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The need to predict, understand, and optimize complex physical and c- mical processes occurring in and around the earth, such as groundwater c- tamination, oil reservoir production, discovering new oil reserves, and ocean hydrodynamics, has been increasingly recognized. Despite their seemingly disparate natures, these geoscience problems have many common mathe- tical and computational characteristics. The techniques used to describe and study them are applicable across a broad range of areas. The study of the above problems through physical experiments, mat- matical theory, and computational techniques requires interdisciplinary col- boration between engineers, mathematicians, computational scientists, and other researchers working in industry, government laboratories, and univ- sities. By bringing together such researchers, meaningful progress can be made in predicting, understanding, and optimizing physical and chemical processes. The International Workshop on Fluid Flow and Transport in Porous - dia was successfully held in Beijing, China, August 2{6, 1999. The aim of this workshop was to bring together applied mathematicians, computational scientists, and engineers working actively in the mathematical and nume- cal treatment of ?uid ?ow and transport in porous media. A broad range of researchers presented papers and discussed both problems and current, state-of-the-art techniques.
The need to predict, understand, and optimize complex physical and c- mical processes occurring in and around the earth, such as groundwater c- tamination, oil reservoir production, discovering new oil reserves, and ocean hydrodynamics, has been increasingly recognized. Despite their seemingly disparate natures, these geoscience problems have many common mathe- tical and computational characteristics. The techniques used to describe and study them are applicable across a broad range of areas. The study of the above problems through physical experiments, mat- matical theory, and computational techniques requires interdisciplinary col- boration between engineers, mathematicians, computational scientists, and other researchers working in industry, government laboratories, and univ- sities. By bringing together such researchers, meaningful progress can be made in predicting, understanding, and optimizing physical and chemical processes. The International Workshop on Fluid Flow and Transport in Porous - dia was successfully held in Beijing, China, August 2{6, 1999. The aim of this workshop was to bring together applied mathematicians, computational scientists, and engineers working actively in the mathematical and nume- cal treatment of ?uid ?ow and transport in porous media. A broad range of researchers presented papers and discussed both problems and current, state-of-the-art techniques.
Fluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work, we investigate the behavior and numerical treatment of multiphase flow in porous media. To be more specific, we take the sequestration of CO2 in geological media as an example. Mathematical modeling and numerical study of carbon sequestration helps to predict both short and long-term behavior of CO2 storage in geological media, which can be a benefit in many ways. This work aims at developing accurate and efficient numerical treatment for problems in porous media on non-rectangular geometries. Numerical treatment of Darcy flow and transport have been developed for many years on rectangular and simplical meshes. However, extra effort is required to extend them to general non-rectangular meshes. In this dissertation work, for flow simulation, we develop new H(div)- conforming mixed finite elements (AT and AT [superscript red] ) which are accurate on cuboidal hexahedra. We also develop the new direct serendipity finite element (DS [subscript r] ), which is H1 -conforming and accurate on quadrilaterals and a special family of hexahedra called truncated cubes. The use of the direct serendipity finite element reduces the number of degrees of freedom significantly and therefore accelerates numerical simulations. For transport, we use the newly developed direct serendipity elements in an enriched Galerkin method (EG), which is locally conservative. The entropy viscosity stabilization is applied to eliminate spurious oscillations. We test the EG-DS [subscript r] method on problems with diffusion, transport, and coupled flow and transport. Finally, we study two-phase flow in heterogeneous porous media with capillary pressure. We work on a new formulation of the problem and force the continuity of the capillary flux with a modification to conquer the degeneracy. The numerical simulation of two-phase flow is conducted on non-rectangular grids and uses the new elements.
