Wendy D. Graham

Field‐scale evaluation of in situ cosolvent flushing for enhanced aquifer remediation

A comprehensive, field-scale evaluation of in situ cosolvent flushing for enhanced remediation of nonaqueous phase liquid (NAPL)-contaminated aquifers was performed in a hydraulically isolated test cell (about 4.3 m × 3.6 m) constructed at a field site at Hill Air Force Base, Utah. This sand-gravel-cobble surficial aquifer, underlain by a deep clay confining unit at about 6 m below ground surface, was contaminated with a multicomponent NAPL as a result of jet fuel and chlorinated solvent disposal during the 1940s and 1950s. The water table within the test cell was raised to create a 1.5 m saturated flow zone that contained the NAPL smear zone. The cosolvent flushing test consisted of pumping about 40,000 L (approximately nine pore volumes) of a ternary cosolvent mixture (70% ethanol, 12% n-pentanol, and 18% water) through the test cell over a period of 10 days, followed by flushing with water for another 20 days. Several methods for assessing site remediation yielded consistent results, indicating that on the average >85% mass of the several target contaminants was removed as a result of the cosolvent flushing; NAPL constituent removal effectiveness was greater (90–99+%) in the upper 1-m zone, in comparison to about 70–80% in the bottom 0.5-m zone near the clay confining unit. Various interacting factors that control the hydrodynamic sweep efficiency, and the NAPL removal effectiveness during cosolvent flushing in this unconfined aquifer are discussed.

Solute Transport Through an Integrated Heterogeneous Soil‐Groundwater System

The coupled transport process through an integrated soil-groundwater system is quantified for kinetically sorbing solute that originates from a time dependent source at the soil surface and is transported by steady random velocity. The derived expressions of ensemble mean solute breakthrough at some arbitrary control plane normal to the mean flow direction involve probability density functions (pdfs) of advective solute travel time through the unsaturated and the saturated zone of the transport domain. A nonstationary travel time pdf is derived for the saturated zone, to account for possible effects of flow nonuniformity due to recharge of water from the unsaturated zone. Nonuniform mean flow in the saturated zone decreases the relative influence of spatial variability within that zone on the ensemble mean solute breakthrough curve. Factors such as the longitudinal extent of the solute source and the unsaturated zone variability become more important for the spreading of the expected solute breakthrough as the degree of flow nonuniformity in the saturated zone increases. This implies that possible far-field simplifications based on the assumption that the transport process in an integrated soil-groundwater system is dominated by the transport conditions in the saturated zone may not be valid in cases with significant groundwater recharge from the unsaturated zone.

Injection mode implications for solute transport in porous media: Analysis in a stochastic Lagrangian Framework

The effect of solute injection mode is examined in the stochastic-advective framework. For three-dimensional heterogeneous aquifers, uniform resident injection of solute results in nonlinear propagation of mass arrival time mean and variance with distance. Injection in flux results in a linear propagation of mean mass arrival time and mass arrival time variance that is both lower and appears to reach a linear regime more rapidly than uniform resident injection. Implementation of instantaneous injections for both modes as boundary conditions for mathematical and numerical models is discussed.

Solute transport through a heterogeneous coupled vadose-saturated zone system with temporally random rainfall

The transport of nonreactive solutes through a coupled, two-dimensional, randomly heterogeneous vadose-saturated zone system subject to temporally random rainfall is predicted by Monte Carlo simulation and compared with previously published analytic results for three different rainfall patterns. The relative contributions of the uncertain inputs (i.e., rainfall and saturated conductivity) to the prediction uncertainty of solute transport are quantified in terms of the statistical moments of the pore water velocity, the plume spatial moments, and solute flux breakthrough curves at downstream control planes. Results show that the mean and variance of the saturated zone pore water velocity were approximately equivalent for the cases of uniform and random rainfall and were well predicted by the analytical relationships developed by Rubin and Bellin [1994]. As a result, the mean plume displacement, estimated by the trajectory of the mean plume center of mass, was found to be nearly identical for these cases. In the temporally random rainfall case, the saturated zone mean plume experienced more spread in the direction of mean flow at early times. However, the asymptotic rates of spatial spreading of the mean solute plumes were found to be approximately equivalent for the uniform and random rainfall cases and well predicted by the approximate expressions for longitudinal macrodispersivity in nonuniform flow proposed by Destouni and Graham [1995]. Random rainfall and random soil properties increased prediction uncertainty of the solute plume behavior in the vadose zone by an order of magnitude when compared with the uniform rain and random soil case. This effect was reduced considerably when the solute entered the saturated zone, where random rainfall produced only slightly larger prediction uncertainty than the uniform rainfall case. The analytic model developed by Destouni and Graham [1995] accurately predicted the temporal breakthrough of the mean solute plume at saturated zone control planes for all cases, if transport through the unsaturated zone accounted for the effects of temporally random rainfall using the methodology developed by Foussereau et al. [2000a, 2000b]. Results of this work indicate that for the humid climates studied here, uncertain rainfall patterns dominate transport prediction uncertainty in the shallow unsaturated zone, while uncertain solute breakthrough to the saturated zone and uncertain hydraulic conductivity dominate prediction uncertainty in the saturated zone.

