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We present an experimental and theoretical study of unsaturated flow in discrete fracture networks. The focus is on the breakthrough time of infiltrating liquid through the fracture networks as well as the spatial distribution of local flow status under a wide range of flow rates. Through visualized experiments, the fluid motion in the fracture network is recorded and analyzed, and gravity‐driven preferential pathways are observed. The location of the breakthrough path is found to be insensitive to the flow rate under the single‐inlet flow condition. Based on analogy with slug migration in a single fracture and considering liquid accumulation due to the capillary barrier effect at the fracture intersections, we propose a theoretical model of liquid breakthrough time through an initially dry fracture network. The theoretical predictions are found to be in excellent agreement with the experimental results. Using the model, we analyze the relative contribution of times needed for liquid migration and for local liquid accumulation to the breakthrough time. We also find that the spatial distribution of local flow status at the steady‐state varies significantly with the flow rate. The improved understanding and the proposed model are of significance for predicting the time required for a fluid/contaminant to reach a certain depth in unsaturated fractured media, and may provide new physical insights on the complex unsaturated flow dynamics. Key Points: We propose a theoretical expression of liquid breakthrough time through an unsaturated fracture networkModel predictions are in excellent agreement with results from carefully controlled visualized experiments of unsaturated flowRelative contribution of times for slug migration and local liquid accumulation to the breakthrough time is analyzed [ABSTRACT FROM AUTHOR]

This paper presents a novel tracking model to detect a d -dimensional random walk radionuclides and toxic chemicals in a fractured medium with minimum time and maximum probability. This model improves the physical and chemical properties of a fractured medium for a long time. It depends on a coordinated search technique with multiple sensors. The radionuclide particle has a linear flows on one direction from d -directions to spread. We consider this particle dispersed through a cylinder path in a very small time. The tracking or searching process in each cylinder path will be done by two sensors which start from any point in the fractured medium (space). The particle's initial position is a vector of random variables with a known probability distribution. More than presenting the analytical solution which shows the existence of a finite tracking technique, we derive some auxiliary results related to optimal tracking technique. Besides that, we derive this optimal tracking technique which minimizes the expected value of the first meeting time between one of the sensors and the radionuclide or the toxic chemical particle. The effectiveness of this model appears in some numerical results. [ABSTRACT FROM AUTHOR]

Wave‐induced fluid flow, an important mechanism in seismic wave attenuation, is considered in the amplitude variation with the offset technique. In a fractured marine carbonate reservoir, fractures and pores develop simultaneously, such that wave‐induced flow is an important mechanism in attenuation caused by the fluid flow between pores as well as between pores and fractures. However, these two types of attenuation are typically investigated separately or studies assume that the pores and fractures are dry or saturated by the same fluid. Rock pores are usually saturated by a mixture of two or more fluids, such that the fracture and pore filling fluids may be different. During variation with offset reservoir prediction and fluid identification, the influence that the porosity, fracture, and fluid have on the P‐wave reflection coefficient should be considered. The patchy saturation model can describe the seismic wave dissipation caused by the wave‐induced flow between pore fluids, whereas the Norris model can describe seismic wave dissipation caused by the fluid flow between fractures and pores. This study considers both the patchy saturation model and Norris model to calculate the amplitude variation with the offset P‐wave reflection coefficient under different conditions. Combining the saturation and Norris models forms a new model, which is regarded as a transversely isotropic medium with a vertical symmetric axis, and can be extended to any incident angle through the relaxation function and the high‐ and low‐frequency elastic limits of the stiffness tensor, where the complete effective stiffness tensor of the new model can be obtained. Finally, the amplitude variation with offset reservoir technology is used to determine the influence of model parameters on the reflection coefficient of P‐waves under different angles and frequencies, including fracture weakness, fluid saturation and pore fluid saturation. [ABSTRACT FROM AUTHOR]

The problem of seismic wave propagation from a source located in a well is considered. Acoustic equations are used to describe the dynamic behavior of the fluid. The damaged zone is described as a porous fluid-saturated medium by applying the Dorovsky model. The elastic approximation is used to describe the dynamic behavior of the surrounding rock. A unified algorithm based on the grid-characteristic approach with curvilinear grids is proposed for full-wave modeling in the entire computational domain. Its distinctive feature is that the necessary contact conditions on the boundary between media with different rheological properties are stated explicitly. The possibility of acoustic diagnostics of the heterogeneity of the damaged zone is numerically explored. [ABSTRACT FROM AUTHOR]

