Porous Media Transport Phenomena E-Book

Faruk Civan

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 616

Veröffentlichungsjahr: 2011

Beschreibung

The book that makes transport in porous media accessible to students and researchers alike Porous Media Transport Phenomena covers the general theories behind flow and transport in porous media--a solid permeated by a network of pores filled with fluid--which encompasses rocks, biological tissues, ceramics, and much more. Designed for use in graduate courses in various disciplines involving fluids in porous materials, and as a reference for practitioners in the field, the text includes exercises and practical applications while avoiding the complex math found in other books, allowing the reader to focus on the central elements of the topic. Covering general porous media applications, including the effects of temperature and particle migration, and placing an emphasis on energy resource development, the book provides an overview of mass, momentum, and energy conservation equations, and their applications in engineered and natural porous media for general applications. Offering a multidisciplinary approach to transport in porous media, material is presented in a uniform format with consistent SI units. An indispensable resource on an extremely wide and varied topic drawn from numerous engineering fields, Porous Media Transport Phenomena includes a solutions manual for all exercises found in the book, additional questions for study purposes, and PowerPoint slides that follow the order of the text.

Leseprobe

Table of Contents

Cover

Title page

Copyright page

Dedication

PREFACE

ABOUT THE AUTHOR

CHAPTER 1 OVERVIEW

1.1 INTRODUCTION

1.2 SYNOPSES OF TOPICS COVERED IN VARIOUS CHAPTERS

CHAPTER 2 TRANSPORT PROPERTIES OF POROUS MEDIA

2.1 INTRODUCTION

2.2 PERMEABILITY OF POROUS MEDIA BASED ON THE BUNDLE OF TORTUOUS LEAKY-TUBE MODEL

2.3 PERMEABILITY OF POROUS MEDIA UNDERGOING ALTERATION BY SCALE DEPOSITION

2.4 TEMPERATURE EFFECT ON PERMEABILITY

2.5 EFFECTS OF OTHER FACTORS ON PERMEABILITY

CHAPTER 3 MACROSCOPIC TRANSPORT EQUATIONS

3.1 INTRODUCTION

3.2 REV

3.3 VOLUME-AVERAGING RULES

3.4 MASS-WEIGHTED VOLUME-AVERAGING RULE

3.5 SURFACE AREA AVERAGING RULES

3.6 APPLICATIONS OF VOLUME AND SURFACE AVERAGING RULES

3.7 DOUBLE DECOMPOSITION FOR TURBULENT PROCESSES IN POROUS MEDIA

3.8 TORTUOSITY EFFECT

3.9 MACROSCOPIC TRANSPORT EQUATIONS BY CONTROL VOLUME ANALYSIS

3.10 GENERALIZED VOLUME-AVERAGED TRANSPORT EQUATIONS

CHAPTER 4 SCALING AND CORRELATION OF TRANSPORT IN POROUS MEDIA

4.1 INTRODUCTION

4.2 DIMENSIONAL AND INSPECTIONAL ANALYSIS METHODS

4.3 SCALING

CHAPTER 5 FLUID MOTION IN POROUS MEDIA

5.1 INTRODUCTION

5.2 FLOW POTENTIAL

5.3 MODIFICATION OF DARCY’S LAW FOR BULK-VERSUS FLUID VOLUME AVERAGE PRESSURES

5.4 MACROSCOPIC EQUATION OF MOTION FROM THE CONTROL VOLUME APPROACH AND DIMENSIONAL ANALYSIS

5.5 MODIFICATION OF DARCY’S LAW FOR THE THRESHOLD PRESSURE GRADIENT

5.6 CONVENIENT FORMULATIONS OF THE FORCHHEIMER EQUATION

