Hydraulic conductivity
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Hydraulic conductivity, symbolically represented as K, is a property of soil or rock, 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, Ksat, describes water movement through saturated media.
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[edit] Derivation through Darcy's law
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
where
- K is the hydraulic conductivity [LT-1 or m s-1];
- κ is the intrinsic permeability of the material [L2 or m2];
- γ is the specific weight of water [ML-2T-2 or N m-3], and;
- μ is the dynamic viscosity of water [ML-1T-1 or kg m-1 s-1].
[edit] Estimation of hydraulic conductivity
[edit] Direct estimation
Hydraulic conductivity can be measured by applying Darcy's law on the material. Such experiments can be conducted by creating a hydraulic gradient between two points, and measuring the flow rate.
[edit] Empirical estimation
Shepherd[1] derived an empirical formula for approximating hydraulic conductivity from grain size analyses:
- K = a(D10)b
where
- a and b are empirically derived terms based on the soil type, and
- D10 is the diameter of the 10 percentile grain size of the material
Note: Shepherd's Figure 3 clearly shows the use of d50, not d10, measured in mm. Therefore the equation should be K = a(d10)b. His figure shows different lines for materials of different types, based on analysis of data from others with d50 up to 10 mm.
[edit] Pedotransfer function
A pedotransfer function (PTF) is a specialized empirical estimation method, used primarily in the soil sciences, however has increasing use in hydrogeology[2]. There are many different PTF methods, however, they all attempt to determine soil properties, such as hydraulic conductivity, given several measured soil properties, such as soil particle size, and bulk density.
[edit] Transmissivity
The transmissivity, T, of an aquifer is a measure of how much water can be transmitted horizontally, such as to a pumping well:
Transmissivity is directly proportional to the aquifer thickness. For a confined aquifer, this remains constant, as the saturated thickness remains constant. The aquifer thickness of an unconfined aquifer is from the base of the aquifer (or the top of the aquitard) to the water table. The water table can fluctuate, which changes the transmissivity of the unconfined aquifer. This may provide positive feedback of a pumping well that is pumping more than can be provided by the aquifer, where the transmissivity drops as the well pumps, thus eventually reducing the aquifer to the height of the pumping well screen.
Transmissivity should not be confused with transmittance, which is the fraction of incident light that passes through a sample.
[edit] Relative properties
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).
[edit] Ranges of values for natural materials
Table of saturated hydraulic conductivity (K) values found in nature
Values are for typical fresh groundwater conditions — using standard values of viscosity and specific gravity for water at 20°C and 1 atm. See the similar table derived from the same source for intrinsic permeability values.[3]
| K (cm/s) | 102 | 101 | 100=1 | 10−1 | 10−2 | 10−3 | 10−4 | 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
[edit] See also
- Aquifer test
- Pedotransfer function–for estimating hydraulic conductivities given soil properties
| physical aquifer properties used in hydrogeology |
|---|
| hydraulic head | hydraulic conductivity | storativity | porosity | water content |
[edit] References
- ^ Shephard, R.G. (1989). "Correlations of permeability and grain-size". Ground Water 27 (5): 633–638.
- ^ Wösten, J.H.M., Pachepsky, Y.A., and Rawls, W.J. (2001). "Pedotransfer functions: bridging the gap between available basic soil data and missing soil hydraulic characteristics" 251: 123–150. DOI:10.1016/S0022-1694(01)00464-4.
- ^ Bear, J. (1972). Dynamics of Fluids in Porous Media. Dover Publications. ISBN 0-486-65675-6.
