Solute Transport In Fractured Rock Research Articles

Non-Fickian solute transport in three-dimensional crossed shear rock fractures at different contact ratios

Solute transport in fractured rocks plays a crucial role in many subsurface processes, such as geothermal resource extraction and carbon capture and storage. This study conducted simulations of non-Fickian solute transport at varying contact ratios and voids in crossed shear fractures. Results indicated that increasing the contact ratio of the crossed fractures intensified the “tailing” phenomenon of non-Fickian solute transport, and has a negative relationship with the solute outflow concentration. Additionally, the anisotropy of intersections and the variations in their void structure both influence the redistribution and mixing of fluid and solute, therefore, we propose a method to determine the solute mixing patterns at the intersection. Ultimately, while the volume and magnitude of the separated vortex domain in the flow field can influence the non-Fickian solute transport, the “tailing” phenomenon is more significantly affected by its magnitude.

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.

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.

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.

Simulation of 3D flow and solute transport in fractured rock at Äspö, Sweden

The code d3f++ developed under the leadership of GRS for simulating 3D flow and solute transport includes an advanced formulation for fracture flow and transport in lower-dimensional elements that has still been in need of qualification. A variety of in-situ experiments in the granitic rock at the Swedish Hard Rock Laboratory Aspo offers an excellent basis for this purpose. Particularly well suited is the work performed in the TRUE Block Scale Project where a hydrostructural model comprising 30 large-scale fractures in a cube-shaped domain with a side length of 200 m has been set up for simulating groundwater flow which in turn forms the basis for reproducing the results of the injection–extraction tracer test “C2”. The present paper deals with modelling 3D flow and solute transport with the code d3f++ as a qualification exercise. The modelling results reveal an excellent representation of the contrasts in flow velocity across the fractures. Also the jumps in tracer concentration along intersecting fractures where waters with different tracer concentrations mix are handled well by the code. Calibration has nevertheless been required in order to achieve a reasonable fit of measured and calculated breakthrough curves.

Particle-Based Workflow for Modeling Uncertainty of Reactive Transport in 3D Discrete Fracture Networks

Fractures are major flow paths for solute transport in fractured rocks. Conducting numerical simulations of reactive transport in fractured rocks is a challenging task because of complex fracture connections and the associated nonuniform flows and chemical reactions. The study presents a computational workflow that can approximately simulate flow and reactive transport in complex fractured media. The workflow involves a series of computational processes. Specifically, the workflow employs a simple particle tracking (PT) algorithm to track flow paths in complex 3D discrete fracture networks (DFNs). The PHREEQC chemical reaction model is then used to simulate the reactive transport along particle traces. The study illustrates the developed workflow with three numerical examples, including a case with a simple fracture connection and two cases with a complex fracture network system. Results show that the integration processes in the workflow successfully model the tetrachloroethylene (PCE) and trichloroethylene (TCE) degradation and transport along particle traces in complex DFNs. The statistics of concentration along particle traces enables the estimations of uncertainty induced by the fracture structures in DFNs. The types of source contaminants can lead to slight variations of particle traces and influence the long term reactive transport. The concentration uncertainty can propagate from parent to daughter compounds and accumulate along with the transport processes.

Influence of surface roughness on fluid flow and solute transport through 3D crossed rock fractures

The influence of surface roughness on fluid flow and solute transport through three-dimensional (3D) crossed rock fractures are investigated by numerical simulations. Three crossed fracture models with different degrees of surface roughness are established by two intersecting rough-walled fractures with four branches. The fracture surface morphological data are measured from three natural fractures in sandstone and granite rock samples. The fluid flow is simulated by solving the Navier-Stokes equations and solute transport is simulated by solving the advective-diffusion equation. By rotating one fracture plane while fixing the other, series of intersection models with different angles between the two crossed fractures are established to investigate the influence of the intersecting angle. Simulation results of the rough-walled fractures are compared with the smooth parallel-plate model, showing that the surface roughness significantly enhances channeling and mixing for fluid flow and solute transport at fracture intersections. The mechanism is that the complex geometry of the intersection for rough-walled models results in reallocation of fluid pathways at the intersection, which consequently affect the mixing behavior depending on the Peclet number. The intersecting angle affects the channeling and mixing behavior because it influences the geometrical structure of the fracture intersection. The correlation between the mixing ratio and the geometrical characteristics of intersections is quantified by a relative roughness parameter. The results reveal that the widely adopted smooth parallel-plate model may lead to significant uncertainty in predicting the solute transport in crossed fractures, especially at intersections with unmated fracture surfaces. The correlation between the mixing ratio and the roughness parameter developed in this study can be incorporated into discrete fracture network models to improve their performance in estimating solute transport in fractured rocks.

