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Geology topics

Allen M. Shapiro

Publications and source records attributed to Allen M. Shapiro.

At least 37 records · Page 2Linked to original sources

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.

Water Resources Research

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) g 1 of η, ζ and τ, whereas the variance of q is shown to depend on the joint pdf g 2 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

Water Resources Research

Stochastic analysis of solute arrival time in heterogeneous porous media

Longitudinal advective solute movement in heterogeneous porous media is investigated by considering the solute arrival time at a plane perpendicular to the mean fluid velocity. The moments of the solute arrival time are defined in terms of the stochastic properties of a statistically anisotropic hydraulic conductivity field. The flux‐averaged concentration is specified by introducing the moments of the arrival time into a probability density function for the arrival time. The quadratic dependence of the arrival time variance on position in the vicinity of an injection point is indicative of a nondiffusive process. For the assumed spatial correlation of the hydraulic conductivity, the variance of the arrival time asymptotically approaches a linear dependence on the position from the injection point similar to a diffusion process. The impact of assuming solute movement to be a diffusive process from the onset of the solute injection causes erroneous estimates of flux‐averaged concentrations at distances from the injection point that are of the order of the correlation length of the hydraulic conductivity. The arrival time analysis and the particle position analysis given in Dagan (1982, 1984) are complementary interpretations of advective solute movement that yield different definitions of the solute concentration; the position analysis intrinsically defines the resident or volume‐averaged concentration, while the flux‐averaged concentration is defined from the arrival time analysis. The temporal variation of the resident and flux‐averaged concentration are similar at a given position for small values of the variance of the hydraulic conductivity, or at distances from the solute injection point that are large relative to correlation length of the hydraulic conductivity.

Water Resources Research

Solute advection in stratified formations

Advection‐dominated solute movement in stratified formations is investigated using a Lagrangian interpretation of particle motion. A probability density function (pdf) for particle position quantifies the expected depth‐integrated resident concentration. A pdf for particle arrival time quantifies the expected depth‐integrated rate of mass arrival, from which the flux‐averaged concentration can be defined. The difference between the flux‐averaged and resident concentrations is shown to be significant for the variability in the hydraulic conductivity that is commonly encountered in field applications. The influence of porosity variations on the advection‐dominated solute movement in stratified porous media is shown to be notable only for large variability in the effective porosity.

Water Resources Research

Pathogen and chemical transport in the karst limestone of the Biscayne aquifer: 3. Use of microspheres to estimate the transport potential of Cryptosporidium parvum oocysts

The vulnerability of a municipal well in the Northwest well field in southeastern Florida to potential contamination by Cryptosporidium parvum oocysts was assessed in a large‐scale, forced‐gradient (convergent) injection and recovery test. The field study involved a simultaneous pulse introduction of a nonreactive tracer (SF 6 , an inert gas) and oocyst‐sized (1.6, 2.9, and 4.9 μ m diameter) carboxylated polystyrene microspheres into karst limestone of the Biscayne aquifer characterized by a complex triple (matrix, touching‐vug, and conduit) porosity. Fractional recoveries 97 m down gradient were inversely related to diameter and ranged from 2.9% for the 4.9 μ m microspheres to 5.8% for 1.6 μ m microspheres. Their centers of mass arrived at the pumping well approximately threefold earlier than that of the nonreactive tracer SF 6 (gas), underscoring the need for use of colloid tracers and field‐scale tracer tests for these kinds of evaluations. In a modified triaxial cell using near in situ chemical conditions, 2.9 and 4.9 μ m microspheres underestimated by fourfold to sixfold the attachment potential of the less electronegative 2.9–4.1 μ m oocysts in the matrix porosity of limestone core samples. The field and laboratory results collectively suggested that it may take 200–300 m of transport to ensure even a 1‐log unit removal of oocysts, even though the limestone surfaces exhibited a substantive capability for their sorptive removal. The study further demonstrated the utility of microspheres as oocyst surrogates in field‐scale assessments of well vulnerability in limestone, provided that differences in attachment behaviors between oocysts and microspheres are taken into account.

