13:20

conference time (CEST, Berlin)

conference time (CEST, Berlin)

Modeling the Effective Properties of Rocks at the Core Sample Scale Taking into Account Pre-loading and Using the Finite Element Method

27/10/2021 13:20 conference time (CEST, Berlin)

Room: G

M. Yakovlev (Fidesys LLC, RUS); I. Bystrov, V. Levin (Lomonosov Moscow State University, RUS); A. Vershinin (Shmidt Institute of Physics of the Earth of RAS, RUS); K. Zingerman, (Tver State University, RUS)

The paper discusses the use of finite element method for modeling the effective properties of rocks on the scale of core sample - a rock sample, extracted from the depths of the Earth using a special type of drilling. Estimation of the effective properties of the core sample is important for geomechanical modeling on a wellbore or a reservoir scale: the resulting effective properties are input data for such calculations. The estimation of core sample properties is performed numerically on the digital (voxel) model of the core sample, which is built using a CT-scan. After that, with the help of a specially developed software module on the voxel model a structured hexahedral mesh is built (each element of which corresponds to one voxel.).
Effective properties are estimated at the representative volume element (RVE) of the core. The RVE is a fragment of the voxel model of the core sample, having a sufficiently large size so that its properties extend to the properties of the core in general. On a RVE in the form of a rectangular parallelepiped, six boundary problems of the theory of elasticity with various boundary conditions are solved, corresponding to three uniaxial tensions of the volume (along each of the coordinate axes) and three shifts (in each of the coordinate planes). The results of solving each boundary value problem are averaged over the volume, which gives effective (average) stress tensors.
Since the core is at a great depth, it is subjected to considerable stress. Therefore, its mechanical properties under the ground and after extracting to the surface can be quite different. In this regard, the numerical modeling of the effective properties of the core sample must be carried out taking into account pre-loading. Preloading (as a pore pressure) is applied to a model for solving the above six elastic boundary problems. In addition, the seventh problem of the theory of elasticity is solved, in which the boundary of the core is tightly fixed, and the pore pressure is still applied. The results of solving the seventh problem solving are also averaged over the volume. All seven problems are solved taking into account geometric nonlinearity. As the effective stress tensors are calculated for the first six problems, an effective tensor is computed for the seventh problem. Then the effective elastic properties of the core sample are calculated as the dependence of the differences on the effective strain tensor.
Calculations are performed using the finite element method with the help of a software module Fidesys Composite of CAE Fidesys. An effect of pore pressure on effective elastic modules of core sample is analyzed. The calculations are carried out for two types of cores: a sandstone (consisting of one mineral, porosity is 21%) and a limestone (consisting of three minerals, porosity 3%). It is shown that even with small porosity, the pore pressure significantly affects the effective elastic properties of the core sample. The dependence of effective properties on pore pressure is practically linear (the report shows the graphs of this dependence for both types of cores.). Thus, an importance of considering initial pre-loading of a core sample for its effective properties estimation is demonstrated.
This work is supported by the Russian Science Foundation under grant 19-71-10008.

Rock Physics, Digital Core, Theory of Elasticity, Effective Properties, Pre-loading, Nonlinearity, Finite Element Method

13:40

conference time (CEST, Berlin)

conference time (CEST, Berlin)

Requirements for Facade Engineers to be Certified in FEA

27/10/2021 13:40 conference time (CEST, Berlin)

Room: G

E. Secillano (Arup, AUS)

The need for facade engineers to learn the fundamentals of FEA and get certified to assess their FEA knowledge are essential and should be considered by professionals in the facade engineering industry. Facade engineers are a new discipline that focuses on the design aspect of the building enclosures. They ensure that the building facade is structurally sound, weather tight, energy efficient, and provides an overall comfort to the occupants. To ensure these aspects are met, facade engineers should have the skills of structural engineers and mechanical engineers. Often facade engineers are task to analyse a rectangular cladding, say for example a glass supported on four sides by a frame, to ensure the facade is adequate against the worst-case conventional load (eg: wind load). They may also require to conduct a thermal calculation of the glass facade to ensure it satisfy the building regulations in their country. To do this, facade engineers will often conduct a simulation using FEA to analyse that the maximum stress in the glass is within the allowable load or to check that the thermal conductivity of the glass is within the limit of the building regulations. However, conducting a simple analysis in FEA could also mislead facade engineers with their limitation in terms of FEA. FEA are often thought as a software where if a user knows which button to click, then they can be considered as a FEA user without understanding the fundamentals such as proper boundary condition, aspect ratio in plate elements, singularity, meshing, etc. In addition to structural requirements, it is often required by many international standards, such as AS1288 in Australia, to conduct a nonlinear analysis when analysing a glass. In addition, thin plate members with deflection greater than half of its thickness are well analysed using geometric nonlinear analysis and solving the differential equation of nonlinear problem are complex and necessitate the use of FEA.