5.7 DETERMINATION OF THE PARAMETERS OF THE FORCHHEIMER EQUATION

5.8 FLOW DEMARCATION CRITERIA

5.9 ENTROPY GENERATION IN POROUS MEDIA

5.10 VISCOUS DISSIPATION IN POROUS MEDIA

5.11 GENERALIZED DARCY’S LAW BY CONTROL VOLUME ANALYSIS

5.12 EQUATION OF MOTION FOR NON-NEWTONIAN FLUIDS

CHAPTER 6 GAS TRANSPORT IN TIGHT POROUS MEDIA

6.1 INTRODUCTION

6.2 GAS FLOW THROUGH A CAPILLARY HYDRAULIC TUBE

6.3 RELATIONSHIP BETWEEN TRANSPORTS EXPRESSED ON DIFFERENT BASES

6.4 THE MEAN FREE PATH OF MOLECULES: FHS VERSUS VHS

6.5 THE KNUDSEN NUMBER

6.6 FLOW REGIMES AND GAS TRANSPORT AT ISOTHERMAL CONDITIONS

6.7 GAS TRANSPORT AT NONISOTHERMAL CONDITIONS

6.8 UNIFIED HAGEN–POISEUILLE-TYPE EQUATION FOR APPARENT GAS PERMEABILITY

6.9 SINGLE-COMPONENT GAS FLOW

6.10 MULTICOMPONENT GAS FLOW

6.11 EFFECT OF DIFFERENT FLOW REGIMES IN A CAPILLARY FLOW PATH AND THE EXTENDED KLINKENBERG EQUATION

6.12 EFFECT OF PORE SIZE DISTRIBUTION ON GAS FLOW THROUGH POROUS MEDIA

CHAPTER 7 FLUID TRANSPORT THROUGH POROUS MEDIA

7.1 INTRODUCTION

7.2 COUPLING SINGLE-PHASE MASS AND MOMENTUM BALANCE EQUATIONS

7.3 CYLINDRICAL LEAKY-TANK RESERVOIR MODEL INCLUDING THE NON-DARCY EFFECT

7.4 COUPLING TWO-PHASE MASS AND MOMENTUM BALANCE EQUATIONS FOR IMMISCIBLE DISPLACEMENT

7.5 POTENTIAL FLOW PROBLEMS IN POROUS MEDIA

7.6 STREAMLINE/STREAM TUBE FORMULATION AND FRONT TRACKING

CHAPTER 8 PARAMETERS OF FLUID TRANSFER IN POROUS MEDIA

8.1 INTRODUCTION

8.2 WETTABILITY AND WETTABILITY INDEX

8.3 CAPILLARY PRESSURE

8.4 WORK OF FLUID DISPLACEMENT

8.5 TEMPERATURE EFFECT ON WETTABILITY-RELATED PROPERTIES OF POROUS MEDIA

8.6 DIRECT METHODS FOR THE DETERMINATION OF POROUS MEDIA FLOW FUNCTIONS AND PARAMETERS

8.7 INDIRECT METHODS FOR THE DETERMINATION OF POROUS MEDIA FLOW FUNCTIONS AND PARAMETERS

CHAPTER 9 MASS, MOMENTUM, AND ENERGY TRANSPORT IN POROUS MEDIA

9.1 INTRODUCTION

9.2 DISPERSIVE TRANSPORT OF SPECIES IN HETEROGENEOUS AND ANISOTROPIC POROUS MEDIA

9.3 GENERAL MULTIPHASE FULLY COMPOSITIONAL NONISOTHERMAL MIXTURE MODEL

9.4 FORMULATION OF SOURCE/SINK TERMS IN CONSERVATION EQUATIONS

9.5 ISOTHERMAL BLACK OIL MODEL OF A NONVOLATILE OIL SYSTEM

9.6 ISOTHERMAL LIMITED COMPOSITIONAL MODEL OF A VOLATILE OIL SYSTEM

9.7 FLOW OF GAS AND VAPORIZING WATER PHASES IN THE NEAR-WELLBORE REGION

9.8 FLOW OF CONDENSATE AND GAS PHASE CONTAINING NONCONDENSABLE GAS SPECIES IN THE NEAR-WELLBORE REGION

9.9 SHAPE-AVERAGED FORMULATIONS

9.10 CONDUCTIVE HEAT TRANSFER WITH PHASE CHANGE

9.11 SIMULTANEOUS PHASE TRANSITION AND TRANSPORT IN POROUS MEDIA CONTAINING GAS HYDRATES

9.12 MODELING NONISOTHERMAL HYDROCARBON FLUID FLOW CONSIDERING EXPANSION/COMPRESSION AND JOULE–THOMSON EFFECTS

CHAPTER 10 SUSPENDED PARTICULATE TRANSPORT IN POROUS MEDIA

10.1 INTRODUCTION

10.2 DEEP-BED FILTRATION UNDER NONISOTHERMAL CONDITIONS

10.3 CAKE FILTRATION OVER AN EFFECTIVE FILTER

CHAPTER 11 TRANSPORT IN HETEROGENEOUS POROUS MEDIA

11.1 INTRODUCTION

11.2 TRANSPORT UNITS AND TRANSPORT IN HETEROGENEOUS POROUS MEDIA

11.3 MODELS FOR TRANSPORT IN FISSURED/FRACTURED POROUS MEDIA