A stochastic model of solute transport in groundwater: Application to the Borden, Ontario, Tracer Test

Results from the Borden tracer test are used to evaluate the performance of the stochastic model developed by Graham and McLaughlin (1989a, b). The model assumes that spatial variations in hydraulic conductivity induce variations in a steady state velocity field which, in turn, induce variations in solute concentration. Analytical expressions for the unconditional ensemble moments of velocity are derived from the unconditional ensemble moments of log hydraulic conductivity. The velocity moments are related to the ensemble moments of concentration by a set of coupled partial differential equations. The dependent variables in these equations are the concentration mean and covariance and the velocity-concentration covariance (or macrodispersive flux). Macrodispersion is not assumed to be Fickian. The moment equations are solved with a dual-grid finite element algorithm. The nonstationary concentration covariances obtained from the finite element solution provide the information needed to condition estimates of velocity and concentration on a small set of concentration measurements. In the Borden application considered here conditioning is performed sequentially, at 85 days and at 260 days after the injection of a pulse of conservative tracer (chloride). The conditional mean concentration provides a better estimate of the true chloride concentration than the unconditional mean. The concentration variance and macrodispersive flux both decrease at conditioning times but gradually increase after the solute plume moves out of the sampling grid. The performance of the stochastic model, as indicated by an analysis of measurement residuals, is generally consistent with the models own estimates of concentration uncertainty.

Comparison of univariate and transfer function models of groundwater fluctuations

Seasonal autoregressive integrated moving average (SARIMA) univariate models and single input-single output transfer function (SARIMA with externalities or SARIMAX) models of groundwater head fluctuations are developed for 21 Upper Floridan aquifer observation wells in northeast Florida. These models incorporate empirical relationships between rainfall input and head response based on historical correlations and cross correlations between these two time series. The magnitude of the forecast error terms indicates that the SARIMA and SARIMAX models explain an average of 84–87% of the variation observed in the monthly piezometric head levels for 1-month lead forecasts. Thus the models account for the dominant processes which affect temporal groundwater fluctuations. Both the SARIMA and SARIMAX models provide unbiased forecasts of piezometric head levels; however, the SARIMAX models produce more accurate forecasts (i.e., smaller forecast probability limits) than the SARIMA models, particularly as lead time increases. Modeling efforts reveal consistent model structures over the study region, with local hydrologic and geologic conditions causing site-specific variability in the time series model parameters.

Optimal estimation of residual non–aqueous phase liquid saturations using partitioning tracer concentration data

Stochastic methods are applied to the analysis of partitioning and nonpartitioning tracer breakthrough data to obtain optimal estimates of the spatial distribution of subsurface residual non–aqueous phase liquid (NAPL). Uncertainty in the transport of the partitioning tracer is assumed to result from small-scale spatial variations in a steady state velocity field as well as spatial variations in NAPL saturation. In contrast, uncertainty in the transport of the nonpartitioning tracer is assumed to be due solely to the velocity variations. Partial differential equations for the covariances and cross cpvariances between the partitioning tracer temporal moments, nonpartitioning tracer temporal moments, residual NAPL saturation, pore water velocity, and hydraulic conductivity fields are derived assuming steady flow in an infinite domain [Gelhar, 1993] and the advection-dispersion equation for temporal moment transport [Harvey and Gorelick, 1995]. These equations are solved using a finite difference technique. The resulting covariance matrices are incorporated into a conditioning algorithm which provides optimal estimates of the tracer temporal moments, residual NAPL saturation, pore water velocity, and hydraulic conductivity fields given available measurements of any of these random fields. The algorithm was tested on a synthetically generated data set, patterned after the partitioning tracer test conducted at Hill AFB by Annable et al. [1997]. Results show that the algorithm successfully estimates major features of the random NAPL distribution. The performance of the algorithm, as indicated by analysis of the “true” estimation errors, is consistent with the theoretical estimation errors predicted by the conditioning algorithm.

