Electric-hydraulic conductivity correlation in fractured crystalline bedrock: Central Landfill, Rhode Island, USA

Remote sensing and geoelectrical methods were used to find water-bearing fractures in the Scituate granite under the Central Landfill of Rhode Island. These studies were necessary to evaluate the integrity of the sanitary landfill and for planning safe landfill extensions. The most useful results were obtained with fracture trace analysis using Landsat and SLAR imagery in combination with ground-based resistivity measurements using Schlumberger vertical electrical soundings based on the assumption of horizontally layered strata. Test borings and packer tests confirmed, in the presence of a lineament and low bedrock resistivity, the probable existence of high bedrock fracture density and high average hydraulic conductivity. However, not every lineament was found to be associated with high fracture density and high hydraulic conductivity. Lineaments alone are not a reliable basis for characterising a landfill site as being affected by fractured bedrock. Horizontal fractures were found in borings located away from lineaments. High values of hydraulic conductivity were correlated with low bedrock resistivities. Bedrock resistivities between 60 and 700 Ω m were associated with average hydraulic conductivities between 4 and 60 cm/day. In some cases very low resistivities were confined to the upper part of the bedrock where the hydraulic conductivity was very large. These types of fractures apparently become narrower in aperture with depth. Bedrock zones having resistivities greater than 1000 Ω m showed, without exception, no flow to the test wells. Plots of bedrock resistivity versus the average hydraulic conductivity indicate that the resistivity decreases with increasing hydraulic conductivity. This relationship is inverse to that found in most unconsolidated sediments and is useful for estimating the hydraulic conductivity in groundwater surveys in fractured bedrock. In appropriate settings such as the Central Landfill site in New England, this electric-hydraulic correlation relationship, supplemented by lineament trace analysis, can be used effectively to estimate the hydraulic conductivity in bedrock from only a limited number of resistivity depth soundings and test wells.     

Imaging Pathways in Fractured Rock Using Three‐Dimensional Electrical Resistivity Tomography

Major challenges exist in delineating bedrock fracture zones because these cause abrupt changes in geological and hydrogeological properties over small distances. Borehole observations cannot sufficiently capture heterogeneity in these systems. Geophysical techniques offer the potential to image properties and processes in between boreholes. We used three‐dimensional cross borehole electrical resistivity tomography (ERT) in a 9 m (diameter) × 15 m well field to capture high‐resolution flow and transport processes in a fractured mudstone contaminated by chlorinated solvents, primarily trichloroethylene. Conductive (sodium bromide) and resistive (deionized water) injections were monitored in seven boreholes. Electrode arrays with isolation packers and fluid sampling ports were designed to enable acquisition of ERT measurements during pulsed tracer injections. Fracture zone locations and hydraulic pathways inferred from hydraulic head drawdown data were compared with electrical conductivity distributions from ERT measurements. Static ERT imaging has limited resolution to decipher individual fractures; however, these images showed alternating conductive and resistive zones, consistent with alternating laminated and massive mudstone units at the site. Tracer evolution and migration was clearly revealed in time‐lapse ERT images and supported by in situ borehole vertical apparent conductivity profiles collected during the pulsed tracer test. While water samples provided important local information at the extraction borehole, ERT delineated tracer migration over spatial scales capturing the primary hydrogeological heterogeneity controlling flow and transport. The fate of these tracer injections at this scale could not have been quantified using borehole logging and/or borehole sampling methods alone.     

Using Domestic Well Records to Determine Fractured Bedrock Watersheds and Recharge Rates

This study presents an approach for delineating groundwater basins and estimating rates of recharge to fractured crystalline bedrock. It entailed the use of completion report data (boring logs) from 2500 domestic wells in bedrock from the Coventry Quadrangle, which is located in northeastern Connecticut and characterized by metamorphic gneiss and schist. Completion report data were digitized and imported into ArcGIS^® for data analysis. The data were processed to delineate groundwater drainage basins for the fractured rock based on flow conditions and to estimate groundwater recharge to the bedrock. Results indicate that drainage basins derived from surface topography, in general, may not correspond with bedrock drainage basins due to scale. Estimates of recharge to the bedrock for the study area indicate that only a small fraction of the precipitation or the amount of water that enters the overburden recharges the rock. The approach presented here can be a useful method for water resource‐related assessments that involve fractured rock aquifers.     