11.4 SPECIES TRANSPORT IN FRACTURED POROUS MEDIA

11.5 IMMISCIBLE DISPLACEMENT IN NATURALLY FRACTURED POROUS MEDIA

11.6 METHOD OF WEIGHTED SUM (QUADRATURE) NUMERICAL SOLUTIONS

11.7 FINITE DIFFERENCE NUMERICAL SOLUTION

REFERENCES

Index

Copyright © 2011 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Civan, Faruk.

 Porous media transport phenomena / Faruk Civan.

p. cm.

 Includes index.

 ISBN 978-0-470-64995-4 (hardback)

 1. Porous materials. I. Title.

 TA418.9.P6C58 2011

 620.1'16--dc22

2011006414

eISBN 978-1-118-08643-8

oISBN 978-1-118-08681-0

ePub ISBN 978-1-118-08680-3

Dedicated to my family with love and appreciation

PREFACE

Many processes in the nature and engineering applications occur in porous media and materials. The mathematical description of such processes in porous materials is usually overwhelmingly complicated. Often, a compromising analysis approach is therefore necessary between complexity of modeling and effort required for the solution of problems of practical interest. This is usually accomplished by emphasizing an averaged representative description and neglecting the details of low-order influence.

This book has been designed to provide an understanding of the fundamentals of the relevant processes. The theory and modeling of the porous material, fluid, and species behavior in porous media are reviewed. The methods for prediction, analysis, and description of the commonly encountered porous media processes are discussed. Emphasis is placed upon practical understanding and implementation with straightforward mathematical treatment.

Transport in porous media is an interesting interdisciplinary subject, which attracted many researchers from various disciplines. This book covers the relevant materials with sufficient detail but without overwhelming the readers. This book can be used for understanding and description of the porous media problems. It may serve as a useful reference and text. This book provides knowledge of the theoretical and practical aspects of porous media transport for various purposes, including conducting laboratory and actual-size tests, model-assisted interpretation of test data, and prediction and simulation of various porous media processes.

Obviously, the abundance of literature available in this area is overwhelming because of the great interdisciplinary nature and the wide variety of potential approaches and applications in porous media. Numerous references have been used in the preparation of this book. However, an encyclopedic presentation of all approaches is not attempted for the purpose of this well-focused book. Rather, I have determined and limited the coverage of the relevant materials in this book to the essential critical bottom-line information required for the analyses and description of porous media processes. I believe this book will form an important basis for readers from which they can begin to explore innovative and creative approaches in dealing with applications in porous media.

