Страница 4 из 4
Предметный указатель:
A
Acid treatment, 404, 420, 428, 448
of fractured limestones, 425, 427, 451, 741
of gas reservoirs, 685, 717
in radial systems, 422, 424, 448, 741
Analogies of porous flow, 139ff., 146, 455, 736
Analytic functions, 182
Anisotropic media, 225ff., 253, 738
partially penetrating wells in, 277ff., 285, 739
resultant permeability in, 227
Averaging procedure, 240
В
Bessel functions, 429ff., 630ff.
definition of, 431
differential equation for, 431, 662
recurrence relations for, 662
Bipolar coordinates, 181
Boundary conditions, 136ff., 146
analytic form of, 139
mixed, 188
at surfaces of discontinuity, 401, 448
Boyle's law, 123, 143
C
Calculus of variations, 235
Capillary zone, 30ff., 292
effect on gravity flow, 372, 373
fluid movements in, 30ff.
Classical hydrodynamics, 125ff., 144
derivation of Darcy's law from 131
discontinuous motion in, 300
Compaction, 14ff.
of clay, 16
effect on fluid migration, 44
effect on permeability, 17
of sand and gravel, 14
Compressible liquids, analytic definition, 132
equation for density distribution of, 133, 145
nonsteady state radial flow of, 630ff., 632, 642, 655
sources and sinks for, 666, 676
steady-state flow of, 627ff., 745
linear flow, 628
radial flow, 628ff.
Conjugate functions, 181, 469
method of, 181ff.
transformations, 186
by electrical models, 242
Connate waters, 40ff.
analyses of, 42
migration of, 43
occurrence of, 40
Conversion factors, 723, 724
Curvilinear coordinates, 725
Cylindrical coordinates, 141, 726
D
Dams, 3
coffer, 221ff., 252, 748
pressure distribution at base of, 193, 201, 202, 207, 248, 737
sand-model experiments on, 205ff., 250
seepage flux under, 208ff., 215ff., 738
seepage through, approximate theory of, 338ff., 377ff., 393, 398
rigorous theory of, 303ff., 314ff., 388ff., 739
Dams, seepage through, study of by electrical models, 318ff., 390,391
stability of, 311
uplift force on, 194, 203, 249, 737, 738
uplift moments on, 194, 203, 249, 737, 738
uplift pressure on, 192, 194
Darcy, conversion table for, 75
definition of, 76
units of, 76
Darcy’s law, 55ff., 136,144, 401, 402, 455, 480, 626, 733
analogy with other physical laws, 140
analytic definition of, 69, 71, 128, 129, 735
for anisotropic media, 226
confirmation of, 178, 208
constant in, 69
deviations from, 62ff., 194
discovery of, 55
range of validity of, 56ff., 67, 68, 144
special form for hydraulics, 72, 294
Deposition of sediments, 24ff.
Dimensional theory, 56
application, to model experiments, 244, 257
to porous flow, 56, 59
Dini series, 656
Drainage by ditches, 288
to deep lying water tables, 331ff., 392, 740
free surfaces in, 327
to shallow water tables, 336ff., 346ff., 394, 740
of sloping sands, 292/, 386, 387, 739
Drive between two wells, 472ff., 502
electrolytic model of, 563
Duhamel's theorem, 631
Dupuit assumptions, 360ff., 373ff., 396
Dupuit-Forchheimer theory, 135, 359ff., 377ff., 385ff.
application to seepage through dams, 314ff.
Dupuit-Forchheimer theory, application of Thiem, 97
equation of, 360, 369
E
"East Texas" field, 460, 625, 639, 642, 668, 672, 673, 675
cross section of, 645
pressure decline in, 644ff., 648, 650ff., 674, 746
pressure distribution about, 652
Edgewater encroachment, 453ff., 499
effect of gravity on, 476, 502
effect of viscosity differences on, 478, 503
line drive, 468
motion of interfaces in, 457, 466ff., 499
Elliptic function transformations, 208ff.
modular functions, 301, 308ff., 312, 313, 729ff.