Analytical and Numerical Modeling of Solute Intrusion,Recovery, and Rebound in Fractured Bedrock

Contaminated groundwater in fractured bedrock can expose ecosystems to undesired levels of risk for extended periods due to prolonged back-diffusion from rock matrix to permeable fractures. Therefore, it is key to characterize the diffusive mass loading (intrusion) of contaminants into the rock matrix for successful management of contaminated bedrock sites. Even the most detailed site characterization techniques often fail to delineate contamination in rock matrix. This study presents a set of analytical solutions to estimate diffusive mass intrusion into matrix blocks, it is recovered by pumping and concentration rebound when pumping ceases. The analytical models were validated by comparing the results with (1) numerical model results using the same model parameters and (2) observed chloride mass recovery, rebound concentration, and concentration in pumped groundwater at a highly fractured bedrock site in Alberta, Canada. It is also demonstrated that the analytical solutions can be used to estimate the total mass stored in the fractured bedrock prior to any remediation thereby providing insights into site contamination history. The predictive results of the analytical models clearly show that successful remediation by pumping depends largely on diffusive intrusion period. The results of initial mass from the analytical model was used to successfully calibrate a three-dimensional discrete fracture network numerical model further highlighting the utility of the simple analytical solutions in supplementing the more detailed site numerical modeling. Overall, the study shows the utility of simple analytical methods to support long-term management of a contaminated fractured bedrock site including site investigations and complex numerical modeling.     

Hydraulic Tomography: 3D Hydraulic Conductivity,Fracture Network,and Connectivity in Mudstone

We present the first demonstration of hydraulic tomography (HT) to estimate the three-dimensional (3D) hydraulic conductivity (K) distribution of a fractured aquifer at high-resolution field scale (HRFS), including the fracture network and connectivity through it. We invert drawdown data collected from packer-isolated borehole intervals during 42 pumping tests in a wellfield at the former Naval Air Warfare Center, West Trenton, New Jersey, in the Newark Basin. Five additional tests were reserved for a quality check of HT results. We used an equivalent porous medium forward model and geostatistical inversion to estimate 3D K at high resolution (K blocks <1 m³), using no strict assumptions about K variability or fracture statistics. The resulting 3D K estimate ranges from approximately 0.1 (highest-K fractures) to approximately 10⁻¹³ m/s (unfractured mudstone). Important estimated features include: (1) a highly fractured zone (HFZ) consisting of a sequence of high-K bedding-plane fractures; (2) a low-K zone that disrupts the HFZ; (3) several secondary fractures of limited extent; and (4) regions of very low-K rock matrix. The 3D K estimate explains complex drawdown behavior observed in the field. Drawdown tracing and particle tracking simulations reveal a 3D fracture network within the estimated K distribution, and connectivity routes through the network. Model fit is best in the shallower part of the wellfield, with high density of observations and tests. The capabilities of HT demonstrated for 3D fractured aquifer characterization at HRFS may support improved in situ remediation for contaminant source zones, and applications in mining, repository assessment, or geotechnical engineering.     

Bioremediation in Fractured Rock: 1. Modeling to Inform Design,Monitoring, and Expectations

Field characterization of a trichloroethene (TCE) source area in fractured mudstones produced a detailed understanding of the geology, contaminant distribution in fractures and the rock matrix, and hydraulic and transport properties. Groundwater flow and chemical transport modeling that synthesized the field characterization information proved critical for designing bioremediation of the source area. The planned bioremediation involved injecting emulsified vegetable oil and bacteria to enhance the naturally occurring biodegradation of TCE. The flow and transport modeling showed that injection will spread amendments widely over a zone of lower‐permeability fractures, with long residence times expected because of small velocities after injection and sorption of emulsified vegetable oil onto solids. Amendments transported out of this zone will be diluted by groundwater flux from other areas, limiting bioremediation effectiveness downgradient. At nearby pumping wells, further dilution is expected to make bioremediation effects undetectable in the pumped water. The results emphasize that in fracture‐dominated flow regimes, the extent of injected amendments cannot be conceptualized using simple homogeneous models of groundwater flow commonly adopted to design injections in unconsolidated porous media (e.g., radial diverging or dipole flow regimes). Instead, it is important to synthesize site characterization information using a groundwater flow model that includes discrete features representing high‐ and low‐permeability fractures. This type of model accounts for the highly heterogeneous hydraulic conductivity and groundwater fluxes in fractured‐rock aquifers, and facilitates designing injection strategies that target specific volumes of the aquifer and maximize the distribution of amendments over these volumes.     

