175:
2793:
2646:
280:
2692:
2605:
2593:
397:
2704:
2755:
2680:
2581:
772:, unit: m) is a part of this, and is a specific property characteristic of the solid skeleton and the microstructure of the porous medium itself, independently of the nature and properties of the fluid flowing through the pores of the medium. This allows to take into account the effect of temperature on the viscosity of the fluid flowing though the porous medium and to address other fluids than pure water,
2728:
73:
2781:
2769:
2805:
32:
2716:
2829:
2745:
2668:
2569:
2817:
2617:
296:
Permeability is a property of porous materials that is an indication of the ability for fluids (gas or liquid) to flow through them. Fluids can more easily flow through a material with high permeability than one with low permeability. The permeability of a medium is related to the
450:
For a rock to be considered as an exploitable hydrocarbon reservoir without stimulation, its permeability must be greater than approximately 100 md (depending on the nature of the hydrocarbon – gas reservoirs with lower permeabilities are still exploitable because of the lower
363:
who first described the flow of water through sand filters for potable water supply. Permeability values for most materials commonly range typically from a fraction to several thousand millidarcys. The unit of square centimetre (cm) is also sometimes used (1 cm = 10 m
2399:
J. P. Bloomfield and A. T. Williams, "An empirical liquid permeability-gas permeability correlation for use in aquifer properties studies". Quarterly
Journal of Engineering Geology & Hydrogeology; November 1995; v. 28; no. Supplement 2; pp. S143–S150.
1023:
1734:
is needed. Pressure can be applied in three directions, and for each direction, permeability can be measured (via Darcy's law in 3D) in three directions, thus leading to a 3 by 3 tensor. The tensor is realised using a 3 by 3
1690:. For example, measurement of permeability through sandstones and shales yielded values from 9.0×10 m to 2.4×10 m for water and between 1.7×10 m to 2.6×10 m for nitrogen gas. Gas permeability of
957:
Tissue such as brain, liver, muscle, etc can be treated as a heterogeneous porous medium. Describing the flow of biofluids (blood, cerebrospinal fluid, etc.) within such a medium requires a full 3-dimensional
550:
1678:
Sometimes permeability to gases can be somewhat different than those for liquids in the same media. One difference is attributable to "slippage" of gas at the interface with the solid when the gas
2486:
1446:
606:
830:
1213:
1542:
1048:
2517:
1410:
1190:
90:
45:
742:
713:
382:
357:
1273:
1575:
1315:
1118:
1097:
924:
902:
684:
1252:
2079:
1619:
1597:
1336:
976:
946:
880:
858:
662:
632:
3673:
3482:
2483:
2463:
2458:
2263:
1703:
2387:
2510:
748:
In naturally occurring materials, the permeability values range over many orders of magnitude (see table below for an example of this range).
137:
51:
2124:
109:
196:
2278:"Poroelasticity as a Model of Soft Tissue Structure: Hydraulic Permeability Reconstruction for Magnetic Resonance Elastography in Silico"
1666:; and that it is a function of the material structure only (and not of the fluid). They explicitly distinguish the value from that of
1657:
502:
301:, but also to the shapes of the pores in the medium and their level of connectedness. Fluid flows can also be influenced in different
116:
2535:
2503:
2441:
2421:
236:
218:
156:
59:
2436:
Wang, H. F., 2000. Theory of Linear
Poroelasticity with Applications to Geomechanics and Hydrogeology, Princeton University Press.
123:
20:
2453:
94:
1492:
2386:
L. J. Klinkenberg, "The
Permeability Of Porous Media To Liquids And Gases", Drilling and Production Practice, 41-200, 1941
1648:
denotes the permeability in a porous medium that is 100% saturated with a single-phase fluid. This may also be called the
1418:
474:), as well as in Civil Engineering when determining whether the ground conditions of a site are suitable for construction.
105:
3185:
3066:
2608:
562:
322:
2214:
1752:
3498:
483:
189:
183:
3098:
2543:
2099:
1050:
is the Darcy flux, or filtration velocity, which describes the bulk (not microscopic) velocity field of the fluid,
83:
3401:
2796:
788:. Given the value of hydraulic conductivity for a studied system, the permeability can be calculated as follows:
794:
200:
3477:
3467:
3339:
3329:
3159:
2897:
2695:
2526:
1744:
2596:
2401:
1785:
These values do not depend on the fluid properties; see the table derived from the same source for values of
1196:
3658:
3317:
3292:
3232:
2912:
2853:
2707:
2044:
310:
130:
2683:
455:
of gas with respect to oil). Rocks with permeabilities significantly lower than 100 md can form efficient
3580:
3391:
3205:
3041:
3016:
2937:
2867:
2846:
2738:
2074:
2049:
1786:
1479:
derived formulas. However, for some simple models of porous media, permeability can be calculated (e.g.,
761:
3668:
3663:
3267:
3076:
2584:
2069:
1699:
1667:
1501:
1031:
2731:
2212:
Guerriero V, et al. (2012). "A permeability model for naturally fractured carbonate reservoirs".
