Transport Phenomena in Porous Media III

Edited by

  • Derek Ingham, Department of Applied Mathematics Ingham Centre for Computational Fluid Dynamics University of Leeds Leeds LS2 9JT UNITED KINGDOM
  • Ioan Pop, Faculty of Mathematics University of Cluj R-3400 Cluj CP 253 ROMANIA

Fluid and flow problems in porous media have attracted the attention of industrialists, engineers and scientists from varying disciplines, such as chemical, environmental, and mechanical engineering, geothermal physics and food science. There has been a increasing interest in heat and fluid flows through porous media, making this book a timely and appropriate resource.Each chapter is systematically detailed to be easily grasped by a research worker with basic knowledge of fluid mechanics, heat transfer and computational and experimental methods. At the same time, the readers will be informed of the most recent research literature in the field, giving it dual usage as both a post-grad text book and professional reference.Written by the recent directors of the NATO Advanced Study Institute session on 'Emerging Technologies and Techniques in Porous Media' (June 2003), this book is a timely and essential reference for scientists and engineers within a variety of fields.
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Mechanical and civil engineers, materials scientists and environmental engineers.


Book information

  • Published: July 2005
  • Imprint: ELSEVIER
  • ISBN: 978-0-08-044490-1

Table of Contents


1 The Double-Decomposition Concept for Turbulent Transport in Porous Media

1.1 Introduction

1.2 Instantaneous Local Transport Equations

1.3 Time- and Volume-Averaging Procedures

1.4 Time-Averaged Transport Equations

1.5 The Double-Decomposition Concept

1.5.1 Basic Relationships

1.6 Turbulent Transport

1.6.1 Momentum Equation

1.7 Heat Transfer

1.7.1 Governing Equations

1.7.2 Turbulent Thermal Dispersion

1.7.3 Local Thermal Equilibrium Hypothesis

1.7.4 Macroscopic Buoyancy Effects

1.8 Mass Transfer

1.8.1 Mean and Turbulent Fields

1.8.2 Turbulent Mass Dispersion

1.9 Concluding Remarks


2 Heat Transfer in Bidisperse Porous Media

2.1 Introduction

2.2 Determination of Transport Properties

2.3 Two-Phase Flow and Boiling Heat Transfer

2.4 Dispersion

2.5 Two-Velocity Model

2.6 Two-Temperature Model

2.7 Forced Convection in A Channel Between Plane Parallel Walls

2.7.1 Uniform Temperature Boundaries: Theory

2.7.2 Uniform Flux Boundaries: Theory

2.7.3 Uniform Temperature Boundaries: Results

2.7.4 Uniform Flux Boundaries: Results

2.7.5 Conjugate Problem

2.7.6 Thermal Development

2.8 Conclusions


3 From Continuum To Porous-Continuum: The Visual Resolution Impact On Modeling Natural Convection in Heterogeneous Media

3.1 Introduction

3.2 Horizontal Heating

3.2.1 Continuum Equations

3.2.2 Porous-Continuum Equations

3.2.3 Heat Transfer Comparison Parameters

3.2.4 Results

3.2.5 Internal Structure Effect

3.3 Heat-Generating Blocks

3.3.1 Mathematical Modeling

3.3.2 Heat Transfer Comparison Parameters

3.3.3 Results

3.4 Conclusion


4 in Integral Transforms for Natural Convection in Cavities Filled With Porous Media

