Allen M. Shapiro

Tracer transport in fractured crystalline rock: Evidence of nondiffusive breakthrough tailing

Extended tailing of tracer breakthrough is often observed in pulse injection tracer tests conducted in fractured geologic media. This behavior has been attributed to diffusive exchange of tracer between mobile fluids traveling through channels in fractures and relatively stagnant fluid between fluid channels, along fracture walls, or within the bulk matrix. We present a field example where tracer breakthrough tailing apparently results from nondiffusive transport. Tracer tests were conducted in a fractured crystalline rock using both a convergent and weak dipole injection and pumping scheme. Deuterated water, bromide, and pentafluorobenzoic acid were selected as tracers for their wide range in molecular diffusivity. The late time behavior of the normalized breakthrough curves were consistent for all tracers, even when the pumping rate was changed. The lack of separation between tracers of varying diffusivity indicates that strong breakthrough tailing in fractured geologic media may be caused by advective transport processes. This finding has implications for the interpretation of tracer tests designed to measure matrix diffusion in situ and the prediction of contaminant transport in fractured rock.

A solute flux approach to transport in heterogeneous formations: 1. The general framework

It is common to represent solute tranport in heterogeneous formations in terms of the resident concentration C(x, t), regarded as a random space function. The present study investigates the alternative representation by q, the solute mass flux at a point of a control plane normal to the mean flow. This representation is appropriate for many field applications in which the variable of interest is the mass of solute discharged through a control surface. A general framework to compute the statistical moments of q and of the associated total solute discharge Q and mass M is established. With x the direction of the mean flow, a solute particle is crossing the control plane at y = η, z = ζ and at the travel (arrival) time τ. The associated expected solute flux value is proportional to the joint probability density function (pdf) g1 of η, ζ and τ, whereas the variance of q is shown to depend on the joint pdf g2 of the same variables for two particles. In turn, the statistical moments of η, ζ and τ depend on those of the velocity components through a system of stochastic ordinary differential equations. For a steady velocity field and neglecting the effect of pore-scale dispersion, a major simplification of the problem results in the independence of the random variables η, ζ and τ. As a consequence, the pdf of η and ζ can be derived independently of τ. A few approximate approaches to derive the statistical moments of η, ζ and τ are outlined. These methods will be explored in paper 2 in order to effectively derive the variances of the total solute discharge and mass, while paper 3 will deal with the nonlinear effect of the velocity variance upon the moments of η, ζ and τ

A solute flux approach to transport in heterogeneous formations: 2. Uncertainty analysis

Uncertainty in the mass flux for advection dominated solute movement in heterogeneous porous media is investigated using the Lagrangian framework developed in paper 1 by Dagan et al. (this issue). Expressions for the covariance of the mass flux and cumulative mass flux are derived as functions of the injection volume and sampling area size relative to the scale of heterogeneity. The result is illustrated for solute advection in three types of heterogeneous porous media: stratified formations, two- and three-dimensional porous media; small perturbation approximation is used for the two- and three-dimensional cases. Variances of the mass flux and cumulative mass flux are evaluated as functions of the injection volume (area) scale versus log-hydraulic conductivity integral scale. The greatest decrease in coefficient of variation (CV) of the mass flux is for the source scale 1–5 times the hydraulic conductivity integral scale; further increase in the source size decreases CV comparatively less. The variance of the cumulative mass flux (or total discharge) indicates that for the source size of 20 hydraulic conductivity integral scales, the transport conditions are almost ergodic. The present results also indicate that the cumulative mass flux is a relatively robust quantity for describing field-scale solute transport.

Effective matrix diffusion in kilometer‐scale transport in fractured crystalline rock

Concentrations of tritium (3H) and dichlorodifluoromethane (CFC-12) in water samples taken from glacial drift and fractured crystalline rock over 4 km2 in central New Hampshire are interpreted to identify a conceptual model of matrix diffusion and the magnitude of the diffusion coefficient. Dispersion and mass transfer to and from fractures has affected the 3H concentration to the extent that the peak 3H concentration of the 1960s is no longer distinguishable. Because of heterogeneity in the bedrock the sparsely distributed chemical data do not warrant a three-dimensional transport model. Instead, a one-dimensional model of CFC-12 and 3H migration along flow lines in the glacial drift and bedrock is used to place bounds on the processes affecting kilometer-scale transport, arid model parameters are varied to reproduce the measured relation between 3H and CFC-12, rather than their spatial distributions. A model of mass exchange to and from fractures that is dependent on the time-varying concentration gradient at fracture surfaces qualitatively reproduces the measured relation between 3H and CFC-12 with an upper bound for the fracture dispersivity approximately equal to 250 m and a lower bound for the effective matrix diffusion coefficient equal to 1 m2 yr−1. The diffusion coefficient at the kilometer scale is at least 3 orders of magnitude greater than laboratory estimates of diffusion in crystalline rock. The large diffusion coefficient indicates that diffusion into an immobile fluid phase (rock matrix) is masked at the kilometer scale by advective mass exchange between fractures with large contrasts in trarismissivity. The measured transmissivity of fractures in the study area varies over more than 6 orders of magnitude. Advective mass exchange from high-permeability fractures to low-permeability fractures results in short migration distances of a chemical constituent in low-permeability fractures over an extended period of time before reentering high-permeability fractures; viewed at the kilometer scale, this process is analogous to the chemical constituent diffusing into and out of an immobile fluid phase.