Water Resources Research

Comment on “Flow and tracer transport in a single fracture: A stochastic model and its relation to some field observations” by L. Moreno et al.

Moreno et al. [1988] (hereinafter referred to as MT) used a particle-tracking scheme to investigate the physics of solute movement in a variable-aperture planar fracture. The spatially heterogeneous fluid velocity was assumed to be the only mechanism of solute movement; local or pore scale dispersion and molecular diffusion were assumed to be negligible. The particle-tracking scheme used by MT consisted of routing particles from node to node in a finite difference grid. In this scheme, the direction of an individual particle is randomly selected and the probability associated with the particle movement in a given direction is proportional to the fluid flux in that direction. The same method was used by Desbarats [1990] to investigate advective transport in aquifers composed of two porous media of different hydraulic conductivities.

Water Resources Research

Cautions and suggestions for geochemical sampling in fractured rock

Collecting water samples for geochemical analyses in open bedrock boreholes or in discrete intervals of boreholes intersected by multiple fractures is likely to yield ambiguous results for ground water chemistry because of the variability in the transmissivity, storativity, and hydraulic head of fractures intersecting the borehole. Interpreting chemical analyses of water samples collected in bedrock boreholes requires an understanding of the hydraulic conditions in the borehole under the ambient flow regime in the aquifer as well as during sampling. Pumping in open boreholes, regardless of the pumping rate and the location of the pump intake, first draws water from the borehole and then from fractures intersecting the borehole. The time at which the volumetric rate of water entering the borehole from fractures is approximately equal to the pumping rate can be identified by monitoring the logarithm of drawdown in the borehole as a function of the logarithm of time. Mixing of water entering the borehole from fractures with water in the borehole must be considered in estimating the time at which the pump discharge is representative of aquifer water. In boreholes intersected by multiple fractures, after the contribution from the borehole volume has diminished, the contribution of fractures to the pump discharge will be weighted according to their transmissivity, regardless of the location of the pump intake. This results in a flux‐averaged concentration in the pump discharge that is biased by the chemical signature of those fractures with the highest transmissivity. Under conditions where the hydraulic head of fractures varies over the length of the borehole, open boreholes will be subject to ambient flow in the water column in the borehole. In some instances, the magnitude of the ambient flow may be similar to the designated pumping rate for collecting water samples for geochemical analyses. Under such conditions, the contributions to the pump discharge from individual fractures will be a function not only of the transmissivity of the fractures, but also of the distribution of hydraulic head in fractures intersecting the borehole. To reduce or eliminate the deleterious effects of conducting geochemical sampling in open boreholes, a straddle‐packer apparatus that isolates a single fracture or a series of closely spaced fractures is recommended. It is also recommended that open boreholes be permanently outfitted with borehole packers or borehole liners in instances where maintaining the hydraulic and chemical stratification in the aquifer is of importance. In a field example, a comparison of results from sampling in an open borehole and in discrete intervals of the same borehole showed dramatic differences in the concentrations of chemical constituents in the water samples, even though chemical field parameters stabilized prior to both open borehole and discrete interval sampling.

Groundwater Monitoring & Remediation

Contamination in fractured-rock aquifers: Research at the former Naval Air Warfare Center, West Trenton, New Jersey

The U.S. Geological Survey and cooperators are studying chlorinated solvents in a fractured sedimentary rock aquifer underlying the former Naval Air Warfare Center (NAWC), West Trenton, New Jersey. Fractured-rock aquifers are common in many parts of the United States and are highly susceptible to contamination, particularly at industrial sites. Compared to 'unconsolidated' aquifers, there can be much more uncertainty about the direction and rate of contaminant migration and about the processes and factors that control chemical and microbial transformations of contaminants. Research at the NAWC is improving understanding of the transport and fate of chlorinated solvents in fractured-rock aquifers and will compare the effectiveness of different strategies for contaminant remediation.

