correlation distance is also reduced greatly due to the presence of the leaky layer.     

Tracer mass recovery in fractured aquifers estimated from multiple well tests

Forced-gradient tracer tests in fractured aquifers often report low mass recoveries. In fractured aquifers, fractures intersected by one borehole may not be intersected by another. As a result (1) injected tracer can follow pathways away from the withdrawal well causing low mass recovery and (2) recovered water can follow pathways not connected to the injection well causing significant tracer dilution. These two effects occur along with other forms of apparent mass loss. If the strength of the connection between wells and the amount of dilution can be predicted ahead of time, tracer tests can be designed to optimize mass recovery and dilution. A technique is developed to use hydraulic tests in fractured aquifers to calculate the conductance (strength of connection) between well pairs and to predict mass recovery and amount of dilution during forced gradient tracer tests. Flow is considered to take place through conduits, which connect the wells to each other and to distant sources or sinks. Mass recovery is related to the proportion of flow leaving the injection well and arriving at the withdrawal well, and dilution is related to the proportion of the flow from the withdrawal well that is derived from the injection well. The technique can be used to choose well pairs for tracer tests, what injection and withdrawal rates to use, and which direction to establish the hydraulic gradient to maximize mass recovery and/or minimize dilution. The method is applied to several tracer tests in fractured aquifers in the Clare Valley, South Australia.     

Stochastic analysis of velocity spatial variability in bounded rectangular heterogeneous aquifers

Transport of inert solutes in two-dimensional bounded heterogeneous porous media is investigated in a stochastic framework. After adopting a first-order approximation of the flow equations, analytical expressions are derived for the velocity covariances. Effects of the boundary conditions and aquifer size upon the statistical moments are analyzed. While the size of the domain is shown to have small influence on the covariances in most cases, the solutions are considerably modified by the boundaries. The results are compared with analytical solutions on infinite domains, and several discrepancies are demonstrated. For example, while the velocity variances on infinite domains are homogeneous, the present results are strongly non-stationary. Finally, the problem is solved numerically by the Monte Carlo simulation method. The results, including the behavior near the boundaries, are shown to be in close agreement with analytical solutions.     

Sustained post-seismic effects on groundwater flow in fractured carbonate aquifers in Central Italy

A sustained increase in spring discharges was monitored after the 2016 Central Italy seismic sequence in the fractured carbonate aquifer of Valnerina–Sibillini Mts. The groundwater surplus recorded between August 2016 and November 2017 was determined to be between 400 and 500 × 10⁶ m³. In fractured aquifers, the post-seismic rise in spring discharges is generally attributed to an increase in bulk permeability caused by the fracture cleaning effect, which is induced by pore pressure propagation. In the studied aquifers, the large amount of additional discharge cannot only be attributed to the enhanced permeability, which was evaluated to be less than 20% after each main seismic event. A detailed analysis of the spring discharge hydrographs and of the water level at five gauging stations was carried out to determine the possible causes of this sudden increase in groundwater outflow. Taking into account the geological and structural framework, a conceptual model of a basin-in-series has been adopted to describe the complex hydrogeological setting, where the thrusts and extensional faults have clearly influenced the groundwater flow directions before and after the seismic sequence. The prevalent portion of the total post-seismic discharge surplus not explained by the increase in permeability has been attributed to changes in the hydraulic gradient that caused seismogenic fault rupture and the disruption in the upgradient sector of the aquifer. The additional flow calculated through the breach of the pre-existing hydrostructural barrier corresponds to approximately 470 × 10⁶ m³. This value is consistent with the total discharge increase measured in the whole study area, validating the proposed conceptual model. Consequently, a shift in the piezometric divide of the hydrogeological system has been induced, causing a potentially permanent change that lowers the discharge amount of the eastern springs.     

Stochastic delineation of capture zones: classical versus Bayesian approach

A Bayesian approach to characterize the predictive uncertainty in the delineation of time-related well capture zones in heterogeneous formations is presented and compared with the classical or non-Bayesian approach. The transmissivity field is modelled as a random space function and conditioned on distributed measurements of the transmissivity. In conventional geostatistical methods the mean value of the log transmissivity and the functional form of the covariance and its parameters are estimated from the available measurements, and then entered into the prediction equations as if they are the true values. However, this classical approach accounts only for the uncertainty that stems from the lack of ability to exactly predict the transmissivity at unmeasured locations. In reality, the number of measurements used to infer the statistical properties of the transmissvity field is often limited, which introduces error in the estimation of the structural parameters. The method presented accounts for the uncertainty that originates from the imperfect knowledge of the parameters by treating them as random variables. In particular, we use Bayesian methods of inference so as to make proper allowance for the uncertainty associated with estimating the unknown values of the parameters. The classical and Bayesian approach to stochastic capture zone delineation are detailed and applied to a hypothetical flow field. Two different sampling densities on a regular grid are considered to evaluate the effect of data density in both methods. Results indicate that the predictions of the Bayesian approach are more conservative.     

