Linear Thermo-Poroelasticity and Geomechanics

Abstract

Most engineering applications estimate the deformation induced by loads by using the linear elasticity theory. The discretization process starts with the equilibrium equation and then develops a displacement formulation that employs the Hooke's law. Problems of practical interest encompass designing of large structures, buildings, subsurface deformation, etc. These applications require determining stresses to compare them with a given failure criteria. One often tackles this way a design or material strength type of problems. For instance, Geomechanics applications in the oil and gas industry assess the induced stresses changes that hydrocarbon production or the injection of fluids, i.e., artificial lift, in a reservoir produce in the surrounding rock mass. These studies often include reservoir compaction and subsidence that pose harmful and costly effects such as in wells casing, cap-rock stability, faults reactivation, and environmental issues as well. Estimating these stress-induced changes and their consequences require accurate elasticity simulations that are usually carried out through finite element (FE) simulations. Geomechanics implies that the flow in porous media simulation must be coupled with mechanics, which causes a substantial increase in CPU time and memory requirements.

A Reduced-Order Gauss-Newton Method for Nonlinear Problems Based on Compressed Sensing for PDE Applications

“…The Newton method for solving square nonlinear problems is one of the most popular techniques used in engineering applications due to its simplicity and fast convergence rate [1][2][3]. However, the quality of the final numerical results is affected by the possible Jacobian's singularity and high nonlinearity.…”

Model order reduction of coupled thermo-hydro-mechanical processes in geo-environmental applications

“…The pore pressure distribution is maximal closer to the glacier front's initial location as expected. The vertical displacement of the rock mass is negative under the glacier (compression) but exhibits positive values outside the glacier, indicating heaving which is typically observed with glacial loading [50]. The non-uniform temperature distribution under the glacier indicates that steady-state condition is not yet reached after 6000 years.…”

“…Despite being widely used in many engineering fields for several years, there are very few studies that explored model order reduction applications to coupled geomechanical problems (e.g. [22,50,87]). Due to the nature of model order reduction where applicability is problem-dependent such that an effective technique for one specific problem is not necessarily guaranteed to work for another problem, development of model reduction techniques that tackle time-dependent and nonlinear coupled systems is particularly challenging.…”

“…Despite being widely used in many engineering fields for several years, there are very few studies that explored model order reduction applications to coupled geomechanical problems [22,50,87]. Model reduction techniques aim at reducing the dimensionality of a system by projecting the reference full order model to a low-dimensional subspace while preserving key information up to an acceptable level of accuracy.…”