This book is intended to provide an effective and comprehensive overview of the fundamentals and the experimental and theoretical approaches present in the area of the transport phenomena in porous media. The mechanisms of processes occurring in porous media are discussed. Various approaches used in the modeling of porous media single- and multiphase transport processes, with and without the thermal, species, and particulate processes, are presented systematically. The techniques available for the analysis and modeling of these processes with well-established approaches are described.

Porous media transport phenomena is an interdisciplinary issue of concern for petroleum, chemical, environmental, geological, geothermal, civil, and mechanical engineers, geologists, physicists, materials scientists, and mathematicians; it considers the simultaneous mass, momentum, and energy transport issues associated with porous matrices, pore fluids, and species; it includes a model-assisted analysis of experimental data and parameter determination issues; and incorporates the recent developments in porous media process analysis and modeling techniques.

This book is written in a concise and practical manner. Emphasis is placed upon the practical understanding, formulation, and application of the relevant processes, mechanisms, and methods without overwhelming with unnecessary details and mathematical complexities. The philosophy and theoretical and technical principles involved in the measurement and experimental techniques are explained. It presents an introductory background at the beginning of the chapters, followed by the relevant theoretical development, application problems for illustration and demonstration purposes, instructive questions and exercise problems for self-practice, and many references for further reading and details.

Most of the topics covered in this book are of common interest and interdisciplinary nature. This book is intended for use by researchers, practicing engineers, professionals, and engineering students involved in porous media applications. This book can be used as a textbook for senior undergraduate and early graduate-level engineering courses. The prerequisites are thermodynamics, fluid mechanics, heat transfer, engineering mathematics, basic computer programming, and basic properties of fluids and porous materials.

This book can be used by many disciplines and professionals for instructional and reference purposes because of its interdisciplinary nature. The material presented in this book has been tested in the courses taught by Dr. Civan at the University of Oklahoma over a period of 30 years. Parts of the materials presented in this book were tested by Dr. Civan in his industry short courses presented at various institutions. The materials presented in this book originate from Dr. Civan’s key papers, and relevant literatures listed in the references as well as the relevant parts taken from Dr. Civan’s course notes prepared for teaching the following courses:

Graduate courses

Fluid Flow through Porous MediaTransport Phenomena in Porous MediaWaterfloodingAdvanced Reservoir EngineeringEnhanced Oil RecoveryProcess Analysis and SimulationNumerical Simulation by Digital Computation

Undergraduate courses

Oil Reservoir EngineeringNatural Gas EngineeringApplied Reservoir Engineering

This book can be used in the following related courses in petroleum, chemical, environmental, civil, and mechanical engineering:

Transport Phenomena in Porous MediaFluid Flow through Porous MediaMass, Momentum, and Energy Transfer in Porous Media

Writing this book was an overwhelming accomplishment, which required the effort and dedication of the author for more than 10 years. Analyzing and condensing the vast amount of information available on this subject to the bottom-line critical presentation in this book was a tedious and laborious task. Some topics were more emphasized than others in the literature. Special undertaking was necessary to tie the loose ends. My dedication and motivation in taking such a responsibility was to make my lifelong learning, teaching, development, and expertise on this topic available for the readers of the book. Like any other information available, the readers should critically examine, test, and apply the information provided in this book in view of the particular conditions and requirements of problems of their interest.

I gratefully acknowledge the following organizations and companies for granting permissions to use various materials included in this book: American Chemical Society, American Geophysical Union, American Institute of Chemical Engineers, American Institute of Physics, American Society of Civil Engineers, American Society of Mechanical Engineers, Begell House Inc. Publishers, Chemical Engineering Education, Elsevier, John Wiley & Sons, Oklahoma Academy of Science, Society of Petroleum Engineers, Society of Petrophysicists and Well Log Analysts, and Springer.

Any comments, corrections, and suggestions by the readers to improve this book are welcome. After all, the overall objective of this book is to serve the readers by providing quality information in this one source.

