Fluid Flow in Porous Media

Fluid Flow in Porous Media Petroleum Engineering 524 Fall 2010 Written by Thomas W. Engler, Ph.D., P.E. Professor of Petroleum Engineering New Mexico Tech Copyright 2010

Table of Contents Chapter 1 Introduction Structure and Properties of Porous Materials Chapter 2 - Porosity 2.1 Fundamentals...2.1 2.2 Geologic Aspects...2.6 2.3 Measurement...2.19 2.4 Compressibility...2.27 2.5 Pore Structure...2.36 Chapter 3 - Permeability 3.1 Factors Affecting Permeability...3.1 3.2.1 Klinkenberg effect 3.2.2 Overburden pressure 3.2.3 Reactive Fluids 3.2 Darcy s Law...3.12 3.3 Porosity Permeability Relationships...3.17 3.4 Distribution of Rock Properties...3.22 3.5 Measurement...3.36 Statics of Fluids in Porous Media Chapter 4 - Saturation 4.1 Saturation...4.1 4.1.1 Irreducible water saturation 4.1.2 Factors affecting fluid saturations 4.1.3 Measurement of fluid saturations 4.2 Resistivity...4.12 Chapter 5 - Multiphase Phenomena 5.1 Wettability...5.1 5.1.1 Saturation distribution in reservoirs 5.2 Capillary Pressure...5.6 5.2.1 Capillary pressure in reservoirs 5.2.2 Entry pressure 5.2.3 Hysteresis Imbibition vs. drainage 5.2.4 Permeability effects 5.2.5 Capillary pressure measurement 5.2.6 Averaging Capillary pressure data

5.3 Relative Permeability...5.17 5.3.1 Two-phase relative permeability 5.3.2 Hysteresis Imbibition vs. drainage 5.3.3 Gas relative permeability 5.3.4 Effect of relative permeability on flow rates 5.3.5 Methods of generating relative permeability data 5.3.6 Three-phase relative permeability 5.3.7 Averaging relative permeability data 5.3.8 Relative permeability/capillary Pressure relationship Physical and Mathematical Theory of Flow Chapter 6 - Flow through porous media 6.1 Applications of Darcy s Law...6.1 3.1.1 Radial Flow 3.1.2 Permeability of combination of layers 3.1.3 Compressible flow 3.1.4 High velocity flow 3.1.5 Flow in fractures 3.1.6 Multiphase flow 6.2Differential equations for fluid flow...6.28 Permeability anisotropy Multiphase flow Chapter 7 - Steady laminar flow of homogeneous fluids 7.1 horizontal, 1D steady state flow...7.1 7.2 streamlines, isopotentials, source/sinks...7.3 7.3 superposition, 2D flow...7.7 Chapter 8 - Transient laminar flow of homogeneous fluids 8.1 Transient flow...8.1 8.2 Superposition in space...8.4 8.3 Unsteady-state Water influx model...8.9 Chapter 9 - Simultaneous flow of immiscible fluids 9.1 Development of equations...9.1 9.2 Steady-state, 1D solution...9.3 9.3 Capillary end effects...9.4 9.4 Frontal advance for unsteady state 1D displacement...9.6 9.4.1 Buckley-Leverett 9.4.2 Displacement performance (constant injection rate) 9.4.3 Determination of relative permeability curves 9.5 Factors that control displacement efficiency...9.19

9.6 Residual oil saturation...9.24 9.7 Limitations of the frontal advance solution...9.26 Chapter 10 - Simultaneous flow of miscible fluids 10.1 mass transport/ Fick s Law... 10.2 miscible displacement in porous media... 10.3 Tracer tests... Chapter x - Acoustic Properties References

CHAPTER 1 Introduction The objectives of this course are to develop an understanding of the basic physical characteristics of porous media and the fluids contained therein, to understand and appreciate the mechanisms that drive fluid flow in porous media and to apply this knowledge to some of the more complex problems of fluid flow through porous media. The first segment of this course investigates structures and properties involved in the flow of fluids in porous media. Building on these physical properties, the next segment involves static properties of fluids. For example, saturation, capillary pressure and relative permeability are included in the description of fluid flow. In essence these topics fall into the category of petrophysics. Petrophysics is the study of the properties of reservoir rocks and their relationship to the contained fluids. [Craft & Hawkins, 1959] Fundamental properties such as the void space in a porous media, porosity, or the ability for the media to transmit fluids, permeability, provide the foundations for reservoir engineering calculations. Further, multiphase flow phenomena such as relative permeability and capillary pressure form the basis for displacement of oil or gas by enhanced recovery processes. It should be easily recognized that geology plays an intimate role in the understanding of rock properties. The deposition, burial and subsequent diagenesis of sediments forms the framework for interconnected pore spaces. For example, porosity can develop through the degree of sorting of grain size during deposition or by dissolution along fractures or molds during diagenesis. The migration of fluids into a reservoir is related to the trapping mechanism and source rock. The third and final segment of this course expands to the physical and mathematical theory of flow. Beginning with the fundamental principles of fluid flow as described by Darcy s Law and conservation laws, governing differential equations are developed for single-phase, steady state and transient flow regimes in one- and twodimensions. And last, applying the multiphase flow phenomena described above, solutions to the immiscible displacement problem will be presented. The outcome of this course is students will obtain the foundations of fluid flow in porous media to apply in future endeavors. 1