Interpretation of single-well tracer tests using fractional-flow dimensions. Part 1: Theory and mathematical models

Generalized equations using fractional-flow dimensions were derived to estimate the Darcy and seepage velocities obtained from the point-dilution and the single-well injection-withdrawal field tests conducted in fractured-rock aquifers. Seepage velocities can only be estimated from single-well tests if the hydraulic conductivity and the hydraulic gradient are known a priori. However, if a radial-convergent test is also performed between two boreholes, the kinematic porosity can be estimated and be used to estimate the seepage velocity from the single-well test results. To apply the generalized equations, the flow dimension and the extent of the flow region must be known. Therefore, the generalized radial flow (GRF) model of Barker (1988; a generalized radial flow model for hydraulic tests in fractured rock. Water Resour Res 24(10):1796–1804) is used to estimate the flow dimension because of its wide range of applications. A pumping test performed on the boreholes will yield an estimate of the fractional-flow dimension by applying the GRF model. Electronic Publication     

Analysis and numerical approximation of Brinkman regularization of two-phase flows in porous media

We consider a system of nonlinear partial differential equations that arises in the modeling of two-phase flows in a porous medium. The phase velocities are modeled using a Brinkman regularization of the classical Darcy’s law. We propose a notion of weak solution for these equations and prove existence of these solutions. An efficient finite difference scheme is proposed and is shown to converge to the weak solutions of this system. The Darcy limit of the Brinkman regularization is studied numerically using the convergent finite difference scheme in two space dimensions as well as using both analytical and numerical tools in one space dimension. The results suggest that the Brinkman regularization may not approximate the accepted entropy solutions of the Darcy model and raise fundamental questions about the use of Brinkman type models in two-phase flows.     

冲洪积平原渗流和管流耦合的辐射井结构

利用新疆阿克苏台兰河流域冲洪积平原区非稳定流抽水试验资料,以辐射井为研究对象,结合辐射管内的水头损失及流态,建立粗颗粒潜水含水层渗流和水平管流耦合的地下水流数值模型。利用数值模型,分析在粗颗粒含水层中辐射管不同根数、不同长度、等效渗透系数、辐射井的井径以及不同含水层的渗透系数、不同降深对辐射井出水量的影响,并且根据各参数的相互关系,提出冲洪积平原辐射井的出水量的经验公式。为优化设计辐射井结构及辐射井布置提供依据,对台兰河地下水库的建设及后期运行管理提供了技术支撑。     

Single-well and large-scale cross-hole tracer experiments in fractured rocks at two sites in Sweden

As part of the Swedish site investigations and research associated with the disposal of spent nuclear fuel, tracer experiments in deep boreholes have been employed in order to characterize solute transport and hydraulic connectivity in the fractured bedrock at two sites??Forsmark and Laxemar-Simpevarp. Performance and analytical results are presented from a suite of tracer experiments in varying scales, from single-hole injection-withdrawal tests, intermediate-scale tests with sorbing tracers, to large-scale connectivity tests over distances up to several hundred meters in major fracture zones or networks of zones. In addition to demonstrating transport connectivity over large distances, a general result is that the single-hole tests, as well as the cross-hole tests with sorbing tracers, have clearly demonstrated the process of solute retention of water-conductive features in the rock at different scales.     

A trigger-tube tracer dilution technique for determining Darcy and apparent velocities of groundwater in dug wells: A case study on phreatic aquiferous formation in Bamenda -Cameroon

The need to understand flow within aquiferous formations for a complete evaluation of groundwater resource and quality control prompts the determination of groundwater velocities through well dilution technique. Well dilution techniques utilize tracer solutions after establishing an initial homogenous condition to monitor the flow rate of ambient groundwater into the wells. Application of dilution techniques in wells makes it feasible to determine the velocities of groundwater in the aquiferous formation surrounding the well. In this study, a simple trigger-tube tracer dilution technique was employed to determine the Darcy and apparent velocities of groundwater in the phreatic aquiferous formation in Bamenda, Cameroon. Eighteen (18) hand dug-wells at different locations within Bamenda were sampled by utilizing sodium chloride (NaCl) as the conservative tracer. Field estimates of groundwater flow velocities in the phreatic aquiferous formation in Bamenda reveal Darcy’s groundwater velocity in the range of 0.39 m/d at Nacho to 130.64 m/d at Foncha Street and apparent velocity in the range of 0.78 m/d at Nacho to 277.86 m/d at Foncha Street. The immense variations in the velocities of groundwater indicate that the groundwater flows at different rates and directions within the aquiferous formation in Bamenda, possibly due to variations in their hydraulic conductivities. Moreover, the spatial variations in the formation types, facies changes, thickness, and layering of the aquiferous formation also contribute to the variation of velocities. Areas with low groundwater velocities are associated with a lower contaminant transport rate when compared to areas with high groundwater velocities. The findings of this study are important for assessing the rates of pollutant movement in the subsurface, as well as the effectiveness and efficacy of the trigger-tube technique in evaluating the hydraulic properties of aquiferous formations.     

