A lumped parameter approach to model the treatment of organic contaminants by a granular iron filled fracture

Zero-valent iron permeable reactive barriers (Fe0-PRBs) have been widely used in unconsolidated media to treat certain dissolved phase organic contaminants, but little attention has been given to their application in fractured porous media. In principle, it is possible to create a Fe0-PRB in a fractured porous medium by injecting an iron slurry mixture into the fracture network. This emplacement method likely results in a complicated system of incompletely iron filled fractures. To aid in the design and performance assessment of such complex systems, representative models must be used that capture the essence of the controlling processes; however, existing models cannot directly account for the complex processes dominating treatment in a partly iron-filled fracture at the required spatial scale. As a first step to address this need, we have developed a modelling approach for an idealized single partly iron filled fracture wherein the physical and chemical processes are represented by a first-order lumped rate parameter. The performance of the developed lumped rate parameter model was examined over a range of conditions by comparing simulation results to those produced by a more comprehensive analytical solution and a numerical model. While some deviations were observed, the lumped parameter model was shown to be valid for a range of iron grain sizes, iron layer thicknesses, open fracture apertures, flow velocities, and reaction rate coefficients. We also demonstrated that the developed lumped parameter approach can represent situations where the system is initially contaminated, and can be used to optimize the thickness of the iron layer. The advantage of this first-order lumped rate parameter model is that it can be used directly in existing discrete fracture models without modifications to their computational framework, and hence will make it possible to approximate the field-scale treatment performance of Fe0-PRBs in fractured porous media.