This book 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. Computational Methods for Multiphase Flows in Porous Media reviews multiphase flow equations and computational methods to introduce basic terminologies and notation. A thorough discussion of practical aspects of the subject is presented in a consistent manner, and the level of treatment is rigorous without being unnecessarily abstract. Each chapter ends with bibliographic information and exercises. This book can be used as a textbook for graduate or advanced undergraduate students in geology, petroleum engineering, and applied mathematics, and as a reference book for professionals in these fields, as well as scientists working in the area of petroleum reservoir simulation. It can also be used 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. List of Figures; List of Tables; Preface; Chapter 1: Introduction; Chapter 2: Flow and Transport Equations; Chapter 3: Rock and Fluid Properties; Chapter 4: Numerical Methods; Chapter 5: Solution of Linear Systems; Chapter 6: Single Phase Flow; Chapter 7: Two-Phase Flow; Chapter 8: The Black Oil Model; Chapter 9: The Compositional Model; Chapter 10: Nonisothermal Flow; Chapter 11: Chemical Flooding; Chapter 12: Flows in Fractured Porous Media; Chapter 13: Welling Modeling; Chapter 14: Special Topics; Chapter 15: Nomenclature; Chapter 16: Units; Bibliography; Index.