Migration of colloids in discretely fractured porous media: effect of colloidal matrix diffusion

Numerical simulations of colloid transport in discretely fractured porous media were performed to investigate the importance of matrix diffusion of colloids as well as the filtration and remobilization of colloidal particles in both the fractures and porous matrix. To achieve this objective a finite element numerical code entitled COLDIFF was developed. The processes that COLDIFF takes into account include advective-dispersive transport of colloids, filtration and remobilization of colloidal particles in both fractures and porous matrix, and diffusive interactions of colloids between the fractures and porous matrix. Three sets of simulations were conducted to examine the importance of parameters and processes controlling colloid migration. First, a sensitivity analysis was performed using a porous block containing a single fracture to determine the relative importance of various phenomenological coefficients on colloid transport. The primary result of the analysis showed that the porosity of the matrix and the process of colloid filtration in fractures play important roles in controlling colloid migration. Second, simulations were performed to replicate and examine the results of a laboratory column study using a fractured shale saprolite. Results of this analysis showed that the filtration of colloidal particles in the porous matrix can greatly affect the tailing of colloid concentrations after the colloid source was removed. Finally, field-scale simulations were performed to examine the effect of matrix porosity, fracture filtration and fracture remobilization on long-term colloid concentration and migration distance. The field scale simulations indicated that matrix diffusion and fracture filtration can significantly reduce colloid migration distance. Results of all three analyses indicated that in environments where porosity is relatively high and colloidal particles are small enough to diffuse out of fractures, the characteristics of the porous matrix that affect colloid transport become more important than those of the fracture network. Because the properties of the fracture network tend to have greater uncertainty due to difficulties in their measurement relative to those of the porous matrix, prediction uncertainties associated with colloid transport in discretely fractured porous media may be reduced.     

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.     

Effects of biofilm growth on flow and transport through a glass parallel plate fracture

The effects of biofilm growth on flow and solute transport through a sandblasted glass parallel plate fracture was investigated. The fracture was inoculated using soil microorganisms. Glucose, oxygen and other nutrients were supplied to support growth. The biomass initially formed discrete clusters attached to the glass surfaces, but over time formed a continuous biofilm. From dye tracer tests conducted during biofilm growth, it was observed that channels and low-permeability zones dominated transport. The hydraulic conductivity of the fracture showed a sigmoidal decrease with time. The hydraulic conductivity was reduced by a factor of 0.033, from 18 to 0.6 cm/s, corresponding to a 72% decrease in the hydraulic aperture, from 500 to 140 microm. In contrast, the mass balance aperture, determined from fluoride tracer tests, remained relatively constant, indicating that the impact of biomass growth on effective fracture porosity was much less than the effect on hydraulic conductivity. Analyses of pre-biofilm tracer tests revealed that both Taylor dispersion and macrodispersion were influencing transport. During biofilm growth, only macrodispersion was dominant. The macrodispersion coefficient alpha(macro) was found to increase logarithmically with hydraulic conductivity reduction.     

Anomalous transport of colloids and solutes in a shear zone

Transport experiments with colloids and radionuclides in a shear zone were conducted during the Colloid and Radionuclide Retardation experiment (CRR) at Nagra's Grimsel Test Site. Breakthrough curves of bentonite colloids and uranine, a non-sorbing solute, were measured in an asymmetric dipole flow field. The colloid breakthrough is earlier than that of uranine. Both breakthrough curves show anomalously long late time tails and the slope of the late time tails for the colloids is slightly higher. Anomalous late time tails are commonly associated with matrix diffusion processes; the diffusive interaction of solutes transported in open channels with the adjacent porous rock matrix or zones of stagnant water. The breakthrough curves for different colloid size classes are very similar and show no signs of fractionation due to their (size-dependent) diffusivity. It is proposed that tailing of the colloids is mainly caused by the structure of the flow field and that for the colloid transport, matrix diffusion is of minor importance. This has consequences for the interpretation of the uranine breakthrough. Comparisons of experimental results with numerical studies and with the evaluation of the colloid breakthrough with continuous time random theory imply that the tailing in the conservative solute breakthrough in this shear zone is not only caused by matrix diffusion. Part of the tailing can be attributed to advective transport in fracture networks and advection in low velocity regions. Models based on the advection-dispersion equation and matrix diffusion do not properly describe the temporal and spatial evolution of colloid and solute transport in such systems with a consistent set of parameters.     

