Predicting Porosity, Permeability, and Tortuosity of Porous Media from Images by Deep Learning Krzysztof M
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Hydrogeology
Hydrogeology Principles of Groundwater Flow Lecture 3 1 Hydrostatic pressure The total force acting at the bottom of the prism with area A is Dividing both sides by the area, A ,of the prism 1 2 Hydrostatic Pressure Top of the atmosphere Thus a positive suction corresponds to a negative gage pressure. The dimensions of pressure are F/L2, that is Newton per square meter or pascal (Pa), kiloNewton per square meter or kilopascal (kPa) in SI units Point A is in the saturated zone and the gage pressure is positive. Point B is in the unsaturated zone and the gage pressure is negative. This negative pressure is referred to as a suction or tension. 3 Hydraulic Head The law of hydrostatics states that pressure p can be expressed in terms of height of liquid h measured from the water table (assuming that groundwater is at rest or moving horizontally). This height is called the pressure head: For point A the quantity h is positive whereas it is negative for point B. h = Pf /ϒf = Pf /ρg If the medium is saturated, pore pressure, p, can be measured by the pressure head, h = pf /γf in a piezometer, a nonflowing well. The difference between the altitude of the well, H, and the depth to the water inside the well is the total head, h , at the well. i 2 4 Energy in Groundwater • Groundwater possess mechanical energy in the form of kinetic energy, gravitational potential energy and energy of fluid pressure. • Because the amount of energy vary from place-to-place, groundwater is forced to move from one region to another in order to neutralize the energy differences. -
Lecture 13: Financial Disasters and Econophysics
Lecture 13: Financial Disasters and Econophysics Big problem: Power laws in economy and finance vs Great Moderation: (Source: http://www.mckinsey.com/business-functions/strategy-and-corporate-finance/our-insights/power-curves-what- natural-and-economic-disasters-have-in-common Analysis of big data, discontinuous change especially of financial sector, where efficient market theory missed the boat has drawn attention of specialists from physics and mathematics. Wall Street“quant”models may have helped the market implode; and collapse spawned econophysics work on finance instability. NATURE PHYSICS March 2013 Volume 9, No 3 pp119-197 : “The 2008 financial crisis has highlighted major limitations in the modelling of financial and economic systems. However, an emerging field of research at the frontiers of both physics and economics aims to provide a more fundamental understanding of economic networks, as well as practical insights for policymakers. In this Nature Physics Focus, physicists and economists consider the state-of-the-art in the application of network science to finance.” The financial crisis has made us aware that financial markets are very complex networks that, in many cases, we do not really understand and that can easily go out of control. This idea, which would have been shocking only 5 years ago, results from a number of precise reasons. What does physics bring to social science problems? 1- Heterogeneous agents – strange since physics draws strength from electron is electron is electron but STATISTICAL MECHANICS --- minority game, finance artificial agents, 2- Facility with huge data sets – data-mining for regularities in time series with open eyes. 3- Network analysis 4- Percolation/other models of “phase transition”, which directs attention at boundary conditions AN INTRODUCTION TO ECONOPHYSICS Correlations and Complexity in Finance ROSARIO N. -
Processes on Complex Networks. Percolation
Chapter 5 Processes on complex networks. Percolation 77 Up till now we discussed the structure of the complex networks. The actual reason to study this structure is to understand how this structure influences the behavior of random processes on networks. I will talk about two such processes. The first one is the percolation process. The second one is the spread of epidemics. There are a lot of open problems in this area, the main of which can be innocently formulated as: How the network topology influences the dynamics of random processes on this network. We are still quite far from a definite answer to this question. 