Numerical simulation of liquefaction in porous media using nonlinear fluid flow law

It is well known that for a sufficiently high seepage velocity, the governing flow law of porous media is nonlinear (J. Computers & Fluids 2010; 39 : 2069–2077). However, this fact has not been considered in the studies of soil‐pore fluid interaction and in conventional soil mechanics. In the present paper, a fully explicit dynamic finite element method is developed for nonlinear Darcy law. The governing equations are expressed for saturated porous media based on the extension of the Biot (J. Appl. Phys. 1941; 12 : 155–164) formulation. The elastoplastic behavior of soil under earthquake loading is simulated using a generalized plasticity theory that is composed of a yield surface along with non‐associated flow rule. Numerical simulations of porous media subjected to horizontal and vertical components of ground motion excitations with different permeability coefficients are carried out; while computed maximum pore water pressure is specially taken into consideration to make the difference between Darcy and non‐Darcy flow regimes tangible. Finally, the effect of non‐Darcy flow on the evaluated liquefaction potential of sand in comparison to conventional Darcy law is examined. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical modeling of the hydraulic signatures of horizontal and inclined faults

Pumping tests in discontinuous media are commonly interpreted using radial/non-radial flow analytical models, which do not account for a large range of multistage real signatures that combine both flow types. The term radial is employed in Barker??s sense, referring to the cross-flow area growth with a flow dimension (n) equal to 2, while multistage refers to a flow response of several time periods with successive n values. Synthetic domains are used to numerically investigate the flow behaviour of faulted media, specifically the effect of fault inclination on multistage signatures. Simulations are performed using single faults surrounded by a permeable matrix to characterize drawdown series and to identify hydrodynamic scenarios associated with some diagnostic multistage n sequences. The n sequence 2 ?C <?2 ?C 2 results from interactions between the matrix and a horizontal to weakly inclined fault, while 2 ?C 1.5 ?C 2 corresponds to a higher fault inclination and is a combination of the generalized horizontally and vertically faulted models. These results improve the interpretation of ambiguous drawdown series from long-term pumping tests. This provides a better hydraulic characterization of faulted environments, allowing assessment of fault and matrix properties such as fault inclination. The approach is successfully tested on real datasets.     

Control‐volume mixed finite element methods

A key ingredient in simulation of flow in porous media is accurate determination of the velocities that drive the flow. Large‐scale irregularities of the geology (faults, fractures, and layers) suggest the use of irregular grids in simulation. This paper presents a control‐volume mixed finite element method that provides a simple, systematic, easily implemented procedure for obtaining accurate velocity approximations on irregular (i.e., distorted logically rectangular) block‐centered quadrilateral grids. The control‐volume formulation of Darcy’s law can be viewed as a discretization into element‐sized “tanks” with imposed pressures at the ends, giving a local discrete Darcy law analogous to the block‐by‐block conservation in the usual mixed discretization of the mass‐conservation equation. Numerical results in two dimensions show second‐order convergence in the velocity, even with discontinuous anisotropic permeability on an irregular grid. The method extends readily to three dimensions.     

