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Numerical Simulation Of Two Phase Flow In Discrete Fractures Using Rayleigh Ritz Finite Element Method
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Book Synopsis Numerical Simulation of Two-phase Flow in Discrete Fractures Using Rayleigh-Ritz Finite Element Method by : Sandeep P. Kaul
Download or read book Numerical Simulation of Two-phase Flow in Discrete Fractures Using Rayleigh-Ritz Finite Element Method written by Sandeep P. Kaul and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Spontaneous imbibition plays a very important role in the displacement mechanism of non-wetting fluid in naturally fractured reservoirs. We developed a new 2D two-phase finite element numerical model, as available commercial simulators cannot be used to model small-scale experiments with different boundary conditions as well as complex boundary conditions such as fractures and vugs. Starting with the basic equation of fluid flow, we derived the non-linear diffusion saturation equation. This equation cannot be put in weighted-integral weak variational form and hence Rayleigh-Ritz finite element method (FEM) cannot be applied. Traditionally, the way around it is to use higher order interpolation functions and use Galerkin FEM or reduce the differentiability requirement and use Mixed FEM formulation. Other FEM methods can also be used, but iterative nature of those methods makes them unsuitable for solving large-scale field problems. But if we truncate the non-linear terms and decouple the dependent variables, from the spatial as well as the temporal domains of the primary variable to solve them analytically, the non-linear FEM problem reduces to a simple weighted integral form, which can be put into its corresponding weak form. The advantage of using Rayleigh-Ritz method is that it has immediate effect on the computation time required to solve a particular problem apart from incorporating complex boundary conditions. We compared our numerical models with the analytical solution of this diffusion equation. We validated the FDM numerical model using X-Ray Tomography (CT) experimental data from the single-phase spontaneous imbibition experiment, where two simultaneously varying parameters of weight gain and CT water saturation were used and then went ahead and compared the results of FEM model to that of FDM model. A two-phase field size example was taken and results from a commercial simulator were compared to the FEM model to bring out the limitations of this approach.
Book Synopsis Numerical Simulation of Fracture Pattern Development and Implications for Fuid Flow by : Adriana Paluszny Rodriguez
Download or read book Numerical Simulation of Fracture Pattern Development and Implications for Fuid Flow written by Adriana Paluszny Rodriguez and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulations are instrumental to understanding flow through discrete fracturegeometric representations that capture the large-scale permeability structure offractured porous media. The contribution of this thesis is threefold: an efficient finite-element finite-volume discretisation of the advection/diffusion flow equations, ageomechanical fracture propagation algorithm to create fractured rock analogues, and a study of the effect of growth on hydraulic conductivity. We describe aniterative geomechanics-based finite-element model to simulate quasi-static crackpropagation in a linear elastic matrix from an initial set of random flaws. Thecornerstones are a failure and propagation criterion as well as a geometric kernel fordynamic shape housekeeping and automatic remeshing. Two-dimensional patternsexhibit connectivity, spacing, and density distributions reproducing en echelon cracklinkage, tip hooking, and polygonal shrinkage forms. Differential stresses at theboundaries yield fracture curving. A stress field study shows that curvature can besuppressed by layer interaction effects. Our method is appropriate to model layeredmedia where interaction with neighbouring layers does not dominate deformation. Geomechanically generated fracture patterns are the input to single-phase flowsimulations through fractures and matrix. Thus, results are applicable to fracturedporous media in addition to crystalline rocks. Stress state and deformation historycontrol emergent local fracture apertures. Results depend on the number of initialflaws, their initial random distribution, and the permeability of the matrix. Straightpathfracture pattern simplifications yield a lower effective permeability in comparisonto their curved counterparts. Fixed apertures overestimate the conductivity ofthe rock by up to six orders of magnitude. Local sample percolation effectsare representative of the entire model flow behaviour for geomechanical apertures. Effective permeability in fracture dataset subregions are higher than the overallconductivity of the system. The presented methodology captures emerging patternsdue to evolving geometric and flow properties essential to the realistic simulation ofsubsurface processes.
