Solute Transport In Fracture Research Articles

Influence of Geometric Characteristics onWaterFlow and Solute Transport atFracture Intersections.

Laboratory experiments and numerical simulations were performed to explore the influence of intersection geometry on fluid flow and solute transport in fractures. Fractures were engraved and sealed into an acrylic plate and two orthogonal intersections with different geometry were constructed. The effects of curvature and relative shear displacement at intersections on preferential flow and solute transport were investigated. By solving the Navier-Stokes (NS) equation, the fluid mixing and solute distribution were predicted. The results showed that the geometric characteristics at the intersection have a significant effect on the preferential flow and solute distribution. The results agreed well with the experimental results, in terms of flow direction, preferential flow rate, and heterogeneous solute distribution. With an increase in curvature, the flow difference between the two outlets increases gradually. Increasing curvature can reduce the preferential flow and weaken the inhomogeneity of solute distribution. An increase of relative shear displacement decreases the pressure gradient and flow rate at the entrance of the two branch fractures, and thereby increases preferential flow and inhomogeneity of solute distribution. The results provide a basis and reference for further exploring the relationship between the geometric characteristics of fracture intersections and flow behaviors.

Variability of travel time of solute particles in single fractures with spatially variable aperture

The arrival time of solutes from the source to a prescribed compliance boundary is a global transport quantity that is of practical interest in many applications, such as risk assessment for environmentally sensitive sites in regulatory analyses. Estimates of uncertainty are necessary and can play an important role in the decision-making process. The objective of this work is therefore to quantify the variability of solute travel time in individual fractures with spatially variable apertures. The variability of solute transport in fractures is largely determined by the heterogeneity of the apertures of naturally occurring rock fractures. To model solute transport, the fracture apertures and flow fields are considered as spatial random functions. Using the relationship between the two-dimensional depth-averaged solute conservation equation and the Fokker-Planck equation, it is possible to formulate the solute convection velocity in such a way that a general expression for the solute travel time variance can be developed by taking into account the effects of the variation in fracture aperture. A closed-form expression for the variance of travel time in the mean flow direction is derived for the case of advection-dominated solute transport. This derived expression allows the analysis of the effects of the variation of the fracture aperture on the variability of the solute travel time.

Hyper-gravity experiment of solute transport in fractured rock and evaluation method for long-term barrier performance

Hyper-gravity experiment enable the acceleration of the long-term transport of contaminants through fractured geological barriers. However, the hyper-gravity effect of the solute transport in fractures are not well understood. In this study, the sealed control apparatus and the 3D printed fracture models were used to carry out 1 ​g and N g hyper-gravity experiments. The results show that the breakthrough curves for the 1 ​g and N g experiments were almost the same. The differences in the flow velocity and the fitted hydrodynamic dispersion coefficient were 0.97–3.12% and 9.09–20.4%, indicating that the internal fractures of the 3D printed fracture models remained stable under hyper-gravity, and the differences in the flow and solute transport characteristics were acceptable. A method for evaluating the long-term barrier performance of low-permeability fractured rocks was proposed based on the hyper-gravity experiment. The solute transport processes in the 1 ​g prototype, 1 ​g scaled model, and N g scaled model were simulated by the OpenGeoSys (OGS) software. The results show that the N g scaled model can reproduce the flow and solute transport processes in the 1 ​g prototype without considering the micro-scale heterogeneity if the Reynolds number (Re) ​≤ ​critical Reynolds number (Recr) and the Peclet number (Pe) ​≤ ​the critical Peclet number (Pecr). This insight is valuable for carrying out hyper-gravity experiments to evaluate the long-term barrier performance of low-permeability fractured porous rock.

