Mathematical Models for Poroelastic Flows PDF Download
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Author: Anvarbek Meirmanov
Publisher: Springer Science & Business Media
ISBN: 9462390150
Category : Mathematics
Languages : en
Pages : 477
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Book Description
The book is devoted to rigorous derivation of macroscopic mathematical models as a homogenization of exact mathematical models at the microscopic level. The idea is quite natural: one first must describe the joint motion of the elastic skeleton and the fluid in pores at the microscopic level by means of classical continuum mechanics, and then use homogenization to find appropriate approximation models (homogenized equations). The Navier-Stokes equations still hold at this scale of the pore size in the order of 5 – 15 microns. Thus, as we have mentioned above, the macroscopic mathematical models obtained are still within the limits of physical applicability. These mathematical models describe different physical processes of liquid filtration and acoustics in poroelastic media, such as isothermal or non-isothermal filtration, hydraulic shock, isothermal or non-isothermal acoustics, diffusion-convection, filtration and acoustics in composite media or in porous fractured reservoirs. Our research is based upon the Nguetseng two-scale convergent method.
Author: Anvarbek Meirmanov
Publisher: Springer Science & Business Media
ISBN: 9462390150
Category : Mathematics
Languages : en
Pages : 477
Get Book
Book Description
The book is devoted to rigorous derivation of macroscopic mathematical models as a homogenization of exact mathematical models at the microscopic level. The idea is quite natural: one first must describe the joint motion of the elastic skeleton and the fluid in pores at the microscopic level by means of classical continuum mechanics, and then use homogenization to find appropriate approximation models (homogenized equations). The Navier-Stokes equations still hold at this scale of the pore size in the order of 5 – 15 microns. Thus, as we have mentioned above, the macroscopic mathematical models obtained are still within the limits of physical applicability. These mathematical models describe different physical processes of liquid filtration and acoustics in poroelastic media, such as isothermal or non-isothermal filtration, hydraulic shock, isothermal or non-isothermal acoustics, diffusion-convection, filtration and acoustics in composite media or in porous fractured reservoirs. Our research is based upon the Nguetseng two-scale convergent method.
Author: Alain P Bourgeat
Publisher: World Scientific
ISBN: 9814548391
Category :
Languages : en
Pages : 534
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Book Description
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: Martin A. Diaz Viera
Publisher: CRC Press
ISBN: 0203113888
Category : Mathematics
Languages : en
Pages : 370
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Book Description
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: Gedeon Dagan
Publisher: Springer Science & Business Media
ISBN: 9401721998
Category : Science
Languages : en
Pages : 293
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Book Description
The main aim of this paper is to present some new and general results, ap plicable to the the equations of two phase flow, as formulated in geothermal reservoir engineering. Two phase regions are important in many geothermal reservoirs, especially at depths of order several hundred metres, where ris ing, essentially isothermal single phase liquid first begins to boil. The fluid then continues to rise, with its temperature and pressure closely following the saturation (boiling) curve appropriate to the fluid composition. Perhaps the two most interesting theoretical aspects of the (idealised) two phase flow equations in geothermal reservoir engineering are that firstly, only one component (water) is involved; and secondly, that the densities of the two phases are so different. This has led to the approximation of ignoring capillary pressure. The main aim of this paper is to analyse some of the consequences of this assumption, especially in relation to saturation changes within a uniform porous medium. A general analytic treatment of three dimensional flow is considered. Pre viously, three dimensional modelling in geothermal reservoirs have relied on numerical simulators. In contrast, most of the past analytic work has been restricted to one dimensional examples.
Author: Martin A. Diaz Viera
Publisher: CRC Press
ISBN: 041566537X
Category : Mathematics
Languages : en
Pages : 372
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Book Description
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 understanding of the physical processes involved in fluid flow and transport. This fact can be attributed to the complexity of the phenomena which include multicomponent fluids, multiphasic flow and rock-fluid interactions. Since its formulation in 1856, Darcy’s law has been generalized to describe multi-phase compressible fluid flow through anisotropic and heterogeneous porous and fractured rocks. Due to the scarcity of information, a high degree of uncertainty on the porous medium properties is commonly present. Contributions to the knowledge of modeling flow and transport, as well as to the characterization of porous media at field scale are of great relevance. This book addresses several of these issues, treated with a variety of methodologies grouped into four parts: I Fundamental concepts II Flow and transport III Statistical and stochastic characterization IV Waves The problems analyzed in this book cover diverse length scales that range from small rock samples to field-size porous formations. They belong to the most active areas of research in porous media with applications in geosciences developed by diverse authors. This book was written for a broad audience with a prior and basic knowledge of porous media. The book is addressed to a wide readership, and it will be useful not only as an authoritative textbook for undergraduate and graduate students but also as a reference source for professionals including geoscientists, hydrogeologists, geophysicists, engineers, applied mathematicians and others working on porous media.