Predicting horizontal velocities from well data

The Imperial College borehole test site consists of four boreholes with depths lying between 260 and 280 m. The boreholes intersect several cyclical sequences of sandstones, mudstones and limestones. The formations are highly laminated and ultrasonic measurements on preserved core have shown that the mudstones are intrinsically anisotropic. Little or no anisotropy is associated with the sandstones and limestones. A scheme is proposed to predict synthetic vertical and horizontal P- and S-wave logs. Combining (an)isotropic effective medium theories, the Gassmann equation and Backus averaging, the scheme extends previous sand-shale models to transversely isotropic rock formations. The model assumes that the anisotropy is due to layering and due to the preferred horizontal orientation of the clay minerals, pores and cracks within the mudstones. The pores and cracks within the sandstones and limestones are randomly orientated. After fitting the model to the ultrasonic data to obtain the unknown parameters, the model successfully predicts the sonic log and the direct arrival times from a cross-hole survey.     

Multiple Well-Shutdown Tests and Site-Scale Flow Simulation in Fractured Rocks

A new method was developed for conducting aquifer tests in fractured-rock flow systems that have a pump-and-treat (P&T) operation for containing and removing groundwater contaminants. The method involves temporary shutdown of individual pumps in wells of the P&T system. Conducting aquifer tests in this manner has several advantages, including (1) no additional contaminated water is withdrawn, and (2) hydraulic containment of contaminants remains largely intact because pumping continues at most wells. The well-shutdown test method was applied at the former Naval Air Warfare Center (NAWC), West Trenton, New Jersey, where a P&T operation is designed to contain and remove trichloroethene and its daughter products in the dipping fractured sedimentary rocks underlying the site. The detailed site-scale subsurface geologic stratigraphy, a three-dimensional MODFLOW model, and inverse methods in UCODE_2005 were used to analyze the shutdown tests. In the model, a deterministic method was used for representing the highly heterogeneous hydraulic conductivity distribution and simulations were conducted using an equivalent porous media method. This approach was very successful for simulating the shutdown tests, contrary to a common perception that flow in fractured rocks must be simulated using a stochastic or discrete fracture representation of heterogeneity. Use of inverse methods to simultaneously calibrate the model to the multiple shutdown tests was integral to the effectiveness of the approach.     

Hydraulic borehole characterization through the application of moment methods to fluid conductivity logs

In any type of groundwater transport problem (contaminant solutes, heat, etc.), knowledge of the location and properties of pathways of increased hydraulic conductivity is essential. However, answering such questions in strongly heterogeneous media, such as fractured rock, can be very difficult and budget-intensive with standard geophysical or hydrogeological field investigations. We present a new testing concept and analysis procedure based on a time sequence of wellbore electric conductivity logs, which provides the exact location and the outflow parameters (transmissivity, formation fluid conductivity) of flowing features (fractures, faults, layers) intercepted by the borehole.Previously the quantitative analysis of this time sequence of electrical conductivity logs was based on a code, called BORE, used to simulate borehole fluid conductivity profiles given these parameters. The present report describes a new direct (not iterative) method for analyzing a short time series of electric conductivity logs which is based on moment quantities of the individual outflow peaks, and applies it to synthetic as well as to field data. The results of the method are promising and are discussed in terms of the method's advantages and limitations. In particular it is shown that the method is capable of reproducing hydraulic properties derived from packer tests well within a factor of three, which is below the range of what is recognized as the accuracy of packer tests themselves. Furthermore the new method is much quicker than the previously used iterative fitting procedure and is even capable of handling transient fracture outflow conditions.     

Transmissivity variations in mudstones

Many people in sub-Saharan Africa have to rely on meager water resources within mudstones for their only water supply. Although mudstones have been extensively researched for their low permeability behavior, little research has been undertaken to examine their ability to provide sustainable water supplies. To investigate the factors controlling the occurrence of usable ground water in mudstone environments, an area of Cretaceous mudstones in southeastern Nigeria was studied over a 3 yr period. Transmissivity (T) variations in a range of mudstone environments were studied. The investigations demonstrate that within the top 40 m of mudstones, transmissivity can be sufficient to develop village water supplies (T > 1 m2/d). Transmissivity is controlled by two factors: low-grade metamorphism and the presence of other, subordinate, lithologies within the mudstones. Largely unaltered mudstones (early diagenetic zone), comprising mainly smectite clays, are mostly unfractured and have a low T of < 0.1 m2/d. Mudstones that have undergone limited metamorphism (late diagenetic zone) comprise mixed layered illite/smectite clays, and ground water is found in widely spaced fracture zones (T > 1 m2/d in large fracture zones; T < 0.1 m2/d away from fracture zones). Mudstones that have been further altered and approach the anchizone comprise illite clays, are pervasively fractured, and have the highest transmissivity values (T > 4 m2/d). Dolerite intrusions in unaltered, smectitic mudstones are highly fractured with transmissivity in the range of 1 < T < 60 m2/d. Thin limestone and sandstone layers can also enhance transmissivity sufficiently to provide community water supplies.     

