资源环境科技发展态势分析平台

We present analytical solutions for transport with bimolecular reactions in a single fracture embedded within an infinite rock matrix. The fracture and matrix are initially assumed to contain one aqueous species (B) at a uniform concentration. A second aqueous species (A) is injected into the fracture and reacts with B and an additional immobile species (N) in the rock matrix. Under these conditions, moving reaction fronts form and propagate along the fracture and into the rock matrix. We employ a composite similarity variable involving two space variables to derive analytical solutions for all species concentrations and the geometry of reaction fronts in the fracture and matrix. The behavior of the reaction-diffusion equations in the rock matrix is posed as a Stefan problem. For uniform advection in the fracture, our analytical solutions establish that the reaction fronts propagate as the square root of time in both the matrix and the fracture. Our analytical solutions agree very well with numerical simulations. We extend our analytical solutions to nonuniform flows in the fracture by invoking a travel-time transformation. We present applications of our analytical solutions to in situ chemical oxidation of dense nonaqueous phase liquids in fractured rock, wherein an oxidant (A, e.g., permanganate) is injected through fractures and consumed by bimolecular reactions with dissolved dense nonaqueous phase liquids (B, e.g., trichloroethylene) and natural organic matter (N) in the fracture and rock matrix. Our analytical solutions are also relevant to a broad class of reactive transport problems in fracture-matrix systems where moving reaction fronts occur.

Plain Language Summary Contamination of groundwater by dense nonaqueous liquids (DNAPLs) is an important environmental concern, because many of these compounds are carcinogens. These chemicals sink through groundwater aquifers and fractured bedrocks and contaminate drinking water aquifers to significant depths. One class of fractured rock aquifers contaminated by DNAPLs is "old" contaminated sites, where entrapped DNAPL within fractures has dissolved over time into the stagnant water held within the rock matrix. Injection of oxidants (e.g., potassium permanganate) is expected to be effective in remediation of these sites, where oxidant is delivered through water circulated within fractures and diffuses out into the rock matrix, reacting with the dissolved DNAPL and eliminating the source. We developed simple mathematical expressions under realistic conditions for the rate of propagation of the reaction front in fracture-matrix system, which defines the boundary and volume of the remediated zone. Ahead of the front (outside the remediated zone), there is still contaminant to clean up, while the contaminant behind the front (in the remediated zone) has been reacted away. The thickness of matrix cleanup is shown to be proportional to the square root of time. These analytical solutions can be applied to design useful strategies for remediation of contaminated fractured rocks.