Geometry‐Based Prediction of Solute Transport Process in Single 3D Rock Fractures Under Laminar Flow Regime

AbstractSubsurface substance migration in the fractured rock aquifer is mainly controlled by fractures, and prediction of solute transport in fractures is important to many geophysical processes and engineering activities. This study explores the possibility of predicting transport process in single rock fractures from measurable physical properties. For this purpose, we conducted a large number of pore‐scale simulations of solute transport in single 3D rock fractures with different apertures and various degrees of roughness. The numerically‐obtained breakthrough curves under laminar flow regime were reproduced with high fidelity by the classic analytical solution within the framework of macroscopic advection‐dispersion theory. The fitted transport coefficients (hydrodynamic dispersion coefficient and transport velocity) were normalized by the parallel‐plate model's values, and were further parameterized by aperture b and roughness parameter σ/b in form of ωeb/ψ + λ(mσ/b − 1)/bn and 1 − α(σ/b)/βb, respectively. By incorporating these parameterized transport coefficients and the modified cubic law into the classic analytical solution, we proposed a new transport predictive model. This model was adaptively degenerated into the classic analytical solution of parallel‐plate model, and was proved to be capable of predicting macroscopic solute transport only relying on arithmetic‐mean mechanical aperture and its standard deviation, without solving the velocity and concentration fields. By the established model, we quantitatively revealed the impacts of aperture and roughness on the breakthrough curve under laminar flow regime. This study puts a step toward predicting solute transport process in fractured rock aquifers with measurable geometric properties.

Quantification of solute transport in a fracture-matrix system using geoelectrical monitoring

Solute transport in fracture is easy to diffuse into the matrix due to the permeability of the matrix. The quantification of solute concentration is particularly important during diffusion and is a challenge for the management of pollutants in a fracture-matrix system. In this paper, sodium chloride as solute, the geoelectrical technology was combined with high density electrical method and conductivity acquisition method to conduct a series of sandbox experiments. In the center of the sandbox is a fracture, and on both sides of the fracture is the matrix. The fracture and matrix in the sandbox form a fracture-matrix system. Loading-flushing process of sodium chloride solution in fracture-matrix system was monitored in real-time and non-destructive. The effect of matrix porosity and flow velocity on solute transport in fracture-matrix system was investigated. The results showed that: 1) Mass transfer rate coefficient (α) and fracture/matrix porosity ratio (β), and tailing exponent of residence time distribution (ω) were quantified by pairing bulk electrical conductivity (BEC) and fluid electrical conductivity (FEC), without the requirement of inverse model calibration. In contrast, the single electrical method still lacks resolution or is not representative in determining solute transport parameters in fracture-matrix system. 2) The matrix porosity had a significant effect on solute transport in fracture-matrix system. With the increase of porosity, the mass transfer rate coefficient (α) increased and the residence time in the matrix decreased. 3) An increase of flow velocity led to a decrease of residence time in the matrix and an increase in mass transfer rate coefficient (α). The solute transport in fracture-matrix system can be quantified by electrical conductivity hysteresis. The results can provide a basis for the management of solute transport in fracture-matrix system

Mass transfer between recirculation zone and main flow domain in fractures: Is the first order rate law valid?

• Recirculation zones (RZs) are present and grow with Reynolds number ( Re ) in fractures when inertial forces are significant. • Mass transfer between RZ and main flow channel results in a late time tailing in residence time distributions. • The first order rate law is robust for describing mass transfer between RZs and main flow channel. A better understanding of solute transport in fractures with immobile zones is critical for many geophysical processes and engineering applications. Although the roles of immobile zones in capturing and releasing solutes leading to non-Fickian transport are well-acknowledged, the mass transfer between immobile and mobile domains using the first order rate law has never been explicitly validated. To this end, we solved fluid flow and solute transport through direct numerical simulations with Reynolds number ( Re ) ranging from 10 to 40, where one kind of immobile zone, i.e., recirculation zones (RZs), are noticeably present and grow with Re . By fitting the analytical solution using the first order rate law to the numerically-derived concentration in RZs, we find that the first order rate law is applicable whenever RZs are noticeably present. Moreover, the mass transfer coefficient increases with Re , and decreases from upstream to downstream in the direction of fluid flow. Hence, the mass transfer coefficient should be precisely determined to accurately capture non-Fickian transport via the first order rate law.

