Simulation of liquid waste buoyancy in a deep heterogeneous aquifer

The results of 3D numerical simulation of coupled flow and transport processes of light-waste migration in heterogeneous aquifer with brine are described. The study is based on the geological data and monitoring of deep-well injection of liquid waste at Chepetsk Mechanical Plant (ChMZ, Glazov). The buoyancy of light waste is simulated for the post-injection period of 300 years using different conceptual models of heterogeneity. The procedure of 3D geostatistical simulation based on transition probability analysis with TSIM code of the reservoir heterogeneity is presented. The results of the ascending waste migration simulation using SEAWAT2000 code indicate that both the variable fluid density and the hydraulic heterogeneity must be considered in the forecast models for determining the possible waste distribution during the injection and the post injection periods.     

Study of Current Underground Injection Control Regulations and Practices in Illinois

In 1984, the Illinois Department of Energy and Natural Resources was required to assess the regulations and practices of the Illinois Underground Injection Control (UIC) program as it relates to Class I hazardous waste disposal wells. Nine injection wells, including two standbys (one inactive), are currently in operation at seven sites in the state. These wells range in depth from 1540 to 5524 feet (470 to 1683m; most inject wastes into porous carbonate formations (two wells inject into a thick sandstone). In 1984, approximately 300 million gallons (1.1 billion liters) of industrial wastes were disposed of in these wells. Acids were the most common waste disposed of, although water made up 70 to 95 percent of the wastes by volume. Illinois has been granted primacy in operating this program.
The geologic environment, consisting of the unit accepting the waste and confining units lying above and below, has the capacity to accept the waste, to retain it, and to protect all underground sources of drinking water (USDW) from contamination by its injection. The geology of Illinois is relatively simple and includes disposal zones and associated confining units suitable for deep-well injection across the central two-thirds of the state.
The regulatory structure for Class I injection wells is generally adequate in concept and scope to ensure containment of injected wastes and to safeguard underground sources of drinking water in Illinois. There is a need to update and strengthen selected portions of the regulatory practices in the areas of waste sampling protocol, chemical analysis of collected waste samples, and evaluation of injection well testing and monitoring data.
A number of technologies exist that can treat and dispose of most hazardous and non-hazardous waste streams. Each of these technologies has associated with it economic, environmental and societal impacts.     

Spatial variability of the poroelastic response of the heterogeneous medium

In this work, a stochastic methodology is applied to analyze the variability of the poroelastic response of the heterogeneous medium at the field scale. To solve the problem analytically, we restrict our attention to the one-dimensional models, where fluid flow as well as deformation occurs in one direction only under a constant applied stress. Assuming statistic homogeneity, the closed-form solutions that describe the variability of fluid pressure head, and a solid's strain and displacement are developed using a spectral approach based on Fourier–Stieltjes representations for the perturbed quantities. The influence of the correlation length of the log hydraulic conductivity on these results is investigated. It is found that the variances of the solid's strain and displacement increase with the correlation length of the log hydraulic conductivity, while the correlation length of the log hydraulic conductivity plays the role in reducing the variability of the specific discharge.     

Numerical method of moments for solute transport in a nonstationary flow field conditioned on hydraulic conductivity and head measurements

The unconditional stochastic studies on groundwater flow and solute transport in a nonstationary conductivity field show that the standard deviations of the hydraulic head and solute flux are very large in comparison with their mean values (Zhang et al. in Water Resour Res 36:2107–2120, 2000; Wu et al. in J Hydrol 275:208–228, 2003; Hu et al. in Adv Water Resour 26:513–531, 2003). In this study, we develop a numerical method of moments conditioning on measurements of hydraulic conductivity and head to reduce the variances of the head and the solute flux. A Lagrangian perturbation method is applied to develop the framework for solute transport in a nonstationary flow field. Since analytically derived moments equations are too complicated to solve analytically, a numerical finite difference method is implemented to obtain the solutions. Instead of using an unconditional conductivity field as an input to calculate groundwater velocity, we combine a geostatistical method and a method of moment for flow to conditionally simulate the distributions of head and velocity based on the measurements of hydraulic conductivity and head at some points. The developed theory is applied in several case studies to investigate the influences of the measurements of hydraulic conductivity and/or the hydraulic head on the variances of the predictive head and the solute flux in nonstationary flow fields. The study results show that the conditional calculation will significantly reduce the head variance. Since the hydraulic head measurement points are treated as the interior boundary (Dirichlet boundary) conditions, conditioning on both the hydraulic conductivity and the head measurements is much better than conditioning only on conductivity measurements for reduction of head variance. However, for solute flux, variance reduction by the conditional study is not so significant.     