Assessment of the groundwater favorability of fractured aquifers from the southeastern Brazil crystalline basement

ABSTRACT

Groundwater favorability maps can aid groundwater exploitation in fractured aquifers, such as those of the Bação and Northern Bonfim complexes (Quadrilátero Ferrífero) southeastern Brazil, bringing alternatives for water supply in regions where water availability is at risk. These maps were obtained by means of the analytic hierarchy process (AHP), using six information levels: the height above the nearest drainage (HAND) model, the declivity map, three lineament maps (morphostructural, radiometric and magnetometric), and the lithological map. The E–W strike of the lineaments was emphasized for the integration, because it is the most frequent and subparallel to the present strike of the maximum principal stress σ₁. The favorability maps were validated by varying the input parameters and comparing the maps with 82 specific capacity values obtained from well tests. Although more data should be necessary to confirm this method, the results are promising and can be tested in other crystalline basement areas.     

Stochastic analysis of bounded unsaturated flow in heterogeneous aquifers: Spectral/perturbation approach

This paper describes a stochastic analysis of steady state flow in a bounded, partially saturated heterogeneous porous medium subject to distributed infiltration. The presence of boundary conditions leads to non-uniformity in the mean unsaturated flow, which in turn causes non-stationarity in the statistics of velocity fields. Motivated by this, our aim is to investigate the impact of boundary conditions on the behavior of field-scale unsaturated flow. Within the framework of spectral theory based on Fourier–Stieltjes representations for the perturbed quantities, the general expressions for the pressure head variance, variance of log unsaturated hydraulic conductivity and variance of the specific discharge are presented in the wave number domain. Closed-form expressions are developed for the simplified case of statistical isotropy of the log hydraulic conductivity field with a constant soil pore-size distribution parameter. These expressions allow us to investigate the impact of the boundary conditions, namely the vertical infiltration from the soil surface and a prescribed pressure head at a certain depth below the soil surface. It is found that the boundary conditions are critical in predicting uncertainty in bounded unsaturated flow. Our analytical expression for the pressure head variance in a one-dimensional, heterogeneous flow domain, developed using a nonstationary spectral representation approach [Li S-G, McLaughlin D. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour Res 1991;27(7):1589–605; Li S-G, McLaughlin D. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour Res 1995; 31(3):541–51], is precisely equivalent to the published result of Lu et al. [Lu Z, Zhang D. Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation. Adv Water Resour 2004;27:775–84].     

Contaminant transport in fractured media: analytical solution and sensitivity study considering pulse,Dirac delta and sinusoid input sources

The analytical solution of one‐dimensional transport for a single species radioactive nuclide, considering the decay term in a single fracture for pulse, Dirac delta, and single sinusoid input sources, has been studied using the Laplace transform method. The dimensionless concentration of the radioactive nuclide in the fracture appears to be a function of space, elapsed time, dispersivity, retardation factor, half‐life of the nuclide, and release time. By comparing different values of groundwater velocity, retardation factor, dispersivity, and release time, the results show that the c/c₀ ratio agrees with the nature of the physical and chemical characteristics of the nuclide in fracture transportation. The dimensionless concentration peak value from a small retardation factor is found to be more sensitive, within a time frame ranging from 10 years to a few hundreds years, than the case with a larger retardation factor for H‐3. Except for a small variation in the peak value, the result is almost the same for pulse and sinusoid inputs when considering the H‐3 nuclide. Analytical solutions during the preliminary screening phase are suitable for performance assessment on radioactive waste disposal sites under a one‐dimensional single fracture condition. Copyright © 2002 John Wiley & Sons, Ltd.     

