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We investigate tracer transport on random discrete fracture networks that are characterized by the statistics of the fracture geometry and hydraulic conductivity. While it is well known that tracer transport through fractured media can be anomalous and particle injection modes can have major impact on dispersion, the incorporation of injection modes into effective transport modeling has remained an open issue. The fundamental reason behind this challenge is that—even if the Eulerian fluid velocity is steady—the Lagrangian velocity distribution experienced by tracer particles evolves with time from its initial distribution, which is dictated by the injection mode, to a stationary velocity distribution. We quantify this evolution by a Markov model for particle velocities that are equidistantly sampled along trajectories. This stochastic approach allows for the systematic incorporation of the initial velocity distribution and quantifies the interplay between velocity distribution and spatial and temporal correlation. The proposed spatial Markov model is characterized by the initial velocity distribution, which is determined by the particle injection mode, the stationary Lagrangian velocity distribution, which is derived from the Eulerian velocity distribution, and the spatial velocity correlation length, which is related to the characteristic fracture length. This effective model leads to a time-domain random walk for the evolution of particle positions and velocities, whose joint distribution follows a Boltzmann equation. Finally, we demonstrate that the proposed model can successfully predict anomalous transport through discrete fracture networks with different levels of heterogeneity and arbitrary tracer injection modes. [ABSTRACT FROM AUTHOR]

Pore-network models were found useful in describing important flow and transport mechanisms and in predicting flow properties of different porous media relevant to numerous fundamental and industrial applications. Pore-networks provide very fast computational framework and permit simulations on large volumes of pores. This is possible due to significant pore space simplifications and linear/exponential relationships between effective properties and geometrical characteristics of the pore elements. To make such relationships work, pore-network elements are usually simplified by circular, triangular, square and other basic shapes. However, such assumptions result in inaccurate prediction of transport properties. In this paper, we propose that pore-networks can be constructed without pore shape simplifications. To test this hypothesize we extracted 3292 2D pore element cross-sections from 3D X-ray microtomography images of sandstone and carbonate rock samples. Based on the circularity, convexity and elongation of each pore element we trained neural networks to predict the dimensionless hydraulic conductance. The optimal neural network provides 90% of predictions lying within the 20% error bounds compared against direct numerical simulation results. Our novel approach opens a new way to parameterize pore-networks and we outlined future improvements to create a new class of pore-network models without pore shape simplifications. [ABSTRACT FROM AUTHOR]

Many islands consist of limestone sedimentary deposits that are better described as a two-aquifer system consisting of an unconfined aquifer (Quaternary sediments) above a fractured aquifer (fractured limestone) in which groundwater heads are closely regulated by tidal fluctuations on both sides of the islands (dual tides). Propagation of tidal signal, reflected in hydraulic head fluctuation in such a two-aquifer system is significantly different from that in a single aquifer system that is often assumed. The Laplace domain solution of the head fluctuation in such a two-aquifer system subjected to dual tides is obtained first and subsequently inverted to yield real-time solution. Unlike previous solutions, Fourier series with complex variables are avoided and Fourier sine transform is used instead. The solution takes into account an instantaneously drainable water table, hydraulic conductivity anisotropy and arbitrary time-dependent tidal fluctuations. The hydraulic connection of the underlying fractured aquifer and the overlying unconfined aquifer is explored in details. The presented solution can be used to evaluate the head fluctuations and the aquifer parameter estimation of the two-aquifer system underneath a strip-shape island subjected to dual tides. The results can be used to determine the optimum piezometer location to estimate hydraulic parameters of the two-aquifer system using groundwater head fluctuation data. Stream-aquifer interaction is similar to the tidal-aquifer interaction if the chemical difference of the salt water and fresh water is not a concern. The developed solution for tidal-aquifer interaction here can also be used to investigate the aquifer response to stream stage variations in river basin aquifers. [ABSTRACT FROM AUTHOR]

Using the first-order analysis, we investigate the spatial cross-correlation between hydraulic conductivity variation and specific discharge (flux) as well as its components measured in a borehole under steady-state flow conditions during cross-hole pumping tests in heterogeneous aquifers. These spatial correlation patterns are found to be quite different from that between the hydraulic conductivity variation and the hydraulic head measurement in the same borehole. This finding suggests that a specific discharge measurement carries non-redundant information about the spatial distribution of heterogeneity, even this measurement is collected from the same location where the head measurement is taken. As such, specific discharge observations should be included in the analysis of hydraulic tomography to increase the resolution of estimated aquifer heterogeneity. Using numerical experiments, we demonstrate the effectiveness of the joint interpretation of both hydraulic heads and fluxes for mapping fracture distributions in a hypothetic geologic medium. [ABSTRACT FROM AUTHOR]

Highlights: [•] Introduction of a novel hydraulic tomography procedure based on travel-time based inversion and application of pilot points. [•] Reconstruction of the hydraulic conductivity field of a three-dimensional, strongly heterogeneous, aquifer analogue. [•] Encountering the computationally burden by parallel computing and subspace regularization. [Copyright &y& Elsevier]

Highlights: [•] Models for simulating heat and water processes in freezing soils are summarized. [•] The sources of existing variations in the Clapeyron equation are explained. [•] Various formulations for the soil freezing curve are reviewed. [•] Best practices to develop a frozen soil hydraulic conductivity model are detailed. [•] Several unresolved questions are highlighted and addressed. [ABSTRACT FROM AUTHOR]

