Computational Geomechanics at MOX
The CompGeo group of the MOX Laboratory gathers researchers in numerical analysis and statistics with the purpose of studying the complex coupled problems related to flow and deformation in the subsurface at different time and space scales, with a focus on energy and risk assessment.
We are investigating geomechanical problems in the presence of faults. We suppose that the physical model consists of two parts: the solid component representing the crust porous material, and the fluid component that represents water and, eventually, oil and/or gas. The solid model is then augmented taking into account the faults, which are, in fact, discontinuities in the volume of rock.
In the last decades, different numerical methods have been employed to describe the state of stress near a fault discontinuity in geomechanical models. The main goals of these methods are to assess the stress build-up and stress release near faults when the pore pressure is perturbed. In particular, we focus on the following challenges:
- the numerical description of the faults as discontinuity surfaces, and the numerical techniques aiming to embed the fault models into the solid equation;
the numerical coupling between the heterogeneous fluid system and porous material equation of the solid component.
Evolution of sedimentary basins
Reconstructing the thermo-mechanical history of a sedimentary basin is a challenging problem in geosciences, but of paramount importance in petroleum engineering.
The post-glacial rebound is mainly affected by the viscosity of the mantle beneath the crust, resulting in a non-local interaction that can be studied only on planet scale. The simulation of this process provides the kinematics of the full basin, giving information about isostatic movements and tilting, that can result in depletion of reservoir.
On the other side, the detailed thermo-mechanical response of a sedimentary basin provides information about hydrocarbon generation and it can be described only locally. This process is the consequence of more complex multi-physics phenomena involving mechanical, geochemical, thermal, geophysical and geological aspects: the pore fluid pressure affects stress, stress changes can lead to fracturing, and fracturing can affect pore fluid pressure.
The coupling of these two models is not trivial but it provides a proper framework for the study of the evolution of sedimentary basins.
Flow in fractured porous media
Subsurface flows are strongly influenced by the presence of fractures. While small and micro-fractures can be easily accounted for changing the permeability tensor, large fractures and faults play a more complex role, acting as paths or barriers for the flow. Their effects are very relevant for many applications such as oil migration, oil recovery, CO2 storage and groundwater contamination and remediation.
The simulation of fractured porous media poses several mathematical and numerical challenges. First of all we need to couple flow and transport in fractures and in the surrounding porous matrix with suitable conditions. Moreover, these two media are characterized by different space scales and velocities. Finally, in realistic cases the construction of a good mesh is a challenging task: for this reason we are studying methods (such as XFEM) that can represent discontinuities avoiding geometric conformity.
Part of the research activity of the CompGeo group at MOX is devoted to the study of seismic wave propagation in complex heterogeneous media. Nowadays, the use of numerical simulations to study the ground motion induced by earthquakes is becoming a normal practice for seismic hazard assessment purposes.
Main focus of the research is the development of geometrically flexible, high order accurate and highly scalable numerical methods for the simulation of earthquake dynamics. Firstly, geometric flexibility is required since the computational domain usually features complicated geometrical shapes as well as sharp media contrasts. Secondly, high order accuracy is needed to well represent the wave propagation field for all periods of interest. Finally, high scalability is mandatory in order to obtain, with reasonable computing efforts, plausible realizations of realistic earthquakes.
This research work has lead to the development of SPEED, an open-source code aims at simulating large-scale seismic events in three-dimensional complex media.