Discrétisation Gradient de Modèles D'écoulements À Dimensions Hybrides Dans Les Milieux Poreux Fracturés PDF Download
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Author: Julian Hennicker
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This thesis investigates the modelling of Darcy flow through fractured porous media and its discretization on general polyhedral meshes. We follow the approach of hybrid dimensional models, invoking a complex network of planar fractures. The models account for matrix-fracture interactions and fractures acting either as drains or as barriers, i.e. we have to deal with pressure discontinuities at matrix-fracture interfaces. In the case of two phase flow, we present two models, which permit to treat gravity dominated flow as well as discontinuous capillary pressure at the material interfaces. The numerical analysis is performed in the general framework of the Gradient Discretisation Method, which is extended to the models under consideration. Two families of schemes namely the Vertex Approximate Gradient scheme (VAG) and the Hybrid Finite Volume scheme (HFV) are detailed and shown to fit in the gradient scheme framework, which yields, in particular, convergence. For single phase flow, we obtain convergence of order 1 via density results. For two phase flow, the existence of a solution is obtained as a byproduct of the convergence analysis. Several test cases are presented. For single phase flow, we study the convergence on different types of meshes for a family of solutions. For two phase flow, we compare the hybrid-dimensional models to the reference equidimensional model, in which fractures have the same dimension as the matrix. This does not only provide quantitative evidence about computational gain, but also leads to deep insight about the quality of the proposed reduced models.
Author: Julian Hennicker
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This thesis investigates the modelling of Darcy flow through fractured porous media and its discretization on general polyhedral meshes. We follow the approach of hybrid dimensional models, invoking a complex network of planar fractures. The models account for matrix-fracture interactions and fractures acting either as drains or as barriers, i.e. we have to deal with pressure discontinuities at matrix-fracture interfaces. In the case of two phase flow, we present two models, which permit to treat gravity dominated flow as well as discontinuous capillary pressure at the material interfaces. The numerical analysis is performed in the general framework of the Gradient Discretisation Method, which is extended to the models under consideration. Two families of schemes namely the Vertex Approximate Gradient scheme (VAG) and the Hybrid Finite Volume scheme (HFV) are detailed and shown to fit in the gradient scheme framework, which yields, in particular, convergence. For single phase flow, we obtain convergence of order 1 via density results. For two phase flow, the existence of a solution is obtained as a byproduct of the convergence analysis. Several test cases are presented. For single phase flow, we study the convergence on different types of meshes for a family of solutions. For two phase flow, we compare the hybrid-dimensional models to the reference equidimensional model, in which fractures have the same dimension as the matrix. This does not only provide quantitative evidence about computational gain, but also leads to deep insight about the quality of the proposed reduced models.
Author: G. Chavent
Publisher: Elsevier
ISBN: 0080875386
Category : Mathematics
Languages : en
Pages : 389
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Book Description
Numerical simulators for oil reservoirs have been developed over the last twenty years and are now widely used by oil companies. The research, however, has taken place largely within the industry itself, and has remained somewhat inaccessible to the scientific community. This book hopes to remedy the situation by means of its synthesized presentation of the models used in reservoir simulation, in a form understandable to both mathematicians and engineers.The book aims to initiate a rigorous mathematical study of the immiscible flow models, partly by using the novel `global pressure' approach in treating incompressible two-phase problems. A finite element approximation technique based on the global pressure variational model is presented, and new approaches to the modelling of various kinds of multiphase flow through porous media are introduced.Much of the material is highly original, and has not been presented elsewhere. The mathematical and numerical models should be of great interest to applied mathematicians, and to engineers seeking an alternative approach to reservoir modelling.
Author: Michel Bilodeau
Publisher: Springer Science & Business Media
ISBN: 0387291156
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Space, structure, and randomness: these are the three key concepts underlying Georges Matheron’s scientific work. He first encountered them at the beginning of his career when working as a mining engineer, and then they resurfaced in fields ranging from meteorology to microscopy. What could these radically different types of applications possibly have in common? First, in each one only a single realisation of the phenomenon is available for study, but its features repeat themselves in space; second, the sampling pattern is rarely regular, and finally there are problems of change of scale. This volume is divided in three sections on random sets, geostatistics and mathematical morphology. They reflect his professional interests and his search for underlying unity. Some readers may be surprised to find theoretical chapters mixed with applied ones. We have done this deliberately. GM always considered that the distinction between the theory and practice was purely academic. When GM tackled practical problems, he used his skill as a physicist to extract the salient features and to select variables which could be measured meaningfully and whose values could be estimated from the available data. Then he used his outstanding ability as a mathematician to solve the problems neatly and efficiently. It was his capacity to combine a physicist’s intuition with a mathematician’s analytical skills that allowed him to produce new and innovative solutions to difficult problems. The book should appeal to graduate students and researchers working in mathematics, probability, statistics, physics, spatial data analysis, and image analysis. In addition it will be of interest to those who enjoy discovering links between scientific disciplines that seem unrelated at first glance. In writing the book the contributors have tried to put GM’s ideas into perspective. During his working life, GM was a genuinely creative scientist. He developed innovative concepts whose usefulness goes far beyond the confines of the discipline for which they were originally designed. This is why his work remains as pertinent today as it was when it was first written.
