The Mathematics of Fluid Flow Through Porous Media. Myron B. Allen, III

The Mathematics of Fluid Flow Through Porous Media

6.2 Variably Saturated Flow 6.3 Two‐fluid Flows 6.4 The Buckley–Leverett Problem 6.5 Viscous Fingering 6.6 Three‐fluid Flows 6.7 Three‐fluid Fractional Flow Analysis

11 7: Flows With Mass Exchange 7.1 General Compositional Equations 7.2 Black‐oil Models 7.3 Compositional Flows in Porous Media 7.4 Fluid‐phase Thermodynamics

12 Appendix A: Dedicated Symbols

13 Appendix B: Useful Curvilinear Coordinates B.1 Polar Coordinates B.2 Cylindrical Coordinates B.3 Spherical Coordinates

14 Appendix C: The Buckingham Pi Theorem C.1 Physical Dimensions and Units C.2 The Buckingham Theorem

15 Appendix D: Surface Integrals D.1 Definition of a Surface Integral D.2 The Stokes Theorem D.3 A Corollary to the Stokes Theorem

16 Bibliography

17 Index

18 End User License Agreement

List of Tables

1 Chapter 3Table 3.1 Isotropic, anisotropic, homogeneous, and inhomogeneous permeability...

2 Chapter 7Table 7.1 Phases in a compositional model.Table 7.2 Derived quantities used in compositional modeling.Table 7.3 Partitioning of pseudospecies in a black‐oil model.Table 7.4 Molar quantities used in compositional reservoir modeling.

3 Appendix ATable A.1 Dedicated symbols for physical quantities.

List of Illustrations

1 Chapter 2Figure 2.1 A reference configuration of a body, showing the referential coor...Figure 2.2 The deformation mapping the reference configuration

onto the bo...Figure 2.3 Regions

and

occupied by a body in two reference configuration...Figure 2.4 Orthonormal basis vectors defining a Cartesian coordinate system....Figure 2.5 A time‐independent region

having oriented boundary

and unit o...Figure 2.6 A region

in three‐dimensional space with unit outward normal ve...Figure 2.7 A cube of material illustrating the interpretations of entries of...Figure 2.8 Coordinate system used to define the depth function

.Figure 2.9 Geometry of the Stokes problem for slow fluid flow around a solid...Figure 2.10 Profile of flow through a thin circular cylinder having radius

Figure 2.11 A reference configuration and the deformation at times

and

f...Figure 2.12 Sketch of a fluid‐saturated porous medium showing three possible...Figure 2.13 Conceptual plot of REV‐averaged volume fraction versus radius of...

2 Chapter 3Figure 3.1 Schematic diagram of Darcy's apparatus for measuring water flow t...Figure 3.2 A piece of mathematical surface in a porous medium, in which shad...Figure 3.3 The transfer of momentum away from a solid object moving through ...Figure 3.4 Experimental configuration used to define 1 darcy.Figure 3.5 Schematic diagram of an array of fixed solid in which viscous eff...Figure 3.6 One‐dimensional flow geometry used to motivate the Forchheimer eq...Figure 3.7 Level sets of

, shown as dashed curves, along with the gradient Figure 3.8 Construction of a scalar potential

such that

, by computing a ...Figure 3.9 A piezometer showing the piezometric head

as the height to whic...Figure 3.10 Geometry of areal flow in a confined aquifer. The elevations

a...Figure 3.11 Fluid flux across the upper confining layer.Figure 3.12 Sandstone core samples. Sample (a) has dark shale streaks parall...Figure 3.13 Direction cosine

between a vector Скачать книгу