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In this article we will discuss about:- 1. Occurrence of Salt Water Intrusion 2. Dispersion 3. Abatement of Sea Water Intrusion 4. Oceanic Island Aquifers 5. Upconing.
Occurrence of Salt Water Intrusion:
Sea water intrusion in coastal aquifers occurs when permeable formations outcrop into a body of sea water and when there is a landward hydraulic gradient. Sea water can be prevented from intruding by maintaining a head of fresh water above it. According to Ghyben-Herzberg principle, the interface will occur at a depth hs below mean sea level (m.s.l.), Fig. 7.1 given by-
(hs + hf) γf = hsγs
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Since the pressure at the point of interface should be equal, and γ = ρg,
hs = γf/(γs – γf) hf = ρf/(ρs – ρf) hf = 1/(Gs – 1)hf …(7.1)
Where hs = depth below m.s.l. where interface occurs; hf = elevation of the ground water table above m.s.l.; ρf = density of fresh water and ρf = density of sea water.
Taking the specific gravity of fresh water as 1 and that of sea water as 1.025 (= Gs), from Eq. (7.1),
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Hs = 40hf …(7.2)
that is, for a rise or fall of g.w.t. or piezometric head by lm will induce a fall or rise, respectively, or of 40 m in the underlying salt water level, even though the response may be greatly delayed.
The net of flow lines and equipotential lines shown in Fig. 7.2 depicts the actual intrusion. Since the total pressure along an equipotential line is constant and the flow lines are sloping upward, the depth to the interface given by the Ghyben-Herzberg relation is less than the actual depth, but the difference is small for flat gradients.
Slope of Interface:
If the water table slope is ‘i’ Fig. 7.3, then from Darcy’s law-
sin i = dh/ds = h/s = v/k …(7.3)
Where v is the velocity of fresh water flow and K is the permeability of the strata. Along this slope, the water table elevation decreases in the direction of flow and hence according to Eq. (7.2), the fresh water-salt water interface should rise. Its slope ф is given by-
sin ф = ρf/ρs – ρf = v/K …(7.4)
Since the boundaries converge, the velocity of fresh water flow increases with distance, and the magnitudes of the slopes increase accordingly. This results in a parabolic interface (see Fig. 7.4 and 7.5).
The interface between fresh water and salt water is theoretically a stream line and no flow across it is possible. However, observations indicate that a narrow mixing zone along the interface exists. This zone results from dispersion occurring in the interface produced by tides, seasonal water table fluctuations, and from molecular diffusion.
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Fresh water due to its lower specific gravity will normally float above a layer of salt water without mixing. But when the ground water levels drop, there will be a tendency for sea water to move landward, displacing the fresh water in the aquifer. A landward sloping ‘fresh water-salt water interface’ will be formed with the depth governed by the Ghyben-Herzberg relationship. As water levels continue to decline, the prism of sea water, designated as the ‘sea water wedge’, will continue to advance until conditions of equilibrium are established. When intrusion takes place, the wedge tends to flatten out and the toe moves somewhat faster than the remaining portion of the interface. The intrusion is a very slow process.
The interface has a parabolic shape which is very similar to the Dupuit’s parabola and is given by-
Where q = seaward fresh water flow per unit width of ocean front; K = permeability of the aquifer and x, y = coordinates of the interface with the origin at the contact of m.s.l. with the land surface, Fig. 7.4.
When x = 0, y0 = 0.741 q/K’
When y = 0, x0 = – 0.275 q/K’
The total length of intrusion measured from x = 0, is given by-
L = K’ H2/2q, when L > H …(7.7)
Where H is the thickness of the aquifer.
The time t (in days) required for the toe of the wedge to move the length L is given by-
i = tnK’ H3/q2ul …(7.8)
Where i = dimensionless factor to be obtained from a master curve; n = porosity of the aquifer material and qul = ultimate fresh water flow per unit width.
It is seen that the wedge toe velocities are very small.
Salt water wedge in a non-leaky artesian aquifer is shown in Fig. 7.5. Replacing H by b in Eq. (7.7), the seaward fresh water flow is given by-
q = K’ b2/2L …(7.9)
Where b is the saturated thickness of the confined aquifer. The length of the intruded wedge is inversely proportional to the fresh water flow. The width of the gap (Xw) through which fresh water escapes to the ocean is approximately given by-
Xw = q/2K’ …(7.10)
Glover (1964) developed the following approximate equation for the shape of the ‘fresh O water-salt water interface’:
y2 – 2qx/K’ – q2/K’2 = 0 …(7.11)
When x = 0, y0 = q/K’ …(7.11(a))
When y = 0, x0 = q/2K’ …(7.11(b))
x0 = width of gap through which fresh water escapes to the ocean (Xw).
If the coordinate distances (x, y) from the shoreline to any point on the interface are found, the fresh water lost into the sea (q, Q) can be determined.