I am indebted to the team at John Wiley & Sons Publishing Company for their support in the preparation and realization of this book.

Faruk Civan, PhD

Norman, Oklahoma

ABOUT THE AUTHOR

Faruk Civan is an M.G. Miller Professor in the Mewbourne School of Petroleum and Geological Engineering at the University of Oklahoma in Norman. Previously, he worked at the Technical University of Istanbul, Turkey. He formerly held the Brian and Sandra O’Brien Presidential and Alumni Professorships. He published a book, Reservoir Formation Damage—Fundamentals, Modeling, Assessment, and Mitigation, from Elsevier Publishing Company, and more than 270 technical articles published in journals, edited books, handbooks, encyclopedia, and conference proceedings, and presented more than 100 invited seminars and/or lectures at various technical meetings, companies, and universities. He holds an advanced degree in engineering from the Technical University of Istanbul, Turkey, a master of science degree from the University of Texas at Austin, and a doctor of philosophy degree from the University of Oklahoma. Civan has served on numerous American Institute of Chemical Engineers and Society of Petroleum Engineers technical committees. He is a member of the American Institute of Chemical Engineers, the Society of Petroleum Engineers, and the editorial boards of several journals. Civan has received 20 honors and awards, including five distinguished lectureship awards and the 2003 SPE Distinguished Achievement Award for Petroleum Engineering Faculty. He teaches short courses on topics of practical importance concerning the various aspects of in situ energy resource development and utilization.

Faruk Civan may be contacted at the Mewbourne School of Petroleum and Geological Engineering, The University of Oklahoma, T301 Energy Center, 100 E. Boyd St., Norman, Oklahoma 73019, USA. Telephone: [phone]; fax: [phone]; e-mail: [email protected].

CHAPTER 1

OVERVIEW

1.1 INTRODUCTION

Processes occurring in porous media and materials are encountered frequently in various engineering applications. The mathematical description of these processes is complicated because of the intricate flow paths, proximity of the pore wall, and mutual interactions of the fluids, particulates, and porous media. Often, a compromising analysis approach is essential in order to circumvent the complexity of modeling in view of the effort required for the solution of problems of practical interest. We can realistically accomplish this task by emphasizing an averaged description capturing the dominant features and neglecting the low order of magnitude details.

Porous Media Transport Phenomena is a comprehensive review and treatise of the fundamental concepts, theoretical background, and modeling approaches required for applications involved in mass, momentum, energy, and species transport processes occurring in porous media. This general inter- and multidisciplinary book provides a comprehensive material and background concerning the description of the behavior of fluids in porous materials.

An updated, concise, practical, convenient, and innovative treatment and presentation of the critical relevant bottom-line issues of transport in porous media is presented, from which all disciplines dealing with processes involving porous materials can benefit. Motivation, description, and executive summary of the various topics covered in this book are presented.

Description and characterization of porous media and processes occurring therein have been attempted by many different methods. The following approaches are among the outstanding methods used for this purpose (Chhabra et al., 2001):

Bundle of capillary tube models. The fluid flowing through the connected pore space is assumed to follow a number of preferential capillary tortuous flow paths (Kozeny, 1927; Carman, 1938, 1956). The wall friction effect of the capillary tubes is considered as exerting resistance to flow. The effect of irregularities (interconnectivity and entanglement) involved in and the interactions (cross-flow) occurring between the fluids flowing through the various capillary flow paths are ignored (Chhabra et al., 2001; Civan, 2001). However, this issue can be alleviated by means of the leaky-tube model (Civan, 2001, 2002b,d, 2003, 2005a).Pack of solid grain models. The drag exerted against fluid flowing through a pack of solid grains of assumed shapes, such as spherical particles, in a prescribed arrangement, such as cubic packing, is considered for prediction of frictional pressure loss during flow (Chhabra et al., 2001). This method has been implemented by three main approaches: (1) correlating the experimental data to express the drag as a function of porosity (pore volume fraction) or solidity, or packing (grain volume fraction) of porous media without considering the solid particle arrangement; (2) predicting the drag by solution of the momentum equations for a prescribed arrangement of solid grains; and (3) adjustment of the drag of a single grain in a cell for intergrain interactions by simulation (Chhabra et al., 2001).Averaging of microscopic field equations. The microscopic conservation equations governing the flow of fluids in porous media are averaged over a representative elementary volume of porous media. However, averaging over time is also carried out for rapid turbulent flow of fluids.Dimensionless empirical correlation methods. Empirical models are developed based on the method of dimensional analysis and empirically obtained mathematical relationships between the relevant dimensionless groups.Hybrid models. These combine the various features of the aformentioned methods.

