J. F. Sykes

Laboratory and model simulations of a LNAPL spill in a variably-saturated sand, 1. Laboratory experiment and image analysis techniques

Abstract A two-dimensional, multiphase flow experiment was conducted in the laboratory. The saturation distribution of a lighter than water non-aqueous-phase liquid (LNAPL) as it migrated through a variably-saturated sand medium was determined using image analysis techniques. The pressures in the water and LNAPL phases were measured using hydrophilic and hydrophobic porous cups connected to a series of pressure transducers and a data acquisition system. The LNAPL inflow and water outflow were also recorded. A series of capillary pressure-saturation experiments were conducted for each two-phase system. The capillary pressures recorded by the pressure transducers were used to calculate the pphase saturations based on a fully hysteretic capillary pressure-saturation algorithm. The static equilibrium capillary pressure-saturation relationships proved to be invalid immediately ahead of the LNAPL front. The capillary pressure-saturation relationship appeared to be dynamic for short periods of time as the LNAPL front arrived at each transducer location. The presence of an entrapped air phase as the LNAPL migrated through the unsaturated zone clearly affected the migration of the LNAPL and the maximum LNAPL saturation reached in the sand medium.

A numerical investigation into factors affecting gas and aqueous phase plumes in the subsurface

Abstract An investigation into the face and transport of volatile organic compounds (VOCs) in the subsurface requires the consideration of contaminant mass in both the aqueous and soil gas phases. As a result of water/gas phase partitioning, contaminated by partitioning from underlying ground water pollution. Conversely, soil gas can be contaminated by partitioning from underlying ground water VOC plumes. This soil gas and aqueous phase interaction has motivated the popularity of soil gas sampling technology as a method of characterizing ground water VOC contamination. A finite-element-based numerical model was developed to accurately simulate the interaction between the soil gas phase and the aqueous phase. This interaction is complicated since the saturation of the aqueous phase varies dramatically across the capillary fringe. The two-phase flow equations for gas and water are used to describe the flow regime, while the advective-dispersive transport of the VOC is considered in both phases. Dissolution and volatilization from a non-mobile non-aqueous phase liquid is included as a volatile organic contaminant source. A deforming mesh allows the model to accurately track the water table movement, and a Eularian-Lagrangian formulation is used to control some of the numerical difficulties associated with the numerical solution of the advection-dispersion equation. An investigation into diffusion of a VOC from below the water table demonstrated that both the frequency and the magnitude of water table fluctuations have a profound influence on the degree of soil gas contamination. Two-dimensional large-scale, long-term simulations were performed to estimate the aqueous and soil gas phase plumes resulting from an immobilized trichloroethylene residual located in the unsaturated zone. The simulation results indicate that these plumes are very sensitive to the vertical position of the contaminant source. In addition, it was determined that seasonal fluctuations in soil gas VOC concentrations are primarily controlled by temperature fluctuations, while ground water VOC concentration fluctuations are primarily a result of infiltration fluctuations.

The importance of fluid entrapment, saturation hysteresis and residual saturations on the distribution of a lighter-than-water non-aqueous phase liquid in a variably saturated sand medium

Abstract A two-dimensional, multiphase flow experiment was conducted in the laboratory and numerically modelled using a finite difference multiphase flow code. Heptane, a lighter-than-water non-aqueous phase liquid (LNAPL), was spilled on a variably saturated sand medium. After the spill was completed, the LNAPL was allowed to distribute itself above the capillary fringe. The water pressure at the base of the experimental box was subsequently raised and lowered on two separate occasions to simulate fluctuating water table conditions. The water and LNAPL pressures were measured using hydrophillic and hydrophobic porous cups connected to pressure transducers and a data acquisition system. The laboratory spill was modelled using a hysteretic and non-hysteretic multiphase flow code. A comparison of the experimental data to the model results illustrates the effects and importance of fluid entrapment and saturation hysteresis.

Laboratory and model simulations of a LNAPL spill in a variably-saturated sand, 2. Comparison of laboratory and model results

Abstract A two-dimensional, multiphase flow experiment was modelled using a finite-difference, multiphase flow and transport code. The laboratory experiment consisted of a lighter-than-water, non-aqueous-phase liquid (LNAPL) spill in a variably-saturated sand. The numerical model allows a non-hysteretic, a partially hysteretic and a fully hysteretic solution. The fully hysteretic algorithm accounts for fluid entrapment, saturation hysteresis and hysteresis in the relative permeability terms. The partially hysteretic model allows air-phase entrapment within the LNAPL as the LNAPL migrates through the unsaturated zone. The fully hysteretic model results were compared to the laboratory pressures and saturations. The importance of hysteresis is clearly illustrated; however, the inclusion of hysteresis substantially increases the computation and storage requirements. The partially hysteretic model predicts the movement of the LNAPL front relatively well but does not account for the hysteretic conditions which persist during the redistribution of the LNAPL after the spill was complete. The laboratory experiment was modelled using an implicit in pressure, explicit in saturation (IMPES) solution and a fully implicit solution. The fully hysteretic IMPES solution with two-point upstream weighting of the relative permeability terms resulted in the best representation of the experimental data for the model scenarios evaluated.

