Representative Values of Hydraulic Properties

by Glenn M. Duffield, President, HydroSOLVE, Inc.

Aquifer tests (pumping tests, slug tests and constant-head tests) are performed to estimate the hydraulic properties of aquifers and aquitards including horizontal and vertical hydraulic conductivity, storativity, specific yield and porosity. The following sections present representative hydraulic property values reported in the literature.

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hydraulic conductivity | transmissivity | anisotropy
storativity | specific yield | porosity

Hydraulic Conductivity (K)

Hydraulic conductivity

Hydraulic conductivity is the rate of flow under a unit hydraulic gradient through a unit cross-sectional area of aquifer (opening A). Transmissivity is the rate of flow under a unit hydraulic gradient through a unit width of aquifer of thickness m (opening B). Diagram from Ferris et al. (1962).

What is hydraulic conductivity? Hydraulic conductivity is a measure of a material's capacity to transmit water. It is defined as a constant of proportionality relating the specific discharge of a porous medium under a unit hydraulic gradient in Darcy's law:

ν = -Ki

where ν is specific discharge [L/T], K is hydraulic conductivity [L/T] and i is hydraulic gradient [dimensionless]. Coefficient of permeability is another term for hydraulic conductivity.

Note that hydraulic conductivity, which is a function of water viscosity and density, is in a strict sense a function of water temperature; however, given the small range of temperature variation encountered in most groundwater systems, the temperature dependence of hydraulic conductivity is often neglected.

What is transmissivity? Transmissivity is the rate of flow under a unit hydraulic gradient through a unit width of aquifer of given saturated thickness. The transmissivity of an aquifer is related to its hydraulic conductivity as follows:

T = Kb

where T is transmissivity [L2/T] and b is aquifer thickness [L].

The following tables show representative values of hydraulic conductivity for various unconsolidated sedimentary materials, sedimentary rocks and crystalline rocks (from Domenico and Schwartz 1990):

Unconsolidated Sedimentary Materials
Material Hydraulic Conductivity
(m/sec)
Gravel 3x10-4 to 3x10-2
Coarse sand 9x10-7 to 6x10-3
Medium sand 9x10-7 to 5x10-4
Fine sand 2x10-7 to 2x10-4
Silt, loess 1x10-9 to 2x10-5
Till 1x10-12 to 2x10-6
Clay 1x10-11 to 4.7x10-9
Unweathered marine clay 8x10-13 to 2x10-9

Sedimentary Rocks
Rock Type Hydraulic Conductivity
(m/sec)
Karst and reef limestone 1x10-6 to 2x10-2
Limestone, dolomite 1x10-9 to 6x10-6
Sandstone 3x10-10 to 6x10-6
Siltstone 1x10-11 to 1.4x10-8
Salt 1x10-12 to 1x10-10
Anhydrite 4x10-13 to 2x10-8
Shale 1x10-13 to 2x10-9

Crystalline Rocks
Material Hydraulic Conductivity
(m/sec)
Permeable basalt 4x10-7 to 2x10-2
Fractured igneous and metamorphic rock 8x10-9 to 3x10-4
Weathered granite 3.3x10-6 to 5.2x10-5
Weathered gabbro 5.5x10-7 to 3.8x10-6
Basalt 2x10-11 to 4.2x10-7
Unfractured igneous and metamorphic rock 3x10-14 to 2x10-10

To Convert Multiply By To Obtain
m/sec 100 cm/sec
m/sec 2.12x106 gal/day/ft2
m/sec 3.2808 ft/sec
Hydraulic conductivity of geologic materials

Hydraulic conductivity of selected consolidated and unconsolidated geologic materials (from Heath 1983).

Hydraulic Conductivity Anisotropy Ratio (Kz/Kr)

An anisotropy ratio relates hydraulic conductivities in different directions. For example, vertical-to-horizontal hydraulic conductivity anisotropy ratio is given by Kz/Kr where Kz is vertical hydraulic conductivity and Kr is radial (horizontal) hydraulic conductivity. Anisotropy in a horizontal plane is given by Ky/Kx where Kx and Ky are horizontal hydraulic conductivities in the x and y directions, respectively.

Todd (1980) reports values of Kz/Kr ranging between 0.1 and 0.5 for alluvium and possibly as low as 0.01 when clay layers are present.

The following table shows representative values of horizontal and vertical hydraulic conductivities for selected rock types (from Domenico and Schwartz 1990):

Material Horizontal Hydraulic Conductivity
(m/sec)
Vertical Hydraulic Conductivity
(m/sec)
Anhydrite 10-14 to 10-12 10-15 to 10-13
Chalk 10-10 to 10-8 5x10-11 to 5x10-9
Limestone,
dolomite
10-9 to 10-7 5x10-10 to 5x10-8
Sandstone 5x10-13 to 10-10 2.5x10-13 to 5x10-11
Shale 10-14 to 10-12 10-15 to 10-13
Salt 10-14 10-14

Storativity (S)

Storativity of a nonleaky confined aquifer

Storativity of a confined (artesian) aquifer (from Ferris et al. 1962).

What is storativity? The storativity of a confined aquifer (or aquitard) is defined as the volume of water released from storage per unit surface area of a confined aquifer (or aquitard) per unit decline in hydraulic head. Storativity is also known by the terms coefficient of storage and storage coefficient.

In a confined aquifer (or aquitard), storativity is defined as

S = Ssb

where S is storativity [dimensionless], Ss is specific storage [L-1] and b is aquifer (or aquitard) thickness [L]. Specific storage is the volume of water that a unit volume of aquifer (or aquitard) releases from storage under a unit decline in head by the expansion of water and compression of the soil or rock skeleton.

