Ground Water

Groundwater Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of lithologic formations. A unit of rock or an unconsolidated deposit is called an aquifer when it can yield a usable quantity of water. The depth at which soil pore spaces or fractures and voids in rock become completely saturated with water is called the water table. Groundwater is recharged from, and eventually flows to, the surface naturally; natural discharge often occurs at springs and seeps, and can form oases or wetlands. Groundwater is also often withdrawn for agricultural, municipal and industrial use by constructing and operating extraction wells. The study of the distribution and movement of groundwater is hydrogeology, also called groundwater hydrology. Typically, groundwater is thought of as liquid water flowing through shallow aquifers, but technically it can also include soil moisture, permafrost (frozen soil), immobile water in very low permeability bedrock, and deep geothermal or oil formation water. Groundwater is hypothesized to provide lubrication that can possibly influence the movement of faults. It is likely that much of the Earth's subsurface contains some water, which may be mixed with other fluids in some instances. Groundwater may not be confined only to the Earth. The formation of some of the landforms observed on Mars may have been influenced by groundwater. There is also evidence that liquid water may also exist in the subsurface of Jupiter's moon Europa. An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. The study of water flow in aquifers and the characterization of aquifers is called hydrogeology. Related terms include: an aquitard, which is an impermeable layer along an aquifer, and an aquiclude (or aquifuge), which is a solid, impermeable area underlying or overlying an aquifer.

The surface of saturated material in an aquifer is known as the water table.

Classification This diagram indicates typical flow directions in a cross-sectional view of a simple confined/unconfined aquifer system. The system shows two aquifers with one aquitard (a confining or impermeable layer), between them, surrounded by the bedrock aquiclude, which is in contact with a gaining stream (typical in humid regions). The water table and unsaturated zone are also illustrated. An aquitard is a zone within the earth that restricts the flow of groundwater from one aquifer to another. An aquitard can sometimes, if completely impermeable, be called an aquiclude or aquifuge. Aquitards are composed of layers of either clay or non-porous rock with low hydraulic conductivity. Saturated versus unsaturated Groundwater can be found at nearly every point in the Earth's shallow subsurface, to some degree; although aquifers do not necessarily contain fresh water. The Earth's crust can be divided into two regions: the saturated zone or phreatic zone (e.g., aquifers, aquitards, etc.), where all available spaces are filled with water, and the unsaturated zone (also called the vadose zone), where there are still pockets of air with some water that can be replaced by water. Saturated means the pressure head of the water is greater than atmospheric pressure (it has a gauge pressure > 0). The definition of the water table is surface where the pressure head is equal to atmospheric pressure (where gauge pressure =0). Unsaturated conditions occur above the water table where the pressure head is negative (absolute pressure can never be negative, but gauge pressure can) and the water which incompletely fills the pores of the aquifer material is under suction.

The water content in the unsaturated zone is held in place by surface adhesive forces and it rises above the water table (the zero gauge pressure isobar) by capillary action to saturate a small zone above the phreatic surface (the capillary fringe) at less than atmospheric pressure. This is termed tension saturation and is not the same as saturation on a water content basis. Water content in a capillary fringe decreases with increasing distance from the phreatic surface. The capillary head depends on soil pore size. In sandy soils with larger pores the head will be less than in clay soils with very small pores. The normal capillary rise in a clayey soil is less than 1.80 m (six feet) but can range between 0.3 and 10 m (1 and 30 ft). [6] The capillary rise of water in a small diameter tube is this same physical process. The water table is the level to which water will rise in a large diameter pipe (e.g. a well) which goes down into the aquifer and is open to the atmosphere. Aquifers versus aquitards Aquifers are typically saturated regions of the subsurface which produce an economically feasible quantity of water to a well or spring (e.g., sand and gravel or fractured bedrock often make good aquifer materials). An aquitard is a zone within the earth that restricts the flow of groundwater from one aquifer to another. An aquitard can sometimes, if completely impermeable, be called an aquiclude or aquifuge. Aquitards comprise layers of either clay or non-porous rock with low hydraulic conductivity. In mountainous areas (or near rivers in mountainous areas), the main aquifers are typically unconsolidated alluvium. They are typically composed of mostly horizontal layers of materials deposited by water processes (rivers and streams), which in cross-section (looking at a two-dimensional slice of the aquifer) appear to be layers of alternating coarse and fine materials. Coarse materials, because of the high energy needed to move them, tend to be found nearer the source (mountain fronts or rivers), while the fine-grained material will make it farther from the source (to the flatter parts of the basin or overbank areas - sometimes called the pressure area). Since there are less fine-grained deposits near the source, this is a place where aquifers are often unconfined (sometimes called the forebay area), or in hydraulic communication with the land surface. Confined versus unconfined There are two end members in the spectrum of types of aquifers; confined and unconfined (with semi-confined being in between). Unconfined aquifers are sometimes also called water table or phreatic aquifers, because their upper boundary is the water table or phreatic surface. (See Biscayne Aquifer.) Typically (but not always) the shallowest aquifer at a given location is unconfined, meaning it does not have a confining layer (an aquitard or aquiclude) between it and the surface. The term "perched" refers to ground water accumulating above a lowpermeability unit or strata, such as a clay layer. This term is generally used to refer to a small local area of ground water that occurs at an elevation higher than a regionally-extensive aquifer. The difference between perched and unconfined aquifers is their size (perched is smaller). If the distinction between confined and unconfined is not clear geologically (i.e., if it is not known if a clear confining layer exists, or if the geology is more complex, e.g., a fractured bedrock aquifer), the value of storativity returned from an aquifer test can be used to determine it (although aquifer tests in unconfined aquifers should be