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.

Effect of Roughness on Conservative Solute Transport through Synthetic Rough Single Fractures

Understanding solute transport in fractured rocks is of particular importance in many applications. Aperture values ranging from 4.7 to 8.7 mm and Reynolds number (Re) values at 9.38~1743.8 were set for investigating fluid flow through synthetic horizontal single smooth and rough fractures. The Brilliant Blue FCF dye was chosen as the tracer to visualize the transport process. This paper focuses on the dispersion process in rough single fractures under non-Darcian flow conditions. Non-Darcian flow existed in both smooth and rough single fractures and the average flow velocity–hydraulic gradient (V–J) relationships were best described by the Forchheimer equation. The main objectives were to check the existing flow and transport models and to study possible correlations between fitting parameters and heterogeneities. The classical advection dispersion equation (ADE) model failed to capture the long-tailing of breakthrough curves (BTCs). Instead, the continuous time random walk (CTRW) model was better at explaining BTCs in both smooth and rough fractures, especially in capturing the long-tailing feature. The non-Darcian coefficient βc in the Forchheimer equation and the coefficient β in the CTRW model appeared to be most relevant for characterizing the heterogeneity of the rough single fractures.

Solute transport in fractured rocks with stagnant water zone and rock matrix composed of different geological layers—Model development and simulations

Key Points A model is developed to describe solute transport in channels in fractures The analytical solution to the Laplace‐transformed concentration is derived Simulations show that diffusion into stagnant water is important

Linked multicontinuum and crack tensor approach for modeling of coupled geomechanics, fluid flow and transport in fractured rock

In this paper, we present a linked multicontinuum and crack tensor approach for modeling of coupled geomechanics, fluid flow, and solute transport in fractured rock. We used the crack tensor approach to calculate effective block-scale properties, including anisotropic permeability and elastic tensors, as well as multicontinuum properties relevant to fracture–matrix interactions and matrix diffusion. In the modeling, we considered stress dependent properties, through stress-induced changes in fracture apertures, to update permeability and elastic tensors. We evaluated the effectiveness and accuracy of our multicontinuum approach by comparing our modeling results with that of three independent discrete fracture network (DFN) models. In two of the three alternative DFN models, solute transport was simulated by particle tracking, an approach very different from the standard solute transport used in our multicontinuum modeling. We compared the results for flow and solute transport through a 20m×20m model domain of fractured rock, including detailed comparison of total flow rate, its distribution, and solute breakthrough curves. In our modeling, we divided the 20m×20m model domain into regular blocks, or continuum elements. We selected a model discretization of 40×40 elements (having a side length of 0.5m) that resulted in a fluid-flow rate equivalent to that of the DFN models. Our simulation results were in reasonably good agreement with the alternative DFN models, for both advective dominated transport (under high hydraulic gradient) and matrix-diffusion retarded transport (under low hydraulic gradient). However, we found pronounced numerical dispersion when using larger grid blocks, a problem that could be remediated by the use of a finer numerical grid resolution, while maintaining a larger grid for evaluation of equivalent properties, i.e. a property grid overlapping the numerical grid. Finally, we encountered some difficulties in using our approach when element sizes were so small that only one or a few fractures intersect an element—this is an area of possible improvement that will be pursued in future research.

Numerical modeling of stress effects on solute transport in fractured rocks

The effects of stress/deformation on fluid flow and contaminant transport in fractured rocks is one of the major concerns for performance and safety assessments of many subsurface engineering problems, especially radioactive waste disposal and oil/gas reservoir fields. However, very little progress has been made to study this issue due to difficulties in both experiments and numerical modeling. The objective of this study is to systematically investigate the influence of stress on solute transport in fractured rocks for the first time, considering different stress and hydraulic pressure conditions. A hybrid approach combining discrete element method (DEM) for stress-flow simulations and a particle tracking algorithm is developed. The impact of matrix diffusion (diffusion of molecular size solutes in and out of the rock matrix, and sorption onto the surface of micropores in rock matrix) is also included. The numerical results show that stress not only significantly changes the solute residence time through the fracture networks, but also changes the solute travel paths. Matrix diffusion plays a dominant role in solute transport when the hydraulic gradient is small, which is often encountered in practice.

