Quantifying Uncertainty in Subsurface Systems E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Geophysical Monograph Series
• Sprache: Englisch

Seitenzahl: 839

Veröffentlichungsjahr: 2018

Beschreibung

Under the Earth's surface is a rich array of geological resources, many with potential use to humankind. However, extracting and harnessing them comes with enormous uncertainties, high costs, and considerable risks. The valuation of subsurface resources involves assessing discordant factors to produce a decision model that is functional and sustainable. This volume provides real-world examples relating to oilfields, geothermal systems, contaminated sites, and aquifer recharge. Volume highlights include: * A multi-disciplinary treatment of uncertainty quantification * Case studies with actual data that will appeal to methodology developers * A Bayesian evidential learning framework that reduces computation and modeling time Quantifying Uncertainty in Subsurface Systems is a multidisciplinary volume that brings together five major fields: information science, decision science, geosciences, data science and computer science. It will appeal to both students and practitioners, and be a valuable resource for geoscientists, engineers and applied mathematicians. Read the Editors' Vox: eos.org/editors-vox/quantifying-uncertainty-about-earths-resources

Leseprobe

Geophysical Monograph Series

180 Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and ImplicationsEric T. DeWeaver, Cecilia M. Bitz, and L.-Bruno Tremblay (Eds.)

181 Midlatitude Ionospheric Dynamics and DisturbancesPaul M. Kintner, Jr., Anthea J. Coster, Tim Fuller‐Rowell, Anthony J. Mannucci, Michael Mendillo, and Roderick Heelis (Eds.)

182 The Stromboli Volcano: An Integrated Study of the 2002–2003 EruptionSonia Calvari, Salvatore Inguaggiato, Giuseppe Puglisi, Maurizio Ripepe, and Mauro Rosi (Eds.)

183 Carbon Sequestration and Its Role in the Global Carbon CycleBrian J. McPherson and Eric T. Sundquist (Eds.)

184 Carbon Cycling in Northern PeatlandsAndrew J. Baird, Lisa R. Belyea, Xavier Comas, A. S. Reeve, and Lee D. Slater (Eds.)

185 Indian Ocean Biogeochemical Processes and Ecological VariabilityJerry D. Wiggert, Raleigh R. Hood, S. Wajih A. Naqvi, Kenneth H. Brink, and Sharon L. Smith (Eds.)

186 Amazonia and Global ChangeMichael Keller, Mercedes Bustamante, John Gash, and Pedro Silva Dias (Eds.)

187 Surface Ocean–Lower Atmosphere ProcessesCorinne Le Quèrè and Eric S. Saltzman (Eds.)

188 Diversity of Hydrothermal Systems on Slow Spreading Ocean RidgesPeter A. Rona, Colin W. Devey, Jérôme Dyment, and Bramley J. Murton (Eds.)

189 Climate Dynamics: Why Does Climate Vary?De‐Zheng Sun and Frank Bryan (Eds.)

190 The Stratosphere: Dynamics, Transport, and ChemistryL. M. Polvani, A. H. Sobel, and D. W. Waugh (Eds.)

191 Rainfall: State of the ScienceFirat Y. Testik and Mekonnen Gebremichael (Eds.)

192 Antarctic Subglacial Aquatic EnvironmentsMartin J. Siegert, Mahlon C. Kennicut II, and Robert A. Bindschadler (Eds.)

193 Abrupt Climate Change: Mechanisms, Patterns, and ImpactsHarunur Rashid, Leonid Polyak, and Ellen Mosley‐Thompson (Eds.)

194 Stream Restoration in Dynamic Fluvial Systems: Scientific Approaches, Analyses, and ToolsAndrew Simon, Sean J. Bennett, and Janine M. Castro (Eds.)

195 Monitoring and Modeling the Deepwater Horizon Oil Spill: A Record‐Breaking EnterpriseYonggang Liu, Amy MacFadyen, Zhen‐Gang Ji, and Robert H. Weisberg (Eds.)

196 Extreme Events and Natural Hazards: The Complexity PerspectiveA. Surjalal Sharma, Armin Bunde, Vijay P. Dimri, and Daniel N. Baker (Eds.)

197 Auroral Phenomenology and Magnetospheric Processes: Earth and Other PlanetsAndreas Keiling, Eric Donovan, Fran Bagenal, and Tomas Karlsson (Eds.)

198 Climates, Landscapes, and CivilizationsLiviu Giosan, Dorian Q. Fuller, Kathleen Nicoll, Rowan K. Flad, and Peter D. Clift (Eds.)

