Modeling of contaminant transport resulting from dissolution of nonaqueous phase liquid pools in saturated porous media

A mathematical model for transient contaminant transport resulting from the dissolution of a single component nonaqueous phase liquid (NAPL) pool in two-dimensional, saturated, homogeneous porous media was developed. An analytical solution was derived for a semi-infinite medium under local equilibrium conditions accounting for solvent decay. The solution was obtained by taking Laplace transforms to the equations with respect to time and Fourier transforms with respect to the longitudinal spatial coordinate. The analytical solution is given in terms of a single integral which is easily determined by numerical integration techniques. The model is applicable to both denser and lighter than water NAPL pools. The model successfully simulated responses of a 1,1,2-trichloroethane (TCA) pool at the bottom of a two-dimensional porous medium under controlled laboratory conditions.Notation a,a ₁ defined in (45a) and (45b), respectively - b defined in (45c) - b vector of true model parameters (n×1) - vector of estimated model parameters (n×1) - c liquid phase solute concentration (solute mass/liquid volume), M/L³ - c _s aqueous saturation concentration (solubility), M/L³ - C dimensionless liquid phase solute concentration, equal toc/c _s - molecular diffusion coefficient, L²/t - ^e effective molecular diffusion coefficient, equal to / ^*, L²/t - D _x longitudinal hydrodynamic dispersion coefficient, L²/t - D _z hydrodynamic dispersion coefficient in the vertical direction, L²/t - e random vector with zero mean (m×1) - erf[x] error function, equal to (2/ ^1/2) - f vector of fitting errors or residuals (m×1) - Fourier operator - _-1 Fourier inverse operator - g vector of model simulated data (m×1) - k mass transfer coefficient, L/t - average mass transfer coefficient, L/t - K _d partition or distribution coefficient (liquid volume/solids mass), L³/M - pool length, L - _o distance between the pool and the origin of the specified Cartesian coordinate system, L - Laplace operator - _-1 Laplace inverse operator - m number of observations - M Laplace/Fourier function defined in (38) - n number of model parameters - N Laplace/Fourier function defined in (39) - p defined in (46) - Pe _x Péclet number, equal toU _x /D _x - Pe _z Péclet number, equal toU _x /D _z - q defined in (47) - R retardation factor - s Laplace transform variable - S objective function - Sh local Sherwood number, equal tok/ _e - Sh _o overall Sherwood number, equal to l/ _e - t time,t - T dimensionless time, equal toU _x t/ - u dummy integration variable - u vector of independent variables - U _x average interstitial velocity, L/t - x spatial coordinate in the longitudinal direction, L - X dimensionless longitudinal length, equal to (x–)/ - y vector of observed data (m×1) - z spatial coordinate in the vertical direction, L - Z dimensionless vertical length, equal toz/ - Fourier transform variable - defined in (37) - defined in (50) - porosity (liquid volume/aquifer volume), L³/L³ - defined in (52a) and (52b), respectively - decay coefficient, t^–1 - dimensionless decay coefficient, equal to /U _x - bulk density of the solid matrix (solids mass/aquifer volume), M/L³ - dummy integration variable - ^* tortuosity     

Determination of radon distribution patterns in the upper soil as a tool for the localization of subsurface NAPL contamination

A radon survey was carried out at an abandoned military airfield, heavily contaminated with non-aqueous phase-liquids (NAPLs). Geo-statistical analysis of the data was used to confirm the validity of the chosen soil gas sampling pattern. The survey revealed a non-uniform distribution of the soil gas radon concentration in the upper soil in spite of a virtually homogenous geological situation. The radon distribution pattern showed minimum zones with radon concentrations decreased by up to 90% with regard to the local background level. The determined radon minimum anomalies could be explicitly associated with the NAPL subsurface contamination. The observed effect is due to the strong partitioning of radon into NAPLs from soil gas or groundwater. Corresponding partitioning coefficients were determined in the laboratory for some NAPL. As result of the study, it was shown that naturally occurring soil gas radon has the potential to be used as an indicator for the localization of subsurface NAPL contamination. As possible options for survey equipment, the AlphaGUARD radon monitor and passive solid-state nuclear track detectors were successfully evaluated.     

