The future of stochastic and upscaling methods in hydrogeology
Geological formations are complex features resulting from geological, mechanical, and physico-chemical processes occurring over a very wide range of length scales and time scales. Transport phenomena ranging from the molecular scale to several hundreds of kilometers may influence the overall behavior of fluid flow in these formations. Heterogeneities that cover a large range of spatial scales play an essential role to channel fluid-flows, especially when they are coupled with non-linearities inherent to transport processes in porous media. These issues have considerable practical importance in groundwater management, and in the oil industry, particularly in solving new problems posed by projects concerned with the trapping of CO2 in the subsurface. In order to manage this complexity, one must be able to prioritize the respective influences of various relevant geological and physico-chemical phenomena occurring at several ranges of length and time scales as well as understand and use the increasingly rich and complex geostatistical models to provide realistic simulations of subsurface conditions. Multiscale simulation of fluid transport in these formations should help engineers to focus on the crucial phenomena that control the flow. This provides a natural framework to integrate data, to solve inverse problems involving large amounts of data, resulting in a reduction of the uncertainties of the subsurface description that must be evaluated. This allows in turn the making of more relevant practical decisions. In this paper, some perspectives on the development of upscaling approaches are presented, highlighting some recent multiscale concepts, discarding the fractured media case. Upscaling can be used as a useful framework to simultaneously manage scale-dependant problems, stochastic approaches and inverse problems. Actual and potential applications of upscaling to the elaboration of subsurface models constrained to observed data, and the management of uncertainties and sensitivity studies in a global multiscale framework is emphasized. In particular, upscaling can help in finding the parameters that control the overall behavior of the flow. Finally, upscaling approaches of non-linear transport equations appear as a new frontier in this area of research.