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Advanced Petroleum Reservoir Simulation : Towards Developing Reservoir Emulators.

By: Contributor(s): Material type: TextTextSeries: Wiley-Scrivener SeriesPublisher: Newark : John Wiley & Sons, Incorporated, 2016Copyright date: ©2016Edition: 2nd edDescription: 1 online resource (594 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781119038788
Subject(s): Genre/Form: Additional physical formats: Print version:: Advanced Petroleum Reservoir SimulationLOC classification:
  • TN870.53.A38 2015
Online resources:
Contents:
Cover -- Title Page -- Copyright Page -- Contents -- Preface -- 1 Introduction -- 1.1 Summary -- 1.2 Opening Remarks -- 1.3 The Need for a Knowledge-Based Approach -- 1.4 Summary of Chapters -- 2 Reservoir Simulation Background -- 2.1 Essence of Reservoir Simulation -- 2.2 Assumptions Behind Various Modeling Approaches -- 2.2.1 Material Balance Equation -- 2.2.2 Decline Curve -- 2.2.3 Statistical Method -- 2.2.4 Analytical Methods -- 2.2.5 Finite-Difference Methods -- 2.2.6 Darcy's Law -- 2.3 Recent Advances in Reservoir Simulation -- 2.3.1 Speed and Accuracy -- 2.3.2 New Fluid-Flow Equations -- 2.3.3 Coupled Fluid Flow and Geo-Mechanical Stress Model -- 2.3.4 Fluid-Flow Modeling Under Thermal Stress -- 2.4 Memory Models -- 2.4.1 Thermal Hysteresis -- 2.4.2 Mathematical and Numerical Models -- 2.5 Future Challenges in Reservoir Simulation -- 2.5.1 Experimental Challenges -- 2.5.2 Numerical Challenges -- 2.5.2.1 Theory of Onset and Propagation of Fractures due to Thermal Stress -- 2.5.2.2 Viscous Fingering during Miscible Displacement -- 3 Reservoir Simulator-Input/Output -- 3.1 Input and Output Data -- 3.2 Geological and Geophysical Modeling -- 3.3 Reservoir Characterization -- 3.3.1 Representative Elementary Volume, REV -- 3.3.2 Fluid and Rock Properties -- 3.3.2.1 Fluid Properties -- 3.3.3 Rock Properties -- 3.4 Upscaling -- 3.4.1 Power Law Averaging Method -- 3.4.2 Pressure-Solver Method -- 3.4.3 Renormalization Technique -- 3.4.4 Multiphase Flow Upscaling -- 3.5 Pressure/Production Data -- 3.6 Phase Saturations Distribution -- 3.7 Reservoir Simulator Output -- 3.8 History Matching -- 3.8.1 History-Matching Formulation -- 3.8.2 Uncertainty Analysis -- 3.8.2.1 Measurement Uncertainty -- 3.8.2.2 Upscaling Uncertainty -- 3.8.2.3 Model Error -- 3.8.2.4 The Prediction Uncertainty -- 3.9 Real-Time Monitoring.
