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Numerical Earth Models (EET 3)

image of Numerical Earth Models (EET 3)
  • By Jean-Laurent Mallet
  • Format: EPUB
  • Publication Year: 2008
  • Number of Pages: 148
  • Language: English
  • Ebook ISBN: 9789462820203

In this book the main problems related to the construction of an Earth-Model are presented and discussed. The first three chapters are dedicated to the classical methods that can be used to build numerical models, in particular, the author proposes:
– some of the classical modeling techniques used in Computer Aided Design (CAD) to model surfaces and their inadequacy for modeling complex geological objects, in particular:
– classical interpolation techniques used to model surfaces;
– topological models used to describe the connections between surfaces and volumes;
– an overview of geomodeling methods dedicated to the discrete modeling of geological objects, in particular:
– the Discrete-Smooth-Interpolation method (DSI);
– meshing techniques to model surfaces and grids;
– a presentation of the classical ?Shared-Earth-Model? (SEM) paradigm consisting in a Structural-Model (SM) plus a Property-Model (PM): SEM = SM + PM
– a discussion concerning the problems raised by the (in) compatibility between the Structural-Model (SM) and the Property-Model (PM).

© 2008 EAGE Publications bv

Table of Contents

Cover
Title Page
Copyright Page
Dedication
Table of contents
Chapter 1 Classical modeling techniques: an overview

1.1 Bezier curves and surfaces
1.1.1 Notion of the Bezier curve
1.1.2 Notion of patch
1.2 Inadequacy of B-methods for geological applications
1.2.1 Goal and use of B-methods
1.2.2 Geomodeling
1.3 Quest for an alternative mathematical model
1.3.1 Automatic Mapping: a dead-end
1.3.2 Level-Set methods
1.4 Moving- Neighborhood technique
1.5 The need for a consistent topological model
1.5.1 Cellular partition
1.5.2 The “Radial-Edge” topological model
1.6 Conclusions

Chapter 2 Discrete Modeling
2.1 Notion of Discrete Model
2.1.1 Need for a new interpolation method
2.2 Discrete Smooth Interpolation (DSI)
2.2.1 Definitions
2.2.2 The simplest example of DSI constraint
2.3 Looking for a DSI solution
2.3.1 Particular case where Ch is empty
2.3.2 General case
2.3.3 A tutorial example
2.4 Some comments on DSI
2.4.1 Divide and conquer
2.4.2 Smoothness constraints
2.4.3 Turning a linear operator into a DSI constraint
2.4.4 Certainty factors
2.5 Level-Sets methods revisited
2.6 Discrete Geostatistics
2.6.1 Sequential stochastic methods
2.6.2 Hybrid stochastic methods
2.7 Meshing techniques
2.7.1 Delaunay partition
2.7.2 Voronoi partition
2.7.3 Extrusion
2.7.4 Marching cubes and marching tetrahedra
2.8 Conclusions

Chapter 3 Seismic interpretation: an introduction
3.1 Centered trigonometric polynomial
3.1.1 Definition
3.1.2 Trigonometric approximation on [- ϖ, + ϖ]
3.1.3 Kernel based representation
3.1.4 Shifting a trigonometric polynomial
3.1.5 Covariances function of trigonometric polynomials
3.1.6 Coherency
3.1.7 Similarity
3.1.8 Homogeneity
3.2 Hilbert transform and analytic signal
3.2.1 Hilbert transform
3.2.2 Analytic signal Z(t) associated with f(t)
3.3 Applications to Seismic Interpretation
3.3.1 Notion of seismic cube: definition and notations
3.3.2 Autopicking of a horizon
3.3.3 Computing 1D seismic attributes
3.3.4 Computing 3D seismic attributes
3.3.5 Autopicking of faults
3.3.6 Aliasing
3.4 Conclusions

Chapter 4 Shared Earth Model ( SEM)
4.1 Shared-Earth-Model approach
4.1.1 Stage #1: Fault-Network Modeling
4.1.2 Stage #2: Horizons modeling
4.1.3 Stage #3: Structural-Model construction (SM)
4.1.4 Stage #4: Property Model construction (PM)
4.1.5 Stage #5: Flow simulation
4.2 What is going wrong with SEMs?
4.2.1 A comment about history matching
4.2.2 Need for a new approach
4.3 Conclusions

Chapter 5 Unified Earth Model ( UEM)
5.1 Introduction
5.1.1 GeoGrids
5.1.2 FlowGrids
5.1.3 Current compromise
5.1.4 On the origin of Stratigraphic-Grids’ limitations
5.1.5 Changing the paradigm
5.2 Parameterizing the subsurface
5.2.1 A space/time mathematical framework
5.2.2 Building a parameterization
5.2.3 Property modeling and uvt-transform
5.2.4 Pitfall to be avoided: the “xyt-transform”
5.2.5 Computing Stratigraphic-Distances
5.3 GeoGrids revisited
5.4 Upscaled permeability tensor
5.4.1 The need for upscaling
5.4.2 Stratigraphic FlowCell
5.4.3 Orthotropic nature of the upscaled permeability tensor
5.5 Unified-Earth-Model approach ( UEM)
5.5.1 Stage #1: Fault-Network Modeling
5.5.2 Stage #2: Horizons modeling
5.5.3 Stage #3: uvt-transform construction
5.5.4 Stage #4: Property Model construction
5.5.5 Stage #5: Flow simulation
5.6 What’s new with UEMs?
5.7 Conclusions

Chapter 6 FlowGrids
6.1 Introduction
6.2 Flow simulators
6.2.1 Problem addressed by flow-simulators
6.2.2 Basic principles of flow-simulators
6.2.3 Notion of Generalized Transmissibility
6.3 Transmissibility estimation
6.3.1 Estimating the transmissibility of a face Fij
6.3.2 1D- harmonic TPFA estimation of transmissibility: isotropic case
6.3.3 Extended validity of equation (6.22)
6.3.4 Stratigraphy-conforming constraint (5.23) revisited
6.3.5 Fault Multiplier
6.4 Proposals for an optimal design of FlowGrids
6.4.1 SS-FlowGrids
6.4.2 Indexing the cells of SS-FlowGrids
6.4.3 Horizontal geometry of FlowCells in a SS- FlowGrid
6.4.4 Optimality of SS-FlowGrids
6.4.5 Flux preservation across stair-stepped faults
6.4.6 Faults Multipliers and SS-FlowGrids
6.4.7 Drawbacks of Stair-Step approximation of faults
6.4.8 Local SS- FlowGrid refinement
6.4.9 Visualizing dynamic properties of “SS-FlowGrids
6.4.10 An example of a SS- FlowGrid
6.5 SS-FlowGrids versus other FlowGrids
6.5.1 Tetrahedral FlowGrids
6.5.2 Full 3D polyhedral FlowGrids
6.5.3 Stream-lines based FlowGrids
6.5.4 Primal-Cookie-Cutter FlowGrids
6.6 Conclusions

Bibliography
Index

References

http://instance.metastore.ingenta.com/content/books/9789462820203
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