Download or read book Mathematical Models for Poroelastic Flows written by Anvarbek Meirmanov and published by Springer Science & Business Media. This book was released on 2013-11-29 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Modelling Of Flow Through Porous Media Proceedings Of The Conference written by Alain P Bourgeat and published by World Scientific. This book was released on 1995-11-30 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Modeling for Flow and Transport Through Porous Media written by Gedeon Dagan and published by Springer Science & Business Media. This book was released on 1991 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical and Numerical Modeling in Porous Media written by Martin A. Diaz Viera and published by CRC Press. This book was released on 2012-07-24 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Mathematical and Numerical Modeling in Porous Media written by Martin A. Diaz Viera and published by CRC Press. This book was released on 2012-07-24 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Analysis of Viscoelastic Flows written by Michael Renardy and published by SIAM. This book was released on 2000-01-01 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.
Download or read book Mathematical Modelling of Flow Through Porous Media written by Alain P. Bourgeat and published by World Scientific Publishing Company Incorporated. This book was released on 1995 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modelling Water Flow in Unsaturated Porous Media written by Adam Szymkiewicz and published by Springer Science & Business Media. This book was released on 2012-10-11 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on two issues related to mathematical and numerical modelling of flow in unsaturated porous media. In the first part numerical solution of the governing equations is discussed, with particular emphasis on the spatial discretization of highly nonlinear permeability coefficient. The second part deals with large scale flow in heterogeneous porous media of binary structure. Upscaled models are developed and it is shown that the presence of material heterogeneities may give rise to additional non-equilibrium terms in the governing equations or to hysteresis in the averaged constitutive relationships.
Download or read book Modeling Density Driven Flow in Porous Media written by Ekkehard O. Holzbecher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling of flow and transport in groundwater has become an important focus of scientific research in recent years. Most contributions to this subject deal with flow situations, where density and viscosity changes in the fluid are neglected. This restriction may not always be justified. The models presented in the book demonstrate immpressingly that the flow pattern may be completely different when density changes are taken into account. The main applications of the models are: thermal and saline convection, geothermal flow, saltwater intrusion, flow through salt formations etc. This book not only presents basic theory, but the reader can also test his knowledge by applying the included software and can set up own models.
Download or read book Mathematical Modeling of Disperse Two Phase Flows written by Christophe Morel and published by Springer. This book was released on 2016-10-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the theoretical foundations of disperse two-phase flows, which are characterized by the existence of bubbles, droplets or solid particles finely dispersed in a carrier fluid, which can be a liquid or a gas. Chapters clarify many difficult subjects, including modeling of the interfacial area concentration. Basic knowledge of the subjects treated in this book is essential to practitioners of Computational Fluid Dynamics for two-phase flows in a variety of industrial and environmental settings. The author provides a complete derivation of the basic equations, followed by more advanced subjects like turbulence equations for the two phases (continuous and disperse) and multi-size particulate flow modeling. As well as theoretical material, readers will discover chapters concerned with closure relations and numerical issues. Many physical models are presented, covering key subjects including heat and mass transfers between phases, interfacial forces and fluid particles coalescence and breakup, amongst others. This book is highly suitable for students in the subject area, but may also be a useful reference text for more advanced scientists and engineers.
Download or read book Mechanics of Poroelastic Media written by A.P.S. Selvadurai and published by Springer Science & Business Media. This book was released on 1996-01-31 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Mechanics of Poroelastic Media the classical theory of poroelasticity developed by Biot is developed and extended to the study of problems in geomechanics, biomechanics, environmental mechanics and materials science. The contributions are grouped into sections covering constitutive modelling, analytical aspects, numerical modelling, and applications to problems. The applications of the classical theory of poroelasticity to a wider class of problems will be of particular interest. The text is a standard reference for researchers interested in developing mathematical models of poroelasticity in geoenvironmental mechanics, and in the application of advanced theories of poroelastic biomaterials to the mechanics of biomaterials.