interpreted differently than confined ones). Confined aquifers have very low storativity values (much less than 0.01, and as little as 10 -5), which means that the aquifer is storing water using the mechanisms of aquifer matrix expansion and the compressibility of water, which typically are both quite small quantities. Unconfined aquifers have storativities (typically then called specific yield) greater than 0.01 (1% of bulk volume); they release water from storage by the mechanism of actually draining the pores of the aquifer, releasing relatively large amounts of water (up to the drainable porosity of the aquifer material, or the minimum volumetric water content). Isotropic versus anisotropic In isotropic aquifers or aquifer layers the hydraulic conductivity (K) is equal for flow in all directions, while in anisotropic conditions it differs, notably in horizontal (Kh) and vertical (Kv) sense. Semi-confined aquifers with one or more aquitards work as an anisotropic system, even when the separate layers are isotropic, because the compound Kh and Kv values are different (see hydraulic conductivity#transmissivity and hydraulic conductivity#resistance). When calculating flow to drains [1] or to wells [2] in an aquifer, the anisotropy is to be taken into account lest the resulting design of the drainage system may be faulty. Hydraulic conductivity Hydraulic conductivity, symbolically represented as K, is a property of vascular plants, 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. Methods of determination

Overview of determination methods

There are two broad categories of determining hydraulic conductivity: •

Empirical approach by which the hydraulic conductivity is correlated to soil properties like pore size and particle size (grain size) distributions, and soil texture

•

Experimental approach by which the hydraulic conductivity is determined from hydraulic experiments using Darcy's law

The experimental approach is broadly classified into: •

Laboratory tests using soil samples subjected to hydraulic experiments

•

Field tests (on site, in situ) that are differentiated into: ○

small scale field tests, using observations of the water level in cavities in the soil

○

large scale field tests, like pump tests in wells or by observing the functioning of existing horizontal drainage systems.

The small scale field tests are further subdivided into: •

infiltration tests in cavities above the water table

•

slug tests in cavities below the water table

Estimation from grain size 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. Darcy's law In fluid dynamics and hydrology, Darcy's law is a phenomenologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments (published 1856)[1] on the flow of water through beds of sand. It also forms the scientific basis of fluid permeability used in the earth sciences.

Description

Diagram showing definitions and directions for Darcy's law. Darcy's law is a simple proportional relationship between the instantaneous discharge rate through a porous medium, the viscosity of the fluid and the pressure drop over a given distance.

The total discharge, Q (units of volume per time, e.g., m³/s) is equal to the product of the permeability (κ units of area, e.g. m²) of the medium, the cross-sectional area (A) to flow, and the pressure drop (Pb − Pa), all divided by the dynamic viscosity μ (in SI units e.g. kg/(m·s) or Pa·s), and the length L the pressure drop is taking place over. The negative sign is needed because fluids flow from high pressure to low pressure. So if the change in pressure is negative (in the x-direction) then the flow will be positive (in the x-direction). Dividing both sides of the equation by the area and using more general notation leads to

where q is the filtration velocity or Darcy flux (discharge per unit area, with units of length per time, m/s) and is the pressure gradient vector. This value of the filtration velocity (Darcy flux), is not the velocity which the water traveling through the pores is experiencing[2]. The pore (interstitial) velocity (v) is related to the Darcy flux (q) by the porosity (φ). The flux is divided by porosity to account for the fact that only a fraction of the total formation volume is available for flow. The pore velocity would be the velocity a conservative tracer would experience if carried by the fluid through the formation.

