Groundwater contamination by dense, non-aqueous phase liquids (DNAPLs) represents a major societal problem both within the United States and worldwide. Costly in situ remediation methods directed at the complete removal of contaminant mass from the subsurface have failed to provide a comprehensive solution to this problem thereby leading to recent, increased interest in an approach to remediation aimed at the reduction of downstream contaminant mass flux. Developing a quantitative understanding of the spatial distribution of DNAPL contamination in the source zone is critical to flux-based remediation and management strategies. Indeed, it has been shown that this source zone architecture is closely linked to downstream behavior of the plume. Unfortunately, the estimation of the source zone architecture is a very challenging inverse problem. We propose an approach to source zone characterization based on the joint, physics-based inversion of hydrological (down-gradient flux and concentration) and geophysical (electrical impedance tomography) data. Our processing approach addresses the ill-posed nature of this inverse problem by employing a novel representation of the source zone. Rather than using the limited data to recover a fine scale, pixilated representation of the spatial distribution of DNAPL, we parameterize the boundaries separating pools, ganglia, and non-contaminated regions. Algorithms are being developed to estimate this geometry along with the space-varying DNAPL saturation in the contaminated zones. Building on recent work in the image processing and computer vision fields, we employ a new form of parametric active contour models to describe the boundaries of the pool and ganglia regions. These models combine the topological flexibility of traditional level set ideas with the low order parametric representation associated with snakes. The performance of our approach is evaluated using an extensive suite of numerical simulations, as well as a set of laboratory-scale experiments. Simulations and experiments will explore (a) the accuracy and utility of Archie-type mixing rules for mapping geophysical to hydrological variables, and (b) the robustness of the method to un-modeled volumetric heterogeneities in both the electrical and hydrological properties of the subsurface. Intellectual Merit: Knowledge gained from this research will improve geometry-based methods for inversion by extending these concepts into hydrology. In addition to advancing the field of hydrology, our research will expand mathematical imaging through the development of new, shape-based methods for multi-modal inverse problems. This research also seeks to quantify the limits associated with using electrical impedance and hydrological data to characterize quasi-static DNAPL source-zone architecture. Broader impact: This project has potential to impact areas of basic science, engineering, and educational training. Proper identification of source zone architecture will provide guidance in designing and choosing appropriate remediation strategies. The methods developed in this project have the potential for application in fields such as earth sciences, medical imaging, and nondestructive evaluation, as the problem of extracting geometric information from highly heterogeneous data sources is widely encountered in all these areas.
The contamination of groundwater by dense, non-aqueous phase liquids (DNAPLs) such as perchloroethylene (PCE) and trichloroethene (TCE) used as industrial degreasers, as part of the dry cleaning process, etc. represents a major societal problem both within the United States and worldwide. Costly remediation methods directed at the complete removal of contaminant mass from the subsurface have failed to provide a comprehensive solution to this problem thereby leading to recent, increased interest in an approach to remediation aimed at the reduction of dissolved contaminant located downstream of the source zone, known as the downstream plume. Critical both to developing remediation strategies aimed at achieving either of these objectives and monitoring their progress is developing a quantitative understanding of the spatial distribution of DNAPL contamination existing at a site prior to remediation. Indeed, it has been shown that this source zone architecture is closely linked to downstream behavior of the dissolved plume. Unfortunately, the estimation of the source zone architecture is a very challenging problem. The current state of the art in this field is based on the use of costly, invasive partitioning inter-well tracer tests, which run the risk of mobilizing DNAPL and can fail to provide complete coverage of the source zone region. In this project, we have developed an approach to characterizing the source zone architecture based on tomographic ideas not too dissimilar to those underlying X-ray based CAT scans, but here adapted to a different set of sensing technologies. Specifically, we consider first data generated using a geophysical method known as Electrical Resistance Tomography (ERT) in which small electrical currents are put into the earth and the resulting voltages are measured at a number of distant locations. These data are sensitivity to the space varying electrical conductivity of the earth which in turn is impacted by the presence (or absence) of DNAPL. In addition to the ERT data we also assume that we have observations of DNAPL concentration collected along a transect downstream from the source zone. These data are related to the source zone contaminant via physical models describing the flow and transport of fluids (water and DNAPL) through the earth. As with X-ray CT or MRI, the goal of our work was to use these two, very different, data sets along with the physics of each to develop a "picture" of the source zone. Unlike CT or MRI where data can be collect all around an individual, here we are limited as to where we can perform ERT measurements and the hydrological data are collected only along one plane. As such, these data are not nearly as rich as can be found in a more typical medical problem and, in the presence of noise and unmodeled physical effect (of which there are many in this application), it is practically impossible to obtain a high resolution image of the subsurface. In a sense, there are too many pixels to be estimated from too little data. Knowing this, we consider an alternate form of the problem where, rather than looking to use the data to recover many, many pixels, we develop a model for the source zone in which the geometry of the region containing significant DNAPL can be described mathematically using relatively few parameters, a couple of hundred rather than tens of thousands of pixels. Using this model, we developed algorithms to estimate the shape-based parameters defining this geometry along with the space-varying DNAPL saturation in the contaminated zones from our multi-modal data set. The approach was demonstrated using realistically generated simulation data. To date it is the only method we know of that can perform such imaging in three dimensions using the exact physics of the two sensing modalities. In addition to this modeling work, the project also involved an experimental component. While ERT is useful, ultimately one would like to employ electrical impedance methods to characterize the structure of the subsurface at a variety of frequencies. It is anticipated that the resulting data would help to mitigate the challenges discussed previously concerning the lack of information in the observations. For this approach to be useful, we would need to know how the electrical properties of DNAPL change with frequency and saturation (i.e., the amount of DNAPL in the pore space of the earth). Technically, there are two such properties at each frequency known as the real and the imaginary part of the DNAPL conductivity. While prior work has pretty well established the relationship between the real conductivity and saturation, less is known about the imaginary part. Our work indicates that this imaginary component is more difficult to measure and exhibits a complex relationship to frequency as well as the state of the subsurface. Obtaining a clearer picture of these phenomena represent an important area of continued investigation for our group.