Two-dimensional stochastic analysis of flow in leaky confined aquifers subject to spatial and periodic leakage

This paper addresses the issue of flow in heterogeneous leaky confined aquifers subject to leakage. The leakage into the confined aquifer is driven by spatial and periodic fluctuations of water table in an overlying phreatic aquifer. The introduction of leakage leads to non-uniformity in the mean head gradient and results in nonstationarity in hydraulic head and velocity fields. Therefore, a nonstationary spectral approach based on Fourier–Stieltjes representations for the perturbed quantities is adopted to account for the spatial variability of nonstationary head fields. Closed-form expressions for the variances of hydraulic head and specific discharge are developed in terms of statistical properties of hydraulic parameters. The results indicate that the spatiotemporal variations in leakage leads to enhanced variability of the hydraulic head and of the specific discharge, which increase with distance from any arbitrary reference point. The coefficient of leakage and the spatial structure of log transmissivity field and of the amplitude of water table fluctuation are critical in quantifying the variability of the hydraulic head and of the specific discharge.     

Differentiation of the Origins of BTX in Ground Water Using Multivariate Plots

Multivariate plots were utilized to create fingerprints of aromatic hydrocarbon residues in ground water. The technique allows hydrogeologists to distinguish between residues of benzene, toluene, ethyl benzene, and total xylenes originating from ground water contact with petroleum in natural deposits and refined petroleum waste products. Examples were taken from deep-well injection of refinery wastes, natural petroleum deposits, municipal and industrial landfill leachates, coal tar and creosote contaminated waters, and varnish industry contaminated ground water. The data were plotted from ASCII files generated through either Lotus 123™ or a database (The Manager™) report program, using a simple Fortran interactive program with Plot88™ subroutines.     

Unsaturated flows in soils with self-similar hydraulic conductivity distribution

In this article, we are concerned with the statistics of steady unsaturated flow in soils with a fractal hydraulic conductivity distribution. It is assumed that the spatial distribution of log hydraulic conductivity can be described as an isotropic stochastic fractal process. The impact of the fractal dimension of this process, the soil pore-size distribution parameter, and the characteristic length scale on the variances of tension head and the effective conductivity is investigated. Results are obtained for one-dimensional and three-dimensional flows. Our results indicate that the tension head variance is scale-dependent for fractal distribution of hydraulic conductivity. Both tension head variance and effective hydraulic conductivity depend strongly on the fractal dimension. The soil pore-size distribution parameter is important in reducing the variability of the unsaturated hydraulic conductivity and of the fluxes.     

Stochastic study of solute transport in a nonstationary medium

A Lagrangian stochastic approach is applied to develop a method of moment for solute transport in a physically and chemically nonstationary medium. Stochastic governing equations for mean solute flux and solute covariance are analytically obtained in the first-order accuracy of log conductivity and/or chemical sorption variances and solved numerically using the finite-difference method. The developed method, the numerical method of moments (NMM), is used to predict radionuclide solute transport processes in the saturated zone below the Yucca Mountain project area. The mean, variance, and upper bound of the radionuclide mass flux through a control plane 5 km downstream of the footprint of the repository are calculated. According to their chemical sorption capacities, the various radionuclear chemicals are grouped as nonreactive, weakly sorbing, and strongly sorbing chemicals. The NMM method is used to study their transport processes and influence factors. To verify the method of moments, a Monte Carlo simulation is conducted for nonreactive chemical transport. Results indicate the results from the two methods are consistent, but the NMM method is computationally more efficient than the Monte Carlo method. This study adds to the ongoing debate in the literature on the effect of heterogeneity on solute transport prediction, especially on prediction uncertainty, by showing that the standard derivation of solute flux is larger than the mean solute flux even when the hydraulic conductivity within each geological layer is mild. This study provides a method that may become an efficient calculation tool for many environmental projects.     

