Kooperativer Bibliotheksverbund

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Format: 1 online resource (xv, 660 pages) : , digital, PDF file(s).

Edition: 1st ed.

ISBN: 1-108-61528-7 , 1-108-59769-6 , 1-108-59141-8

Content: This book provides a self-contained introduction to the simulation of flow and transport in porous media, written by a developer of numerical methods. The reader will learn how to implement reservoir simulation models and computational algorithms in a robust and efficient manner. The book contains a large number of numerical examples, all fully equipped with online code and data, allowing the reader to reproduce results, and use them as a starting point for their own work. All of the examples in the book are based on the MATLAB Reservoir Simulation Toolbox (MRST), an open-source toolbox popular popularity in both academic institutions and the petroleum industry. The book can also be seen as a user guide to the MRST software. It will prove invaluable for researchers, professionals and advanced students using reservoir simulation methods. This title is also available as Open Access on Cambridge Core.

Note: Title from publisher's bibliographic system (viewed on 23 Jul 2019). , Cover -- Half-title -- Title page -- Copyright information -- Contents -- Preface -- 1 Introduction -- 1.1 Petroleum Recovery -- 1.2 Reservoir Simulation -- 1.3 Outline of the Book -- 1.4 The First Encounter with MRST -- Part I Geological Models and Grids -- 2 Modeling Reservoir Rocks -- 2.1 Formation of Sedimentary Rocks -- 2.2 Creation of Crude Oil and Natural Gas -- 2.3 Multiscale Modeling of Permeable Rocks -- 2.3.1 Geological Characterization -- 2.3.2 Representative Elementary Volumes -- 2.3.3 Microscopic Models: The Pore Scale -- 2.3.4 Mesoscopic Models -- 2.4 Modeling Rock Properties -- 2.4.1 Porosity -- 2.4.2 Permeability -- 2.4.3 Other Parameters -- 2.5 Property Modeling in MRST -- 2.5.1 Homogeneous Models -- 2.5.2 Random and Lognormal Models -- 2.5.3 The 10th SPE Comparative Solution Project: Model 2 -- 2.5.4 The Johansen Formation -- 2.5.5 SAIGUP: Shallow-Marine Reservoirs -- 3 Grids in Subsurface Modeling -- 3.1 Structured Grids -- 3.2 Unstructured Grids -- 3.2.1 Delaunay Tessellation -- 3.2.2 Voronoi Diagrams -- 3.2.3 General Tessellations -- 3.2.4 Using an External Mesh Generator -- 3.3 Stratigraphic Grids -- 3.3.1 Corner-Point Grids -- 3.3.2 2.5D Unstructured Grids -- 3.4 Grid Structure in MRST -- 3.5 Examples of More Complex Grids -- 3.5.1 SAIGUP: Model of a Shallow-Marine Reservoir -- 3.5.2 Composite Grids -- 3.5.3 Control-Point and Boundary Conformal Grids -- 3.5.4 Multiblock Grids -- Part II Single-Phase Flow -- 4 Mathematical Models for Single-Phase Flow -- 4.1 Fundamental Concept: Darcy's Law -- 4.2 General Flow Equations for Single-Phase Flow -- 4.3 Auxiliary Conditions and Equations -- 4.3.1 Boundary and Initial Conditions -- 4.3.2 Injection and Production Wells -- 4.3.3 Field Lines and Time-of-Flight -- 4.3.4 Tracers and Volume Partitions -- 4.4 Basic Finite-Volume Discretizations -- 4.4.1 Two-Point Flux-Approximation. , 4.4.2 Discrete div and grad Operators -- 4.4.3 Time-of-Flight and Tracer -- 5 Incompressible Solvers for Single-Phase Flow -- 5.1 Basic Data Structures in a Simulation Model -- 5.1.1 Fluid Properties -- 5.1.2 Reservoir States -- 5.1.3 Fluid Sources -- 5.1.4 Boundary Conditions -- 5.1.5 Wells -- 5.2 Incompressible Two-Point Pressure Solver -- 5.3 Upwind Solver for Time-of-Flight and Tracer -- 5.4 Simulation Examples -- 5.4.1 Quarter Five-Spot -- 5.4.2 Boundary Conditions -- 5.4.3 