Stochastic analysis of transport in unsaturated heterogeneous soils uder transient flow regimes

Approximate analytic solutions are developed to predict the transport of inert solutes in variably saturated, randomly heterogeneous porous media subject to a random boundary flux condition. The mean and variance of solute mass flux past a series of vadose zone control planes are determined using a Lagrangian approach. The method requires the specification of an advective travel time probability density function (pdf) between the soil surface and the control planes and an impulse response function which quantifies the specific flow and transport processes that affect the solute along an individual streamline in the soil. In this study an advective-dispersive impulse response function for inert solute is assumed, and an advective travel time pdf is derived from the statistics of the boundary flux and soil properties using a one-dimensional transient vadose zone flow model [Foussereau et al., this issue]. Monte Carlo simulations are conducted using random boundary flux sequences and spatially correlated random hydraulic conductivity fields in a multidimensional variably saturated flow and transport code to test the analytic model assumptions. The analytic model accurately predicts the ensemble mean solute flux breakthrough curves for a variety of soil-climate combinations. The general behavior of the coefficient of variation of solute flux is also accurately reproduced; however, the minimum coefficient of variation at the mean center of mass was slightly underpredicted in most cases. Results show that for shallow soils in humid climates, boundary flux variability dominates soil variability in determining the uncertainty of solute transport predictions in the vadose zone.

Evaluation of in situ cosolvent flushing dynamics using a network of spatially distributed multilevel samplers

A network of multilevel samplers was used to evaluate the spatial patterns in contaminant extraction during an in situ cosolvent flushing field test. The study was conducted in an isolation test cell installed in a fuel contaminated site at Hill Air Force Base, Utah. Partitioning tracer tests, conducted before and after the cosolvent flush, were used to estimate the spatial distribution of nonaqueous phase liquids (NAPL) and the effectiveness of cosolvent flushing for removing NAPL. Samples collected during the cosolvent flushing test were used to visualize the extraction process. The results of these two analyses showed similar spatial trends in mass removal and were in general agreement with observations based on soil core data. In general, the cosolvents were more effective in the upper portion of the flow domain and had slightly lower mass removal effectiveness in the lower portion of the flow domain. In this region, tracers indicated slower transport rates and higher NAPL saturations. The spatial analysis also indicated that cosolvent was trapped in the capillary fringe increasing the time required to displace the cosolvent from the aquifer. These results demonstrate the value of spatial information for performance assessment and improving in situ flushing design strategies.

Stochastic analysis of transient flow in unsaturated heterogeneous soils

A stochastic unsaturated water flow model is developed for heterogeneous soils subject to a transient flow regime. Equations are developed for a fully three-dimensional soil profile, and results are presented for an example one-dimensional problem. The model predicts the mean and covariance of the soil water content, Darcys flux, and pore water velocity as a function of the boundary flux and saturated hydraulic conductivity statistics. The statistics of the pore water velocity can be used to predict solute transport in soils, as shown by Foussereau et al. [this issue]. Approximate flow-related moment equations are solved analytically in the Laplace domain. Then, the analytical results are numerically inverted using a modified fast Fourier transform algorithm. The model predictions are compared to results obtained from Monte Carlo simulations for two different boundary flux patterns characteristic of humid climates and two different soil types (a fine sand and a sandy loam). Comparing the approximate solutions of the statistical moments to the outputs of the Monte Carlo simulations shows (1) the dominance of the boundary flux variability over that of the saturated conductivity on the overall prediction uncertainty, particularly at shallow depths, and (2) the good performance of the stochastic unsaturated flow model, particularly for fine-textured soils subject to boundary fluxes with coefficients of variation up to ∼1.5. As the boundary flux coefficient of variation increases and the soil becomes coarser, the model performance deteriorates because the flow system becomes significantly more nonlinear.