Equation of continuity, 121
derivation of, 122
steady-state form of, 123
for incompressible liquids, 124 for variable permeability, 402, 448
Equation of state, 123, 131, 143
Equations of motion, 131, 145
for compressible liquids, 133, 735, 736
for gases, 133, 736
for incompressible liquids, 132, 735
Erosion, 346, 355, 395, 740
Euler sum formula, 443
F
Filter beds, 403, 404
Finite line source, 181, 247
flow into infinite sand from, 181
flow into a well from, 186,191, 737
pressure distribution about, 184
Five-spot flood, 569
conductivity of, 585ff., 615, 744
Five-spot flood, efficiency of, 596, 597, 613, 616, 745
flooding history of, 570, 743
pressure distribution in, 577, 586
Fluidity, 459
Fourier-Bessel series, 633
Fourier equation, 134
elementary solutions of, 630
Green's function for, 661ff.
source and sink solutions of, 666ff..
Fourier integral, 227, 417, 450, 732
Fourier series, 156ff., 168, 245, 379, 417, 441, 450, 633, 634, 662
cosine series, 156, 159, 441
sine series, 157, 161
Fourier's law, 140
Fractured limestones, 409ff., 450
acid treatment of, 425, 427, 450, 741
bounded systems, 417
effective permeability of, 417
as gas reservoirs, 685, 718
resistivities of, 415, 416, 450
Free surfaces, 243, 256, 287ff., 365, 385
hodograph for, 302
parabolic, 325, 391
refraction of, 401
in seepage from ditches, 327ff., 335
shape in dams, 314 ff.
slope, at inflow surfaces, 291
at outflow surfaces, 291
Friction factor, 58
chart, 60, 61
G
Gamma function, 267, 419
Gas coning, 701ff.
conditions for, 702
Gas drive, 455
Gases, analytic definition of, 132, 672
equation for density distribution of, 133, 145, 679
nonsteady-state flow of, 704ff.
drainage of closed reservoirs, 708, 712, 721
Gases, nonsteady-state flow of, transients in, 705, 715
permeability measurements with, 91
steady-state flow of, 679ff.
gravity-flow systems, 684, 717
linear, 680, 716, 747
multiple-well systems, 704, 720
nonuniform-permeability systems, 685, 717
three-dimensional systems, 683, 717
two-dimensional problems, 682, 717
two-fluid systems, 686, 718
Gas-oil ratios, 687, 718
effect of tubing on, 696ff., 719, 720, 748
for communicating gas and oil zones, 689ff., 719, 748
for noncommunicating gas and oil zones, 692ff., 719, 748
relation to oil recovery, 688, 748
Gauss' theorem of the mean, 174, 231
Grain diameter "average", 15, 61
Gravity-flow systems, 287ff.
approximate theory of, 377ff., 398
composite pressure-head and, 375ff., 398, 741
exact solutions for, 323ff., 391
of gases, 684, 717
sand-model studies of, 365ff., 397ff.
treatment, by electrical models, 318ff., 390
by Hopf and Trefitz, 292ff., 387
by method of hodographs, 300ff., 387
Green's function, 169ff., 246, 511
conformal mapping by, 197
definition of, 169
graphical construction of, 237
mixed, 189
for nonsteady-state flow, 661ff.
relation to method of images, 180
symmetry of, 171
for two-dimensional systems, 727
Green's reciprocation theorem, 228, 246
Green's theorem, 236
Ground waters, 28ff.