Computational Methods for Multiphase Flows in Porous Media offers a fundamental and practical introduction to the use of computational methods, particularly finite element methods, in the simulation of fluid flows in porous media. It is the first book to cover a wide variety of flows, including single-phase, two-phase, black oil, volatile, compositional, nonisothermal, and chemical compositional flows in both ordinary porous and fractured porous media. In addition, a range of computational methods are used, and benchmark problems of nine comparative solution projects organized by the Society of Petroleum Engineers are presented for the first time in book form. The book reviews multiphase flow equations and computational methods to introduce basic terminologies and notation. A thorough discussion of practical aspects of the subjects is presented in a consistent manner, and the level of treatment is rigorous without being unnecessarily abstract. Audience: this book can be used as a textbook for graduate or advanced undergraduate students in geology, petroleum engineering, and applied mathematics; as a reference book for professionals in these fields, as well as scientists working in the area of petroleum reservoir simulation; as a handbook for employees in the oil industry who need a basic understanding of modeling and computational method concepts; and by researchers in hydrology, environmental remediation, and some areas of biological tissue modeling. Calculus, physics, and some acquaintance with partial differential equations and simple matrix algebra are necessary prerequisites.
The past decade has seen remarkable growth in research related to petroleum reseIVoir simulation. This growth reflects several developments, not the least of which is the increased interest in oil recovery technologies requiring sophisticated engineer ing. Augmenting this interest has been the broader availability of supercomputers capable of handling the tremendous computational demands of a typical reseIVoir simulator. The field of reseIVoir simulation incorporates several major facets of applied mathematics. First, in view of the varieyt and complexity of the processes encoun tered, it is imperative that the modeler adopt a systematic approach to establishing the equations governing reseIVoir flows. Second, the mathematical structure of these flow equations needs to be carefully analyzed in order to develop appropriate and efficient numerical methods for their solution. Third, since some aspects of the discretized flow equations are typically stiff, one must develop efficient schemes for solving large sparse systems of linear equations. This monograph has three parts, each devoted to one of these three aspects of reseIVoir modeling. The text grew out of a set of lectures presented by the authors in the autumn of 1986 at the IBM Scientific Center in Bergen, Norway. We feel that it is only appropriate to caution the reader that many of the ideas that we present in this monograph do not reflect standard approaches in petroleum reseIVoir simulation. In fact, our aim is to outline promising new ways of attacking reseIVoir simulation prob lems, rather than to compile another textbook for the mainstream.
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.
The June 2001 conference brought together mathematicians, computational scientists, and engineers working on the mathematical and numerical treatment of fluid flow and transport in porous media. This collection of 43 papers from that conference reports on recent advances in network flow modeling, parallel computation, optimization, upscaling, uncertainty reduction, media characterization, and chemically reactive phenomena. Topics include modeling horizontal wells using hybrid grids in reservoir simulation, a high order Lagrangian scheme for flow through unsaturated porous media, and a streamline front tracking method for two- and three- phase flow. No index. Annotation copyrighted by Book News, Inc., Portland, OR.
William T. Sha first proposed the novel porous media formulation in an article in Nuclear Engineering and Design in 1980. The novel porous media formulation represented a new, flexible and unified approach to solve real-world engineering problems. It uses the concept of volume porosity, directional surface porosities, distributed resistance and distributed heat source and sink. Most practical engineering problems involve many complex shapes and sizes of solid internal structures whose distributed resistance is impossible to quantify accurately. The concept of directional surface porosities eliminates the sole reliance on empirical estimation of the distributed resistance of complex-shaped structures often involved in the analysis. The directional surface porosities thus greatly improve the resolution and modeling accuracy and facilitate mock-ups of numerical simulation models of real engineering systems. Both the continuum and conventional porous media formulations are subsets of the novel porous media formulation.
The study of multiphase flow through porous media is undergoing intense development, mostly due to the recent introduction of new methods. After the profound changes induced by percolation in the eighties, attention is nowadays focused on the pore scale. The physical situation is complex and only recently have tools become available that allow significant progress to be made in the area. This volume on Multiphase Flow in Porous Media, which is also being published as a special issue of the journal Transport in Porous Media, contains contributions on the lattice-Boltzmann technique, the renormalization technique, and semi-phenomenological studies at the pore level. Attention is mostly focused on two- and three-phase flows. These techniques are of tremendous importance for the numerous applications of multiphase flows in oil fields, unsaturated soils, the chemical industry, and environmental sciences.