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2005 | Buch

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Mathematical Methods and Modelling in Hydrocarbon Exploration and Production

herausgegeben von: Dr. Armin Iske, Dr. Trygve Randen

Verlag: Springer Berlin Heidelberg

Buchreihe : Mathematics in Industry

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Hydrocarbon exploration and production incorporate great technology challenges for the oil and gas industry. In order to meet the world's future demand for oil and gas, further technological advance is needed, which in turn requires research across multiple disciplines, including mathematics, geophysics, geology, petroleum engineering, signal processing, and computer science.

This book addresses important aspects and fundamental concepts in hydrocarbon exploration and production. Moreover, new developments and recent advances in the relevant research areas are discussed, whereby special emphasis is placed on mathematical methods and modelling. The book reflects the multi-disciplinary character of the hydrocarbon production workflow, ranging from seismic data imaging, seismic analysis and interpretation and geological model building, to numerical reservoir simulation. Various challenges concerning the production workflow are discussed in detail.

The thirteen chapters of this joint work, authored by international experts from academic and industrial institutions, include survey papers of expository character as well as original research articles. Large parts of the material presented in this book were developed between November 2000 and April 2004 through the European research and training network NetAGES, "Network for Automated Geometry Extraction from Seismic". The new methods described here are currently being implemented as software tools at Schlumberger Stavanger Research, one of the world's largest service providers to the oil industry.

Inhaltsverzeichnis

Frontmatter

Seismic Interpretation

Introduction to Seismic Texture

Summary

This chapter introduces the concept of seismic texture analysis. Several seismic textures and their geological messages are described with respect to depositional history and reservoir quality. Finally, a strategy of how to automatically map these textures is recommended and limitations of this method are mentioned.

Jürgen Schlaf, Trygve Randen, Lars Sønneland

Atlas of 3D Seismic Attributes

Summary

Seismic attributes have been a common tool in seismic data analysis since the mid to late seventies. Seismic attributes may highlight geological or geophysical effects, thus leading to a quicker analysis of the data. In the early works, seismic attributes were to a large degree limited to capture 1D effects occurring along the vertical seismic trace. Since the mid nineties, extensions to multi-trace attributes have become more popular. In this chapter we present a set of three-dimensional attributes for seismic data analysis. The attributes are designed to highlight the seismic expression of faults and stratigraphic features, and are designed to be genuine 3D with no implicit directionality bias on the result. The chapter is written to be an introduction to the technology. Feasibility tests of some of the approaches can be found in the chapter [4] of Carrillat and Vallès.

Trygve Randen, Lars Sønneland

The Use of Structure Tensors in the Analysis of Seismic Data

Summary

The first and second order structure tensors, simply estimated by differencing the image, can be used to quantify the local structure of seismic data and their departure from laminar structure. They can be used to distinguish chaotic regions as well as regions of interest, like mounds and horizon terminations from stratified regions. They have been well established in the processing of 2D images, but their application to 3D volume data is still a largely unexplored field of research. This chapter reviews the properties of these tensors and their application to image processing in general, and demonstrates their usefulness in the analysis of 2D and 3D seismic data.

Maria Faraklioti, Maria Petrou

Automated Structural Interpretation Through Classification of Seismic Horizons

Summary

A novel method for extracting geometry primitives from seismic data is presented. All events in the 3D seismic cube will be detected and can be combined into geometric primitives based on similarities in the local wave form. No assumptions of continuity in the geometric primitives are required. The geometric primitives can therefore represent faulted horizons, which furthermore facilitates quantification of the fault displacement.

The accuracy with which the local waveform can be represented is defined as a user input, implying that subtle lateral changes in the reflectivity can be detected and exploited. This characteristic enables analysis of stratigraphic variations along horizons.

Hilde G. Borgos, Thorleif Skov, Lars Sønneland

Automatic Fault Extraction Using Artificial Ants

Summary

A high-level fault interpretation workflow using automatically extracted surfaces is presented. The first step of the workflow is to generate a fault attribute that enhances the discontinuities in the seismic data. Fault-like surfaces are then extracted using an algorithm called ant tracking. The surfaces are then loaded into an analysis tool where the interpreter, by interactively working with the surfaces, decides on the final interpretation. The interpreter works on two levels in the analysis tool. Firstly, on the system level, where the fault surfaces are split into separate systems according to their strikes. Faults that are created at the same time period typically form a fault system. This separation is geologically meaningful and gives the interpreter an overview of the structural history of the area. Secondly, the interpreter groups and modifies individual surfaces within each fault system to form the final interpretation. The workflow is demonstrated as a case study of two fields offshore mid Norway.

Stein Inge Pedersen, Thorleif Skov, Trygve Randen, Lars Sønneland

Geological Model Building

Geological Modelling and Reservoir Simulation

Summary

The main mathematical techniques used in building geological models for input to fluid flow simulation are reviewed. The subject matter concerns the entire geological and reservoir simulation modelling workflow relating to the subsurface. To provide a realistic illustration of a complete fluid flow model, a short outline of two-phase incompressible flow through porous media is given. The mathematics of model building is discussed in a context of seismic acquisition, processing and interpretation, well logging and geology. Grid generation, geometric modelling and spatial statistics are covered in considerable detail. A few new results in the area of geostatistics are proved. In particular the equivalence of radial basis functions, general forms of kriging and minimum curvature methods is shown. A Bayesian formulation of uncertainty assessment is outlined. The theory of inverse problems is discussed in a general way, from both deterministic and statistical points of view. There is a brief discussion of upscaling. A case for multiscale geological modelling is made and the outstanding research problems to be solved in building multiscale models from many types of data are discussed.