Structured versus Unstructured Stencils -- 5.4.4 Using Peaceman Well Models -- 6 Consistent Discretizations on Polyhedral Grids -- 6.1 The TPFA Method Is Not Consistent -- 6.2 The Mixed Finite-Element Method -- 6.2.1 Continuous Formulation -- 6.2.2 Discrete Formulation -- 6.2.3 Hybrid Formulation -- 6.3 Finite-Volume Methods on Mixed Hybrid Form -- 6.4 The Mimetic Method -- 6.5 Monotonicity -- 6.6 Discussion -- 7 Compressible Flow and Rapid Prototyping -- 7.1 Implicit Discretization -- 7.2 A Simulator Based on Automatic Differentiation -- 7.2.1 Model Setup and Initial State -- 7.2.2 Discrete Operators and Equations -- 7.2.3 Well Model -- 7.2.4 The Simulation Loop -- 7.3 Pressure-Dependent Viscosity -- 7.4 Non-Newtonian Fluid -- 7.5 Thermal Effects -- Part III Multiphase Flow -- 8 Mathematical Models for Multiphase Flow -- 8.1 New Physical Properties and Phenomena -- 8.1.1 Saturation -- 8.1.2 Wettability -- 8.1.3 Capillary Pressure -- 8.1.4 Relative Permeability -- 8.2 Flow Equations for Multiphase Flow -- 8.2.1 Single-Component Phases -- 8.2.2 Multicomponent Phases -- 8.2.3 Black-Oil Models -- 8.3 Model Reformulations for Immiscible Two-Phase Flow -- 8.3.1 Pressure Formulation -- 8.3.2 Fractional-Flow Formulation in Phase Pressure -- 8.3.3 Fractional-Flow Formulation in Global Pressure -- 8.3.4 Fractional-Flow Formulation in Phase Potential -- 8.3.5 Richards' Equation. , 8.4 The Buckley-Leverett Theory of 1D Displacements -- 8.4.1 Horizontal Displacement -- 8.4.2 Gravity Segregation -- 8.4.3 Front Tracking: Semi-Analytical Solutions -- 9 Discretizing Hyperbolic Transport Equations -- 9.1 A New Solution Concept: Entropy-Weak Solutions -- 9.2 Conservative Finite-Volume Methods -- 9.3 Centered versus Upwind Schemes -- 9.3.1 Centered Schemes -- 9.3.2 Upwind or Godunov Schemes -- 9.3.3 Comparison of Centered and Upwind Schemes -- 9.3.4 Implicit Schemes -- 9.4 Discretization on Unstructured Polyhedral Grids -- 10 Solvers for Incompressible Immiscible Flow -- 10.1 Fluid Objects for Multiphase Flow -- 10.2 Sequential Solution Procedures -- 10.2.1 Pressure Solvers -- 10.2.2 Saturation Solvers -- 10.3 Simulation Examples -- 10.3.1 Buckley-Leverett Displacement -- 10.3.2 Inverted Gravity Column -- 10.3.3 Homogeneous Quarter Five-Spot -- 10.3.4 Heterogeneous Quarter Five-Spot: Viscous Fingering -- 10.3.5 Buoyant Migration of CO[sub(2)] in a Sloping Sandbox -- 10.3.6 Water Coning and Gravity Override -- 10.3.7 The Effect of Capillary Forces - Capillary Fringe -- 10.3.8 Norne: Simplified Simulation of a Real-Field Model -- 10.4 Numerical Errors -- 10.4.1 Splitting Errors -- 10.4.2 Grid Orientation Errors -- 11 Compressible Multiphase Flow -- 11.1 Industry-Standard Simulation -- 11.2 Two-Phase Flow without Mass Transfer -- 11.3 Three-Phase Relative Permeabilities -- 11.3.1 Relative Permeability Models from ECLIPSE 100 -- 11.3.2 Evaluating Relative Permeabilities in MRST -- 11.3.3 The SPE 1, SPE 3, and SPE 9 Benchmark Cases -- 11.3.4 A Simple Three-Phase Simulator -- 11.4 PVT Behavior of Petroleum Fluids -- 11.4.1 Phase Diagrams -- 11.4.2 Reservoir Types and Their Phase Behavior during Recovery -- 11.4.3 PVT and Fluid Properties in Black-Oil Models -- 11.5 Phase Behavior in ECLIPSE Input Decks -- 11.6 The Black-Oil Equations. , 11.6.1 The Water Component -- 11.6.2 The Oil Component -- 11.6.3 The Gas Component -- 11.6.4 Appearance and Disappearance of Phases -- 11.7 Well Models -- 11.7.1 Inflow-Performance Relationships -- 11.7.2 Multisegment Wells -- 11.8 Black-Oil Simulation with MRST -- 11.8.1 Simulating the SPE 1 Benchmark Case -- 