Contaminant transport in fractured chalk: laboratory and field experiments

Laboratory experiments were performed on chalk samples from Denmark and Israel to determine diffusion and distribution coefficients. Batch tests were used to define sorption isotherms for naphthalene and o-xylene. Linear sorption isotherms were observed and described with Henry-isotherms. Because of the high purity and low contents of clay minerals and organic carbon, Danish and white Israeli chalk generally have low retardation capacities. Contrarily, gray Israeli chalk, with organic carbon fractions as high as 1.092%, remarkably retards organic contaminants. The K(OC) concept is not applicable to predicting distribution coefficients based on the organic carbon content in the chalk samples. Effective diffusivities of o-xylene, naphthalene, and several artificial tracers were determined using through-diffusion experiments. Based on measured diffusion coefficients and available literature values, a chalk specific exponent of 2.36 for Archie's law was derived, allowing a satisfactory estimate of relative diffusivities in chalk. A field-scale tracer test with uranine and lithium was performed in the Negev desert (Israel) to examine the transferability of diffusivities determined on small rock samples in the laboratory. Due to low recovery rates of the tracer, a modified single fissure dispersion model was used for inverse modeling of the breakthrough curves. Resulting diffusivities deviate insignificantly from the laboratory values, which are considered to be representative for the investigated part of the aquifer and applicable in transport models.     

Semi-analytical solutions for solute transport in fractured porous media using a strip source of finite width

Transient and steady-state analytical solutions are derived to investigate solute transport in a fractured porous medium consisting of evenly spaced, parallel discrete fractures. The solutions incorporate a finite width strip source, longitudinal and transverse dispersion in the fractures, source decay, aqueous phase decay, one-dimensional diffusion into the matrix, sorption to fracture walls, and sorption within the matrix. The solutions are derived using Laplace and Fourier transforms, and inverted by interchanging the order of integration and utilizing a numerical Laplace inversion algorithm. The solutions are verified for simplified cases by comparison to solutions derived by Batu [Batu V. A generalized two-dimensional analytical solution for hydrodynamic dispersion in bounded media with the first-type condition at the source. Wat Resour Res 1989;25(6):1125] and Sudicky and Frind [Sudicky EA, Frind EO. Contaminant transport in fractured porous media: analytical solutions for a system of parallel fractures. Wat Resour Res 1982;18(6):1634]. The application of the solutions to a fractured sandstone demonstrates that narrower source widths and larger values of transverse dispersivity both lead to lower downstream concentrations in the fractures and shorter steady-state plumes. The incorporation of aqueous phase decay and source concentration decay both lead to lower concentrations and shorter plumes, with even moderate amounts of decay significantly shortening the persistence of contamination.     

Simulating conservative tracers in fractured till under realistic timescales

Discrete-fracture and dual-porosity models are infrequently used to simulate solute transport through fractured unconsolidated deposits, despite their more common application in fractured rock where distinct flow regimes are hypothesized. In this study, we apply four fracture transport models--the mobile-immobile model (MIM), parallel-plate discrete-fracture model (PDFM), and stochastic and deterministic discrete-fracture models (DFMs)--to demonstrate their utility for simulating solute transport through fractured till. Model results were compared to breakthrough curves (BTCs) for the conservative tracers potassium bromide (KBr), pentafluorobenzoic acid (PFBA), and 1,4-piperazinediethanesulfonic acid (PIPES) in a large-diameter column of fractured till. Input parameters were determined from independent field and laboratory methods. Predictions of Br BTCs were not significantly different among models; however, the stochastic and deterministic DFMs were more accurate than the MIM or PDFM when predicting PFBA and PIPES BTCs. DFMs may be more applicable than the MIM for tracers with small effective diffusion coefficients (De) or for short timescales due to differences in how these models simulate diffusion or incorporate heterogeneities by their fracture networks. At large scales of investigation, the more computationally efficient MIM and PDFM may be more practical to implement than the three-dimensional DFMs, or a combination of model approaches could be employed. Regardless of the modeling approach used, fractures should be incorporated routinely into solute transport models in glaciated terrain.     

