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

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