5.1 Percolation 5.1.1 Introduction to percolation Percolation is one of the simplest processes that exhibit the critical phenomena or phase transition. This means that there is a parameter in the system, whose small change yields a large change in the system behavior. To define the percolation process, consider a graph, that has a large connected component. In the classical settings, percolation was actually studied on infinite graphs, whose vertices constitute the set Zd, and edges connect each vertex with nearest neighbors, but we consider general random graphs. We have parameter ϕ, which is the probability that any edge present in the underlying graph is open or closed (an event with probability 1 − ϕ) independently of the other edges. Actually, if we talk about edges being open or closed, this means that we discuss bond percolation. It is also possible to talk about the vertices being open or closed, and this is called site percolation. -
Continuum Mechanics of Two-Phase Porous Media
Continuum mechanics of two-phase porous media Ragnar Larsson Division of material and computational mechanics Department of applied mechanics Chalmers University of TechnologyS-412 96 Göteborg, Sweden Draft date December 15, 2012 Contents Contents i Preface 1 1 Introduction 3 1.1 Background ................................... 3 1.2 Organizationoflectures . .. 6 1.3 Coursework................................... 7 2 The concept of a two-phase mixture 9 2.1 Volumefractions ................................ 10 2.2 Effectivemass.................................. 11 2.3 Effectivevelocities .............................. 12 2.4 Homogenizedstress ............................... 12 3 A homogenized theory of porous media 15 3.1 Kinematics of two phase continuum . ... 15 3.2 Conservationofmass .............................. 16 3.2.1 Onephasematerial ........................... 17 3.2.2 Twophasematerial. .. .. 18 3.2.3 Mass balance of fluid phase in terms of relative velocity....... 19 3.2.4 Mass balance in terms of internal mass supply . .... 19 3.2.5 Massbalance-finalresult . 20 i ii CONTENTS 3.3 Balanceofmomentum ............................. 22 3.3.1 Totalformat............................... 22 3.3.2 Individual phases and transfer of momentum change between phases 24 3.4 Conservationofenergy . .. .. 26 3.4.1 Totalformulation ............................ 26 3.4.2 Formulation in contributions from individual phases ......... 26 3.4.3 The mechanical work rate and heat supply to the mixture solid . 28 3.4.4 Energy equation in localized format . ... 29 3.4.5 Assumption about ideal viscous fluid and the effective stress of Terzaghi 30 3.5 Entropyinequality ............................... 32 3.5.1 Formulation of entropy inequality . ... 32 3.5.2 Legendre transformation between internal energy, free energy, entropy and temperature 3.5.3 The entropy inequality - Localization . .... 34 3.5.4 Anoteontheeffectivedragforce . 36 3.6 Constitutiverelations. -
Understanding Complex Systems: a Communication Networks Perspective
1 Understanding Complex Systems: A Communication Networks Perspective Pavlos Antoniou and Andreas Pitsillides Networks Research Laboratory, Computer Science Department, University of Cyprus 75 Kallipoleos Street, P.O. Box 20537, 1678 Nicosia, Cyprus Telephone: +357-22-892687, Fax: +357-22-892701 Email: [email protected], [email protected] Technical Report TR-07-01 Department of Computer Science University of Cyprus February 2007 Abstract Recent approaches on the study of networks have exploded over almost all the sciences across the academic spectrum. Over the last few years, the analysis and modeling of networks as well as networked dynamical systems have attracted considerable interdisciplinary interest. These efforts were driven by the fact that systems as diverse as genetic networks or the Internet can be best described as complex networks. On the contrary, although the unprecedented evolution of technology, basic issues and fundamental principles related to the structural and evolutionary properties of networks still remain unaddressed and need to be unraveled since they affect the function of a network. Therefore, the characterization of the wiring diagram and the understanding on how an enormous network of interacting dynamical elements is able to behave collectively, given their individual non linear dynamics are of prime importance. In this study we explore simple models of complex networks from real communication networks perspective, focusing on their structural and evolutionary properties. The limitations and vulnerabilities of real communication networks drive the necessity to develop new theoretical frameworks to help explain the complex and unpredictable behaviors of those networks based on the aforementioned principles, and design alternative network methods and techniques which may be provably effective, robust and resilient to accidental failures and coordinated attacks. -