Matrix diffusion-derived plume attenuation in fractured bedrock

Matrix diffusion can attenuate the rate of plume migration in fractured bedrock relative to the rate of ground water flow for both conservative and nonconservative solutes of interest. In a system of parallel, equally spaced constant aperture fractures subject to steady-state ground water flow and an infinite source width, the degree of plume attenuation increases with time and travel distance, eventually reaching an asymptotic level. The asymptotic degree of plume attenuation in the absence of degradation can be predicted by a plume attenuation factor, beta, which is readily estimated as R' (phi(m)/phi(f)), where R' is the retardation factor in the matrix, phi(m) is the matrix porosity, and phi(f) is the fracture porosity. This dual-porosity relationship can also be thought of as the ratio of primary to secondary porosity. Beta represents the rate of ground water flow in fractures relative to the rate of plume advance. For the conditions examined in this study, beta increases with greater matrix porosity, greater matrix fraction organic carbon, larger fracture spacing, and smaller fracture aperture. These concepts are illustrated using a case study where dense nonaqueous phase liquid in fractured sandstone produced a dissolved-phase trichloroethylene (TCE) plume approximately 300 m in length. Transport parameters such as matrix porosity, fracture porosity, hydraulic gradient, and the matrix retardation factor were characterized at the site through field investigations. In the fractured sandstone bedrock examined in this study, the asymptotic plume attenuation factors (beta values) for conservative and nonconservative solutes (i.e., chloride and TCE) were predicted to be approximately 800 and 12,210, respectively. Quantitative analyses demonstrate that a porous media (single-porosity) solute transport model is not appropriate for simulating contaminant transport in fractured sandstone where matrix diffusion occurs. Rather, simulations need to be conducted with either a discrete fracture model that explicitly incorporates matrix diffusion, or a dual-continuum model that accounts for mass transfer between mobile and immobile zones. Simulations also demonstrate that back diffusion from the matrix to fractures will likely be the time-limiting factor in reaching ground water cleanup goals in some fractured bedrock environments.     

Analysis of a vertical dipole tracer test in highly fractured rock

The results of a vertical dipole tracer experiment performed in highly fractured rocks of the Clare Valley, South Australia, are presented. The injection and withdrawal piezometers were both screened over 3 m and were separated by 6 m (midpoint to midpoint). Due to the long screen length, several fracture sets were intersected, some of which do not connect the two piezometers. Dissolved helium and bromide were injected into the dipole flow field for 75 minutes, followed by an additional 510 minutes of flushing. The breakthrough of helium was retarded relative to bromide, as was expected due to the greater aqueous diffusion coefficient of helium. Also, only -25% of the total mass injected of both tracers was recovered. Modeling of the tracer transport was accomplished using an analytical one-dimensional flow and transport model for flow through a fracture with diffusion into the matrix. The assumptions made include: streamlines connecting the injection and withdrawal point can be modeled as a dipole of equal strength, flow along each streamline is one dimensional, and there is a constant Peclet number for each streamline. In contrast to many other field tracer studies performed in fractured rock, the actual travel length between piezometers was not known. Modeling was accomplished by fitting the characteristics of the tracer breakthrough curves (BTCs), such as arrival times of the peak concentration and the center of mass. The important steps were to determine the fracture aperture (240 microm) based on the parameters that influence the rate of matrix diffusion (this controls the arrival time of the peak concentration); estimating the travel distance (11 m) by fitting the time of arrival of the centers of mass of the tracers; and estimating fracture dispersivity (0.5 m) by fitting the times that the inflection points occurred on the front and back limbs of the BTCs. This method works even though there was dilution in the withdrawal well, the amount of which can be estimated by determining the value that the modeled concentrations need to be reduced to fit the data (approximately 50%). The use of two tracers with different diffusion coefficients was not necessary, but it provides important checks in the modeling process because the apparent retardation between the two tracers is evidence of matrix diffusion and the BTCs of both tracers need to be accurately modeled by the best fit parameters.     