3620:
3472:
3429:
3322:
3247:
2784:
2630:
2299:
2223:
2186:
2139:
1773:
will yield the principal directions of flow where flow is parallel to the pressure gradient, and the
1736:
1682:
is comparable to the pore size (about 0.01 to 0.1 μm at standard temperature and pressure). See also
635:
467:
3396:
3386:
2927:
2887:
2860:
2635:
2625:
638:
through the porous medium (i.e., the average flow velocity calculated as if the fluid was the only
2671:
3653:
3347:
3056:
2839:
2758:
2289:
2174:
2155:
1465:
1345:
1127:
3648:
3444:
3190:
3081:
2902:
2484:
Florida Method of Test For
Concrete Resistivity as an Electrical Indicator of its Permeability
2478:
2437:
2417:
2327:
2248:
2064:
1866:
1683:
1480:
1472:
724:
695:
460:
367:
342:
257:
1464:
under steady state conditions or, more generally, by application of various solutions to the
1258:
3494:
3381:
3272:
3237:
3212:
3071:
2892:
2317:
2307:
2231:
2194:
2147:
1740:
1476:
963:
3527:
2792:
2645:
1553:
1282:
1103:
1053:
909:
887:
669:
3610:
3434:
3352:
3287:
3282:
3180:
3046:
2917:
2772:
2691:
2604:
2490:
2468:
1883:
1715:
1449:
1222:
1018:{\displaystyle {\boldsymbol {q}}=-{\frac {1}{\eta }}{\boldsymbol {\kappa }}\cdot \nabla P}
785:
306:
279:
253:
2592:
2303:
2227:
2190:
2143:
427:
The concept of permeability is of importance in determining the flow characteristics of
3557:
3449:
3366:
3170:
2932:
2922:
2808:
2703:
2469:
Graphical depiction of different flow rates through materials of differing permeability
2322:
2277:
1766:
1691:
1687:
1679:
1604:
1582:
1461:
1321:
931:
865:
843:
647:
639:
617:
489:
273:
2754:
2679:
2580:
396:
3642:
3585:
3424:
3302:
3297:
3021:
2942:
2159:
1758:
757:
261:
2367:"Chapter 2: Physical Properties and Principles | Freeze and Cherry Groundwater Book"
2235:
2198:
2151:
466:
The concept also has many practical applications outside of geology, for example in
3605:
3600:
3590:
3570:
3257:
3200:
3031:
2748:
2054:
1770:
1471:
Permeability needs to be measured, either directly (using Darcy's law), or through
428:
331:
326:
269:
1599:
is a dimensionless constant that is related to the configuration of the flow-paths
2366:
1662:
3615:
3312:
3195:
3134:
1774:
1727:
1695:
440:
360:
72:
2727:
2473:
2345:
1656:
These terms refer to the quality that the permeability value in question is an
3439:
3419:
3307:
3119:
3114:
3036:
3026:
2907:
2780:
2768:
2652:
2572:
2059:
959:
471:
16:
Measure of the ability of a porous material to allow fluids to pass through it
2312:
3595:
3575:
3461:
3277:
3262:
2878:
2820:
2804:
2719:
2620:
1879:
1873:
1711:
1707:
1121:
781:
687:
493:
452:
432:
302:
2715:
2495:
2331:
2828:
2744:
2667:
1660:
of the medium, not a spatial average of a heterogeneous block of material
3625:
3512:
3242:
3217:
3144:
3061:
3051:
2474:
Web-based porosity and permeability calculator given flow characteristics
1789:, which are specific to the material through which the fluid is flowing.
1622:
1339:
716:
298:
2568:
492:
which relates discharge (flow rate) and fluid physical properties (e.g.
3565:
3537:
3222:
3149:
3139:
3129:
3124:
2832:
2173:
Bense, V.F.; Gleeson, T.; Loveless, S.E.; Bour, O.; Scibek, J. (2013).
1889:
1757:
The tensor is positive definite because the energy being expended (the
463:). Unconsolidated sands may have permeabilities of over 5000 md.
444:
2816:
2616:
3547:
3542:
3532:
3522:
3454:
3252:
3227:
3175:
2985:
1813:
1731:
1216:
967:
2125:"Tortuosity of porous media: Image analysis and physical simulation"
756:
The global proportionality constant for the flow of water through a
2294:
966:
hydraulic permeability is replaced with the hydraulic permeability
313:. Permeability is also affected by the pressure inside a material.
3000:
1826:
1460:
Permeability is typically determined in the lab by application of
777:
276:
or an unconsolidated material) to allow fluids to pass through it.
3487:
2995:
2990:
2980:
2975:
2970:
2955:
2657:
1850:
1844:
1830:
1819:
1761:
of fluid flow and negative pressure gradient) is always positive
545:{\displaystyle v={\frac {k}{\eta }}{\frac {\Delta P}{\Delta x}}}
2499:
1630:
Absolute permeability (aka intrinsic or specific permeability)
1495:
for viscous flow in a pipe, permeability can be expressed as:
1276:
436:
391:
168:
66:
25:
1448:, where k is the scalar hydraulic permeability, and 1 is the
2123:
Fu, Jinlong; Thomas, Hywel R.; Li, Chenfeng (January 2021).
309:; the mechanisms by which this occurs are the subject of
768:, unit: m/s). Permeability, or intrinsic permeability, (
488:
Permeability is part of the proportionality constant in
496:), to a pressure gradient applied to the porous media:
408:
1702:, when considering the optimal extraction of gas from
1607:
1585:
1556:
1504:
1441:{\displaystyle {\boldsymbol {\kappa }}=k\mathbb {1} }
1421:
1348:
1324:
1285:
1261:
1225:
1199:
1130:
1106:
1056:
1034:
979:
934:
912:
890:
868:
846:
797:
727:
698:
672:
650:
620:
565:
505:
370:
345:
744:
is the thickness of the bed of the porous medium (m)
601:{\displaystyle k=v{\frac {\eta \Delta x}{\Delta P}}}
3556:
3511:
3410:
3374:
3365:
3338:
3158:
3107:
3094:
3009:
2963:
2954:
2877:
2555:
2542:
97:. Unsourced material may be challenged and removed.