New Jersey

BAT3 Analyzer: Real-time data display and interpretation software for the multifunction bedrock-aquifer transportable testing tool (BAT3)

The BAT3 Analyzer provides real-time display and interpretation of fluid pressure responses and flow rates measured during geochemical sampling, hydraulic testing, or tracer testing conducted with the Multifunction Bedrock-Aquifer Transportable Testing Tool (BAT3) (Shapiro, 2007). Real-time display of the data collected with the Multifunction BAT3 allows the user to ensure that the downhole apparatus is operating properly, and that test procedures can be modified to correct for unanticipated hydraulic responses during testing. The BAT3 Analyzer can apply calibrations to the pressure transducer and flow meter data to display physically meaningful values. Plots of the time-varying data can be formatted for a specified time interval, and either saved to files, or printed. Libraries of calibrations for the pressure transducers and flow meters can be created, updated and reloaded to facilitate the rapid set up of the software to display data collected during testing with the Multifunction BAT3. The BAT3 Analyzer also has the functionality to estimate calibrations for pressure transducers and flow meters using data collected with the Multifunction BAT3 in conjunction with corroborating check measurements. During testing with the Multifunction BAT3, and also after testing has been completed, hydraulic properties of the test interval can be estimated by comparing fluid pressure responses with model results; a variety of hydrogeologic conceptual models of the formation are available for interpreting fluid-withdrawal, fluid-injection, and slug tests.

Open-File Report

Characterizing Hydraulic Properties and Ground-Water Chemistry in Fractured-Rock Aquifers: A User's Manual for the Multifunction Bedrock-Aquifer Transportable Testing Tool (BAT3)

A borehole testing apparatus has been designed to isolate discrete intervals of a bedrock borehole and conduct hydraulic tests or collect water samples for geochemical analyses. This borehole testing apparatus, referred to as the Multifunction Bedrock-Aquifer Transportable Testing Tool (BAT3), includes two borehole packers, which when inflated can form a pressure-tight seal against smooth borehole walls; a pump apparatus to withdraw water from between the two packers; a fluid-injection apparatus to inject water between the two packers; pressure transducers to monitor fluid pressure between the two packers, as well as above and below the packers; flowmeters to monitor rates of fluid withdrawal or fluid injection; and data-acquisition equipment to record and store digital records from the pressure transducers and flowmeters. The generic design of this apparatus was originally discussed in United States Patent Number 6,761,062 (Shapiro, 2004). The prototype of the apparatus discussed in this report is designed for boreholes that are approximately 6 inches in diameter and can be used to depths of approximately 300 feet below land surface. The apparatus is designed to fit in five hard plastic boxes that can be shipped by overnight freight car-riers. The equipment can be assembled rapidly once it is removed from the shipping boxes, and the length of the test interval (the distance between the two packers) can be adjusted to account for different borehole conditions without reconfiguring the downhole components. The downhole components of the Multifunction BAT3 can be lowered in a borehole using steel pipe or a cable; a truck mounted winch or a winch and tripod can be used for this purpose. The equipment used to raise and lower the downhole components of the Multifunction BAT3 must be supplied on site, along with electrical power, a compressor or cylinders of compressed gas to inflate the packers and operate downhole valves, and the proper length of tubing to connect the packers, the submersible pump, and other downhole components to land surface. Borehole geophysical logging must be conducted prior to deploying the Multifunction BAT3 in bedrock boreholes. In particular, it is important to identify the borehole diameter as a function of depth to avoid placing the packers over rough sections of the borehole, where they may be damaged during inflation. In addition, it is advantageous to identify the location of fractures intersecting the borehole wall, for example, using an acoustic televiewer log or a borehole camera. A knowledge of fracture locations is helpful in designing the length of the test interval and the locations where hydraulic tests and geochemical sampling are to be conducted. The Multifunction BAT3 is configured to conduct both fluid-injection and fluid-withdrawal tests. Fluid-injection tests are used to estimate the hydraulic properties of low-permeability fractures intersecting the borehole. The lower limit of the transmissivity that can be estimated using the configuration of the Multifunction BAT3 described in this report is approximately 10-3 square feet per day (ft2/d). Fluid-withdrawal tests are used to collect water samples for geochemical analyses and estimate the hydraulic properties of high-permeability fractures intersecting the borehole. The Multifunction BAT3 is configured with a submersible pump that can support pumping rates ranging from approximately 0.05 to 2.5 gallons per minute, and the upper limit of the of the transmissivity that can be estimated is approximately 104 ft2/d. The Multifunction BAT3 also can be used to measure the ambient hydraulic head of a section of a bedrock borehole, and to conduct single-hole tracer tests by injecting and later withdrawing a tracer solution.