This book presents a concise review and treatise of the relevant developments and theoretical foundations required for understanding, investigation, and formulation of processes involving porous media. The overall objective is to provide the readers with one source to acquire the bottom-line information in a convenient and practical manner. This book is written to provide engineering students, scientists, professionals, and practicing engineers with an updated and comprehensive review of the knowledge accumulated in the literature on the understanding, mathematical treatment, and modeling of the processes involving porous media, fluid, and species interactions and transport. However, presentation is limited to the most critical information needed for applications of practical importance and further developments without overwhelming the readers with unnecessary encyclopedic details.

Fundamental theories, principles, and methods involved in the analysis and modeling of single- and multiphase fluid and species transport in porous media are covered. Special emphasis is placed on the phenomenological modeling of the processes involved in the transport of fluids, species, and particulates in porous materials, oil and gas recovery, geothermal energy recovery, and groundwater contamination and remediation. This book presents the fundamental knowledge and the recent developments in the analysis, formulation, and applications of flow through porous materials. Formulation of mass, momentum, and energy transport phenomena and rate processes; model-assisted analysis of experimental data; and modeling of processes occurring in porous media are described in a practical manner and are illustrated by various example problems. Experimental and measurement techniques used for the study of the processes in porous media and for the determination of relevant process parameters are described and demonstrated by applications.

Among the topics covered in this book are characterization of porous materials; phenomenological description of commonly encountered processes, formulation of equations for mathematical description of porous media transport, and their associated initial and/or boundary conditions; analyses of porous media processes by various approaches including constitutive relationships, dimensional analysis, control volume conservation analysis, and representative volume and time averaging; development and applications of the multiphase transport models, including the noncompositional, limited compositional, and fully compositional types; treatment of potential flow, phase transition, physical and chemical reactions, porous media deformation, particulates, heterogeneity, and anisotropy; and basic numerical simulation examples. Examples exploring and demonstrating the applications of the various formulations are presented for instructional purposes, and exercise problems are provided at the end of the chapters for further practice on the subject matter. Most problems dealing with porous media transport involve subsurface porous media, and therefore some examples given in this book relate to processes occurring in such media. The state of the knowledge is presented in plain language with equal emphasis on the various topics in a uniform format and nomenclature using the consistent International System of Units (SI). Instructive figures are presented to explain the relevant phenomena, mechanisms, and modeling approaches and results. A comprehensive list of relevant references is provided at the end of the book.

1.2 SYNOPSES OF TOPICS COVERED IN VARIOUS CHAPTERS

This book contains 11 chapters covering the most critical topics and formulation of porous media transport phenomena. Chapter 1 presents an overview and executive summaries of the various topics covered in this book.