4.1 Introduction

4.2 Two-Dimensional Problem

4.3 Three-Dimensional Problem

4.4 Results and Discussion

4.5 Conclusions


5 A Porous Medium Approach for The Thermal Analysis of Heat Transfer Devices

5.1 Introduction

5.2 Thermal Analysis of Microchannel Heat Sinks

5.2.1 High-Aspect-Ratio Microchannels

5.2.2 Low-Aspect-Ratio Microchannels

5.3 Thermal Analysis of Internally Finned Tubes

5.3.1 Mathematical Formulation and theoretical Solutions

5.3.2 Velocity and Temperature Distributions

5.3.3 Optimizationof thermal Performance

5.3.4 Comments On The Averaging Direction

5.4 Conclusions


6 Local Thermal Non-Equilibrium in Porous Medium Convection

6.1 Introduction

6.2 Governing Equations

6.3 Conditions for the Validity of LTE

6.4 Free Convection Boundary Layers

6.4.1 General Formulation

6.4.2 Results for Stagnation Point Flow

6.4.3 Results for A Vertical Flat Plate

6.4.4 General Comments

6.5 Forced Convection Past A Hot Circular Cylinder

6.6 Stability of Free Convection

6.7 Conclusions


7 Three-Dimensional Numerical Models for Periodically Fully-Developed Heat and Fluid Flows Within Porous Media

7.1 Introduction

7.2 Three-Dimensional Numerical Model for Isotropic Porous Media

7.2.1 Numerical Model

7.2.2 Governing Equations and Periodic Boundary Conditions

7.2.3 Method of Computation

7.2.4 Macroscopic Pressure Gradient and Permeability

7.3 Quasi-Three-Dimensional Numerical Model for Anisotropic Porous Media

7.3.1 Periodic Thermal Boundary Conditions

7.3.2 Quasi-Three-Dimensional Solution Procedure for Anisotropic Arrays of Infinitely Long Cylinders

7.3.3 Effect of Cross Flow Angle On the Euler and Nusselt Numbers

7.3.4 Effect of Yaw Angle On the Euler and Nusselt Numbers

7.4 Large Eddy Simulation of Turbulent Flow in Porous Media

7.4.1 Large Eddy Simulation and Numerical Model

7.4.2 Velocity Fluctuations and Turbulent Kinetic Energy

7.4.3 Macroscopic Pressure Gradient in Turbulent Flow

7.5 Conclusions


8 Entropy Generation in Porous Media

8.1 Introduction

8.2 A Short History of the Second Law of thermodynamics

8.3 Governing Equations

8.3.1 Continuity Equation

8.3.2 Momentum Balance Equation

8.3.3 Energy Equation

8.3.4 Entropy Generation

8.4 Entropy Generation in A Porous Cavity and Channel

8.4.1 Entropy Generation in A Porous Cavity

8.4.2 Entropy Generation in A Porous Channel

8.5 Conclusions


9 Thermodiffusion in Porous Media

9.1 Introduction

9.2 Literature Review

9.2.1 Measurement Techniques of the Soret Coefficient

9.2.2 Mathematical and Numerical Techniques

9.3 Fundamental Equations of thermodiffusion

9.3.1 Haase Model

9.3.2 Kempers Model

9.3.3 Firoozabadi Model

9.4 Fundamental Equations in Porous Media

9.5 Numerical Solution Technique

9.6 Mesh Sensitivity Analysis

9.7 Results and Discussion

9.7.1 Comparison of Molecular and thermodiffusion Coefficients for Water Alcohol Mixtures

9.7.2 Calculation of Molecular and thermodiffusion Coefficients for Hydrocarbon Mixtures

9.7.3 Convection in A Square Cavity

9.7.4 Convection in A Rectangular Cavity

9.8 Conclusions


10 Effect of Vibration On The Onset of Double-Diffusive Convection in Porous Media

10.1 Introduction

10.2 Mathematical Formulation

10.2.1 Direct Formulation

10.2.2 Time-Averaged Formulation

10.2.3 Scale Analysis Method

10.2.4 Time-Averaged System of Equations

10.3 Linear Stability Analysis

10.3.1 Infinite Horizontal Porous Layer

10.3.2 Limiting Case of the Long-Wave Mode

10.3.3 Convective Instability Under Static Gravity (No Vibration)

10.4 Comparison of the Results With Fluid Media

10.5 Numerical Method

10.5.1 Vertical Vibration

10.5.2 Horizontal Vibration

10.6 The Onset of thermo-Solutal Convection Under The Influence of Vibration Without Soret Effect

10.6.1 Linear Stability Analysis

10.7 Conclusions


11 Combustion in Porous Media: Fundamentals and Applications

11.1 Introduction

11.2 Previous Works

11.3 Characteristics of Combustion in Porous Media