Uncertainty quantification of radionuclide migration in fractured granite

Deep geological disposal is a widely accepted approach for safe management and long-term disposal of high-level radioactive waste (HLW). However, high uncertainty associated with subsurface properties of fractured rocks is a significant obstacle to practical safety assessment of HLW disposal. In this study, we develop an integrated statistical framework for uncertainty quantification of radionuclide migration related to the geological disposal of HLW. We employ a response surface methodology integrated with Monte Carlo simulations of radionuclide migration in fractured granite to perform global sensitivity and statistical analysis by coupling the uncertainty quantification tool, PSUADE, and radionuclide migration simulator, FRACPIPE. FRACPIPE is a semi-analytical simulator that models solute transport in fractures and matrix slabs with an arbitrary-length decay chain and an arbitrary time-varying influent concentration history by considering a variety of transport mechanisms. The statistical risk metrics include nuclide breakthrough (BT) time, total release dose, single nuclide release dose, and single nuclide flux. The global sensitivity analysis identifies fracture aperture, matrix diffusion coefficient, hydraulic gradient, and dispersivity as the most sensitive parameters. Considering the uncertainty ranges for independent variables (e.g., dispersivity, hydraulic gradient, fracture spacing, fracture aperture, sorption distribution coefficient, matrix diffusion, and matrix porosity), we apply post-processing results of Monte Carlo simulations to conduct statistical analysis of the risk metrics. Under this studied condition, the average BT time for radionuclides at 1000 m is between 85 and 331 thousand years. This study provides valuable insights into the impact of input parameter (independent variables) uncertainty and sensitivity on radionuclide migration behavior in an HLW repository.

Comparing heat and solute transport in a discrete rock fracture of variable aperture

In this study, we have compared heat and solute transport in a discrete fracture using numerical modeling. Fracture aperture heterogeneity was described using geostatistical properties with fracture aperture means of up to 1000 μm, variances of 10,000 µm2 and isotropic correlation lengths up to 10 m. Groundwater flow in the matrix was assumed to be negligible and flow in the fracture was set to values typical for natural groundwater conditions with velocities less than 100 m/day and associated hydraulic gradients of less than 0.05. A uniform isotropic thermal conductivity of 2 W/m °C was set for the matrix. Based on 50 realizations, three-dimensional and two-dimensional conduction in the matrix and in the fracture, respectively, play an important role in controlling the development and the shape of the thermal plume under natural flow conditions. In contrast, solute transport exhibits limited penetration depth in the matrix. The results of this research indicate that, contrary to solute transport in discrete fracture settings where channeling is sometimes a major contributor to solute migration rates, no significant thermal channeling is observed under natural groundwater flow conditions. The use of tracer experiments or the monitoring of solute transport in fractured rock will not therefore provide a reliable prediction of the migration of heat in the same setting.

Multi-gene genetic programming expressions for simulating solute transport in fractures

In lieu of process-based models, evolutionary artificial intelligence techniques can yield accurate expressions describing complex phenomena. In the current study, closed-form expressions are developed to predict solute transport in a fracture-matrix system as a function of the parameters that describe relevant physical and chemical processes. The study adopts a multi-gene genetic programming approach to approximate a solution of the classical advection–dispersion equation for reactive transport in single, parallel-plate fractures. The approach is employed to obtain an accurate relationship between the hydraulic, geological, and chemical parameters of the fracture-matrix system as inputs and an ensemble of breakthrough curves as outputs. Solutions generated by the developed model showed good agreement with those of corresponding analytical and numerical models. Computationally, the developed approach is highly efficient, particularly when compared with the analytical solution, which typically requires relatively fine discretization to calculate the long-tailed breakthrough curves. Therefore, future work could extend the developed model to simulate field-scale networks and include additional and more complex transport phenomena. This approach advances solute transport behavior predictions through being simpler and computationally more efficient than currently adopted techniques, which is important as the scale of simulation increases from that of a single fracture to a network.