A passive-discrete water sampler for monitoring seepage

This paper presents the design of the passive-discrete water sampler (PDWS) which has been developed to facilitate investigations of flow partitioning in fractured rocks. The PDWS continuously isolates seeping water into discrete samples while monitoring the seepage rate. The PDWS was used in a flow and transport experiment that investigated fracture-matrix interactions. During the experiment, a mix of conservative tracers with significantly different diffusion coefficients (lithium bromide [LiBr] and pentafluorobenzoic acid [PFBA]) was introduced along a fault located in fractured tuffs, and water seeping through the lower end of the fault was collected by the PDWS and analyzed for tracer concentrations. Preliminary results from this investigation show that samples of effluent captured by the PDWS effectively retained temporal changes in the chemical signature, while providing seepage rates.     

Irreversible sorption of benzene in sandy aquifer materials

Hydrocarbon compounds in aquifers are generally known to show a retardation effect due to sorption onto the surfaces of solid particles. In this study, we investigated the effect of sorption on the transport of benzene in sandy aquifer materials by conducting batch and column tests for both sandy aquifer materials and sandy materials to which had been added 0·5% powdered activated carbon. The batch test was conducted by equilibrating dry materials with benzene solutions of various initial concentrations, and by analysing the concentrations of benzene in the initial and equilibrated solutions using high‐performance liquid chromatography (HPLC). The column test was performed to monitor the concentrations of effluent versus time, known as a breakthrough curve (BTC). We injected KCl and benzene solutions as tracers into the inlet boundary as two different types of square pulse and step, and monitored the effluent concentrations at the exit boundary under a steady‐state condition using an electrical conductivity meter and HPLC. Simulation of benzene transport was performed using the convective–dispersive equation model with the distribution coefficients obtained from the batch test and the transport parameters of the conservative solute KCl from the column test. The observed BTCs of KCl and benzene for pulse injection showed that the arrival times of the peaks of both tracers coincided well, but the relative peak concentration of benzene was much lower than that of KCl. Comparison of the simulated and observed BTCs showed a great discrepancy for all cases of injection mode and material texture, indicating the absence of retardation effect. These results reveal that the predominant process affecting the benzene transport in the sandy aquifer materials is an irreversible sorption rather than retardation. This tentative conclusion was verified by simulation of benzene transport using an irreversible sorption parameter that led to a good agreement between the simulated and observed BTCs. Copyright © 2002 John Wiley & Sons, Ltd.     

Solute movement through intact columns of cryoturbated Upper Chalk

Cryoturbated Upper Chalk is a dichotomous porous medium wherein the intra‐fragment porosity provides water storage and the inter‐fragment porosity provides potential pathways for relatively rapid flow near saturation. Chloride tracer movement through 43 cm long and 45 cm diameter undisturbed chalk columns was studied at water application rates of 0·3, 1·0, and 1·5 cm h^?1. Microscale heterogeneity in effluent was recorded using a grid collection system consisting of 98 funnel‐shaped cells each 3·5 cm in diameter. The total porosity of the columns was 0·47 ± 0·02 m³ m^?3, approximately 13% of pores were ≥ 15 µm diameter, and the saturated hydraulic conductivity was 12·66 ± 1·31 m day^?1. Although the column remained unsaturated during the leaching even at all application rates, proportionate flow through macropores increased as the application rate decreased. The number of dry cells (with 0 ml of effluent) increased as application rate decreased. Half of the leachate was collected from 15, 19 and 22 cells at 0·3, 1·0, 1·5 cm h^?1 application rates respectively. Similar breakthrough curves (BTCs) were obtained at all three application rates when plotted as a function of cumulative drainage, but they were distinctly different when plotted as a function of time. The BTCs indicate that the columns have similar drainage requirement irrespective of application rates, as the rise to the maxima (C/C_o) is almost similar. However, the time required to achieve that leaching requirement varies with application rates, and residence time was less in the case of a higher application rate. A two‐region convection–dispersion model was used to describe the BTCs and fitted well (r² = 0·97–0·99). There was a linear relationship between dispersion coefficient and pore water velocity (correlation coefficient r = 0·95). The results demonstrate the microscale heterogeneity of hydrodynamic properties in the Upper Chalk. Copyright © 2007 John Wiley & Sons, Ltd.     

