Abstract
The impact of heterogeneities on solute transport in the subsurface has been the focus of intensive<br />research in recent years. Anomalous dispersion at the field-scale is partly attributed to physical nonequilibrium<br />effects such as solute transfer between different regions with highly contrasted characteristics<br />(permeability, porosity, ...).<br />With large-scale non-equilibrium effects, macroscopic miscible flow cannot be described using the<br />classical advective-dispersive transport equation. An up-scaling method must be used in order to take into<br />account the heterogeneities, and give a macroscopic representation of solute transport. This change of<br />scale problem has been treated theoretically by different up-scaling techniques, such as the method of<br />large-scale volume averaging. This method calculates the transport equations and the effective properties<br />at a given scale by an averaging process over the equations corresponding to the lower scale. In this way,<br />the large-scale properties are given explicitly from a local representation of heterogeneities through a set<br />of three closure problems. The resulting model is an extension of dual-porosity models, with the<br />capability of dealing with fully "mobile-mobile" systems. Several one-equation models are derived and<br />compared (asymptotic behavior, local equilibrium assumption, non-equilibrium case).<br />A numerical procedure is proposed to solve the closure problems for any geometry, and therefore<br />calculate the macroscopic transport coefficients. In order to test the two-equation model, theoretical<br />results are compared to numerical experiments in the case of stratified and nodular systems. Then, we<br />explore the possibility of using this two-medium treatment in connection with a geo-statistical<br />representation of the heterogeneities. Random stratified systems and bi-dimensionnal random media are<br />studied, the results show a reasonable agreement between theory and experiment.