Using radon-222 to study coastal groundwater/surface-water interaction in the Crau coastal aquifer (southeastern France)

Radon has been used to determine groundwater velocity and groundwater discharge into wetlands at the southern downstream boundary of the Crau aquifer, southeastern France. This aquifer constitutes an important high-quality freshwater resource exploited for agriculture, industry and human consumption. An increase in salinity occurs close to the sea, highlighting the need to investigate the water balance and groundwater behavior. Darcy velocity was estimated using radon activities in well waters according to the Hamada “single-well method” (involving comparison with radon in groundwater in the aquifer itself). Measurements done at three depths (7, 15 and 21 m) provided velocity ranging from a few mm/day to more than 20 cm/day, with highest velocities observed at the 15-m depth. Resulting hydraulic conductivities agree with the known geology. Waters showing high radon activity and high salinity were found near the presumed shoreline at 3,000 years BP, highlighting the presence of ancient saltwater. Radon activity has also been measured in canals, rivers and ponds, to trace groundwater discharges and evaluate water balance. A model of the radon spatial evolution explains the observed radon activities. Groundwater discharge to surface water is low in pond waters (4 % of total inputs) but significant in canals (55 l/m²/day).     

Engineering characterization of hydraulic properties in a pilot rock cavern for underground LNG storage

Feasibility of storing LNG in a lined rock cavern was evaluated using a pilot cryogenic rock cavern constructed in Daejeon, Korea. The pilot program included hydrogeological and engineering characterization of the rock mass around the cavern, design and construction of a drainage system, and pilot operation of the cryogenic cavern. An appropriate drainage system is most important to protect the containment system of LNG from thermal shocks due to ice lenses and hydrostatic pressure of groundwater. As a part of the pilot program, this study focused on the evaluation of hydraulic and engineering properties of the rock mass around the cavern. For this purpose, engineering logging of the rock cores, single and cross-hole hydraulic tests, and recharge/drainage tests were performed using seven drilled holes with different trends and plunges. Three main joint sets were found from the logging of the rock cores, acoustic borehole televiewer, and window mapping. The orientations of the three major joint sets were 60/209, 40/171, and 29/331, which can provide the main groundwater flow paths. Mean RQD values ranged from 56 to 88, which were classified as fair and good, although varying with depth along single boreholes. Hydraulic conductivity from the single and cross-hole hydraulic tests estimated in the order of 10⁻⁶ or 10⁻⁷ m/s and corresponding transmissivity ranged between 10⁻⁵ and 10⁻⁶ m²/s. Permeable intervals identified from the hydraulic tests were mostly located above the cavern roof. Below the roof, the permeable zone was difficult to observe. According to the hydraulic communication tests performed for some designated intervals, hydraulic connection between boreholes was highly varied with depth or location, which indicated a very different distribution of water conducting joint sets along the boreholes. When water was injected at R1 with constant or varying flow rates, monotonous and stable seepage was observed at observation boreholes. From this, some stable drainage was expected even in relatively heavy rainfalls. When designing the drainage system of the cavern, the drainage holes should be orientated to maximize frequency of encountering the major joint sets and the permeable intervals identified from this study.     

磁共振探测估算含水层渗透系数的原位试验研究

通过一个完整的磁共振探测（MRS）、钻探、抽水试验过程,开展了MRS估算含水层渗透系数的原位试验研究。在分析MRS估算渗透系数准确性的基础上,系统剖析了引起准确性差异的主要因素,并对进一步提高估算效果提出了建议。结果显示：（1）采用现阶段常用的参数设置,与抽水试验计算值相比,MRS估算渗透系数的差值为抽水试验计算值的17.59%。（2）MRS推断的含水层顶板、底板埋深与钻孔揭示的信息相比,差值分别为4.11m、1.03m,表明其对估算渗透系数准确性的影响较小。（3）CP值是影响估算准确性的重要因素,其值为10-9数量级符合大多数地层的特点。另外,通过在已知渗透系数的钻孔附近进行MRS,从而获取CP参考值,应用该值估算的渗透系数准确性高于常用的参数设置。（4）指数a、b设置方面,应用Seevers公式（a=1、b=2）的估算效果优于Kenyon公式（a=4、b=2）。本成果有助于提高MRS估算渗透系数方法在野外条件下的适用性。     

Fractional flow dimensions and hydraulic properties of a fracture-zone aquifer, Leppävirta, Finland