The hydrogeological properties of the matrix of the chalk in the Lublin coal basin (southeast Poland)

Abstract

An analysis of a series of chalk samples from the Lublin coal basin reveals that its matrix is a very porous but only slightly permeable porous medium; its water reserves are hardly susceptible to gravity drainage. The interconnected porosity of the chalk matrix diminishes with depth, probably because of the increase in lithostatic pressure.     

Dilution tests in a low-permeability fractured aquifer: matrix diffusion effect

A point dilution test is commonly used in single-borehole tracer experiments designed to determine the Darcy velocity of a formation. This method is based on the concept that, in a borehole, a tracer's concentration declines as a consequence of the water flux. Based on theoretical simulations and field observations, this study indicates that for low-permeability, yet highly porous fractured formations, the common practice of excluding the effect of diffusive mass flux between the dissolved tracer within the borehole and the surrounding matrix may lead to significant errors in the assessment of the Darcy velocity. This conclusion was confirmed by a model adapted to simulate experimental data collected from a tracer test performed in a vertical, large-diameter (25-cm) borehole drilled along a subvertical fracture intersecting a chalk formation.     

Contaminant transport in a fracture with spatially variable aperture in the presence of monodisperse and polydisperse colloids

A quasi-three-dimensional particle tracking model is developed to characterize the spatial and temporal effects of advection, molecular diffusion, Taylor dispersion, fracture wall deposition, matrix diffusion, and co-transport processes on two discrete plumes (suspended monodisperse or polydisperse colloids and dissolved contaminants) flowing through a variable aperture fracture situated in a porous medium. Contaminants travel by advection and diffusion and may sorb onto fracture walls and colloid particles, as well as diffuse into and sorb onto the surrounding porous rock matrix. A kinetic isotherm describes contaminant sorption onto colloids and sorbed contaminants assume the unique transport properties of colloids. Sorption of the contaminants that have diffused into the matrix is governed by a first-order kinetic reaction. Colloids travel by advection and diffusion and may attach onto fracture walls; however, they do not penetrate the rock matrix. A probabilistic form of the Boltzmann law describes filtration of both colloids and contaminants on fracture walls. Ensemble-averaged breakthrough curves of many fracture realizations are used to compare arrival times of colloid and contaminant plumes at the fracture outlet. Results show that the presence of colloids enhances contaminant transport (decreased residence times) while matrix diffusion and sorption onto fracture walls retard the transport of contaminants. Model simulations with the polydisperse colloids show increased effects of co-transport processes.     

Estimation of water saturation dependence of dispersion in unsaturated porous media: experiments and modelling analysis

In the dispersion theory, a linear relationship has been verified between the coefficient of hydrodynamic dispersion and water velocity, both in saturated and in unsaturated porous media. But for unsaturated soils the variability of flow directions and microscopic velocities can be larger than in saturated soils because of the lower degree of water saturation. This leads to an increased dispersion. Therefore, relationships between water content and relative water velocity fluctuations and water content together with the coefficient of dispersivity in unsaturated porous media respectively have been investigated systematically by displacement experiments in glass beads and coarse-textured sandy soil columns. The breakthrough curves (BTCs) of chloride showed that an increase of solute mixing with a decrease of water content was caused by an increase of flow velocity fluctuations for different pathways. In order to explain the observed tailing effect in unsaturated flow, two mathematical models were used to fit theoretically derived nonlinear functions of water content dependent dispersivities for both porous media. The close agreement between the observed and computed results suggests that the theoretical model of hydrodynamic dispersion can be extended to transport in unsaturated porous media, providing that BTCs of the effluent water are used to estimate representative dispersivity parameters of soils.     

