An Introduction to Reservoir Simulation Using MATLAB/GNU Octave: User Guide for the MATLAB Reservoir Simulation Toolbox (MRST)

✍ Scribed by Knut-Andreas Lie

• Publisher: Cambridge University Press
• Year: 2019
• Tongue: English
• Leaves: 678
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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