Abstract Background One of the current problems in studying the mechanical properties and behavior of structurally inhomogeneous media with cracks is the characterization of acoustic wave propagation. This is especially important in Geomechanics and prognosis of earthquakes. Methods In this work, the authors propose an approach that could simplify characterization of wave propagation in medium with cracks. It is based on homogenization procedure performed at a set of equations characterizing acoustic wave propagation in media weakened by fractures under condition of external distributed loading. Such kind of loading in most cases is close to the real one in case of consideration of Geomechanics problems. Results On the basis of the proposed homogenization technique, we performed characterization of elastic properties and plane acoustic waves propagation in a pre-loaded linear elastic medium weakened by a large amount of cracks. We have investigated two special cases of loading: uniaxial compression and complex compression. We have also studied how the wavespeeds depend on averaged concentration and distribution of craks. Conclusions Effective elastic properties were theoretically characterized for fractured media under external loading. The results revealed high dependency of the longitudinal wave propagation speed on the relation between stresses reasoned by an external loading.

Characterizing the groundwater flow pattern in a landslide would help to establish a monitor-warning system to predict the movement of a highly concealed and extremely hazard translational landslide. The complex fracture network in this type of landslide affects the rainfall infiltration process and the groundwater flow. In this paper, multi-tracer tests, injection tests and electrical resistivity tomography were used to investigate the hydrogeological characteristics and groundwater dynamics of the Kualiangzi translational rock landslide, which is located in the northeast of the Sichuan Basin, China. The study results indicate that there are two kinds of groundwater flow mode, in the landslide, the concentrated mode and the dispersed mode. Tracer and injection test results indicate that the groundwater flow in the landslide is mainly controlled by a vertical preferential flow pathway (concentrated mode), of which the direction is approximately perpendicular to the sliding direction of the landslide. The main runoff direction in the middle of this landslide is southwest according to electrical resistivity tomography. The hydraulic conductivity in the preferential direction is more than 3750 times larger than that perpendicular to the direction. The groundwater flow along the weathered sandstone and mudstone media in the vicinity of the slip surface is very slow (dispersed mode). The results reveal the existence of a preferential flow pathway. The hydrogeological conceptual model is considered as an unbounded domain with an anisotropic medium in the whole area. This hydrogeological model clearly describes the hydrological conditions, and can help establish a monitor-warning system in a translational landslide. [ABSTRACT FROM AUTHOR]

Abstract This study aimed at investigating the impact of injection sites including i) matrix and ii) fracture when polymers of PVA, PAM, and CMC are injected at different concentrations within a fractured medium. The experimental results showed that PAM for all concentrations had a high recovery factor (RF) when its injection site is matrix and also at low concentrations. PAM has performed better due to its higher viscosity as well as its high capillary pressure in water-wet condition. In different pore sizes, the amount of shear rate that will be applied to the polymers will vary, which is why in the case of PAM injection in the fracture, the tendency of polymer to penetrate through the grains is more than fracture. CMC at low concentrations of 100 and 1000 ppm cannot wash the oil effectively. However, for a concentration of 5000 ppm, it has maximum breakthrough time as well as the maximum RF of 96% and 83% when it is injected via the matrix and fracture, respectively. These efficiencies are approximately 15% and 10% higher than that of PAM although PAM is more viscous of nearly three-fold. PVA can ultimately sweep 12% of the OOIP when its 5000-ppm solution is injected from the matrix. Graphical abstract Image 1 Highlights • Impact of shear rate on polymer invasion through grains instead of fracture. • Superiority of CMC than PAM in terms of recovery factor at high concentrations. • Breakthrough time postponement when grains are considered for polymer injection. • Weak performance of PVA compared to that of PAM and CMC. [ABSTRACT FROM AUTHOR]

