SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Desenvolvimento de um simulador substituto de reservatório multiescala acoplado com geomecânica

Orientador: Philippe Remy Bernard DevlooTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de GeociênciasResumo: Os softwares de simulação de reservatórios são utilizados como ferramentas para o entendimento dos reservatórios de petróleo e eventualmente, para diagnosticar anomalias operacionais. O aumento da potência computacional permite aos engenheiros de reservatórios desenvolver modelos geológicos mais realistas, refinados e com uma grande quantidade de dados de entrada. Alguns exemplos são os modelos multi-físicos que acoplam efeitos geomecânicos, térmicos, geoquímicos e modelos que incluem múltiplas escalas inerentes aos modelos de campo completo. Estes modelos são geralmente caros, porque o cálculo direto de um modelo geocelular refinado gera enormes sistemas lineares de equações. Quando é considerado o efeito da deformação geomecânica com o fluxo de fluido através de meios porosos, um sistema muito grande de equações associado com a elasticidade é acoplado a um sistema igualmente grande de equações, associadas ao fluxo de fluido e ao transporte de massa. Portanto, a maioria das simulações são realizadas sem considerar o acoplamento geomecânico. Essas simulações ignoram fenômenos físicos que podem ter sérios impactos ambientais, como ativação de falhas, subsidência e outros. Neste trabalho desenvolve-se um inovador método multiescala que permite diretamente simular um modelo geocelular fino em uma maneira econômica. Um modelo substituto também foi desenvolvido para simular a deformação geomecânica acoplada ao modelo de fluido. O objetivo é obter aproximações do problema multifísico não linear descrito pelas equações multifásicas poroelásticas. Para atingir esse objetivo, diferentes tecnologias de elementos finitos são integradas dentro de um simulador de reservatórios, resolvendo problemas que incluem um modelo geocelular com diferentes escalas, acoplado a um modelo substituto de deformação geomecânica. O modelo matemático é escrito em uma forma adequada para a estrutura de elementos finitos do NeoPZ. Em cada passo de tempo, a aproximação é obtida como uma sequência de problemas elásticos, de Darcy e de transporte. Cada componente nesta sequência é tratado por um esquema numérico diferente e / ou espaço de aproximação; em primeiro lugar, um modelo substituto, inspirado na teoria das inclusões poroelásticas, é usado para o cálculo da deformação geomecânica das rochas; em segundo lugar, utiliza-se um método multi-escala baseado na aproximação mista de equações multifásicas; em terceiro lugar, para a convecção das fases, uma aproximação mista multi-escala do campo de velocidade de Darcy é usada, em conjunto com um esquema de upwind de primeira ordem. O potencial da abordagem numérica é demonstrado através de vários exemplos bidimensionais e tridimensionais, em que os reservatórios são simulados usando malhas não estruturadas. Todas as simulações foram executadas usando estruturas computacionais de baixo custoAbstract: Reservoir simulation softwares are used as a tool to understand the behavior of petroleum reservoirs and, eventually, to diagnose operating anomalies. The increased computational power allows reservoir engineers to develop more realistic geological models, that are very refined and have a large amount of input data. As an example, multi-physics models couple geomechanical, thermal, geochemical effects and include multiple scales inherent to full field models. These models are generally costly, because the direct calculation of a refined geocellular model, generates huge linear systems of equations. When coupling the geomechanical deformation with fluid flow through porous media, a very large system of equations associated with elasticity, is coupled to an equally large system of equations, which is associated with fluid flow and mass transport. Therefore, most simulations are performed without considering the geomechanical coupling. These simulations ignore physical phenomena that can have serious environmental impacts such as fault activation, land subsidence and others. In this work an innovative multiscale method is developed, allowing the direct simulation of a fine geocellular model in a cost-effective way. A surrogate model has also been developed for simulating the geomechanical deformation coupled to the fluid model. The goal is obtain approximations for the nolinear multiphysic problem decribed by the multiphase poroelastic equations. In order to attain this goal, different finite element technologies are integrated within a reservoir simulator, solving problems that include a geocellular model with different scales, coupled with a surrogate model of geomechanical deformation. The mathematical model is written in a form suitable for the NeoPZ finite element framework. At each timestep, the approximation is obtained as a sequence of elastic, Darcy's and transport problems. Each component in this sequence is treated by a different numerical scheme and/or approximation space; first, a surrogate model, inspired on the theory of poroelastic inclusions, is used for the calculation of the geomechanical deformation of rocks; second, a multiscale method based on mixed approximation of multiphase equations is used; third, for the convection of the phases, a mixed multiscale approximation of the Darcy's velocity field is used together with a first-order upwind scheme. The potential of the numerical approach is demonstrated through several bi-dimensional and three-dimensional examples, in which reservoirs are simulated using unstructured meshes. All simulations have been executed using low cost computational structuresDoutoradoExplotaçãoDoutor em Ciências e Engenharia de Petróle

