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Inverse Theory for Petroleum Reservoir Characterization and History Matching

ISBN-10: 052188151X

ISBN-13: 9780521881517

Edition: 2008

Authors: Ning Liu, Dean S. Oliver, Albert C. Reynolds

List price: $168.00
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This book is a guide to the use of inverse theory for estimation and conditional simulation of flow and transport parameters in porous media. It describes the theory and practice of estimating properties of underground petroleum reservoirs from measurements of flow in wells, and it explains how to characterize the uncertainty in such estimates. Early chapters present the reader with the necessary background in inverse theory, probability and spatial statistics. The book demonstrates how to calculate sensitivity coefficients and the linearized relationship between models and production data. It also shows how to develop iterative methods for generating estimates and conditional realizations. The text is written for researchers and graduates in petroleum engineering and groundwater hydrology and can be used as a textbook for advanced courses on inverse theory in petroleum engineering. It includes many worked examples to demonstrate the methodologies and a selection of exercises.
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Book details

List price: $168.00
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 5/1/2008
Binding: Hardcover
Pages: 394
Size: 7.00" wide x 9.75" long x 0.75" tall
Weight: 2.090

Ning Liu holds a Ph.D. from the University of Oklahoma in petroleum engineering and now works as a Reservoir Simulation Consultant at Chevron Energy Technology Company. Dr Liu is a recipient of the Outstanding PhD Scholarship Award at the University of Oklahoma and the Student Research Award from the International Association for Mathematical Geology (IAMG). Her areas of interest are history matching, uncertainty forecasting, production optimization, and reservoir management.

Dean Oliver is the Mewbourne Chair Professor in the Mewbourne School of Petroleum and Geological Engineering at the University of Oklahoma, where he was the Director for four years. Prior to joining the University of Oklahoma, he worked for seventeen years as a research geophysicist, staff reservoir engineer, and research scientist in reservoir characterization for Chevron and for Saudi Aramco. He also spent six years as a professor in the Petroleum Engineering Department at the University of Tulsa. Professor Oliver has been awarded 'best paper of the year' awards from two journals and received the SPE Reservoir Description and Dynamics Award in 2004. He is currently the Executive Editor of SPE Journal. His research interests are in inverse theory, reservoir characterization, uncertainty quantification, and optimization.

Albert Reynolds is Professor of Petroleum Engineering and Mathematics, holder of the McMan chair in Petroleum Engineering, and Director of the TUPREP Research Consortium at the University of Tulsa. He has published over 100 technical articles and one previous book, and is well known for his contributions to pressure transient analysis and optimization based history matching. Professor Reynolds has won the Society of Petroleum Engineers (SPE) Distinguished Achievement Award for Petroleum Engineering Faculty, the SPE Reservoir Description and Dynamics Award and the SPE Formation Award. He became an SPE Distinguished Member in 1999.

The forward problem
The inverse problem
Examples of inverse problems
Density of the Earth
Acoustic tomography
Steady-state 1D flow in porous media
History matching in reservoir simulation
Estimation for linear inverse problems
Characterization of discrete linear inverse problems
Solutions of discrete linear inverse problems
Singular value decomposition
Backus and Gilbert method
Probability and estimation
Random variables
Expected values
Bayes' rule
Descriptive geostatistics
Geologic constraints
Univariate distribution
Multi-variate distribution
Gaussian random variables
Random processes in function spaces
Production data
Logs and core data
Seismic data
The maximum a posteriori estimate
Conditional probability for linear problems
Model resolution
Doubly stochastic Gaussian random field
Matrix inversion identities
Optimization for nonlinear problems using sensitivities
Shape of the objective function
Minimization problems
Newton-like methods
Levenberg-Marquardt algorithm
Convergence criteria
Line search methods
Computational examples
Sensitivity coefficients
The Frechet derivative
Discrete parameters
One-dimensional steady-state flow
Adjoint methods applied to transient single-phase flow
Adjoint equations
Sensitivity calculation example
Adjoint method for multi-phase flow
Evaluation of uncertainty with a posteriori covariance matrix
Quantifying uncertainty
Introduction to Monte Carlo methods
Sampling based on experimental design
Gaussian simulation
General sampling algorithms
Simulation methods based on minimization
Conceptual model uncertainty
Other approximate methods
Comparison of uncertainty quantification methods
Recursive methods
Basic concepts of data assimilation
Theoretical framework
Kalman filter and extended Kalman filter
The ensemble Kalman filter
Application of EnKF to strongly nonlinear problems
1D example with nonlinear dynamics and observation operator
Example - geologic facies