268
8. Applications of Groundwater Quality Models
Substituting Eq. (8.2.17b) into this equation, we obtain the following equation for the average hydraulic head h. of seawater
Using a parallel derivation, we can also obtain the following equation for the
average hydraulic head h, of fresh water
V' (K b V'h) Sb oh, (*Oh. *Oh,)
- . ''I. ,+ 'f 'fTt- n P. at-p,Tt
oh,
+om-+Q,=O
ot
'
(8.2.24)
where the source and sink term covers pumping, recharge and infiltration
of rainfall; and IX is a coefficient, IX = 0 for confined water while IX = 1 for
phreatic water. For the sake of simplifying the notation, h. and h, are still
written as h. and h" but it should be remembered that they are only functions
of x, y, and t. Equations (8.2.23) and (8.2.24) can be expressed in the scalar
form as
(8.2.25)
and
oh, (* oh. * Oh,) oh, 0 ( Oh,)
S,b,Tt - n P. at - P, Tt + IXnTt - ox K,,,b, ox
-~(K, b, Oh,) + Q, = O.
oy y oy
(8.2.26)
To solve the two equations, appropriate initial and boundary conditions
must be given. Boundary conditions along the coast are not easy to determine. It is incorrect to let h, be equal to the level of seawater along the coast,
because the fresh water flows towards the sea. As a result, the boundary line
should be the seepage surface of the fresh water. If the overflow of the fresh
water can be determined, the coast line may be regarded as a flux boundary.
Of course, the overflow is, in fact, also unknown, but it might be determined
as apart of the parameter identification by solving the inverse problem.
Bear (1979) suggested the adoption of the third-type of boundary conditi on. Along the co ast line, for the fresh water equation, it is defined as
h, [*h *h ] oh, 0
- + P. • - P, , ~ = ,
IX
un
(8.2.27)
8. Applications of Groundwater Quality Models
Substituting Eq. (8.2.17b) into this equation, we obtain the following equation for the average hydraulic head h. of seawater
Using a parallel derivation, we can also obtain the following equation for the
average hydraulic head h, of fresh water
V' (K b V'h) Sb oh, (*Oh. *Oh,)
- . ''I. ,+ 'f 'fTt- n P. at-p,Tt
oh,
+om-+Q,=O
ot
'
(8.2.24)
where the source and sink term covers pumping, recharge and infiltration
of rainfall; and IX is a coefficient, IX = 0 for confined water while IX = 1 for
phreatic water. For the sake of simplifying the notation, h. and h, are still
written as h. and h" but it should be remembered that they are only functions
of x, y, and t. Equations (8.2.23) and (8.2.24) can be expressed in the scalar
form as
(8.2.25)
and
oh, (* oh. * Oh,) oh, 0 ( Oh,)
S,b,Tt - n P. at - P, Tt + IXnTt - ox K,,,b, ox
-~(K, b, Oh,) + Q, = O.
oy y oy
(8.2.26)
To solve the two equations, appropriate initial and boundary conditions
must be given. Boundary conditions along the coast are not easy to determine. It is incorrect to let h, be equal to the level of seawater along the coast,
because the fresh water flows towards the sea. As a result, the boundary line
should be the seepage surface of the fresh water. If the overflow of the fresh
water can be determined, the coast line may be regarded as a flux boundary.
Of course, the overflow is, in fact, also unknown, but it might be determined
as apart of the parameter identification by solving the inverse problem.
Bear (1979) suggested the adoption of the third-type of boundary conditi on. Along the co ast line, for the fresh water equation, it is defined as
h, [*h *h ] oh, 0
- + P. • - P, , ~ = ,
IX
un
(8.2.27)