The scale dependence of dispersivity in multi-faces heterogeneous aquifer systems

Early work on stochastic modeling of the transport of inert solutes in porous media assumed that log conductivity could be characterized by a single, finite integral scale representing the spatial correlation of log conductivity. In this study, we focused on representing log conductivity across different scales so that the integral scale may be neither finite nor single valued. We characterize the scaling of the variance and correlation of log conductivity, and the macrodispersivity, through considering a multitude of field observations and scaling experiments. Based on a general composite covariance function of log conductivity in multi-faces sediments, we developed the macrodispersion coefficient equations for the solute transport in three-dimensional porous formations. Then we derived the longitudinal dispersivity to show the scale dependence of this parameter. With an example, the time evolution trends and the relative contributions of the auto- and cross-facies transition terms to the macrodispersion have been discussed. Sensitivity analysis indicates that the values of the longitudinal dispersion coefficient are positively correlated to facies mean length and the difference of the mean log conductivity between different facies. The longitudinal dispersivity coefficient also shows clearly a linear dependence on the composite variance of the log conductivity in the multi-facies sediments. The scientific results from this study provide a methodology to compute the effective dispersivity using aquifer structure and statistical parameters.