Simulation of solute transport using a coupling model based on finite volume method in fractured rocks

The discrete version of solute transport equation for porous matrix depicted with the continuum model and the discrete fractured-network model are derived for fractured rocks with the Finite Volume Method (FVM). The two models are coupled according to the continuity condition of hydraulic head and concentration and the conservation of flow flux and mass flux in the contact plane between porous matrix and fractures. Numerical results show that the simulated concentration of the coupling model based on the FVM agrees well with that from analytical solution, which demonstrates that the coupling model can effectively be applied to the simulation of solute transport in fractured rocks.

Variable‐density groundwater flow and solute transport in fractured rock: Applicability of the Tang et al. [1981] analytical solution

The effect of fluid density variations on mixed convective (advective and density‐driven) transport in fractured rock is examined. Assuming a representative natural hydraulic gradient in a vertical fracture, breakthrough curves for variable‐density systems are shown to be significantly different from those with constant‐density conditions for even very small solute source concentrations (as low as approximately 2.3 g L−1 total dissolved solids, corresponding to 6.4% of seawater salinity). We compare analytical solutions with results of fully coupled numerical simulations of variable‐density groundwater flow and solute transport in fractured rock. Current analytical solutions for solute transport in fractured rock do not account for fluid density variations and therefore fail to predict variable‐density transport. Using a mixed convection ratio analysis, we determine the hydrogeologic conditions where variable‐density transport is important and hence when analytical solutions fail to predict variable‐density transport in fractured rock. We present a modified velocity term that includes a density‐driven flow component in a vertical fracture to account for fluid density variations. The modified velocity term is incorporated into the standard Tang et al. (1981) analytical solution. The original density‐invariant analytical solution is shown to be applicable near a solute source and at early time, while the velocity‐modified density‐variant solution gives very good results for long‐term and far‐field behavior. These results suggest that analytical solutions may still be useful for analyzing variable‐density transport in fractured rock. This study has implications for the analysis of dense plume transport in fractured rock where reliable long‐term predictions are important.

Non-Fickian dispersion in a single fracture

Solute transport in fractured rocks is of major interest in many applications, from the petroleum industry to ground water management. This work focuses on the dispersion process in a transparent replica of a real single fracture. The fracture exhibits strong changes in heterogeneity, with the first half very heterogeneous and the second half fairly homogeneous. Three models have been used to interpret the tracer experiments: the classical advection-dispersion equation (ADE), the continuous time random walk (CTRW), and the stratified model. The main goals were to test these models and to study possible correlations between fitting parameters and heterogeneities. As expected, the solution derived from the ADE equation appears to be unable to model long-time tailing behavior. On the other hand, the results confirm the CTRW robustness and the coefficient β seems well correlated to heterogeneities. Finally, the stratified model is also able to describe non-Fickian dispersion. The parameters defined by this model are correlated to the heterogeneities of the fracture.

Scale Dependence of the Effective Matrix Diffusion Coefficient: Some Analytical Results

Matrix diffusion is an important process affecting solute transport in fractured rock, and the matrix diffusion coefficient is a key parameter for describing this process. Previous studies have indicated that effective matrix diffusion coefficient values obtained from a number of field tracer tests are enhanced in comparison with local values and may increase with test scale. In this communication, we develop analytical expressions for the effective matrix diffusion coefficient for two simple fracture–matrix systems and demonstrate that heterogeneities in the rock matrix at different scales may contribute to the scale dependence of the effective matrix diffusion coefficient.