A Method for Predicting Chloride Concentrations in Leachate at Natural Attenuation Landfills in the Precambrian Shield Regions of Ontario, Canada

Natural attenuation landfill sites continue to be the preferred method of domestic waste disposal in the Precambrian Shield regions of Ontario due to economic factors. The main challenge in siting these landfills is ensuring that there will be no adverse impact on off-site water resources. Impact risk assessments are generally based on estimated volumes and strengths of chloride in the leachate. While volumes can be estimated using simple water balances, peak chloride concentration predictions are based on judgment and are quite variable. Since design chloride strengths dictate the size of the required attenuation zone, overestimating concentrations will typically make it impossible to find a suitable site, while underestimating concentrations increases the potential for adverse off-site impacts occurring.
Hydrogeological data from active and closed landfills in the Precambrian Shield region were collected to help develop a reliable method of predicting peak chloride concentrations in leachate. This study focused on 21 sites located on relatively permeable sandy soils since landfills underlain by low permeability clayey soils retain leachate similar to lined facilities.
Linear regression analyses were conducted to determine if source chloride concentrations at the "sand" sites are significantly influenced by waste thickness, fill area, waste volume, waste deposition rate, hydraulic conductivity, upgradient flow length, depth to the water table, and moisture surplus.
A strong relationship (R = 0.957) was found to exist between source chloride concentrations and waste volume. This empirical volume versus chloride regression equation can be used as the basis for establishing design chloride concentrations at new natural attenuation landfills developed over sandy soils in the Precambrian Shield regions of Ontario. An alternative risk assessment approach is required for sites developed over clay soils.     

Numerical Modeling of Methane Leakage from a Faulty Natural Gas Well into Fractured Tight Formations

Horizontal drilling and hydraulic fracturing have enabled hydrocarbon recovery from unconventional reservoirs, but led to natural gas contamination of shallow groundwaters. We describe and apply numerical models of gas‐phase migration associated with leaking natural gas wells. Three leakage scenarios are simulated: (1) high‐pressure natural gas pulse released into a fractured aquifer; (2) continuous slow leakage into a tilted fractured formation; and (3) continuous slow leakage into an unfractured aquifer with fluvial channels, to facilitate a generalized evaluation of natural gas transport from faulty natural gas wells. High‐pressure pulses of gas leakage into sparsely fractured media are needed to produce the extensive and rapid lateral spreading of free gas previously observed in field studies. Transport in fractures explains how methane can travel vastly different distances and directions laterally away from a leaking well, which leads to variable levels of methane contamination in nearby groundwater wells. Lower rates of methane leakage (≤1 Mcf/day) produce shorter length scales of gas transport than determined by the high‐pressure scenario or field studies, unless aquifers have low vertical permeabilities (≤1 millidarcy) and fractures and bedding planes have sufficient tilt (～10°) to allow a lateral buoyancy component. Similarly, in fractured rock aquifers or where permeability is controlled by channelized fluvial deposits, lateral flow is not sufficiently developed to explain fast‐developing gas contamination (0‐3 months) or large length scales (～1 km) documented in field studies. Thus, current efforts to evaluate the frequency, mechanism, and impacts of natural gas leakage from faulty natural gas wells likely underestimate contributions from small‐volume, low‐pressure leakage events.     

Using data assimilation method to calibrate a heterogeneous conductivity field and improve solute transport prediction with an unknown contamination source

Hydraulic conductivity distribution and plume initial source condition are two important factors affecting solute transport in heterogeneous media. Since hydraulic conductivity can only be measured at limited locations in a field, its spatial distribution in a complex heterogeneous medium is generally uncertain. In many groundwater contamination sites, transport initial conditions are generally unknown, as plume distributions are available only after the contaminations occurred. In this study, a data assimilation method is developed for calibrating a hydraulic conductivity field and improving solute transport prediction with unknown initial solute source condition. Ensemble Kalman filter (EnKF) is used to update the model parameter (i.e., hydraulic conductivity) and state variables (hydraulic head and solute concentration), when data are available. Two-dimensional numerical experiments are designed to assess the performance of the EnKF method on data assimilation for solute transport prediction. The study results indicate that the EnKF method can significantly improve the estimation of the hydraulic conductivity distribution and solute transport prediction by assimilating hydraulic head measurements with a known solute initial condition. When solute source is unknown, solute prediction by assimilating continuous measurements of solute concentration at a few points in the plume well captures the plume evolution downstream of the measurement points.     