Movement of Road Salt to a Small New Hampshire Lake

Runoff of road salt from an interstate highway in New Hampshire has led to contamination of a lake and a stream that flows into the lake, in spite of the construction of a diversion berm to divert road salt runoff out of the lake drainage basin. Chloride concentration in the stream has increased by over an order of magnitude during the 23 yr since the highway was opened, and chloride concentration in the lake has tripled. Road salt moves to the lake primarily via the contaminated stream, which provides 53% of all the chloride to the lake and only 3% of the total streamflow to the lake. The stream receives discharge of salty water from leakage through the diversion berm. Uncontaminated ground water dilutes the stream downstream of the berm. However, reversals of gradient during summer months, likely caused by transpiration from deciduous trees, result in flow of contaminated stream water into the adjacent ground water along the lowest 40-m reach of the stream. This contaminated ground water then discharges into the lake along a 70-m-wide segment of lake shore. Road salt is pervasive in the bedrock between the highway and the lake, but was not detected at all of the wells in the glacial overburden. Of the 500 m of shoreline that could receive discharge of saly ground water directly from the highway, only a 50-m-long segment appears to be contaminated.

Assessing the vulnerability of a municipal well field to contamination in a karst aquifer

Proposed expansion of extractive lime-rock mines near the Miami–Dade County Northwest well field and Everglades wetland areas has garnered intense scrutiny by government, public, environmental stakeholders, and the media because of concern that mining will increase the risk of pathogen contamination. Rock mines are excavated to the same depth as the well fields primary producing zone. The underlying karst Biscayne aquifer is a triple-porosity system characterized by (1) a matrix of interparticle porosity and separate vug porosity; (2) touching-vug porosity that forms preferred, stratiform passageways; and, less commonly, (3) conduit porosity formed by thin solution pipes, bedding-plane vugs, and cavernous vugs. Existing ground-water flow and particle tracking models do not provide adequate information regarding the ability of the aquifer to limit the advective movement of pathogens and other contaminants. Chemical transport and colloidal mobility properties have been delineated using conservative and microsphere-surrogate tracers for Cryptosporidium parvum . Forced-gradient tests were executed by introducing conservative tracers into injection wells located 100 m (328 ft) from a municipal-supply well. Apparent mean advective velocity between the wells is one to two orders of magnitude greater than previously measured. Touching-vug, stratiform flow zones are efficient pathways for tracer movement at the well field. The effective porosity for a continuum model between the point of injection and tracer recovery ranges from 2 to 4 percent and is an order of magnitude smaller than previously assumed. Existing well-field protection zones were established using porosity estimates based on specific yield. The effective, or kinematic, porosity of a Biscayne aquifer continuum model is lower than the total porosity, because high velocities occur along preferential flow paths that result in faster times of travel than can be represented with the ground-water flow equation. Tracer tests indicate that the relative ease of contaminant movement to municipal supply wells is much greater than previously considered.

Pathogen and chemical transport in the karst limestone of the Biscayne aquifer: 1. Revised conceptualization of groundwater flow

[1] The Biscayne aquifer is a highly transmissive karst limestone that serves as the sole source of drinking water to over two million residents in south Florida. The aquifer is characterized by eogenetic karst, where the most transmissive void space can be an interconnected, touching-vug, biogenically influenced porosity of biogenic origin. Public supply wells in the aquifer are in close proximity to lakes established by surface mining. The mining of the limestone has occurred to the same depths as the production wells, which has raised concerns about pathogen and chemical transport from these surface water bodies. Hydraulic and forced gradient tracer tests were conducted to augment geologic and geophysical studies and to develop a hydrogeologic conceptual model of groundwater flow and chemical transport in the Biscayne aquifer. Geologic and geophysical data indicate multiple, areally extensive subhorizontal preferential flow zones of vuggy limestone separated by rock with a matrix pore system. The hydraulic response from an aquifer test suggests that the Biscayne aquifer behaves as a dual-porosity medium; however, the results of the tracer test showed rapid transport similar to other types of karst. The tracer test and concurrent temperature logging revealed that only one of the touching-vug flow zones dominates transport near the production wells. On the basis of the rising limb of the breakthrough curve, the dispersivity is estimated to be less than 3% of the tracer travel distance, which suggests that the fastest flow paths in the formation are likely to yield limited dilution of chemical constituents.