Diffusive Transport of Volatile Pollutants in Nonaqueous-Phase Liquid Contaminated Soil: A Fractal Model

Volatile organic chemicals from nonaqueous phase liquids trapped in soil spread quickly both into the atmosphere and the groundwater system, resulting in long-lasting pollution of the environment. The extent and speed of spread is strongly influenced by the heterogeneities present in the soil, which interact with the various mechanisms of transport in a complex manner. A semi-analytical model is presented to investigate the effect of soil-heterogeneities on the spreading of pollutants from a nonaqueous phase liquid trapped in a soil. Based on field evidence, soil heterogeneities are modeled as a self-similar fractal process, and diffusive transport of organic chemicals in such a substrate is studied. Various mechanisms of, and resistance to, transport of these contaminants are considered, and it is illustrated how each of these are altered by the presence of heterogeneities. More specifically, it is shown that, while the transport processes at early time are governed by volatilization and dissolution and are quite unaffected by the heterogeneities, the transport processes at late time are strongly dependent on the heterogeneities of the soil and its sorption characteristics. In addition, how failure to recognize these heterogeneities in the soil may result in unsuccessful design of appropriate remediation techniques is discussed.     

Acoustically Enhanced Ganglia Dissolution and Mobilization in a Monolayer of Glass Beads

A pore network consisting of a monolayer of glass beads was constructed for experimental investigation of the effects of acoustic waves on the dissolution and mobilization of perchloroethylene (PCE) ganglia. Dissolution experiments were conducted with acoustic wave frequencies ranging from 75 to 225 Hz at a constant pressure amplitude of 3.68 kPa applied to the inlet of the monolayer. Ganglia mobilization experiments were conducted with a constant acoustic wave frequency of 125 Hz and acoustic pressure amplitudes ranging from 0 to 39.07 kPa. Effluent dissolved PCE concentrations were observed to increase in the presence of acoustic waves with the greatest increase (over 300%) occurring at the lowest frequency employed (75 Hz). Acoustic waves were also observed to mobilize otherwise immobile PCE ganglia, break them apart, and further enhance dissolution.     

Role of NAPL Thermal Properties in the Effectiveness of Hot Water Flooding

Hot water flooding is a thermal nonaqueous phase liquid (NAPL) recovery technology originally developed in the petroleum industry that has recently been proposed for enhanced recovery of NAPLs in the contaminated subsurface. This technology, however, has received relatively little laboratory or numerical modeling investigation in the contaminant hydrology community. In this study the utility of flooding NAPL contaminated source zones at elevated water temperatures was investigated. Simulations were conducted using 16 different geostatistical representations of an actual field site. Two NAPLs were selected for this study—a light NAPL with hydraulic properties that have moderate temperature dependencies and a dense NAPL with significant viscosity temperature dependency. For these two NAPLs, flooding the source zone with water at elevated temperatures resulted in enhanced NAPL recovery. However, injection of hot water also resulted in accelerated downward movement of coal tar DNAPL due to the reduced viscosity at elevated temperatures. NAPL recovery was also dependent on the source zone architecture with greater NAPL mass recovery when the NAPL was localized in a small volume at high saturations. These results suggest that hot water flooding can significantly speed up the recovery of viscous NAPLs and, as such, is a powerful technique for the remediation of viscous NAPLs.     

Local Mass Transfer Correlations for Nonaqueous Phase Liquid Pool Dissolution in Saturated Porous Media

Local mass transfer correlations are developed to describe the rate of interface mass transfer of single component nonaqueous phase liquid (NAPL) pools in saturated subsurface formations. A threedimensional solute transport model is employed to compute local mass transfer coefficients from concentration gradients at the NAPL–water interface, assuming that the aqueous phase concentration along the NAPL–water interface is constant and equal to the solubility concentration. Furthermore, it is assumed that the porous medium is homogeneous, the interstitial fluid velocity steady and the dissolved solute may undergo firstorder decay or may sorb under local equilibrium conditions. Powerlaw expressions relating the local Sherwood number to appropriate local Peclet numbers are developed for both rectangular and elliptic/circular source geometries. The proposed power law correlations are fitted to numerically generated data and the correlation coefficients are determined using nonlinear least squares regression. The estimated correlation coefficients are found to be direct functions of the interstitial fluid velocity, pool dimensions, and pool geometry.     