Critical Percolation As a Framework to Analyze the Training of Deep Networks
Published as a conference paper at ICLR 2018 CRITICAL PERCOLATION AS A FRAMEWORK TO ANALYZE THE TRAINING OF DEEP NETWORKS Zohar Ringel Rodrigo de Bem∗ Racah Institute of Physics Department of Engineering Science The Hebrew University of Jerusalem University of Oxford [email protected]. [email protected] ABSTRACT In this paper we approach two relevant deep learning topics: i) tackling of graph structured input data and ii) a better understanding and analysis of deep networks and related learning algorithms. With this in mind we focus on the topological classification of reachability in a particular subset of planar graphs (Mazes). Doing so, we are able to model the topology of data while staying in Euclidean space, thus allowing its processing with standard CNN architectures. We suggest a suitable architecture for this problem and show that it can express a perfect solution to the classification task. The shape of the cost function around this solution is also derived and, remarkably, does not depend on the size of the maze in the large maze limit. Responsible for this behavior are rare events in the dataset which strongly regulate the shape of the cost function near this global minimum. We further identify an obstacle to learning in the form of poorly performing local minima in which the network chooses to ignore some of the inputs. We further support our claims with training experiments and numerical analysis of the cost function on networks with up to 128 layers. 1 INTRODUCTION Deep convolutional networks have achieved great success in the last years by presenting human and super-human performance on many machine learning problems such as image classification, speech recognition and natural language processing (LeCun et al. -
Coupled Multiphase Flow and Poromechanics: 10.1002/2013WR015175 a Computational Model of Pore Pressure Effects On
PUBLICATIONS Water Resources Research RESEARCH ARTICLE Coupled multiphase flow and poromechanics: 10.1002/2013WR015175 A computational model of pore pressure effects on Key Points: fault slip and earthquake triggering New computational approach to coupled multiphase flow and Birendra Jha1 and Ruben Juanes1 geomechanics 1 Faults are represented as surfaces, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, capable of simulating runaway slip USA Unconditionally stable sequential solution of the fully coupled equations Abstract The coupling between subsurface flow and geomechanical deformation is critical in the assess- ment of the environmental impacts of groundwater use, underground liquid waste disposal, geologic stor- Supporting Information: Readme age of carbon dioxide, and exploitation of shale gas reserves. In particular, seismicity induced by fluid Videos S1 and S2 injection and withdrawal has emerged as a central element of the scientific discussion around subsurface technologies that tap into water and energy resources. Here we present a new computational approach to Correspondence to: model coupled multiphase flow and geomechanics of faulted reservoirs. We represent faults as surfaces R. Juanes, embedded in a three-dimensional medium by using zero-thickness interface elements to accurately model [email protected] fault slip under dynamically evolving fluid pressure and fault strength. We incorporate the effect of fluid pressures from multiphase flow in the mechanical -
Arxiv:1504.02898V2 [Cond-Mat.Stat-Mech] 7 Jun 2015 Keywords: Percolation, Explosive Percolation, SLE, Ising Model, Earth Topography
