Contaminant transport in sets of parallel finite fractures with fracture skins

Abstract

Analysis of flow and transport in double/dual-porosity or fractured formations is a problem with important theoretical and practical applications. We present steady-state and transient solutions for solute transport in a finite system of parallel fractures with fracture skins. Solute transport in the fractures is by advection and hydrodynamic dispersion. Concentrations are attenuated by diffusion into the porous matrix. Radioactive decay and sorption in the skin, the matrix, and along the fracture walls are included. Our analysis extends previous studies by considering both finite fracture lengths and the effects of fracture skins. Our results conform to these studies when considering large, but finite fractures without skins. For transient solutions, we use a numerical inversion of the Laplace transforms and also present a series solution. Steady-state solutions are closed form analytical solutions. The results of these analyses can be used for the verification of numerical models used in predicting or retrodicting flow and transport in fractured porous media and for sensitivity analyses. The steady-state analyses are shown to be satisfactory for sensitivity analyses. We utilize data for cesium-137 and from the Permian Brushy Canyon Sandstone of west Texas in the sensitivity analyses to show the effects of fracture skins. The analyses indicate increased distances of transport with thicker skins of lower porosity and lower diffusivity. Retardation effects were smaller in magnitude. Analysis of transport in dual-porosity systems should consider the effects of fracture skins because they are ubiquitous in nature and are present in many, if not most, hydraulically active near-surface fractures.