Delineating a recharge area for a spring using numerical modeling, Monte Carlo techniques, and geochemical investigation

Recharge areas of spring systems can be hard to identify, but they can be critically important for protection of a spring resource. A recharge area for a spring complex in southern Wisconsin was delineated using a variety of complementary techniques. A telescopic mesh refinement (TMR) model was constructed from an existing regional-scale ground water flow model. This TMR model was formally optimized using parameter estimation techniques; the optimized "best fit" to measured heads and fluxes was obtained by using a horizontal hydraulic conductivity 200% larger than the original regional model for the upper bedrock aquifer and 80% smaller for the lower bedrock aquifer. The uncertainty in hydraulic conductivity was formally considered using a stochastic Monte Carlo approach. Two-hundred model runs used uniformly distributed, randomly sampled, horizontal hydraulic conductivity values within the range given by the TMR optimized values and the previously constructed regional model. A probability distribution of particles captured by the spring, or a "probabilistic capture zone," was calculated from the realistic Monte Carlo results (136 runs of 200). In addition to portions of the local surface watershed, the capture zone encompassed areas outside of the watershed--demonstrating that the ground watershed and surface watershed do not coincide. Analysis of water collected from the site identified relatively large contrasts in chemistry, even for springs within 15 m of one another. The differences showed a distinct gradation from Ordovician-carbonate-dominated water in western spring vents to Cambrian-sandstone-influenced water in eastern spring vents. The difference in chemistry was attributed to distinctive bedrock geology as demonstrated by overlaying the capture zone derived from numerical modeling over a bedrock geology map for the area. This finding gives additional confidence to the capture zone calculated by modeling.     

Fracture control of ground water flow and water chemistry in a rock aquitard

There are few studies on the hydrogeology of sedimentary rock aquitards although they are important controls in regional ground water flow systems. We formulate and test a three-dimensional (3D) conceptual model of ground water flow and hydrochemistry in a fractured sedimentary rock aquitard to show that flow dynamics within the aquitard are more complex than previously believed. Similar conceptual models, based on regional observations and recently emerging principles of mechanical stratigraphy in heterogeneous sedimentary rocks, have previously been applied only to aquifers, but we show that they are potentially applicable to aquitards. The major elements of this conceptual model, which is based on detailed information from two sites in the Maquoketa Formation in southeastern Wisconsin, include orders of magnitude contrast between hydraulic diffusivity (K/S(s)) of fractured zones and relatively intact aquitard rock matrix, laterally extensive bedding-plane fracture zones extending over distances of over 10 km, very low vertical hydraulic conductivity of thick shale-rich intervals of the aquitard, and a vertical hydraulic head profile controlled by a lateral boundary at the aquitard subcrop, where numerous surface water bodies dominate the shallow aquifer system. Results from a 3D numerical flow model based on this conceptual model are consistent with field observations, which did not fit the typical conceptual model of strictly vertical flow through an aquitard. The 3D flow through an aquitard has implications for predicting ground water flow and for planning and protecting water supplies.     

Understanding of hydraulic properties from configurations of stochastically distributed fracture networks

A systematic investigation of the effect of configurations of stochastically distributed fracture networks on hydraulic behaviour for fractured rock masses could provide either quantitative or qualitative correlation between the structural configuration of the fracture network and its corresponding hydraulic behaviour, and enhance our understanding of appropriate application of groundwater flow and contaminant transport modelling in fractured rock masses. In this study, the effect of block sizes, intersection angles of fracture sets, standard deviations of fracture orientation, and fracture densities on directional block hydraulic conductivity and representative elementary volume is systematically investigated in two dimensions by implementing a numerical discrete fracture fluid flow model and incorporating stochastically distributed fracture configurations. It is shown from this investigation that the configuration of a stochastically distributed fracture network has a significant quantitative or qualitative effect on the hydraulic behaviour of fractured rock masses. Compared with the deterministic fracture configurations that have been extensively dealt with in a previous study, this investigation is expected to be more practical and adequate, since fracture geometry parameters are inherently stochastically distributed in the field. Moreover, the methodology and approach presented in this study may be generally applied to any fracture system in investigating the hydraulic behaviours from configurations of the fracture system while establishing a ‘bridge’ from the discrete fracture network flow modelling to equivalent continuum modelling in fractured rock masses. Copyright © 2007 John Wiley & Sons, Ltd.     