Example 1:
By conductivity measurements in a well in a coastal aquifer extending 4 km along the shore, the interface was located at a depth of 20 m below msl at 100 m from the shore, inland. The depth of the homogeneous aquifer is 30 m below m.s.l. and has a permeability of 50 m/day. What is the rate of fresh water flow into the sea and the width of gap at the shore bottom through which it escapes into the sea? What is the position of the toe of the saltwater wedge? Use Glover’s method.
If due to ground water exploitation, the fresh water flow into the sea is reduced by 80% how far the toe will eventually move?
Solution:
Dispersion:
Dispersion of the interface is the phenomenon that the fresh water-salt water interface is not sharp, but is represented by a narrower or wider transition zone in which the amount of total solids increases more or less rapidly from the landward to the seaward side. Calculations can be made for lines of equal total solids, say 1,500 or 2,000 ppm and this can be assumed as the interface. Data from electrical logging of bore holes can be used to demarcate the fresh water- sea water interface.
A dispersion zone and the dynamics of ground water flow in coastal areas cause a variation of the location of the interface between fresh and salt water from what would be expected by a strict application of Ghyben-Herzberg principle.
Example 2:
From the collection and interpretation of hydrologic, geologic and geochemical data, the following information was obtained.
Width of aquifer – 2.8 km
Thickness of aquifer – 30 m
Porosity of aquifer material – 10%
Difference in specific gravity – 0.03
Permeability of the aquifer – 48.9 m/day
From conductivity measurements in two observation wells located at 150 and 225 m from the shore (landward side) the 1,500 ppm line was found to be located at 15 and 22.5 m, respectively, below the top of the aquifer. Determine the fresh water-sea water interface.
Solution:
From Darcy’s law, Fig. 7.6,
Length of instruction, from Eq. (7.7),
L = K’ H2/2q = 48.9(0.03)302/2(2.76) = 239 m
At the time of investigation, the toe of the interface will be located at 239 m landward from the shore. The depth of the interface in between the toe and the shore can be computed from Eq. (7.12) and the complete interface can be located.
Since L is inversely proportional to q, if further ground water exploitation is proposed at the rates of Q/4, Q/3, Q/2 and 3Q/4, (Q = 2,800 q), the seaward fresh water flows will be 3Q/4, 2Q/3, Q/2 and Q/4, and the corresponding lengths of intrusion will be 4L/3, 3L/2, 2L and 4L, respectively. Using 3q/4, 2q/3, q/2 and q/4 in Eq. (7.11), the depth of interface can be worked out for any ground water exploitation.
The position and shape of the interface for the various cases have been worked out and shown in Fig. 7.7. The time when the toe will advance and reach its final length of intrusion or any other length in between can be calculated from the Eq. (7.8). This will show the rate of landward sea water intrusion and will be very useful for planning ground water exploitation in coastal areas.
Abatement of Sea Water Intrusion:
Intrusion can be controlled by reducing pumping, by increasing supply, or by forming some type of barrier. A physical barrier may be formed by actually constructing a cut off wall, using sheet piling, concrete, puddle clay etc. A protective trough may be developed by a line of pumping wells, properly spaced along the coast, Fig. 7.8. These wells produce a mixture of saline and fresh water, resulting in a considerable waste of fresh water. The pumping costs involved and the waste of otherwise usable waters are major factors to be considered in evaluating the practicability of protecting a ground water basin by maintaining a pumping trough.
A ground water mound or ridge may be created by concentrated recharge of the aquifer. A series of spreading grounds or injection wells, or a combination of both, could be utilised, as dictated, by the geologic conditions encountered. The use of fresh water barriers by ground water recharge to prevent sea water intrusion, is practised extensively on the sea coast of southern California. The fresh water barrier should be for enough inland to force all the wedge back seaward. Otherwise, the fresh water will separate the wedge and force the landward wedge still farther inland, creating a saline wave, Fig. 7.9.
A continuous programme for the collection and interpretation of hydrologic, geologic and water quality data has to be initiated to halt and abate sea water intrusion in all basins known to be affected at present. It was found by UNDP investigations that along the Madras coast at the rates of extraction of ground water during 1966, the movement of sea water interface was at the rate of 120 m / year and the limits of extractions were recommended to halt and abate this intrusion.
Due to over pumping to meet the ever increasing industrial and agricultural demands, the ground water levels in the Madras coastal aquifers dropped by more than 25 to 30 m during 1970 causing a reversal of the hydraulic gradient and movement of seawater interface towards land at the rate of 120 to 150 m per year. The GWT was falling at a gradient of 1 m per km towards sea. The interface was located at 60 m depth (below m.s.l.) at 3 km inland. From Glover’s method, Eq. (7.11), assuming K= 50 m/day-
q = K’ y2/2x = (0.025 × 50)602/2 × 3000 = 0.75 m3/day/m
Or
0.75 × 1000 = 750 m3/day per km of coastline
The methods suggested for controlling the seawater intrusion into coastal aquifers are:
(i) Modification of Pumping:
Modification of pumping, i.e., reduction and rearrangement of pattern of pumping draft. By this method the over-draft causing intrusion can be eliminated enabling the ground water levels to rise above m.s.l. and to maintain a seaward gradient.