content in unconsolidated surface sediments, 30
fluctuations in level of, 364
movements, below water table, 34, 38
in capillary zone, 30
occurrence of, 28
H
Hodographs, method of, 300ff., 387
application of inversion transformations to, 300, 301, 332
for constant-potential surfaces, 302, 388
definition of, 301
for free surfaces, 302, 387
for impermeable boundaries, 301, 388
for seepage through dams, 304
for surfaces of seepage, 302, 388
Homogeneous fluids, definition of, 4
equations for, 131, 132
I
Images, method of, 175, 247
application to partially penetrating wells, 265, 266
in homogeneous media, 410
infinite sets of, 186
relation to Green's function, 180
Incompressible liquids, 123
equation, for pressure distribution, 132, 145
of state for, 123, 132
radial flow of, 150
Infinite line source, 175
Infinite-well arrays, 523
pressure distribution about, 526, 528, 537, 544
resistance of, 529, 540
staggered arrays, 545, 611
Infinite-well arrays, three-line arrays, 540ff., 610, 743
shielding in, 543, 610
two-line arrays, 530ff., 609, 743
shielding in, 533, 535, 536, 610, 743
Initial conditions, 136, 138
Irrigation problems, 353, 394
К
Kelvin equation, 457
L
Laplace's equation, 133, 134, 140, 430
in curvilinear coordinates, 726
in cylindrical coordinates, 141
methods of solution:
arithmetic mean, 234
balayage, 234
graphical, 237, 254, 339, 738
model experiments, 241ff., 255, 256
numerical, 238, 255
separation of variables, 430
variational, 235, 254
Ritz, 235
Trefitz, 236
solutions of, 430
exact for gravity-flow systems, 323ff., 391
periodic, 168
polar coordinate, 163
in spherical coordinates, 142, 259
for two-dimensional liquid flow, 150, 244
uniqueness of solution, 139, 433
Laws of flow, 59
for gases, 66
for liquids, 59, 61, 63, 64
Limestones, acid treatment of, 420ff.
flow in fractured, 409ff.
structure of, 20ff.
Linear encroachment, 459ff., 500, 742
Linear sheet flow, 324, 391
Line drive, 175, 246
electrolytic model for, 563, 564, 566, 567
encroachment from, 468ff., 501, 742
flux into well from, 178, 736
into infinite-well arrays, 524ff., 609
Line-drive floods, 568
conductivity of, 582ff., 615, 744
flooding history of, 569, 743
pressure distribution in, 579, 582
Line-of-сгеер theory, 201, 202, 204, 249
M
Maxwell's law, 140
Model experiments, 241, 255
dimensional requirements for, 243, 257,
electrical, 241ff.
electrolytic, 241, 255
for flooding networks, 561ff., 612
for seepage under dams, 208, 220
graphite, 242, 486, 498
for water coning, 486, 498
gravity flow, 243, 256, 318ff., 390
circuit for, 319
for seepage through dams, 318ff.
sheet conduction, 242, 256
circuit for, 575
for flooding networks, 577ff., 614
sand models, 241
of gravity-flow systems, 365ff.
for seepage from ditches. 349, 352
for seepage under dams, 205, 206, 208
Multiple-well systems, 507ff.
for gas sands, 704
N
Nonuniform-permeability systems, 400ff.
flux in, 407, 741
for gas flow, 685, 717
pressure distribution in, 406, 414
О
Offsetting, 546ff., 611
multiple-line, 552ff., 612, 743
example of, 556ff.
single-line, 548ff., 611, 743
pressure distribution in, 551
Ohm's law, 140
Open-bottom wells, 282
P
Packing of porous media, 10ff.
of natural materials, 13
relation to porosity, 79
of spheres, 10ff.
Partially penetrating wells, 263ff.
in anisotropic sands, 277ff., 285, 739
in gas sands, 684, 686, 748
potential distribution for, 270, 271, 283, 498
application to coning problem, 488ff.
production capacities of, 274ff., 284, 438, 739
maximal, without water coning, 495
in stratified sands, 429ff., 438, 742
Permeability, 69ff.
calculation, for gases, 78, 733
for liquids, 77, 733
continuous variations of, 401ff.
conversion table for, 75
definition of, 10, 71, 72, 294
dimensions of, 72
discontinuous variations in, 403ff.
effect of compaction on, 17
effective, for anisotropic media, 227
Permeability, effective, for filter beds, 403
of fractures, 417, 425, 449, 741
for hydraulic problems, 72, 294
measurement of, 76ff.
consolidated sands, 85
apparatus for, 86ff.
with gases, 91
gas vs. liquids, 91, 93
with liquids, 89
in the field, 93ff.
calculation of, 95ff., 733ff.
correction factors, 96, 734
unconsolidated sands, 79ff.
apparatus for, 81
nomenclature, 76
typical values of, 101
anisotropic character of, 111
for consolidated sands, 103ff.