The Xiamaling oil shale generated through Rhodophyta over 800 Ma ago

A suit of oil shales, predominated by black argillaceous silicalite and finely laminated black-brown shale, has been discovered in a set of carbonaceous-siliceous mudstone formations (350 m in thickness) in the third member of Xiamaling Formation of the Upper Proterozoic Qingbaikou Series (900―873 MaBP), Xiahuayuan, Hebei Province, China. The oil shale, combustible with strong bitumen odour, has su- per-high TOC contents ranging from 21.4% to 22.9%, bitumen “A” contents from 0.58% to 0.88% and oil length from 5.29% to 10.57%. The ultrathin section observation of the shale and the identification of its kerogen demonstrate that its hydrocarbon-generative parent material is mainly benthonic Rhodophyta whose specific tetrasporangia are legible and abundant. It is rarely reported in the literature that such a hydrocarbon-generative parent material, composed mainly of Rhodophyta and with extraordinarily high contents of TOC and bitumen “A”, developed into a set of high-quality source rocks. The extracts of the oil shale are characteristic of richness in 17α(H)-diahopanes and n-alkyl tricyclic terpenoids but low in steranes. Such a biomarker feature is obviously different from that of the extracts from other Proterozoic marine carbonate source rocks of the studied area. Since the biological constitution of this oil shale is rather simple, it is clear that these biomarkers most likely represent to certain extent the specific mo- lecular constitutions of the benthonic Rhodophyta identified in the ultrathin sections of the samples. Studies on its lithologic association and depositional sequences suggest that this suit of the carbona- ceous-siliceous mudstone formation, which contains oil shales, was probably developed in an under- compensation deep-bay environment when a maximum transgression occurred during the formation of the third member of Xiamaling Formation. The high concentration of SiO2 in this organic-rich rock and the positive correlation between TOC and some trace elements such as P, Cu, Ni, W and Mo indicate that this suit of rocks was affected by activities of bottom thermal currents as deposited.     

Hydraulic Conductivity Calibration of Logging NMR in a Granite Aquifer,Laramie Range,Wyoming

In granite aquifers, fractures can provide both storage volume and conduits for groundwater. Characterization of fracture hydraulic conductivity (K) in such aquifers is important for predicting flow rate and calibrating models. Nuclear magnetic resonance (NMR) well logging is a method to quickly obtain near-borehole hydraulic conductivity (i.e., K_NMR) at high-vertical resolution. On the other hand, FLUTe flexible liner technology can produce a K profile at comparable resolution but requires a fluid driving force between borehole and formation. For three boreholes completed in a fractured granite, we jointly interpreted logging NMR data and FLUTe K estimates to calibrate an empirical equation for translating borehole NMR data to K estimates. For over 90% of the depth intervals investigated from these boreholes, the estimated K_NMR are within one order of magnitude of K_FLUTe. The empirical parameters obtained from calibrating the NMR data suggest that “intermediate diffusion” and/or “slow diffusion” during the NMR relaxation time may occur in the flowing fractures when hydraulic aperture are sufficiently large. For each borehole, “intermediate diffusion” dominates the relaxation time, therefore assuming “fast diffusion” in the interpretation of NMR data from fractured rock may lead to inaccurate K_NMR estimates. We also compare calibrations using inexpensive slug tests that suggest reliable K_NMR estimates for fractured rock may be achieved using limited calibration against borehole hydraulic measurements.     