This work is concerned with the role of geometrical properties of fractures on oil displacement efficiency during solvent injection to heavy oil. Here, a series of solvent injection processes were conducted on one-quarter five-spot fractured micromodels that were initially saturated with the heavy oil, at a fixed flow rate condition. The oil recovery was measured using image analysis of the continuously provided pictures. The results show that for the range of experiments performed here, the maximum oil recovery happens at a fracture orientation angle of 45 degrees. Also, increasing the number of fractures leads to a higher oil recovery factor by solvent in 45 degrees, while it does not change significantly for the case of a 90-degree inclination. By increasing the fracture spacing, the oil recovery factor decreased. When fractures are distributed along the mean flow direction, oil recovery is higher than the case where the fractures are more dispersed and are not in the mean flow direction. In the presence of discontinuous fractures, the oil recovery factor decreases in comparison with the case of continuous fractures. The results of this work might be helpful for better understanding the role of fractures during miscible injection processes, which might be used to develop new mathematical models in such a reservoir. [ABSTRACT FROM AUTHOR]

Abstract: In a geological storage context, the durability of nuclear glass is first and foremost determined by its alteration rate and by the surface being leached. This surface is comprised of a network of three-dimensional cracks due to the stress relief generated by the cooling of glass packages. In order to improve the methods employed so far for quantifying the impact of a fissure network on the life time of glass packages in geological disposal, we have developed a software, referred to as FraGMA, which can be used to generate a realistic 2D geometry of the fissure network inside the glass based on mechanistic analogies. This type of tool is required for providing a mesh adapted to the calculation codes simulating water flow and glass alteration in such a medium. The main principles of this tool have been developed and its parameters have been defined based on the analysis of theoretical fracture processes and observations of real fissure networks. The 2D networks developed using FraGMA are compared with cross-sections of real networks. It is outlined that the general structure of the fracture maps is correctly reproduced, compared to the observations; consequently, it is relevant to apply the tool for further studies in order to generate more complex crack networks, and to study the channeling in such structures, as expected by the strong organized pattern of the experimental fracture maps. [ABSTRACT FROM AUTHOR]

The major objectives of this study are to analytically and experimentally determine the residual resistance factor in the fractured medium based on the polymer solution properties and operational conditions. The parameters considered in this study are the polymer concentration, power law constitutive equation parameter, and salt concentration, sulfonation content of polymer, temperature, and molecular weight of the water soluble polymers which are used in polymer flooding for enhanced oil recovery. The results indicated that residual resistance factor in fractured medium is dependent on the coil overlap parameter and power law equation parameter of polymer. The coil overlap parameter is a dimensionless number consists of intrinsic viscosity and polymer concentration. Since intrinsic viscosity is a function of polymer diameter in medium conditions, to predict the residual resistance factor in fracture medium, an experimental correlation is generated for determination of the molecular diameter of polymer based on polymer molecular weight, temperature, salt concentration, and sulfonation content. [ABSTRACT FROM AUTHOR]

Karst aquifers are characterized by spatial heterogeneity due to the presence of highly permeable channels and conduits in low-permeable fractured rocks (matrix block). Recent studies have reported a close relationship between surface and subsurface water in karstic regions due to the water flow through a complicated network of paths formed by fracture intersections. Subsurface flow in karstified aquifers ranges between conduit flow, in large passages with relatively high flow velocities, and diffuse flow, in the matrix block where Darcy’s law is still valid. In this paper, we present the simulation of a complex karstified aquifer system in Crete, Greece, where the presence of main faults drastically affects the regional flow. A discrete fracture approach in conjunction with an equivalent porous medium approach was adopted to simulate the mixed flow in the area of interest. The simulation results have shown that the length and the orientation of the dominant faults, primarily during the rainy season, affect the flow field. [ABSTRACT FROM AUTHOR]

This article presents a numerical analysis on anomalous transport behavior in a heterogeneous fractured porous reservoir using streamlines. The authors developed a streamline simulator with a direct quadrilateral mesh generator to investigate the correlated effects of hydrological properties. Quadrilateral grids were made by constructing boundary loops automatically. The mesh generator showed reliable shapes and did not need to construct another control volume for a conventional transport model. Solute was transported using a streamline approach on the irregular grids with various values of permeabilities between matrix and fracture. Breakthrough curve has a skewed characteristic similar at a real heterogeneous medium. The trajectories of streamline, the distribution of pressure, and the skewed breakthrough confirm the applicability of our model at both porous and fractured medium. [ABSTRACT FROM AUTHOR]

