286
8. Applications of Groundwater Quality Models
(2)
Z2 = min max hj\ jE"',
(8.3.30)
k
j
where '" is a set of injection weHs. This objective is to minimize the cost of
water injection.
(3)
Z3 = max min Cf, jE"',
(8.3.31 )
k
j
This objective aims at saving the expense for the treatment of recharge
water. The total objective may be a certain weighted combination of these
objectives.
The constraints of this problem include:
1. The total extraction must meet the demand, i.e.,
L Q~ = D\
(8.3.32)
iE1t
where D k represents the water demand in the kth interval.
2. The total recharge water must reach the amount of recharge, i.e.,
L QJ = R\
(8.3.33)
jE '"
where R k is the amount of waste water to be injected into the aquifer
during the kth interval.
3. Extraction and injection should not surpass the capability of the equipment, i.e.,
Q~ ~ Qt, QJ ~ Qj,
(8.3.34)
(i E n)
(j E "')
where Qt and Qj* are the maximum capabilities of pumping and injection,
respectively.
4. Water quality standard in the extraction weHs should be satisfied, i.e.,
C~I ::; C*, i E n,
(8.3.35)
where C* is the given standard of water quality.
Eqs. (8.3.29) to (8.3.35) compose a multi-objective programming problem.
It can be divided into two correlated subproblems. If hydraulic management
is the major objective, we can first solve the subproblem of water quantity
defined by Eqs. (8.3.29) and (8.3.30) in conjunction with the constraints
(8.3.32) to (8.3.34). Its solution provides the scheme of water quantity aHocation for each of the management intervals. Then, take the scheme as the
source and sink term to obtain the flow velo city distribution. FinaHy, solve
the management subproblem of water quality as defined in Eq. (8.3.31) with
the additional constraints (8.3.35). Willis (1979) gave a hypothetical example
to illustrate the use of the above method in building models for groundwater
hydraulic management and quality management.
8. Applications of Groundwater Quality Models
(2)
Z2 = min max hj\ jE"',
(8.3.30)
k
j
where '" is a set of injection weHs. This objective is to minimize the cost of
water injection.
(3)
Z3 = max min Cf, jE"',
(8.3.31 )
k
j
This objective aims at saving the expense for the treatment of recharge
water. The total objective may be a certain weighted combination of these
objectives.
The constraints of this problem include:
1. The total extraction must meet the demand, i.e.,
L Q~ = D\
(8.3.32)
iE1t
where D k represents the water demand in the kth interval.
2. The total recharge water must reach the amount of recharge, i.e.,
L QJ = R\
(8.3.33)
jE '"
where R k is the amount of waste water to be injected into the aquifer
during the kth interval.
3. Extraction and injection should not surpass the capability of the equipment, i.e.,
Q~ ~ Qt, QJ ~ Qj,
(8.3.34)
(i E n)
(j E "')
where Qt and Qj* are the maximum capabilities of pumping and injection,
respectively.
4. Water quality standard in the extraction weHs should be satisfied, i.e.,
C~I ::; C*, i E n,
(8.3.35)
where C* is the given standard of water quality.
Eqs. (8.3.29) to (8.3.35) compose a multi-objective programming problem.
It can be divided into two correlated subproblems. If hydraulic management
is the major objective, we can first solve the subproblem of water quantity
defined by Eqs. (8.3.29) and (8.3.30) in conjunction with the constraints
(8.3.32) to (8.3.34). Its solution provides the scheme of water quantity aHocation for each of the management intervals. Then, take the scheme as the
source and sink term to obtain the flow velo city distribution. FinaHy, solve
the management subproblem of water quality as defined in Eq. (8.3.31) with
the additional constraints (8.3.35). Willis (1979) gave a hypothetical example
to illustrate the use of the above method in building models for groundwater
hydraulic management and quality management.