Hydraulic conductivity, mathematically represented as $K$, is a property of soil or rock, in the vadose zone or groundwater, that describes the ease with which water can move through pore spaces or fractures. It depends on the intrinsic permeability of the material and on the degree of saturation. Saturated hydraulic conductivity, $Ks$, describes water movement through saturated media.

Transmissivity, $T$, is a measure of how much water an aquifer can transmit horizontally. It depends on the aquifer's saturated hydraulic conductivity and thickness, $b$:

$T\; =\; Ks\; *\; b$

Transmissivity is important in studies of hydrogeology.

Hydraulic conductivity is the proportionality constant in Darcy's law, which relates the amount of water which will flow through a unit cross-sectional area of aquifer under a unit gradient of hydraulic head. It is analogous to the thermal conductivity of materials in heat conduction, or 1/resistivity in electrical circuits. The hydraulic conductivity (k — the English letter "kay") is specific to the flow of a certain fluid (typically water, sometimes oil or air); intrinsic permeability (κ — the Greek letter "kappa") is a parameter of a porous media which is independent of the fluid. This means that, for example, k will go up if the water in a porous medium is heated (reducing the viscosity of the water), but κ will remain constant. The two are related through the following equation

$k\; =\; \backslash frac\{\backslash kappa\; \backslash gamma\}\{\backslash mu\}$

Where γ is the unit weight of water (with units of force per volume, N/m³ or lbf/ft³), μ is the dynamic viscosity of water (with units of pascal seconds (Pa·s), poise, or lbf·s/ft²) and κ is the intrinsic permeability (units of m² or the oil industry unit of the darcy).

Relative properties

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Because of their high porosity and permeability, sand and gravel aquifers have higher hydraulic conductivity than clay or unfractured granite aquifer. Sand or gravel aquifers would thus be easier to extract water from (e.g., using a pumping well) because of their high transmissivity, compared to clay or unfractured bedrock aquifers.

Hydraulic conductivity has units with dimensions of length per time (e.g., m/s, ft/day and gal/(day/ft²) ); transmissivity then has units with dimensions of length squared per time. The following table gives some typical ranges (illustrating the many orders of magnitude which are likely) for k values.

Hydraulic conductivity (k) is the most complex and important of the hydrogeologic aquifer properties; values found in nature:

• range over many orders of magnitude (the distribution is often considered to be lognormal),
• vary a large amount through space (sometimes considered to be randomly spatially distributed, or stochastic in nature),
• are directional (in general k is a symmetric second-rank tensor; e.g., vertical k values can be several orders of magnitude smaller than horizontal k values),
• are scale dependent (testing a m³ of aquifer will generally produce different results than a similar test on only a cm³ sample of the same aquifer),
• must be determined indirectly through field pumping tests, laboratory column flow tests or inverse computer simulation, (sometimes also from grain size analyses), and
• are very dependent (in a non-linear way) on the water content, which makes solving the unsaturated flow equation difficult. In fact, the variably saturated k for a single material varies over a wider range than the saturated k values for all types of materials (see chart below for an illustrative range of the latter).

Ranges of values for natural materials

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Table of saturated hydraulic conductivity (k) values found in nature

(for typical fresh groundwater conditions (viscosity and specific gravity))

k (cm/s)

100

10

1

0.1

0.01

0.001

0.0001

10−5

10−6

10−7

10−8

10−9

10−10

k (ft/day)

105

10,000

1,000

100

10

1

0.1

0.01

0.001

0.0001

10−5

10−6

10−7

Relative Permeability

Pervious

Semi-Pervious

Impervious

Aquifer

Good

Poor

None

Unconsolidated Sand & Gravel

Well Sorted Gravel

Well Sorted Sand or Sand & Gravel

Very Fine Sand, Silt, Loess, Loam

Unconsolidated Clay & Organic

Peat

Layered Clay

Fat / Unweathered Clay

Consolidated Rocks

Highly Fractured Rocks

Oil Reservoir Rocks

Fresh Sandstone

Fresh Limestone, Dolomite

Fresh Granite

Source: modified from Bear, 1972

See also

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• Aquifer test
• Permeability (geology)

References

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• Bear, Jacob, 1972. Dynamics of Fluids in Porous Media, Dover. — A very mathematical, rigorous treatment of the subject, and an inexpensive Dover book. ISBN 0486656756

Hydrology | Water | Civil engineering | Soil mechanics | Soil physics

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