Abstract: Physical properties of many natural and man-made materials can be modelled using the concept of poroelasticity. Some porous materials, in addition to the network of pores, contain larger inhomogeneities such as inclusions, cavities, fractures or cracks. A common method of detecting such inhomogeneities is based on the use of elastic wave scattering. We consider interaction of a normally incident time-harmonic longitudinal plane wave with a circular crack imbedded in a porous medium governed by Biot’s equations of dynamic poroelasticity. The problem is formulated in cylindrical co-ordinates as a system of dual integral equations for the Hankel transform of the wave field, which is then reduced to a single Fredholm integral equation of the second kind. It is found that the scattering that takes place is predominantly due to wave induced fluid flow between the pores and the crack. The scattering magnitude depends on the size of the crack relative to the slow wave wavelength and has it’s maximum value when they are of the same order. [Copyright &y& Elsevier]

Natural fractured media are highly unpredictable because of existing complex structures at the fracture and at the network levels. Fractures are by themselves heterogeneous objects of broadly distributed sizes, shapes, and orientations that are interconnected in large correlated networks. With little field data and evidence, numerical modeling can provide important information on the underground hydraulic phenomena. However, it must overcome several barriers. First, the complex network structure produces a structure difficult to mesh. Second, the absence of a priori homogenization scale, along with the double fracture and network heterogeneity levels, requires the calculation of large but finely resolved fracture networks resulting in very large simulation domains. To tackle these two related issues, we reduce the highly complex geometry of the fractures by applying a local transformation that suppresses the cumbersome meshing configurations while keeping the networks fundamental, geological, and geometrical characteristics. We show that the flow properties are marginally affected while the problem complexity (i.e., memory capacity and resolution time) can be divided by orders of magnitude. The goal of this article is to propose a method of resolution which takes into account the geometrical complexity met in the networks and which makes it possible to treat a few thousand fractures. The principal aim of this article is to present a tool to slowly modify the structures of the fracture networks to have a good quality mesh with a marginal loss in precision. [ABSTRACT FROM AUTHOR]

This article presents numerical analyses on diffusion trend for the fractured media with fractal properties by pressure transient data. The authors develop a discrete fracture model with random fracture pattern and a power-law length distribution, which has not been fully considered in the previous fractal modeling. From the model presented, the fractal dimension and conductivity index is determined, and the pressure behavior is analyzed for the range of length exponent ( a ) of power-law from 1 and 3. Various fractal geometries are examined depending on the morphology of fractures. A single fractal characteristic is observed in the media dominated by long ( a 3), and two distinct fractal dimensions in pertinently mixed system of long and small fractures (2 < a < 3). Also, pressure transient behaviors in the mixed system show their unique characteristics, corresponding to each fractal dimension respectively. It is shown that diffusion effect is relatively small in the early time influenced by a few long fractures, and becomes larger in the late time by long and small fractures. [ABSTRACT FROM AUTHOR]

A Eulerian moment expansion through the first order of σ p2( p = f, m) (σ p2 is the velocity variance in the fracture, p = f, or matrix, p = m, domain) is developed for solute transport in a nonstationary, fractured medium. A dual-permeability model is applied to describe the conceptualized fractured medium where solute convection and dispersion in both the fracture and matrix domains are considered. Hydraulic conductivity distrbutions in both fracture and matrix domains are nonstationary. The stochastic governing equations for the mean concentration and concentration covariance are analytically derived. A numerical method (a finite difference method) is applied to obtain the solutions. The developed method is applied to study solute transport in stationary and nonstationary fractured media. The study results indicate that medium nonstationarity significantly influences the solute transport process. The nonstationary transport theory relaxes many assumptions adopted in stationary theories and paves the way for applying the theory to many environmental projects, especially for uncertainty analysis of solute transport. [ABSTRACT FROM AUTHOR]