Interpretation of injection-withdrawal tracer experiments conducted between two wells in a large single fracture

Tracer experiments conducted using a flow field established by injecting water into one borehole and withdrawing water from another are often used to establish connections and investigate dispersion in fractured rock. As a result of uncertainty in the uniqueness of existing models used for interpretation, this method has not been widely used to investigate more general transport processes including matrix diffusion or advective solute exchange between mobile and immobile zones of fluid. To explore the utility of the injection-withdrawal method as a general investigative tool and with the intent to resolve the transport processes in a discrete fracture, two tracer experiments were conducted using the injection-withdrawal configuration. The experiments were conducted in a fracture which has a large aperture (>500 microm) and horizontally pervades a dolostone formation. One experiment was conducted in the direction of the hydraulic gradient and the other in the direction opposite to the natural gradient. Two tracers having significantly different values of the free-water diffusion coefficient were used. To interpret the experiments, a hybrid numerical-analytical model was developed which accounts for the arcuate shape of the flow field, advection-dispersion in the fracture, diffusion into the matrix adjacent to the fracture, and the presence of natural flow in the fracture. The model was verified by comparison to a fully analytical solution and to a well-known finite-element model. Interpretation of the tracer experiments showed that when only one tracer, advection-dispersion, and matrix diffusion are considered, non-unique results were obtained. However, by using multiple tracers and by accounting for the presence of natural flow in the fracture, unique interpretations were obtained in which a single value of matrix porosity was estimated from the results of both experiments. The estimate of porosity agrees well with independent measurements of porosity obtained from core samples. This suggests that: (i) the injection-withdrawal method is a viable tool for the investigation of general transport processes provided all relevant experimental conditions are considered and multiple conservative tracers are used; and (ii) for the conditions of the experiments conducted in this study, the dominant mechanism for exchange of solute between the fracture and surrounding medium is matrix diffusion.     

Transport of a non-volatile contaminant in unsaturated porous media in the presence of colloids

Stable colloidal particles can travel long distances in subsurface environments and carry particle-reactive contaminants with them to locations further than predicted by the conventional advective-dispersive transport equation. When such carriers exist in a saturated porous medium, the system can be idealized as consisting of three phases: an aqueous phase, a carrier phase, and a stationary solid matrix phase. However, when colloids are present in an unsaturated porous medium, the system representation should include one more phase, i.e. the air phase. In the work reported, a mathematical model was developed to describe the transport and fate of the colloidal particles and a non-volatile contaminant in unsaturated porous media. The model is based on mass balance equations in a four-phase porous medium. Colloid mass transfer mechanisms among aqueous, solid matrix, and air phases, and contaminant mass transfer between aqueous and colloid phases are represented by kinetic expressions. Governing equations are non-dimensionalized and solved to investigate colloid and contaminant transport in an unsaturated porous medium. A sensitivity analysis of the transport model was utilized to assess the effects of several parameters on model behavior. The colloid transport model matches successfully with experimental data of Wan and Wilson. The presence of air-water interface retards the colloid transport significantly counterbalancing the facilitating effect of colloids. However, the retardation of contaminant transport by colloids is highly dependent on the properties of the contaminant and the colloidal surface.     

The influence of system complexity on bacterial transport in saturated porous media

A series of miscible-displacement column experiments were conducted under saturated flow conditions to systematically investigate the influence of physical and biological complexity on bacterial activity and fate in the presence and absence of a non-sorbing growth substrate, salicylate. Bacterial elution was monitored for three different systems; System I--a sterilized, inoculated, well-sorted sand, System II--a sterilized, inoculated, heterogeneous loamy sand (Hayhook), and System III--two different unsterilized loamy sands (Hayhook and Vinton) each with their associated indigenous microbial community. Results show that System I behaved ideally with respect to both cell and substrate transport, wherein: (1) growth occurred in response to substrate addition, (2) cell elution increased in response to the substrate pulse, and (3) breakthrough curves were reproducible for both substrate and cell elution. In contrast, System II showed ideal behavior with respect to substrate transport but showed variable behavior for cell transport. Further, there was no measurable growth in response to substrate addition and no increase in cell elution during the salicylate pulse. System III exhibited non-ideal behavior for both substrate and cell transport. Of particular interest is the fact that the indigenous communities of the two soils behaved differently. Specifically, for the Hayhook soil, an increased elution response was observed for the heterotrophic population while the salicylate-degrading community was preferentially retained in the column. In contrast for the Vinton soil, the substrate pulse did not elicit an elution response from either the heterotrophic or salicylate-degrading community from the culturable, indigenous Vinton microorganisms. For Systems II and III, the observed variability appears to be associated with the biological component of the system, since sterile controls were reproducible. This type of systematic study is critical for understanding cell and substrate transport behavior in complex, heterogeneous systems, and illustrates the potential uncertainty associated with measurements in such systems.     