Specification of Matrix Cleanup Goals in Fractured Porous Media

Semianalytical transient solutions have been developed to evaluate what level of fractured porous media (e.g., bedrock or clay) matrix cleanup must be achieved in order to achieve compliance of fracture pore water concentrations within a specified time at specified locations of interest. The developed mathematical solutions account for forward and backward diffusion in a fractured porous medium where the initial condition comprises a spatially uniform, nonzero matrix concentration throughout the domain. Illustrative simulations incorporating the properties of mudstone fractured bedrock demonstrate that the time required to reach a desired fracture pore water concentration is a function of the distance between the point of compliance and the upgradient face of the domain where clean groundwater is inflowing. Shorter distances correspond to reduced times required to reach compliance, implying that shorter treatment zones will respond more favorably to remediation than longer treatment zones in which back‐diffusion dominates the fracture pore water response. For a specified matrix cleanup goal, compliance of fracture pore water concentrations will be reached sooner for decreased fracture spacing, increased fracture aperture, higher matrix fraction organic carbon, lower matrix porosity, shorter aqueous phase decay half‐life, and a higher hydraulic gradient. The parameters dominating the response of the system can be measured using standard field and laboratory techniques.     

Heat Tracing in a Fractured Aquifer with Injection of Hot and Cold Water

Heat as a tracer in fractured porous aquifers is more sensitive to fracture-matrix processes than a solute tracer. Temperature evolution as a function of time can be used to differentiate fracture and matrix characteristics. Experimental hot (50 °C) and cold (10 °C) water injections were performed in a weathered and fractured granite aquifer where the natural background temperature is 30 °C. The tailing of the hot and cold breakthrough curves, observed under different hydraulic conditions, was characterized in a log–log plot of time vs. normalized temperature difference, also converted to a residence time distribution (normalized). Dimensionless tail slopes close to 1.5 were observed for hot and cold breakthrough curves, compared to solute tracer tests showing slopes between 2 and 3. This stronger thermal diffusive behavior is explained by heat conduction. Using a process-based numerical model, the impact of heat conduction toward and from the porous rock matrix on groundwater heat transport was explored. Fracture aperture was adjusted depending on the actual hydraulic conditions. Water density and viscosity were considered temperature dependent. The model simulated the increase or reduction of the energy level in the fracture-matrix system and satisfactorily reproduced breakthrough curves tail slopes. This study shows the feasibility and utility of cold water tracer tests in hot fractured aquifers to boost and characterize the thermal matrix diffusion from the matrix toward the flowing groundwater in the fractures. This can be used as complementary information to solute tracer tests that are largely influenced by strong advection in the fractures.     

Plume Detachment and Recession Times in Fractured Rock

The influence of source zone concentration reduction on solute plume detachment and recession times in fractured rock was investigated using new semianalytical solutions to transient solute transport in the presence of advection, dispersion, sorption, matrix diffusion, and first-order decay. Novel aspects of these solutions are: (1) the source zone concentration behavior is simulated using a constant concentration with the option for either an instantaneous reduction to zero concentration or an exponentially decaying source zone concentration initiated at some time (t^*) after the source is introduced, and (2) different biodegradation rates in the fracture and rock matrix. These solutions were applied for sandstone bedrock and revealed that biodegradation in the matrix, not the fracture, may be the most significant attenuation mechanism and therefore may dictate remediation time scales. Also, instantaneous and complete source concentration reduction in aged plumes may not be beneficial with respect to plume response because back-diffusion can sustain plume migration for long periods of time. Moderate source zone concentration reduction has a similar impact on the rate of advance of the leading edge of the plume as aggressive concentration reduction. If the source zone concentration reduction half-life is less than the plume decay half-life, then volatile organic compound (VOC) mass sequestered in the rock matrix will ultimately dictate plume persistence and not the presence of the source zone.     

