Connectivity metrics for subsurface flow and transport

Understanding the role of connectivity for the characterization of heterogeneous porous aquifers or reservoirs is a very active and new field of research. In that framework, connectivity metrics are becoming important tools to describe a reservoir. In this paper, we provide a review of the various metrics that were proposed so far, and we classify them in four main groups. We define first the static connectivity metrics which depend only on the connectivity structure of the parameter fields (hydraulic conductivity or geological facies). By contrast, dynamic connectivity metrics are related to physical processes such as flow or transport. The dynamic metrics depend on the problem configuration and on the specific physics that is considered. Most dynamic connectivity metrics are directly expressed as a function of an upscaled physical parameter describing the overall behavior of the media. Another important distinction is that connectivity metrics can either be global or localized. The global metrics are not related to a specific location while the localized metrics relate to one or several specific points in the field. Using these metrics to characterize a given aquifer requires the possibility to measure dynamic connectivity metrics in the field, to relate them with static connectivity metrics, and to constrain models with those information. Some tools are already available for these different steps and reviewed here, but they are not yet routinely integrated in practical applications. This is why new steps should be added in hydrogeological studies to infer the connectivity structure and to better constrain the models. These steps must include specific field methodologies, interpretation techniques, and modeling tools to provide more realistic and more reliable forecasts in a broad range of applications.