Block-effective dispersivity in heterogeneous media: Effects of porosity and distribution coefficient variability

The concept of block-effective dispersivity represents the difference between the classic macrodispersivity values and the dispersivity captured by the numerical grid. We use Monte Carlo simulations of flow and transport in two-dimensional random conductivity, porosity, and distribution coefficient fields to explore the influence of spatial variability on the block-effective dispersivity. Different correlation structures between porosity, distribution coefficient, and hydraulic conductivity are assumed,positive correlation, negative correlation, and no-correlation using random fields with exponential covariance. Different grid sizes are also simulated from very fine grids (grid-cell size is smaller than the correlation length) to coarse grid (grid-cell size is larger than the correlation length). Results suggest that it is important to examine the role of distribution coefficient and/or porosity variability, and the possible correlation between them in calculating block-effective dispersivity. When porosity and/or distribution coefficient is positively correlated with conductivity, block-effective longitudinal dispersivity is smaller than the case of random conductivity with constant variables while the block-effective transverse dispersivity is larger than the case of constant variables. The negative correlation case leads to the opposite results. When porosity and/or distribution coefficient is spatially variable but uncorrelated to the hydraulic conductivity, block-effective macrodispersivity is slightly different than the case of constant variables.