Characteristics of Fluid Flow and Solute Transport in Multicrossed Rough Rock Fractures Based on Three-Dimensional Simulation

Fluid flow and solute transport in rock fractures are important for controlling pollutant migration in groundwater and radionuclide migration in nuclear waste disposal. The quantitative characterization of fluid flow and mass transport in crossed fractures is the key to defining solute transport in a fracture network. In this study, the characteristics of fluid flow and solute transport in rock fractures were investigated through experiments and simulation. The surface topography of these fractures was reconstructed using 3D laser scanning technology. The solute transport in crossed parallel plates and rough fractures with intersecting angles of 30°, 60°, 90°, 120°, and 150° was investigated under different initial conditions. Results show that the intersection angle and fluid velocity significantly affect the fluid flow pattern at the intersection. As the flow velocity and intersection angle increase, streamlines at the intersection of rough fractures are unevenly distributed. The fluid tends to seep into the dominant channel and has different degrees of channeling flow at the intersection of fractures. An eddy phenomenon is observed at the intersection, indicating that the seepage behavior transforms into a non-Darcy flow. As the Peclet number (Pe) increases, solute migration and diffusion gradually decrease; however, the convection part gradually increases. Thus, the solute transport mode gradually changes into a streamline path mode at the intersection of fractures.

Effect of slippery boundary on solute transport in rough-walled rock fractures under different flow regimes

Fundamental understanding of solute transport behaviors in rock fractures is of great importance to many hydrogeological processes. The fate of fluid-borne solutes is inherently linked to fluid flow process in rock fractures, which is usually theoretically and numerically analyzed under the assumption of classic no-slip boundary condition. However, fluid slippage at rock surfaces is possibly present in some geological environments, such as hydrophilicity change in rock surfaces exposed to organic substances, or the immobile wetting film covering rock surfaces. These situations would induce a non-zero velocity at the boundary walls for flowing fluid, i.e., fluid slippage, which leads to a violation of the no-slip assumption. Nonetheless, the effect of slippery boundary on fluid-borne solute transport is poorly understood for rock fractures. This study systematically investigated the slippery boundary effect on solute transport in rough-walled rock fractures under different flow regimes. A series of pore-scale simulation results showed that the slippery boundary has a profound influence on both microscale and macroscale solute transport behaviors in rock fractures. Such an influence became more significant with increasing hydraulic gradient, accompanied by the flow regime transitioning from Darcy to non-Darcian. For Darcy flow regime, the slippery boundary exerted its influence on solute transport by altering velocity distribution pattern in rock fracture; while for non-Darcian flow regime, the enlarged eddy volume and promoted mass transfer process by the slippery boundary profoundly affected solute transport behaviors. Further discussion indicated that the predictive models with parameters estimated from the conventional no-slip boundary condition cannot directly apply to the slip one. Moreover, the effect of slippery boundary would possibly have an impact on larger-scale fractured rock aquifers which requires further verification. The results and findings enrich the understanding of solute transport in fractured rocks where the slippery boundary is prevalently present, and contribute to developing predictive models for complex geological environments.

Numerical Research of Fluid Flow and Solute Transport in Rough Fractures under Different Normal Stress

The effects of roughness and normal stress on hydraulic properties of fractures are significant during the coupled shear flow test. Knowing the laws of fluid flow and solute transport in fractures is essential to ensure the nature and safety of geological projects. Although many experiments and numerical simulations of coupled shear flow test have been conducted, there is still a lack of research on using the full Navier-Stokes (N-S) equation to solve the real flow characteristics of fluid in three-dimensional rough fractures. The main purpose of this paper is to study the influence of roughness and normal stress on the fluid flow and solute transport through fractures under the constant normal stiffness boundary condition. Based on the corrected successive random addition (SRA) algorithm, fracture surfaces with different roughness expressed by the Hurst coefficient ( H ) were generated. By applying a shear displacement of 5 mm, the sheared fracture models with normal stresses of 1 MPa, 3 MPa, and 5 MPa were obtained, respectively. The hydraulic characteristics of three-dimensional fractures were analyzed by solving the full N-S equation. The particle tracking method was employed to obtain the breakthrough curves based on the calculated flow field. The numerical method was verified with experimental results. It has been found that, for the same normal stress, the smaller the fracture H value is (i.e., more tough the fracture is), the larger the mechanical aperture is. The ratio of hydraulic aperture to mechanical aperture ( e h / e m ) decreases with the increasing of normal stress. The smaller the H value, the effect of the normal stress on the ratio e h / e m is more significant. The variation of transmissivity of fractures with the flow rate exhibits similar manner with that of e h / e m . With the normal stress and H value increasing, the mean velocity of particles becomes higher and more particles move to the outlet boundary. The dispersive transport behavior becomes obvious when normal stress is larger.