Chapter 2 presents the transport properties of porous media. The effects of pore connectivity, the valve action of pore throats, and cementation are considered in a bundle of tortuous, leaky capillary tubes of flow for a macroscopic model of permeability of porous media. Practical straight-line plotting and parameter determination schemes are presented for convenient correlation of the porosity–permeability of porous media using a simplified macroscopic model. The permeability of porous media is correlated by means of a single continuous function over the full range of porosity using a power-law flow unit equation. The parameters of the power-law flow unit equation incorporate the fractal attributes of interconnected pore space into a bundle of tortuous, leaky hydraulic tube model of porous media. These parameters are strong functions of the coordination number of porous media and are significantly different from those of the Kozeny–Carman equation. The mathematical relationships of the power-law parameters to the coordination number are also presented. The associated analysis also lends itself to the physical interpretation of the pore connectivity and cementation factor in terms of the relationship of permeability to porosity. From a practical point of view, the primary advantage of the present macroscopic modeling approach is that it leads to a single, simple, compact, and convenient equation, which can be readily incorporated into the modeling of porous media processes without adding appreciable complexity and computational burden into large-scale field simulations. This macroscopic model is an improvement over the Kozeny–Carman equation, which has a more limited application. It is more beneficial than the microscopic pore-scale network models because it requires significantly less computational burden while providing sufficient accuracy for large field-scale applications.

Chapter 3 presents the macroscopic transport equations. First, the methodology for temporal, spatial, and double averaging of microscopic conservation equations for derivation of the porous media macroscopic conservation equations is presented and illustrated by several examples. The volume and mass-weighted volume averaging of the microscopic equation of conservation results in different macroscopic equations. Properly formulated closure schemes, such as the gradient theory, are required for formulation of terms involving the averages of the products of various quantities representing deviations from their volume-average values. It is emphasized that both time and space averaging are necessary by means of double decomposition for macroscopic description of processes involving transport through coarse porous media, where the pore fluid volume is large enough to undergo some turbulence effects. Second, the methodology for direct derivation of the porous media conservation equations by control volume analysis is presented as an alternative approach, which can provide different insights into the nature of macroscopic equations.

Chapter 4 presents the scaling and correlation of transport in porous media. Applications of dimensional and inspection analysis methods to porous media processes are demonstrated and elaborated. Their outstanding advantages and disadvantages are delineated. The benefits of using normalized variables are emphasized. Important dimensionless groups and mathematical relationships are derived and applied for several cases. Analysis and interpretation of experimental results using dimensionless groups and self-similarity transformations are presented. Strategies for effective scaling and generalization of experimental results are discussed.

Chapter 5 presents the fluid motion in porous media. The equation of motion for single-phase fluid flow through porous media is derived by various approaches, including the analysis of forces acting on fluid based on dimensional analysis and a control volume momentum balance approach. Resistive forces associated with pore surface and pore throat are characterized by the capillary orifice model of porous media. Several issues are emphasized, including the porous media averaging of the pressure and shear stress terms, the effect of porous media heterogeneity and anisotropy, source terms, correlation of parameters, flow demarcation criteria, entropy generation, viscous dissipation, generalization of Darcy’s law, non-Newtonian versus Newtonian fluid rheology, and threshold pressure gradient that must be overcome for fluid to flow through porous media.

Chapter 6 presents the gas transport in tight porous media. The flow of gases through tight porous media is treated differently from liquids. Walls of tight pores in porous media interfere with the mean free motion of gas molecules and cause a strong deviation from Darcy’s law. Darcy’s law cannot describe the flow of gas in tight formations under the Knudsen and slip flow conditions because Darcy’s law was designed to represent the viscous flow by analogy to liquid flow. A multiple-mechanism transfer model can provide an accurate description of gas flow in tight porous media. A Darcy-like equation using an apparent permeability is presented by considering the gas transport by several mechanisms, which may occur in tight pore spaces under different Knudsen number criteria. This equation incorporates the Knudsen, transition, slip, viscous, surface diffusion, and condensate flow mechanisms into the description of gas flow, each prevailing under different conditions. The characteristics of porous media are represented by fractal description and by considering the pore size distribution. Various issues involved in the proper derivation of relevant formulas based on the realization of the preferential flow paths in porous media by means of a bundle of tortuous tubes are presented. The mechanisms, characteristic parameters, and modeling of gas transport through tight porous media under various conditions are reviewed. Formulations and methodology are described for accurate and meaningful correlations of data considering the effect of the characteristic parameters of porous media, including intrinsic permeability, porosity, and tortuosity, as well as the apparent gas permeability, rarefaction coefficient, and Klinkenberg gas slippage factor.