Modeling the effects of nonlinear equilibrium sorption on the transport of solute plumes in saturated heterogeneous porous media

Transport of sorbing solutes in 2D steady and heterogeneous flow fields is modeled using a particle tracking random walk technique. The solute is injected as an instantaneous pulse over a finite area. Cases of linear and Freundlich sorption isotherms are considered. Local pore velocity and mechanical dispersion are used to describe the solute transport mechanisms at the local scale. This paper addresses the impact of the degree of heterogeneity and correlation lengths of the log-hydraulic conductivity field as well as negative correlation between the log-hydraulic conductivity field and the log-sorption affinity field on the behavior of the plume of a sorbing chemical. Behavior of the plume is quantified in terms of longitudinal spatial moments: center-of-mass displacement, variance, 95% range, and skewness. The range appears to be a better measure of the spread in the plumes with Freundlich sorption because of plume asymmetry. It has been found that the range varied linearly with the travelled distance, regardless of the sorption isotherm. This linear relationship is important for extrapolation of results to predict behavior beyond simulated times and distances. It was observed that the flow domain heterogeneity slightly enhanced the spreading of nonlinearly sorbing solutes in comparison to that which occurred for the homogeneous flow domain, whereas the spreading enhancement in the case of linear sorption was much more pronounced. In the case of Freundlich sorption, this enhancement led to further deceleration of the solute plume movement as a result of increased retardation coefficients produced by smaller concentrations. It was also observed that, except for plumes with linear sorption, correlation between the hydraulic conductivity and the sorption affinity fields had minimal effect on the spatial moments of solute plumes with nonlinear sorption.     

Transport of kinetically sorbing solutes in heterogeneous sediments with multimodal conductivity and hierarchical organization across scales

Solute transport in subsurface environments is controlled by geological heterogeneity over multiple scales. In reactive transport characterized by a low Damköhler number, it is also controlled by the rate of kinetic mass transfer. A theory for addressing the impact of sedimentary texture on the transport of kinetically sorbing solutes in heterogeneous porous formations is derived using the Lagrangian-based stochastic methodology. The resulting model represents the hierarchical organization of sedimentary textures and associated modes of log conductivity (K) for sedimentary units through a hierarchical Markov Chain. The model characterizes kinetic sorption using a spatially uniform linear reversible rate expression. Our main interest is to investigate the effect of sorption kinetics relative to the effects of K heterogeneity on the dispersion of a reactive plume. We study the contribution of each scale of stratal architecture to the dispersion of kinetically sorbing solutes in the case of a low Damköhler number. Examples are used to demonstrate the time evolution and relative contributions of the auto- and cross-transition probability terms to dispersion. Our analysis is focused on the model sensitivity to the parameters defined at each hierarchical level (scale) including the integral scales of K spatial correlation, the anisotropy ratio, the indicator correlation scales, and the contrast in mean K between facies defined at different scales. The results show that the anisotropy ratio and integral scales of K have negligible effect upon the longitudinal dispersion of sorbing solutes. Furthermore, dispersion of sorbing solutes depends mostly on indicator correlation scales, and the contrast of the mean conductivity between units at different scales.     

Matrix Diffusion Effects on Contaminant Migration from an Injection Well in Fractured Sandstone

Deep-well injection into fractured sandstone is an option for the disposal of contaminated mine dewatering discharge from an open pit uranium mine. As part of the assessment of potential contaminant migration from deep-well injection, the effect of matrix diffusion was evaluated. An analytical mathematical model was developed for the simulation of the radial movement of a contaminant front away from an injection point under steady flow conditions in a planar fracture with uniform properties. The model includes the effects of advection in the fracture, diffusion of contaminants from the fracture into the rock matrix, and equilibrium adsorption on the fracture surface as well as in the rock matrix. Effective diffusion coefficients obtained from laboratory experiments on 11 intact core samples varied from 3.4 × 10⁻⁸ to 3.2 × 10⁻⁷ cm²/s. Model simulations were made with diffusion coefficient values in this range and with single-fracture injection rates estimated from fracture frequencies in boreholes, and from bulk hydraulic conductivity values obtained from field tests. Because of matrix diffusion, the rate of outward movement of the front of the nonreactive contaminants from the injection well is much slower than the rate of water flow in the fractures. Simulations of the movement of contaminants that undergo adsorption indicate that even a small distribution coefficient for the rock matrix causes the contaminants to remain very close to the injection well during the one-year period. The results of the simplified model demonstrate that matrix diffusion is an important process that cannot be neglected in the assessment of a waste disposal scheme located in fractured porous rock. However, in order to make a definitive assessment of the capability of matrix diffusion and associated matrix adsorption to significantly limit the extent of contaminant migration around injection wells, it would be necessary to conduct field tests such as a preliminary or experimental injection.     