One-dimensional simulation of solute transfer in saturated–unsaturated porous media using the discontinuous finite elements method

A one-dimensional transport model for simulating water flow and solute transport in homogeneous–heterogeneous, saturated–unsaturated porous media is presented. The model is composed of a combination of accurate numerical algorithms for solving the nonlinear Richard's and advection–dispersion equations (ADE). The mixed form of Richard's equation is solved using a standard finite element method (FEM) with primary variable switching. The transport equation is solved using operator splitting, with the discontinuous finite element method (DFE) for discretization of the advective term. A slope limiting procedure for DFE avoids numerical instabilities but creates very limited numerical dispersion for high Peclet numbers. An implicit finite differences scheme (FD) is used for the dispersive term.The unsaturated flow and transport model (Wamos-T) is applied to a variety of rigorous problems including transient flow, heterogeneous medium and abrupt variations of velocity in magnitude and direction due to time-varying boundary conditions. It produces accurate and mass-conservative solutions for a very large range of grid Peclet numbers. The Wamos-T model is a good and robust alternative for the simulation of mass transport in unsaturated domain.     

The effect of surface-active solutes on water flow and contaminant transport in variably saturated porous media with capillary fringe effects

Organic contaminants that decrease the surface tension of water (surfactants) can have an effect on unsaturated flow through porous media due to the dependence of capillary pressure on surface tension. We used an intermediate-scale 2D flow cell (2.44 x 1.53 x 0.108 m) packed with a fine silica sand to investigate surfactant-induced flow perturbations. Surfactant solution (7% 1-butanol and dye tracer) was applied at a constant rate at a point source located on the soil surface above an unconfined synthetic aquifer with ambient groundwater flow and a capillary fringe of approximately 55 cm. A glass plate allowed for visual flow and transport observations. Thirty instrumentation stations consist of time domain reflectometry probes and tensiometers measured in-situ moisture content and pressure head, respectively. As surfactant solution was applied at the point source, a transient flow perturbation associated with the advance of the surfactant solution was observed. Above the top of the capillary fringe the advance of the surfactant solution caused a visible drainage front that radiated from the point source. Upon reaching the capillary fringe, the drainage front caused a localized depression of the capillary fringe below the point source because the air-entry pressure decreased in proportion to the decrease in surface tension caused by the surfactant. Eventually, a new capillary fringe height was established. The height of the depressed capillary fringe was proportional to height of the initial capillary fringe multiplied by the relative surface tension of the surfactant solution. The horizontal transport of surfactant in the depressed capillary fringe, driven primarily by the ambient groundwater flow, caused the propagation of a wedge-shaped drying front in the downgradient direction. Comparison of dye transport during the surfactant experiment to dye transport in an experiment without surfactant indicated that because surfactant-induced drainage decreased the storage capacity of the vadose zone, the dye breakthrough time to the water table was more than twice as fast when the contaminant solution contained surfactant. The extensive propagation of the drying front and the effect of vadose zone drainage on contaminant breakthrough time suggest the importance of considering surface tension effects on unsaturated flow and transport in systems containing surface-active organic contaminants or systems, where surfactants are used for remediation of the vadose zone or unconfined aquifers.     

The effect of entrapped nonaqueous phase liquids on tracer transport in heterogeneous porous media: laboratory experiments at the intermediate scale

This work considers the applicability of conservative tracers for detecting high-saturation nonaqueous-phase liquid (NAPL) entrapment in heterogeneous systems. For this purpose, a series of experiments and simulations was performed using a two-dimensional heterogeneous system (10x1.2 m), which represents an intermediate scale between laboratory and field scales. Tracer tests performed prior to injecting the NAPL provide the baseline response of the heterogeneous porous medium. Two NAPL spill experiments were performed and the entrapped-NAPL saturation distribution measured in detail using a gamma-ray attenuation system. Tracer tests following each of the NAPL spills produced breakthrough curves (BTCs) reflecting the impact of entrapped NAPL on conservative transport. To evaluate significance, the impact of NAPL entrapment on the conservative-tracer breakthrough curves was compared to simulated breakthrough curve variability for different realizations of the heterogeneous distribution. Analysis of the results reveals that the NAPL entrapment has a significant impact on the temporal moments of conservative-tracer breakthrough curves.