Upscaling of single-and two-phase flow in reservoir engineering by Bruining, Hans

Table of Contents: “…Sheet I contains the permeabilities 2.A.5 The sheet for the well flow potential <BR>2.A.6 The sheet for Productivity/Injectivity indexes 2.A.7 The sheet for the wells 2.A.8 The sheet for flow calculations 2.B Finite element calculations 2.C Sketch of proof of the effective medium approximation formula 2.D Homogenization 3 Time dependent problems in porous media flow 3.1 Transient Pressure Equation 3.1.1 Boundary conditions 3.1.2 The averaged problem in two space dimensions 3.1.3 The problem in radial symmetry 3.1.4 Boundary conditions for radial diffusivity equation 3.1.5 Dimensional analysis for the radial pressure equation; adapted from lecture notes of Larry Lake 3.1.6 Solution of the radial diffusivity equation with the help of Laplace transformation 3.1.7 Laplace transformation 3.1.8 Self similar solution 3.1.9 The dimensional draw-down pressure <BR>3.2 Pressure build up 3.2.2 Time derivatives of pressure response 3.2.3 Practical limitations of pressure build up testing 3.3 Formulation in a bounded reservoir 3.4 Non-Darcy flow 3.A About Boundary condition at r = reD 3.A.1 Exercise, Stehfest algorithm 3.B Rock compressibility 3.B.1 Physical model 3.B.2 Mass balance in constant control volume 3.C Equations disregarding the grain velocity in Darcy's law 3.D Superposition principle 3.E Laplace inversion with the Stehfest algorithm [223] 3.F EXCEL numerical Laplace inversion programme 3.F.1 Alternative inversion techniques 4 Multi-Phase Flow 4.1 Capillary Pressure function 4.1.1 Interfacial tension and capillary rise 4.1.2 Exercise, Laplace formula 4.1.3 Exercise, Young's law 4.1.4 Application to conical tube; Relation between capillary pressure and saturation 4.1.5 Relation between the pore radius and the square root of the permeability divided by the porosity. 4.1.6 Non-dimensionalizing the capillary pressure 4.1.7 Exercise, Ratio grain diameter / pore throat diameter 4.1.8 Three phase capillary pressures 4.1.9 Experimental set up and measurements of capillary pressure 4.1.10 Cross-dip capillary equilibrium 4.1.11 Exercise, Capillary desaturation curve 4.2 Relative permeabilities 4.2.1 Exercise, Brooks-Corey rel-perms 4.2.2 LET relative permeability model 4.2.3 Estimate of the LET parameters 4.2.4 Exercise, Residual oil and Rel-perm 4.3 Theory of Buckley-Leverett 4.3.1 Exercise, Vertical upscaling relative permeability 4.4 Material balance 4.4.1 Solutions of the theory of Buckley-Leverett 4.4.2 Equation of motion (Darcy's Law) and the fractional flow function 4.4.3 Analytical solution of the equations <BR>4.4.4 Construction of the analytical solution; requirement of the entropy condition 4.4.5 Exercise, Buckley Leverett profile with EXCEL 4.4.6 Derivation of the shock condition 4.4.7 Analytical calculation of the production behavior 4.4.8 Exercise, Buckley Leverett production file 4.4.9 Exercise, Analytical Buckley Leverett production curve 4.4.10 Determination of relative permeabilities from production data and pressure measurements 4.4.11 Determination of the relative permeabilities by additional measurement of the pressure drop 4.5 Finite volume approach to obtain the finite difference equations for the Buckley Leverett problem 4.5.1 Exercise, Numerical solution of Buckley Leverett problem 4.6 Vertical equilibrium as a basis for upscaling of relative permeabilities and fractional flow functions 4.6.1 Dake's Upscaling procedure for relative permeabilities 4.6.2 Exercise, Sorting factor dependence 4.6.3 Hopmans's formulation 4.7 Physical Theory of Interface Models 4.7.1 Derivation of interface equation of motion and productions for segregated flow 4.7.2 Stationary interface (Mobility number < Gravity number +1) 4.7.3 Exercise, Interface angle calculations 4.7.4 Production behavior for stationary solution, i.e., M < G + 1 4.8 Non-stationary interface 4.8.1 The volume balance in the form of an interface equation 4.8.2 Dietz-Dupuit-approximation 4.8.3 Approximate Equilibrium Equation 4.8.4 Derivation of flow rate Qwx from Darcy's law 4.8.5 Quasi Stationary Solution of the Dietz-Dupuit Equation for M < G + 1 4.8.6 Exercise, Shock solution versus interface angle solution 4.8.7 Analytical Solutions 4.8.8 Analytical expressions for the interface as a function of position in the reservoir 4.8.9 Analytical expressions for the production behavior 4.8.10 Summary of analytical procedure for interface models 4.8.11 Exercise, Advantage of M G + 1 4.A Numerical approach for interface models 4.A.1 Exercise. …”
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Virtual reality technology by Burdea, Grigore, Coiffet, Philippe