4 Reservoir Simulators: Problems, Shortcomings, and Some Solution Techniques -- 4.1 Multiple Solutions in Natural Phenomena -- 4.1.1 Knowledge Dimension -- 4.2 Adomian Decomposition -- 4.2.1 Governing Equations -- 4.2.2 Adomian Decomposition of Buckley-Leverett Equation -- 4.2.3 Results and Discussions -- 4.3 Some Remarks on Multiple Solutions -- 5 Mathematical Formulation of Reservoir Simulation Problems -- 5.1 Black Oil Model and Compositional Model -- 5.2 General Purpose Compositional Model -- 5.2.1 Basic Definitions -- 5.2.2 Primary and Secondary Parameters and Model Variables -- 5.2.3 Mass Conservation Equation -- 5.2.4 Energy Balance Equation -- 5.2.5 Volume Balance Equation -- 5.2.6 The Motion Equation in Porous Medium -- 5.2.7 The Compositional System of Equations and Model Variables -- 5.3 Simplification of the General Compositional Model -- 5.3.1 The Black Oil Model -- 5.3.2 The Water Oil Model -- 5.4 Some Examples in Application of the General Compositional Model -- 5.4.1 Isothermal Volatile Oil Reservoir -- 5.4.2 Steam Injection Inside a Dead Oil Reservoir -- 5.4.3 Steam Injection in Presence of Distillation and Solution Gas -- 6 The Compositional Simulator Using Engineering Approach -- 6.1 Finite Control Volume Method -- 6.1.1 Reservoir Discretization in Rectangular Coordinates -- 6.1.2 Discretization of Governing Equations -- 6.1.2.1 Components Mass Conservation Equation -- 6.1.2.2 Energy Balance Equation -- 6.1.3 Discretization of Motion Equation -- 6.2 Uniform Temperature Reservoir Compositional Flow Equations in a 1-D Domain -- 6.3 Compositional Mass Balance Equation in a Multidimensional Domain -- 6.3.1 Implicit Formulation of Compositional Model in Multidimensional Domain -- 6.3.2 Reduced Equations of Implicit Compositional Model in Multidimensional Domain -- 6.3.3 Well Production and Injection Rate Terms.
6.3.3.1 Production Wells -- 6.3.3.2 Injection Wells -- 6.3.4 Fictitious Well Rate Terms (Treatment of Boundary Conditions) -- 6.4 Variable Temperature Reservoir Compositional Flow Equations -- 6.4.1 Energy Balance Equation -- 6.4.2 Implicit Formulation of Variable Temperature Reservoir Compositional Flow Equations -- 6.5 Solution Method -- 6.5.1 Solution of Model Equations Using Newton's Iteration -- 6.6 The Effects of Linearization -- 6.6.1 Case 1: Single Phase Flow of a Natural Gas -- 6.6.2 Effect of Interpolation Functions and Formulation -- 6.6.3 Effect of Time Interval -- 6.6.4 Effect of Permeability -- 6.6.5 Effect of Number of Gridblocks -- 6.6.6 Spatial and Transient Pressure Distribution Using Different Interpolation Functions -- 6.6.7 CPU Time -- 6.6.8 Case 2: An Oil/water Reservoir -- 7 Development of a New Material Balance Equation for Oil Recovery -- 7.1 Summary -- 7.2 Introduction -- 7.3 Mathematical Model Development -- 7.3.1 Permeability Alteration -- 7.3 Porosity Alteration -- 7.4 Pore Volume Change -- 7.4.1 A Comprehensive MBE with Memory for Cumulative Oil Recovery -- 7.5 Numerical Simulation -- 7.5.1 Effects of Compressibilities on Dimensionless Parameters -- 7.4.2 Comparison of Dimensionless Parameters Based on Compressibility Factor -- 7.4.3 Effects of M on Dimensionless Parameter -- 7.4.4 Effects of Compressibility Factor with M Values -- 7.4.5 Comparison of Models Based on RF -- 7.4.6 Effects of M on MBE -- 7.5 Conclusions -- Appendix Chapter 7: Development of an MBE for a Compressible Undersaturated Oil Reservoir -- 8 State-of-the-art on Memory Formalism for Porous Media Applications -- 8.1 Summary -- 8.2 Introduction -- 8.3 Historical Development of Memory Concept -- 8.3.1 Constitutive Equations -- 8.3.2 Application of Memory in Diffusion in Porous Media -- 8.3.3 Definition of Memory.
