G Hattori

Numerical Simulation of Fracking in Shale Rocks: Current State and Future Approaches

Extracting gas from shale rocks is one of the current engineering challenges but offers the prospect of cheap gas. Part of the development of an effective engineering solution for shale gas extraction in the future will be the availability of reliable and efficient methods of modelling the development of a fracture system, and the use of these models to guide operators in locating, drilling and pressurising wells. Numerous research papers have been dedicated to this problem, but the information is still incomplete, since a number of simplifications have been adopted such as the assumption of shale as an isotropic material. Recent works on shale characterisation have proved this assumption to be wrong. The anisotropy of shale depends significantly on the scale at which the problem is tackled (nano, micro or macroscale), suggesting that a multiscale model would be appropriate. Moreover, propagation of hydraulic fractures in such a complex medium can be difficult to model with current numerical discretisation methods. The crack propagation may not be unique, and crack branching can occur during the fracture extension. A number of natural fractures could exist in a shale deposit, so we are dealing with several cracks propagating at once over a considerable range of length scales. For all these reasons, the modelling of the fracking problem deserves considerable attention. The objective of this work is to present an overview of the hydraulic fracture of shale, introducing the most recent investigations concerning the anisotropy of shale rocks, then presenting some of the possible numerical methods that could be used to model the real fracking problem.

Damage identification in multifield materials using neural networks

Abstract Smart materials structures with multifield coupling properties have been widely used in the latter years. Some methodologies have been developed to study fracture problems in piezoelectric and magnetoelectroelastic (MEE) materials using the boundary element method (BEM). However, relatively limited attention has been paid to inverse problems. Identification problems are usually ill-conditioned, which implies that gradient search methods might not have a good performance, whilst Newton-based search methods are computationally expensive. Additionally, the presence of noise in the measured data affects the convergence of these methods. In this paper, we study the application of neural networks to damage identification of multifield materials, in particular to MEE materials. A particular training set division has been applied to improve the identification results, even for high noise levels. A hypersingular BEM is used to obtain the solution of the direct problem (elastic displacements and magnetic and electric potentials) and create the training set.

Influence of the main contact parameters in finite element analysis of elastic bodies in contact.

One of the key issues in solving contact problems is the correct choice of the contact parameters. The contact stiffness, the penetration limit and the contact algorithm are some of the parameters that have to be adjusted. There are no methodologies available in the literature for choosing the contact parameters, relying only on the user experience for this important task. In this work we investigate how the contact parameters behave in a commercial finite element analysis software. We will show that while the contact stiffness has great influence on the finite element analysis, other parameters will not affect it significantly. Some contact examples are shown to illustrate the performance of the contact parameters during the solution of a contact problem.

An Acceleration Approach for Fracture Problems in the Extended Boundary Element Method (XBEM) Framework

In this paper we investigate the use of the adaptive cross approximation (ACA) in the extended boundary element method (XBEM) framework. The proposed XBEM formulation is an implicit enrichment approach, where the stress intensity factors (SIF) are obtained with the displacements, eliminating the need of further post-processing to calculate these parameters. However, it is known that the boundary element formulation has drawbacks with respect to the matrix of the linear system of equations. Such matrices are unsymmetric and fully populated, which can be computationally expensive for large fracture problems containing multiple boundaries. We will show that ACA has the potential to accelerate the computational time without reducing the accuracy of the solution.