A composite L1 parameter estimator for model fitting in groundwater flow and solute transport simulation

This paper proposes a composite L1 parameter estimator to solve the inverse problems in groundwater flow and solute transport modeling. The estimator is formulated using a weighted L1 norm as the error measure between the vector of the observed hydraulic heads and solute concentrations and the corresponding vector of the heads and concentrations computed from a finite element model for steady state groundwater flow and solute transport in a two-dimensional areal confined aquifer system. The parameters currently considered are the hydraulic conductivities, the dispersivities, the porosities of the aquifer system, and the solute source concentration(s). The gradients of the state variables with respect to the parameters are computed analytically using a formulation stemming from the finite element model for the state variables. The solutions to two hypothetical groundwater parameter estimation problems are presented to illustrate that the proposed estimator does have the property of being fairly accurate and, more significantly, being robust in handling observation data containing certain outliers.

Stochastic simulations of NAPL mass transport in variably saturated heterogeneous porous media.

A multiphase flow and transport numerical model is developed to study the effects of porous media heterogeneities on residual NAPL mass partitioning and transport of dissolved and/or volatilized NAPL mass in variably saturated media. The results indicate the significance of porous media heterogeneity in influencing the mass transfer processes and NAPL transport in the subsurface. Among the parameters investigated in this study, the heterogeneity of the permeability field has the most significant influence on the NAPL mass partitioning and transport. In general, the heterogeneity of the porous media properties enhances the NAPL mass plume spreading in both the water phase and the gas phase while the influence on the water phase is much more significant. Overall, the porous media property heterogeneities tend to increase the accumulation of NAPL mass in the water phase. The nonequilibrium mass transfer processes result in the expected trend of decreasing the NAPL mass dissipation rate and causing long-term groundwater contamination.

Parameter identification and uncertainty analysis for variably saturated flow

Abstract This study investigates variably saturated groundwater flow in the vicinity of a sanitary landfill. A Conjugate gradient method with an objective function that includes both pressure terms and travel time terms is used for parameter identification. The uncertainty in calculated travel time is estimated using both a moment method and a Latin hypercube direct parameter sampling method. The adjoint operator technique is an important component of both the parameter identification procedure and the moment method uncertainty analysis.

Fitting a groundwater contaminant transport model by L1 and L2 parameter estimators

Abstract This paper presents a study on the use of linear and nonlinear L1-norm parameter estimators to fit an analytical groundwater contaminant transport model with nonuniform contaminant source distributions. The model solution is obtained as a superposition of an analytical solution developed by Cleary (Cleary, R.W., Analytical Models for Groundwater Pollution and Hydrology, 208 Long Island Groundwater Pollution Study, draft report, vol. 3, Princeton University, NJ, 1978). Comparisons with the commonly used linear and nonlinear L2-norm estimators are conducted. The posterior statistical inference theory by Nyquist (Nyquist, H., Commun. Statist.-Theor. Meth., 1983, 12, 2511-24) and Gonin and Money (Gonin, G. & Money, A.H., Commun. Statist.-Theor. Meth., 1985, 14, 827-40) is used to provide the posterior covariance matrix and the probability distribution for the unknown parameter vector. As the conclusion, it is suggested that in view of the nature of groundwater contaminant transport modeling, L1-norm estimators may be preferred as robust alternatives to L2-norm estimators in solving parameter estimation problems.

A moment method for calculating groundwater flow uncertainty: the analysis of a landfill.

The numerical analysis or modelling of groundwater flow and solute migration in support of remedial investigation studies or applications for the development of sanitary landfills is a multi-step process. In the first step, a conceptual model of the site is developed. This description delineates the spatial domain, designates the lithologic zones assigning preliminary values to the hydraulic conductivities and porosities and establishes the boundary condition configuration. Modelling is then used to evaluate the conceptual model; an important objective being the confirmation of the conceptual model description and parameter selection. For many groundwater studies, little or no modelling analyses are undertaken. It is assumed that the posed conceptual model is correct. When modelling is included in a remedial investigation study or landfill application, it is usually deterministic in nature; the techniques of parameter estimation and stochastic modelling as described in the literature are rarely used. Many hydro-geologists feel that these techniques are too theoretical for practical use. While this may be true for some methods, some uncertainty techniques can be applied to practical problems.

Parameter Identification and Uncertainty Analysis for Variably Saturated Flow

This study investigates variably saturated groundwater flow in the vicinity of a sanitary landfill. A Conjugate gradient method with an objective function that includes both pressure terms and travel time terms is used for parameter identification. The uncertainty in calculated travel time is estimated using both a moment method and a Latin hypercube direct parameter sampling method. The adjoint operator technique is an important component of both the parameter identification procedure and the moment method uncertainty analysis.