Download or read book Multiphase Mechanisms and Fluid Dynamics in Gas Injection Eor Processes written by Madhav Kulkarni and published by LAP Lambert Academic Publishing. This book was released on 2011-06 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work attempts to address six key questions: (i) do we continue to 'fix the problems' of gravity segregation in the horizontal gas floods or find an effective alternative?, (ii) is there a 'happy-medium' between single-slug and WAG processes that would outperform both?, (iii) what are the controlling multiphase mechanisms and fluid dynamics in gravity drainage processes?, (iv) what are the mechanistic issues relating to gravity drainage?, and (v) how can we model the novel GAGD process using traditional analytical and empirical theories and (vi) what are the roles of the classical displacement, versus drainage in the GAGD process? The primary original contributions of this work to the existing literature are: (i) proof of concept of two new gas injection processes, and (ii) preliminary mechanistic and dynamic differences between the drainage and displacement phenomenon have been identified and a new mechanism to characterize the process fluid mechanics have been proposed.

Download or read book Multiphase Fluid Flow in Porous and Fractured Reservoirs written by Yu-Shu Wu and published by Gulf Professional Publishing. This book was released on 2015-09-23 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiphase Fluid Flow in Porous and Fractured Reservoirs discusses the process of modeling fluid flow in petroleum and natural gas reservoirs, a practice that has become increasingly complex thanks to multiple fractures in horizontal drilling and the discovery of more unconventional reservoirs and resources. The book updates the reservoir engineer of today with the latest developments in reservoir simulation by combining a powerhouse of theory, analytical, and numerical methods to create stronger verification and validation modeling methods, ultimately improving recovery in stagnant and complex reservoirs. Going beyond the standard topics in past literature, coverage includes well treatment, Non-Newtonian fluids and rheological models, multiphase fluid coupled with geomechanics in reservoirs, and modeling applications for unconventional petroleum resources. The book equips today’s reservoir engineer and modeler with the most relevant tools and knowledge to establish and solidify stronger oil and gas recovery. Delivers updates on recent developments in reservoir simulation such as modeling approaches for multiphase flow simulation of fractured media and unconventional reservoirs Explains analytical solutions and approaches as well as applications to modeling verification for today’s reservoir problems, such as evaluating saturation and pressure profiles and recovery factors or displacement efficiency Utilize practical codes and programs featured from online companion website

Download or read book Computational Methods in Multiphase Flow IV written by A.A. Mammoli and published by WIT Press. This book was released on 2007-05-11 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluid Dynamics is one of the most important topics of applied mathematics and physics. Together with complex flows and turbulence, multiphase flows remains one of the most challenging areas of computational mechanics, and even seemingly simple problems remain unsolved to date. Multiphase flows are found in all areas of technology, at all length scales and flow regimes. The fluids involved can be compressible or incompressible, linear or nonlinear. Because of the complexity of the problem, it is often essential to utilize advanced computational and experimental methods to solve the complex equations that describe them. Challenges in these simulations include nonlinear fluids, treating drop breakup and coalescence, characterizing phase structures, and many others.This volume brings together work presented at the Fourth International Conference on Computational and Experimental Methods in Multiphase and Complex Flows. Featured topics include: Suspensions; Bubble and Drop Dynamics; Flow in Porous Media; Interfaces; Turbulent Flow; Injectors and Nozzles; Particle Image Velocimetry; Macroscale Constitutive Models; Large Eddy Simulation; Finite Volumes; Interface Tracking Methods; Biological Flows; Environmental Multiphase Flow; Phase Changes and Stochastic Modelling.

Download or read book Multiphase Flow Dynamics 2 written by Nikolay Ivanov Kolev and published by Springer Science & Business Media. This book was released on 2011-11-03 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-phase flows are part of our natural environment such as tornadoes, typhoons, air and water pollution and volcanic activities as well as part of industrial technology such as power plants, combustion engines, propulsion systems, or chemical and biological industry. The industrial use of multi-phase systems requires analytical and numerical strategies for predicting their behavior. .In its fourth extended edition the successful monograph package “Multiphase Flow Daynmics” contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations, providing a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present second volume the methods for describing the mechanical interactions in multiphase dynamics are provided. This fourth edition includes various updates, extensions, improvements and corrections. "The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended,” BERND PLATZER, ZAAM In the present second volume the methods for describing the mechanical interactions in multiphase dynamics are provided. This fourth edition includes various updates, extensions, improvements and corrections. "The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended,” BERND PLATZER, ZAAM "The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended,” BERND PLATZER, ZAAM