199 Dynamics of the Earth’s Radiation Belts and Inner MagnetosphereDanny Summers, Ian R. Mann, Daniel N. Baker, and Michael Schulz (Eds.)

200 Lagrangian Modeling of the AtmosphereJohn Lin (Ed.)

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204 The Galápagos: A Natural Laboratory for the Earth SciencesKaren S. Harpp, Eric Mittelstaedt, Noémi d’Ozouville, and David W. Graham (Eds.)

205 Modeling Atmospheric and Oceanic Flows: Insightsfrom Laboratory Experiments and Numerical SimulationsThomas von Larcher and Paul D. Williams (Eds.)

206 Remote Sensing of the Terrestrial Water CycleVenkat Lakshmi (Ed.)

207 Magnetotails in the Solar SystemAndreas Keiling, Caitríona Jackman, and Peter Delamere (Eds.)

208 Hawaiian Volcanoes: From Source to Surface Rebecca Carey, Valerie Cayol, Michael Poland, and Dominique Weis (Eds.)

209 Sea Ice: Physics, Mechanics, and Remote SensingMohammed Shokr and Nirmal Sinha (Eds.)

210 Fluid Dynamics in Complex Fractured‐Porous SystemsBoris Faybishenko, Sally M. Benson, and John E. Gale (Eds.)

211 Subduction Dynamics: From Mantle Flow to Mega DisastersGabriele Morra, David A. Yuen, Scott King, Sang Mook Lee, and Seth Stein (Eds.)

212 The Early Earth: Accretion and DifferentiationJames Badro and Michael Walter (Eds.)

213 Global Vegetation Dynamics: Concepts and Applications in the MC1 ModelDominique Bachelet and David Turner (Eds.)

214 Extreme Events: Observations, Modeling and EconomicsMario Chavez, Michael Ghil, and Jaime Urrutia‐Fucugauchi (Eds.)

215 Auroral Dynamics and Space WeatherYongliang Zhang and Larry Paxton (Eds.)

216 Low‐Frequency Waves in Space PlasmasAndreas Keiling, Dong‐Hun Lee, and Valery Nakariakov (Eds.)

217 Deep Earth: Physics and Chemistry of the Lower Mantle and CoreHidenori Terasaki and Rebecca A. Fischer (Eds.)

218 Integrated Imaging of the Earth: Theory and ApplicationsMax Moorkamp, Peter G. Lelievre, Niklas Linde, and Amir Khan (Eds.)

219 Plate Boundaries and Natural HazardsJoao Duarte and Wouter Schellart (Eds.)

220 Ionospheric Space Weather: Longitude and Hemispheric Dependences and Lower Atmosphere Forcing Timothy Fuller‐Rowell, Endawoke Yizengaw, Patricia H. Doherty, and Sunanda Basu (Eds.)

221 Terrestrial Water Cycle and Climate Change Natural and Human‐Induced ImpactsQiuhong Tang and Taikan Oki (Eds.)

222 Magnetosphere‐Ionosphere Coupling in the Solar SystemCharles R. Chappell, Robert W. Schunk, Peter M. Banks, James L. Burch, and Richard M. Thorne (Eds.)

223 Natural Hazard Uncertainty Assessment: Modeling and Decision SupportKarin Riley, Peter Webley, and Matthew Thompson (Eds.)

224 Hydrodynamics of Time‐Periodic Groundwater Flow: Diffusion Waves in Porous MediaJoe S. Depner and Todd C. Rasmussen (Auth.)

225 Active Global SeismologyIbrahim Cemen and Yucel Yilmaz (Eds.)

226 Climate ExtremesSimon Wang (Ed.)

227 Fault Zone Dynamic ProcessesMarion Thomas (Ed.)

228 Flood Damage Survey and Assessment: New Insights from Research and PracticeDaniela Molinari, Scira Menoni, and Francesco Ballio (Eds.)

229 Water‐Energy‐Food Nexus – Principles and PracticesP. Abdul Salam, Sangam Shrestha, Vishnu Prasad Pandey, and Anil K Anal (Eds.)

230 Dawn–Dusk Asymmetries in Planetary Plasma EnvironmentsStein Haaland, Andrei Rounov, and Colin Forsyth (Eds.)

231 Bioenergy and Land Use ChangeZhangcai Qin, Umakant Mishra, and Astley Hastings (Eds.)

232 Microstructural Geochronology: Planetary Records Down to Atom ScaleDesmond Moser, Fernando Corfu, James Darling, Steven Reddy, and Kimberly Tait (Eds.)

