alt="bold e Subscript j"/> in one orthonormal basis a...
3 Chapter 4Figure 4.1 Geometry of the Dupuit–Thiem model.Figure 4.2 Definition of the drawdown
at an observation well.Figure 4.3 Calculation of transmissivity using drawdown data.Figure 4.4 A two‐dimensional region
with an external boundary
and a well...Figure 4.5 Two‐dimensional region
used to model the region
in Figure 4.4...Figure 4.6 Graphs of the Theis solution for vertically averaged piezometric ...Figure 4.7 Hypothetical plot of drawdown versus
for the Theis method.Figure 4.8 Schematic diagram of a vertical slice through an unconfined aquif...Figure 4.9 Weak solution to the porous medium equation showing a nondifferen...Figure 4.10 Location of the advancing front
as a function of time.
4 Chapter 5Figure 5.1 Qualitative illustration of Taylor diffusion. (a) Parabolic veloc...Figure 5.2 Mechanical dispersion effects. (a) Solute spreading as a result o...Figure 5.3 Initial concentration profile
for a sample initial‐value proble...Figure 5.4 Geometry of the method of characteristics, showing a hypothetical...Figure 5.5 (a) An admissible initial curve for a first‐order PDE. This curve...Figure 5.6 The solution
to the moving plume problem at two different times...Figure 5.7 Graph of the fundamental solution to the heat equation showing th...Figure 5.8 Graph of moving front solutions 5.36 to the advection–diffusion e...Figure 5.9 Snapshot of a numerical solution to the moving‐front problem usin...Figure 5.10 Snapshot of a numerical solution to the moving‐front problem usi...Figure 5.11 (a) Linear isotherm. (b) Freundlich isotherms for different valu...Figure 5.12 Graph of the ramp‐like initial concentration profile for the ini...Figure 5.13 Characteristic curves associated with the initial‐value problem ...Figure 5.14 Resolution to the problem of intersecting characteristics in Fig...Figure 5.15 Chord on the isotherm defining the speed of the adsorbate concen...Figure 5.16 Graphs of the solution
at several time levels, showing the for...
5 Chapter 6Figure 6.1 A piece
of smooth surface with boundary
, which is parametrize...Figure 6.2 A curved interface
with the pressure on the concave side being ...Figure 6.3 Wetting fluid
and nonwetting fluid
in a tube with contact ang...Figure 6.4 Capillary rise of water in a tube open at the top to the air.Figure 6.5 Capillary rise of water in a bundle of tubes having different rad...Figure 6.6 Typical capillary pressure curves showing the effects of hysteres...Figure 6.7 Schematic profile of soil in the near‐surface region, showing the...Figure 6.8 Schematic diagram of a tensiometer showing the water‐saturated po...Figure 6.9 Graph of a typical pressure head
for variably saturated flow in...Figure 6.10 Graph of a typical unsaturated hydraulic conductivity
for vari...Figure 6.11 An advancing moisture content front showing a wetting front, dow...Figure 6.12 Typical relative permeability curves.Figure 6.13 Typical fractional flow function associated with relative permea...Figure 6.14 One‐dimensional flow geometry used in the Buckley–Leverett probl...Figure 6.15 Ramp‐shaped initial condition used in the initial‐value problem ...Figure 6.16 Graphic solution to the Buckley–Leverett problem: Part (a) shows...Figure 6.17 Saturation shock in the solution to the Buckley–Leverett problem...Figure 6.18 Welge tangent construction to determine the saturation
at the ...Figure 6.19 Characteristic curves for the Buckley–Leverett problem showing t...Figure 6.20 Classical solution to the Buckley–Leverett problem with nonzero ...Figure 6.21 Characteristic curves for the Buckley–Leverett solution showing ...Figure 6.22 Oil production rate as a function of time predicted by the Buckl...Figure 6.23 Welge's graphic construction of the average oil saturation
at ...Figure 6.24 Schematic diagram of viscous fingering: A more mobile injected f...Figure 6.25 Geometry of the initially planar displacement front
separating...Figure 6.26 Perturbation
to the initial displacement front
.Figure 6.27 The perturbation as a level surface of the function
, showing a...Figure 6.28 A ternary diagram for three‐phase saturations showing the geomet...Figure 6.29 Saturation profiles for gas, oil, and water used in Exercise 6.1...Figure 6.30 Hypothetical three‐phase relative permeability contour plots sho...Figure 6.31 Saturation ternary diagram showing the reduced ternary diagram a...Figure 6.32 Two families of integral curves in the reduced ternary diagram d...Figure 6.33 Two saturation routes connecting the constant states
and
via...Figure 6.34 Saturation profile for the three‐phase displacement modeled by t...
6 Chapter 7Figure 7.1 Flow chart for equation‐of‐state thermodynamic calculations in a ...
7 Appendix BFigure B.1 Cylindrical coordinates.Figure B.2 Spherical coordinates.
8 Appendix DFigure D.1 A parametrized surface
showing the unit normal vector
and the...
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