[PDF] Stochastic Models Of Flow Through Porous Media eBook

Author : Dongxiao Zhang
Publisher : Elsevier
Page : 371 pages
File Size : 29,33 MB
Release : 2001-10-11
Category : Mathematics
ISBN : 0080517773

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Stochastic Methods for Flow in Porous Media: Coping with Uncertainties explores fluid flow in complex geologic environments. The parameterization of uncertainty into flow models is important for managing water resources, preserving subsurface water quality, storing energy and wastes, and improving the safety and economics of extracting subsurface mineral and energy resources. This volume systematically introduces a number of stochastic methods used by researchers in the community in a tutorial way and presents methodologies for spatially and temporally stationary as well as nonstationary flows. The author compiles a number of well-known results and useful formulae and includes exercises at the end of each chapter. Balanced viewpoint of several stochastic methods, including Greens' function, perturbative expansion, spectral, Feynman diagram, adjoint state, Monte Carlo simulation, and renormalization group methods Tutorial style of presentation will facilitate use by readers without a prior in-depth knowledge of Stochastic processes Practical examples throughout the text Exercises at the end of each chapter reinforce specific concepts and techniques For the reader who is interested in hands-on experience, a number of computer codes are included and discussed

Author : Martin A. Diaz Viera
Publisher : CRC Press
Page : 370 pages
File Size : 49,88 MB
Release : 2012-07-24
Category : Mathematics
ISBN : 0203113888

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Porous media are broadly found in nature and their study is of high relevance in our present lives. In geosciences porous media research is fundamental in applications to aquifers, mineral mines, contaminant transport, soil remediation, waste storage, oil recovery and geothermal energy deposits. Despite their importance, there is as yet no complete

Author : Mickaële Le Ravalec
Publisher : Editions Technips
Page : 0 pages
File Size : 46,72 MB
Release : 2005
Category : Fluid dynamics
ISBN : 9782710808640

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In order to understand fluid flows in underground porous formations, engineers need to produce models, in the form of grid systems populated with physical properties such as permeability and porosity. This procedure is of crucial importance but it is also problematic. It is crucially important in determining where and how fluids flow; reservoir or aquifer modeling is used to plan field development, optimize oil production with the judicious selection of well locations, assess contaminant migration, design capture zones, and so on. It is problematic, because there is never enough data available to describe with certainty the spatial distribution of permeability and porosity on a given scale. Given the complex heterogeneity of natural porous media, the fundamental question is: how can this reality be incorporated in models? This textbook refers to geostatistics and optimization to review the whole workflow for modern reservoir characterization and to provide an original solution. A CD-ROM with a software called GO is supplied with this book. It provides tools to answer the illustrative exercises proposed and to help the reader to develop intuitive understanding. This book is written at a comprehensible level for students who have had calculus, linear algebra and some exposure to differential equations. It should also serve already-practicing engineers in oil reservoirs, environment and hydrology.

Author : Alain P Bourgeat
Publisher : World Scientific
Page : 534 pages
File Size : 17,67 MB
Release : 1995-11-30
Category :
ISBN : 9814548391

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This proceedings volume contains contributions from leading scientists working on modelling and numerical simulation of flows through porous media and on mathematical analysis of the equations associated to the modelling. There is a number of contributions on rigorous results for stochastic media and for applications to numerical simulations. Modelling and simulation of environment and pollution are also subject of several papers. The published material herein gives an insight to the state of the art in the field with special attention for rigorous discussions and results.

Author : Don Kulasiri
Publisher : Elsevier
Page : 253 pages
File Size : 33,51 MB
Release : 2002-11-22
Category : Mathematics
ISBN : 0080541801

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Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas are explained in an intuitive manner wherever possible with out compromising rigor. The solute transport problem in porous media saturated with water had been used as a natural setting to discuss the approaches based on stochastic dynamics. The work is also motivated by the need to have more sophisticated mathematical and computational frameworks to model the variability one encounters in natural and industrial systems. This book presents the ideas, models and computational solutions pertaining to a single problem: stochastic flow of contaminant transport in the saturated porous media such as that we find in underground aquifers. In attempting to solve this problem using stochastic concepts, different ideas and new concepts have been explored, and mathematical and computational frameworks have been developed in the process. Some of these concepts, arguments and mathematical and computational constructs are discussed in an intuititve manner in this book.

Author : Gedeon Dagan
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 40,22 MB
Release : 1991
Category : Mathematics
ISBN : 9780792316169

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This book contains a selection of articles presented at an International Workshop on `Mathematical Modeling for Flow and Transport Through Porous Media'. The major topics of the meeting were free and moving boundary problems, structured media, multiphase flow, scale problems, stochastic aspects, parameter identification and optimization problems. The volume also represents a few contributions on the incorporation of chemical and biological processes in mathematical models for transport in porous media. The book is directed at researchers active in porous media, mathematical modeling, petroleum and geotechnical engineering and environmental sciences.

Author : Viorel Barbu
Publisher : Springer
Page : 209 pages
File Size : 28,15 MB
Release : 2016-09-30
Category : Mathematics
ISBN : 3319410695

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Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.