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.
Hydraulic Conductivity (K)
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
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
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|
|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|
|Rock Type||Hydraulic Conductivity
|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|
|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|
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
|Vertical Hydraulic Conductivity
|Anhydrite||10-14 to 10-12||10-15 to 10-13|
|Chalk||10-10 to 10-8||5x10-11 to 5x10-9|
|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|
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 (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).
|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|
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
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
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 (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.
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:
The following table shows representative values of specific yield for various geologic materials (from Morris and Johnson 1967):
|Material||Specific Yield (%)|
|Sandstone, fine grained||21|
|Sandstone, medium grained||27|
|Till, predominantly silt||6|
|Till, predominantly sand||16|
|Till, predominantly gravel||16|
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|
|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|
|Rock Type||Porosity (%)|
|Sandstone||14 - 49|
|Siltstone||21 - 41|
|Claystone||41 - 45|
|Shale||1 - 10|
|Limestone||7 - 56|
|Dolomite||19 - 33|
|Rock Type||Porosity (%)|
|Basalt||3 - 35|
|Weathered granite||34 - 57|
|Weathered gabbro||42 - 45|
See also: Argonne National Laboratory