 In order to characterize the hydraulic properties of an aquifer in Finland comprising two subvertical fracture zones, observation-well responses were matched with generalized radial flow (GRF) type curves. The responses in six wells out of seven are consistent with the GRF model. The fractional flow dimensions (1–1.2 and 1.5) were determined by regression analysis of straight-line slopes and type-curve matching. In each test, the flow dimensions in the neighboring fracture zone range from 2–2.25. Comparisons of the late-time responses with the asymptotic GRF solution and the flow dimensions obtained by reversing the pumping and observation points suggest homogeneous hydraulic properties. Deviations in responses can be explained by flow-path tortuosity. After assessments of the extent of the flow and radial distances along the fracture system, hydraulic conductivities and storativities were determined from the results of the type-curve matching procedure. The obtained hydraulic conductivities are 1.3×10^–5 to 7.9×10^–5 m/s and 5.0×10^–6 to 2.5×10^–5 m/s for the western and the eastern fracture zones, respectively. The results were verified by applying them to analytical solutions for pumping wells. The calculated pumping-well responses are consistent with the observations. The analysis of flow dimension also enhances qualitative interpretations on the hydrogeology of fracture zones. Received, April 1997 · Revised, September 1997 · Accepted, May 1998     

Implication of surface modified NZVI particle retention in the porous media: Assessment with the help of 1-D transport model

Retention of surface-modified nanoscale zero-valent iron (NZVI) particles in the porous media near the point of injection has been reported in the recent studies. Retention of excess particles in porous media can alter the media properties. The main objectives of this study are, therefore, to evaluate the effect of particle retention on the porous media properties and its implication on further NZVI particle transport under different flow conditions. To achieve the objectives, a one-dimensional transport model is developed by considering particle deposition, detachment, and straining mechanisms along with the effect of changes in porosity resulting from retention of NZVI particles. Two different flow conditions are considered for simulations. The first is a constant Darcy’s flow rate condition, which assumes a change in porosity, causes a change in pore water velocity and the second, is a constant head condition, which assumes the change in porosity, influence the permeability and hydraulic conductivity (thus Darcy’s flow rate). Overall a rapid decrease in porosity was observed as a result of high particle retention near the injection points resulting in a spatial distribution of deposition rate coefficient. In the case of constant head condition, the spatial distribution of Darcy’s velocities is predicted due to variation in porosity and hydraulic conductivity. The simulation results are compared with the data reported from the field studies; which suggests straining is likely to happen in the real field condition.     

A trigger-tube tracer dilution technique for determining Darcy and apparent velocities of groundwater in dug wells: A case study on phreatic aquiferous formation in Bamenda-Cameroon

The need to understand flow within aquiferous formations for a complete evaluation of groundwater resource and quality control prompts the determination of groundwater velocities through well dilution technique. Well dilution techniques utilize tracer solutions after establishing an initial homogenous condition to monitor the flow rate of ambient groundwater into the wells. Application of dilution techniques in wells makes it feasible to determine the velocities of groundwater in the aquiferous formation surrounding the well. In this study, a simple trigger-tube tracer dilution technique was employed to determine the Darcy and apparent velocities of groundwater in the phreatic aquiferous formation in Bamenda, Cameroon. Eighteen(18) hand dug-wells at different locations within Bamenda were sampled by utilizing sodium chloride(NaCl) as the conservative tracer. Field estimates of groundwater flow velocities in the phreatic aquiferous formation in Bamenda reveal Darcy's groundwater velocity in the range of 0.39 m/d at Nacho to 130.64 m/d at Foncha Street and apparent velocity in the range of 0.78 m/d at Nacho to 277.86 m/d at Foncha Street. The immense variations in the velocities of groundwater indicate that the groundwater flows at different rates and directions within the aquiferous formation in Bamenda, possibly due to variations in their hydraulic conductivities. Moreover, the spatial variations in the formation types, facies changes, thickness, and layering of the aquiferous formation also contribute to the variation of velocities. Areas with low groundwater velocities are associated with a lower contaminant transport rate when compared to areas with high groundwater velocities. The findings of this study are important for assessing the rates of pollutant movement in the subsurface, as well as the effectiveness and efficacy of the trigger-tube technique in evaluating the hydraulic properties of aquiferous formations.     

Substantiation of debris flow velocity from super-elevation: a numerical approach

The use of super-elevations that a forced vortex flow leaves on the valley walls of a curved flume is a plausible approach toward estimating debris flow velocities in earthquake-induced geo-hazard studies. The centrifugal force of a speeding flow is responsible for a higher flow depth on the outer bend. However, in reality, a flow is not steady, and only the highest flow-marks are left at the outer and inner bends of the flow, which can lead to an inaccurate estimation of the actual velocity. Seeing the real scenario of the field, a series of numerical flume tests using smoothed particle hydrodynamics (SPH) is conducted to validate the estimation of debris flow velocities from flow-marks. Velocities estimated from flow-marks are lower than real velocities near the source region, but they converge to real velocities as the distance to the source increases. Based on several simulations, a best-fit line is proposed for adjusting debris flow velocity from mud-marks, and it is used to estimate flow velocities of the well-documented debris event called “Shiraito river debris flow,” which happened near the rim of the Hakone Crater, Kanagawa Prefecture, Japan, ensuing from the 1923 Great Kanto earthquake.     