Evaluating the transport and removal of chromate using pyrite and biotite columns

To remove chromate from a wastewater, a porous permeable reactive barrier system (PRBS), using pyrite and biotite, was adapted. This study included bench‐scale column experiments to evaluate the efficiency of the PRBS and investigate the reaction process. The total chromium concentration of the effluent from the biotite and pyrite columns reached the influent concentration of 0·10 mM after passing through more than 150 pore volumes (PVs) and 27 PVs respectively, and remained constant thereafter. The Cr^VI concentration in the effluent from the biotite column became constant at about 0·08 mM , accounting for approximately 80% of the influent concentration, after passing through 200 PVs. Moreover, in the pyrite column, the Cr^VI concentration remained at about 0·01 mM , 10% of the input level, after passing through 116 PVs. This shows that both columns maintained their levels of chromate reduction once the Cr^VI breakthrough curves (BTCs) had reached the steady state, though the steady‐state output concentration of total chromium had reached the influent level. The variances of the iron concentration closely followed those of the chromium. The observed data for both columns were fitted to the predicted BTCs calculated by CXTFIT, a program for estimating the solute transport parameters from experimental data. The degradation coefficient µ of the total chromium BTCs for both columns was zero, suggesting the mechanisms for the removal of chromate limit the µ of the Cr^VI BTCs. The Cr^VI degradation of the pyrite column (6·60) was much greater than that of the biotite column (0·27). In addition, the Cr^VI retardation coefficient R of the pyrite column (253) was also larger than that of the biotite column (125). The R values for the total chromium BTCs from both columns were smaller than those of the Cr^VI BTC. Whereas the total chromium BTC for the pyrite column showed little retardation (1·5), the biotite column showed considerable retardation (80). The results for the 900 °C heat‐treated biotite column were analogous to those of the control column (quartz sand). This suggests that the heat‐treated biotite played no role in the retardation and removal of hexavalent chromium. The parameters of the heat‐treated biotite were calculated to an R of 1·2 and µ of 0·01, and these values confirmed quantitatively that the heated biotite had little effect on the transport of Cr^VI. These solute transport parameters, calculated by CXTFIT from the data obtained from the column tests, can provide quantitative information for the evaluation of bench‐ or field‐scale columns as a removal technology for Cr^VI in wastewater or contaminated groundwater. Copyright © 2006 John Wiley & Sons, Ltd.     

An equivalent medium model for wave simulation in fractured porous rocks

Seismic wave propagation in reservoir rocks is often strongly affected by fractures and micropores. Elastic properties of fractured reservoirs are studied using a fractured porous rock model, in which fractures are considered to be embedded in a homogeneous porous background. The paper presents an equivalent media model for fractured porous rocks. Fractures are described in a stress‐strain relationship in terms of fracture‐induced anisotropy. The equations of poroelasticity are used to describe the background porous matrix and the contents of the fractures are inserted into a matrix. Based on the fractured equivalent‐medium theory and Biot's equations of poroelasticity, two sets of porosity are considered in a constitutive equation. The porous matrix permeability and fracture permeability are analysed by using the continuum media seepage theory in equations of motion. We then design a fractured porous equivalent medium and derive the modified effective constants for low‐frequency elastic constants due to the presence of fractures. The expressions of elastic constants are concise and are directly related to the properties of the main porous matrix, the inserted fractures and the pore fluid. The phase velocity and attenuation of the fractured porous equivalent media are investigated based on this model. Numerical simulations are performed. We show that the fractures and pores strongly influence wave propagation, induce anisotropy and cause poroelastic behaviour in the wavefields. We observe that the presence of fractures gives rise to changes in phase velocity and attenuation, especially for the slow P‐wave in the direction parallel to the fracture plane.