Author: Willem Hundsdorfer
Publisher: Springer Science & Business Media
ISBN: 3662090171
Category : Technology & Engineering
Languages : en
Pages : 479
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Book Description
Unique book on Reaction-Advection-Diffusion problems
Author: Ion Paraschivoiu
Publisher: Presses inter Polytechnique
ISBN: 9782553011306
Category : Science
Languages : en
Pages : 568
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Book Description
Author: Pierre M. Adler
Publisher: Oxford University Press, USA
ISBN: 0199666512
Category : Science
Languages : en
Pages : 184
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Book Description
This book provides a systematic treatment of the geometrical and transport properties of fractures, fracture networks, and fractured porous media. It is divided into two major parts. The first part deals with geometry of individual fractures and of fracture networks. The use of the dimensionless density rationalizes the results for the percolation threshold of the networks. It presents the crucial advantage of grouping the numerical data for various fracture shapes. The second part deals mainly with permeability under steady conditions of fractures, fracture networks, and fractured porous media. Again the results for various types of networks can be rationalized by means of the dimensionless density. A chapter is dedicated to two phase flow in fractured porous media.
Author: D.W. Peaceman
Publisher: Elsevier
ISBN: 0080868606
Category : Technology & Engineering
Languages : en
Pages : 191
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Book Description
The use of numerical reservoir simulation with high-speed electronic computers has gained wide acceptance throughout the petroleum industry for making engineering studies of a wide variety of oil and gas reservoirs throughout the world. These reservoir simulators have been designed for use by reservoir engineers who possess little or no background in the numerical mathematics upon which they are based. In spite of the efforts to improve numerical methods to make reservoir simulators as reliable, efficient, and automatic as possible, the user of a simulator is faced with a myriad of decisions that have nothing to do with the problem to be solved. This book combines a review of some basic reservoir mechanics with the derivation of the differential equations that reservoir simulators are designed to solve.
Author: Knut-Andreas Lie
Publisher: Cambridge University Press
ISBN: 1108492436
Category : Business & Economics
Languages : en
Pages : 677
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Book Description
Presents numerical methods for reservoir simulation, with efficient implementation and examples using widely-used online open-source code, for researchers, professionals and advanced students. This title is also available as Open Access on Cambridge Core.
Author: Ismael Herrera
Publisher: John Wiley & Sons
ISBN: 1118207203
Category : Technology & Engineering
Languages : en
Pages : 259
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Book Description
A powerful, unified approach to mathematical and computational modeling in science and engineering Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective models, it also enables them to apply these models to any macroscopic physical system. Mathematical Modeling in Science and Engineering focuses on models in which the processes to be modeled are expressed as systems of partial differential equations. It begins with an introductory discussion of the axiomatic formulation of basic models, setting the foundation for further topics such as: Mechanics of classical and non-classical continuous systems Solute transport by a free fluid Flow of a fluid in a porous medium Multiphase systems Enhanced oil recovery Fluid mechanics Throughout the text, diagrams are provided to help readers visualize and better understand complex mathematical concepts. A set of exercises at the end of each chapter enables readers to put their new modeling skills into practice. There is also a bibliography in each chapter to facilitate further investigation of individual topics. Mathematical Modeling in Science and Engineering is ideal for both students and professionals across the many disciplines of science and engineering that depend on mathematical and computational modeling to predict and understand complex systems.
Author: Philippe Gourbesville
Publisher: Springer
ISBN: 9812876154
Category : Science
Languages : en
Pages : 616
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Book Description
This book is a collection of extended papers based on presentations given during the SIMHYDRO 2014 conference, held in Sophia Antipolis in June 2014. It focuses on the modeling and simulation of fast hydraulic transients, on 3D modeling, and on uncertainties and multiphase flows. The book explores both the limitations and performance of current models and presents the latest developments based on new numerical schemes, high-performance computing, multiphysics and multiscale methods, and better interaction with field or scale model data. It addresses the interests of practitioners, stakeholders, researchers and engineers active in this field.