Book Synopsis Adaptive Finite Element Method for Multiphase Flow and Poroelasticity by : Hanyu Li
Download or read book Adaptive Finite Element Method for Multiphase Flow and Poroelasticity written by Hanyu Li and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation of subsurface flow for applications such as carbon sequestration and nuclear waste deposit has always been a computational challenge. The main reason points to the strong nonlinearity inherited in the governing equations that describe the multiphysics phenomena. The enormous number of unknowns and small timesteps required for stable Newtonian convergence make this type of problems computationally exhaustive. To address this issue, we introduce adaptive finite element approaches guided by a posteriori error estimators to improve computational efficiency. A space-time discretization scheme with temporal and spatial mesh adaptivity is formulated for multiphase flow system. The solution algorithm adopts a geometric multigrid procedure that starts with solving the system in the coarsest resolution and locally refines the mesh in both space and time. Error estimators that measure the spatial and temporal discretization error are employed to guide such an adaptivity. These estimators provide a global upper bound on the dual norm of the residual and the non-conformity of the numerical solution. Results from two-phase immiscible and three-phase miscible flow are presented to confirm solution accuracy and computational efficiency as compared to the uniformly fine timestep and fine spatial discretization solution. We also resolve the common issue of high frequency residuals in multigrid methods by local residual minimization and dynamic advection-diffusion coupling to achieve additional computational speedup and stability. In addition to the multiphase flow models, we also study the Biot system that couples poromechanics with flow. A posteriori error estimators are derived with the flow and mechanics solved by mixed finite element formulation and continuous Galerkin respectively in a fixed-stress split algorithm. The effectivity of such estimators is validated by Mandel’s problem which enable us to compute the a priori error with its analytical solution. We demonstrate the efficiency of the estimators for adaptive mesh refinement using a fractured porous media example. The validity of the novel stopping criterion which balances the fixed-stress algorithm error with the discretization error is confirmed afterwards. We aim to ultimately provide efficient computations for high fidelity models from carbon sequestration and underground hydrogen storage scenarios
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Adaptive Finite Element Methodology for 2D Simulation of Two-phase Flow Through Porous Media by :
Download or read book An Adaptive Finite Element Methodology for 2D Simulation of Two-phase Flow Through Porous Media written by and published by . This book was released on 1994 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: A scheme for the accurate simulation of two-phase flow through porous media, utilizing adaptive finite element methods is presented. The theoretical equations and their approximation using Galerkin's method is covered, followed by a discussion of a dynamically refined mesh which preserves piece wise solutions across transition elements. Finally, comparisons are made between results of computed simulations and laboratory experiments. The paper uses the processes occurring in a water coning scenario, a problem of particular interest to petroleum engineers, to illustrate the method.
Download or read book Master's Theses Directories written by and published by . This book was released on 2004 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Education, arts and social sciences, natural and technical sciences in the United States and Canada".
Book Synopsis Numerical Methods in Fracture Mechanics by : A. R. Luxmoore
Download or read book Numerical Methods in Fracture Mechanics written by A. R. Luxmoore and published by . This book was released on 1978 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical simulation of fracture processes in concrete structures combining the discrete and the smeared approaches by :
Download or read book Numerical simulation of fracture processes in concrete structures combining the discrete and the smeared approaches written by and published by . This book was released on 1906 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: O presente trabalho consiste na elaboração de um modelo para simulação numérica do fraturamento em estruturas de concreto utilizando-se o Método dos Elementos Finitos econceitos da Mecânica da Fratura aplicada ao concreto. A característica mais importante deste modelo está na transição do processo de fraturamento distribuído para o processo discreto à medida em que as deformações se localizam em uma certa região da estrutura. Com isto, pode-se tirar proveito das principais vantagens apresentadas pelos dois processos, ao mesmo tempo em que se eliminam algumas de suas maiores desvantagens. A simulação é suportada por um pré-processador para geração automática da malha de elementos finitos e por uma sofisticada estrutura de dados topológica que assegura a consistência da malha gerada. A fissura discreta é inserida em uma região de comportamento plástico selecionada pelo programa, e somente esta região é rediscretizada após a inserção e propagaçãoda fissura. Todo o processo é monitorado pelo usuário através da mesma interface gráfica. A análise pelo processo distribuído é desenvolvida através de um modelo plástico não-associado e algumas dificuldades numéricas são encontradas na tentativa de representar o comportamento da estrutura nas proximidades da carga máxima e no regime pós-pico. Um procedimento numérico é proposto para contornar estas dificuldades.
Book Synopsis A Front-capturing Method for the Numerical Simulation of Dispersed Two-phase Flow by : Emil Rustam Ardeshir Coyagee
Download or read book A Front-capturing Method for the Numerical Simulation of Dispersed Two-phase Flow written by Emil Rustam Ardeshir Coyagee and published by . This book was released on 2007 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Application of the Finite Element Method to Two-phase Flow in Porous Media by : Vilgeir Dalen
Download or read book Application of the Finite Element Method to Two-phase Flow in Porous Media written by Vilgeir Dalen and published by . This book was released on 1977 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Simulation of Fracture Propagation Based on Finite Element Method and Peridynamics by : Yanan Sun
Download or read book Numerical Simulation of Fracture Propagation Based on Finite Element Method and Peridynamics written by Yanan Sun and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Engineering Index Annual written by and published by . This book was released on 1992 with total page 2264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its creation in 1884, Engineering Index has covered virtually every major engineering innovation from around the world. It serves as the historical record of virtually every major engineering innovation of the 20th century. Recent content is a vital resource for current awareness, new production information, technological forecasting and competitive intelligence. The world?s most comprehensive interdisciplinary engineering database, Engineering Index contains over 10.7 million records. Each year, over 500,000 new abstracts are added from over 5,000 scholarly journals, trade magazines, and conference proceedings. Coverage spans over 175 engineering disciplines from over 80 countries. Updated weekly.