Chapter 7 presents the coupling fluid mass and motion in porous media. The flow of fluids through porous media under isothermal conditions requires the simultaneous solution of the mass and momentum conservation equations. Hence, this chapter describes the coupling of these two equations in various applications of practical importance involving single- and multiphase fluid systems. The concept of the leaky-tank model is introduced, allowing for the determination of the essential parameters of flow occurring in porous media around the wells. Special convenient formulations are derived for fractional flow, end-point mobility, and streamline/stream tube flow descriptions. Applications of the method of superposition, images, and front tracking are described for potential flow problems. Numerical solutions of various problems are presented for instructional purposes.

Chapter 8 presents the characterization of parameters for fluid transfer. A review of the methods required for defining and determining the essential parameters affecting fluid transport through porous media is presented. Wettability and wall drag, wettability index, capillary pressure and measurement, relative permeability and measurement, temperature dependence, and interfacial drag are discussed. Application of the Arrhenius equation is reviewed for the correlation of the temperature effect on wettability-related properties of material, including the work of immiscible displacement, unfrozen water content, wettability index, and fluid saturation in porous media. The correlation with the Arrhenius equation provides useful information about the activation energy requirements associated with the imbibition and drainage processes involving the flow of immiscible fluids in porous materials. Determination of the relative permeability and capillary pressure from laboratory core tests by direct and indirect methods based on steady-state and unsteady-state core flow tests is described.

Chapter 9 presents the modeling transport in porous media. Applications of coupled mass, momentum, and energy conservation equations are discussed and presented for various problems. Transport of species through porous media by different mechanisms is described. Dispersivity and dispersion in heterogeneous and anisotropic porous media issues are reviewed. Formulation of compositional multiphase flow through porous media is presented in the following categories: the general multiphase, fully compositional nonisothermal mixture model, the isothermal black oil model of nonvolatile oil systems, the isothermal limited compositional model of volatile oil systems, and shape-averaged models. Formulation of source/sink terms in conservation equations is discussed. Analyses and formulations of problems involving phase change and transport in porous media, such as gas condensation, freezing/thawing of moist soil, and production of natural gas from hydrate-bearing formations, are presented.

Chapter 10 presents the modeling of particulate transport in porous media. Formulation of deep-bed and cake filtration processes involving particle transport and retention, and resulting porosity and permeability variation in porous media, is described. Phenomenological modeling considering temperature variation and particle transport by advection and dispersion is discussed. Temperature dependence is accounted for through the filtration rate coefficient and porous matrix thermal deformation. Other factors affecting the filtration coefficient and permeability are considered by means of empirical correlations. Applications are presented concerning the transport of colloids and particles through porous media and compressible cake filtration involving smaller particles packing through the large particles that form the skeleton of the filter cake. The effect of dispersion mechanism and temperature variation on particle transport and retention, and the consequent porosity and permeability impairment, is demonstrated by several examples.

Chapter 11 presents the modeling of transport in heterogeneous porous media. This chapter presents formulations and solutions that apply to heterogeneous systems having various transport units in fractured porous media, where the permeability of the fracture system is relatively greater than that of the porous matrix, and therefore the fractures form the preferential flow paths while the matrix forms a source of fluid for fractures. The objectives of this chapter are to develop an understanding of the mechanism of the matrix-to-fracture fluid transfer by the various processes and the formulation of transport in fractured porous media. The analytical and numerical solutions are presented for relatively simplified cases and systems undergoing an imbibition-drive matrix-to-fracture fluid transfer.