Fractional Derivative Modeling on Solute Non-Fickian Transport in a Single Vertical Fracture

Solute transport in a single vertical fracture (SVF) cannot be reliably described by the classical advection-dispersion equation (ADE) model, due to the heterogeneity nature of fracture. This study conducted a group of experiments to investigate chloride ion transport in the SVFs under different rough-walled conditions, and then applied a time fractional advection-dispersion equation (F-ADE) model to offer an accurate description. A comparison between F-ADE model and a classical ADE model in describing experimental data, was also carried out. Results show that the FADE model is better than the ADE model in describing the breakthrough curve and heavy-tail phenomenon of solute transport in the fracture. Especially in the experiments with lower flow rate and higher roughness fracture, the FADE model can offer an accurate description, indicating that it is a promising tool for characterizing solute transport heterogeneous vertical fracture.

Effect of adsorption, radioactive decay and fractal structure of matrix on solute transport in fracture.

Reservoir contamination by various contaminants including radioactive elements is an actual environmental problem for all developed countries. Analysis of mass transport in a complex environment shows that the conventional diffusion equation based on Fick's Law fails to model the anomalous character of the diffusive mass transport observed in the field and laboratory experiments. These complex processes can be modelled by non-local advection-diffusion equations with temporal and spatial fractional derivatives. In the present paper, fractional differential equations are used for modelling the transport of radioactive materials in a fracture surrounded by the porous matrix of fractal structure. A new form of fractional differential equation for modelling migration of the radioactive contaminant in the fracture is derived and justified. Solutions of particular boundary value problems for this equation were found by application of the Laplace transform. Through the use of fractional derivatives, the model accounts for contaminant exchange between fracture and surrounding porous matrix of fractal geometry. For the case of an arbitrary time-dependent source of radioactive contamination located at the inlet of the fracture, the exact solutions for solute concentration in the fracture and surrounding porous medium are obtained. Using the concept of a short memory, an approximate solution of the problem of radioactive contaminant transport along the fracture surrounded by the fractal type porous medium is also obtained and compared with the exact solution. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

Quantitative characterization of solute transport in fractures with different surface roughness based on ten Barton profiles

In order to understand the transport mechanism of solute through naturally fractured rocks, it is important to quantitatively characterize the influence of varying surface roughness on fluid flow and solute transport. Rough-walled fracture geometry models with different joint roughness coefficients (JRC) were generated based on MATLAB pixel analyses of ten standard Barton profiles. Fluid flow and solute transport in the 2D rough-walled fractures were simulated by solving the Navier-Stokes-equation (NSE) and the transport equation for different pressure drops (i.e., 5, 10, and 20Pa). The simulation results show that the evolution of the solute-concentration field within rough-walled fractures is significantly dependent on surface roughness. Analysis of the breakthrough curves (BTCs) and residence time distributions (RTDs) indicated that rough fracture surfaces with large JRCs played a significant role in weakening the non-Fickian transport characteristics (i.e., early arrival and long tail) under the same pressure drop. It was found that the solute-concentration-distribution index (CDI), i.e., a metric for quantifying the longevity of the tail, increased with the JRCs and decreased with an increase in pressure drops. This result demonstrates that decreasing the surface roughness increases the Péclet number (Pe) and enhances advection process in solute transport, resulting in an increase in the non-uniform concentration distribution and shortened the long tail. Inverse modeling of the BTCs shows that rough fracture surfaces with large JRCs decrease the effective dispersion coefficient and Pe, suggesting that rough fracture surfaces decrease the advection and dispersion processes and delay the early arrival. These results provide more comprehensive understanding of the role of surface roughness in solute transport through fractures. Based on the relationships between JRC value and effective dispersion coefficient, a prediction method was established to predict the non-Fickian transport and the JRC value, and the practical cases further proved the feasibility of the prediction method.