1769:(being both symmetric and positive definite). The
1613:
1591:
1569:
1536:
1440:
1415:Connecting this expression to the isotropic case,
1404:
1330:
1309:
1267:
1246:
1207:
1184:
1112:
1091:
1042:
1017:
940:
918:
896:
874:
852:
824:
736:
707:
678:
656:
626:
600:
544:
376:
351:
2346:"CalcTool: Porosity and permeability calculator"
2459:Tailoring porous media to control permeability
2266:, an application of Darcy's law, at iMechanica
2100:"Reading: Porosity and Permeability | Geology"
2080:Electrical resistivity measurement of concrete
329:(m). A practical unit for permeability is the
2511:
8:
962:treatment of the tissue. In this case the
904:is the dynamic viscosity of the fluid, Pa·s
359:10 m). The name honors the French Engineer
287:permeability tests in geotechnical drawings
60:Learn how and when to remove these messages
3371:
3104:
2960:
2552:
2518:
2504:
2496:
825:{\displaystyle k=K{\frac {\eta }{\rho g}}}
2321:
2311:
2293:
1781:Ranges of common intrinsic permeabilities
1606:
1584:
1561:
1555:
1528:
1509:
1503:
1481:random close packing of identical spheres
1434:
1433:
1422:
1420:
1393:
1384:
1372:
1363:
1352:
1347:
1323:
1298:
1289:
1284:
1260:
1238:
1229:
1224:
1200:
1198:
1173:
1154:
1145:
1134:
1129:
1105:
1080:
1071:
1060:
1055:
1035:
1033:
1001:
991:
980:
978:
933:
911:
889:
867:
845:
807:
796:
726:
697:
671:
649:
619:
575:
564:
522:
512:
504:
369:
344:
237:Learn how and when to remove this message
219:Learn how and when to remove this message
157:Learn how and when to remove this message
1887:
1877:
1871:
1865:
1862:
1854:
1848:
1843:
1824:
1817:
1811:
1791:
1777:represent the principal permeabilities.
1487:Permeability model based on conduit flow
948:is the acceleration due to gravity, m/s.
278:
182:This article includes a list of general
2091:
1423:
1208:{\displaystyle {\boldsymbol {\kappa }}}
1201:
1036:
1002:
981:
2479:Multiphase fluid flow in porous media
2249:Multiphase fluid flow in porous media
106:"Permeability" materials science
7:
95:adding citations to reliable sources
3674:In situ geotechnical investigations
2414:Dynamics of Fluids in Porous Media,
664:is the permeability of a medium (m)
642:present in the porous medium) (m/s)
305:by brittle deformation of rocks in
268:) is a measure of the ability of a
1765:The permeability tensor is always
1621:is the average, or effective pore
1537:{\displaystyle k_{I}=C\cdot d^{2}}
1262:
1009:
882:is the hydraulic conductivity, m/s
752:Relation to hydraulic conductivity
728:
699:
589:
581:
533:
525:
188:it lacks sufficient corresponding
14:
2536:Offshore geotechnical engineering
1043:{\displaystyle {\boldsymbol {q}}}
926:is the density of the fluid, kg/m
41:This article has multiple issues.
2827:
2815:
2803:
2791:
2779:
2767:
2753:
2743:
2726:
2714:
2702:
2690:
2678:
2666:
2644:
2615:
2603:
2591:
2579:
2567:
1839:Unconsolidated clay and organic
395:
173:
71:
30:
2236:10.1016/j.marpetgeo.2012.11.002
2199:10.1016/j.earscirev.2013.09.008
2152:10.1016/j.earscirev.2020.103439
1809:Unconsolidated sand and gravel
1751:The tensor is symmetric by the
82:needs additional citations for
49:or discuss these issues on the
21:Permeability (electromagnetism)
1577:is the intrinsic permeability
1468:for unsteady flow conditions.
1390:
1381:
1369:
1360:
1357:
1349:
1295:
1286:
1235:
1226:
1215:is the hydraulic permeability
1170:
1163:
1151:
1142:
1139:
1131:
1077:
1068:
1065:
1057:
1:
3186:Mechanically stabilized earth
325:unit for permeability is the
2938:Hydraulic conductivity tests
2464:Permeability of Porous Media
2215:Marine and Petroleum Geology
1753:Onsager reciprocal relations
3499:Stress distribution in soil
3690:
2649:Pore pressure measurement
2264:Controlling Capillary Flow
1405:{\displaystyle ^{-1}^{-2}}
1185:{\displaystyle ^{-1}^{-1}}
970:so that Darcy's Law reads
481:
335:(d), or more commonly the
18:
3402:Preconsolidation pressure
2797:Standard penetration test
2533:
2276:Sowinski, Damian (2021).
2253:Transport in porous media
2175:"Fault zone hydrogeology"
2104:courses.lumenlearning.com
1841:
1834:
1803:
1800:
1797:
1726:To model permeability in
1493:Hagen–Poiseuille equation
283:Symbol used to represent
2898:California bearing ratio
2696:Rotary-pressure sounding
2527:Geotechnical engineering
2313:10.3389/fphy.2020.617582
953:Anisotropic permeability
737:{\displaystyle \Delta x}
708:{\displaystyle \Delta P}
484:Fick's laws of diffusion
377:{\displaystyle \approx }
352:{\displaystyle \approx }
264:(commonly symbolized as
19:Not to be confused with
3318:Geosynthetic clay liner
3293:Expanded clay aggregate
2913:Proctor compaction test
2854:Crosshole sonic logging
2840:Nuclear densometer test
2597:Geo-electrical sounding
2045:Fault zone hydrogeology
1863:Highly fractured rocks
1268:{\displaystyle \nabla }
311:fault zone hydrogeology
203:more precise citations.
3581:Earthquake engineering
3392:Lateral earth pressure
3017:Hydraulic conductivity
2868:Wave equation analysis
2847:Exploration geophysics
2739:Deformation monitoring
2708:Rotary weight sounding
2454:Defining Permeability
2075:Klinkenberg correction
2050:Hydraulic conductivity
1825:Very fine sand, silt,
1787:hydraulic conductivity
1730:media, a permeability
1654:specific permeability.