Download or read book Flow Interpretation Implications for Poro Elastic Modeling written by and published by . This book was released on 2010 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basis of poro-elastic modeling is a set of assumptions about the nature of the porous media and the fluid that fill its void spaces. The basic assumptions are: (1) the solid matrix is homogenous, elastically deformable, and chemically inert with respect to the fluid, (2) the fluid is single phase and Newtonian, (3) the flow is in the laminar range, (4) there is an explicit one-to-one relationship between porosity and permeability, and (5) the fluid flow is governed by Darcy's law. There are two basic interpretations of Darcy's law. The primary interpretation in poro-elastic acoustics is to assume that Darcy's law is a restatement of Poisseuille's law for porous media applications. This restatement can be extended for bundles of capillary tubes, and non-straight tubes. This gives rise to a linear equation that predicts the acoustic dispersion, and attenuation for acoustic waves in a porous media. Unfortunately, simulations of fluid flow in Hele-Shaw cells suggest that for porous media consisting of face-centered-cubically packed spheres the Poisseuille law treatment is incorrect. Both the distribution of fluid velocity, and viscous drag are incorrect. The second interpretation is to assume that Darcy's law is a macro-scale statistically derived flow relationship derived from underlying micro-scale processes. This methods gives rise to a model that inherently includes flow geometry, and variations in permeability and porosity. The statistical model allows for the definition of permeability such that the tortuosity of the fluid paths are explicitly included in both the permeability and the inertial effects. Additional fluid dynamic phenomena, such as inertial effects, internal friction and local accelerations among others can be included in the calculation.
Download or read book Mathematical Theory of Compressible Fluid Flow written by Richard Von Mises and published by . This book was released on 1966 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Models of Fluid Dynamics written by Rainer Ansorge and published by Wiley-VCH. This book was released on 2009-07-10 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Without sacrificing scientific strictness, this introduction to the field guides readers through mathematical modeling, the theoretical treatment of the underlying physical laws and the construction and effective use of numerical procedures to describe the behavior of the dynamics of physical flow. The book is carefully divided into three main parts: - The design of mathematical models of physical fluid flow; - A theoretical treatment of the equations representing the model, as Navier-Stokes, Euler, and boundary layer equations, models of turbulence, in order to gain qualitative as well as quantitative insights into the processes of flow events; - The construction and effective use of numerical procedures in order to find quantitative descriptions of concrete physical or technical fluid flow situations. Both students and experts wanting to control or predict the behavior of fluid flows by theoretical and computational fluid dynamics will benefit from this combination of all relevant aspects in one handy volume.
Download or read book Asymptotic Modelling of Fluid Flow Phenomena written by Radyadour Kh. Zeytounian and published by Springer Science & Business Media. This book was released on 2002-01-31 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: for the fluctuations around the means but rather fluctuations, and appearing in the following incompressible system of equations: on any wall; at initial time, and are assumed known. This contribution arose from discussion with J. P. Guiraud on attempts to push forward our last co-signed paper (1986) and the main idea is to put a stochastic structure on fluctuations and to identify the large eddies with a part of the probability space. The Reynolds stresses are derived from a kind of Monte-Carlo process on equations for fluctuations. Those are themselves modelled against a technique, using the Guiraud and Zeytounian (1986). The scheme consists in a set of like equations, considered as random, because they mimic the large eddy fluctuations. The Reynolds stresses are got from stochastic averaging over a family of their solutions. Asymptotics underlies the scheme, but in a rather loose hidden way. We explain this in relation with homogenizati- localization processes (described within the §3. 4 ofChapter 3). Ofcourse the mathematical well posedness of the scheme is not known and the numerics would be formidable! Whether this attempt will inspire researchers in the field of highly complex turbulent flows is not foreseeable and we have hope that the idea will prove useful.
Download or read book Mathematical Model of Flow of Fluid in Porous Media written by Hong Li and published by . This book was released on 1997 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications written by Mehrdad Massoudi and published by MDPI. This book was released on 2020-04-16 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geothermal energy is the thermal energy generated and stored in the Earth's core, mantle, and crust. Geothermal technologies are used to generate electricity and to heat and cool buildings. To develop accurate models for heat and mass transfer applications involving fluid flow in geothermal applications or reservoir engineering and petroleum industries, a basic knowledge of the rheological and transport properties of the materials involved (drilling fluid, rock properties, etc.)—especially in high-temperature and high-pressure environments—are needed. This Special Issue considers all aspects of fluid flow and heat transfer in geothermal applications, including the ground heat exchanger, conduction and convection in porous media. The emphasis here is on mathematical and computational aspects of fluid flow in conventional and unconventional reservoirs, geothermal engineering, fluid flow, and heat transfer in drilling engineering and enhanced oil recovery (hydraulic fracturing, CO2 injection, etc.) applications.
