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8. Applications of Groundwater Quality Models
8.2.2 Fresh Water-Seawater Interfaces
Pinder and Page (1976), and Bear (1979) gave a complete mathematical
statement for the case of an abrupt interface. Assurne that the distribution of
hydraulic heads in the seawater region is h s ' and in the fresh water region, is
h f . The governing equations are given below:
In seawater:
ohs
Ss 7ft + V . qs = 0,
(8.2.1a)
qs= -KsVhs'
(8.2.1 b)
in fresh water:
oh f
Srat + V·qf = 0,
(8.2.2a)
qf = -KfVh f ,
(8.2.2b)
where Ss and Sf' K s and K f , qs and qf are the specific storage coefficients (or
specific yields if in unconfined aquifer), hydraulic conductivities and Darcy's
velocities in seawater region and fresh water region, respectively.
The gradient operator V is defined as:
o. o. 0 k
V = ox I + oyJ + OZ '
where i, j, and kare unit vectors along the co ordinate axes.
Assurne that the equation of the sharp interface is
F(x, y, Z, t) = O.
Pressure balance must be satisfied on the interface, that is
pf(h f - zd = Ps(hs - Zl)'
(8.2.3)
(8.2.4)
where Ps and Pf are the densities of seawater and fresh water, respectively; and
Z 1 is the elevation of the interface. From Eq. (8.2.4), we have
Pshs - pfh f
Zl =
,
Ps - Pf
which can be written as
*
Pf
Pf = - - .
Ps - Pf
(8.2.5)
If h s and h f can be solved from Eqs. (8.2.1) and (8.2.2), then the elevation of
the interface Z 1 may be obtained from Eq. (8.2.5). Thus, the equation of the
interface can be expressed by
F(x, y, Z, t) == Z - Z 1 (x, y, t) = O.
(8.2.6)