8.4 State-of-the-art Memory-Based Models -- 8.5 Basset Force: A History Term -- 8.6 Anomalous Diffusion: A memory Application -- 8.6.1 Fractional Order Transport Equations and Numerical Schemes -- 8.7 Future Trends -- 8.8 Conclusion -- 9 Modeling Viscous Fingering During Miscible Displacement in a Reservoir -- 9.1 Improvement of the Numerical Scheme -- 9.1.1 The Governing Equation -- 9.1.2 Finite Difference Approximations -- 9.1.2.1 Barakat-Clark FTD Scheme -- 9.1.2.2 DuFort-Frankel Scheme -- 9.1.3 Proposed Barakat-Clark CTD Scheme -- 9.1.4 Accuracy and Truncation Errors -- 9.1.5 Some Results and Discussion -- 9.1.6 Influence of Boundary Conditions -- 9.2 Application of the New Numerical Scheme to Viscous Fingering -- 9.2.1 Stability Criterion and Onset of Fingering -- 9.2.2 Base Stable Case -- 9.2.3 Base Unstable Case -- 9.2.4 Parametric Study -- 9.2.4.1 Effect of Injection Pressure -- 9.2.4.2 Effect of Overall Porosity -- 9.2.4.3 Effect of Mobility Ratio -- 9.2.4.4 Effect of Longitudinal Dispersion -- 9.2.4.5 Effect of Transverse Dispersion -- 9.2.4.6 Effect of Aspect Ratio -- 9.2.5 Comparison of Numerical Modeling Results with Experimental Results -- 9.2.5.1 Selected Experimental Model -- 9.2.5.2 Physical Model Parameters -- 9.2.5.3 Comparative Study -- 9.2.5.4 Concluding Remarks -- 10 An Implicit Finite-Difference Approximation of Memory-Based Flow Equation in Porous Media -- 10.1 Summary -- 10.2 Introduction -- 10.3 Background -- 10.4 Theoretical Development -- 10.4.1 Mass Conservation -- 10.4.2 Composite Variable, ƞ -- 10.4.3 Implicit Formulation -- 10.6 Numerical Simulation -- 10.7 Results and Discussion -- 10.8 Conclusion -- 11 Towards Modeling Knowledge and Sustainable Petroleum Production -- 11.1 Essence of Knowledge, Science, and Emulation -- 11.1.1 Simulation vs. Emulation -- 11.1.2 Importance of the First Premise and Scientific Pathway.
11.1.3 Mathematical Requirements of Nature Science -- 11.1.4 The Meaningful Addition -- 11.1.5 "Natural" Numbers and the Mathematical Content of Nature -- 11.2 The Knowledge Dimension -- 11.2.1 The Importance of Time as the Fourth Dimension -- 11.3 Aphenomenal Theories of Modern Era -- 11.3.1 Examples of Linearization and Linear Thinking -- 11.3.2 The Knowledge-Based Cognition Process -- 11.4 Towards Modeling Truth and Knowledge -- 11.5 The Single-Parameter Criterion -- 11.5.1 Science Behind Sustainable Technology -- 11.5.2 A New Computational Method -- 11.5.3 Towards Achieving Multiple Solutions -- 11.6 The Conservation of Mass and Energy -- 11.6.1 The Avalanche Theory -- 11.6.2 Aims of Modeling Natural Phenomena -- 11.6.3 Challenges of Modeling Sustainable Petroleum Operations -- 11.6.4 The Criterion: The Switch that Determines the Direction at a Bifurcation Point -- 11.6.4.1 Some Applications of the Criterion -- 11.7 The Need for Multidimensional Study -- 11.8 Assessing the Overall Performance of a Process -- 11.9 Implications of Knowledge-Based Analysis -- 11.9.1 A General Case -- 11.9.2 Impact of Global Warming Analysis -- 11.9.3 Examples of Knowledge-based Simulation -- 12 Reservoir Simulation of Unconventional Reservoirs -- 12.1 Introduction -- 12.2 Material Balance Equations -- 12.3 New Fluid Flow Equations -- 12.4 Coupled Fluid Flow and Geo-mechanical Stress Model -- 12.5 Fluid Flow Modeling under Thermal Stress -- 12.6 Challenges of Modeling Unconventional Gas Reservoirs -- 12.7 Comprehensive Modeling -- 12.7.1 Governing Equations -- 12.7.2 Darcy's Model -- 12.7.3 Forchheimer's Model -- 12.7.4 Modified Brinkman's Model -- 12.7.5 The Comprehensive Model -- 13 Final Conclusions -- References and Bibliography -- Appendix A -- Index -- EULA.
