Block-effective Dispersivity in Heterogeneous Media: Effects of Porosity and Distribution Coefficient Variability

Abstract

Stochastic theories have been developed that linkThe concept of block-effective dispersivity the kinematics of dispersion to the spatial covariance of represents the difference between the classic hydraulic conductivity and derive formulas to calculate macrodispersivity values and the dispersivity captured the macrodispersivity as a function of time and travel by the numerical grid.We use Monte Carlo distance [1][2][3][4]. In these theories, the natural logarithm simulations offlow and transport in two-dimensional of hydraulic conductivity (ln K) is modeled as a random conductivity, porosity, and distribution random field; and the resulting macrodispersivities coefficient fields to explore the influence of spatial become functions of the statistical nature of the variability on the block-effective dispersivity. Diferent hydraulic conductivity distribution. correlation structures between porosity, distribution This macrodispersion is arising from the coefficient, and hydraulic conductivity are assumed; heterogeneous local-scale material structure.A positive correlation, negative correlation, and nofundamental assumption associated with the concept of correlation using random fields with exponential macrodispersion is that the velocity field is represented covariance. Different grid sizes are also simulated only through its expected value and that the from very fine grids (grid-cell size is smaller than the macrodispersivity tensor accounts for all the effects of correlation length) to coarse grid (grid-cell size is unmodeled spatial variability of the velocity field. On larger than the correlation length). Results suggest the other extreme, a detailed description of the velocity that it is important to examine the role of distribution field can be modeled with only a local dispersivity coefficient andlor porosity variability, and the possible value (in the order of the one measured in the lab).correlation between them in calculating block-effectiveThe latter approach has been extensively used in many dispersivity.When porosity andlor distribution large scale numerical simulations to validate the coefficient is positively correlated with conductivity, applicability of the stochastic theories. In this block-effective longitudinal dispersivity is smaller than approach, numerical models with grid-cell size (A) the case of random conductivity with constant smaller than the correlation scale of hydraulic variables while the block-effective transverse conductivity (A) are modeled to capture all the spatial dispersivity is larger than the case of constant variability of the velocity field [5][6][7][8]. Modeling the variables. The negative correlation case leads to the velocity field through a detailed description of the opposite results. When porosity andlor distribution hydraulic conductivity field and a local dispersivity coefficient is spatially variable but uncorrelated to the may be computationally intensive and an upscaled hydraulic conductivity, block-effective numerical grid with cells larger than the correlation ...