1650:intrinsic permeability
1615:
1593:
1571:
1538:
1442:
1406:
1332:
1311:
1269:
1248:
1209:
1186:
1114:
1093:
1044:
1019:
942:
920:
898:
876:
860:is the permeability, m
854:
826:
762:hydraulic conductivity
738:
709:
680:
658:
628:
602:
546:
378:
353:
288:
2759:Settlement recordings
2684:Rock control drilling
2585:Cone penetration test
2179:Earth-Science Reviews
2132:Earth-Science Reviews
2070:Relative permeability
1700:petroleum engineering
1674:Permeability to gases
1668:relative permeability
1646:Absolute permeability
1616:
1594:
1572:
1570:{\displaystyle k_{I}}
1539:
1443:
1407:
1333:
1312:
1310:{\displaystyle ^{-1}}
1270:
1249:
1210:
1187:
1115:
1113:{\displaystyle \eta }
1094:
1092:{\displaystyle ^{-1}}
1045:
1020:
943:
921:
919:{\displaystyle \rho }
899:
897:{\displaystyle \eta }
877:
855:
827:
739:
710:
681:
679:{\displaystyle \eta }
659:
629:
603:
547:
379:
354:
303:lithological settings
282:
3621:Agricultural science
3323:Cellular confinement
2282:Frontiers in Physics
1722:Permeability tensor
1605:
1583:
1554:
1502:
1419:
1346:
1342:field in the fluid,
1322:
1283:
1259:
1247:{\displaystyle ^{2}}
1223:
1197:
1128:
1104:
1054:
1032:
977:
932:
910:
888:
866:
844:
795:
725:
696:
670:
648:
618:
563:
503:
468:chemical engineering
368:
343:
91:improve this article
3513:Numerical analysis
3397:Overburden pressure
3387:Pore water pressure
3167:Shoring structures
3042:Reynolds' dilatancy
2943:Water content tests
2928:Triaxial shear test
2888:Soil classification
2861:Pile integrity test
2412:Bear, Jacob, 1972.
2304:2021FrP.....8..637S
2228:1990MarPG...7..410M
2191:2013ESRv..127..171B
2144:2021ESRv..21203439F
1860:Consolidated rocks
1822:or sand and gravel
690:of the fluid (Pa·s)
439:reservoirs, and of
3488:Slab stabilisation
3468:Stability analysis
2489:2011-06-16 at the
2348:. www.calctool.org
1658:intensive property
1611:
1589:
1567:
1534:
1466:diffusion equation
1438:
1402:
1328:
1307:
1265:
1244:
1205:
1182:
1110:
1089:
1040:
1015:
938:
916:
894:
872:
850:
822:
734:
705:
676:
654:
624:
598:
542:
407:. You can help by
374:
349:
289:
3636:
3635:
3507:
3506:
3483:Sliding criterion
3445:Response spectrum
3361:
3360:
3191:Pressure grouting
3090:
3089:
2950:
2949:
2903:Direct shear test
2609:Permeability test
2065:Petroleum geology
2036:
2035:
1855:Unweathered clay
1745:positive definite
1684:Knudsen diffusion
1614:{\displaystyle d}
1592:{\displaystyle C}
1387:
1366:
1355:
1331:{\displaystyle P}
1292:
1277:gradient operator
1232:
1148:
1137:
1074:
1063:
999:
941:{\displaystyle g}
875:{\displaystyle K}
853:{\displaystyle k}
820:
657:{\displaystyle k}
627:{\displaystyle v}
596:
552:(for linear flow)
540:
520:
461:petroleum geology
425:
424:
258:materials science
247:
246:
239:
229:
228:
221:
167:
166:
159:
141:
64:
3681:
3495:Bearing capacity
3382:Effective stress
3372:
3273:Land reclamation
3213:Land development
3108:Natural features
3105:
3072:Specific storage
2961:
2893:Atterberg limits
2831:
2819:
2807:
2795:
2783:
2771:
2757:
2747:
2732:Screw plate test
2730:
2718:
2706:
2694:
2682:
2670:
2648:
2619:
2607:
2595:
2583:
2571:
2553:
2520:
2513:
2506:
2497:
2424:
2410:
2404:
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2261:
2255:
2246:
2240:
2239:
2209:
2203:
2202:
2170:
2164:
2163:
2129:
2120:
2114:
2113:
2111:
2110:
2096:
1792:
1706:sources such as
1698:is important in
1665:
1642:
1641:
1637:
1620:
1618:
1617:
1612:
1598:
1596:
1595:
1590:
1576:
1574:
1573:
1568:
1566:
1565:
1543:
1541:
1540:
1535:
1533:
1532:
1514:
1513:
1447:
1445:
1444:
1439:
1437:
1426:
1411:
1409:
1408:
1403:
1401:
1400:
1388:
1385:
1380:
1379:
1367:
1364:
1356:
1353:
1337:
1335:
1334:
1329:
1316:
1314:
1313:
1308:
1306:
1305:
1293:
1290:
1274:
1272:
1271:
1266:
1253:
1251:
1250:
1245:
1243:
1242:
1233:
1230:
1214:
1212:
1211:
1206:
1204:
1191:
1189:
1188:
1183:
1181:
1180:
1162:
1161:
1149:
1146:
1138:
1135:
1119:
1117:
1116:
1111:
1098:
1096:
1095:
1090:
1088:
1087:
1075:
1072:
1064:
1061:
1049:
1047:
1046:
1041:
1039:
1024:
1022:
1021:
1016:
1005:
1000:
992:
984:
947:
945:
944:
939:
925:
923:
922:
917:
903:
901:
900:
895:
881:
879:
878:
873:
859:
857:
856:
851:
831:
829:
828:
823:
821:
819:
808:
786:organic solvents
771:
767:
743:
741:
740:
735:
714:
712:
711:
706:
685:
683:
682:
677:
663:
661:
660:
655:
633:
631:
630:
625:
607:
605:
604:
599:
597:
595:
587:
576:
551:
549:
548:
543:
541:
539:
531:
523:
521:
513:
420:
417:
399:
392:
383:
381:
380:
375:
358:
356:
355:
350:
242:
235:
224:
217:
213:
210:
204:
199:this article by
190:inline citations
177:
176:
169:
162:
155:
151:
148:
142:
140:
99:
75:
67:
56:
34:
33:
26:
3689:
3688:
3684:
3683:
3682:
3680:
3679:
3678:
3639:
3638:
3637:
3632:
3611:Earth materials
3552:
3514:
3503:
3412:
3406:
3357:
3334:
3288:Earth structure
3283:Erosion control
3181:Ground freezing
3171:Retaining walls
3154:
3096:
3086:
3047:Angle of repose
3005:
2946:
2880:
2873:
2872:
2833:Visible bedrock
2785:Simple sounding
2773:Shear vane test
2549:instrumentation
2548:
2546:
2538:
2529:
2524:
2491:Wayback Machine
2450:
2433:
2428:
2427:
2411:
2407:
2398:
2394:
2385:
2381:
2372:
2370:
2365:
2364:
2360:
2351:
2349:
2344:
2343:
2339:
2275:
2274:
2270:
2262:
2258:
2247:
2243:
2211:
2210:
2206:
2172:
2171:
2167:
2127:
2122:
2121:
2117:
2108:
2106:
2098:
2097:
2093:
2088:
2041:
1783:
1724:
1716:coalbed methane
1676:
1661:
1643:
1639:
1635:
1633:
1632:
1603:
1602:
1581:
1580:
1557:
1552:
1551:
1524:
1505:
1500:
1499:
1489:
1458:
1450:identity tensor
1417:
1416:
1389:
1368:
1344:
1343:
1320:
1319:
1294:
1281:
1280:
1257:
1256:
1234:
1221:
1220:
1195:
1194:
1169:
1150:
1126:
1125:
1120:is the dynamic
1102:
1101:
1076:
1052:
1051:
1030:
1029:
975:
974:
955:
930:
929:
908:
907:
886:
885:
864:
863:
842:
841:
812:
793:
792:
776:, concentrated
769:
765:
754:
723:
722:
719:difference (Pa)
715:is the applied
694:
693:
686:is the dynamic
668:
667:
646:
645:
616:
615:
588:
577:
561:
560:
532:
524:
501:
500:
486:
480:
421:
415:
412:
405:needs expansion
390:
366:
365:
341:
340:
339:(md) (1 d
319:
294:
270:porous material
254:fluid mechanics
243:
232:
231:
230:
225:
214:
208:
205:
195:Please help to
194:
178:
174:
163:
152:
146:
143:
100:
98:
88:
76:
35:
31:
24:
17:
12:
11:
5:
3687:
3685:
3677:
3676:
3671:
3666:
3661:
3659:Soil mechanics
3656:
3651:
3641:
3640:
3634:
3633:
3631:
3630:
3629:
3628:
3618:
3613:
3608:
3603:
3598:
3593:
3588:
3583:
3578:
3573:
3568:
3562:
3560:
3558:Related fields
3554:
3553:
3551:
3550:
3545:
3540:
3535:
3530:
3525:
3519:
3517:
3509:
3508:
3505:
3504:
3502:
3501:
3492:
3491:
3490:
3485:
3480:
3478:Classification
3475:
3470:
3459:
3458:
3457:
3452:
3450:Seismic hazard
3447:
3437:
3432:
3427:
3422:
3416:
3414:
3408:
3407:
3405:
3404:
3399:
3394:
3389:
3384:
3378:
3376:
3369:
3363:
3362:
3359:
3358:
3356:
3355:
3350:
3344:
3342:
3336:
3335:
3333:
3332:
3327:
3326:
3325:
3320:
3315:
3310:
3300:
3295:
3290:
3285:
3280:
3275:
3270:
3265:
3260:
3255:
3250:
3245:
3240:
3235:
3230:
3225:
3220:
3215:
3210:
3209:
3208:
3203:
3198:
3193:
3188:
3183:
3178:
3173:
3164:
3162:
3156:
3155:
3153:
3152:
3147:
3142:
3137:
3132:
3127:
3122:
3117:
3111:
3109:
3102:
3092:
3091:
3088:
3087:
3085:
3084:
3079:
3077:Shear strength
3074:
3069:
3064:
3059:
3054:
3052:Friction angle
3049:
3044:
3039:
3034:
3029:
3024:
3019:
3013:
3011:
3007:
3006:
3004:
3003:
2998:
2993:
2988:
2983:
2978:
2973:
2967:
2965:
2958:
2952:
2951:
2948:
2947:
2945:
2940:
2935:
2933:Oedometer test
2930:
2925:
2923:Sieve analysis
2920:
2915:
2910:
2905:
2900:
2895:
2890:
2885:
2883:
2875:
2874:
2871:
2870:
2864:
2863:
2857:
2856:
2850:
2849:
2843:
2842:
2836:
2835:
2824:
2823:
2812:
2811:
2809:Total sounding
2800:
2799:
2788:
2787:
2776:
2775:
2764:
2763:
2762:
2761:
2751:
2735:
2734:
2723:
2722:
2711:
2710:
2699:
2698:
2687:
2686:
2675:
2674:
2663:
2662:
2661:
2660:
2655:
2641:
2640:
2639:
2638:
2633:
2628:
2612:
2611:
2600:
2599:
2588:
2587:
2576:
2575:
2564:
2563:
2561:
2550:
2540:
2539:
2534:
2531:
2530:
2525:
2523:
2522:
2515:
2508:
2500:
2494:
2493:
2481:
2476:
2471:
2466:
2461:
2456:
2449:
2448:External links
2446:
2445:
2444:
2432:
2429:
2426:
2425:
2405:
2392:
2379:
2358:
2337:
2268:
2256:
2241:
2204:
2165:
2115:
2090:
2089:
2087:
2084:
2083:
2082:
2077:
2072:
2067:
2062:
2057:
2052:
2047:
2040:
2037:
2034:
2033:
2030:
2027:
2024:
2021:
2018:
2015:
2012:
2009:
2006:
2003:
2000:
1997:
1994:
1987:
1986:
1983:
1980:
1977:
1974:
1971:
1968:
1965:
1962:
1959:
1956:
1953:
1950:
1947:
1940:
1939:
1936:
1933:
1930:
1927:
1924:
1921:
1918:
1915:
1912:
1909:
1906:
1903:
1900:
1893:
1892:
1886:
1876:
1870:
1864:
1861:
1857:
1856:
1853:
1847:
1842:
1840:
1836:
1835:
1833:
1823:
1816:
1810:
1806:
1805:
1802:
1801:Semi-pervious
1799:
1796:
1782:
1779:
1767:diagonalizable
1763:
1762:
1755:
1747:(SPD matrix):
1723:
1720:
1704:unconventional
1692:reservoir rock
1688:constrictivity
1680:mean free path
1675:
1672:
1631:
1628:
1627:
1626:
1610:
1600:
1588:
1578:
1564:
1560:
1545:
1544:
1531:
1527:
1523:
1520:
1517:
1512:
1508:
1488:
1485:
1457:
1454:
1436:
1432:
1429:
1425:
1413:
1412:
1399:
1396:
1392:
1383:
1378:
1375:
1371:
1362:
1359:
1351:
1327:
1317:
1304:
1301:
1297:
1288:
1264:
1254:
1241:
1237:
1228:
1203:
1192:
1179:
1176:
1172:
1168:
1165:
1160:
1157:
1153:
1144:
1141:
1133:
1124:of the fluid,
1109:
1099:
1086:
1083:
1079:
1070:
1067:
1059:
1038:
1026:
1025:
1014:
1011:
1008:
1004:
998:
995:
990:
987:
983:
954:
951:
950:
949:
937:
927:
915:
905:
893:
883:
871:
861:
849:
838:
837:
833:
832:
818:
815:
811:
806:
803:
800:
760:is called the
753:
750:
746:
745:
733:
730:
720:
704:
701:
691:
675:
665:
653:
643:
636:fluid velocity
623:
609:
608:
594:
591:
586:
583:
580:
574:
571:
568:
554:
553:
538:
535:
530:
527:
519:
516:
511:
508:
479:
476:
423:
422:
402:
400:
389:
386:
373:
348:
318:
315:
293:
290:
262:Earth sciences
245:
244:
227:
226:
209:September 2014
181:
179:
172:
165:
164:
79:
77:
70:
65:
39:
38:
36:
29:
15:
13:
10:
9:
6:
4:
3:
2:
3686:
3675:
3672:
3670:
3667:
3665:
3662:
3660:
3657:
3655:
3652:
3650:
3647:
3646:
3644:
3627:
3624:
3623:
3622:
3619:
3617:
3614:
3612:
3609:
3607:
3604:
3602:
3599:
3597:
3594:
3592:
3589:
3587:
3586:Geomorphology
3584:
3582:
3579:
3577:
3574:
3572:
3569:
3567:
3564:
3563:
3561:
3559:
3555:
3549:
3546:
3544:
3541:
3539:
3536:
3534:
3531:
3529:
3526:
3524:
3521:
3520:
3518:
3516:
3510:
3500:
3496:
3493:
3489:
3486:
3484:
3481:
3479:
3476:
3474:
3471:
3469:
3466:
3465:
3463:
3460:
3456:
3453:
3451:
3448:
3446:
3443:
3442:
3441:
3438:
3436:
3433:
3431:
3430:Consolidation
3428:
3426:
3425:Frost heaving
3423:
3421:
3418:
3417:
3415:
3409:
3403:
3400:
3398:
3395:
3393:
3390:
3388:
3385:
3383:
3380:
3379:
3377:
3373:
3370:
3368:
3364:
3354:
3351:
3349:
3346:
3345:
3343:
3341:
3337:
3331:
3328:
3324:
3321:
3319:
3316:
3314:
3311:
3309:
3306:
3305:
3304:
3303:Geosynthetics
3301:
3299:
3298:Crushed stone
3296:
3294:
3291:
3289:
3286:
3284:
3281:
3279:
3276:
3274:
3271:
3269:
3266:
3264:
3261:
3259:
3256:
3254:
3253:Cut-and-cover
3251:
3249:
3246:
3244:
3241:
3239:
3236:
3234:
3231:
3229:
3226:
3224:
3221:
3219:
3216:
3214:
3211:
3207:
3204:
3202:
3199:
3197:
3194:
3192:
3189:
3187:
3184:
3182:
3179:
3177:
3174:
3172:
3169:
3168:
3166:
3165:
3163:
3161:
3157:
3151:
3148:
3146:
3143:
3141:
3138:
3136:
3133:
3131:
3128:
3126:
3123:
3121:
3118:
3116:
3113:
3112:
3110:
3106:
3103:
3100:
3093:
3083:
3080:
3078:
3075:
3073:
3070:
3068:
3065:
3063:
3060:
3058:
3055:
3053:
3050:
3048:
3045:
3043:
3040:
3038:
3035:
3033:
3030:
3028:
3025:
3023:
3022:Water content
3020:
3018:
3015:
3014:
3012:
3008:
3002:
2999:
2997:
2994:
2992:
2989:
2987:
2984:
2982:
2979:
2977:
2974:
2972:
2969:
2968:
2966:
2962:
2959:
2957:
2953:
2944:
2941:
2939:
2936:
2934:
2931:
2929:
2926:
2924:
2921:
2919:
2916:
2914:
2911:
2909:
2906:
2904:
2901:
2899:
2896:
2894:
2891:
2889:
2886:
2884:
2882:
2876:
2869:
2866:
2865:
2862:
2859:
2858:
2855:
2852:
2851:
2848:
2845:
2844:
2841:
2838:
2837:
2834:
2830:
2826:
2825:
2822:
2818:
2814:
2813:
2810:
2806:
2802:
2801:
2798:
2794:
2790:
2789:
2786:
2782:
2778:
2777:
2774:
2770:
2766:
2765:
2760:
2756:
2752:
2750:
2746:
2742:
2741:
2740:
2737:
2736:
2733:
2729:
2725:
2724:
2721:
2720:Sample series
2717:
2713:
2712:
2709:
2705:
2701:
2700:
2697:
2693:
2689:
2688:
2685:
2681:
2677:
2676:
2673:
2669:
2665:
2664:
2659:
2656:
2654:
2651:
2650:
2647:
2643:
2642:
2637:
2634:
2632:
2629:
2627:
2624:
2623:
2622:
2618:
2614:
2613:
2610:
2606:
2602:
2601:
2598:
2594:
2590:
2589:
2586:
2582:
2578:
2577:
2574:
2570:
2566:
2565:
2562:
2559:
2554:
2551:
2545:
2544:Investigation
2541:
2537:
2532:
2528:
2521:
2516:
2514:
2509:
2507:
2502:
2501:
2498:
2492:
2488:
2485:
2482:
2480:
2477:
2475:
2472:
2470:
2467:
2465:
2462:
2460:
2457:
2455:
2452:
2451:
2447:
2443:
2442:0-691-03746-9
2439:
2435:
2434:
2430:
2423:
2422:0-486-65675-6
2419:
2415:
2409:
2406:
2403:
2396:
2393:
2389:
2383:
2380:
2368:
2362:
2359:
2347:
2341:
2338:
2333:
2329:
2324:
2319:
2314:
2309:
2305:
2301:
2296:
2291:
2287:
2283:
2279:
2272:
2269:
2265:
2260:
2257:
2254:
2250:
2245:
2242:
2237:
2233:
2229:
2225:
2221:
2217:
2216:
2208:
2205:
2200:
2196:
2192:
2188:
2184:
2180:
2176:
2169:
2166:
2161:
2157:
2153:
2149:
2145:
2141:
2137:
2133:
2126:
2119:
2116:
2105:
2101:
2095:
2092:
2085:
2081:
2078:
2076:
2073:
2071:
2068:
2066:
2063:
2061:
2058:
2056:
2053:
2051:
2048:
2046:
2043:
2042:
2038:
2031:
2028:
2025:
2022:
2019:
2016:
2013:
2010:
2007:
2004:
2001:
1998:
1995:
1993:(millidarcy)
1992:
1989:
1988:
1984:
1981:
1978:
1975:
1972:
1969:
1966:
1963:
1960:
1957:
1954:
1951:
1948:
1945:
1942:
1941:
1937:
1934:
1931:
1928:
1925:
1922:
1919:
1916:
1913:
1910:
1907:
1904:
1901:
1898:
1895:
1894:
1891:
1885:
1881:
1875:
1868:
1867:Oil reservoir
1859:
1858:
1852:
1846:
1838:
1837:
1832:
1828:
1821:
1815:
1808:
1807:
1795:Permeability
1794:
1793:
1790:
1788:
1780:
1778:
1776:
1772:
1768:
1760:
1759:inner product
1756:
1754:
1750:
1749:
1748:
1746:
1742:
1738:
1733:
1729:
1721:
1719:
1717:
1713:
1709:
1705:
1701:
1697:
1693:
1689:
1685:
1681:
1673:
1671:
1669:
1664:
1663:equation 2.28
1659:
1655:
1651:
1647:
1638:
1629:
1624:
1608:
1601:
1586:
1579:
1562:
1558:
1550:
1549:
1548:
1529:
1525:
1521:
1518:
1515:
1510:
1506:
1498:
1497:
1496:
1494:
1491:Based on the
1486:
1484:
1482:
1478:
1474:
1469:
1467:
1463:
1456:Determination
1455:
1453:
1451:
1430:
1427:
1397:
1394:
1376:
1373:
1341:
1325:
1318:
1302:
1299:
1278:
1255:
1239:
1218:
1193:
1177:
1174:
1166:
1158:
1155:
1123:
1107:
1100:
1084:
1081:
1028:
1027:
1012:
1006:
996:
993:
988:
985:
973:
972:
971:
969:
965:
961:
952:
935:
928:
913:
906:
891:
884:
869:
862:
847:
840:
839:
835:
834:
816:
813:
809:
804:
801:
798:
791:
790:
789:
787:
783:
779:
775:
763:
759:
758:porous medium
751:
749:
731:
721:
718:
702:
692:
689:
673:
666:
651:
644:
641:
637:
621:
614:
613:
612:
592:
584:
578:
572:
569:
566:
559:
558:
557:
536:
528:
517:
514:
509:
506:
499:
498:
497:
495:
491:
485:
477:
475:
473:
469:
464:
462:
458:
454:
448:
446:
442:
438:
434:
430:
419:
416:February 2016
410:
406:
403:This section
401:
398:
394:
393:
387:
385:
371:
362:
346:
338:
334:
333:
328:
324:
316:
314:
312:
308:
304:
300:
291:
286:
281:
277:
275:
271:
267:
263:
259:
255:
251:
241:
238:
223:
220:
212:
202:
198:
192:
191:
185:
180:
171:
170:
161:
158:
150:
139:
136:
132:
129:
125:
122:
118:
115:
111:
108: –
107:
103:
102:Find sources:
96:
92:
86:
85:
80:This article
78:
74:
69:
68:
63:
61:
54:
53:
48:
47:
42:
37:
28:
27:
22:
3669:Porous media
3664:Soil physics
3606:Biogeography
3601:Hydrogeology
3591:Soil science
3571:Geochemistry
3330:Infiltration
3258:Cut and fill
3201:Soil nailing
3067:Permeability
3032:Bulk density
2749:Inclinometer
2672:Ram sounding
2557:
2413:
2408:
2395:
2382:
2371:. Retrieved
2369:. 2016-09-08
2361:
2350:. Retrieved
2340:
2285:
2281:
2271:
2259:
2252:
2244:
2219:
2213:
2207:
2182:
2178:
2168:
2135:
2131:
2118:
2107:. Retrieved
2103:
2094:
2055:Hydrogeology
1990:
1943:
1896:
1818:Well sorted
1812:Well sorted
1784:
1771:eigenvectors
1764:
1725:
1677:
1653:
1649:
1645:
1644:
1546:
1490:
1470:
1459:
1414:
956:
773:
755:
747:
610:
555:
487:
465:
456:
449:
429:hydrocarbons
426:
413:
409:adding to it
404:
388:Applications
336:
330:
327:square metre
320:
295:
292:Permeability
284:
265:
250:Permeability
249:
248:
233:
215:
206:
187:
153:
144:
134:
127:
120:
113:
101:
89:Please help
84:verification
81:
57:
50:
44:
43:Please help
40:
3616:Archaeology
3340:Foundations
3313:Geomembrane
3196:Slurry wall
3135:Water table
3099:Interaction
3095:Structures
3082:Sensitivity
2879:Laboratory
2222:: 115–134.
2185:: 171–192.