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Cover -- Title Page -- Copyright Page -- Contents -- Preface -- 1 Introduction -- 1.1 Summary -- 1.2 Opening Remarks -- 1.3 The Need for a Knowledge-Based Approach -- 1.4 Summary of Chapters -- 2 Reservoir Simulation Background -- 2.1 Essence of Reservoir Simulation -- 2.2 Assumptions Behind Various Modeling Approaches -- 2.2.1 Material Balance Equation -- 2.2.2 Decline Curve -- 2.2.3 Statistical Method -- 2.2.4 Analytical Methods -- 2.2.5 Finite-Difference Methods -- 2.2.6 Darcy's Law -- 2.3 Recent Advances in Reservoir Simulation -- 2.3.1 Speed and Accuracy -- 2.3.2 New Fluid-Flow Equations -- 2.3.3 Coupled Fluid Flow and Geo-Mechanical Stress Model -- 2.3.4 Fluid-Flow Modeling Under Thermal Stress -- 2.4 Memory Models -- 2.4.1 Thermal Hysteresis -- 2.4.2 Mathematical and Numerical Models -- 2.5 Future Challenges in Reservoir Simulation -- 2.5.1 Experimental Challenges -- 2.5.2 Numerical Challenges -- 2.5.2.1 Theory of Onset and Propagation of Fractures due to Thermal Stress -- 2.5.2.2 Viscous Fingering during Miscible Displacement -- 3 Reservoir Simulator-Input/Output -- 3.1 Input and Output Data -- 3.2 Geological and Geophysical Modeling -- 3.3 Reservoir Characterization -- 3.3.1 Representative Elementary Volume, REV -- 3.3.2 Fluid and Rock Properties -- 3.3.2.1 Fluid Properties -- 3.3.3 Rock Properties -- 3.4 Upscaling -- 3.4.1 Power Law Averaging Method -- 3.4.2 Pressure-Solver Method -- 3.4.3 Renormalization Technique -- 3.4.4 Multiphase Flow Upscaling -- 3.5 Pressure/Production Data -- 3.6 Phase Saturations Distribution -- 3.7 Reservoir Simulator Output -- 3.8 History Matching -- 3.8.1 History-Matching Formulation -- 3.8.2 Uncertainty Analysis -- 3.8.2.1 Measurement Uncertainty -- 3.8.2.2 Upscaling Uncertainty -- 3.8.2.3 Model Error -- 3.8.2.4 The Prediction Uncertainty -- 3.9 Real-Time Monitoring.

4 Reservoir Simulators: Problems, Shortcomings, and Some Solution Techniques -- 4.1 Multiple Solutions in Natural Phenomena -- 4.1.1 Knowledge Dimension -- 4.2 Adomian Decomposition -- 4.2.1 Governing Equations -- 4.2.2 Adomian Decomposition of Buckley-Leverett Equation -- 4.2.3 Results and Discussions -- 4.3 Some Remarks on Multiple Solutions -- 5 Mathematical Formulation of Reservoir Simulation Problems -- 5.1 Black Oil Model and Compositional Model -- 5.2 General Purpose Compositional Model -- 5.2.1 Basic Definitions -- 5.2.2 Primary and Secondary Parameters and Model Variables -- 5.2.3 Mass Conservation Equation -- 5.2.4 Energy Balance Equation -- 5.2.5 Volume Balance Equation -- 5.2.6 The Motion Equation in Porous Medium -- 5.2.7 The Compositional System of Equations and Model Variables -- 5.3 Simplification of the General Compositional Model -- 5.3.1 The Black Oil Model -- 5.3.2 The Water Oil Model -- 5.4 Some Examples in Application of the General Compositional Model -- 5.4.1 Isothermal Volatile Oil Reservoir -- 5.4.2 Steam Injection Inside a Dead Oil Reservoir -- 5.4.3 Steam Injection in Presence of Distillation and Solution Gas -- 6 The Compositional Simulator Using Engineering Approach -- 6.1 Finite Control Volume Method -- 6.1.1 Reservoir Discretization in Rectangular Coordinates -- 6.1.2 Discretization of Governing Equations -- 6.1.2.1 Components Mass Conservation Equation -- 6.1.2.2 Energy Balance Equation -- 6.1.3 Discretization of Motion Equation -- 6.2 Uniform Temperature Reservoir Compositional Flow Equations in a 1-D Domain -- 6.3 Compositional Mass Balance Equation in a Multidimensional Domain -- 6.3.1 Implicit Formulation of Compositional Model in Multidimensional Domain -- 6.3.2 Reduced Equations of Implicit Compositional Model in Multidimensional Domain -- 6.3.3 Well Production and Injection Rate Terms.