Berea, 106
Berea grit, 104
Bradford, 103, 105, 109
Clarendon, 104, 106, 109, 110
Cromwell, 107, 108
Gilcrease, 107
Glen Rose, 108
Johnson, 107
Kane, 106
Olean, 106
Onondaga, 105
Pechelbroon, 108
Robinson, 103
Salt, 104
School Land, 106
Speechley, 102, 104, 107
Tokio, 108
Venango, 103, 104, 106, 109, 110
Wanette, 108
Wilcox, 103, 106
Windfall, 104
Woodbine, 103, 105, 647
of continuous cores, 109
of unconsolidated sands, 113
units for, 74
variation, with cementation, 73
with grain size, 70
with porosity, 12, 80
Petroleum fluids, 47ff.
accumulation of, 50
migration of, 50
occurrence of, 47
source of, 48
traps for, 52
Piezometric surface, 355, 369
Poisseuille's law, 56, 57, 71
Poisson's integral, 174, 231, 308
generalized, proof of, 732
Porosity, 10
calculation of, 114, 735
of consolidated rocks, 103ff., 118
of continuous cores, 109
determination of,
consolidated sands, 113ff.
Barnes methods, 117
Melcher-Nutting method, 114
Russel method, 115
Washburn-Bunting method, 116
unconsolidated sands, 81
effect on permeability, 12, 80
of natural materials, 13
of sphere packings, 12
Porous media, definition of, 7
nature of, 10ff.
Potential, 129
velocity, 129, 137, 145, 182, 287
Potential distributions, about partially penetrating wells, 270, 271, 283
in radial systems, 260
in spherical systems, 260
for stratified sands, 436
Potential theory, 149ff., 455, 456ff.
Pressure distributions, 77
under dams, 193, 201, 202, 737, 738
in flooding networks, 577ff., 582ff., 614
about infinite-well arrays, 526, 528, 537, 544, 551
in inhomogeneous systems, 406, 414
for line-drive flow into well, 178
in linear gas flow, 680, 681
Pressure distributions, in linear systems, 77
in radial systems, 151, 152
arbitrary, over boundaries, 163
in Woodbine sand, 652
Pressure rise in wells, 640ff., 672, 746
R
Radial encroachment, 462ff., 500, 742
Radial flow, 150
of compressible liquids, 628, 632ff.,640, 642ff.
of gases, 682, 747
of incompressible liquids, 150
flux in, 153, 736
effect of well diameter on, 156
gravity flow, 365ff., 397, 740
Kozeny's theory of, 365
sand-model studies of, 368ff., 397ff.
in inhomogeneous media, 403ff., 448, 741
pressure distribution, 151, 152, 155
velocity distribution, 151, 152, 155
Reservoirs, 50ff.
closed, 653, 675
interference effects in, 664ff., 676
pressure decline in, 658, 659, 675, 747
producing gas, 70S
pressure decline in, 712, 714, 749
production decline in, 710, 749
single well in, 653ff., 657ff.
Reynolds number, 57ff.
variation of flow with, 58ff.
for porous media, 59ff., 67, 68
for sand free flow, 58
Rocks, kinds of, 17ff.
screen analyses of, 15
structure of, 22ff.
S
Sanded liner, 439ff., 452
effect on production capacity, 444, 446, 742
in gas wells, 686
Schwarz-Christoffel theorem, 197, 209, 210, 213, 215, 242, 248, 332, 333, 388
generalization of, 297
Seepage flux, under coffer dams, 224, 252, 738
under dams with piling, 218, 251, 738
under dams without piling, 212, 251, 738
through dams with sloping faces, 333, 337, 338ff.., 393
through dams with vertical faces, 303ff., 314, 389, 739
out of ditches, 327, 331, 334, 338, 346ff., 392, 394, 740
general formula, 214, 738
in radial gravity flow, 372, 397, 740
Separation of variables, 430ff.