Download or read book Particulates And Continuum Multiphase Fluid Dynamics written by Shao L. Soo and published by Routledge. This book was released on 2018-12-19 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treating multiphase systems with emphasis on the aspect of fluid dynamics and as an introduction to research in multiphase flow, this book covers definitive concepts, methods, and theories which have been validated by experimental results. A textbook for college seniors and graduate students and a research reference, it is a coherent presentation that facilitates the understanding of physical interactions. The book's focus is fluid dynamics, with extension to other transport processes of heat and mass transfer, and chemical relations to illustrate applications of multiphase flow. The exercise problems at the end of each chapter assist the reader in formulating and solving physical problems and gaining a sense of magnitude of interacting effects and events. Extended details and corollaries are also included in these exercise problems. Some of the topics in the exercise problems may also be incorporated as topics for the lectures.

Download or read book Energy Geotechnics written by Alessio Ferrari and published by Springer. This book was released on 2018-08-23 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects selected full papers presented at the International Symposium on Energy Geotechnics 2018 (SEG-2018), held on 25th – 28th September 2018, at the Swiss Federal Institute of Technology in Lausanne (EPFL). It covers a wide range of topics in energy geotechnics, including energy geostructures, energy geostorage, thermo-hydro-chemo-mechanical behaviour of geomaterials, unconventional resources, hydraulic stimulation, induced seismicity, CO2 geological storage, and nuclear waste disposal as well as topics such as tower and offshore foundations. The book is intended for postgraduate students, researchers and practitioners working on geomechanics and geotechnical engineering for energy-related applications.

Download or read book Multiphase Flow Dynamics 3 written by Nikolay Ivanov Kolev and published by Springer Science & Business Media. This book was released on 2007-06-08 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to allow the application of the theory from all the three volumes also to processes in combustion engines a systematic set of internally consistent state equations for diesel fuel gas and liquid valid in broad range of changing pressure and temperature are provided also in Volume 3. Erlangen, October 2006 Nikolay Ivanov Kolev Table of contents 1 Some basics of the single-phase boundary layer theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 Flow over plates, velocity profiles, share forces, heat transfer. . . . . . . . . . . . . . . . . . . . 1 1. 1. 1 Laminar flow over the one site of a plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1. 2 Turbulent flow parallel to plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 2 Steady state flow in pipes with circular cross sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 2. 1 Hydraulic smooth wall surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 2. 2 Transition region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 2. 3 Complete rough region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 2. 4 Heat transfer to fluid in a pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1. 3 Transient flow in pipes with circular cross sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2 Introduction to turbulence of multi-phase flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2. 1 Basic ideas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2. 2 Isotropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2. 3 Scales, eddy viscosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2. 3. 1 Small scale turbulent motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2. 3. 2 Large scale turbulent motion, Kolmogorov-Pandtl expression. . . . . . . . . 42 2. 4 k-eps framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3 Sources for fine resolution outside the boundary layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3. 1 Bulk sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3. 1. 1 Deformation of the velocity field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3. 1. 2 Blowing and suction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Download or read book Relaxation Schemes for Multiphase Multicomponent Flow in Gas Injection Processes written by Shalini B. Krishnamurthy and published by . This book was released on 2008 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relaxation schemes for multiphase, multicomponent flow in gas injection processes.

Download or read book Multiphase Flow written by S. Hernández and published by WIT Press. This book was released on 2020-06-03 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research included in this volume focuses on using synergies between experimental and computational techniques to gain a better understanding of all classes of multiphase and complex flow. The included papers illustrate the close interaction between numerical modellers and researchers working to gradually resolve the many outstanding issues in our understanding of multiphase flow. Recently multiphase fluid dynamics have generated a great deal of attention, leading to many notable advances in experimental, analytical and numerical studies. Progress in numerical methods has permitted the solution of many practical problems, helping to improve our understanding of the physics involved. Multiphase flows are found in all areas of technology and the range of related problems of interest is vast, including astrophysics, biology, geophysics, atmospheric process, and many areas of engineering.