Recent advances in percolation theory and its applications Abbas Ali Saberi aDepartment of Physics, University of Tehran, P.O. Box 14395-547,Tehran, Iran bSchool of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5531, Tehran, Iran Abstract Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied to describe a large variety of natural, technological and social systems. Percolation models serve as important universality classes in critical phenomena characterized by a set of critical exponents which correspond to a rich fractal and scaling structure of their geometric features. We will first outline the basic features of the ordinary model. Over the years a variety of percolation models has been introduced some of which with completely different scaling and universal properties from the original model with either continuous or discontinuous transitions depending on the control parameter, di- mensionality and the type of the underlying rules and networks. We will try to take a glimpse at a number of selective variations including Achlioptas process, half-restricted process and spanning cluster-avoiding process as examples of the so-called explosive per- colation. We will also introduce non-self-averaging percolation and discuss correlated percolation and bootstrap percolation with special emphasis on their recent progress. Directed percolation process will be also discussed as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. In the past decade, after the invention of stochastic L¨ownerevolution (SLE) by Oded Schramm, two-dimensional (2D) percolation has become a central problem in probability theory leading to the two recent Fields medals. -
Percolation Theory Are Well-Suited To
Models of Disordered Media and Predictions of Associated Hydraulic Conductivity A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science By L AARON BLANK B.S., Wright State University, 2004 2006 Wright State University WRIGHT STATE UNIVERSITY SCHOOL OF GRADUATE STUDIES Novermber 6, 2006 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY L Blank ENTITLED Models of Disordered Media and Predictions of Associated Hydraulic Conductivity BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science. _______________________ Allen Hunt, Ph.D. Thesis Advisor _______________________ Lok Lew Yan Voon, Ph.D. Department Chair _______________________ Joseph F. Thomas, Jr., Ph.D. Dean of the School of Graduate Studies Committee on Final Examination ____________________ Allen Hunt, Ph.D. ____________________ Brent D. Foy, Ph.D. ____________________ Gust Bambakidis, Ph.D. ____________________ Thomas Skinner, Ph.D. Abstract In the late 20th century there was a spill of Technetium in eastern Washington State at the US Department of Energy Hanford site. Resulting contamination of water supplies would raise serious health issues for local residents. Therefore, the ability to predict how these contaminants move through the soil is of great interest. The main contribution to contaminant transport arises from being carried along by flowing water. An important control on the movement of the water through the medium is the hydraulic conductivity, K, which defines the ease of water flow for a given pressure difference (analogous to the electrical conductivity). The overall goal of research in this area is to develop a technique which accurately predicts the hydraulic conductivity as well as its distribution, both in the horizontal and the vertical directions, for media representative of the Hanford subsurface. -
Theoretical and Computational Poromechanics from 14:30 to 16:30 Via Ferrata 3, Pavia Carlo Callari, Università Del Molise
DIPARTIMENTO DI INGEGNERIA CIVILE E ARCHITETTURA DOTTORATO IN INGEGNERIA CIVILE E ARCHITETTURA UNIVERSITÀ DEGLI STUDI DI PAVIA SHORT COURSE ON JUNE, 22, 23, 24, 25, 26 THEORETICAL AND COMPUTATIONAL POROMECHANICS FROM 14:30 TO 16:30 VIA FERRATA 3, PAVIA CARLO CALLARI, UNIVERSITÀ DEL MOLISE Detailed Outline MOTIVATIONS: The role of poromechanics in civil, environmental and medical engineering: problem analysis and material modeling PART 1: Mechanics of fully saturated porous media with compressible phases Biot's thermodynamics and constitutive equations: • Thermodynamics of barotropic and inviscid fluids • Fluid mass balance in the porous medium • Local forms of first and second principles • Clausius-Duhem inequality • Transport laws • General form of constitutive laws for the porous medium • Linear poroelasticity and extension to poro-elastoplasticity • Fluid-to-solid and solid-to-fluid limit uncoupled influences • Strain-dependent permeability models Finite element formulations for porous media: • Boundary conditions for mechanical and fluid-flow fields • Formulation of mechanical and fluid-flow problems • Extension to non-linear response Research applications to saturated porous media: • 2D response of dam and rock mass to reservoir operations • Tunnel face stability • Poroelastic damage and applications to hydrocarbon wells PART 2: Extension to multiphase fluids Biot's thermodynamics and poroelastic laws: • General hyperelastic laws for three-phase porous media • Generalized Darcy law • Constitutive equations from the theory of mixtures -