Stress and strain fields for overdamped slug tests in aquifer materials,and resulting conservation equation

Two theories may be used to analyze overdamped variable‐head (slug) tests in aquifer materials. The first theory assumes that the solid matrix strain has a negligible influence. The second theory takes into account some elastic and immediate strain. Something is wrong with these theories because they yield different hydraulic conductivity values. This paper explains what is wrong after establishing the strain‐stress elastic equations for a slug test in 2 ideal conditions: plane strain and spherical symmetry. The equations show that the radial contraction (or elongation) and tangential elongation (or contraction) yield a null volumetric strain. As a result, the conservation is described by the Laplace equation, which is used by the first theory. This first theory is the only one to yield correct solutions. The diffusion equation, with storativity, which is used by the second theory, is physically ill founded for slug tests in aquifers. This new proof scientifically confirms previously raised doubts and experimental proofs that the second theory is ill founded.     

Micro- and macro-behaviour of fluid flow through rock fractures: an experimental study

Microscopic and macroscopic behaviour of fluid flow through rough-walled rock fractures was experimentally investigated. Advanced microfluidic technology was introduced to examine the microscopic viscous and inertial effects of water flow through rock fractures in the vicinity of voids under different flow velocities, while the macroscopic behaviour of fracture flow was investigated by carrying out triaxial flow tests through fractured sandstone under confining stresses ranging from 0.5 to 3.0 MPa. The flow tests show that the microscopic inertial forces increase with the flow velocity with significant effects on the local flow pattern near the voids. With the increase in flow velocity, the deviation of the flow trajectories is reduced but small eddies appear inside the cavities. The results of the macroscopic flow tests show that the linear Darcy flow occurs for mated rock fractures due to small aperture, while a nonlinear deviation of the flow occurs at relatively high Reynolds numbers in non-mated rock fracture (Re?>?32). The microscopic experiments suggest that the pressure loss consumed by the eddies inside cavities could contribute to the nonlinear fluid flow behaviour through rock joints. It is found that such nonlinear flow behaviour is best matched with the quadratic-termed Forchheimer equation.     

Pathline tracing on fully unstructured control-volume grids

The trend toward unstructured grids in subsurface flow modeling has prompted interest in the issue of streamline or pathline tracing on unstructured grids. Streamline tracing on unstructured grids is problematic because a continuous velocity field is required for the calculation, while numerical solutions to the groundwater flow equations provide velocity in discretized form only. A method for calculating flow streamlines or pathlines from a finite-volume flow solution is presented. The method uses an unconstrained least squares method on interior cells and a constrained least squares method on boundary cells to approximate cell-centered velocities, which can then be continuously interpolated to any point in the domain of interest. Two-dimensional tests demonstrate that the method correctly reproduces uniform and corner-to-corner flow on fully unstructured grids. In three dimensions using regular hexahedral grids, the method agrees well with established semianalytical methods. Tests also demonstrate that the method produces physically realistic results on fully unstructured three-dimensional grids.     

Assessment of groundwater residence times in the pore aquifers of the River Elbe Basin

An area covering assessment of the groundwater residence times for the upper pore aquifers in the River Elbe Basin was performed. Residence times were determined by combining groundwater velocities and flow distances along each flow-path to the surface waters using a two-dimensional model approach. Groundwater velocity was calculated as a function of hydraulic conductivity, hydraulic gradient and effective yield of pore space. Flow paths were obtained by an analysis of the morphology of the groundwater table. The mean groundwater residence time in the pore aquifers of the River Elbe Basin was quantified to about 25 years. A strong temporal blurring in the different regions between less than one year and more than 250 years was obtained. For the regional groundwater management in the Elbe Basin the groundwater residence times are an important parameter, which helps to take into account the temporal dimension in the assessment of the impact of political measures aiming at the improvement of groundwater quality with regard to diffuse pollutants (e.g. nitrate).