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 2010Table 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 data5.3 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 ..........................9.199.6 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 ReferencesCHAPTER 1 – Introduction 1 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