A general three-dimensional numerical model for single-phase, slightly compressible flow through fractured porous media is introduced. It is based on a discrete fracture representation. Applications to the simulation of pressure drawdown well tests are presented, for complex situations where the well intercepts a random fracture network with various fracture densities and conductivities. The well pressure response can be modeled as a function of its interconnectivity with the fracture network. [ABSTRACT FROM AUTHOR]

Flow in fractured porous media was first investigated by Barenblatt and Zheltov [1960] and Barenblatt et al. [1960] by means of the double-porosity model. A direct, exact, and complete numerical solution of the flow in such media is given in this paper for arbitrary distributions of permeabilities in the porous matrix and in the fracture network. The fracture network and the porous matrix are automatically meshed; the flow equations are discretized by means of the finite volume method. This code has been so far applied to incompressible fluids and to statistically homogeneous media which are schematized as spatially periodic media. Some results pertaining to random networks of polygonal fractures are presented and discussed; they show the importance of the percolation threshold of the fracture network and possibly of the porous matrix. Moreover, the influence of the fracture shape can be taken into account by means of the excluded volume. [ABSTRACT FROM AUTHOR]

Dual velocity (often called dual porosity) models exist to describe a variety of solute transport processes. These exist for both chemical and geochemical systems. All current models reviewed in this paper can be represented by a generalized form. Characteristics of the solutions are obtained by investigating moments of the solution. Of particular interest is the simple asymptotic behavior. To verify the approach, an example problem is investigated where the exact analytical solution is compared to the asymptotic solution. It is shown that many dual velocity models can be well-represented by the inclusion of an increased dispersion term in a simpler single velocity model. [ABSTRACT FROM AUTHOR]

Coal permeability is known to be affected by the sorption-induced strain. Indeed, coal swells with gas sorption and shrinks with desorption, which is likely to modify the cleat aperture and thus the permeability. Coal permeability evolution is crucially important for either Coalbed Methane production (CBM) or Carbon dioxide Capture and Storage (CCS). A model is developed at the scale of the fractures to take into account the hydro-mechanical couplings observed experimentally. It is implemented in the finite element code Lagamine. This numerical model is developed at the scale of the fractures and the matrix blocks. Fractures are modelled with interface elements specially adapted to manage sorption/desorption by taking into account the Langmuir's isotherm (Langmuir, 1918). In the matrix blocks, the sorption strain is assumed proportional to the adsorbed gas content. Depending on the boundary conditions, sorption strain affects the stress state and thus the fracture aperture. Contrary to macroscale models (Bertrand et al. 2017), this model does not require the use of shape factors since the geometry can be explicitly represented. The implementation of the model is validated by comparison with the analytical solution on a simple geometry. The model is finally used to simulate gas injection on a representative elementary volume (REV) made up few matrix blocks. This modelling highlights the interests of a numerical approach to compute the permeability evolution compared to a porosity-based model. [ABSTRACT FROM AUTHOR]

• The spatiotemporal distribution of fluid phases is strongly influenced by the aperture field anisotropy. • Anisotropy leads to stretched invading clusters, decreased fluid trapping, and increased relative permeabilities in the displacing direction. • Empirical equations are proposed to link the relative permeabilities to the anisotropy factor. The void space geometry of rough fractures is one of most important factors controlling two-phase flow in fractured media. This paper presents a numerical study on the effect of aperture field anisotropy on two-phase flow properties in rough fractures. By using a power spectrum based method, we generate multiple realizations of synthetic rough fractures with aperture fields of different anisotropy factors. Fluid–fluid displacement in these fractures is simulated by a modified invasion percolation model. It is found that the spatiotemporal distribution of fluid phases is strongly influenced by the aperture field anisotropy. On average, both the nonwetting phase saturation and the entrapped wetting phase saturations at breakthrough decrease with increasing anisotropy factor; but the specific interfacial area is larger for a higher anisotropy ratio. Relative permeabilities to both phases in the direction parallel to the displacement increase with the anisotropy factor, indicating a reduced phase interference due to aperture field anisotropy. Empirical equations are proposed to link the relative permeabilities to the anisotropy factor. These results improve our understanding of immiscible displacement in rough fractures and can be useful for predicting two-phase flow in fractured media at the large scale where geomechanical and chemical processes produce anisotropic roughness. [ABSTRACT FROM AUTHOR]