Kent S. Novakowski

The interpretation of a tracer experiment conducted in a single fracture under conditions of natural groundwater flow

The development of conceptual models to describe the hydrogeology of sparsely fractured media requires the characterization of the properties of discrete fractures at the field scale. In this study, a tracer experiment conducted under conditions of natural groundwater flow in a discrete fracture in an interbedded shale and limestone sequence is interpreted. This experiment, which was initiated by injecting a small quantity of tracer into the fracture plane, involved monitoring tracer movement using 27 boreholes within a 35×40 m area. Test data revealed a tracer plume which spread both longitudinally and transversely in the direction of mean groundwater flow. The field breakthrough curves were interpreted using a two-dimensional finite element transport model that incorporated longitudinal and transverse dispersion, diffusion into the rock matrix, and constant fracture aperture. Additional simulations which incorporated the effects of aperture variability were conducted in a Monte Carlo format by varying the spatial correlation and variance of the aperture field. The constant aperture analysis found that the mean aperture determined from the tracer experiment was approximately 20% greater than the mean aperture measured by hydraulic methods. Values of matrix porosity ranging between 1 and 3%, a constant longitudinal dispersivity of 0.1 m, and a large range in transverse dispersivity from 0.01 to 0.22 m were required to simulate the data. Trends of increasing aperture and matrix porosity with distance were observed, suggesting that tracer transport followed increasingly tortuous pathways. Although the variable aperture simulations were not fitted to the field data, the aperture field having an isotropic spatial correlation length of 0.5 m and variance of 10,000 μm2 provided simulated plumes that appeared to be most similar to the shape and concentration of the field plume. Evidence from the hydraulic measurement of the aperture distribution suggests that this is a reasonable estimate of the natural aperture field.

The analysis of tracer experiments conducted in divergent radial flow fields

Analytical models are developed to interpret tracer experiments conducted in divergent flow fields. The models account for the mixing of tracer in both the source and observation wells and for the diffusion of tracer into adjacent aquitards. A solution for the particular case of an observation well of infinitesimally small volume is also presented. Solutions are derived for both resident and flux concentrations and for macroscopically discontinuous conditions at both the inlet and outlet boundaries. The solutions for resident and flux concentration are identical when the mixing volume in the observation well is of finite volume. Two tracer experiments were conducted in a horizontally fractured shale to demonstrate the application of the new analytical models. Experiments were conducted with observation wells of finite volume and using a new sampling packer which eliminates the volume of the observation well. The results show that for experiments conducted in fractured media, the analytical model developed in this paper provides an improved fit to the shape of the concentration curve relative to models which do not account for mixing in the source and observation wells. Alternatively, by modifying the field method such that the volume of the observation well is eliminated using the sampling packer, either conventional models or the new model for concentration in the formation will provide equally suitable fits to the concentration data.

Humic acid enhanced remediation of an emplaced diesel source in groundwater.: 1. Laboratory-based pilot scale test

The enhanced solubility of petroleum-derived compounds in humic acid solutions is the basis for a new groundwater remediation technology. In this unique pilot-scale test, a stationary contaminant source consisting of diesel fuel was placed below the water table in a model sand aquifer (1.2 x 5.5 x 1.8-m deep) and flushed with water at a flow rate of 2 cm/h over 5 years. At 51 days, laboratory grade humic acid was added to the water and maintained at a level of approximately 0.8 g/l. The addition of humic acid had only a small impact on the aqueous transport of the BTEX components, which were rapidly dissolved from the diesel, but had a large effect on the flushing of PAHs, including methylated naphthalenes (MNs). Binding to aqueous humic acid enhanced the solubilization of MNs two- to tenfold. During aqueous transport, biodegradation of the BTEX and PAHs occurred, limiting the lateral and longitudinal extent of the diesel contaminant plume in the model aquifer. It appears that through enhanced solubilization, the overall biodegradation rate of the MNs was increased. As the various MNs were depleted from the diesel source, the MN plume shrank and then disappeared.