233 Global Flood Hazard: Applications in Modeling, Mapping and ForecastingGuy Schumann, Paul D. Bates, Giuseppe T. Aronica, and Heiko Apel (Eds.)

234 Pre‐Earthquake Processes: A Multidisciplinary Approach to Earthquake Prediction StudiesDimitar Ouzounov, Sergey Pulinets, Katsumi Hattori, and Patrick Taylor (Eds.)

235 Electric Currents in Geospace and BeyondAndreas Keiling, Octav Marghitu, and Michael Wheatland (Eds.)

Geophysical Monograph 236

Quantifying Uncertainty in Subsurface Systems

Céline ScheidtLewis LiJef Caers

This Work is a co‐publication of the American Geophysical Union and John Wiley and Sons, Inc.

This Work is a co‐publication between the American Geophysical Union and John Wiley & Sons, Inc.

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AUTHORS

Céline ScheidtSenior Research EngineerDepartments of Energy Resources EngineeringStanford University, Stanford, CA, USA

Lewis LiDoctoral StudentDepartments of Energy Resources EngineeringStanford University, Stanford, CA, USA

Jef CaersProfessor of Geological SciencesDirector, Stanford Center for Earth Resources ForecastingStanford University, Stanford, CA, USA

CONTRIBUTORS

Ognjen GrujicDepartment of Energy Resources Engineering, Stanford University, Stanford, CA, USA

Thomas HermansUniversity of Liege, Liege, Belgium

Kate MaherDepartment of Geological Sciences, Stanford University, Stanford, CA, USA

Jihoon ParkDepartment of Energy Resources Engineering, Stanford University, Stanford, CA, USA

Carla Da SilvaAnadarko, The Woodlands, TX, USA

Troels Norvin VilhelmsenDepartment of Geoscience, Aarhus University, Aarhus, Denmark

Guang YangDepartment of Energy Resources Engineering, Stanford University, Stanford, CA, USA

PREFACE

“I think that when we know that we actually do live in uncertainty, then we ought to admit it; it is of great value to realize that we do not know the answers to different questions. This attitude of mind – this attitude of uncertainty – is vital to the scientist, and it is this attitude of mind which the student must first acquire”

Richard P. Feynman, Noble Laureate in Physics, 1965

This book offers five substantial case studies on decision making under uncertainty for subsurface systems. The strategies and workflows designed for these case studies are based on a Bayesian philosophy, tuned specifically to the particularities of the subsurface realm. Models are large and complex; data are heterogeneous in nature; decisions need to address conflicting objectives; the subsurface medium is created by geological processes that are not always well understood; and expertise of a large variety of scientific and engineering disciplines need to be synthesized.

There is no doubt that we live in an uncertain time. With growing population, resources such as energy, materials, water, and food will become increasingly critical in their exploitation. The subsurface offers many such resources, important to the survival of humankind. Drinking water from groundwater systems is gaining in importance, as aquifers are natural purifiers and can store large volumes. However, the groundwater system is fragile, subject to contamination from agriculture practices and industries. Before renewables become the dominant energy sources, oil and gas will remain a significant resource in the next few decades. Geothermal energy both deep (power) and shallow (heating) can contribute substantially to alleviating reliance on fossil fuels. Mining minerals used for batteries will aid in addressing intermittency of certain renewables, but mining practices will need to address environmental concerns.

Companies and governmental entities involved in the extraction of these resources face considerable financial risk because of the difficulty in accessing the poorly understood subsurface and the cost of engineering facilities. Decisions regarding exploration methods, drilling, extraction methods, and data‐gathering campaigns often need to balance conflicting objectives: resource versus environmental impact, risk versus return. This can be truly addressed only if one accepts uncertainty as integral part of the decision game. A decision based on a deterministic answer when uncertainty is prevailing is simply a poor decision, regardless of the outcome. Decisions and uncertainty are part of one puzzle; one does not come before the other.

Uncertainty on key decision variables such as volumes, rates of extraction, time of extraction, spatiotemporal variation on fluid movements needs to be quantified. Uncertainty quantification, in this book shortened to UQ, requires a complex balancing of several fields of expertise such as geological sciences, geophysics, data science, computer science, and decision analysis. We gladly admit that we do not have a single best solution to UQ. The aim of this book is to provide the reader with a principled approach, meaning a set of actions motivated by a mathematical philosophy based on axioms, definitions, and algorithms that are well understood, repeatable, and reproducible, as well as a software to reproduce the results of this book. We consider uncertainty not simply to be some posterior analysis but a synthesized discipline steeped in scientific ideas that are still evolving. Ten chapters provide insight into our way of thinking on UQ.