Determination by experimental approach There are relatively simple and inexpensive laboratory tests that may be run to determine the hydraulic conductivity of a soil: constant-head method and fallinghead method. Laboratory methods Constant-head method The constant-head method is typically used on granular soil. This procedure allows water to move through the soil under a steady state head condition while the quantity (volume) of water flowing through the soil specimen is measured over a period of time. By knowing the quantity Q of water measured, length L of specimen, cross-sectional area A of the specimen, time t required for the quantity of water Q to be discharged, and head h, the hydraulic conductivity can be calculated:

where v is the flow velocity. Using Darcy's Law:

and expressing the hydraulic gradient i as:

where h is the difference of hydraulic head over distance L, yields:

Solving for K gives:

Falling-head method The falling-head method is very similar to the constant head methods in its initial setup; however, the advantage to the falling-head method is that can be used for both fine-grained and coarse-grained soils. The soil sample is first saturated under a specific head condition. The water is then allowed to flow through the soil without maintaining a constant pressure head[3].

In-situ (field) methods Augerhole method There are also in-situ methods for measuring the hydraulic conductivity in the field. When the water table is shallow, the augerhole method, a slug test, can be used for determining the hydraulic conductivity below the water table. The method was developed by Hooghoudt (1934) [4] in The Netherlands and introduced in the US by Van Bavel en Kirkham (1948) [5] . The method uses the following steps: 1. an augerhole is perforated into the soil to below the water table 2. water is bailed out from the augerhole 3. the rate of rise of the water level in the hole is recorded 4. the K-value is calculated from the data as

[6]

:

Kh = C (Ho-Ht) / t

Cumulative frequency distribution (lognormal) of hydraulic conductivity (X-data) where: Kh = horizontal saturated hydraulic conductivity (m/day), H = depth of the waterlevel in the hole relative to the water table in the soil (cm), Ht = H at time t, Ho = H at time t = 0, t = time (in seconds) since the first measurement of H as Ho, and F is a factor depending on the geometry of the hole: F = 4000r / h'(20+D/r)(2−h'/D) where: r = radius of the cylindrical hole (cm), h' is the average depth of the water level in the hole relative to the water table in the soil (cm) , found as h'=(Ho+Ht)/2 , and D is the the depth of the bottom of the hole relative to the water table in the soil (cm). The picture shows a large variation of K-values measured with the augerhole method in an area of 100 ha [7] . The ratio between the highest and lowest values is 25. The cumulative frequency distribution is lognormal and was made with the CumFreq program. Related magnitudes Transmissivity

An aquifer may consist of n soil layers. The transmissivity for horizontal flow (Ti) of the i − th soil layer with a saturated thickness di and horizontal hydraulic conductivity Khi is: Ti = Khi di Transmissivity is directly proportional to horizontal permeability (Khi) and thickness (di). Expressing Khi in m/day and di in m, the transmissivity (Ti) is found in units m2/day. The transmissivity is a measure of how much water can be transmitted horizontally, such as to a pumping well. Transmissivity should not be confused with the similar word transmittance used in optics, meaning the fraction of incident light that passes through a sample. The total transmissivity (Tt) of the aquifer is

[6]

:

Tt = Σ Ti = Σ Khi di where Σ signifies the summation over all layers: i= 1, 2, 3, . . .n The apparent horizontal hydraulic conductivity (KhA) of the aquifer is: KhA = Tt / Dt where Dt is the total thickness of the aquifer: Dt= Σ di , with i= 1, 2, 3, . . .n The transmissivity of an aquifer can be determined from pumping tests

[8]

.