Abstract: The assessment of hydraulic conductivity of heterogeneous aquifers is a difficult task using traditional hydrogeological methods (e.g., steady state or transient pumping tests) due to their low spatial resolution. Geophysical measurements performed at the ground surface and in boreholes provide additional information for increasing the resolution and accuracy of the inverted hydraulic conductivity field. We used a stochastic joint inversion of Direct Current (DC) resistivity and self-potential (SP) data plus in situ measurement of the salinity in a downstream well during a synthetic salt tracer experiment to reconstruct the hydraulic conductivity field between two wells. The pilot point parameterization was used to avoid over-parameterization of the inverse problem. Bounds on the model parameters were used to promote a consistent Markov chain Monte Carlo sampling of the model parameters. To evaluate the effectiveness of the joint inversion process, we compared eight cases in which the geophysical data are coupled or not to the in situ sampling of the salinity to map the hydraulic conductivity. We first tested the effectiveness of the inversion of each type of data alone (concentration sampling, self-potential, and DC resistivity), and then we combined the data two by two. We finally combined all the data together to show the value of each type of geophysical data in the joint inversion process because of their different sensitivity map. We also investigated a case in which the data were contaminated with noise and the variogram unknown and inverted stochastically. The results of the inversion revealed that incorporating the self-potential data improves the estimate of hydraulic conductivity field especially when the self-potential data were combined to the salt concentration measurement in the second well or to the time-lapse cross-well electrical resistivity data. Various tests were also performed to quantify the uncertainty in the inverted hydraulic conductivity field. [Copyright &y& Elsevier]

Abstract: Parameters of functions to describe soil hydraulic properties are derived from measurements by means of parameter estimation. Of crucial importance here is the choice of correct constraints in the parameter space. Often, the parameters are mere shape parameters without physical meaning, giving flexibility to the model. A fundamental requirement is that the hydraulic functions are monotonic: the retention function and the conductivity function can only decrease as the capillary suction increases. A stricter physical requirement for the conductivity function is that its decrease with respect to saturation is at least linear. This linear decrease would occur if all pores of a capillary bundle had an equal radius. In the first part of this contribution, we derive constraints for the so-called tortuosity parameter of the Mualem conductivity model, which allow highest possible flexibility on one hand and guarantee physical consistency on the other hand. In combination with the retention functions of Brooks and Corey, van Genuchten, or Durner, such a constraint can be expressed as a function of the pore-size distribution parameters. In the second part, we show that a common modification of retention models, which is applied to reach zero water content at finite suction, can lead to the physically unrealistic case of increasing water content with increasing suction. We propose a solution for this problem by slightly modifying these models and introducing a correct parameter constraint. [Copyright &y& Elsevier]

Abstract: A steady/quasi-steady model is developed for predicting flow into a partially penetrating well with skin zone in a confined aquifer overlying an impervious layer. The model takes into account flow through the bottom of the wellbore, finite skin thickness and finite horizontal and vertical extent of the aquifer. Moreover, the solution can be easily extended to include the mixed-type boundary condition at the well face, where a Dirichlet in the form of a specified hydraulic head and a Neumann in the form of zero flux coexist at the same time at different portions of the well face. The validity of the proposed solution is tested by comparing a few results obtained from the developed model with corresponding results obtained by analytical and numerical means. The study shows that, among other factors remaining constant, both the horizontal and vertical extent of an artesian aquifer, thickness of the skin zone, bottom flow and conductivity contrast of the skin and formation zones, play an important part in deciding flow to a well dug in the aquifer, and hence these factors must be considered while analyzing the problem. The model proposed here can be used to estimate skin thickness as well as hydraulic conductivities of the skin and formation zones of a well with skin zone in an artesian aquifer underlain by an impervious layer by utilizing pumping test data falling in the steady or quasi-steady state of a typical pumping test. As the proposed solution is of a general nature in the sense that it can handle, apart from partial penetration and bottom flow, the finite size skin zone and finite horizontal and vertical extent of an artesian aquifer together with the mixed-type boundary condition at the well face, it is hoped that the predictions coming out of the model will be more realistic than those obtained using solutions developed with more stringent assumptions. [ABSTRACT FROM AUTHOR]

• A physically-based model is presented to calculate hydraulic conductivity of stony soils. • Rock fragments can be permeable and effective saturated and unsaturated hydraulic conductivity of a stony soil can be calculated for all matric potentials. • The model considers the effect of shape and orientation of rock fragments. • The model is also valid for high volumetric rock fragment contents where existing approaches are not applicable. Despite a longstanding interest in understanding the effects of rock fragments on soil hydraulic properties, physically-based models to describe the effective hydraulic conductivity of stony soils are still rare. The conductivity of stony soils is mostly described by simple scaling approaches, assuming impermeable rock fragments. We present a model based on the general effective medium (GEM) theory to calculate the effective hydraulic conductivity of stony soils. The model accounts for the volumetric content, shape, and orientation of rock fragments in the main direction of water flow. Rock fragments can either be permeable or impermeable in the model which allows to calculate the effective unsaturated hydraulic conductivity curve of stony soils over the full range of soil matric potentials. Existing models assume rock fragments to be isolated and their application is therefore limited to low to moderately stony soils. In GEM model interaction between rock fragments is allowed, which makes it applicable in stony soils with high contents of rock fragments. The mathematical simplicity of the model makes it suitable for practical applications and provides a strong theoretical basis for improving predictions of flow and transport in hydrological models applied in forested and agricultural watersheds and mountainous areas. [ABSTRACT FROM AUTHOR]