Chapter 1 introduces the five case studies: an oil reservoir in Libya, a groundwater system in Denmark, a geothermal source for heating buildings in Belgium, a contaminated aquifer system in Colorado, and an unconventional hydrocarbon resource in Texas. In each case study, we introduce the formulation of the decision problem, the types of data used, and the complexity of the modeling problem. Common to all these cases is that the decision problem involves simple questions: Where do we drill? How much is there? How do we extract? What data to gather? The models involved on the other hand are complex and high dimensional, the forward simulators time‐consuming. The case studies set the stage.

Chapter 2 introduces the reader to some basic notions in decision analysis. Decision analysis is a science, with its own axioms, definitions, and heuristics. Properly formulating the decision problem, defining the key decision variables, the data used to quantify these, and the objectives of the decision maker are integral to such decision analysis. Value of information is introduced as a formal framework to assess the value of data before acquiring it.

Chapter 3 provides an overview of the various data science methods that are relevant to UQ problems in the subsurface. Representing the subsurface requires a high‐dimensional model parametrization. To make UQ problems manageable, some form of dimension reduction is needed. In addition, we focus on several methods of regression such as Gaussian process regression and CART (classification and regression trees) that are useful for statistical learning and development of statistical proxy models. Monte Carlo is covered extensively as this is instrumental to UQ. Methods such as importance sampling and sequential importance resampling are discussed. Lastly, we present the extension of Monte Carlo to Markov chain Monte Carlo and bootstrap; both are methods to address uncertainty and confidence.

Chapter 4 is dedicated to sensitivity analysis (SA). Although SA could be part of Chapter 3, because of its significance to UQ, we dedicate a single chapter to it. Our emphasis will be on global SA and more specifically Monte Carlo‐based SA since this family of methods (Sobol’, regionalized sensitivity analysis, CART) provides key insight into understanding what model variables most impact data and prediction variables.

Chapter 5 introduces the philosophy behind Bayesian methods: Bayesianism. We provide a historical context to why Bayes has become one of the leading paradigms to UQ, having evolved from other paradigms such as induction, deduction, and falsification. The most important contribution of Thomas Bayes is the notion of the prior distribution. This notion is critical to UQ in the subsurface, simply because of the poorly understood geological medium that drives uncertainty. The chapter, therefore, ends with a discussion on the nature of prior distributions in the geosciences, how one can think about them and how they can be established from physical, rather than statistical principles.

Chapter 6 then extends on Chapter 5 by discussion on the role of prior distribution in inverse problems. We provide a brief overview of both deterministic and stochastic inversion. The emphasis lies on how quantification of geological heterogeneity (e.g., using geostatistics) can be used as prior models to solve inverse problems, within a Bayesian framework.

Chapter 7 is perhaps the most novel technical contribution of this book. This chapter covers a collection of methods termed Bayesian evidential learning (BEL). Previous chapters indicated that one of the major challenges in UQ is model realism (geological) as well as deal with large computing times in forward models related to data and prediction responses. In this chapter, we present several methods of statistical learning, where Monte Carlo is used to generate a training set of data and prediction variables. This Monte Carlo approach requires the specification of a prior distribution on the model variables. We show how learning the multivariate distribution of data and prediction variables allows for predictions based on data without complex model inversions.

Chapter 8 presents various strategies addressing the decision problem of the various case studies introduced in Chapter 1. The aim is not to provide the best possible method but to outline choices in methods and strategies in combination to solve real‐world problems. These strategies rely on materials presented in Chapters 2–7.

Chapter 9 provides a discussion of the various software components that are necessary for the implementation of the different UQ strategies presented in the book. We discuss some of the challenges faced when using existing software packages as well as provide an overview of the companion code for this book.

Chapter 10 concludes this book by means of seven questions that formulate important challenges that when addressed may move the field of UQ forward in impactful ways.