Author :Hans-Jörg G. Diersch Publisher :Springer Science & Business Media ISBN 13 :364238739X Total Pages :1018 pages Book Rating :4.6/5 (423 download)
Download or read book FEFLOW written by Hans-Jörg G. Diersch and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 1018 pages. Available in PDF, EPUB and Kindle. Book excerpt: FEFLOW is an acronym of Finite Element subsurface FLOW simulation system and solves the governing flow, mass and heat transport equations in porous and fractured media by a multidimensional finite element method for complex geometric and parametric situations including variable fluid density, variable saturation, free surface(s), multispecies reaction kinetics, non-isothermal flow and multidiffusive effects. FEFLOW comprises theoretical work, modeling experiences and simulation practice from a period of about 40 years. In this light, the main objective of the present book is to share this achieved level of modeling with all required details of the physical and numerical background with the reader. The book is intended to put advanced theoretical and numerical methods into the hands of modeling practitioners and scientists. It starts with a more general theory for all relevant flow and transport phenomena on the basis of the continuum approach, systematically develops the basic framework for important classes of problems (e.g., multiphase/multispecies non-isothermal flow and transport phenomena, discrete features, aquifer-averaged equations, geothermal processes), introduces finite-element techniques for solving the basic balance equations, in detail discusses advanced numerical algorithms for the resulting nonlinear and linear problems and completes with a number of benchmarks, applications and exercises to illustrate the different types of problems and ways to tackle them successfully (e.g., flow and seepage problems, unsaturated-saturated flow, advective-diffusion transport, saltwater intrusion, geothermal and thermohaline flow).
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1977 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Book Synopsis The Finite Element Method Set by : O. C. Zienkiewicz
Download or read book The Finite Element Method Set written by O. C. Zienkiewicz and published by Elsevier. This book was released on 2005-11-25 with total page 1863 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM. Written by the leading professors in their fields, the three books cover the basis of the method, its application to solid mechanics and to fluid dynamics.* This is THE classic finite element method set, by two the subject's leading authors * FEM is a constantly developing subject, and any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in these books * Fully up-to-date; ideal for teaching and reference
Book Synopsis The Finite Element Method and Applications in Engineering Using ANSYS® by : Erdogan Madenci
Download or read book The Finite Element Method and Applications in Engineering Using ANSYS® written by Erdogan Madenci and published by Springer. This book was released on 2015-02-10 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers theoretical and practical knowledge of the finite element method. The book equips readers with the skills required to analyze engineering problems using ANSYS®, a commercially available FEA program. Revised and updated, this new edition presents the most current ANSYS® commands and ANSYS® screen shots, as well as modeling steps for each example problem. This self-contained, introductory text minimizes the need for additional reference material by covering both the fundamental topics in finite element methods and advanced topics concerning modeling and analysis. It focuses on the use of ANSYS® through both the Graphics User Interface (GUI) and the ANSYS® Parametric Design Language (APDL). Extensive examples from a range of engineering disciplines are presented in a straightforward, step-by-step fashion. Key topics include: • An introduction to FEM • Fundamentals and analysis capabilities of ANSYS® • Fundamentals of discretization and approximation functions • Modeling techniques and mesh generation in ANSYS® • Weighted residuals and minimum potential energy • Development of macro files • Linear structural analysis • Heat transfer and moisture diffusion • Nonlinear structural problems • Advanced subjects such as submodeling, substructuring, interaction with external files, and modification of ANSYS®-GUI Electronic supplementary material for using ANSYS® can be found at http://link.springer.com/book/10.1007/978-1-4899-7550-8. This convenient online feature, which includes color figures, screen shots and input files for sample problems, allows for regeneration on the reader’s own computer. Students, researchers, and practitioners alike will find this an essential guide to predicting and simulating the physical behavior of complex engineering systems."
Book Synopsis International Aerospace Abstracts by :
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1999 with total page 1042 pages. Available in PDF, EPUB and Kindle. Book excerpt:
