The Interaction of Saltwater/Freshwater in Coastal Aquifiers

By : Putika Ashfar K

Freshwater and saltwater interaction in coastal aquifiers are influenced by density difference,

which is cause invisible interface between them. The density of water is gradually change from freshwater

to saltwater area. The partition zone of separation between salt and fresh water in estuary are usually

called as pycnocline zone.

Figure 1: Saltwater interface in an unconfined coastal aquifier according to the Ghyben Herzberg relation

Excessive pumping of groundwater will cause seawater movement toward the aquifier. The

seawater diverts upside, and it causes deterioration of water quality in coastal aquifiers. The most

fundamental relation between saltwater and freshwater in coastal area is Ghyben-Herzberg relation. The

Ghyben-Hezberg relation is the fundamental analytical model to describe saline water intrusion problem.

We can define the pizometric head in the saltwater zone and freshwater zone respectively using Ghyben -

Herzberg equation as :

ℎ𝑠 =𝜌𝑓

𝜌𝑠−𝜌𝑓ℎ𝑓 ≈ 40 ℎ𝑓..................(1)

Where hs and hf are the pizometric head in the saltwater zone and freshwater zone, ρs and ρf are the

saltwater and freshwater density. For example, we can calculate the length of salwater wedge and the

position of interface between fresh and salt water using Ghyben Herzberg relation as follows :

The density of fresh water is (ρf ) =1 gr/cm3 and the density of seawater is( ρs )= 1,025 gr/cm3. The water

level in two wells from the shoreline are 0,5 m and 1 m, and the distance between them is 1000 m.

K = 10 m/d , b = 50 m

We can see here the illustration of longitudinal section in coastline

Figure 2: Longitudinal section of interface between salt and fresh water

Length of saltwater wedge

𝑥 =1

2

(𝜌𝑠 − 𝜌𝑓)𝐾𝑧2

𝜌𝑓𝑄′… … … … … . (2)

we can calculate the discharge from aquifier to sea per unit length of shoreline

𝑄 ′ = 𝐾𝑏𝑑ℎ

𝑑𝑥

𝑄 ′ = 10𝑚

𝑑. 50 𝑚.

(1𝑚 − 0,5𝑚)

1000 𝑚= 0,25 𝑚3𝑑

𝑥 =1

2

(1,025 𝑔𝑟/𝑐𝑚3 − 1 𝑔𝑟/𝑐𝑚3) 10𝑚𝑑

40𝑧2

2

1𝑔𝑟

𝑐𝑚3 . 1 𝑔𝑟/𝑐𝑚3 = 0,5 𝑧2

The position of interface

𝐿 =1

2

(𝜌𝑠 − 𝜌𝑓)𝐾𝑏2

𝜌𝑓 𝑄′ … … … … . . … (3)

𝑥 =1

2

(1,025 𝑔𝑟/𝑐𝑚3 − 1 𝑔𝑟/𝑐𝑚3) 10𝑚𝑑

50𝑚2

1𝑔𝑟

𝑐𝑚3 . 1 𝑔𝑟/𝑐𝑚3 = 1250 𝑚

The interface would be risen if the number of pumping wells are not controlled. Upconing (zh) is

the rise of interface as a result of groundwater pumping. We can limiting seawater intrusion by control on

pumping. Reducing pumping rates and number of pumped way are two examples to controls on pumping.

X

Figure 3: Upconing phenomena in coastal aquifier

Upconing of interface can be calculated as follows :

𝑧ℎ = 𝑄′𝜌𝑓

2𝜋𝐾𝑑(𝜌𝑠 − 𝜌𝑓)… … … … … . . (4)

The maximum pumping rate (Qmax) have to be calculated to control the number of pumped wells.

𝑄𝑚𝑎𝑥 ≤ 0,6𝜋𝑑2𝐾(𝜌𝑠 − 𝜌𝑓)

𝜌𝑓… … … … (5)

In practice, the Ghyben-Herzberg relation and modified Ghyben-Herzberg which is uses the observed

piezometric head in saltwater zone, can be used for preminary estimates the location of saltwater-

freshwater interface. The procedure of estimation in a field investigation is as follows :

1. Collect data of a shallow wells network use for observation of water table head

2. Piezometer can be used to measure freshwater head and estimates submarine groundwater

discharge.

Figure 4 : Longitudinal section of piezometric position to estimate groundwater discharge in

coastal area

Nested piezometers are located along a transect of the coastal zone to estimate the submarine

groundwater discharge

∆𝑧𝑗

∆ℎ𝑗

𝑞𝑣 = ∑ 𝐾𝑗𝑤𝐿∆ℎ𝑗

∆𝑧𝑗

𝑟

𝑗=1

… … … … … … … … … . (5)

In which :

r = number of nested piezometer

Kj = hydraulic conductivity of sediments where the piezometer are opened to groundwater flow

L = width of coastal zone, perpendicular to the plane along the coast zonewhich has submarine

discharge flow toward the ocean

w = width of the zone of influence of nested piezometers in the plane

Δhj = the vertical hydraulic head difference at the jth nested piezometer

Δzj= vertical distance between the piezometers screen intervals.

3. Contour lines showing the freshwater head are drawn using an interpolation technique (kriging

method)

4. Contour maps showing the elevation of saltwater/freshwater interface can be obtained by the

Ghyben-Herzberg relation. The location of aquifier bottom can be found from geological maps.

Then, the intersection of the interface and aquifier bottom boundary which can represents

saltwater toe location can be traced and the location of saltwater wedge can be deliniated.

Figure 5:Tracking saltwater toe location

References:

[1] Bear, J. Cheng, AH-D, Sorek, S., D.Ouzar. Seawater Intrusion in Coastal Aquifiers-Concepts,

Methods and Practices. Kluwer Academics Publishers. Dordrecht. The Netherlands. 164-167. 1999

[2] Zetsker, Igor. S., Dzhamalov. Submarine Groundwater. Taylor and Francis Group. New York. US. 48-

49. 2007