Evaluation of simplified mass transfer models to simulate the impacts of source zone architecture on nonaqueous phase liquid dissolution in heterogeneous porous media

Abstract

Nonaqueous phase liquid (NAPL) dissolution was studied in three-dimensional (3D) heterogeneous experimental aquifers (25.5 cm × 9 cm × 8.5 cm) with two different longitudinal correlation lengths (2.1 cm and 1.1 cm) and initial spill volumes (22.5 ml and 10.5 ml). Spatial and temporal distributions of NAPL during dissolution were measured using magnetic resonance imaging (MRI). At high NAPL spill volume, average effluent concentrations initially increased during dissolution, as NAPL pools transitioned to NAPL ganglia, and then decreased as the total NAPL–water interfacial area decreased over time. Experimental results were used to test six dissolution models: (i and ii) a one-dimensional (1D) model using either specific NAPL–water interfacial area values estimated from MR images at each time step (i.e., 1D quasi-steady state model), or an empirical mass transfer ( Sh′) correlation (i.e., 1D transient model), (iii and iv) a multiple analytical source superposition technique (MASST) using either the NAPL distribution determined from MR images at each time step (i.e., MASST steady state model), or the NAPL distribution determined from mass balance calculations (i.e., MASST transient model), (v) an equilibrium streamtube model, and (vi) a 3D grid-scale pool dissolution model (PDM) with a dispersive mass flux term. The 1D quasi-steady state model and 3D PDM captured effluent concentration values most closely, including some concentration fluctuations due to changes in the extent of flow reduction. The 1D transient, MASST steady state and transient, and streamtube models all showed a monotonic decrease in effluent concentration values over time, and the streamtube model was the most computationally efficient. Changes during dissolution of the effective NAPL–water interfacial area estimated from imaging data are similar to changes in effluent concentration values. The 1D steady state model incorporates estimates of the effective NAPL–water interfacial area directly at each time point; the 3D PDM does so indirectly through mass balance and a relative permeability function, which causes reduced water flow through high saturation NAPL regions. Hence, when model accuracy is required, the results indicate that a surrogate of this effective interfacial area is required. Approaches to include this surrogate in the MASST and streamtube models are recommended.