Seven-spot flood, 571
conductivity of, 587ff., 615, 744
efficiency of, 597ff., 613ff., 745
flooding history of, 571ff., 744
pressure distribution in, 578, 588
Sheet piling under dams, 201, 250
effect, on pressure under dams, 201, 202, 207, 738
on seepage flux, 218, 251, 738
on uplift force, 203, 249, 738
on uplift moment, 203, 249, 738
pressure drop over, 201, 202, 219, 248, 738
Sloping sand, drainage of, 292ff., 386, 387
flux caught'by ditch in, 298, 387, 739
limiting streamlines in, 299, 300
Soil samplers, 82
Spherical coordinates, 142, 726
Spherical flow, 259ff., 282
flux in, 260, 282, 739
Spherical flow, potential distribution in, 260, 282
velocity distribution in, 260, 282
Staggered line-drive flood, 579, 615
conductivity of, 584, 592ff., 615, 744
efficiency of, 596ff., 615, 616, 745
pressure distribution in, 580, 592
Steady state, definition, 123, 134, 621
continuous succession of, 621ff., 660, 707
flow of gases in, 680ff.
incompressible-liquid systems in, 621ff., 670, 745
liquid flow in, 149ff.
Stokes-Navier equations, 56, 126, 128, 130, 144
Stream function, 183
interchange with potential, 231, 253
Streamlines, 183
interchange with equipotentials, 231, 253
refraction of, 401
Subirrigation, 354, 394, 740
Subsurface fluids, 26
classification of, 28
Surfaces of discontinuity, 400, 448
boundary conditions at, 401, 448
in gas-flow systems, 685
refraction of streamlines at, 401
Surface of seepage, 243, 256, 289ff., 365, 386
hodograph for, 302
T
Thalweg, 35
Three-dimensional problems, 258ff.
of gas flow, 683, 717
Tile drainage, 356ff., 395, 740
Turbulent flow, 58, 62ff.
Two-dimensional problems, 149ff.
of gas flow, 682, 717
Two-fluid systems, 453ff.
in EC-IS sands, 686, 718
U
Unsymmetrical flow, 163ff., 168
for compressible liquids, 661ff., 676
for eccentric boundaries, 169ff.
V
Viscous flow, 57, 61, 63,125, 136, 144
W
Water coning, 480ff., 503 ff.
analytical theory of, 487ff., 504
critical nature of, 485
equilibrium condition for, 481
in gas sands, 686, 687, 718
maximal pressure drops, without, 493, 505, 742
maximal production rates, without, 495, 506, 742
model experiments on, 486, 498
shapes of cones in, 486, 493
suppression by shale lenses of, 496ff., 506
Water drive, 454
line drive, 468
between two wells, 472
Water-drive field, 635
production decline in, 635ff., 672
Water flooding, 454, 560ff., 612
comparison of networks, 600, 602ff., 617
conductivities of, 580ff., 613
efficiencies of, 593ff., 613
history of, 560
model experiments on, 561ff., 612
natural, 454
pressure distributions in, 577ff.
Water-logging, 355, 740
Well battery, 518, 742
Well diameter, effect on flux, of partially penetrating wells, 275, 276, 284
in radial flow, 156
in spherical flow, 262
Well displacement, effect on flux, 172, 173, 736
Well groups, 507ff.
in gas reservoirs, 704
infinite groups, 523ff., 743
small, in circular region, 509ff., 607
battery on circle, 518, 742
five wells, 515
four wells, 514, 742
mutual interferences, 519, 607, 608
nine wells, 516
sixteen wells, 517
Well groups, .small, three wells, 513, 742
two wells, 512, 742
supplied by line drive, 521ff., 743
Well spacing, 512, 608
in infinite arrays, 535, 555
in small well groups, 513ff.
Woodbine sand, 103, 645, 647, 653, 672
expansion of water in, 625, 646, 674
permeability of, 103, 105, 647
pressure distribution in, 652
structure contours on, 644
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