Crosswell seismic investigation of hydraulically conductive, fractured bedrock near Mirror Lake, New Hampshire

Abstract Near Mirror Lake, New Hampshire (USA), hydraulically conductive, fractured bedrock was investigated with the crosswell seismic method to determine whether this method could provide any information about hydraulic conductivity between wells. To this end, crosswell seismic data, acoustic logs from boreholes, image logs from boreholes, and single borehole hydraulic tests were analyzed. The analysis showed that, first, the P-wave velocities from the acoustic logs tended to be higher in schist than they were in granite. (Schist and granite were the dominant rock types). Second, the P-wave velocities from the acoustic logs tended to be low near fractures. Third, the hydraulic conductivity was always low (always less than to 10−8 m/s) where no fractures intersected the borehole, but the hydraulic conductivity ranged from low to high (from less than to 10−10 m/s to 10−4 m/s) where one or more fractures intersected the borehole. Fourth, high hydraulic conductivities were slightly more frequent when the P-wave velocity was low (less than 5200 m/s) than when it was high (greater than or equal to 5200 m/s). The interpretation of this statistical relation was that the fractures tended to increase the hydraulic conductivity and to lower the P-wave velocity. This statistical relation was applied to a velocity tomogram to create a map showing the probability of high hydraulic conductivity; the map was consistent with results from independent hydraulic tests.

Transport Equations for Fractured Porous Media

With the advent of analyzing geological settings as possible sites for hazardous waste isolation, the modeling of transport phenomena in fractured rock has been a topic of increasing interest. In studies to date, the means by which transport phenomena in fractured rock have been mathematically visualized has taken two distinct routes. The need for different conceptualizations of fractured rock has arisen due to the diverse nature of fracturing in rock formations. Usually, the length scale of a given transport problem, in relation to the intensity of fracturing, varies from one rock formation to the next. In some instances, there may exist only a few significant fractures (of a given fracture family) over the length scale of the transport problem. In other situations, the length scale of the transport problem may encompass large numbers of interconnected fractures. These observations have led to conceptualizations of fractured rock as either a system of individual and possibly interconnected fractures in a permeable or impermeable host rock, or as one or more overlapping fluid continua, in a manner similar to the mathematical treatment of granular porous materials. The assumptions implicit in the use of each of these conceptualizations are discussed in this chapter along with a selective review of the recent literature. A detailed analysis of the discrete fracture and continuum conceptualizations of fractured rock is provided by developing the appropriate equations of mass, momentum and energy transport for each conceptualization.

Integration of stable carbon isotope, microbial community, dissolved hydrogen gas, and 2HH2O tracer data to assess bioaugmentation for chlorinated ethene degradation in fractured rocks

An in situ bioaugmentation (BA) experiment was conducted to understand processes controlling microbial dechlorination of trichloroethene (TCE) in groundwater at the Naval Air Warfare Center (NAWC), West Trenton, NJ. In the BA experiment, an electron donor (emulsified vegetable oil and sodium lactate) and a chloro-respiring microbial consortium were injected into a well in fractured mudstone of Triassic age. Water enriched in ²H was also injected as a tracer of the BA solution, to monitor advective transport processes. The changes in concentration and the δ¹³C of TCE, cis-dichloroethene (cis-DCE), and vinyl chloride (VC); the δ²H of water; changes in the abundance of the microbial communities; and the concentration of dissolved H₂ gas compared to pre- test conditions, provided multiple lines of evidence that enhanced biodegradation occurred in the injection well and in two downgradient wells. For those wells where the biodegradation was stimulated intensively, the sum of the molar chlorinated ethene (CE) concentrations in post-BA water was higher than that of the sum of the pre-BA background molar CE concentrations. The concentration ratios of TCE/(cis-DCE+VC) indicated that the increase in molar CE concentration may result from additional TCE mobilized from the rock matrix in response to the oil injection or due to desorption/diffusion. The stable carbon isotope mass-balance calculations show that the weighted average ¹³C isotope of the CEs was enriched for around a year compared to the background value in a two year monitoring period, an effective indication that dechlorination of VC was occurring. Insights gained from this study can be applied to efforts to use BA in other fractured rock systems. The study demonstrates that a BA approach can substantially enhance in situ bioremediation not only in fractures connected to the injection well, but also in the rock matrix around the well due to processes such as diffusion and desorption. Because the effect of the BA was intensive only in wells where an amendment was distributed during injection, it is necessary to adequately distribute the amendments throughout the fractured rock to achieve substantial bioremediation. The slowdown in BA effect after a year is due to some extend to the decrease abundant of appropriate microbes, but more likely the decreased concentration of electron donor.