## 1. Introduction

[2] Dense nonaqueous phase liquids (DNAPLs) present in the subsurface frequently persist as sources of long-term groundwater contamination. Even though DNAPL source zone remediation strategies have been the subject of extensive research to date, it remains a challenge to reliably predict the evolution of DNAPL source zones in the subsurface and the associated effect on downgradient effluent concentrations. Numerous studies have shown that source zone architecture has a strong impact on mass transfer from the DNAPL to the aqueous phase [*Christ et al*., 2006; *Fure et al*., 2006; *Lemke and Abriola*, 2006; *DiFilippo et al*., 2010]. As a result, uncertainties related to source zone spatial characteristics often hinder the accurate prediction of downstream concentrations. At the same time, the spatial evolution of the source zone itself is governed by the kinetics of mass transfer from the DNAPL to the aqueous phase (i.e., dissolution). Understanding the complex interplay between the DNAPL source zone architecture and the resulting effluent concentration is essential to addressing the problem of DNAPL source zone remediation.

[3] To date, the dissolution of DNAPLs has been studied under a wide variety of conditions, by both physical and numerical experiments and across most scales. It is well established that local equilibrium is often an invalid assumption, and that kinetic effects occur under most realistic conditions, when soil and source zone heterogeneity exist [*Unger et al*., 1998; *Maji and Sudicky*, 2008]. To capture these kinetic effects at the local, representative elementary volume (REV) scale, multiphase numerical simulators typically implement the single resistance, linear driving force model:

where *J* is the mass flux from the DNAPL to the water phase, *k _{la}* is the mass transfer coefficient,

*a*is the effective normalized interfacial area between the DNAPL and the water phase, is the effective solubility of the DNAPL, is the bulk aqueous phase concentration, and is the difference in concentration between the DNAPL-water interface and the bulk aqueous phase.

^{n}[4] To predict the dissolution flux using equation (1), interfacial area estimates are needed. Such estimates are also needed to experimentally determine *k _{la}*. In the absence of ways to measure interfacial areas, the traditional approach has been to lump the mass transfer coefficient and the interfacial area into a single coefficient , and then develop empirical correlations that relate system variables to the modified Sherwood number, , where

*d*is the mean particle diameter and is the molecular diffusion coefficient. Such correlations have been developed by many studies under a variety of experimental conditions [

_{m}*Miller et al*., 1990;

*Powers et al*., 1994b;

*Imhoff et al*., 1994;

*Saba and Illangasekare*, 2000;

*Nambi and Powers*, 2003]. However, because these correlations are specific to the system they were developed in, they can be reliably extrapolated to different systems only when calibrated. Without proper calibration, extrapolation can lead to significant errors [

*Powers et al*., 1992;

*Nambi and Powers*, 2003]. This is rather restricting, since most correlations were developed in homogeneous systems of low dimensionality, for simple, emplaced source zones, while they are typically needed for heterogeneous systems of high dimensionality and DNAPL source zones of complex architecture.

[5] The above problems can be overcome by separately considering the mass transfer coefficient, *k _{la}*, and the interfacial area,

*a*, when modeling dissolution. To predict

^{n}*k*,

_{la}*Pfannkuch*[1984] and

*Powers et al*. [1994a] developed empirical models that relate the Sherwood number to the aqueous phase velocity,

*v*. However, the validity of these

_{x}*k*models is uncertain, since they have not been sufficiently compared to experimental data, especially for complex DNAPL systems [

_{la}*Powers et al*., 1994a;

*Seagren et al*., 1999]. Validating

*k*models is complicated, because it requires interfacial area estimates. Existing studies have used interfacial area estimates based on idealized geometries of DNAPL pools or ganglia [

_{la}*Dekker and Abriola*, 2000;

*Rathfelder et al*., 2001]. While it is likely that such idealizations do not reflect the complexity of real DNAPL source zones, the impact of this simplification on predicting dissolution rates has not been quantified thus far in the literature.

[6] Alternatively, interfacial areas can be modeled using the thermodynamic theory [*Morrow*, 1970]. The thermodynamic theory for interfacial areas is based on the principle that work done during DNAPL drainage and imbitition translates to the formation or destruction of DNAPL-water interfaces. This explicitly links interfacial areas to capillary pressure-saturation constitutive relationships, and renders the thermodynamic model suitable for REV-scale multiphase models, without requiring geometric assumptions or parameter calibration. The thermodynamic interfacial area model has shown potential to provide accurate estimates of interfacial areas [*Dobson et al*., 2006; *Porter et al*., 2010]. Recently, the approach was modified to incorporate saturation history [*Grant and Gerhard*, 2007a], and was utilized successfully to predict effluent concentrations from a two-dimensional DNAPL source zone [*Grant and Gerhard*, 2007b]. However, this study was performed at a low hydraulic gradient, so that changes in mass transfer rates were only caused by interfacial area variations, while the mass transfer coefficient was constant. At higher velocities, the mass transfer coefficient depends on water velocities and is affected by relative permeability and flow bypassing effects. These effects result in more complex mass transfer dynamics, and prevail in aquifers with high hydraulic gradients or significant flow focusing. The extent to which these effects impact depletion rates, and ultimately, the remediation potential of complex DNAPL source zones is not yet clearly understood.

[7] In this study, we present the first evaluation of the thermodynamically based dissolution model at high velocities, for complex DNAPL source zones, in three-dimensional heterogeneous systems. The model is tested using the experimental data set of *Zhang et al*. [2008], that includes high resolution, three-dimensional, local DNAPL saturations, as well as average and local effluent concentrations, obtained from experimental flow cells. To simulate dissolution, the thermodynamic model for interfacial areas is combined with the *Pfannkuch* [1984] *k _{la}* model. DNAPL infiltration is modeled using hysteretic DNAPL infiltration-redistribution constitutive relationships. The models are implemented within the multiphase numerical model COMPSIM [

*Sleep and Sykes*, 1993], and simulations are performed without any parameter calibration, to evaluate the model's ability to predict dissolution based solely on soil properties and DNAPL release conditions, and for arbitrary source zone architectures. Upon validation of the model, the spatial and temporal variations of mass transfer rates are investigated and the controlling processes are identified. Finally, the results are compared to alternative models for both mass transfer coefficients and interfacial areas.