Author: Adelina Georgescu
Publisher: World Scientific
ISBN: 9814289574
Category : Mathematics
Languages : en
Pages : 418
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Book Description
1. Mathematical models governing fluid flows stability. 1.1. General mathematical models of thermodynamics. 1.2. Classical mathematical models in thermodynamics of fluids. 1.3. Classical mathematical models in thermodynamics. 1.4. Classical perturbation models. 1.5. Generalized incompressible Navier-Stokes model -- 2. Incompressible Navier-Stokes fluid. 2.1. Back to integral setting; involvement of dynamics and bifurcation. 2.2. Stability in semidynamical systems. 2.3. Perturbations; asymptotic stability; linear stability. 2.4. Linear stability. 2.5. Prodi's linearization principle. 2.6. Estimates for the spectrum of Ã. 2.7. Universal stability criteria -- 3. Elements of calculus of variations. 3.1. Generalities. 3.2. Direct and inverse problems of calculus of variations. 3.3. Symmetrization of some matricial ordinary differential operators. 3.4. Variational principles for problems (3.3.1)-(3.3.7). 3.5. Fourier series solutions for variational problems -- 4. Variants of the energy method for non-stationary equations. 4.1. Variant based on differentiation of parameters. 4.2. Variant based on simplest symmetric part of operators. 4.3. Variants based on energy splitting -- 5. Applications to linear Bénard convections. 5.1. Magnetic Bénard convection in a partially ionized fluid. 5.2. Magnetic Bénard convection for a fully ionized fluid. 5.3. Convection in a micro-polar fluid bounded by rigid walls. 5.4. Convections governed by ode's with variable coefficients -- 6. Variational methods applied to linear stability. 6.1. Magnetic Bénard problem with Hall effect. 6.2. Lyapunov method applied to the anisotropic Bénard problem. 6.3. Stability criteria for a quasi-geostrophic forced zonal flow. 6.4. Variational principle for problem (5.3.1), (5.3.2). 6.5. Taylor-Dean problem -- 7. Applications of the direct method to linear stability. 7.1. Couette flow between two cylinders subject to a magnetic field. 7.2. Soret-Dufour driven convection. 7.3. Magnetic Soret-Dufour driven convection. 7.4. Convection in a porous medium. 7.5. Convection in the presence of a dielectrophoretic force. 7.6. Convection in an anisotropic M.H.D. thermodiffusive mixture. 7.7. Inhibition of the thermal convection by a magnetic field. 7.8. Microconvection in a binary layer subject to a strong Soret effect. 7.9. Convection in the layer between the sea bed and the permafrost.
Author: Myron B. Allen, III
Publisher: John Wiley & Sons
ISBN: 1119663873
Category : Mathematics
Languages : en
Pages : 226
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Book Description
Master the techniques necessary to build and use computational models of porous media fluid flow In The Mathematics of Fluid Flow Through Porous Media, distinguished professor and mathematician Dr. Myron B. Allen delivers a one-stop and mathematically rigorous source of the foundational principles of porous medium flow modeling. The book shows readers how to design intelligent computation models for groundwater flow, contaminant transport, and petroleum reservoir simulation. Discussions of the mathematical fundamentals allow readers to prepare to work on computational problems at the frontiers of the field. Introducing several advanced techniques, including the method of characteristics, fundamental solutions, similarity methods, and dimensional analysis, The Mathematics of Fluid Flow Through Porous Media is an indispensable resource for students who have not previously encountered these concepts and need to master them to conduct computer simulations. Teaching mastery of a subject that has increasingly become a standard tool for engineers and applied mathematicians, and containing 75 exercises suitable for self-study or as part of a formal course, the book also includes: A thorough introduction to the mechanics of fluid flow in porous media, including the kinematics of simple continua, single-continuum balance laws, and constitutive relationships An exploration of single-fluid flows in porous media, including Darcy’s Law, non-Darcy flows, the single-phase flow equation, areal flows, and flows with wells Practical discussions of solute transport, including the transport equation, hydrodynamic dispersion, one-dimensional transport, and transport with adsorption A treatment of multiphase flows, including capillarity at the micro- and macroscale Perfect for graduate students in mathematics, civil engineering, petroleum engineering, soil science, and geophysics, The Mathematics of Fluid Flow Through Porous Media also belongs on the bookshelves of any researcher who wishes to extend their research into areas involving flows in porous media.
Author: Ulrich Hornung
Publisher: Springer Science & Business Media
ISBN: 1461219205
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This book offers a systematic, rigorous treatment of upscaling procedures related to physical modeling for porous media on micro-, meso- and macro-scales, including detailed studies of micro-structure systems and computational results for dual-porosity models.
Author: G. Chavent
Publisher: Elsevier
ISBN: 9780080875385
Category : Technology & Engineering
Languages : en
Pages : 375
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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: Tomáš Bodnár
Publisher: Springer Nature
ISBN: 3030396398
Category : Mathematics
Languages : en
Pages : 647
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Book Description
This contributed volume is based on talks given at the August 2016 summer school “Fluids Under Pressure,” held in Prague as part of the “Prague-Sum” series. Written by experts in their respective fields, chapters explore the complex role that pressure plays in physics, mathematical modeling, and fluid flow analysis. Specific topics covered include: Oceanic and atmospheric dynamics Incompressible flows Viscous compressible flows Well-posedness of the Navier-Stokes equations Weak solutions to the Navier-Stokes equations Fluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.
