Topics In Stability Analysis Of Multi Layer Hele Shaw And Porous Media Flows
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Topics In Stability Analysis Of Multi Layer Hele Shaw And Porous Media Flows
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Author : Craig Robert Gin
language : en
Publisher:
Release Date : 2015
Topics In Stability Analysis Of Multi Layer Hele Shaw And Porous Media Flows written by Craig Robert Gin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
We study the linear stability of multi-layer Hele-Shaw flows. This topic has many useful applications including the design of efficient enhanced oil recovery techniques. We study four problems: two in a rectilinear flow geometry and two in a radial flow geometry. The first of these involves a characterization of the eigenvalues and eigenfunctions of the eigenvalue problem which results from the stability analysis of three-layer rectilinear flows in which the middle layer has variable viscosity. The resulting eigenvalue problem is a Sturm-Liouville problem in which the eigenvalues appear in the boundary conditions. For the case of an increasing viscous profile, we find that there is an infinite number of eigenvalues that increase without bound. By connecting the problem to a related regular Sturm-Liouville problem, we are able to prove the completeness of the eigenfunctions in a certain Sobolev space. We then provide an in-depth analysis of the case where the viscous profile of the middle layer is exponential. We find an explicit sequence of numbers which alternate with the eigenvalues. The second problem involves the stability of three-layer rectilinear Hele-Shaw flows in which there is diffusion of polymer within the middle layer of fluid. We first reformulate the eigenvalue problem using dimensionless quantities. We then revisit an old theorem about the stabilizing effect of diffusion and give a new proof. An efficient and accurate pseudo-spectral Chebyshev method is used to show that the stabilizing effect of diffusion is, in fact, drastic. We proceed to consider the stability of multi-layer Hele-Shaw flows in a radial flow geometry. We first study the case of an arbitrary number of fluid layers with constant viscosity. We provide upper bounds on the growth rate of disturbances and use them to provide conditions for stabilization of the flow. We also show that the equations for rectilinear flow can be obtained as a certain limit of radial flow. For the specific case of three-layer flows, we give exact expressions for the growth rate and explore the asymptotic limits of a thick and thin intermediate layer. We finish by using these exact expressions to study the effects of important parameters of the problem. We conclude that large values of interfacial tension can completely stabilize the flow and that decreasing the curvature of the interfaces by pumping in additional fluid has a non-monotonic effect on stability. We then consider three-layer radial flows in which the intermediate layer has variable viscosity. In order to use a similar analysis to that which is done in the previous problems, we define a change of variables that fixes the basic solution. In this new coordinate system, we are able to formulate the eigenvalue problem that governs the growth rate of disturbances. We define a measure based on the eigenvalue problem which leads to a Hilbert space in which the problem is self-adjoint. We also derive upper bounds on the growth rate, analogous to ones previously found for variable viscosity rectilinear flows. We then undertake a numerical study of the eigenvalue problem and find that variable viscosity flows, if chosen properly, can be less unstable than constant viscosity flows. Finally, we give details on our numerical method which is used throughout. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155543
Stability And Wave Motion In Porous Media
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Author : Brian Straughan
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
Stability And Wave Motion In Porous Media written by Brian Straughan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Technology & Engineering categories.
This book describes several tractable theories for fluid flow in porous media. The important mathematical quations about structural stability and spatial decay are address. Thermal convection and stability of other flows in porous media are covered. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed. In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail. A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1980
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mechanics, Applied categories.
Two Phase Flow In Porous Media
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Author : Kimberly Renee Spayd
language : en
Publisher:
Release Date : 2012
Two Phase Flow In Porous Media written by Kimberly Renee Spayd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Fundamental Studies Of Fluid Mechanics And Stability In Porous Media Progress Report
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Author :
language : en
Publisher:
Release Date : 1991
Fundamental Studies Of Fluid Mechanics And Stability In Porous Media Progress Report written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
This report summarizes accomplished and proposed work for the fundamental studies of fluid mechanics and stability in porous media. Topics discussed include: viscous fingering in miscible displacements; polymer flow interactions in free shear layers of viscoelastic fluids; effect of nonmonotonic viscosity profiles on the stability of miscible displacements in porous media; and references. (JL).
Fundamental Studies Of Fluid Mechanics And Stability In Porous Media
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Author :
language : en
Publisher:
Release Date : 1991
Fundamental Studies Of Fluid Mechanics And Stability In Porous Media written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
This report summarizes accomplished and proposed work for the fundamental studies of fluid mechanics and stability in porous media. Topics discussed include: viscous fingering in miscible displacements; polymer flow interactions in free shear layers of viscoelastic fluids; effect of nonmonotonic viscosity profiles on the stability of miscible displacements in porous media; and references. (JL).
Handbook Of Porous Media
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Author : Kambiz Vafai
language : en
Publisher: CRC Press
Release Date : 2005-03-30
Handbook Of Porous Media written by Kambiz Vafai and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-30 with Science categories.
Over the last three decades, advances in modeling flow, heat, and mass transfer through a porous medium have dramatically transformed engineering applications. Comprehensive and cohesive, Handbook of Porous Media, Second Edition presents a compilation of research related to heat and mass transfer including the development of practical applications
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1995
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.
Flow In Porous Rocks
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Author : Andrew W. Woods
language : en
Publisher: Cambridge University Press
Release Date : 2015
Flow In Porous Rocks written by Andrew W. Woods and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Business & Economics categories.
This book provides simplified models explaining flows in heterogeneous rocks, their physics and energy production processes, for researchers, energy industry professionals and graduate students.
The Finite Volume Method In Computational Fluid Dynamics
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Author : F. Moukalled
language : en
Publisher: Springer
Release Date : 2015-08-13
The Finite Volume Method In Computational Fluid Dynamics written by F. Moukalled and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-13 with Technology & Engineering categories.
This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.