Detection of the water level in fractured phreatic aquifers using nuclear magnetic resonance (NMR) geophysical measurements

Correlation of geophysical data collected using the NMR method in the Negev Desert, Israel, with hydrogeological data from nearby observation wells is presented. The experiment was conducted near Kibbutz Revivim in the Besor drainage system (Fig. 1). The objective of the survey was to detect groundwater layers in the Quaternary cover filling and Eocene fractured aquifers down to a depth of 100 m. The experiment was performed using a combination of two different geophysical techniques, namely the NMR and time domain electromagnetic (TDEM) methods. The geophysical results were verified by measuring the water level in three observation wells, two of which were drilled several months after the geophysical survey was carried out.The water level measured in these follow-up observation wells shortly after drilling did not coincide with the geophysical data. However, it settled over a period of time and finally stabilized at a depth very similar to that obtained from the NMR measurements. This phenomenon is caused by the fractured nature of the phreatic aquifer. Since the flow of water in such aquifers is confined by the fractures, the appearance of water in the well during or shortly after drilling is determined solely by the intersection of the well and the fracture. Our experiments showed that geophysical measurements in fractured phreatic aquifers may have a distinct advantage over direct borehole measurements, since the former average the depth to the water table over large areas (several thousand square meters) while the latter are limited by the area of the borehole cross-section (several tens of square centimeters).     

Incorporation of conceptual and parametric uncertainty into radionuclide flux estimates from a fractured granite rock mass

Detailed numerical flow and radionuclide simulations are used to predict the flux of radionuclides from three underground nuclear tests located in the Climax granite stock on the Nevada Test Site. The numerical modeling approach consists of both a regional-scale and local-scale flow model. The regional-scale model incorporates conceptual model uncertainty through the inclusion of five models of hydrostratigraphy and five models describing recharge processes for a total of 25 hydrostratigraphic–recharge combinations. Uncertainty from each of the 25 models is propagated to the local-scale model through constant head boundary conditions that transfer hydraulic gradients and flow patterns from each of the model alternatives in the vicinity of the Climax stock, a fluid flux calibration target, and model weights that describe the plausibility of each conceptual model. The local-scale model utilizes an upscaled discrete fracture network methodology where fluid flow and radionuclides are restricted to an interconnected network of fracture zones mapped onto a continuum grid. Standard Monte Carlo techniques are used to generate 200 random fracture zone networks for each of the 25 conceptual models for a total of 5,000 local-scale flow and transport realizations. Parameters of the fracture zone networks are based on statistical analysis of site-specific fracture data, with the exclusion of fracture density, which was calibrated to match the amount of fluid flux simulated through the Climax stock by the regional-scale models. Radionuclide transport is simulated according to a random walk particle method that tracks particle trajectories through the fracture continuum flow fields according to advection, dispersion and diffusional mass exchange between fractures and matrix. The breakthrough of a conservative radionuclide with a long half-life is used to evaluate the influence of conceptual and parametric uncertainty on radionuclide mass flux estimates. The fluid flux calibration target was found to correlate with fracture density, and particle breakthroughs were generally found to increase with increases in fracture density. Boundary conditions extrapolated from the regional-scale model exerted a secondary influence on radionuclide breakthrough for models with equal fracture density. The incorporation of weights into radionuclide flux estimates resulted in both noise about the original (unweighted) mass flux curves and decreases in the variance and expected value of radionuclide mass flux.     

Comparative study of methods for WHPA delineation

Human activities, whether agricultural, industrial, commercial, or domestic, can contribute to ground water quality deterioration. In order to protect the ground water exploited by a production well, it is essential to develop a good knowledge of the flow system and to adequately delineate the area surrounding the well within which potential contamination sources should be managed. Many methods have been developed to delineate such a wellhead protection area (WHPA). The integration of more information on the geologic and hydrogeologic characteristics of the study area increases the precision of any given WHPA delineation method. From a practical point of view, the WHPA delineation methods allowing the simplest and least expensive integration of the available information should be favored. This paper presents a comparative study in which nine different WHPA delineation methods were applied to a well and a spring in an unconfined granular aquifer and to a well in a confined highly fractured rock aquifer. These methods range from simple approaches to complex computer models. Hydrogeological mapping and numerical modeling with MODFLOW-MODPATH were used as reference methods to respectively compare the delineation of the zone of contribution and the zone of travel obtained from the various WHPA methods. Although applied to simple ground water flow systems, these methods provided a relatively wide range of results. To allow a realistic delineation of the WHPA in aquifers of variable geometry, a WHPA delineation method should ensure a water balance and include observed or calculated regional flow characteristics.     

