The Boundaries Influence in Trending Hydraulic Conductivity Fields

We analyze the impact of the boundary conditions on flow and transport solutions for the case of a two-dimensional heterogeneous medium with a linear trend in the mean log-conductivity. The influence of the boundaries is analyzed for different values of the domain size and aspect ratio, and different directions of the trend respect to the mean flow direction. The analysis involving a steady, spatially nonstationary velocity field, is developed by using the stochastic finite element method. Results of this study show that the impact of the trend in finite domains may disagree with that obtained in unbounded domains and it is more complex. The trend alters the result obtained for the medium with stationary conductivity, leading to a larger or smaller value of the macrodispersion coefficients, depending on the size and aspect ratio of the domain, and this effect may vary with the travel distance from the solute source. Moreover in limited domains here analyzed also for particles starting at distance of several integral scales from the boundaries and traveling in the middle of the domain, the behavior of macrodispersion coefficients is affected by the boundary conditions and the influence of the trend on longitudinal and transverse macrodispersion coefficients may vary with the imposed constraints.