Application of Finite and Spectral Element Methods for Rock Modeling at Different Scales

This presentation was made at the 2019 NAFEMS World Congress in Quebec Canada

Resource Abstract

The article considers an application of finite and spectral element methods implemented in simulation software CAE Fidesys for geomechanical problems at different scales. At the pore scale it’s used in order to estimate effective geomechanical and thermal properties (Levin, 2000 and Levin, 2013) of the rock samples based on their digital models (obtained from either the CT scan data or virtual representative volumetric element of the pore space). Using this method dynamically variable porosities/permeabilities (based on the matrix bulk volume and fracture aperture changes) could be directly computed. These properties are used further at other scales as input material parameters. It is assumed that the structure of the solid’s material may be changed in the process of loading. For example, pores and (or) inclusions may be originated in the material (i.e. the mechanical properties of the material may be changed in some regions). The approach used develops the technique presented in (Levin, 2016 and Levin, 2015). A representative volume which mechanical behavior represents the properties of material as a whole is extracted from the body. The static problem of nonlinear elasticity is solved for this volume at given loads applied to its boundary. Then the strains and stresses are averaged over the representative volume (area), and the effective constitutive equations are constructed as a relation between the average strains and the average stresses. The effective properties are found in the form of generalized Hooke law for anisotropic materials. Numerical experiments (as opposed to real ones) allow changing material properties, constitutive relations, pore pressure. CAE Fidesys was used to build periodic cells of arbitrary geometries and relative orientations of fractures and inclusions (analytical models usually consider only the case of uniformly distributed fractures of the same shape and size).

One of the key problems of geomechanics is the determination of technological parameters, for which the rock will maintain its stability. The different rock’s properties (modulus of elasticity, Poisson's ratio, density, friction and dilatancy angles, strength and yield strengths for tension and compression, adhesion, porosity, permeability, compressibility, etc) should be taken into account. In addition, the rock is prestressed, which is determined by the components of the generally anisotropic nonuniform stress tensor. When drilling a bit generates a pressure on the rock, thereby deforming it and redistributing the stresses (superposition of finite deformations), causing the reaction of the rock to the applied impact. Accordingly, a geomechanical modeling of a rock stability taking into account a 3D realistic geometry of the prestressed solid with layers/faults intersecting is required. A nonlinear analysis using poroelastoplastic models under finite strains and their redistribution and spectral element method for high numerical resolution of plastic shear bands is applied. In particular, this helps in determining of the optimal technological parameters to compensate geomechanical stresses in the rock.

Document Details

AuthorVershinin. A
Date 18th June 2019
OrganisationFidesys LLC


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