11.4 Applications

11.5 Porous Burners

11.6 Mathematical Modeling

11.7 Results and Discussion

11.8 Radial Burner

11.9 Conclusions

11.10 Possible Future Work


12 Reactive Transport in Porous Media-Concepts and Numerical Approaches

12.1 Introduction

12.2 Quantitative Geochemistry

12.3 Analytical Description of Reactive Transport

12.4 Examples

12.4.1 Equilibrium Example 1

12.4.2 Equilibrium Example 2

12.4.3 Equilibrium and Kinetics Example 1

12.4.4 Equilibrium and Kinetics Example 2

12.5 Numerical Approaches

12.5.1 Speciation Calculations

12.5.2 Transport Modeling

12.5.3 Transport and Reaction Coupling

12.6 Numerical Errors

12.7 Implementation in Matlab

12.8 Example Models

12.8.1 Three-Species Model

12.8.2 Calcite Dissolution Test Case (ID)

12.8.3 Two-Dimensional Modeling

12.9 Conclusions


13 Numerical and Analytical Analysis of the Thermosolutal Convection in An Annular Field: Effect of thermodiffusion

13.1 Introduction

13.2 Mathematical Model

13.2.1 Numerical Solution

13.3 Analytical Solution

13.4 Results and Discussion

13.5 Conclusions


14 Pore-Scale Transport Phenomena in Porous Media

14.1 Introduction

14.2 Conjugated Transport Phenomena With Pore Structure

14.2.1 Conjugated Phenomena in Sludge Drying

14.2.2 Effect of Inner Evaporation On The Pore Structure

14.3 Transport-Reaction Phenomena

14.3.1 Reaction in A Porous Solid

14.3.2 Experimental Investigation

14.4 Boiling and Interfacial Transport

14.4.1 Experimental Observations

14.4.2 Static Description of Primary Bubble Interface

14.4.3 Replenishment and Dynamic Behavior of the Interface

14.4.4 Interfacial Heat and Mass Transfer At Pore Level

14.5 Freezing and Thawing

14.5.1 Experimental Facility

14.5.2 Sludge Agglomerates During Freezing

14.5.3 Botanical Tissues During Freezing

14.6 Two-Phase Flow Behavior

14.6.1 Experimental Observation

14.6.2 Critical Diameter

14.6.3 Transport of Small Bubbles

14.6.4 Transport of Big Bubbles

14.7 Conclusion


15 Dynamic Solidification in A Water-Saturated Porous Medium Cooled From Above

15.1 Introduction

15.2 Mathematical Formulation

15.2.1 Two-Dimensional Model

15.2.2 A Reduced One-Dimensional Model

15.3 Numerical Results

15.3.1 Development of A Solid Layer and Convecting Flow

15.3.2 Amplitude and Phase Lag of the Oscillating Solid-Liquid Interface

15.4 Experimental Results

15.4.1 Experimental Apparatus and Procedure

15.4.2 Ice-Layer Thickness At Steady State

15.4.3 Average Nusselt Number and Vertical Temperature Variation At Steady State

15.4.4 Oscillating Cooling Temperature and the Response of Ice-Layer

15.4.5 Amplitude and Phase Lag Against Oscillating Cooling Temperature

15.5 Conclusion


16 Application of Fluid Flows Through Porous Media in Fuel Cells

16.1 Introduction

16.2 Operation Principles of Fuel Cells

16.3 Governing Equations for The Fluid Flows in Porous Electrodes

16.3.1 Equations for The Fluid Flow and Mass Transfer in Fuel Cells

16.3.2 Heat Generation and Transfer in Fuel Cells

16.3.3 The Electric Field in Fuel Cells

16.4 Multicomponent Gas Transport in Porous Electrodes

16.4.1 Convective Transport

16.4.2 Diffusive Transport

16.5 CFD Model Predictions of Fuel Cells

16.6 Concluding Remarks


17 Modeling The Effects of Faults and Fractures On Fluid Flow in Petroleum Reservoirs

17.1 Introduction

17.2 Single and Multiphase Flow

17.3 Modeling Flow in Petroleum Reservoirs Where Faults Act As Barriers

17.3.1 Numerical Modeling of the Permeability of Fault Rocks

17.3.2 Modeling Flow in Complex Damage Zones

17.3.3 Incorporation of Fault Properties Into Production Simulation Models

17.3.4 Knowledge Gaps and Future Directions

17.4 Modeling Flow in Reservoirs Where Faults and Fractures Act As Conduits

17.4.1 Overview of Existing Discrete Fracture Models

17.4.2 Technical Description of the Methodology

17.4.3 An Example of Flow Simulation in A Fractured Reservoir

17.5 Discussion and Conclusions