What is specific storage? Specific storage is related to the compressibilities of the aquifer (or aquitard) and water as follows:

Ss = ρg(α + neβ)

where ρ is mass density of water [M/L3], g is gravitational acceleration (= 9.8 m/sec2) [L/T2], α is aquifer (or aquitard) compressibility [T2L/M], ne is effective porosity [dimensionless], and β is compressibility of water (= 4.4x10-10 m sec2/kg or Pa-1) [T2L/M].

Storativity of an unconfined (water-table) aquifer

Storativity of an unconfined (water-table) aquifer (from Ferris et al. 1962).

In an unconfined aquifer (or aquitard), storativity is given by

S = Sy + Ssb

where Sy is specific yield. Because Ssb is typically small in comparison to Sy, storativity in an unconfined aquifer is often simply equated with specific yield.

The storativity of a confined aquifer, which varies with specific storage and aquifer thickness, typically ranges from 5x10-5 to 5x10-3 (Todd 1980); in unconfined aquifers, storativity ranges from 0.1 to 0.3 (Lohman 1972).

The following table provides representative values of specific storage for various geologic materials (Domenico and Mifflin [1965] as reported in Batu [1998]):

Material Ss (ft-1)
Plastic clay 7.8x10-4 to 6.2x10-3
Stiff clay 3.9x10-4 to 7.8x10-4
Medium hard clay 2.8x10-4 to 3.9x10-4
Loose sand 1.5x10-4 to 3.1x10-4
Dense sand 3.9x10-5 to 6.2x10-5
Dense sandy gravel 1.5x10-5 to 3.1x10-5
Rock, fissured 1x10-6 to 2.1x10-5
Rock, sound < 1x10-6

To Convert Divide By To Obtain
ft-1 0.3048 m-1

Freeze and Cherry (1979) provided the following compressibility values for various aquifer materials:

Material Compressibility, α (m2/N or Pa-1)
Clay 10-8 to 10-6
Sand 10-9 to 10-7
Gravel 10-10 to 10-8
Jointed rock 10-10 to 10-8
Sound rock 10-11 to 10-9

Pa-1 = m2/N = m sec2/kg

Example Calculations
  1. Use compressibility data to estimate the storativity of a 35-ft thick confined sand aquifer (assume ρ = 1000 kg/m3 and ne = 0.3).

    S = Ssb = ρg(α + neβ)b = (1000 kg/m3)(9.8 m/sec2) [10-8 m2/N + (0.3) (4.4x10-10 m2/N)](35 ft)(0.3048 m/ft) = 1.1x10-3

    How much does the expansion of water contribute to the total storativity in this example?

    Sw = ρgneβb = (1000 kg/m3)(9.8 m/sec2)(0.3) (4.4x10-10 m2/N)(35 ft)(0.3048 m/ft) = 1.4x10-5


  2. Use specific storage data to estimate storativity for the same aquifer given in the preceding example.

    S = Ssb = (5x10-5 ft-1)(35 ft) = 1.8x10-3

Specific Yield (Sy)

Specific retention, specific yield and total porosity

Specific retention (Sr), specific yield (Sy) and total porosity (n) (from Heath 1983).

What is specific yield? Specific yield is defined as the volume of water released from storage by an unconfined aquifer per unit surface area of aquifer per unit decline of the water table.

Bear (1979) relates specific yield to total porosity as follows:

n = Sy + Sr

where n is total porosity [dimensionless], Sy is specific yield [dimensionless] and Sr is specific retention [dimensionless], the amount of water retained by capillary forces during gravity drainage of an unconfined aquifer. Thus, specific yield, which is sometimes called effective porosity, is less than the total porosity of an unconfined aquifer (Bear 1979).

Heath (1983) reports the following values (in percent by volume) for porosity, specific yield and specific retention:

Material Porosity (%) Specific
Yield (%)
Specific
Retention (%)
Soil 55 40 15
Clay 50 2 48
Sand 25 22 3
Gravel 20 19 1
Limestone 20 18 2
Sandstone (unconsolidated) 11 6 5
Granite 0.1 0.09 0.01
Basalt (young) 11 8 3

The following table shows representative values of specific yield for various geologic materials (from Morris and Johnson 1967):

Material Specific Yield (%)
Gravel, coarse 21
Gravel, medium 24
Gravel, fine 28
Sand, coarse 30
Sand, medium 32
Sand, fine 33
Silt 20
Clay 6
Sandstone, fine grained 21
Sandstone, medium grained 27
Limestone 14
Dune sand 38
Loess 18
Peat 44
Schist 26
Siltstone 12
Till, predominantly silt 6
Till, predominantly sand 16
Till, predominantly gravel 16
Tuff 21

Porosity (n)

Void volume, total volume and porosity

Void volume, total volume and porosity (from Heath 1983).

What is porosity? Porosity is defined as the void space of a rock or unconsolidated material:

n = Vv/VT

where n is porosity [dimensionless], Vv is void volume [L3] and VT is total volume [L3].

The following tables show representative porosity values for various unconsolidated sedimentary materials, sedimentary rocks and crystalline rocks (from Morris and Johnson 1967):

Unconsolidated Sedimentary Materials
Material Porosity (%)
Gravel, coarse 24 - 37
Gravel, medium 24 - 44
Gravel, fine 25 - 39
Sand, coarse 31 - 46
Sand, medium 29 - 49
Sand, fine 26 - 53
Silt 34 - 61
Clay 34 - 57

Sedimentary Rocks
Rock Type Porosity (%)
Sandstone 14 - 49
Siltstone 21 - 41
Claystone 41 - 45
Shale 1 - 10
Limestone 7 - 56
Dolomite 19 - 33

Crystalline Rocks
Rock Type Porosity (%)
Basalt 3 - 35
Weathered granite 34 - 57
Weathered gabbro 42 - 45

See also: Argonne National Laboratory

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