Download or read book Multiphase Transport of Hydrocarbons in Pipes written by Juan J. Manzano-Ruiz and published by John Wiley & Sons. This book was released on 2024-03-26 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiphase Transport of Hydrocarbons in Pipes An introduction to multiphase flows in the oil and gas industry The term ‘multiphase flow’ refers to the concurrent flow of oil and/or gas, alongside other substances or materials such as production water, chemical inhibitors, and solids (e.g. sand). This is a critical topic in the oil and gas industry, where the presence of multiple flow phases in pipelines affects deliverability, generates serious complications in predicting flow performance for system design and operation, and requires specific risk mitigation actions and continuous maintenance. Chemical and Mechanical Engineers interested in working in this industry will benefit from understanding the basic theories and practices required to model and operate multiphase flows through pipelines, wells, and other components of the production system. Multiphase Transport of Hydrocarbons in Pipes meets this need with a comprehensive overview of five decades of research into multiphase flow. Incorporating fundamental theories, historic and cutting-edge multiphase flow models, and concrete examples of current and future applications. This book provides a sound technical background for prospective or working engineers in need of understanding this crucial area of industry. Readers will also find: Fundamental principles supporting commercial software Detailed tools for estimating multiphase flow rates through flowlines, wells, and more Integration of conservation principles with thermodynamic and transport properties Coverage of legacy and modern simulation models This book is ideal for flow assurance engineers, facilities engineers, oil and gas production engineers, and process engineers, as well as chemical and mechanical engineering students looking to work in any of these roles.

Download or read book Multiphase Flow Dynamics 2 written by Nikolay Ivanov Kolev and published by Springer Science & Business Media. This book was released on 2007-05-21 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-phase flows are part of our natural environment such as tornadoes, typhoons, air and water pollution and volcanic activities as well as part of industrial technology such as power plants, combustion engines, propulsion systems, or chemical and biological industry. The industrial use of multi-phase systems requires analytical and numerical strategies for predicting their behavior. In its third extended edition this book contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations. This book provides a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present second volume the mechanical and thermal interactions in multiphase dynamics are provided. This third edition includes various updates, extensions, improvements and corrections.

Download or read book Machine Learning for Subsurface Characterization written by Siddharth Misra and published by Gulf Professional Publishing. This book was released on 2019-10-12 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine Learning for Subsurface Characterization develops and applies neural networks, random forests, deep learning, unsupervised learning, Bayesian frameworks, and clustering methods for subsurface characterization. Machine learning (ML) focusses on developing computational methods/algorithms that learn to recognize patterns and quantify functional relationships by processing large data sets, also referred to as the "big data." Deep learning (DL) is a subset of machine learning that processes "big data" to construct numerous layers of abstraction to accomplish the learning task. DL methods do not require the manual step of extracting/engineering features; however, it requires us to provide large amounts of data along with high-performance computing to obtain reliable results in a timely manner. This reference helps the engineers, geophysicists, and geoscientists get familiar with data science and analytics terminology relevant to subsurface characterization and demonstrates the use of data-driven methods for outlier detection, geomechanical/electromagnetic characterization, image analysis, fluid saturation estimation, and pore-scale characterization in the subsurface. Learn from 13 practical case studies using field, laboratory, and simulation data Become knowledgeable with data science and analytics terminology relevant to subsurface characterization Learn frameworks, concepts, and methods important for the engineer’s and geoscientist’s toolbox needed to support

Download or read book Multiphase Flow Dynamics 1 written by Nikolay Ivanov Kolev and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-phase flows are part of our natural environment such as tornadoes, typhoons, air and water pollution and volcanic activities as well as part of industrial technology such as power plants, combustion engines, propulsion systems, or chemical and biological industry. The industrial use of multi-phase systems requires analytical and numerical strategies for predicting their behavior. In its third extended edition this monograph contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations, providing a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present first volume the fundamentals of multiphase dynamics are provided. This third edition includes various updates, extensions and improvements in all book chapters.

