Simulating Dissolution of the Most Soluble Compounds from Complex NAPLs Using Equilibrium Partitioning
Michael J. Gefell and Deviyani Gurung Anchor QEA, LLC
Equilibrium partitioning simulations can be used to estimate the time required to deplete the most soluble components from complex NAPLs that contain a significant insoluble fraction.Figure 1 – Sketch of empirical sand tank model with dissolving coal tar NAPL zone (based on Eberhardt and Grathwohl 2002).
They measured dissolved concentrations of volatile organic compounds (VOCs) and polycyclic aromatic hydrocarbons (PAHs) on selected dates over a 354-day period at a monitoring well immediately downgradient from the NAPL zone. Aqueous concentrations remained at approximate effective solubility for an extended period (Figure 2). Naphthalene and indene had the highest initial effective solubility values, and their concentrations remained at approximate effective solubility until 120 and 50 water pore volume exchanges, respectively, were flushed through the NAPL zone. Subsequently, the concentrations for both compounds dropped by multiple orders of magnitude. Eberhardt and Grathwohl (2002) called the initial drop in concentration for each compound the arrival of the “dissolution front.”Figure 2 – MT3D model results (black solid and dashed lines) and empirical concentrations (red squares) for naphthalene (a) and indene (b) downgradient of coal tar NAPL zone. Solid line is model result with the initial Kd value calculated using Equation 1. Dashed line is model result with Kd and α optimized to match both datasets.
They presented an equation to calculate the delay, or retardation, of the dissolution front for a given compound relative to the water velocity within the NAPL zone based on the ratio of the mass of that compound in the NAPL versus its mass in the aqueous phase in the NAPL zone. Effective Distribution Coefficient Equating Eberhardt and Grathwohl’s retardation equation to the standard retardation equation for equilibrium partitioning to organic carbon leads to the following equation for an effective distribution coefficient that approximates mass transfer—to the aqueous phase from multicomponent NAPL containing a significant relatively insoluble fraction—for a specific soluble chemical (compound i) (Gefell and Gurung 2022; in press):Kd = (ρ0 fi,o n2 S0) / (ρb Ci,sat nc) (EQ-1)
where: Kd is the effective distribution coefficient [cm3/g], ρ0 is the NAPL density [g/cm3], fi,o is the mass fraction (not mole fraction) of compound i in NAPL [dimensionless], n is soil total porosity [dimensionless], S0 is the NAPL saturation (i.e., the fraction of the soil void space occupied by NAPL [dimensionless]), ρb is the soil dry bulk density [g/cm3], Ci,sat is the effective solubility for compound i (i.e., the equilibrium concentration of compound i dissolved in water in contact with NAPL [g/cm3]), and nc is the effective porosity in the NAPL zone (total porosity minus the NAPL-filled porosity) [dimensionless]. This approach assumes the NAPL undergoes little or no change other than the dissolution of the most soluble compounds from the NAPL. Numerical Modeling The effective Kd method was demonstrated using a one-dimensional numerical solute transport model (MT3D; Zheng 1990) with 100 cells representing a flowline through the center of the NAPL zone in Eberhardt and Grathwohl’s sand tank model. Each MT3D cell was a 1 cm cube. Simulations were performed for the most soluble PAH (naphthalene) and VOC (indene). Indene was selected rather than benzene because indene had a higher effective solubility, and the indene data were easier to extract from the published data graphs. Of the chemical components in the coal tar sample, naphthalene and indene represented only 15% of the total initial coal tar mass, but 76% of the total aqueous mass of all identified NAPL components in equilibrium with water. Most of the 30 identified NAPL components had initial effective solubilities orders of magnitude lower than those for naphthalene and indene. For each modeled compound, the initial aqueous concentration in the simulated NAPL zone (in the center of the numerical model grid) was set at the reported effective solubility value (Eberhardt and Grathwohl 2002). To represent the initial mass of each compound sorbed in the NAPL, Kd values were calculated using Equation 1 based on data presented by Eberhardt and Grathwohl 2002. Longitudinal dispersivity (α) was initially set equal to 5 cm, which is one-tenth of the NAPL zone width parallel to flow. The model was first run using the Kd values calculated using Equation 1. Then, for comparison, Kd and α were adjusted to optimize the model fit and evaluate the difference between the optimized Kd and the initial Kd estimate.Eberhardt, C., and P. Grathwohl, 2002. “Time scales of organic contaminant dissolution from complex source zones: coal tar pools vs. blobs.” Journal of Contaminant Hydrology 59:45‑66.
Gefell, M.J., and D. Gurung, 2022. “Predicting Multicomponent NAPL Dissolution Using an Equilibrium Partitioning Model, With Demonstration Using Empirical Data.” 2022 Northwest Remediation Conference (Tacoma, Washington); October 6, 2022. Available at: https://nwremediation.com/wp-content/uploads/2B_Gefell.pdf. Gefell, M.J., and D. Gurung, in press. “Modeling Dissolution of Soluble Compounds from Multi-Component NAPL Using a Desorption Approximation.” Accepted for publication in Groundwater.Shen, X., D. Lampert, S. Ogle, S., and D. Reible, 2018. “A software tool for simulating contaminant transport and remedial effectiveness in sediment environments.” Environmental Modelling & Software 109: 104-113.
Zheng, C., 1990. MT3D: A Modular Three-Dimensional Transport Model for Simulation of Advection, Dispersion, and Chemical Reaction of Contaminants in Groundwater Systems. S.S. Papadopulos & Associates, Inc. Rockville, Maryland. October 17, 1990.
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