Influence of the water table When a soil layer is above the water table, it is not saturated and does not contribute to the transmissivity. When the soil layer is entirely below the water table, its saturated thickness corresponds to the thickness of the soil layer itself. When the water table is inside a soil layer, the saturated thickness corresponds to the distance of the water table to the bottom of the layer. As the water table may behave dynamically, this thickness may change from place to place or from time to time, so that the transmissivity may vary accordingly. In a semi-confined aquifer, the water table is found within a soil layer with a negligibly small transmissivity, so that changes of the total transmissivity (Dt) resulting from changes in the level of the water table are negligibly small. When pumping water from an unconfined aquifer, where the water table is inside a soil layer with a significant transmissivity, the water table may be drawn down whereby the transmissivity reduces and the flow of water to the well diminishes. Resistance The resistance to vertical flow (Ri) of the i − th soil layer with a saturated thickness di and vertical hydraulic conductivity Kvi is: Ri = di / Kvi Expressing Kvi in m/day and di in m, the resistance (Ri) is expressed in days. The total resistance (Rt) of the aquifer is [6] : Rt = Σ Ri = Σ di / Kvi

where Σ signifies the summation over all layers: i= 1, 2, 3, . . .n The apparent vertical hydraulic conductivity (KvA) of the aquifer is: KvA = Dt / Rt where Dt is the total thickness of the aquifer: Dt = Σ di , with i= 1, 2, 3, . . .n The resistance plays a role in aquifers where a sequence of layers occurs with varying horizontal permeability so that horizontal flow is found mainly in the layers with high horizontal permeability while the layers with low horizontal permeability transmit the water mainly in a vertical sense. Anisotropy When the horizontal and vertical hydraulic conductivity (Khi and Kvi) of the i − th soil layer differ considerably, the layer is said to be anisotropic with respect to hydraulic conductivity. When the apparent horizontal and vertical hydraulic conductivity (KhA and KvA) differ considerably, the aquifer is said to be anisotropic with respect to hydraulic conductivity. An aquifer is called semi-confined when a saturated layer with a relatively small horizontal hydraulic conductivity (the semi-confining layer or aquitard) overlies a layer with a relatively high horizontal hydraulic conductivity so that the flow of groundwater in the first layer is mainly vertical and in the second layer mainly horizontal. The resistance of a semi-confining toplayer of an aquifer can be determined from pumping tests [8] . When calculating flow to drains [9] or to a well field [10] in an aquifer with the aim to control the water table, the anisotropy is to be taken into account, otherwise the result may be erroneous. Relative properties Because of their high porosity and permeability, sand and gravel aquifers have higher hydraulic conductivity than clay or unfractured granite aquifers. 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 one of the most complex and important of the properties of aquifers in hydrogeology as the 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 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.[11] K (cm/s)

10² 101

K (ft/day)

105

Relative Permeability

Pervious

Aquifer

Good

100= 10− 10− 10−1 10−2 3 10−5 10−6 10−7 4 1

10,00 1,000 100 10 0

Unconsolidate Well d Sand & Sorted Gravel Gravel

0.0 0.00 10− 0.0001 10−5 6 10−7 1 1 Impervious

Poor

None

Well Sorted Very Fine Sand, Sand or Sand Silt, Loess, Loam & Gravel Peat

Highly Rocks

0.1

Semi-Pervious

Unconsolidate d Clay & Organic Consolidated Rocks

1

10− 10−1 10−8 9 0

Layered Clay

Fat / Unweathered Clay

Fresh Fresh Fractured Oil Reservoir Fresh Sandston Limestone, Rocks Granite e Dolomite

Source: modified from Bear, 1972 Storativity Storativity is the volume of water released from storage per unit decline in hydraulic head in the aquifer, per unit area of the aquifer, or:

Values of specific yield, from Johnson (1967) min

avg

Storativity is the vertically integrated specific storage value for a confined aquifer or aquitard. For a confined Unconsolidated deposits homogeneous aquifer or aquitard they are Clay 0 simply related by: Sandy clay (mud) Silt where b is the thickness of aquifer. Storativity is a dimensionless quantity, and Fine sand ranges between 0 and the effective porosity of the aquifer; although for Medium sand confined aquifers, this number is usually much less than 0.01. Coarse sand The storage coefficient of an unconfined aquifer is approximately equal to the Gravelly sand specific yield, Sy, since the release from Fine gravel specific storage, Ss is typically orders of magnitude less. Medium gravel Specific yield Specific yield, also known as the drainable porosity, is a ratio, less than or equal to the effective porosity, indicating the volumetric fraction of the bulk aquifer volume that a given aquifer will yield when all the water is allowed to drain out of it under the forces of gravity:

where

Coarse gravel

ma x

2

5

3

7

12

3

18 19

10

21 28

15

26 32

20

27 35

20

25 35

21

25 35

13

23 26

12

22 26

Consolidated deposits Fine-grained sandstone

21

Medium-grained sandstone

27

Limestone

14

Schist

26

Siltstone

12

Vwd is the volume of water drained, Tuff and Other deposits

21

VT is the total rock or material Dune sand volume Loess It is primarily used for unconfined aquifers, since the elastic storage component, Ss, is Peat relatively small and usually has an insignificant contribution. Specific yield Till, predominantly silt

38 18 44 6

can be close to effective porosity, but there are several subtle things which make this value more complicated than it seems. Some water always remains in the formation, even after drainage; it clings to the grains of sand and clay in the formation. Also, the value of specific yield may not be fully realized until very large times, due to complications caused by unsaturated flow.