On the Displacement of NAPL Lenses and Plumes in a Phreatic Aquifer

The movement of an LNAPL lens above a sloping or horizontal water table, and a DNAPL lens above an impermeable surface is discussed. The governing equations are derived, using the vertical equilibrium approach and assuming the water mobility to be much greater than that of the NAPL. Analytical solutions are obtained for onedimensional movement of a lens along a sloping water table. They describe the lens movement with the formation of a jump at the leading front (large-scale approximation), and the distribution of NAPL in the transition zone near the jump (smallscale approximation). A model,describing the movement of a lens, taking into account NAPL retention,is proposed. Approximate onedimensional solutions for the movement of a NAPL lens along sloping or horizontal surfaces under such conditions are presented for this model. Some approximate analytical solutions for twodimensional lens (plume) formation and movement are obtained for the case of a point source at a sloping surface.     

Regression and Dimensional Analysis for Modeling Two‐Phase Flow

Numerical models describing multiphase flow phenomena are typically used to predict the displacement of water during the infiltration of nonaqueous phase liquids (NAPLs) into a groundwater system. In this paper, the applicability of regression and dimensional analysis to develop simple tools to bypass these time consuming numerical simulations is assessed. In particular, the infiltration of NAPL through a vertical, homogeneous soil column initially saturated with water is quantified. Two output variables defining the extent of infiltration were considered – the elevation of the NAPL front and the volume of NAPL which had entered the system. Dimensional analysis was initially performed to identify dimensionless terms associated with the underlying relations between these two output variables and the input variables (independent variables and system parameters). Artificial neural network techniques were then employed to develop regression equations for approximating the input–output relationships over a given domain. Application of these equations illustrated the interrelationships among capillary, buoyancy, and viscous forces driving the NAPL infiltration process.     

Small-scale forward smouldering experiments for remediation of coal tar in inert media

This paper presents a series of experiments conducted to assess the potential of smouldering combustion as a novel technology for remediation of contaminated land by water-immiscible organic compounds. The results from a detailed study of the conditions under which a smouldering reaction propagates in sand embedded with coal tar are presented. The objective of the study is to provide further understanding of the governing mechanisms of smouldering combustion of liquids in porous media. A small-scale apparatus consisting of a 100-mm in diameter quartz cylinder arranged in an upward configuration was used for the experiments. Thermocouple measurements and visible digital imaging served to track and characterize the ignition and propagation of the smouldering reaction. These two diagnostics are combined here to provide valuable information on the development of the reaction front. Post-treatment analyses of the sand were used to assess the amount of coal tar remaining in the soil. Experiments explored a range of inlet airflows and fuel concentrations. The smouldering ignition of coal tar was achieved for all the conditions presented here and self-sustained propagation was established after the igniter was turned off. It was found that the combustion is oxygen limited and peak temperatures in the range 800–1080 °C were observed. The peak temperature increased with the airflow at the lower range of flows but decreased with airflow at the higher range of flows. Higher airflows were found to produce faster propagation. Higher fuel concentrations were found to produce higher peak temperatures and slower propagation. The measured mass removal of coal tar was above 99% for sand obtained from the core and 98% for sand in the periphery of the apparatus.     

Smoothed Particle Hydrodynamics Model of Non-Aqueous Phase Liquid Flow and Dissolution

A smoothed particle hydrodynamics model was developed to simulate the flow of mixtures of aqueous and non-aqueous phase liquids in porous media and the dissolution of the non-aqueous phase in the aqueous phase. The model was used to study the effects of pore-scale heterogeneity and anisotropy on the steady state dense non-aqueous phase liquid (DNAPL) saturation when gravity driven DNAPL displaces water from initially water saturated porous media. Pore-scale anisotropy was created by using co-oriented non-overlapping elliptically shaped grains to represent the porous media. After a steady state DNAPL saturation was reached, water was injected until a new steady state DNAPL saturation was reached. The amount of trapped DNAPL was found to be greater when DNAPL is displaced in the direction of the major axes of the soil grains than when it is displaced in the direction of the minor axes of the soil grains. The amount of trapped DNAPL was also found to increase with decreasing initial saturation of the continuous DNAPL phase. For the conditions used in our simulations, the saturation of the trapped DNAPL with a smaller initial DNAPL saturation was more than 3 times larger than the amount of trapped DNAPL with a larger initial saturation. These simulations were carried out assuming that the DNAPL did not dissolve in water. Simulations including the effect of dissolution of DNAPL in the aqueous phase were also performed, and effective (macroscopic) mass transfer coefficients were determined. The U.S. Government’s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.