Minimal research has been conducted to examine dissolution and remediation of NAPL located in lower-permeability (K) media. The purpose of this research was to investigate dissolution of non-uniformly distributed residual NAPL located in lower-K media and how mass transfer was affected. Additionally, in situ chemical oxidation (ISCO) effectiveness using KMnO₄ in the laboratory and field was examined. A series of column and flow cell experiments were conducted with trichloroethene (TCE). For uniformly distributed residual NAPL control experiments, reduced interfacial pool area and resonance time were likely the most important mass transfer limitation. For non-uniformly distributed residual NAPL, by-pass flow attributed to reduced effective permeability was initially the most important factor affecting nonideal mass transfer. Dissolution times increased with physical heterogeneity due to bypass flow. Mass transfer was more non-ideal for non-uniformly distributed NAPL. Nonideal mass transfer was most pronounced for non-uniformly distributed NAPL in lower-K zones. NAPL location influences dissolution behavior and ultimately remediation. Mass flux reduction versus mass reduction comparisons for the experiments exhibited how mass transfer trends vary between systems. The effectiveness of KMnO₄ ISCO of residual TCE located in lower-K media was examined. KMnO₄ solution was flushed through a flow cell followed by water flushing to evaluate long-term mass flux behavior, which was then compared to a water-flush control. For water flushing following KMnO₄ flushing, mass flux was similar to the control experiment. However, since contaminant mass was reduced, the number of pore volumes required for complete TCE removal via water flushing was estimated to be reduced by half. 1,1-Dichloroethene (DCE) is thought to be located in lower permeability strata adjacent to the water table at the Samsonite Building Area. Eight injection wells were emplaced in the source zone area, with well screens spanning the vadose and saturated zones, and injected with ~250 kg of 1.7% KMnO₄ solution. Bench-scale studies using core material determined that DCE was readily degraded by KMnO₄, even at lower reagent concentrations (< 1 mM). The natural oxidant demand was determined to be 1.0 x 10⁻⁵ g of KMnO₄/g of sediment. Aqueous DCE levels dropped below detection after KMnO₄ solution was present.

The goal of optimal transport is to map a source probability measure to a destination one with the minimum possible cost. However, the optimal mapping might not be feasible under some practical constraints. One such example is to realize a transport mapping through an information bottleneck. As the optimal mapping may induce infinite mutual information between the source and the destination, the existence of an information bottleneck forces one to resort to some suboptimal mappings. Investigating this type of constrained optimal transport problems is clearly of both theoretical significance and practical interest. In this work, we substantiate a particular form of constrained optimal transport in the context of quantum-to-classical systems by establishing an Output-Constrained Rate-Distortion Theorem similar to the classical case introduced by Yuksel et al. This theorem develops a noiseless communication channel and finds the least required transmission rate R and common randomness Rc to transport a sufficiently large block of n i.i.d. source quantum states, to samples forming a perfectly i.i.d. classical destination distribution, while maintaining the distortion between them. The coding theorem provides operational meanings to the problem of Rate-Limited Optimal Transport, which finds the optimal transportation from source to destination subject to the rate constraints on transmission and common randomness. We further provide an analytical evaluation of the quantum-to-classical rate-limited optimal transportation cost for the case of qubit source state and Bernoulli output distributions with unlimited common randomness. The evaluation results in a transcendental system of equations whose solution provides the rate-distortion curve of the transportation protocol. We further extend this theorem to continuous-variable quantum systems by employing a clipping and quantization argument and using our discrete coding theorem. Moreover, we derive an analytical solution for rate-limited Wasserstein distance of 2nd order for Gaussian quantum systems with Gaussian output distribution. We also provide a Gaussian optimality theorem for the case of unlimited common randomness, showing that Gaussian measurement optimizes the rate in a system with Gaussian source and destination. / Thesis / Doctor of Philosophy (PhD) / We establish a coding theorem for rate-limited quantum-classical optimal transport systems with limited classical common randomness. The coding theorem, referred to as the output-constrained rate-distortion theorem, characterizes the rate region of measurement protocols on a product quantum source state for faithful construction of a given classical destination distribution while maintaining the source-destination distortion below a prescribed threshold with respect to a general distortion observable. This theorem provides a solution to the problem of rate-limited optimal transport, which aims to find the optimal cost of transforming a source quantum state to a destination distribution via a measurement channel with a limited classical communication rate. The coding theorem is further extended to cover Bosonic continuous-variable quantum systems. The analytical evaluation is provided for the case of a qubit measurement system with unlimited common randomness, as well as the case of Gaussian quantum systems.