Channel network concept: an integrated approach to visualize solute transport in fractured rocks

The advection-dispersion equation, ADE, has commonly been used to describe solute transport in fractured rock. However, there is one key question that must be addressed before the mathematical form of the so-called Fickian dispersion that underlies the ADE takes on physical meaning in fractures. What is the required travel distance, or travel time, before the Fickian condition is met and the ADE becomes physically reasonable? A simple theory is presented to address this question in tapered channels. It is shown that spreading of solute under forced-gradient flow conditions is mostly dominated by advective mechanisms. Nevertheless, the ADE might be valid under natural flow conditions. Furthermore, several concerns are raised in this paper with regard to using the concept of a field-scale matrix diffusion coefficient in fractured rocks. The concerns are mainly directed toward uncertainties and potential bias involved in finding the continuum model parameters. It is illustrated that good curve fitting does not ensure the physical reasonability of the model parameters. It is suggested that it is feasible and adequate to describe flow and transport in fractured rocks as taking place in three-dimensional networks of channels, as embodied in the channel network concept. It is argued that this conceptualization provides a convenient framework to capture the impacts of spatial heterogeneities in fractured rocks and can accommodate the physical mechanisms underlying the behavior of solute transport in fractures. All these issues are discussed in relation to analyzing and predicting actual tracer tests in fractured crystalline rocks.

Non-Fickian Solute Transport in a Single Fracture of Marble Parallel Plate

Accurate prediction of solute transport processes in a fracture aquifer is an important task not only for proper management of the groundwater but also for pollution control. A key issue of this task is how to accurately obtain the experimental data and to analyze the solute transport in fracture in subsurface hydrology, which would greatly help us to understand the releasing mechanism and transport of the solute in a fracture. In this study, a fracture experiment is conducted in a laboratory based on previous studies. The fracture used with a length of 60 cm and a width of 10 cm is sealed with glass glue to avoid leakage of tracer due to uneven fracture walls. The sodium chloride (NaCl) solute is injected from the left of the fracture. And an electrical conductivity monitoring system is installed on the right of the fracture. Then breakthrough curves (BTCs) of solute transport are fitted using the classical advection-dispersion equation (ADE) and the truncation power-law function (TPL) model in the package of the continuous time random walk (CTRW). The results show that the flow satisfies non-Darcian law in the experimental conditions, which can be better fitted using the Forchheimer equation and Izbash equation. The solute transport presents non-Fickian phenomena and shows a long tailing. The fitting results of the TPL model are far better than ADE in fitting the long tailing at three different flow velocities. Furthermore, electrical conductivity monitoring method not only is effective but also has an advantage of no disturbance to water and concentration fields in a fracture.

Assumptions of the analytical solution for solute transport in a fracture–matrix system

This study focuses on numerical modeling of fluid flow and solute transport in rough-walled rock fractures and fracture-matrix systems, with the main aim to investigate the impacts of fracture surface roughness on flow and transport processes in rock fractures. Both 2D and 3D fracture models were built from laser-scanned surface tomography of a real granite rock sample, to consider realistic features of surface tomography and potential asperity contacts. The flow was simulated by directly solving the Navier-Stokes equations (NSE) and the transport was modeled by solving the advection-dispersion equation (ADE) in the entire domain of fracture-matrix system, including matrix diffusion process. Such direct simulations provided detailed flow and concentration fields for quantitatively analysis of flow and transport behavior. The detailed analysis of surface roughness decomposition, complex flow patterns (i.e., channeling, transverse and eddy flows), effective advective flow apertures, effective transmissivity, effective dispersivity, residence time, transport resistance and specific surface area demonstrated significant impacts of realistic fracture surface roughness on fluid flow and solute transport processes in rock fractures. The results show that the surface roughness and shear displacement caused asperity contacts significantly enhance nonlinearity and complexity of flow and transport processes in rough-walled fractures and fracture-matrix systems. The surface roughness also causes invasion flows in intersected fractures which enhance solute mixing at fracture intersections. Therefore, the fracture surface roughness is an important source of uncertainty in application of such simplified models like cubic law (CL) for fluid flow and analytical solutions for solute transport in rock fractures. The research conducted advances our understanding of realistic flow and transport processes in natural fractured rocks. The results are useful for model validation/extension, uncertainty analysis/quantification and laboratory experiments design in the context of various applications related to fracture flow and transport.