Uncertainty Estimation in One‐Dimensional Heat Transport Model for Heterogeneous Porous Medium

In many practical applications, the rates for ground water recharge and discharge are determined based on the analytical solution developed by Bredehoeft and Papadopulos (1965) to the one‐dimensional steady‐state heat transport equation. Groundwater flow processes are affected by the heterogeneity of subsurface systems; yet, the details of which cannot be anticipated precisely. There exists a great deal of uncertainty (variability) associated with the application of Bredehoeft and Papadopulos' solution (1965) to the field‐scale heat transport problems. However, the quantification of uncertainty involved in such application has so far not been addressed, which is the objective of this wok. In addition, the influence of the statistical properties of log hydraulic conductivity field on the variability in temperature field in a heterogeneous aquifer is also investigated. The results of the analysis demonstrate that the variability (or uncertainty) in the temperature field increases with the correlation scale of the log hydraulic conductivity covariance function and the variability of temperature field also depends positively on the position.     

ALLUVIAL CHARACTERISTICS,GROUNDWATER–SURFACE WATER EXCHANGE AND HYDROLOGICAL RETENTION IN HEADWATER STREAMS

Conservative solute injections were conducted in three first-order montane streams of different geological composition to assess the influence of parent lithology and alluvial characteristics on the hydrological retention of nutrients. Three study sites were established: (1) Aspen Creek, in a sandstone–siltstone catchment with a fine-grained alluvium of low hydraulic conductivity (1·3×10⁻⁴ cm/s), (2) Rio Calaveras, which flows through volcanic tuff with alluvium of intermediate grain size and hydraulic conductivity (1·2×10⁻³ cm/s), and (3) Gallina Creek, located in a granite/gneiss catchment of coarse, poorly sorted alluvium with high hydraulic conductivity (4·1×10⁻³ cm/s). All sites were instrumented with networks of shallow groundwater wells to monitor interstitial solute transport. The rate and extent of groundwater–surface water exchange, determined by the solute response in wells, increased with increasing hydraulic conductivity. The direction of surface water–groundwater interaction within a stream was related to local variation in vertical and horizontal hydraulic gradients. Experimental tracer responses in the surface stream were simulated with a one-dimensional solute transport model with inflow and storage components (OTIS). Model-derived measures of hydrological retention showed a corresponding increase with increasing hydraulic conductivity. To assess the temporal variability of hydrological retention, solute injection experiments were conducted in Gallina Creek under four seasonal flow regimes during which surface discharge ranged from baseflow (0·75 l/s in October) to high (75 l/s during spring snowmelt). Model-derived hydrological retention decreased with increasing discharge. The results of our intersite comparison suggest that hydrological retention is strongly influenced by the geologic setting and alluvial characteristics of the stream catchment. Temporal variation in hydrological retention at Gallina Creek is related to seasonal changes in discharge, highlighting the need for temporal resolution in studies of the dynamics of surface water–groundwater interactions in stream ecosystems. © 1997 by John Wiley & Sons, Ltd.     

Combining 3D Hydraulic Tomography with Tracer Tests for Improved Transport Characterization

Hydraulic tomography (HT) is a method for resolving the spatial distribution of hydraulic parameters to some extent, but many details important for solute transport usually remain unresolved. We present a methodology to improve solute transport predictions by combining data from HT with the breakthrough curve (BTC) of a single forced‐gradient tracer test. We estimated the three dimensional (3D) hydraulic‐conductivity field in an alluvial aquifer by inverting tomographic pumping tests performed at the Hydrogeological Research Site Lauswiesen close to Tübingen, Germany, using a regularized pilot‐point method. We compared the estimated parameter field to available profiles of hydraulic‐conductivity variations from direct‐push injection logging (DPIL), and validated the hydraulic‐conductivity field with hydraulic‐head measurements of tests not used in the inversion. After validation, spatially uniform parameters for dual‐domain transport were estimated by fitting tracer data collected during a forced‐gradient tracer test. The dual‐domain assumption was used to parameterize effects of the unresolved heterogeneity of the aquifer and deemed necessary to fit the shape of the BTC using reasonable parameter values. The estimated hydraulic‐conductivity field and transport parameters were subsequently used to successfully predict a second independent tracer test. Our work provides an efficient and practical approach to predict solute transport in heterogeneous aquifers without performing elaborate field tracer tests with a tomographic layout.     