Open-File Report

Interpretation of prematurely terminated air-pressurized slug tests

An air-pressurized slug test consists of applying a constant pressure to the column of air in a well, monitoring the declining water level, and then releasing the air pressure and monitoring the recovering water level. Such tests offer a means of estimating formation transmissivity and storativity without extensive downhole equipment and the associated safety risks. This paper analyzes data from prematurely terminated tests. A solution to the boundary-value problem for the declining and recovering water level during an air-pressurized slug test is developed for an arbitrary time-dependent air pressure applied to the well. Type curves are generated to estimate formation transmissivity and storativity from the recovering water level associated with prematurely, terminated tests. The application of the type curves is illustrated in a series of actual tests.

Ground Water

Hydrogeologic controls on ground-water discharge to the Washington METRO subway tunnel near the Medical Center station and Crossover, Montgomery County, Maryland

Excessive water intrusion has been observed inside several of the Washington Metropolitan Area Transit Authority subway tunnels, with the worst leakage occurring along the Red Line tunnels and stations north of Dupont Circle in Washington, D.C. These tunnels were constructed in bedrock that contains permeable (water-bearing) joints and fractures. Excessive water leakage through the walls and water inside the underground facilities has damaged mechanical and electrical components in the tunnel, and has escalated the deterioration rate of the rail system. The U.S. Geological Survey and the Washington Metropolitan Area Transit Authority have worked cooperatively on a study from 200003 to describe and quantify the factors controlling ground-water flow into the Red Line subway tunnel near the Medical Center Station and Crossover in Montgomery County, Maryland. The Red Line near the Medical Center Station and Crossover passes through or beneath the gneissic Sykesville Formation and the biotite-hornblende tonalite member of the Georgetown Intrusive Suite, both of which contain numerous fractures. The mapped foliation and joints of the Sykesville Formation in the vicinity of the Medical Center Station and Crossover are generally orientated north-south. Fractures in the Sykesville Formation in outcrops appear to be poorly connected. In the biotite-hornblende tonalite member of the Georgetown Intrusive Suite, the general orientation of the mapped foliation and joints is east-west. In contrast to the fractures in the Sykesville Formation, the fractures in the Georgetown Intrusive Suite in outcrops appear to be more numerous and have a greater degree of connectivity. Fractures intersecting four bedrock wells near the Medical Center Station and Crossover that were drilled into the biotite-hornblende tonalite member of the Georgetown Intrusive Suite show an east-west orientation matching the foliation and joints shown on geologic maps. The excessive water intrusion at the Medical Center Station and Crossover could be the result of its location within the Georgetown Intrusive Suite. The abrupt changes in the mapped directions of ground-water flow based on the hydraulic heads at the contact between the Sykesville Formation and biotite-hornblende tonalite member of the Georgetown Intrusive Suite could also be the result of the change in fracturing between these two lithologies. Saprolite, a residual of soft, red/brown to gray clay from decomposed crystalline rock, overlies the bedrock and varies from about 20 to 55 feet thick, depending on location. On the basis of a slug test conducted in the lower part of the saprolite near the Medical Center Station and Crossover, transmissivity and storativity of the saprolite were estimated to be 10 feet squared per day and 10-6 , respectively. The transmissivity of fractures intersecting bedrock boreholes drilled in the biotite-hornblende tonalite member of the Georgetown Intrusive Suite varies over five orders of magnitude, from a maximum of approximately 10 feet squared per day to the detection limit of the in situ testing apparatus, which is approximately 10-4 feet squared per day. In general, the transmissivity of fractures intersecting the boreholes increases with depth. The low transmissivity of bedrock fractures in close proximity to the saprolite is likely to be caused by the fractures being filled with byproducts of rock weathering, resulting in reduced permeability. 2 Hydrogeologic Controls on Ground-Water Discharge to the Washington METRO Subway Tunnel The bulk transmissivity of the bedrock aquifer is approximately 3.7 feet squared per day, as determined from an aquifer test conducted by pumping a 240-foot-deep borehole and monitoring the drawdown over 3 days in the pumped borehole and several observation boreholes. In general, the hydraulic head decreases with depth in bedrock boreholes, indicating the potential for downward ground-water flow. Based on hydraulic head values mea

