Coupled simulation of faulted porous media

Abstract : Poromechanical models are currently of common use in a number of engineering applications, including the management of deep hydrocarbon reservoirs, used for both production and storage purposes, and the exploitation of groundwater resources from shallow multi-aquifer systems. Recently, an increasing interest is set at introducing discontinuity surfaces in the numerical models to simulate the mechanics of geological faults. For instance, such an activity is of paramount importance for ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids.
The stable numerical modelling of coupled poromechanics and the ground rupture formation, however, is still a challenging task because of several issues, namely: (1) the pore pressure numerical instability, (2) the strong non-linearity induced by the fault activation, (3) the large number of unknowns, and (4) the severe ill-conditioning of the discrete problem. A number of different approaches have been proposed in recent years to alleviate such difficulties. Among them, Mixed Finite Element formulations of coupled poromechanics and the use of Lagrange multipliers to prescribe the contact constraints on the fault surfaces can help alleviate the numerical oscillations and provide a mass-conservative approach, but typically give rise to very large and ill-conditioned systems of algebraic equations.
In the present work, the mathematical weak formulation of the problem is modified in order to take into account the frictional energy along the activated fault portion according to the principle of maximum plastic dissipation. This helps providing stable solutions with a fast convergence of the non-linear fault problem. Moreover, a novel class of efficient block preconditioners is developed with the aim of accelerating the convergence of Krylov subspace methods in complex real-world applications. The main idea relies on building cheap and effective approximations of the two-level Schur complement using a physics-based approach. A purely algebraic formulation is also advanced, thus allowing for the extension to different kinds of coupled multi-physics problems.
Applications of the proposed approach are presented in problems related to the generation of ground fractures due to groundwater withdrawal in arid regions, fault reactivation in active hydrocarbon reservoirs, and the exploitation of groundwater resources from a regional multi-aquifer system.

Bio : Massimiliano Ferronato got the Degree in Civil Engineering at the University of Padova (Italy) in 1998 and the PhD in Numerical Geomechanics at the Technology University of Delft (The Netherlands) in 2003. Currently, he is Associate Professor at the Department of Civil, Environmental and Architectural Engineering of the University of Padova, with teaching duties in the Numerical Methods classes.
He has authored and co-authored more than 150 scientific papers published in international journals, books and proceedings of international conferences, and delivered invited talks and lectures in several renowned symposia. The main scientific interests concern the numerical solution of the partial differential equations governing the mechanics of saturated and partially saturated porous media, with engineering applications in the field of subsurface hydrology and petroleum engineering. He has been involved in a number of projects related to the numerical simulation of the geomechanical behavior of deep producing reservoirs, geological formations used for storage purposes, e.g., CO2 sequestration, and shallow multi-aquifer systems, including the analysis of fault activation, fissure generation, failure risk and land subsidence. The main scientific contributions concern the development and implementation of efficient and robust numerical models, based on Finite Element, Mixed Finite Element and Finite Volume methods, for the simulation of geomechanical and fluid-dynamical processes in the subsurface. Particular care is paid to the implementation of accurate iterative solvers for the linear systems arising from such applications. He is the co-author of a number of original algorithms for both sequential and parallel computational architectures, with the aim of accelerating the convergence and improving the robustness of iterative linear solvers.