A stochastic LATIN method for stochastic and parameterized elastoplastic analysis

The LATIN method has been developed and successfully applied to a variety of deterministic problems, but few work has been developed for nonlinear stochastic problems. This paper presents a stochastic LATIN method to solve stochastic and/or parameterized elastoplastic problems. To this end, the stochastic solution is decoupled into spatial, temporal and stochastic spaces, and approximated by the sum of a set of products of triplets of spatial functions, temporal functions and random variables. Each triplet is then calculated in a greedy way using a stochastic LATIN iteration. The high efficiency of the proposed method relies on two aspects: The nonlinearity is efficiently handled by inheriting advantages of the classical LATIN method, and the randomness and/or parameters are effectively treated by a sample-based approximation of stochastic spaces. Further, the proposed method is not sensitive to the stochastic and/or parametric dimensions of inputs due to the sample description of stochastic spaces. It can thus be applied to high-dimensional stochastic and parameterized problems. Four numerical examples demonstrate the promising performance of the proposed stochastic LATIN method

Finite element method for coupled thermo-hydro-mechanical processes in discretely fractured and non-fractured porous media

Numerical analysis of multi-field problems in porous and fractured media is an important subject for various geotechnical engineering tasks such as the management of geo-resources (e.g. engineering of geothermal, oil and gas reservoirs) as well as waste management. For practical usage, e.g. for geothermal, simulation tools are required which take into account both coupled thermo-hydro-mechanical (THM) processes and the uncertainty of geological data, i.e. the model parametrization. For modeling fractured rocks, equivalent porous medium or multiple continuum model approaches are often only the way currently due to difficulty to handle geomechanical discontinuities. However, they are not applicable for prediction of flow and transport in subsurface systems where a few fractures dominates the system behavior. Thus modeling coupled problems in discretely fractured porous media is desirable for more precise analysis. The subject of this work is developing a framework of the finite element method (FEM) for modeling coupled THM problems in discretely fractured and non-fractured porous media including thermal water flow, advective-diffusive heat transport, and thermoporoelasticity. Pre-existing fractures are considered. Systems of discretely fractured porous media can be considered as a problem of interacted multiple domains, i.e. porous medium domain and discrete fracture domain, for hydraulic and transport processes, and a discontinuous problem for mechanical processes. The FEM is required to take into account both kinds of the problems. In addition, this work includes developing a methodology for the data uncertainty using the FEM model and investigating the uncertainty impacts on evaluating coupled THM processes. All the necessary code developments in this work has been carried out with a scientific open source project OpenGeoSys (OGS). In this work, fluid flow and heat transport problems in interactive multiple domains are solved assuming continuity of filed variables (pressure and temperature) over the two domains. The assumption is reasonable if there are no infill materials in fractures. The method has been successfully applied for several numerical examples, e.g. modeling three-dimensional coupled flow and heat transport processes in discretely fractured porous media at the Gross Schoenebck geothermal site (Germany), and three-dimensional coupled THM processes in porous media at the Urach Spa geothermal site (Germany). To solve the mechanically discontinuous problems, lower-dimensional interface elements (LIEs) with local enrichments have been developed for coupled problems in a domain including pre-existing fractures. The method permits the possibility of using existing flow simulators and having an identical mesh for both processes. It enables us to formulate the coupled problems in monolithic scheme for robust computation. Moreover, it gives an advantage in practice that one can use existing standard FEM codes for groundwater flow and easily make a coupling computation between mechanical and hydraulic processes. Example of a 2D fluid injection problem into a single fracture demonstrated that the proposed method can produce results in strong agreement with semi-analytical solutions. An uncertainty analysis of THM coupled processes has been studied for a typical geothermal reservoir in crystalline rock based on the Monte-Carlo method. Fracture and matrix are treated conceptually as an equivalent porous medium, and the model is applied to available data from the Urach Spa and Falkenberg sites (Germany). Reservoir parameters are considered as spatially random variables and their realizations are generated using conditional Gaussian simulation. Two reservoir modes (undisturbed and stimulated) are considered to construct a stochastic model for permeability distribution. We found that the most significant factors in the analysis are permeability and heat capacity. The study demonstrates the importance of taking parameter uncertainties into account for geothermal reservoir evaluation in order to assess the viability of numerical modeling

State Of the Art Report in the fields of numerical analysis and scientific computing. Final version as of 16/02/2020 deliverable D4.1 of the HORIZON 2020 project EURAD.: European Joint Programme on Radioactive Waste Management

Document information Project Acronym EURAD Project Title European Joint Programme on Radioactive Waste Management Project Type European Joint Programme (EJP) EC grant agreement No. 847593 Project starting / end date 1 st June 2019-30 May 2024 Work Package No. 4 Work Package Title Development and Improvement Of NUmerical methods and Tools for modelling coupled processes Work Package Acronym DONUT Deliverable No. 4.