An evaluation of boundary conditions for one-dimensional solute transport: 1. Mathematical development

The Laplace transform method is employed to obtain the solution to several boundary value problems in which mixing occurs in reservoirs attached to a porous medium. Flow is assumed to be uniformly one-dimensional throughout the porous medium. Solutions are obtained for both continuous and discontinuous concentrations at the reservoir-medium boundary and for resident and flux-averaged concentrations. A mass balance conducted on each solution shows that neither continuity condition can be proved generally superior. An evaluation of the parametric sensitivity of the solutions is also conducted and shows that the distinction between the continuity conditions and the flux and resident concentrations is only important at small Peclet numbers. The only exception to this is the distinction between flux-averaged versus resident continuous concentrations in a finite solution domain. In this case, the flux concentrations were found to be insensitive to the volume of the downstream reservoir and, consequently, the flux and resident concentrations can differ substantially for larger reservoirs. In consideration of the general behavior of the solutions, three conceptual problems were identified which must be investigated by physical modeling: (1) determination of the appropriate solution at small Peclet number, (2) the possibility that dispersive mass flux occurs from the upstream reservoir under conditions of continuous concentration, and (3) the use of the flux transformation for continuous concentration in a finite solution domain. The physical modeling is discussed in a companion paper.

The Radial Diffusion Method: 2. A semianalytical model for the determination of effective diffusion coefficients, porosity, and adsorption

A model for interpreting diffusional transport in porous geological materials is developed. The model is based on a laboratory method described in a companion paper [van der Kamp et al., this issue] by which radial diffusion from or into a cylindrical reservoir in a core-sized sample is measured. The model accounts for radial diffusion, mass balance in the reservoir, linear adsorption, decay or transformation, and periodic abstraction of samples. The model is derived using the Laplace transform method for both finite and semi-infinite domains. For conditions where solute concentrations equilibrate (i.e., in finite diameter samples), a simple expression is derived that can be used to interpret the results for effective porosity and a retardation factor. It is demonstrated that the method can provide independent measures of the effective diffusion coefficient, adsorption, and effective porosity when the results are interpreted using the model. Several real and hypothetical diffusion experiments are presented to illustrate the use of the model.

Preliminary interpretation of tracer experiments conducted in a discrete rock fracture under conditions of natural flow

The authors present a preliminary analysis of tracer experiments conducted on a natural horizontal fracture system in shale and limestone at a depth of roughly 10 m. An array of 27 boreholes on 5 m spacings was placed into this fracture system, and apertures of the fractures were determined hydraulically at each hole. A conservative tracer was injected into one borehole, and monitored in the array. The tracer transport process was modeled by a one dimensional model, and indicates that transverse dispersion, and diffusion in the matrix are the predominant processes which inhibit tracer migration, and result in spreading.

An evaluation of boundary conditions for one‐dimensional solute transport: 2. Column experiments

As the result of a theoretical comparison of analytical models for one-dimensional solute transport (Novakowski, this issue), it has been found that to reconcile the substantial differences observed between the models under conditions of large dispersion, a physical modeling study of the processes of solute transport in the vicinity of boundaries must be undertaken. The physical modeling is conducted using columns ranging in diameter from 76 to 352 mm and length from 300 to 400 mm. Geological materials of either large or small coefficient of dispersion are employed as packing for the columns. Reservoirs of finite volume are located at the inlet and outlet boundaries of each column. Using a conservative fluorescent tracer, experiments are conducted to investigate the use of macroscopic continuity in concentration at the boundaries, and the use of the flux-averaged transformation for this boundary value problem. Concentration of the tracer was determined noninvasively from both the inlet and outlet reservoirs and, for some experiments, resident concentration was determined from within the interior of the column by excavation. Results of the experiments conducted using different volumes of the outlet reservoir show that the analytical model for flux concentration accounting for macroscopic continuity in concentration at the boundaries only poorly simulates the physical mixing process in the outlet reservoir. In addition, the results of the experiments conducted in which resident concentrations were determined from the interior of the column show that the concept of macroscopic continuity is not supported by physical evidence at either the inlet or outlet boundary. Thus, the analytical model in which concentration at the boundaries is macroscopically discontinuous best simulates the solute transport processes for this boundary value problem. Unfortunately, the solutions for resident and flux concentration with these boundary conditions are identical and further distinction between these models cannot be undertaken. Analytical inversion of the Laplace domain solution is also presented.