(ii) Artificial Recharge:
Artificial recharge by spreading areas (for unconfined aquifers) and recharge wells (for confined aquifers).
(iii) Pumping Trough:
A line of pumping wells constructed parallel to the coast would form a trough and the gradients created would limit sea water intrusion to a stationary wedge inland of the trough, as shown in Fig. 7.8 for a confined aquifer. This reduces the usable storage capacity of the basin and is costly to install and operate.
(iv) Pressure Ridge:
In an unconfined aquifer recharge from spreading areas could create a fresh water ridge. In a confined aquifer, a line of recharge wells could form a ridge of the piezometric surface, Fig. 7.9. A small amount of recharge water would run waste into the sea, the remainder moving landward to supply part of the pumping draft.
(v) Subsurface Barrier:
The construction of a subsurface barrier prevents inflow of seawater, Fig. 7.11. This method has limited applicability for very shallow aquifers and is expensive initially. In Germany a method known as ‘sealing wall method’ has been developed and is being used extensively in German open cast mines to totally eliminate seepage of saline water or reduce it to an insignificant amount. While the initial cost is there, the recurring cost will be nil.
Oceanic Island Aquifers:
Since oceanic islands are relatively permeable, sea water is in contact with ground water on all sides. Ground water replenishment is entirely by rainfall and only a limited amount of fresh water is available. A fresh water lens, Fig. 7.10 (a) is formed by the radial movement of ground water towards the coast. An approximate fresh water boundary can be determined, from the boundary condition hs = O where r = R, given by-
Where hs = depth below m.s.l. to the fresh water boundary (interface) at radius r;K= permeability of the aquifer; r = radial distance to the point where the depth is hs; R = radius of the island; P = recharge rate from rainfall.
If the specific gravities of sea water and fresh water are taken as 1.025 and 1.0 respectively, then the denominator in Eq. (7.13) becomes 0.05125 K. Thus, the depth to salt water at any location is a function of the rainfall recharge, size of the island and permeability of the aquifer. Substantial fresh water supplies are more likely to be found on large islands with large recharge and low permeability.
When an island well is pumped at a rate as to lower water table near to m.s.l., the fresh water-salt water equilibrium is disturbed and the salt water will rise as a cone to enter the well, Fig. 7.10 (b). To prevent sea water intrusion, the drawdown should be a minimum so as to draw fresh water only from top of the lens. Many islands get water supplies from infiltration galleries consisting of horizontal collecting tunnels.
Pumping Island Aquifer—Steady Unconfined Flow with Rainfall:
To derive an equation for the phreatic surface of an island aquifer of radius R with an effective rainfall rate P, when a central well is pumped at a rate Qw, Fig. 7.12.
Example 3:
A circular island of 600 m radius has an effective rainfall of 5 mm/day. A central well 30 cm in diameter is pumped at a constant rate of 30 m3/hr. K for the island aquifer is 25 m/day. The depth of sea around the island is 10 m. What is the drawdown in the well and at the water divide?
If the sea around the island is contributing, the hydraulic gradient line would be sloping downwards and inwards at every point, line b in Fig. 7.12. If a water divide exists at a radial distance of x, then the entire pumpage is being contributed by rainfall. So, the area contributing is obtained from Eq. (7.14)
Upconing:
In coastal aquifers, where the fresh ground water is underlain by saline water, pumping in a well causes the fresh water-salt water interface to rise below the well in response to the pressure reduction on the interface due to the drawdown of the ground water table around the well. This is called ‘upconing’, Fig. 7.13. If the well discharge is relatively high or if the bottom of the well is close to the interface, the salt water cone may enter into the well causing the well discharge to be a mixture of fresh and salt water.
Bear and Dagan (1968) developed an expression for the rise of salt water cone below the centre of the pumping well, and a simplified form for long duration pumping is-
z = Q/2πK’l …(7.18)
Where z = rise of cone and I = depth of interface below the well bottom prior to pumping.
From Eq. (7.18) safe depths and pumping rates of wells to prevent entry of saline water, can be determined.
Example 4:
A well screen 1 m in length is located 15 m below the ground water table in an unconfined aquifer having a permeability of 20 m/day. The fresh water-sea water interface exists at a depth of 36 m below the water table. What is the maximum discharge that can be sustained from the well without causing the salt water to intrude into the well?
Solution:
The interface should not be allowed to rise more than one-third the distance between the bottom of the well and the original interface elevation. For this the maximum sustained discharge from the well is given by Eq. (7.18).
z = Q/2πK’ l
1/3 (36 – 16) – Q/2π(0.025 × 20)(36 – 16)
Therefore, Q = 418 m3/day or 290 1pm