Download or read book Multiphase Flow Dynamics 4 written by Nikolay Ivanov Kolev and published by Springer Science & Business Media. This book was released on 2011-09-24 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present Volume 4 of the successful monograh package “Multiphase Flow Dynamics”is devoted to selected Chapters of the multiphase fluid dynamics that are important for practical applications but did not find place in the previous volumes. The state of the art of the turbulence modeling in multiphase flows is presented. As introduction, some basics of the single phase boundary layer theory including some important scales and flow oscillation characteristics in pipes and rod bundles are presented. Then the scales characterizing the dispersed flow systems are presented. The description of the turbulence is provided at different level of complexity: simple algebraic models for eddy viscosity, simple algebraic models based on the Boussinesq hypothesis, modification of the boundary layer share due to modification of the bulk turbulence, modification of the boundary layer share due to nucleate boiling. The role of the following forces on the mathematical description of turbulent flows is discussed: the lift force, the lubrication force in the wall boundary layer, and the dispersion force. A pragmatic generalization of the k-eps models for continuous velocity field is proposed containing flows in large volumes and flows in porous structures. A Methods of how to derive source and sinks terms for multiphase k-eps models is presented. A set of 13 single- and two phase benchmarks for verification of k-eps models in system computer codes are provided and reproduced with the IVA computer code as an example of the application of the theory. This methodology is intended to help other engineers and scientists to introduce this technology step-by-step in their own engineering practice. In many practical application gases are solved in liquids under given conditions, released under other conditions and therefore affecting technical processes for good of for bad. Useful information on the solubility of oxygen, nitrogen, hydrogen and carbon dioxide in water under large interval of pressures and temperatures is collected, and appropriate mathematical approximation functions are provided. In addition methods for the computation of the diffusion coefficients are described. With this information solution and dissolution dynamics in multiphase fluid flows can be analyzed. For this purpose the non-equilibrium absorption and release on bubble, droplet and film surfaces under different conditions is mathematically described. A systematic set of internally consistent state equations for diesel fuel gas and liquid valid in broad range of changing pressure and temperature is provided. This new second edition includes various updates, extensions, improvements and corrections. In many practical application gases are solved in liquids under given conditions, released under other conditions and therefore affecting technical processes for good of for bad. Useful information on the solubility of oxygen, nitrogen, hydrogen and carbon dioxide in water under large interval of pressures and temperatures is collected, and appropriate mathematical approximation functions are provided. In addition methods for the computation of the diffusion coefficients are described. With this information solution and dissolution dynamics in multiphase fluid flows can be analyzed. For this purpose the non-equilibrium absorption and release on bubble, droplet and film surfaces under different conditions is mathematically described. A systematic set of internally consistent state equations for diesel fuel gas and liquid valid in broad range of changing pressure and temperature is provided. This new second edition includes various updates, extensions, improvements and corrections.

Download or read book Asphaltene Deposition written by Francisco M. Vargas and published by CRC Press. This book was released on 2018-05-16 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: As global consumption of fossil fuels such as oil increases, previously abundant sources have become depleted or plagued with obstructions. Asphaltene deposition is one of such obstructions which can significantly decrease the rate of oil production. This book offers concise yet thorough coverage of the complex problem of asphaltene precipitation and deposition in oil production. It covers fundamentals of chemistry, stabilization theories and mechanistic approaches of asphaltene behavior at high temperature and pressure. Asphaltene Deposition: Fundamentals, Prediction, Prevention, and Remediation explains techniques for experimental determination of asphaltene precipitation and deposition and different modeling tools available to forecast the occurrence and magnitude of asphaltene deposition in a given oil field. It discusses strategies for mitigation of asphaltene deposition using chemical inhibition and corresponding challenges, best practices for asphaltene remediation, current research, and case studies.

Download or read book Multiphase Flow Dynamics written by Marcio Ferreira Martins and published by Springer Nature. This book was released on 2022-04-01 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents isothermal and non-isothermal multiphase flows with and without phase change or chemical reactions. Six main axes of multiphase flow are covered in a strategic order: Multiphase Flow in Industry, Multiphase Flow Measurement and Instrumentation, Multiphase Flow With Phase Change & Chemical Reactions, Multiphase Flow Modeling, Experimental Multiphase Flow, and Wet and Dry Particulate Systems. Each part is opened by mini-reviews written by internationally prominent researchers from the academy and industry. The content is of interest to researchers and engineers working in mining, oil and gas, power, nuclear, chemical process, space, food, biomedical, micro and nanotechnology, and other industries.

Download or read book Computational Methods for Multiphase Flows in Porous Media written by Zhangxin Chen and published by SIAM. This book was released on 2006-01-01 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.