A Systems Description of Flow Through Porous Media (eBook)
XV, 119 Seiten
Springer International Publishing (Verlag)
978-3-319-00260-6 (ISBN)
The introductory part of the course, i.e. the systems description of flow through porous media, forms the topic of this brief monograph. The main objective is to present the classic reservoir simulation equations in a notation that facilitates the use of concepts from the systems-and-control literature. Although the theory is limited to the relatively simple situation of horizontal two-phase (oil-water) flow, it covers several typical aspects of porous-media flow.
The first chapter gives a brief review of the basic equations to represent single-phase and two-phase flow. It discusses the governing partial-differential equations, their physical interpretation, spatial discretization with finite differences, and the treatment of wells. It contains well-known theory and is primarily meant to form a basis for the next chapter where the equations will be reformulated in terms of systems-and-control notation.
The second chapter develops representations in state-space notation of the porous-media flow equations. The systematic use of matrix partitioning to describe the different types of inputs leads to a description in terms of nonlinear ordinary-differential and algebraic equations with (state-dependent) system, input, output and direct-throughput matrices. Other topics include generalized state-space representations, linearization, elimination of prescribed pressures, the tracing of stream lines, lift tables, computational aspects, and the derivation of an energy balance for porous-media flow.
The third chapter first treats the analytical solution of linear systems of ordinary differential equations for single-phase flow. Next it moves on to the numerical solution of the two-phase flow equations, covering various aspects like implicit, explicit or mixed (IMPES) time discretizations and associated stability issues, Newton-Raphson iteration, streamline simulation, automatic time-stepping, and other computational aspects. The chapter concludes with simple numerical examples to illustrate these and other aspects such as mobility effects, well-constraint switching, time-stepping statistics, and system-energy accounting.
The contents of this brief should be of value to students and researchers interested in the application of systems-and-control concepts to oil and gas reservoir simulation and other applications of subsurface flow simulation such as CO2 storage, geothermal energy, or groundwater remediation.
PREFACE1. POROUS-MEDIA FLOW1.1 Introduction1.2 Notation1.3 Single-phase flow1.3.1 Governing equations1.3.2 Finite-difference discretization1.3.3 Example 1 – Single-phase flow in a simple reservoir1.3.4 Incompressible flow1.3.5 Mass-conservative formulation1.3.6 Well models1.4 Two-phase flow 1.4.1 Governing equations1.4.2 Nature of the equations1.4.3 Relative permeabilities1.4.4 Example 2 – Two-phase flow in a simple reservoir1.4.5 Buckley-Leverett equation1.4.6 Linear approximation1.4.7 Formation volume factors1.4.8 Finite-difference discretization1.4.9 Example 3 – Inverted five-spot1.4.10 Sources of nonlinearity1.4.11 Incompressible flow1.4.12 Fluid velocities 2. SYSTEM MODELS2.1 System equations2.1.1 Partial-differential equations2.1.2 Ordinary-differential equations2.1.3 State-space representation2.1.4 Linearized equations2.2 Single-phase flow2.2.1 System equations2.2.2 Example 1 continued – Location matrix 2.2.3 Prescribed pressures and flow rates2.2.4 Well models2.2.5 Example 1 continued – Well model2.2.6 Elimination of prescribed pressures2.2.7 System energy2.3 Two-phase flow2.3.1 System equations2.3.2 Well operating constraints2.3.3 Computational aspects2.3.4 Lift tables2.3.5 Control valves2.3.6 Streamlines2.3.7 System energy 3 SYSTEM RESPONSE3.1 Free response3.1.1 Homogeneous equation 3.1.2 Diagonalization3.1.3 Stability3.1.4 Singular system matrix3.1.5 Example 1 continued – Free response3.2 Forced response3.2.1 Nonhomogeneous equation3.2.2 Diagonalization and modal analysis3.2.3 Singular system matrix3.3 Numerical simulation3.3.1 Explicit Euler discretization3.3.2 Implicit Euler discretization3.3.3 Picard and Newton-Raphson iteration3.3.4 Numerical stability3.3.5 IMPES3.3.6 Computational aspects3.3.7 Control aspects3.3.8 Stream line simulation3.4 Examples3.4.1 Example 1 continued – Stability3.4.2 Example 2 continued – Mobility effects3.4.3 Example 3 continued – Well constraints3.4.4 Example 3 continued – Time-stepping statistics3.4.5 Example 3 continued – System energyNOMENCLATUREINDEX
Erscheint lt. Verlag | 23.5.2013 |
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Reihe/Serie | SpringerBriefs in Earth Sciences |
Zusatzinfo | XV, 119 p. 26 illus. |
Verlagsort | Cham |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik |
Naturwissenschaften ► Geowissenschaften | |
Technik ► Bauwesen | |
Schlagworte | numerical simulation • Petroleum Engineering • Porous-media Flow • Reservoir Engineering • Reservoir Simulation • Smart Fields • subsurface flow • Systems and Control • Textbook on Flow through Porous Media |
ISBN-10 | 3-319-00260-0 / 3319002600 |
ISBN-13 | 978-3-319-00260-6 / 9783319002606 |
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