6.3.3.1 Production Wells -- 6.3.3.2 Injection Wells -- 6.3.4 Fictitious Well Rate Terms (Treatment of Boundary Conditions) -- 6.4 Variable Temperature Reservoir Compositional Flow Equations -- 6.4.1 Energy Balance Equation -- 6.4.2 Implicit Formulation of Variable Temperature Reservoir Compositional Flow Equations -- 6.5 Solution Method -- 6.5.1 Solution of Model Equations Using Newton's Iteration -- 6.6 The Effects of Linearization -- 6.6.1 Case 1: Single Phase Flow of a Natural Gas -- 6.6.2 Effect of Interpolation Functions and Formulation -- 6.6.3 Effect of Time Interval -- 6.6.4 Effect of Permeability -- 6.6.5 Effect of Number of Gridblocks -- 6.6.6 Spatial and Transient Pressure Distribution Using Different Interpolation Functions -- 6.6.7 CPU Time -- 6.6.8 Case 2: An Oil/water Reservoir -- 7 Development of a New Material Balance Equation for Oil Recovery -- 7.1 Summary -- 7.2 Introduction -- 7.3 Mathematical Model Development -- 7.3.1 Permeability Alteration -- 7.3 Porosity Alteration -- 7.4 Pore Volume Change -- 7.4.1 A Comprehensive MBE with Memory for Cumulative Oil Recovery -- 7.5 Numerical Simulation -- 7.5.1 Effects of Compressibilities on Dimensionless Parameters -- 7.4.2 Comparison of Dimensionless Parameters Based on Compressibility Factor -- 7.4.3 Effects of M on Dimensionless Parameter -- 7.4.4 Effects of Compressibility Factor with M Values -- 7.4.5 Comparison of Models Based on RF -- 7.4.6 Effects of M on MBE -- 7.5 Conclusions -- Appendix Chapter 7: Development of an MBE for a Compressible Undersaturated Oil Reservoir -- 8 State-of-the-art on Memory Formalism for Porous Media Applications -- 8.1 Summary -- 8.2 Introduction -- 8.3 Historical Development of Memory Concept -- 8.3.1 Constitutive Equations -- 8.3.2 Application of Memory in Diffusion in Porous Media -- 8.3.3 Definition of Memory.