Site characterization in densely fractured dolomite: comparison of methods

One of the challenges in characterizing fractured-rock aquifers is determining whether the equivalent porous medium approximation is valid at the problem scale. Detailed hydrogeologic characterization completed at a small study site in a densely fractured dolomite has yielded an extensive data set that was used to evaluate the utility of the continuum and discrete-fracture approaches to aquifer characterization. There are two near-vertical sets of fractures at the site; near-horizontal bedding-plane partings constitute a third fracture set. Eighteen boreholes, including five coreholes, were drilled to a depth of approximately 10.6 m. Borehole geophysical logs revealed several laterally extensive horizontal fractures and dissolution zones. Flowmeter and short-interval packer testing identified which of these features were hydraulically important. A monitoring system, consisting of short-interval piezometers and multilevel samplers, was designed to monitor four horizontal fractures and two dissolution zones. The resulting network consisted of >70 sampling points and allowed detailed monitoring of head distributions in three dimensions. Comparison of distributions of hydraulic head and hydraulic conductivity determined by these two approaches suggests that even in a densely fractured-carbonate aquifer, a characterization approach using traditional long-interval monitoring wells is inadequate to characterize ground water movement for the purposes of regulatory monitoring or site remediation. In addition, traditional multiwell pumping tests yield an average or bulk hydraulic conductivity that is not adequate for predicting rapid ground water travel times through the fracture network, and the pumping test response does not appear to be an adequate tool for assessing whether the porous medium approximation is valid.     

Modeling unsaturated flow in a layered formation under quasi-steady state conditions using geophysical data constraints

The identification of vadose zone flow parameters and solute travel time from the surface to the water table are key issues for the assessment of groundwater vulnerability. In this paper we use the results of time-lapse monitoring of the vadose zone in a UK consolidated sandstone aquifer using cross-hole zero-offset radar to assess and calibrate models of water flow in the vadose zone. The site under investigation is characterized by a layered structure, with permeable medium sandstone intercalated by finer, less permeable, laminated sandstone. Information on this structure is available from borehole geophysical (gamma-ray) logs. Monthly cross-hole radar monitoring was performed from August 1999 to February 2001, and shows small changes of moisture content over time and fairly large spatial variability with depth. One-dimensional Richards’ equation modeling of the infiltration process was performed under spatially heterogeneous, steady state conditions. Both layer structure and Richards’ equation parameters were simulated using a nested Monte Carlo approach, constrained via geostatistical analysis on the gamma-ray logs and on a priori information regarding the possible range of hydraulic parameters. The results of the Monte Carlo analysis show that, in order to match the radar-derived moisture content profiles, it is necessary to take into account the vertical scale of measurements, with an averaging window size of the order of the antenna length and the Fresnel zone width. Flow parameters cannot be uniquely identified, showing that the system is over parameterized with respect to the information content of the (nearly stationary) radar profiles. Estimates of travel time of water across the vadose zone are derived from the simulation results.     

浙江温州北部地区白垩系地层划分与对比

本文根据温州北部地区的火山一沉积岩地层的剖面,进行了岩石地层、生物地层、年代地层的综合研究和区域对比,针对以往1：25万、1：20万和1：5万区域地质调查的划分和归属提出了新的看法。浙东南下白垩统火山一沉积岩分为上、下两个岩系,下岩系称磨石山群,上岩系称永康群。研究认为,温州北部地区的火山-沉积岩系主体为下白垩统下岩系的磨石山群,并非均为上岩系的永康群馆头组;在永嘉枫林、澄田一带的火山-沉积岩地层分别属于磨石山群大爽组和茶湾组,而桥下一带的沉积岩地层则属于永康群馆头组。     

A constitutive model for water flow in unsaturated fractured rocks

A conceptual model for describing effective saturation in fractured hard rock is presented. The fracture network and the rock matrix are considered as an equivalent continuum medium where each fracture is conceptualized as a porous medium of granular structure and the rock matrix is assumed to be impermeable. The proposed model is based on the representation of a rough‐walled fracture by an equivalent porous medium, which is described using classical constitutive models. A simple closed‐form equation for the effective saturation is obtained when the van Genuchten model is used to describe saturation inside fractures and fractal laws are assumed for both aperture and number of fractures. The relative hydraulic conductivity for the fractured rock is predicted from a simple relation derived by Liu and Bodvarsson. The proposed constitutive model contains three independent parameters, which may be obtained by fitting the proposed effective saturation curve to experimental data. Two of the model parameters have physical meaning and can be identified with the reciprocal of the air entry pressure values in the fractures of minimum and maximum apertures. Effective saturation and relative hydraulic conductivity curves match fairly well the simulated constitutive relations obtained by Liu and Bodvarsson. Copyright © 2008 John Wiley & Sons, Ltd.     

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.