1804:Impervious
1775:eigenvalues
1739:being both
1728:anisotropic
1696:source rock
1477:empirically
1462:Darcy's law
960:anisotropic
556:Therefore:
490:Darcy's law
478:Description
441:groundwater
361:Henry Darcy
307:fault zones
201:introducing
3643:Categories
3473:Mitigation
3455:Shear wave
3440:Earthquake
3435:Compaction
3420:Permafrost
3411:Phenomena/
3308:Geotextile
3233:Embankment
3223:Excavation
3160:Earthworks
3120:Vegetation
3115:Topography
3037:Thixotropy
3027:Void ratio
3010:Properties
2908:Hydrometer
2653:Piezometer
2573:Core drill
2431:References
2402:(abstract)
2388:(abstract)
2373:2023-05-02
2352:2008-05-30
2295:2012.03993
2138:: 103439.
2109:2022-01-14
2060:Permeation
1473:estimation
482:See also:
472:filtration
337:millidarcy
272:(often, a
184:references
147:April 2008
117:newspapers
46:improve it
3654:Hydrology
3596:Hydrology
3576:Petrology
3464:analysis
3462:Landslide
3367:Mechanics
3278:Track bed
3263:Fill dirt
3248:Terracing
2821:Trial pit
2636:Statnamic
2621:Load test
2160:229386129
2086:Footnotes
1880:limestone
1874:sandstone
1798:Pervious
1741:symmetric
1712:tight gas
1708:shale gas
1522:⋅
1424:κ
1395:−
1374:−
1300:−
1263:∇
1202:κ
1175:−
1156:−
1122:viscosity
1108:η
1082:−
1010:∇
1007:⋅
1003:κ
997:η
989:−
914:ρ
892:η
814:ρ
810:η
782:petroleum
729:Δ
700:Δ
688:viscosity
674:η
590:Δ
582:Δ
579:η
534:Δ
526:Δ
518:η
494:viscosity
453:viscosity
372:≈
347:≈
52:talk page
3649:Aquifers
3626:Agrology
3515:software
3413:problems
3243:Causeway
3218:Landfill
3145:Subgrade
3062:Porosity
3057:Cohesion
2487:Archived
2416:Dover.
2332:36340954
2039:See also
1884:dolomite
1849:Layered
1623:diameter
1340:pressure
717:pressure
445:aquifers
299:porosity
3566:Geology
3538:SVSlope
3348:Shallow
3268:Grading
3206:Tieback
3150:Subsoil
3140:Bedrock
3130:Topsoil
3125:Terrain
2918:R-value
2881:testing
2631:Dynamic
2558:in situ
2556:Field (
2323:9635531
2300:Bibcode
2288:: 637.
2224:Bibcode
2187:Bibcode
2140:Bibcode
2032:0.0001
2008:10,000
1905:0.0001
1890:granite
1634:)": -->
1547:where:
1338:is the
1275:is the
634:is the
611:where:
470:(e.g.,
384:10 d).
285:in situ
197:improve
131:scholar
3548:Plaxis
3543:UTEXAS
3533:SVFlux
3523:SEEP2D
3375:Forces
3228:Trench
3176:Gabion
2986:Gravel
2626:Static
2440:
2420:
2330:
2320:
2158:
2029:0.001
2011:1,000
1902:0.001
1888:Fresh
1878:Fresh
1872:Fresh
1869:rocks
1814:gravel
1737:matrix
1732:tensor
1475:using
1217:tensor
1062:Length
968:tensor
964:scalar
778:brines
186:, but
133:
126:
119:
112:
104:
3528:STABL
3001:Loess
2964:Types
2290:arXiv
2251:From
2156:S2CID
2128:(PDF)
2026:0.01
1899:(cm)
1827:loess
1714:, or
836:where
784:, or
640:phase
459:(see
457:seals
332:darcy
317:Units
138:JSTOR
124:books
3353:Deep
2996:Loam
2991:Peat
2981:Sand
2976:Silt
2971:Clay
2956:Soil
2658:Well
2438:ISBN
2418:ISBN
2328:PMID
2023:0.1
2014:100
1946:(m)
1851:clay
1845:Peat
1831:loam
1820:sand
1743:and
1694:and
1686:and
1636:edit
1136:Mass
1073:Time
774:e.g.
435:and
321:The
274:rock
260:and
110:news
3238:Cut
2547:and
2318:PMC
2308:doi
2232:doi
2195:doi
2183:127
2148:doi
2136:212
2017:10
2005:10
2002:10
1999:10
1996:10
1985:10
1982:10
1979:10
1976:10
1973:10
1970:10
1967:10
1964:10
1961:10
1958:10
1955:10
1952:10
1949:10
1938:10
1935:10
1932:10
1929:10
1926:10
1923:10
1920:10
1917:10
1914:10
1911:10
1908:10
1652:or
1483:).
443:in
437:gas
433:oil
431:in
411:.
252:in
93:by
3645::
3497:*
2326:.
2316:.
2306:.
2298:.
2284:.
2280:.
2230:.
2220:40
2218:.
2193:.
2181:.
2177:.
2154:.
2146:.
2134:.
2130:.
2102:.
2020:1
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1829:,
1718:.
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1670:.
1452:.
1279:,
1219:,
780:,
447:.
323:SI
256:,
55:.
3101:)
3097:(
2560:)
2519:e
2512:t
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2390:.
2376:.
2355:.
2334:.
2310::
2302::
2292::
2286:8
2238:.
2234::
2226::
2201:.
2197::
2189::
2162:.
2150::
2142::
2112:.
1991:k
1944:k
1897:k
1640:]
1625:.
1609:d
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1511:I
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1435:1
1431:k
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1391:]
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1382:[
1377:1
1370:]
1365:L
1361:[
1358:]
1354:M
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1326:P
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1291:L
1287:[
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1231:L
1227:[
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1167:T
1164:[
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1147:L
1143:[
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1132:[
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1069:[
1066:]
1058:[
1037:q
1013:P
994:1
986:=
982:q
936:g
870:K
848:k
817:g
805:K
802:=
799:k
770:k
766:K
764:(
732:x
703:P
652:k
622:v
593:P
585:x
573:v
570:=
567:k
537:x
529:P
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510:=
507:v
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414:(
266:k
240:)
234:(
222:)
216:(
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160:)
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145:(
135:·
128:·
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