8.4 State-of-the-art Memory-Based Models -- 8.5 Basset Force: A History Term -- 8.6 Anomalous Diffusion: A memory Application -- 8.6.1 Fractional Order Transport Equations and Numerical Schemes -- 8.7 Future Trends -- 8.8 Conclusion -- 9 Modeling Viscous Fingering During Miscible Displacement in a Reservoir -- 9.1 Improvement of the Numerical Scheme -- 9.1.1 The Governing Equation -- 9.1.2 Finite Difference Approximations -- 9.1.2.1 Barakat-Clark FTD Scheme -- 9.1.2.2 DuFort-Frankel Scheme -- 9.1.3 Proposed Barakat-Clark CTD Scheme -- 9.1.4 Accuracy and Truncation Errors -- 9.1.5 Some Results and Discussion -- 9.1.6 Influence of Boundary Conditions -- 9.2 Application of the New Numerical Scheme to Viscous Fingering -- 9.2.1 Stability Criterion and Onset of Fingering -- 9.2.2 Base Stable Case -- 9.2.3 Base Unstable Case -- 9.2.4 Parametric Study -- 9.2.4.1 Effect of Injection Pressure -- 9.2.4.2 Effect of Overall Porosity -- 9.2.4.3 Effect of Mobility Ratio -- 9.2.4.4 Effect of Longitudinal Dispersion -- 9.2.4.5 Effect of Transverse Dispersion -- 9.2.4.6 Effect of Aspect Ratio -- 9.2.5 Comparison of Numerical Modeling Results with Experimental Results -- 9.2.5.1 Selected Experimental Model -- 9.2.5.2 Physical Model Parameters -- 9.2.5.3 Comparative Study -- 9.2.5.4 Concluding Remarks -- 10 An Implicit Finite-Difference Approximation of Memory-Based Flow Equation in Porous Media -- 10.1 Summary -- 10.2 Introduction -- 10.3 Background -- 10.4 Theoretical Development -- 10.4.1 Mass Conservation -- 10.4.2 Composite Variable, ƞ -- 10.4.3 Implicit Formulation -- 10.6 Numerical Simulation -- 10.7 Results and Discussion -- 10.8 Conclusion -- 11 Towards Modeling Knowledge and Sustainable Petroleum Production -- 11.1 Essence of Knowledge, Science, and Emulation -- 11.1.1 Simulation vs. Emulation -- 11.1.2 Importance of the First Premise and Scientific Pathway.

11.1.3 Mathematical Requirements of Nature Science -- 11.1.4 The Meaningful Addition -- 11.1.5 "Natural" Numbers and the Mathematical Content of Nature -- 11.2 The Knowledge Dimension -- 11.2.1 The Importance of Time as the Fourth Dimension -- 11.3 Aphenomenal Theories of Modern Era -- 11.3.1 Examples of Linearization and Linear Thinking -- 11.3.2 The Knowledge-Based Cognition Process -- 11.4 Towards Modeling Truth and Knowledge -- 11.5 The Single-Parameter Criterion -- 11.5.1 Science Behind Sustainable Technology -- 11.5.2 A New Computational Method -- 11.5.3 Towards Achieving Multiple Solutions -- 11.6 The Conservation of Mass and Energy -- 11.6.1 The Avalanche Theory -- 11.6.2 Aims of Modeling Natural Phenomena -- 11.6.3 Challenges of Modeling Sustainable Petroleum Operations -- 11.6.4 The Criterion: The Switch that Determines the Direction at a Bifurcation Point -- 11.6.4.1 Some Applications of the Criterion -- 11.7 The Need for Multidimensional Study -- 11.8 Assessing the Overall Performance of a Process -- 11.9 Implications of Knowledge-Based Analysis -- 11.9.1 A General Case -- 11.9.2 Impact of Global Warming Analysis -- 11.9.3 Examples of Knowledge-based Simulation -- 12 Reservoir Simulation of Unconventional Reservoirs -- 12.1 Introduction -- 12.2 Material Balance Equations -- 12.3 New Fluid Flow Equations -- 12.4 Coupled Fluid Flow and Geo-mechanical Stress Model -- 12.5 Fluid Flow Modeling under Thermal Stress -- 12.6 Challenges of Modeling Unconventional Gas Reservoirs -- 12.7 Comprehensive Modeling -- 12.7.1 Governing Equations -- 12.7.2 Darcy's Model -- 12.7.3 Forchheimer's Model -- 12.7.4 Modified Brinkman's Model -- 12.7.5 The Comprehensive Model -- 13 Final Conclusions -- References and Bibliography -- Appendix A -- Index -- EULA.

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