Field-scale effective matrix diffusion coefficient for fractured rock: Results from literature survey

Matrix diffusion is an important mechanism for solute transport in fractured rock. We recently conducted a literature survey on the effective matrix diffusion coefficient, D m e, a key parameter for describing matrix diffusion processes at the field scale. Forty field tracer tests at 15 fractured geologic sites were surveyed and selected for the study, based on data availability and quality. Field-scale D m e values were calculated, either directly using data reported in the literature, or by reanalyzing the corresponding field tracer tests. The reanalysis was conducted for the selected tracer tests using analytic or semi-analytic solutions for tracer transport in linear, radial, or interwell flow fields. Surveyed data show that the scale factor of the effective matrix diffusion coefficient (defined as the ratio of D m e to the lab-scale matrix diffusion coefficient, D m, of the same tracer) is generally larger than one, indicating that the effective matrix diffusion coefficient in the field is comparatively larger than the matrix diffusion coefficient at the rock-core scale. This larger value can be attributed to the many mass-transfer processes at different scales in naturally heterogeneous, fractured rock systems. Furthermore, we observed a moderate, on average trend toward systematic increase in the scale factor with observation scale. This trend suggests that the effective matrix diffusion coefficient is likely to be statistically scale-dependent. The scale-factor value ranges from 0.5 to 884 for observation scales from 5 to 2000 m. At a given scale, the scale factor varies by two orders of magnitude, reflecting the influence of differing degrees of fractured rock heterogeneity at different geologic sites. In addition, the surveyed data indicate that field-scale longitudinal dispersivity generally increases with observation scale, which is consistent with previous studies. The scale-dependent field-scale matrix diffusion coefficient (and dispersivity) may have significant implications for assessing long-term, large-scale radionuclide and contaminant transport events in fractured rock, both for nuclear waste disposal and contaminant remediation.

An interpretation of potential scale dependence of the effective matrix diffusion coefficient

Matrix diffusion is an important process for solute transport in fractured rock, and the matrix diffusion coefficient is a key parameter for describing this process. Previous studies have indicated that the effective matrix diffusion coefficient values, obtained from a large number of field tracer tests, are enhanced in comparison with local values and may increase with test scale. In this study, we have performed numerical experiments to investigate potential mechanisms behind possible scale-dependent behavior. The focus of the experiments is on solute transport in flow paths having geometries consistent with percolation theories and characterized by multiple local flow loops formed mainly by small-scale fractures. The water velocity distribution through a flow path was determined using discrete fracture network flow simulations, and solute transport was calculated using a previously derived impulse-response function and a particle-tracking scheme. Values for effective (or up-scaled) transport parameters were obtained by matching breakthrough curves from numerical experiments with an analytical solution for solute transport along a single fracture. Results indicate that a combination of local flow loops and the associated matrix diffusion process, together with scaling properties in flow path geometry, seems to be an important mechanism causing the observed scale dependence of the effective matrix diffusion coefficient (at a range of scales).

Combined interpretation of radar, hydraulic, and tracer data from a fractured-rock aquifer near Mirror Lake, New Hampshire, USA

An integrated interpretation of field experimental cross-hole radar, tracer, and hydraulic data demonstrates the value of combining time-lapse geophysical monitoring with conventional hydrologic measurements for improved characterization of a fractured-rock aquifer. Time-lapse difference-attenuation radar tomography was conducted during saline tracer experiments at the US Geological Survey Fractured Rock Hydrology Research Site near Mirror Lake, Grafton County, New Hampshire, USA. The presence of electrically conductive saline tracer effectively illuminates permeable fractures or pathways for geophysical imaging. The geophysical results guide the construction of three-dimensional numerical models of ground-water flow and solute transport. In an effort to explore alternative explanations for the tracer and tomographic data, a suite of conceptual models involving heterogeneous hydraulic conductivity fields and rate-limited mass transfer are considered. Calibration data include tracer concentrations, the arrival time of peak concentration at the outlet, and steady-state hydraulic head. Results from the coupled inversion procedure suggest that much of the tracer mass migrated outside the three tomographic image planes, and that solute is likely transported by two pathways through the system. This work provides basic and site-specific insights into the control of permeability heterogeneity on ground-water flow and solute transport in fractured rock.

Scale Dependency of the Effective Matrix Diffusion Coefficient

It has been recognized that matrix diffusion is an important process for retarding solute transport in fractured rock. Based on analyses of tracer transport data from a number of field tests, we demonstrate for the first time that the effective matrix‐diffusion coefficient may be scale dependent and generally increases with test scale. A preliminary theoretical explanation of this scale dependency is also presented, based on the hypothesis that solute travel paths within a fracture network are fractals.