Estimation of vertical water and heat fluxes in the semi-confined aquifers in tokyo metropolitan area,japan

Groundwater circulation is known to be one of the agents responsible for the redistribution of geothermal energy by acting as a source or sink in the course of its movement through porous media. Heat transport in groundwater systems is considered to be a coupled process and the theory based on this was used to analyse temperature profiles of 30 thermally stable observation wells in a deep, semi-confined aquifer system in the Tokyo Metropolitan area. Vertical water fluxes in the semi-confined aquifers and the associated upward heat fluxes were estimated from a heat flux equation that describes convection and conduction processes of heat transport in one dimension. The vertical downward water fluxes in Shitamachi lowland, Musashino and Tachikawa terraces were 0.69.26.91 × 10^?9, 1.46-70.92 × 10^?9 and 2.61.2204 × 10^?9 m/s, respectively. A vertical upward water flux of 1.80-33.60 × 10^?9 m/s was estimated in Shitamachi lowland. The water flux generally decreased with increasing depth for observation wells which intercepted more than one semi-confining layer. The estimated upward heat fluxes for Shitamachi lowland, Musashino and Tachikawa terraces were 0.32-1.12, 0.49-1.21 and 1.00-11.62 W/m², respectively. The heat flux was highest in Tachikawa terrace where a major fault, the Tachikawa fault, is located. Generally, the estimated heat flux was higher in the semi-confining layers than in the aquifers. Areas with heat sources and sinks as well as groundwater flow patterns in the semi-confined aquifers were revealed by heat flux and temperature distributions in the study area.     

Hydraulic head applications of flow logs in the study of heterogeneous aquifers

Permeability profiles derived from high-resolution flow logs in heterogeneous aquifers provide a limited sample of the most permeable beds or fractures determining the hydraulic properties of those aquifers. This paper demonstrates that flow logs can also be used to infer the large-scale properties of aquifers surrounding boreholes. The analysis is based on the interpretation of the hydraulic head values estimated from the flow log analysis. Pairs of quasi-steady flow profiles obtained under ambient conditions and while either pumping or injecting are used to estimate the hydraulic head in each water-producing zone. Although the analysis yields localized estimates of transmissivity for a few water-producing zones, the hydraulic head estimates apply to the far-field aquifers to which these zones are connected. The hydraulic head data are combined with information from other sources to identify the large-scale structure of heterogeneous aquifers. More complicated cross-borehole flow experiments are used to characterize the pattern of connection between large-scale aquifer units inferred from the hydraulic head estimates. The interpretation of hydraulic heads in situ under steady and transient conditions is illustrated by several case studies, including an example with heterogeneous permeable beds in an unconsolidated aquifer, and four examples with heterogeneous distributions of bedding planes and/or fractures in bedrock aquifers.     

Numerical study on tide-driven submarine groundwater discharge and seawater recirculation in heterogeneous aquifers

There are many factors affecting submarine groundwater discharge (SGD). However, systematic study of the influences of these factors is still limited. In this study, numerical modeling is performed to quantitatively explore the influences of various factors on SGD in a coastal aquifer. In such locations, tidal and terrestrial hydraulic gradients are the primary forces driving fresh and salt water movement. Unlike steady-state flow, dynamic fresh and salt water mixing at the near-shore seafloor may form an intertidal mixing zone (IMZ) near the surface. By constructing a general SGD model, the effects of various model components such as boundary conditions, model geometry and hydraulic parameters are systematically studied. Several important findings are obtained from the study results: (1) Previous studies have indicated there will be a freshwater discharge tube between the classic transition zone and the IMZ. However, this phenomenon may become unclear with the increase of heterogeneity and anisotropy of the medium’s conductivity field. (2) SGD and IMZ are both more sensitive to the vertical anisotropy ratio of hydraulic conductivity (K_x/K_z) than to the horizontal ratio (K_x/K_y). (3) Heterogeneity of effective porosity significantly affects SGD and IMZ. (4) Increase of the storage coefficient decreases fresh water discharge but increases mixing salt water discharge and total SGD. The increase will also change the shape of the IMZ. (5) Variation of dispersivities does not affect SGD, but significantly changes the distributions of the IMZ and the whole mixing zone. These findings will be helpful to the sampling design of field studies of SGD and to the application of dynamic SGD models to field sites for model development and calibration.     

地面核磁共振技术勘查西北干旱浅层地下水效果浅析

地面核磁共振技术勘查地下水是一种新的应用领域,该技术是目前国际上唯一的能直接进行地下水勘查的技术.我所自一九九九年引进法国Numis仪器以来,先后在陕西黄土区、宁南黄土区等地开展寻找不同类型浅层地下水的试验工作,取得了一定的野外成果.本文是在分析总结这些成果的基础上,针对存在的问题如强干扰背景下勘查结果的可靠性,同一测点"8”字型与"正方形”发射线框二者勘查结果比较等方面进行探讨分析.