Facade, FEA, Numerical Simulation, Enclosures

14:00

conference time (CEST, Berlin)

conference time (CEST, Berlin)

Poroelastoplastic Modeling of Shear Banding Nearby the Borehole Using Spectral Element Method and CUDA

27/10/2021 14:00 conference time (CEST, Berlin)

Room: G

A. Vershinin, V. Levin (Fidesys LLC, RUS); Y. Podladchikov (Lomonosov Moscow State University, CHE)

The presentation considers a generalization of classical Biot's equations to the poroelastoplastic medium in order to simulate a shear banding phenomena taking place around the borehole drilled in the prestressed solid under the artificial depression leading to the change in the pore pressure in the surrounding rock as well as redistribution of stresses and accumulated plastic strains. The mathematical problem formulation consists of a coupled system of dynamic poroelastoplastic equations in a solid skeleton and a saturating fluid for the small strains case (geometrically linear formulation): equilibrium equations, Darcy's law, and constitutive stress-strain and pore pressure relations. Different physically nonlinear relations are taken into account: dynamic porosity and permeability dependent on the pore pressure and volumetric strains, non-associative poroplasticity taken into account irreversible plastic strans and change in fluid volume content, dynamic poroelastic moduli (bulk, shear, Biot etc) dependent on the current porocity.
A set of nonlinear PDEs is solved using a novel approach based on the fully explicit time integration scheme and the high order spectral element method (SEM) space discretization scheme. Two numerical algorithms are analyzed and compared with each other: the first one is based on the direct Lagrangian formalism leading to the full displacement integration and accumulation of the full plastic strains at each loading step, the second one is based on the Euler formalism leading to the seeking a numerical solution in terms of the relative displacements at each loading step (i.e. velocities) and accumulated stresses. Both approaches are implemented for solving quasi-static poroelastoplastic equations using pseudo-transient scheme with the inertia and dissipative terms allowing one to converge to the static solution at each loading "time" step. Obtained numerical results as well as the performance of both approaches are analyzed and compared with CAE Fidesys for the Drucker-Prager plasticity.
CUDA technology is used to parallelize the implemented algorithm on the massively parallel Tesla V100 GPU. Different optimization strategies and details of parallelizing spectral element method using CUDA are discussed. In particular, an algorithm for the mapping of an unstructured spectral element mesh of an arbitrary order onto the grid of blocks of GPU multilevel thread hierarchy is presented. CUDA kernels' design, memory access patterns, synchronization issues are considered. Performance analysis is given for different SEM orders and mesh sizes as well as for the different floating-point precisions.
The reported study was funded by Russian Science Foundation project -19-77-10062.
References
[1] M.A. Biot “Theory of propagation of elastic waves in a fluid-saturated porous solid,” in J. Acoust. Soc. Am., 28, pp. 168-191 (1956).
[2] Charara M, Vershinin A, Deger E, Sabitov D and Pekar G 2011 3D spectral element method simulation of sonic logging in anisotropic viscoelastic media SEG Expanded Abstracts 30 pp 432–437
[3] Duretz, T., Souche, A., de Borst, R., & Le Pourhiet, L. (2018). The benefits of using a consistent tangent operator for viscoelastoplastic computations in geodynamics. Geochemistry, Geophysics, Geosystems, 19.
[4] O. Coussy, Poromechanics, John Wiley and Sons, 2004.
[5] Komatitsch D and Vilotte J-P 1998 The spectral element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures Bulletin of Seismological Society of America 88(2)
[6] Levin V, Zingerman K, Vershinin A, Freiman E and Yangirova A 2013 Numerical analysis of the stress concentration near holes originating in previously loaded viscoelastic bodies at finite strains International Journal of Solids and Structures 50(20-21)
[7] Yarushina, V. M. & Podladchikov, Y. Y. (De)compaction of porous viscoelastoplastic media: Model formulation. J. Geophys. Res. Solid Earth 120, 4146–4170 (2015).
References
[8] CAE Fidesys website www.cae-fidesys.com

Biot model, spectral element method, GPU, CUDA, porous medium, shear bands