We want to thank several people who made important contributions to this book, directly and indirectly. This book would not have been possible without the continued support of the Stanford Center for Reservoir Forecasting. The unrestricted funding provided over the last 30 years has aided us in working on case studies as well as fundamental research that focuses on synthesis in addition to many technical contributions in geostatistics, geophysics, data science, and others. We would also like to thank our esteemed colleagues at Stanford University and elsewhere, who have been involved in many years of discussion around this topic. In particular, we would like to thank Tapan Mukerji (Energy Resources Engineering & Geophysics), who has been instrumental in educating us on decision analysis as well as on the geophysical aspects of this book. Kate Maher (Earth System Science) provided important insights into the modeling of the case study on uranium contamination. We thank the members of the Ensemble project funded by the Swiss government, led by Philippe Renard (University of Neuchatel), Niklas Linde (University of Lausanne), Peter Huggenberger (University of Basel), Ivan Lunati (University of Lausanne), Grégoire Mariethoz (University of Lausanne), and David Ginsbourger (University of Bern). To our knowledge, this was one of the first large‐scale governmental project involving both research and education for quantifying uncertainty in the subsurface. We would also like to thank Troels Vilhelmsen (University of Aarhus) for the short but intensive collaboration on the Danish groundwater case. We welcome the data provided by Wintershall (Michael Peter Suess) and Andarko (Carla Da Silva). The Belgian case was done with Thomas Hermans (University of Gent), when he was postdoctoral researcher at Stanford. Discussions with Fréderic Nguyen (University of Liege) were also instrumental for that case study. We would also like to thank Emanuel Huber (University of Basel) for the construction of the hydrological (DNAPL) test case used in Chapters 3 and 4 during his postdoc at Stanford.

PhD students also have been integral part of this work, at Stanford and elsewhere. In particular, we would like to thank Addy Satija, Orhun Aydin, Ognjen Grujic, Guang Yang, Jihoon Park, Markus Zechner, and Adrian Barfod (University of Aarhus).

The thumbtack game on decision analysis was introduced to us by Reidar Bratvold (University of Stavanger). Early reviews on Chapter 5 (Bayesianism) by Klaus Mosegaard (University of Kopenhagen), Don Dodge (Retired, San Francisco), and Matthew Casey (The Urban School, San Francisco) were instrumental to the writing and clarity of the chapter. We also thank Darryl Fenwick (Kappa Engineering) for early reviews of Chapters 4 and 6 and for many fruitful discussions. We are very grateful to the 10 anonymous reviewers and the Wiley editors for their critical comments.

We hope you enjoy our work.

Céline ScheidtLewis LiJef Caers

1The Earth Resources Challenge

Co-Authored by: Troels Norvin Vilhelmsen1, Kate Maher2, Carla Da Silva3, Thomas Hermans4, Ognjen Grujic5, Jihoon Park5, and Guang Yang5

1Department of Geoscience, Aarhus University, Aarhus, Denmark

2Department of Geological Sciences, Stanford University, Stanford, CA, USA

3Anadarko, The Woodlands, TX, USA

4University of Liege, Liege, Belgium

5Department of Energy Resources Engineering, Stanford University, Stanford, CA, USA

1.1. WHEN CHALLENGES BRING OPPORTUNITIES

Humanity is facing considerable challenges in the 21st century. Population is predicted to grow well into this century and saturate between 9 and 10 billion somewhere in the later part. This growth has led to climate change (see the latest IPCC reports), has impacted the environment, and has affected ecosystems locally and globally around the planet. Virtually no region exists where humans have had no footprint of some kind [Sanderson et al., 2002]; we now basically “own” the ecosystem, and we are not always a good Shepard. An increasing population will require an increasing amount of resources, such as energy, food, and water. In an ideal scenario, we would transform the current situation of unsustainable carbon‐emitting energy sources, polluting agricultural practices and contaminating and over‐exploiting drinking water resources, into a more sustainable and environmentally friendly future. Regardless of what is done (or not), this will not be an overnight transformation. For example, natural gas, a green‐house gas (either as methane or burned into CO2), is often called the blue energy toward a green future. But its production from shales (with vast amounts of gas and oil reserves, 7500 Tcf of gas, 400 billion barrels of oil, US Energy Information, December 2014) has been questioned for its effect on the environment from gas leaks [Howarth et al., 2014] and the unsolved problem of dealing with the waste water it generates. Injecting water into kilometer‐deep wells has caused significant earthquakes [Whitaker, 2016], and risks to contamination of the groundwater system are considerable [Osborn et al., 2011].

Challenges bring opportunities. The Earth is rich in resources, and humanity has been creative and resourceful in using the Earth to advance science and technology. Batteries offer promising energy storage devices that can be connected to intermittent energy sources such as wind and solar. Battery technology will likely develop further from a better understanding of Earth materials. The Earth provides a naturally emitting heat source that can be used for energy creation or heating of buildings. In this book, we will contribute to exploration and exploitation of geological resources. The most common of such resources are briefly described in the following:

Fossil fuels