A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules for the Modular Modeling System of the U.S
Prepared in cooperation with the Bureau of Reclamation, Yakama Nation, and the Washington State Department of Ecology A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules for the Modular Modeling System of the U.S. Geological Survey Scientific Investigations Report 2006–5318 U.S. Department of the Interior U.S. Geological Survey Cover: Photograph of Clark WEll No. 1, located on the north side of the Moxee Valley in North Yakima, Washington. The well is located in township 12 north, range 20 east, section 6. The well was drilled to a depth of 940 feet into an artesian zone of the Ellensburg Formation, and completed in 1897 at a cost of $2,000. The original flow from the well was estimated at about 600 gallons per minute, and was used to irrigate 250 acres in 1900 and supplied water to 8 small ranches with an additional 47 acres of irrigation. (Photograph was taken by E.E. James in 1897, and was printed in 1901 in the U.S. Geological Survey Water-Supply and Irrigation Paper 55.) A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules for the Modular Modeling System of the U.S. Geological Survey By J.J. Vaccaro Prepared in cooperation with the Bureau of Reclamation, Yakama Nation, and Washington State Department of Ecology Scientific Investigations Report 2006–5318 U.S. Department of the Interior U.S. Geological Survey U.S. Department of the Interior DIRK KEMPTHORNE, Secretary U.S. Geological Survey Mark D. Myers, Director U.S. Geological Survey, Reston, Virginia: 2007 For product and ordering information: World Wide Web: http://www.usgs.gov/pubprod Telephone: 1-888-ASK-USGS For more information on the USGS--the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment: World Wide Web: http://www.usgs.gov Telephone: 1-888-ASK-USGS Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. -
POROMECHANICS of POROUS and FRACTURED RESERVOIRS Jishan Liu, Derek Elsworth KIGAM, Daejeon, Korea May 15-18, 2017
POROMECHANICS OF POROUS AND FRACTURED RESERVOIRS Jishan Liu, Derek Elsworth KIGAM, Daejeon, Korea May 15-18, 2017 1. Poromechanics – Flow Properties (Jishan Liu) 1:1 Reservoir Pressure System – How to calculate overburden stress and reservoir pressure Day 11 1:2 Darcy’s Law – Permeability and its changes, reservoir classification 1:3 Mass Conservation Law – flow equations 1:4 Steady-State Behaviors – Solutions of simple flow problems 1:5 Hydraulic Diffusivity – Definition, physical meaning, and its application in reservoirs 1:6 Rock Properties – Their Dependence on Stress Conditions Day 1 ……………………………………………………………………………………………………………... 2. Poromechanics – Fluid Storage Properties (Jishan Liu) 2:1 Fluid Properties – How they change and affect flow Day 2 2:2 Mechanisms of Liquid Production or Injection 2:3 Estimation of Original Hydrocarbons in Place 2:4 Estimation of Ultimate Recovery or Injection of Hydrocarbons 2:5 Flow – Deformation Coupling in Coal 2:6 Flow – Deformation Coupling in Shale Day 2 ……………………………………………………………………………………………………………... 3. Poromechanics –Modeling Porous Medium Flows (Derek Elsworth) 3:1 Single porosity flows - Finite Element Methods [2:1] Lecture Day 3 3:2 2D Triangular Constant Gradient Elements [2:3] Lecture 3:3 Transient Behavior - Mass Matrices [2:6] Lecture 3:4 Transient Behavior - Integration in Time [2:7] Lecture 3:5 Dual-Porosity-Dual-Permeability Models [6:1] Lecture Day 3 ……………………………………………………………………………………………………………... 4. Poromechanics –Modeling Coupled Porous Medium Flow and Deformation (Derek Elsworth) 4:1 Mechanical properties – http://www.ems.psu.edu/~elsworth/courses/geoee500/GeoEE500_1.PDF Day 4 4:2 Biot consolidation – http://www.ems.psu.edu/~elsworth/courses/geoee500/GeoEE500_1.PDF 4:3 Dual-porosity poroelasticity 4:4 Mechanical deformation - 1D and 2D Elements [5:1][5:2] Lecture 4:5 Coupled Hydro-Mechanical Models [6:2] Lecture Day 4 ……………………………………………………………………………………………………………..