4 Groundwater movement
Groundwater flows underground in response to elevation differences (downwards) and pressure differences (from areas of high pressure to areas of low pressure). Near the water table, this means that groundwater usually flows 'downhill', i.e. from a higher level to a lower level, just as it would on the surface. The difference in energy between two points that are l metres apart horizontally on a sloping water table is determined by the difference in height (h) between them (Figure 7). This height is called the head of water. The slope of the water table is called the hydraulic gradient and is defined as h/l. The rate of groundwater movement (Q; the volume of water flowing in unit time, with units of m3 s−1) is related to the hydraulic gradient by Darcy's law (Box 1):
In Equation 1, K is the hydraulic conductivity and is defined as the volume of water that will flow through a unit cross-sectional area of rock per unit time, under a unit hydraulic gradient and at a specified temperature. The units of hydraulic conductivity are metres per second (m s−1) or metres per day. A is the cross-sectional area at right angles to the flow path.
The hydraulic conductivity depends on the properties of the rock that allow water to flow through it (its permeability) and also on the properties of the water. Unlike hydraulic conductivity, permeability is an intrinsic property of the rock, so it is the same whatever the nature of the fluid flowing through the rock — whether water, as in this instance, or oil or gas. The hydraulic conductivity (K), however, depends on the density and viscosity of the fluid, so it will vary accordingly. When the fluid is water, the most important factor that affects the hydraulic conductivity is temperature. For example, an increase in water temperature from 5 °C to about 30 °C will double the hydraulic conductivity and, from Darcy's law, will therefore double the speed at which the groundwater flows.
Box 1 Henry Darcy
Darcy's law is named after Henry Darcy, who was born in Dijon in France in 1803. He trained as an engineer, and worked to solve the problem of providing drinking water in Dijon, which at the time had no reliable and safe supply. Darcy designed a water supply system for the city from a large spring 10 km away, piped to standpipes in the city, providing Dijon with its first good water supply.
Darcy also carried out experiments into the science of water flow and derived the relationship between the speed of flow and the hydraulic gradient which is now known as Darcy's law. This was published in 1856, together with his work on water supply, under the title Les Fontaines Publiques de la Ville de Dijon.
Rocks can be divided into two broad categories — permeable and impermeable — on the basis of their hydraulic conductivity. Rocks generally regarded as permeable have hydraulic conductivities of 1 m per day or more.
Hydraulic conductivity is proportional to permeability (permeability is discussed in greater detail in Section 6). So from Darcy's law (Equation 1) it can be deduced that in a rock of constant hydraulic conductivity (K), and hence of constant permeability for a given fluid, the rate (Q) at which the groundwater flows will increase as the hydraulic gradient (h/l, the slope of the water table) increases.
Groundwater flows in the direction of the hydraulic gradient (the maximum slope of the water table) at least for groundwater near the top of the saturated zone and where the rock is isotropic (has similar properties in all directions). If there are fissures, for example, and these are in a different orientation to the hydraulic gradient, the direction of flow will be greatly affected by the fissure orientation. Groundwater flow directions can be deduced from contour maps of the water table, as the direction of maximum slope is at right-angles to the water table contours. In Figure 8 directions of flow are added to the water table contour map in Figure 5a. In Question 2 we deduced that the water table in this area sloped down to the north-east, so the direction of groundwater flow was also to the north-east.
This flow of groundwater in the direction of the slope of the water table is only part of the picture, for groundwater is also in motion at greater depths, where it generally moves in a curved path rather than a straight line when seen in cross-section (Figure 9), towards a stream or river, a spring, or even a well. This path is the result of movement towards an area of discharge, such as the stream.
In addition to the natural discharge at streams, rivers or springs, groundwater can be extracted from wells. The water table around a well from which water is being pumped will fall, forming a cone of depression (Figure 10). The shape and extent of the cone of depression depend on the hydraulic conductivity of the rock, the rate of pumping, and the duration of pumping. The difference in height between the water table before pumping and the level of water in the well during pumping is called the drawdown.
At a coast, groundwater normally discharges into the sea because the water table slopes down towards sea level (Figure 11). Rocks under the sea, however, are generally saturated with seawater (saline groundwater). The boundary between fresh groundwater and saline groundwater usually slopes downward inland from the coast, with denser saline groundwater wedging under the less dense fresh groundwater below the land. The depth below sea level of the interface between fresh and saline groundwater at any point (h2 on Figure 11) depends on the height of the water table above sea level (h1). Along this interface the pressures due to the head of denser saline water and the less dense fresh water must balance. This means that the depth of the saline water below sea level (h2) is about forty times the height of the water table above sea level (h1). (The 'forty' comes from the difference in densities of fresh water and seawater.) So if the water table near a coast is, say, 5 m above sea level (that is, h1 = 5 m), then the depth to the saline groundwater below the water table should be:
If the densities of the fresh or saline water vary, so will the 40 : 1 ratio of h2 to h1. This can happen where brackish waters form the interface with fresh water, because the interface between fresh groundwater and saline groundwater is usually not as sharp as is implied in Figure 11. Instead there is normally a zone, at least a few metres in thickness, where the fresh and saline groundwaters mix. The water in this zone is less saline than seawater; that is, it is brackish water. Also the level of the sea rises and falls with the tides, and there are variations in the rate of discharge of fresh groundwater to the sea. Factors such as these bring about changes in the position of the interface, and can promote mixing of fresh water and seawater. Figure 12 shows a zone of mixing between 200 m and 500 m wide off the coast of Florida.
Seawater intrusion into wells can become a problem where large amounts of groundwater are extracted near a coast, so that saline groundwater moves inland. This is called a saline intrusion. If the water table is lowered by high rates of extraction (h1 is reduced), the position of the interface between the fresh and saline groundwater rises (h2 is reduced), so the wells may eventually fill with saline water and become useless for supplying fresh water. These problems can become acute on small islands, where a lens-shaped body of fresh groundwater usually overlies saline groundwater (Figure 13).
Saline intrusion along coasts can be controlled by limiting the rate at which groundwater is removed so that the water table remains above sea level and slopes down towards the coast. Providing the hydraulic gradient is seawards, fresh groundwater will flow in this direction, preventing further saline intrusion. This method of control is practised in eastern England. Saline intrusion can also be controlled by injecting fresh water into the ground. This can either be surplus water collected during wet months or water of low quality which would otherwise be discharged into the sea. The water is injected into the ground by secondary wells situated between the main extraction wells and the coast. Sewage effluent is used to control saline intrusions by this method on the western coast of the United States and in Israel.