Saltwater Intrusion - Ghyben-Herzberg Relation

Ghyben-Herzberg Relation

The first physical formulations of saltwater intrusion were made by W. Badon-Ghijben (1888, 1889) and A. Herzberg (1901), thus called the Ghyben-Herzberg relation. 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.

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

the thickness of the freshwater zone above sea level is represented as and that below sea level is represented as . The two thicknesses and, are related by and where is the density of freshwater and 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

.

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 fewer assumptions and can be applied more generally.