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

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

Stochastic analysis of groundwater flow in aquifers with leakage

 Stochastic analysis of one- and two-dimensional flow through a shallow semi-confined aquifer with spatially variable hydraulic conductivity K represented by a stationary (statistically homogeneous) random process is carried out by using the spectral technique. The hydraulic head covariance functions for flows in a semi-confined aquifer bounded by a leaky layer above and an impervious stratum below are derived by assuming that the randomness forcing the head variation to originate from the hydraulic conductivity field of the aquifer. The head covariance functions are studied using two convenient forms of the logarithmic hydraulic conductivity process. The results demonstrate the significant reduction in the head variances and covariances due to the presence of a leaky layer. The hydraulic head correlation distance is also reduced greatly due to the presence of the leaky layer.     

Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data

This paper presents the extension of the self-calibrating method to the coupled inverse modelling of groundwater flow and mass transport. The method generates equally likely solutions to the inverse problem that display the variability as observed in the field and are not affected by a linearisation of the state equations. Conditioning to the state variables is measured by an objective function including, among others, the mismatch between the simulated and measured concentrations. Conditioning is achieved by minimising the objective function by gradient-based methods. The gradient contains the partial derivatives of the objective function with respect to: log conductivities, log storativities, prescribed heads at boundaries, retardation coefficients and mass sources. The derivatives of the objective function with respect to log conductivity are the most cumbersome and need the most CPU-time to be evaluated. For this reason, to compute this derivative only advective transport is considered. The gradient is calculated by the adjoint-state method. The method is demonstrated in a controlled, synthetic study, in which the worth of concentration data is analysed. It is shown that concentration data are essential to improve transport predictions and also help to improve aquifer characterisation and flow predictions, especially in the upstream part of the aquifer, even in the case that a considerable amount of other experimental data like conductivities and heads are available. Besides, conditioning to concentration data reduces the ensemble variances of estimated transmissivity, hydraulic head and concentration.     

Application of Electromagnetic Logging to Contamination Investigations in Glacial Sand-and-Gravel Aquifers

Electromagnetic (EM) logging provides an efficient method for high-resolution, vertical delineation of electrically conductive contamination in glacial sand-and-gravel aquifers. LM. gamma, and lithologic logs and specific conductance data from sand-and-gravel aquifers at five sites in the northeastern United States were analyzed to define the relation of KM conductivity to aquifer lithology and water quality. Municipal waste disposal, septic waste discharge, or highway deicing salt application at these sites has caused contaminant plumes in which the dissolved solids concentration and specific conductance of ground water exceed background levels by as much as 10 to 20 limes.
The major hydrogeologic factors that affected KM log response at the five sites were the dissolved solids concentration of the ground water and the silt and clay content in the aquifer. KM conductivity of sand and gravel with uncontaminated water ranged from less than 5 to about 10 millisiemens per meter (mS/m); that of silt and clay zones ranged from about 15 to 45 mS/m: and that of the more highly contaminated zones in sand and gravel ranged from about 10 to more than 80 mS/m. Specific conductance of water samples from screened intervals in sand and gravel at selected monitoring well installations was significantly correlated with KM conductivity.
CM logging can be used in glacial sand-and-gravel aquifer investigations to (1) determine optimum depths for the placement of monitoring well screens: (2) provide a nearly continuous vertical profile of specific conductance to complement depth-specific water quality samples; and (3) identify temporal changes in water quality through sequential logging. Detailed lithologic or gamma logs, preferably both, need to be collected along with the F.M logs to define zones in which elevated EM conductivity is caused by the presence of sill and clay beds rather than contamination.     

Scale effect and calibration of contaminant transport models

The influence on solute transport of the small-scale spatial variation of aquifer hydraulic conductivity (K) was analyzed by comparing results from fine-grid (2 m by 2 m) simulations of a synthetic heterogeneous aquifer to those from coarse-grid (8 m by 4 m) simulations of an equivalent homogeneous aquifer. Realizations of the K field of the heterogeneous aquifer were generated, using the Monte Carlo approach, from a lognormal distribution with mean log K of 2 (K in m/d) and three levels of log K variance of 0.1, 0.5, and 1.0. Numerical simulation results show that the average standard deviation of point concentrations increased from 1.21 to 5.78 when the value of log K variance was increased from 0.1 to 1.0. The average discrepancy between modeled concentrations (obtained from a coarse-grid deterministic numerical simulation) and the actual mean point concentrations (obtained from fine-grid Monte Carlo numerical simulations) increased from 0.91 to 4.23 with the increase in log K variance. The results from this study illustrate the uncertainty in predictions from contaminant transport models due to their inability to simulate the effects of heterogeneities at scales smaller than the model grid.