Chris L. Farmer

Geological Model Building: A Hierarchical Segmentation Approach

Summary

A new approach towards model building with the promise of significantly shortening the turnaround time of 3D model building is presented. By introducing a unified framework, efficient representation of models throughout the lifecycle of a reservoir is enabled, all the way from velocity to simulation models. All levels of resolution are maintained and handled simultaneously and information is structured according to geological understanding. This enables the interpreter to work with pre-generated geological objects, rather than spending time creating them in the first place. Consequently, more time is spent being creative, gaining a better understanding of the reservoir. Furthermore, the framework enables use of new semi- or fully automatic interpretation schemes and provides real-time user interaction with large volumes.

Erik Monsen, Trygve Randen, Lars Sønneland, Jan E. Odegard

Mapping 3D Geo-Bodies Based on Level Set and Marching Methods

Summary

In this chapter, a simplified method for mapping objects based on the level set method is introduced. Level set and marching methods are used to map connected volumes within 3D seismic data. The simpler marching method solves the stationary problem stated by the level set formulation. The evolution of the object, from a seed point to the boundary, is described by a differential equation.

Stine Kjersti Richardsen, Trygve Randen

Modern Techniques in Seismic Tomography

Summary

This chapter is focussed on two local inverse kinematic problems of seismology, concerning reflected rays and refracted rays. Both model problems are reduced to a sequence of 2D problems, where theoretical and numerical results are offered. In the case of reflected rays, it is shown how to select a stable problem of recovering a velocity distribution in a layer, by using travel time measurements along rays with one reflection on the boundary. This way, a simple inversion algorithm is obtained for the linearized near a constant velocity case. In the case of refracted rays, a Newton-type algorithm for finding the 3D velocity distribution from 3D travel time measurements is constructed for the local inverse kinematic problem. To this end, a sound velocity that increases linearly with depth is chosen as a first approximation. With this particular choice for the linearization, the underlying problem reduces to a sequence of 2D Radon transforms in discs.

Alexander A. Boukhgueim

Reservoir Modelling and Simulation

From 3D Seismic Facies to Reservoir Simulation: An Example From the Grane Field

Summary

A new seismic to simulation workflow is proposed, where the aim is the reduction of the overall turn-around time, from seismic data acquisition to reservoir model building and simulation. To this end, new automated procedures are established: firstly, for discriminating seismic data into three-dimensional seismic facies, and secondly, for building a voxel-based reservoir model.

This chapter is divided into three parts. In the first part, automated three-dimensional seismic facies mapping is discussed, where both the stratigraphic and the structural framework of the seismic data are reflected. The resulting seismic facies are then identified with lithologies by calibration against well data.

In the second part, automated voxel grid extraction for reservoirs is explained. The required input is the voxel size together with the top and bottom horizons delimiting the reservoir extents. The calibrated three-dimensional seismic facies are then used to associate each voxel with porosity and permeability values. This last automated step results in a voxel-based reservoir model.

Finally, in the third part, an application of the new workflow is presented. To this end, a case study for the Grane field is used. The selected simulation scenario models a three-phase reservoir life.

Alexis Carrillat, Brice Vallès

Reservoir Flow Simulation by Adaptive ADER Schemes

Summary

In this chapter, an extension of ADER schemes is presented in order to solve both linear and nonlinear scalar conservation laws on unstructured triangulations. The proposed scheme is conservative and belongs to the class of finite volume schemes. It combines high order reconstruction techniques with a high order flux evaluation method to update cell average values through fluxes across cell interfaces. The ADER approach results in an explicit, one-step scheme based on the solution of generalized Riemann problems across cell interfaces. Moreover, the triangulation is adaptively modified during the simulation to effectively combine high order accuracy with locally refined meshes and therefore reduce the computational costs. The required adaption rules for the refinement and coarsening of the triangular mesh rely on a customized error indicator. Numerical experiments confirm the expected orders of accuracy and show the good performance of the proposed scheme for linear and nonlinear problems. Finally, the adaptive ADER schemes are applied to a test case from oil industry, which plays an important role in the modelling of fluid flow in petroleum reservoirs.

Martin Käser, Armin Iske

Optimal Multivariate Interpolation

Summary

In this chapter, we are concerned with the problem of multivariate data interpolation. The main focus lies on the concept of minimizing a quadratic form which, in practice, emerges from a physical model, subject to the interpolation constraints. The approach is a natural extension of the one-dimensional polynomial spline interpolation. Besides giving a basic outline of the mathematical framework, we design a fast numerical scheme and analyze the performance quality. We finally show that optimal interpolation is closely related to standard linear stochastic estimation methods.

Tobias Werther

A Method for Ranking CO2 Flow Models Using Seismic Modeling and Time-Lapse Data

Summary

A method for discriminating between different reservoir flow models using forward modeling and time-lapse seismic is presented. A rock-physical model is used in order to generate synthetic time-lapse acoustic responses based on flow model predictions. From the acoustic properties a pull-down caused by modifications in acoustic velocity is calculated and compared to real measurements. Full synthetic seismograms are also generated. The method has been applied to the Sleipner CO₂ sequestration project where time-lapse seismic is used to monitor the injected gas. Different vertical migration processes of the CO₂ may explain the observed time-lapse response. In this chapter, this new methodology is used in order to discriminate between these processes.

Magne Lygren, Erik Lindeberg, Per Bergmo, Geir Vaaland Dahl, Kristine Årland Halvorsen, Trygve Randen, Lars Sønneland

Backmatter

Titel: Mathematical Methods and Modelling in Hydrocarbon Exploration and Production
herausgegeben von: Dr. Armin Iske
Dr. Trygve Randen
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-540-26493-4
Print ISBN: 978-3-540-22536-2
DOI: https://doi.org/10.1007/b137702