Groundwater-related subsidence

Groundwater surface drawdown Groundwater-related subsidence is the subsidence (or the sinking) of land resulting from groundwater extraction, and a major problem in the developing world as major metropolises swell without adequate regulation and enforcement, as well as a being a common problem in the developed world. One estimate has 80% of serious land subsidence problems associated with the excessive extraction of groundwater [1], making it a growing problem throughout the world. Groundwater is considered to be one of the last 'free' resources. Anybody who can afford to drill, can draw up merely according to the their ability to pump. However, as seen in the figure, the act of pumping draws down the free surface of the groundwater table, and can affect a large region. Thus, the extraction of groundwater becomes a Tragedy of the commons, with high economic externalities. Perhaps as a consequence of global warming, the desert areas of the world are requiring more and more water for growing populations, and agriculture. In the San Joaquin Valley of the United States, groundwater pumping for crops has gone on for generations. This has resulted in the entire valley sinking an extraordinary amount, as shown in the figure. Fortunately, there is little consequence in a wide, flat, agricultural basin, since the settlement is uniform. Total settlement can only be determined by surveys and GPS measurements. As the groundwater is pumped out, the effective stress changes, precipitating consolidation, which is non-reversible. Thus, the total volume of the silts and clays is reduced, resulting in the lowering of the surface. The damage at the surface is much greater if there is differential settlement, or large-scale features, such as sinkholes. The only known method to prevent this condition, is by pumping less groundwater, which is extremely difficult to enforce, when many people own water wells. Attempts are being made to directly recharge aquifers, but this still a preliminary effort.

Groundwater in rock formations Groundwater may exist in underground rivers (e.g. caves where water flows freely underground). This may occur in eroded limestone areas known as karst topography which make up only a small percentage of Earth's area. More usual is that the pore spaces of rocks in the subsurface are simply saturated with water — like a kitchen sponge — which can be pumped out and used for agricultural, industrial or municipal uses. Seawater intrusion Generally, in very humid or undeveloped regions, the shape of the water table mimics the slope of the surface. The recharge zone of an aquifer near the seacoast is likely to be inland, often at considerable distance. In these coastal areas, a lowered water table may induce sea water to reverse the flow toward the sea. Sea water moving inland is called a saltwater intrusion. Alternatively, salt from mineral beds may leach into the groundwater of its own accord. Saltwater intrusion Saltwater intrusion is the movement of saline water into freshwater aquifers. Most often, it is caused by ground-water pumping from coastal wells,[1] or from construction of navigation channels or oil field canals. The channels and canals provide conduits for salt water to be brought into fresh water marshes. But salt water intrusion can also occur as the result of a natural process like a storm surge from a hurricane.[2] Saltwater intrusion occurs in virtually all coastal aquifers, where they are in hydraulic continuity with seawater. Ghyben-Herzberg relation The first physical formulations of saltwater intrusion were made by W. BadonGhijben (1888, 1889) and A. Herzberg (1901), thus called the Ghyben-Herzberg relation.[5] They derived analytical solutions to approximate the intrusion behavior, which are based on a number of assumptions that do not hold in all field cases.

[1]

The figure shows the Ghyben-Herzberg relation. In the equation,

the thickness of the freshwater zone above sea level is represented as h and that below sea level is represented as z. The two thicknesses h and z, are related by ρf and ρs where ρf is the density of freshwater and ρs is the density of saltwater. Freshwater has a density of about 1.000 grams per cubic centimeter (g/cm3) at 20 °C, whereas that of seawater is about 1.025 g/cm3. The equation can be simplified to .[1] The Ghyben-Herzberg ratio states, for every foot of fresh water in an unconfined aquifer above sea level, there will be forty feet of fresh water in the aquifer below sea level. In the 20th century the higher computing power allowed the use of numerical methods (usually finite differences or finite elements) that need less assumptions and can be applied more generally.[citation needed]