FLOW AND TRANSPORT IN BIMODAL HETEROGENEOUS FORMATIONS

A spatial correlation model is presented for the case of a spatially distributed, bimodal attribute. This model can be used for modeling the hydraulic conductivity in sand-shale or sand-clay formations or in fractured rocks, where the conductivities of the fractured and nonfractured rocks display dramatically different spatial structures. In the proposed model each of the modes is defined by a different multivariate probability density function and correlation scale. A length scale other than the one specified for each mode is used to characterize the relative distribution of the modes in space. Effective conductivity and transport parameters are then defined and analyzed. In developing the transport parameters our goal is to see the effects of the different scales and the different modes on transport. Unlike the case of a unimodal distribution, the macrodispersion is not a linear function of the total variance of the population, and the relative contributions of the variabilities of the different modes are determined by the ratios between the various length scales. We found that the effects of the large-scale variability on longitudinal spread become significant only after a large travel distance, but that its contribution to lateral spread occurs at a relatively early travel time.