Comparative analysis of analytical and numerical solutions for hydraulic properties upscaling in fractured media

The investigation of hydro-mechanical properties in rock formations is of utmost importance for several geological and engineering applications, e.g. for carbon-dioxide or hydrogen underground storage, exploitation of groundwater, geothermal or oil and gas reservoirs, hydrothermal ore deposits, and the mechanics of earthquakes. In particular, modeling fluid flow into networks of discontinuities (i.e. faults and fractures) is a key task in all these studies. Due to the high complexity of such processes, involving a significant number of feedbacks and occurring at different spatial and time scales, the achievement of a satisfying representation of the physical problem remains a challenge.

In the last decades, a variety of modeling approaches have been proposed in literature, accounting for different orders of complexity and using several computational methods. Analytical solutions are commonly based on simplistic assumptions about the process, allowing for simple fracture geometries and/or implying incompressible Newtonian fluids; as well as about the medium, considered elastic and permeable (or impermeable). Nevertheless, these solutions are still widely employed, as they provide significantly quick, first-order solutions compared to more sophisticated approaches.

On the other hand numerical models, typically accounting for a higher number of parameters and concurrent effects, are expected to return more realistic solutions. Those based on Finite Element Methods (FEMs) or similarly discretized domains, for example, permit to model the fractured rock mass with information that can be inferred from geological surveys and geophysical techniques.

As anticipated, important limitations in the use of more advanced modeling approaches could be the computing time and model size or resolution, not always allowing for cost-efficient solutions. In this study, we aim at a comprehensive review and benchmarking of the main classes of existing methods, comparing their results obtained for an identical dataset. In this way, we are able to highlight the advantages and disadvantages of each technique, defining the differences in accuracy and the ranges of applicability of these methods. 

The outcomes of our work are intended as a cross-benchmarking among available models, as well as a starting point for the future development of novel improved techniques in the field of fluid flows dynamics in networks of discontinuities.