Evidence of non-Darcy flow and non-Fickian transport in fractured media at laboratory scale

Abstract. During a risk assessment procedure as well as when dealing with cleanup and monitoring strategies, accurate predictions of solute propagation in fractured rocks are of particular importance when assessing exposure pathways through which contaminants reach receptors. Experimental data obtained under controlled conditions such as in a laboratory allow to increase the understanding of the fundamental physics of fluid flow and solute transport in fractures. In this study, laboratory hydraulic and tracer tests have been carried out on an artificially created fractured rock sample. The tests regard the analysis of the hydraulic loss and the measurement of breakthrough curves for saline tracer pulse inside a rock sample of parallelepiped shape (0.60 × 0.40 × 0.08 m). The convolution theory has been applied in order to remove the effect of the acquisition apparatus on tracer experiments. The experimental results have shown evidence of a non-Darcy relationship between flow rate and hydraulic loss that is best described by Forchheimer's law. Furthermore, in the flow experiments both inertial and viscous flow terms are not negligible. The observed experimental breakthrough curves of solute transport have been modeled by the classical one-dimensional analytical solution for the advection–dispersion equation (ADE) and the single rate mobile–immobile model (MIM). The former model does not properly fit the first arrival and the tail while the latter, which recognizes the existence of mobile and immobile domains for transport, provides a very decent fit. The carried out experiments show that there exists a pronounced mobile–immobile zone interaction that cannot be neglected and that leads to a non-equilibrium behavior of solute transport. The existence of a non-Darcian flow regime has showed to influence the velocity field in that it gives rise to a delay in solute migration with respect to the predicted value assuming linear flow. Furthermore, the presence of inertial effects enhance non-equilibrium behavior. Instead, the presence of a transitional flow regime seems not to exert influence on the behavior of dispersion. The linear-type relationship found between velocity and dispersion demonstrates that for the range of imposed flow rates and for the selected path the geometrical dispersion dominates the mixing processes along the fracture network.

Experimental study of the non-darcy flow and solute transport in a channeled single fracture

The characterization of fracture rocks is always a key issue in understanding the flow and solute transport in fractured media. This article studies the solute transport in a Channeled Single Fracture (CSF), a single fracture with contact in certain areas. The flow in a CSF often has preferential pathways and the transport in a CSF often has Break Through Curves (BTCs) with long tails. The Surface Contact Ratio (SCR), the ratio of the contact area to the total fracture area, is an important indicator for the fracture surface roughness. To study the flow and solute transport in a CSF, a controlled physical model is constructed and a series of flow and tracer test experiments are carried out. Under our experimental conditions, the flow in a CSF is found to follow the Forchheimer equation J = av + bv 2, where J and v are the hydraulic gradient and the average pore velocity, respectively and a and b are two parameters related to the viscous and inertial flow components, respectively. Furthermore, it is found that b decreases with the decrease of SCR. For the solute transport, it is found that the BTCs often deviate from the traditional Fickian behavior, by the early-arrival and the long tailing. More interestingly, the observed BTCs often have a double-peak or a multi-peak, that would be difficult to explain using the existing transport theory such as the Advection-Dispersion Equation (ADE). In addition, the longitudinal dispersion coefficient D L is found to be scale-dependent in a CSF and the D L – l relationship is of exponential type.