Table of Contents: “…6.5.1.2 Continuous Level- of- Detail Management -- 6.5.1.3 Adaptive Level- of- Detail Management Using Foveated Rendering -- 6.5.1.4 Adaptive Level- of- Detail Management Guaranteeing Frame Time -- 6.5.2 Cell Segmentation -- 6.5.2.1 Automatic Cell Segmentation -- 6.5.2.2 3D Cell Segmentation -- 6.6 Conclusions -- 6.7 Review Questions -- References -- Chapter 7 Virtual Reality Programming -- 7.1 Scene Graphs and Toolkits -- 7.1.1 Scene Graphs -- 7.1.1.1 Internal Scene Graphs -- 7.1.1.2 Distributed Scene Graphs -- 7.2 Toolkits -- 7.2.1 Java3D -- 7.2.1.1 Java 3D Model Geometry and Appearance -- 7.2.1.2 Java3D Scene Graph -- 7.2.1.3 Java3D Sensors and Behaviors -- 7.2.1.4 Java3D Networking -- 7.2.2 The Vizard Toolkit -- 7.2.2.1 Vizard Model Geometry and Appearance -- 7.2.2.2 Vizard Scene Graph -- 7.2.2.3 Vizard Sensors and Behaviors -- 7.2.2.4 Vizard Physics Engine -- 7.2.2.5 Vizard OpenHaptics Plug- in -- 7.2.2.6 Vizard Networking -- 7.2.3 The OpenHaptics Toolkit -- 7.2.3.1 OpenHaptics Integration with the Graphics Pipeline -- 7.2.3.2 OpenHaptics QuickHaptics Micro API -- 7.2.3.3 OpenHaptics Haptic Device to Screen Mapping -- 7.2.3.4 OpenHaptics Unity Plugin -- 7.3 Unity 3D Game Engine -- 7.3.1 The Game Engine -- 7.3.2 Game Production Pipeline -- 7.3.2.1 The Pre- production Pipeline Stage -- 7.3.2.2 The Production Pipeline Stage -- 7.3.2.3 The Post- production Pipeline Stage -- 7.3.3 Unity 3D Game Programming -- 7.3.3.1 Creating a New Project in Unity -- 7.3.3.2 The Unity Editor -- 7.3.3.3 Unity Game Objects -- 7.3.3.4 Physics Programming in Unity -- 7.3.3.5 Scripting in Unity -- 7.3.3.6 Artificial Intelligence in Unity Gaming -- 7.4 Conclusions -- 7.5 Review Questions -- References -- Chapter 8 Human Factors in Virtual Reality -- 8.1 Methodology and Technology -- 8.1.1 The Experimental Protocol -- 8.1.2 Institutional Review and Participant Consent.…”
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Chemical analysis of antibiotic residues in food

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