Water-Resources Investigations Report

Fractured-rock aquifers, understanding an increasingly important source of water

Ground water is one of the Nation's most important natural resources. It provides drinking water to communities, supports industry and agriculture, and sustains streams and wetlands. A long record of contributions exists in understanding ground-water movement in sand and gravel aquifers; historically, these aquifers were easily accessible and the first to be investigated. With increased demand for water, communities are looking to fractured-rock aquifers, where water moves through fractures in the rock. Fractures, however, may not always convey or store large quantities of water. Understanding ground-water flow through fractured-rock aquifers is an area of ground-water research that will have increasing importance to our Nation over the coming years. Many areas of the United States rely on fractured-rock aquifers for water supply. In addition, areas experiencing population growth in the Northeast, Southeast, and mountainous regions of the West are likely to rely heavily on water supplies from fractured-rock aquifers. Finding water for thirsty communities, however, is not the only societal issue requiring an understanding of ground-water flow in fractured rock. Land-use practices affect water quality in fractured-rock aquifers, particularly where ground water flows rapidly through fractures. Fractured rock aquifers also are viewed as potential repositories for radioactive and other types of waste, where it is desirable for the ground water to be inaccessible or move at a very slow rate.

Fact Sheet

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.

Water Resources Research

A Graphical-User Interface for the U. S. Geological Survey's SUTRA Code using Argus ONE (for simulation of variable-density saturated-unsaturated ground-water flow with solute or energy transport)

This report describes a Graphical-User Interface (GUI) for SUTRA, the U.S. Geological Survey (USGS) model for saturated-unsaturated variable-fluid-density ground-water flow with solute or energy transport,which combines a USGS-developed code that interfaces SUTRA with Argus ONE, a commercial software product developed by Argus Interware. This product, known as Argus Open Numerical Environments (Argus ONE TM ), is a programmable system with geographic-information-system-like (GIS-like) functionality that includes automated gridding and meshing capabilities for linking geospatial information with finite-difference and finite-element numerical model discretizations. The GUI for SUTRA is based on a public-domain Plug-In Extension (PIE) to Argus ONE that automates the use of ArgusONE to: automatically create the appropriate geospatial information coverages (information layers) for SUTRA, provide menus and dialogs for inputting geospatial information and simulation control parameters for SUTRA, and allow visualization of SUTRA simulation results. Following simulation control data and geospatial data input bythe user through the GUI, ArgusONE creates text files in a format required for normal input to SUTRA,and SUTRA can be executed within the Argus ONE environment. Then, hydraulic head, pressure, solute concentration, temperature, saturation and velocity results from the SUTRA simulation may be visualized. Although the GUI for SUTRA discussed in this report provides all of the graphical pre- and post-processor functions required for running SUTRA, it is also possible for advanced users to apply programmable features within Argus ONE to modify the GUI to meet the unique demands of particular ground-water modeling projects.

Open-File Report