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Copyright by Yang Xue 2013 The Dissertation Committee for Yang Xue Certifies that this is the approved version of the following dissertation: NOVEL STOCHASTIC INVERSION METHODS AND WORKFLOW FOR RESERVOIR CHARACTERIZATION AND MONITORING Committee: Mrinal K. Sen, Supervisor Robert H. Tatham Sergey Fomel Kyle T. Spikes Sanjay Srinivasan Long Jin NOVEL STOCHASTIC INVERSION METHODS AND WORKFLOW FOR RESERVOIR CHARACTERIZATION AND MONITORING by Yang Xue, Dipl.-Ing. Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY The University of Texas at Austin December 2013 To my parents Musheng Cao and Li Xue To my husband Liqing Huang Acknowledgements The course of my Ph. D studying and the writing of this dissertation would not have been possible without the supports from so many people as follows. First of all, I would like to express my deepest appreciations to my supervisor, Dr. Mrinal K. Sen, for his financial supports, helps and guidance during the entire Ph. D course. As a student from a different background, Dr. Sen gave me the opportunity to develop my research interest in the exploration geophysics, provided me the exciting research subjects and helped me explore ideas. Without his patient guidance, persistent helps, constant inspirations, and great efforts in editing this dissertation, this journey would not have brought me so much fun and this dissertation would never have shaped. I would also like to give special thanks to my committee members, Dr. Robert Tatham, Dr. Fomel Sergey, Dr. Kyle Spikes, Dr. Sanjay Srinivasan, and Dr. Long Jin for their time, energy and insightful comments provided valuable inputs to my dissertation. In addition, I sincerely thank Dr. Clark R. Wilson and Dr. Zong-liang Yang, who supported me in the first semester of study. My thanks also go to Dr. Paul Stoffa and Dr. Zhiwen Deng for their kind discussions, from which I benefited a lot. I also sincerely thank Philip Guerrero, Margo Grace, Judy Sansom and Nancy Hard for your administrative assistances. Many thanks also go to Jackson School of Geosciences, sponsors of Edger Forum and Shell Oil Company for the financial support during my research. Special thanks go to quantitative reservoir management (QRM) team at Shell Oil Company, who financially supported my research for two year, offered me the exciting projects, allowed me to work on the projects at the Shell office for more than one year, provided me the excellent in- v house software, hardware and many learning opportunities, and allows me to publish my work at Shell. I must thank Dr. Long Jin and Dr. Eduardo Jimenez again for their nice teaching, helpful guidance and supervising during my visit at Shell. It has been a lot of fun working with them and learning from them. Without their collaboration, the projects would not have gone through smoothly. I would also want to thank other team members and experts from Shell, Dr. Denial Weber, Dr. Javier Ferrandis, Dr. Jaap Leguijt, Dr. Paul Gelderblom, Dr. Tim Barker, Dr. Rocky Detomo, Dr. Jorge Lopez, Dr. Paul van den Hoek, Dr. Detlef Hohl and Dr. Hans Potters for their constructive comments and generous help in my research. I also thank EAGE (European Association of Geoscientists and Engineers) for the permission to include chapter four and five of my dissertation, which were originally presented at EAGE conference meeting at London, 2013. I owe a debt of gratitude to my families for standing behind me all the time. My mother, Musheng Cao, and my father, Li Xue, always stresses the importance of education and provided me the opportunities of studying across three continents. These ten years experiences of studying and living abroard made my life quite different and so exciting. I am also grateful to my husband, Liqing Huang, not only for his endless love and tolerance, but also for his accompany and encouragement through the exploring journey. He is the sources of my strength and he makes my life so colorful. vi Novel Stochastic inversion methods and workflow for reservoir characterization and monitoring Yang Xue, PhD The University of Texas at Austin, 2013 Supervisor: Mrinal K. Sen Reservoir models are generally constructed from seismic, well logs and other related datasets using inversion methods and geostatistics. It has already been recognized by the geoscientists that such a process is prone to non-uniqueness. Practical methods for estimation of uncertainty still remain elusive. In my dissertation, I propose two new methods to estimate uncertainty in reservoir models from seismic, well logs and well production data. The first part of my research is aimed at estimating reservoir impedance models and their uncertainties from seismic data and well logs. This constitutes an inverse problem, and we recognize that multiple models can fit the measurements. A deterministic inversion based on minimization of the error between the observation and forward modeling only provides one of the best-fit models, which is usually band-limited. A complete solution should include both models and their uncertainties, which requires drawing samples from the posterior distribution. A global optimization method called very fast simulated annealing (VFSA) is commonly used to approximate posterior distribution with fast convergence. Here I address some of the limitations of VFSA by developing a new stochastic inference method, named Greedy Annealed Importance Sampling (GAIS). GAIS combines VFSA with greedy importance sampling (GIS), which vii uses a greedy search in the important regions located by VFSA to attain fast convergence and provide unbiased estimation. I demonstrate the performance of GAIS on post- and pre-stack data from real fields to estimate impedance models. The results indicate that GAIS can estimate both the expectation value and the uncertainties more accurately than using VFSA alone. Furthermore, principal component analysis (PCA) as an efficient parameterization method is employed together with GAIS to improve lateral continuity by simultaneous inversion of all traces. The second part of my research involves estimation of reservoir permeability models and their uncertainties using quantitative joint inversion of dynamic measurements, including synthetic production data and time-lapse seismic related data. Impacts from different objective functions or different data sets on the model uncertainty and model predictability are investigated as well. The results demonstrate that joint inversion of production data and time-lapse seismic related data (water saturation maps here) reduces model uncertainty, improves model predictability and shows superior performance than inversion using one type of data alone. viii Table of Contents List of Figures ........................................................................................................ xi Chapter 1: Introduction ...........................................................................................1 1.1 Inverse problem in exploration geophysics ...........................................1 1.2 Bayes theorem ........................................................................................2 1.3 Methods for geophysical inversion ........................................................5 1.4 Simultaneous seismic inversion .............................................................9 1.5 Reservoir monitoring ...........................................................................11 Chapter 2: Overview of stochastic inversion ........................................................15 2.1 Importance sampling ............................................................................16 2.2 Markov Chain ......................................................................................19 2.3 Metropolis sampling ............................................................................20 2.4 Global optimization methods ...............................................................22 2.4.1 Metropolis simulated annealing .........................................22 2.3.2 Very fast simulated annealing ............................................26 2.4.3 Genetic algorithm...............................................................29 2.4.4 Particle swarm optimization ..............................................31 2.4.5 Summary of global optimization methods .........................34 2.4 Joint approach (annealed importance sampling)..................................34 2.5 Current shortcomings and new objectives ...........................................37 Chapter 3: Novel stochastic seismic inversion using Greedy Annealed Importance Sampling (GAIS) ..........................................................................................40 3.1 Introduction ..........................................................................................40 3.2 Background: greedy importance sampling ..........................................44 3.3 Methodology: greedy annealed importance sampling (GAIS) ............52 3.4 Application of GAIS to seismic inversion ...........................................53 3.5 Synthetic test of GAIS in seismic inversion ........................................56 3.6 Inversion of post-stack seismic data ....................................................62 3.7 Inversion of pre-stack seismic data ......................................................69 ix 3.8 Discussions and conclusions ................................................................85