11.8.2 Comparison against a Commercial Simulator -- 11.8.3 Limitations and Potential Pitfalls -- 12 The AD-OO Framework for Reservoir Simulation -- 12.1 Overview of the Simulator Framework -- 12.2 Model Hierarchy -- 12.2.1 PhysicalModel - Generic Physical Models -- 12.2.2 ReservoirModel - Basic Reservoir Models -- 12.2.3 Black-Oil Models -- 12.2.4 Models of Wells and Production Facilities -- 12.3 Solving the Discrete Model Equations -- 12.3.1 Assembly of Linearized Systems -- 12.3.2 Nonlinear Solvers -- 12.3.3 Selection of Time-Steps -- 12.3.4 Linear Solvers -- 12.4 Simulation Examples -- 12.4.1 Depletion of a Closed/Open Compartment -- 12.4.2 An Undersaturated Sector Model -- 12.4.3 SPE 1 Instrumented with Inflow Valves -- 12.4.4 The SPE 9 Benchmark Case -- 12.5 Improving Convergence and Reducing Runtime -- Part IV Reservoir Engineering Workflows -- 13 Flow Diagnostics -- 13.1 Flow Patterns and Volumetric Connections -- 13.1.1 Volumetric Partitions -- 13.1.2 Time-of-Flight Per Partition Region: Improved Accuracy -- 13.1.3 Well Allocation Factors -- 13.2 Measures of Dynamic Heterogeneity -- 13.2.1 Flow and Storage Capacity -- 13.2.2 Lorenz Coefficient and Sweep Efficiency -- 13.3 Residence-Time Distributions -- 13.4 Case Studies -- 13.4.1 Tarbert Formation: Volumetric Connections -- 13.4.2 Heterogeneity and Optimized Well Placement -- 13.5 Interactive Flow Diagnostics Tools -- 13.5.1 Synthetic 2D Example: Improving Areal Sweep -- 13.5.2 SAIGUP: Flow Patterns and Volumetric Connections -- 14 Grid Coarsening -- 14.1 Grid Partitions. , 14.1.1 Uniform Partitions -- 14.1.2 Connected Partitions -- 14.1.3 Composite Partitions -- 14.2 Coarse Grid Representation in MRST -- 14.2.1 Subdivision of Coarse Faces -- 14.3 Partitioning Stratigraphic Grids -- 14.3.1 The Johansen Aquifer -- 14.3.2 The SAIGUP Model -- 14.3.3 Near Well Refinement for CaseB4 -- 14.4 More Advanced Coarsening Methods -- 14.5 A General Framework for Agglomerating Cells -- 14.5.1 Creating Initial Partitions -- 14.5.2 Connectivity Checks and Repair Algorithms -- 14.5.3 Indicator Functions -- 14.5.4 Merge Blocks -- 14.5.5 Refine Blocks -- 14.5.6 Examples -- 14.6 Multilevel Hierarchical Coarsening -- 14.7 General Advice and Simple Guidelines -- 15 Upscaling Petrophysical Properties -- 15.1 Upscaling for Reservoir Simulation -- 15.2 Upscaling Additive Properties -- 15.3 Upscaling Absolute Permeability -- 15.3.1 Averaging Methods -- 15.3.2 Flow-Based Upscaling -- 15.4 Upscaling Transmissibility -- 15.5 Global and Local-Global Upscaling -- 15.6 Upscaling Examples -- 15.6.1 Flow Diagnostics Quality Measure -- 15.6.2 A Model with Two Facies -- 15.6.3 SPE 10 with Six Wells -- 15.6.4 Complete Workflow Example -- 15.6.5 General Advice and Simple Guidelines -- Appendix The MATLAB Reservoir Simulation Toolbox -- A.1 Getting Started with the Software -- A.1.1 Core Functionality and Add-on Modules -- A.1.2 Downloading and Installing -- A.1.3 Exploring Functionality and Getting Help -- A.1.4 Release Policy and Version Numbers -- A.1.5 Software Requirements and Backward Compatibility -- A.1.6 Terms of Usage -- A.2 Public Data Sets and Test Cases -- A.3 More About Modules and Advanced Functionality -- A.3.1 Operating the Module System -- A.3.2 What Characterizes a Module? -- A.3.3 List of Modules -- A.4 Rapid Prototyping Using MATLAB and MRST -- A.5 Automatic Differentiation in MRST -- References -- Index -- Usage of MRST Functions.

Additional Edition: ISBN 1-108-49243-6

Language: English

URL: Volltext  (kostenfrei)

URL: Inhaltstext

URL: https://doi.org/10.1017/9781108591416