Identifying watershed-scale barriers to groundwater flow: Lineaments in the Canadian Shield

Lineament identifi cation is a standard but controversial hydrogeologic practice. In this study, we present a rigorous examination of the hydrology of lineaments in a crystalline bedrock setting. Lineaments are reinterpreted as watershed-scale hydraulic barriers, in contrast to previous interpretations as fractured conduits that focus recharge and fl ow. In the study area, an ~900 km 2 watershed underlain by the granitic and gneissic terrain of the Canadian Shield, bedrock lineaments are associated with linear lake shores and perennial wetland complexes. Lineaments were identifi ed using a robust multi-image method and characterized by remote sensing, fracture mapping, drilling, hydraulic characterization, and numerical simulation of a coupled groundwater‐surface-water system. Results indicate that two principal lineament sets are oriented parallel to fracture and fault orientations, and thus lineaments are interpreted as structural features, either fault zones or fracture zones with limited displacement. Faulted lineaments are more effectively identifi ed by digital elevation model (DEM) topographic data rather than Landsat tonal imagery. Hydrogeological characterization and geomatic data indicate that the fractured bedrock underlying lineaments is composed of poorly connected zones of reduced permeability due to fault zone and/or fl uid fl ow processes. Field data and numerical simulations suggest that lineament areas are barriers to recharge and fl ow in this setting as a result of permeability reduction. Integrated data sets and models of lineament permeability that are geologically realistic result in a better understanding of fractured bedrock aquifers and patterns of flfl ow in the brittle uppermost crust.

Fecal Indicator Bacteria Variability in Samples Pumped from Monitoring Wells

The detection of microbiological contamination in drinking water from groundwater wells is often made with a limited number of samples that are collected using traditional geochemical sampling protocols. The objective of this study is to examine the variability of fecal indicator bacteria, as observed using discrete samples, due to pumping. Two wells were instrumented as multilevel piezometers in a bedrock aquifer, and bacterial enumeration was conducted on a total of 166 samples (for total coliform, fecal coliform, Escherichia coli, and fecal streptococci) using standard membrane filtration methods. Five tests were conducted using pumping rates ranging from 0.3 to 17 L/min in a variety of purging scenarios, which included constant and variable (incremental increase and decrease) flow. The results clearly show a rapid and reproducible, 1 to 2 log-unit decrease in fecal indicator bacteria at the onset of pumping to stabilized, low-level concentrations prior to the removal of three to five well volumes. The pumping rate was not found to be correlated with the magnitude of observed bacterial counts. Based on the results, we suggest sampling protocols for fecal indicator bacteria that include multiple collections during the course of pumping, including early-time samples, and consider other techniques such as microscopic enumeration when assessing the source of bacteria from the well-aquifer system.

A note on a method for measuring the transport properties of a formation using a single well

For some subsurface investigations of contaminant transport, particularly those conducted in consolidated material, the costs related to well construction prohibit the installation of a comprehensive field of monitoring wells. To alleviate this problem for fractured, low-porosity formations, a method for measuring transport properties using a single well was developed. The method involves the injection of fluid and tracer over a short duration which establishes a radial source condition in the formation. Following this the ambient flow is allowed to carry the tracer back through the injection well where tracer concentration is monitored passively, in situ. To interpret the experimental results, a numerical model was adapted to account for the mass balance of solute in the source/monitoring well during the injection and monitoring periods. The model accommodates advection-dispersion, adsorption, decay, and matrix diffusion in a framework of fractures having a variety of geometries. To illustrate the use of the method, a field experiment was conducted using a single well which is intersected by a discrete horizontal fracture in a flat-lying shale and limestone formation. Interpretation of the results agreed well with the interpretation of other tracer experiments conducted previously in the same fracture plane. This suggests that the method may yield defensible estimates of transport properties such as matrix porosity and groundwater velocity in geological formations that are expensive and difficult to characterize.